Modelling and Optimization of Photovoltaic Cells, Modules, and Systems (Springer Theses) 9811611106, 9789811611100

Table of contents :
Supervisor’s Foreword
Abstract
Publications Related to This Thesis
Journal Publications
Conference Publications
Acknowledgements
Contents
Symbols
1 Introduction
1.1 Motivation
1.2 Research Objectives
1.3 Author's Original Contributions
1.4 Thesis Structure
References
2 Background and Literature Review
2.1 Review of the Photovoltaic Field
2.1.1 Solar Cells
2.1.2 Solar Modules
2.1.3 Photovoltaic Systems
2.2 Review of the Optimization Field
2.2.1 Optimization Problem
2.2.2 Optimization Algorithms
2.3 Summary
References
3 On the Optimization for the Grid Metallization Design of Si-Based Solar Cells and Modules
3.1 Introduction
3.2 Modelling of Cell and Module Performance
3.3 Estimation of Silver Consumption
3.4 Estimation of the Fabrication Cost
3.5 Optimization Under Standard Test Conditions
3.5.1 Optimization Problem
3.5.2 Optimization Algorithms
3.5.3 Case Study
3.5.4 Results and Discussion
3.5.5 Experimental Validation
3.5.6 Summary
3.6 Optimization Under Real-World Conditions
3.6.1 Approach
3.6.2 Case Study
3.6.3 Optimization Algorithm
3.6.4 Results and Discussion
3.6.5 Summary
References
4 Optimization and Cost-Effectiveness Analysis Between Si-Based Monofacial and Bifacial Grid-Connected PV Systems
4.1 Introduction
4.2 Data Processing
4.3 Irradiance Model
4.4 PV Energy Generation
4.5 Cost and LCOE Estimations
4.6 Case Study
4.6.1 Weather Parameters
4.6.2 Module Performance Parameters
4.6.3 Cost Parameters
4.7 Results and Discussion
4.7.1 Monofacial AMO Versus Bifacial AMO
4.7.2 Monofacial AMO Versus Bifacial VMO
4.7.3 Sensitivity Analysis
4.8 Summary
References
5 Optimal Diesel Replacement Strategy for the Progressive Introduction of PV and Batteries
5.1 Introduction
5.2 Modelling of PV Hybrid Systems
5.2.1 Diesel Generators
5.2.2 Solar Panels
5.2.3 Batteries
5.2.4 Spinning Reserve
5.3 Problem Formulation
5.3.1 Traditional Problem Formulation
5.3.2 Diesel Replacement Formulation
5.4 Algorithms
5.4.1 Sizing Algorithm
5.4.2 Scheduling Algorithm
5.5 Case Study
5.6 Results and Discussion
5.6.1 Results from (P1)
5.6.2 Results from (P2)
5.7 Summary
References
6 On the Dispatch Strategy Optimization for PV Hybrid Systems in Real Time
6.1 Introduction
6.2 Real Time Simulator
6.3 Algorithms
6.3.1 Benchmark Algorithm 1: DG Backup Based
6.3.2 Benchmark Algorithm 2: Spinning Reserve Based
6.3.3 Proposed Algorithm: Forecast Based
6.4 Case Study
6.5 Results and Discussion
6.6 Summary
References
7 Conclusions and Proposed Future Works
7.1 Conclusions
7.2 Proposed Future Work
Appendix A Influence of Grid Metallization Design in Cell/Module
A.1 Photovoltaic Current Density Estimation
A.1.1 Direct Impact Contribution
A.1.2 Backsheet Influence
A.1.3 Albedo Influence
A.2 Dark Saturation Current Densities Estimation
A.3 Area Weighted Series Resistance Estimation
A.4 Table of Results Under STC
Appendix B Weather Data Processing
B.1 Data Filtering
B.2 Data Filling
B.3 Typical Meteorological Year Data Estimation
Appendix C Approaches to Estimate the Front and Rear Irradiance Reaching the Module
C.1 Front Surface Irradiance
C.2 Rear Surface Irradiance
Appendix D Polar Contour Plots
Appendix E Scheduling Algorithm Applied for PV Hybrid Systems

Citation preview

Springer Theses Recognizing Outstanding Ph.D. Research

Carlos David Rodríguez Gallegos

Modelling and Optimization of Photovoltaic Cells, Modules, and Systems

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

Theses may be nominated for publication in this series by heads of department at internationally leading universities or institutes and should fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder (a maximum 30% of the thesis should be a verbatim reproduction from the author’s previous publications). • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to new PhD students and scientists not expert in the relevant field. Indexed by zbMATH.

More information about this series at http://www.springer.com/series/8790

Carlos David Rodríguez Gallegos

Modelling and Optimization of Photovoltaic Cells, Modules, and Systems Doctoral Thesis accepted by National University Of Singapore

Author Carlos David Rodríguez Gallegos Solar Energy Research Institute of Singapore National University of Singapore Singapore, Singapore

Supervisor Assoc. Prof. Sanjib Kumar Panda Power and Energy Systems Department of Electrical and Computer Engineering National University of Singapore Singapore, Singapore

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-981-16-1110-0 ISBN 978-981-16-1111-7 (eBook) https://doi.org/10.1007/978-981-16-1111-7 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Supervisor’s Foreword

The installation of Solar Photovoltaic (PV) systems has been consistently increasing over the past decade or so due to the reduction in cost in the solar PV panels as well as the energy storage devices to overcome the concerns regarding climate change and potential depletion of non-renewable sources in the near future. Therefore, it is expected that this trend is likely to continue in the following years and decades as further favorable conditions are being presented such as the decrease in their fabrication cost, increase in their electrical efficiency, potential for scalability and noiseless electrical power generation. These systems are gaining more share on the overall electricity production, and although research on this technology has resulted in current system installations with a lower cost of electricity generation than the traditional ones for multiple countries, there is still space for improvements as the aim is to keep on enhancing the PV system properties so that these installations will not only be desired to help fight climate change, but also as an economic investment by producing cheap electricity. Consequently, the thesis written by Carlos aims to study the current limitations in the area of photovoltaics and propose strategies to overcome them by applying optimization approaches. While there are previous studies focusing on this aim, this thesis goes a step further as it employs the state-of-the-art optimization algorithms to tackle in the best way several different problems from this field at different levels, i.e. starting from the optimization of the manufacturing process of the solar cells and modules and finalizing with improvements of operation at the system level under different configurations and improving the energy efficiency of the system. This study not only contains simulation analyses but also provides experimental test results in order to justify the work carried out. This thesis also offers a summary on the literature review to cover the full spectrum of the technical and economic aspects of PV while also providing a thorough explanation on the current challenges. This work employs detailed use of mathematical modelling approaches to accurately simulate the performance of solar cells, modules and systems while explaining in detail how are these developed and applied. Furthermore, it employs real data regarding weather, cell and module parameters as well as real conditions of PV systems that will be relevant not only to researchers v

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Supervisor’s Foreword

but also to the industry. This thesis work will then be a great source of information in the PV field and will be of great interest to multiple readers. Singapore, Singapore November 2020

Sanjib Kumar Panda, Ph.D., FIEEE

Abstract

The world’s population is increasing day by day. This increase, together with the desire of people to achieve a better quality of life, leads to a continuous rise in energy consumption. At present, most of the primary energy is obtained from non-renewable sources. Their supply however is limited and their usage produces a considerable amount of greenhouse gas emissions, which are known to contribute to climate change. Therefore, renewable energy sources are the only way forward to achieve a sustainable use of the available energy resources and to reach the “< 2 °C” global warming aim documented in the Paris Agreement. Among the different sources of renewable energy, solar energy is highly promising due to the enormous amount of energy provided by the Sun almost anywhere on the planet. Apart from solar thermal applications, which work best in areas with high direct irradiance, the most widely use of solar energy is the direct conversion into electricity using the so-called “photovoltaic” (PV) effect. The accumulated installed PV capacity has reached a value of around 400 GWp by 2017. Although this technology has achieved a certain level of maturity, it still has room and needs for further improvements to increase efficiencies and lower cost. Hence, the overall objective of this work is to study the current limitations in the area of PV and propose strategies to overcome them by applying optimization approaches. Different studies were performed to optimize the performance at the cell, module, and system levels. These are summarized in the following paragraphs. An advanced optimization approach to enhance the electrical performance and reduce the fabrication cost of monofacial and bifacial crystalline Si-based cells and modules, by optimizing their metallization design (number and dimensions of fingers, busbars, and interconnector ribbons) under standard test conditions and realworld conditions, is proposed. Different from the existing works in the literature, the proposed one is able to handle all the required optimization variables in parallel, by applying multiobjective and robust techniques. With respect to grid connected systems, although research has previously aimed to estimate the extra production from bifacial installation in comparison to monofacial ones, no proper cost-effectiveness analysis has been performed. Therefore, this work optimizes the module orientation designs for monofacial and bifacial vii

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Abstract

systems and compares their cost-effectiveness (based on the levelized cost of electricity) worldwide to determine the conditions in which bifacial PV installations are preferable. Off-grid systems have also been examined in this work, focusing on the hybridization of systems originally composed of diesel generators by adding solar panels and batteries. While the addition of these sources could achieve future savings, high initial investments are typically required for their installation (resulting in insurmountable capital requirements in many scenarios). Therefore, this work proposes a diesel replacement strategy to reduce the required investment, while assuring high savings at the end of the project lifespan. The proposed approach defines an optimal process to add solar panels and batteries over time based on the yearly savings from diesel. In addition, with respect to the energy dispatch strategy of these hybrid systems, this thesis also provides a technique to enhance their daily savings by considering future load and irradiance scenarios based on forecasting algorithms. The obtained results were compared with benchmark algorithms showing the extra savings produced from the one proposed here.

Publications Related to This Thesis Journal Publications 1.

2.

3.

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5.

6.

C. D. Rodríguez-Gallegos, O. Gandhi, J. M. Yacob Ali, V. Shanmugam, T. Reindl, and S. K. Panda, “On the grid metallization optimization design for monofacial and bifacial Si-based PV modules for real-world conditions,” IEEE Journal of Photovoltaics, vol. 9, no. 1, pp. 112–118, 2019. C. D. Rodríguez-Gallegos, J. P. Singh, J. M. Y. Ali, O. Gandhi, S. Nalluri, A. Kumar, V. Shanmugam, L. M. Aguilar, M. Bieri, T. Reindl, and S. K. Panda, “PVGO: A multiobjective and robust optimization approach for the grid metallization design of Si based solar cells and modules,“Progress in Photovoltaics: Research and Applications”, vol. 27, no. 2, pp. 113–135, 2019. C. D. Rodríguez-Gallegos, M. Bieri, O. Gandhi, J. P. Singh, T. Reindl, and S. K. Panda, “Monofacial vs bifacial Si-based PV modules: Which one is more cost-effective?,” Solar Energy, vol. 176, pp. 412–438, 2018. C. D. Rodríguez-Gallegos, O. Gandhi, M. Bieri, T. Reindl, and S. K. Panda, “A diesel replacement strategy for off-grid systems based on progressive introduction of PV and batteries: An Indonesian case study,” Applied Energy, vol. 229, pp. 1218–1232, 2018. C. D. Rodríguez-Gallegos, D. Yang, O. Gandhi, M. Bieri, T. Reindl, and S. K. Panda, “A multi-objective and robust optimization approach for sizing and placement of PV and batteries in off-grid systems fully operated by diesel generators: An Indonesian case study,” Energy, vol. 160, pp. 410–429, 2018. C. D. Rodríguez-Gallegos, O. Gandhi, D. Yang, M. S. Alvarez-Alvarado, W. Zhang, T. Reindl, and S. K. Panda, “A siting and sizing optimization approach for PV-battery-diesel hybrid systems,” IEEE Transactions on Industry Applications, vol. 54, no. 3, pp. 2637–2645, 2018.

Conference Publications 1.

2.

3.

C. D. Rodríguez-Gallegos, O. Gandhi, T. Reindl, and S. K. Panda, “PHSO: A Graphic User Interface Optimizer for the Sizing Design of the PV Hybrid Systems,” in 33rd European Photovoltaic Solar Energy Conference and Exhibition (EU PVSEC), Amsterdam, The Netherlands, pp. 2375–2379, 2017. C. D. Rodríguez-Gallegos, M. S. Alvarez-Alvarado, O. Gandhi, D. Yang, W. Zhang, T. Reindl, and S. K. Panda, “Placement and sizing optimization for PVbattery-diesel hybrid systems,” in The 4th IEEE International Conference on Sustainable Energy Technologies (ICSET 2016), Hanoi, Vietnam, pp. 83–89, IEEE, 2016. C. D. Rodríguez-Gallegos, K. Rahbar, M. Bieri, O. Gandhi, T. Reindl, and S. K. Panda, “Optimal PV and storage sizing for PV-battery-diesel hybrid systems,” in IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society (IECON), Florence, Italy, pp. 3080–3086, IEEE, 2016.

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Publications Related to This Thesis

C. D. Rodríguez-Gallegos, and T. M. Walsh, “Conceptual design for a standalone solar photovoltaic powered peltier air conditioner,” in Proceedings of the World Engineer’ s Summit (WES) on Climate Change 2015, Singapore, pp. 350–360, 2015.

Acknowledgements

I would first like to thank God for all the blessings he has given me. I am thankful to my parents for all their support and sacrifices and to my brothers for acting as my role models. I am very grateful to Prof. Armin Aberle for his support while applying for this Ph.D. position and for allowing me to choose the research topic to pursue at the Solar Energy Research Institute of Singapore (SERIS). I also want to thank my supervisors, Prof. Sanjib Kumar Panda and Dr. Thomas Reindl, for all their support and guidance during this Ph.D. Whenever I had a challenge while doing my research (either due to a lack of knowledge or lack of equipment), they would immediately help me to ensure that I could do my Ph.D. in an optimal way. My work employed different weather parameters measured in Singapore by SERIS. Thanks to this data I was able to perform my investigations. As such, I am grateful to their team members (current and previous), among them, André Nobre, Soe Pyae, Zhao Lu, and Marek Kubis. At SERIS I had the luck to meet true experts in their field who were always willing to share their knowledge and collaborate in research. In particular, I want to thank Monika Bieri (most knowledgeable person in economics I have ever met), Jai Prakash (who taught me many things about bifacial technologies and PV modules), and Katayoun Rahbar (who introduced me to the basics of the optimization algorithms). In Singapore, I had the fortune to meet very good friends; the time with them helped me to learn more about other cultures, relax, and have fun. Although there are many, I want to thank in particular Oktoviano Gandhi, Jaffar Moideen, Dazhi Yang, Amit Singh, Kanakesh Nheralatt, Bala Muralidhar, Du Hui, Can Yesilyurt, and Kareem Ali. In addition, I want to thank Okto for helping me improve my research approaches. Thanks to the many discussions we had and for always be willing to proofread my journal and conference papers, as well as this thesis. Lastly, I am very grateful to NUS and SERIS for allowing me to pursue my Ph.D. under them and to their staff who were, in general, very friendly and helpful.

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Author’s Original Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 5 6 7

2 Background and Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Review of the Photovoltaic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Solar Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Photovoltaic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Review of the Optimization Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Optimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 9 9 10 12 17 17 17 19 20

3 On the Optimization for the Grid Metallization Design of Si-Based Solar Cells and Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Modelling of Cell and Module Performance . . . . . . . . . . . . . . . . . . . . 3.3 Estimation of Silver Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Estimation of the Fabrication Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Optimization Under Standard Test Conditions . . . . . . . . . . . . . . . . . . 3.5.1 Optimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.5 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Optimization Under Real-World Conditions . . . . . . . . . . . . . . . . . . . . 3.6.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.6.2 3.6.3 3.6.4 3.6.5 References

Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....................................................

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4 Optimization and Cost-Effectiveness Analysis Between Si-Based Monofacial and Bifacial Grid-Connected PV Systems . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Irradiance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 PV Energy Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Cost and LCOE Estimations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Weather Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Module Performance Parameters . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Cost Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.1 Monofacial AMO Versus Bifacial AMO . . . . . . . . . . . . . . . . . 4.7.2 Monofacial AMO Versus Bifacial VMO . . . . . . . . . . . . . . . . . 4.7.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 51 53 53 54 55 58 58 58 62 65 72 73 74 77 78

5 Optimal Diesel Replacement Strategy for the Progressive Introduction of PV and Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Modelling of PV Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Diesel Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Solar Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Spinning Reserve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Traditional Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Diesel Replacement Formulation . . . . . . . . . . . . . . . . . . . . . . . 5.4 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Sizing Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Results from (P1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Results from (P2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

6 On the Dispatch Strategy Optimization for PV Hybrid Systems in Real Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Real Time Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Benchmark Algorithm 1: DG Backup Based . . . . . . . . . . . . . 6.3.2 Benchmark Algorithm 2: Spinning Reserve Based . . . . . . . . 6.3.3 Proposed Algorithm: Forecast Based . . . . . . . . . . . . . . . . . . . . 6.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xv

111 111 112 113 114 114 115 116 117 119 120

7 Conclusions and Proposed Future Works . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.2 Proposed Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Appendix A: Influence of Grid Metallization Design in Cell/Module . . . . 127 Appendix B: Weather Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Appendix C: Approaches to Estimate the Front and Rear Irradiance Reaching the Module . . . . . . . . . . . . . . . . . . . . . . . 141 Appendix D: Polar Contour Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Appendix E: Scheduling Algorithm Applied for PV Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Symbols

#fc #ppf #rc αbi αmo β0 [%] β1 [%/year] βcell βmodule t[h] l[%] lDG [years] lfloat [years] lm [m] lS [year] η[%] η[%] ηBAT,inv [%] ηc [%] ηd [%] ηmax [%] ηPV,inv [%] γ[%/◦ C] κdiesel [l] πBAT [%] πivt [%]

number of external front contacts per string to get the IV curve at the cell level number of particles forming the pareto front number of external rear per string contacts to get the IV curve at the cell level 1 for bifacial module, 0 for monofacial 1 for monofacial module, 0 for bifacial initial degradation of solar panels annual degradation rate of solar panels 1 for solar cell, 0 for solar module 1 for solar module, 0 for solar cell slot size remaining system losses lifetime of diesel generators battery float lifetime module length system lifetime efficiency when a particular optimization variable is modified based on Varunc efficiency weighted average efficiency of battery inverters battery charging efficiency battery discharging efficiency maximum efficiency from the pareto front weighted average efficiency of PV inverters power temperature coefficient of solar panels diesel consumption percentage of the battery inverter cost that needs to be paid to extend the inverter warranty percentage of the PV inverter cost for warranty extension xvii

xviii

πPV [%] ρ ρAA ρAV ρBB_f [m] ρBB_r [m] ρb [m]   2 ρc_ge m   ρc_gp+ m2 ρfi_f [m] ρfi_r [m] ρir [m] ρm_r [m] σ[%/month] θ m [◦ ] θrl [◦ ] LCOE[USD cents/kWh] εload εPV cell_f [%] cell_r [%] ref_f [%] ref_r[%]  Ac_nm m2 Acell m2 aDG [l/kWh] Am [◦ ] ar As [◦ ]  Atotal m2 Auc (j)[cm2 ] AM AMa AOIf [◦ ] ARel_fi_f [0, 1] ARel_fi_r [0, 1] b bDG [l/kWh] Balini [USD]

Symbols

percentage of the PV inverter cost that needs to be paid to extend the inverter warranty albedo minimum albedo value at which bifacial AMO systems are more cost-effective than the monofacial AMO ones minimum albedo value at which bifacial VMO systems are more cost-effective than the monofacial AMO ones line resistivity of the front side busbar line resistivity of the rear side busbar line resistivity of the base contact resistivity between the grid/emitter contact resistivity between the grid/p+ layer line resistivity of the front side finger line resistivity of the rear side finger line resistivity of the interconnector ribbons resistivity of the rear side metal layer battery self discharge module tilt angle angular division of light reflected from backsheet difference between the monofacial and bifacial LCOE uncertainty coefficient for loads uncertainty coefficient for PV shading percentage of the cell at the front side shading percentage of the cell at the rear side front side shading percentage of reference cell rear side shading percentage of reference cell non-metallized cell area solar cell area coefficient of diesel consumption module azimuth angle angular loss coefficient sun azimuth angle total area of the PV device unit cell area of the jth rs contributor air mass absolute air mass angle of incidence between the DNI radiation and the normal of the front surface of the module optical aspect ratio of the front side finger optical aspect ratio of the rear side finger bifaciality factor of a solar module coefficient of diesel consumption yearly initial balance

Symbols

Bond20y [%] CPV,Wp  [USD/W  p] cAg USD/g CBank,amor [USD] CBank,int [USD] CBAT,inv [USD] cBAT,inv [USD/kW] cBAT,OM [USD/year/kW] CBAT,OM [USD] CBAT,rep [USD] cBAT [USD/kWh] CBAT [USD] cDG,OM [USD/year/kW] CDG,OM [USD] cDG [USD/kW] CDG [USD] cdiesel [USD/l] Cdiesel[USD]  cf_min  USD/W  p cf USD/Wp Cini,inv [USD] cinsu [%] Cinsu [USD] cmb [%] Cown [USD] cPV,ins,lab [USD/Wp ] cPV,ins,mat [USD/Wp ] cPV,ins [USD/Wp ] cPV,inv [USD/Wp ] cPV,OM,lab [USD/year/Wp ] cPV,OM,mat [USD/year/Wp ] cPV,OM [USD/year/Wp ] CPV,OM [USD] cPV [USD/Wp ] CPV [USD] Ct [USD] Cwar [USD] CO2e [gCO2 ] BAT,inv [gCO2 ] CO2e BAT CO2e [gCO2 ]

xix

20-year bond yield total system cost per Wp silver cost per unit mass bank amortization payment bank interest payment total cost due to battery inverters battery inverter cost O&M cost for batteries total O&M cost from batteries battery replacement cost battery cost total battery acquisition cost O&M cost for diesel generators total O&M cost from diesel generators diesel generator cost total acquisition cost of diesel generators diesel price total cost due to diesel consumption minimum fabrication cost from pareto front fabrication cost of solar cell or solar module PV system initial investment yearly insurance cost factor total insurance cost for PV system cost relation between bifacial and monofacial module price to reach the same LCOE part of the initial investment paid directly by the project owner installation cost of the PV system related to the labor installation cost of the PV system related to the materials installation cost of the PV system PV inverter cost yearly O&M cost factor for PV system related to the labor yearly O&M cost factor for PV system related to the materials yearly O&M cost factor for PV system total O&M cost from PV system acquisition cost of solar panels total cost of PV system total cost to produce the PV device total warranty extension cost of the PV inverter CO2 equivalent life cycle emissions CO2e emissions of the battery inverters CO2e emissions of the batteries

xx DG CO2e [gCO2 ] diesel [gCO2 ] CO2e PV,ins CO2e [gCO2 ] PV,inv CO2e [gCO2 ] PV [gCO2 ] CO2e Cortax [%] CostBAT [USD]

cs[m]  DAg_f g/m3   3 DAg_pads  g/m  DAg_r g/m3 DHI [W/m2 ] DNI [W/m2 ] DR[%] dtBank [year] E[kWh] Ed [Wh/Wp /day] (y) EPV [Wh] El[m] Eqc [%] EWBB_f [%] EWfi_f [%] EWir [%] f1 FM_f [0, 1] FM_r [0, 1] GHI [W/m2 ] gvf hBB_f [m] hBB_r [m] hir [m] hmg [m] hpads [m] I0 [W/m2 ] Idiff,f [W/m2 ] Idiff,r [W/m2 ] Idir,f [W/m2 ] Idir,r [W/m2 ] Id [Wh/m2 /day] If [W/m2 ]

Symbols

CO2e emissions of the diesel generators CO2e emissions of the diesel CO2e emissions of the solar panel installations CO2e emissions of the PV inverters CO2e emissions of the solar panels Corporate income tax cost related to the batteries installation for a particular year cell spacing silver content of the front paste (front busbars and fingers) silver content of the silver pads silver content of the rear paste (rear busbars and fingers) diffuse horizontal irradiance direct normal irradiance discount rate bank debt tenor battery lifetime discharging energy daily average energy production total energy generation of the PV system for year y surface elevation Equity cost effective width of the front side busbars effective width of the front side fingers effective width of the interconnector ribbons spectral irradiance contribution front side metallization fraction rear side metallization fraction global horizontal irradiance ground view factor average height of the front side busbar average height of the rear side busbar height of the interconnector ribbons module height measured between the module lowest edge and ground height of the silver pads extraterrestrial irradiance normal to a surface diffuse irradiance contribution from If diffuse irradiance contribution from Ir direct irradiance contribution from If direct irradiance contribution from Ir daily average effective irradiation module front side irradiance

Symbols

Ignd,f [W/m2 ] Ignd,r [W/m2 ] Iin [USD] Impp [A] Ir [W/m2 ] Iuc (j)[A] IR[%] IRBank [%]  2 jL mA/cm   2 jo1_b mA/cm   2 jo1_n+ _met  mA/cm  2 jo1_n+ mA/cm   jo1_p_AlBSF mA/cm2 2 jo1_p+ _met  mA/cm  2 jo1_p+ mA/cm 2 jo1_r  mA/cm  2 jo1 mA/cm   2 j o2_f_met  mA/cm  jo2_n+ mA/cm2  2 jo2_p+ mA/cm   2 mA/cm jo2_r_met   2 jo2 mA/cm   jph_ab mA/cm2 jph_bs mA/cm2   jph_di_f  mA/cm2 jph_di_r mA/cm2  jph_ref_f  mA/cm2 2 mA/cm jph_ref_r   2 jph mA/cm lBank [%] lcell [m] lpads [m] LCOE[USD/kWh] LCOEip [%] lightpp [%] lightsp [%] m Ag [%]   mAg_BB_f  g mAg_BB_r g mAg_fi_f  g mAg_fi_r g  mAg_min g  mAg_pads g

xxi

ground irradiance contribution from If ground irradiance contribution from Ir initial investment current at maximum power point module rear side irradiance total current generated at the unit cell inflation rate bank interest rate load current density jo1 contribution from the base jo1 contribution at the emitter-metal interface jo1 contribution from the emitter jo1 contribution at the base-Al-BSF interface jo1 contribution at rear p+ -metal interface jo1 contribution from the p+ rear layer jo1 contribution from the rear side dark saturation current density of diode 1 jo2 contribution from the front metal contacts jo2 contribution from the emitter jo2 contribution from the rear p+ rear layer jo2 contribution from the rear metal contacts dark saturation current density of diode 2 jph contribution due to the albedo factor jph contribution due to light reflected from the backsheet jph contribution at the front side due to direct light jph contribution at the rear side due to direct light jph of a reference solar cell at the front side jph of a reference solar cell at the rear side photovoltaic current density bank loan cell length length of the silver pads levelized cost of electricity LCOE improvement percentage of p polarized light percentage of s polarized light total silver consumption when a particular optimization variable is modified based on Varunc silver consumption due to front side busbars silver consumption due to rear side busbars silver consumption due to front side fingers silver consumption due to rear side fingers minimum silver consumption from the pareto front silver consumption due to the silver pads

xxii

  mAg g Mrp [%] n1 n2 nag nair NBAT nBAT nBB ncs nc nDG nfi_f nglass nlb_max npads NPV nPV Np nr Ns Objsen [%] Pc,max [kW] Pc [kW ] Pd,max [kW ] PDG,nominal [kW ] PDG,min [kW ] PDG [kW ] Pd [kW ] Pload [kW ] Ploss (j)[W] PPV [W] PSTC,f [Wp ] r(j)[cm2 ] rBB_f [cm2 ] rBB_r [cm2 ] rbr [cm2 ] Rbs [%] rb [cm2 ]

Symbols

total silver consumption Market risk premium ideality number of diode 1 ideality number of diode 2 number of silver pads per column air refractive index total number of batteries installed until a particular year number of batteries number of busbars and interconnector ribbons number of subdivisions of the cell spacing distance number of solar cells columns within a module number of diesel generators number of front side fingers glass refractive index maximum number of light bouncing from backsheet number of silver pads per column total number of solar panels installed until a particular year number of solar panels number of string of cells connected in parallel number of solar cells rows within a module number of cells connected in series maximum sensitivity of the objective functions maximum charging power from batteries charging power from battery inverters maximum discharging power from batteries nominal power of diesel generators minimum power from diesel generators power produced by diesel generators discharging power from battery inverters load demand power loss at the unit cell due to the jth contributor of rs power produced from the PV system direct power production from the installed solar panels when light reaches only the front side under standard test conditions area weighted series resistance of the jth contributor of rs area weighted front side busbar resistance area weighted rear side busbar resistance area weighted bussing ribbon resistance backsheet weighted average reflectance area weighted base resistance

Symbols

rc_ge [cm2 ] rc_gp+ [cm2 ] Reff (j)[] re [cm2 ] rfi_f [cm2 ] rfi_r [cm2 ] rir_cs [cm2 ] rir_f [cm2 ] rir_r [cm2 ] rm_r [cm2 ] rp+ [cm2 ] rp [cm2 ] Rsh_e [Ω/] Rsh_p+ [Ω/] rs [cm2 ] rlcir,f rldir,f rlgnd,f rlhor,f rlsky,f S[kWh] S0 [kWh] Sdiesel [USD] sf_f [m] sf_r [m] SOC[%] SOCmax [%] SOCmin [%] SR[W ] SRBAT [W ] SRDG [W ] svf Ta [◦ C] Tc [◦ C] TINOCT [◦ C]

xxiii

area weighted contact resistance between the front grid and the emitter area weighted contact resistance between the rear grid and the p+ layer effective resistance of the jth contributor of rs area weighted emitter resistance area weighted front side finger resistance area weighted rear side finger resistance area weighted cell spacing interconnector ribbon resistance area weighted front side interconnector ribbon resistance area weighted rear side interconnector ribbon resistance area weighted rear side metal layer resistance area weighted resistance of the p+ layer area weighted shunt resistance sheet resistance of the emitter sheet resistance of the p+ layer area weighted series resistance reflection losses of light reaching the front surface for the circumsolar component of the Perez4 model reflection losses of light reaching the front surface for the Idir,f irradiance reflection losses of light reaching the front surface for the Ignd,f irradiance reflection losses of light reaching the front surface for the horizon component of the Perez4 model reflection losses of light reaching the front surface for the sky component of the Perez4 model current battery capacity initial battery capacity savings on diesel for a particular year geometrical constant geometrical constant battery state of charge maximum state of charge minimum state of charge total spinning reserve spinning reserve from batteries spinning reserve from diesel generators sky view factor ambient temperature temperature of the solar cell installed normal operating cell temperature

xxiv

TNOCT [◦ C] temp[K] Thb [m] Thglass [mm] Thm_r [m] u VL [V] Vmpp [V] vt [V] Varunc [%] wBAT [years] wBB_f [m] wBB_r [m] wcell [m] wfi_f [m] wfi_r [m] wir [m] wivt [year] wpads [m] wPV [years] xmount [◦ C] z[◦ ]

Symbols

normal operating cell temperature temperature of the PV device thickness of the base glass thickness thickness of the rear side metal layer DG status (0 if DG is OFF, otherwise 1) load voltage voltage at maximum power point thermal voltage uncertainty of the optimization variable warranty period of battery inverters width of front side busbars width of the rear side busbar cell width width of front side fingers width of rear side fingers width of the interconnector ribbons warranty period of PV inverters width of the silver pads warranty period of PV inverters mounting structure dependent parameter sun zenith angle

Chapter 1

Introduction

1.1 Motivation The world’s population is increasing day by day. This increase, together with the desire of people to achieve a better quality of life, leads to a continuous rise in energy consumption, as can be seen from Fig. 1.1. This figure shows the contribution from different energy sources to the world primary energy consumption. At present, most of the primary energy is obtained from non-renewable sources, the supply of which, as their name indicates, is limited. Based on the production levels and nonrenewable known reserves in 2017, the number of years reserve left for coal, oil and natural gas are estimated to be 134, 50.2 and 52.6, respectively [1]. Although factors such as the future discovery of unknown non-renewable reserves can help to increase the previous values, the issue is that at one point in time the non-renewable reserves will be depleted. In addition, non-renewable sources produce a considerable amount of greenhouse gas (GHG) emissions which are known to contribute to the climate change. As a consequence, most of the countries have ratified the Paris Agreement [2], which aims to limit the global temperature increase to be well below 2 ◦ C. According to the agreement, these countries are expected to set targets to reduce their GHG emissions. Therefore, it is imperative to address these challenges by reducing energy consumption (e.g. through energy efficiency measures) and promoting the use of renewable sources. Many countries have set targets to achieve a minimum renewable generation, which is often accompanied by supporting policies. For example, China aims to reach an accumulated installed capacity of renewable sources of 770 GW by 2020. By the same year, Australia aims to generate 20% of its electricity supply from renewables, and India aims to reach a total installed capacity of 100 GW for solar, 60 GW for Wind, 10 GW for biomass, and 5 GW for hydropower by 2022 [3]. Among the different sources of renewable energy, solar energy is highly promising due to considerable amount of energy provided by the sun almost anywhere in the planet. To have a better understanding on the previous statement, Fig. 1.2 shows the estimated worldwide energy demand in 2015 in comparison to the yearly energy potential from other renewables sources (excluding solar), the expected energy pro© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7_1

1

2

1 Introduction

Fig. 1.1 Historical primary energy consumption worldwide (adapted from [1, 4])

Fig. 1.2 Solar energy potential showing the relation between the yearly energy provided by the sun (yellow), other renewable energy sources (green), estimated non-renewable reserves (black), and the 2015 world energy demand (violet) (adapted from [5])

1.1 Motivation

3

Fig. 1.3 Historical PV accumulated installed capacity, PV yearly installed capacity and PV electricity production (adapted from [9–11])

duced from the known non-renewable reserves and the yearly solar energy potential (solar energy reaching the land masses). Solar cells then appear as the basic elements which directly convert energy from light into electricity based on the photovoltaic (PV) effect. At the beginning of their commercialization, solar panels (composed of solar cells) were very expensive (above 20 USD/Wp in 1984 [6]), limiting their adoption mostly to space applications [7]. Nevertheless, due to suitable support schemes (e.g. the renewable energy act in Germany in the early 2000s) and continuous improvement in manufacturing, their cost has reduced over time, reaching a current value of around 0.21 USD/Wp [8], allowing for the PV installation capacity to increase significantly. This can be seen in Fig. 1.3, which shows the accumulated and yearly PV installed capacity worldwide (reaching values of around 500 GWp and 100 GWp by 2018, respectively [9]). In addition, Fig. 1.3 also presents the percentage of the electricity generation coming from PV worldwide (2.58% by 2018 [9]) showing a steady increase with time.

1.2 Research Objectives Based on the discussions provided in Sect. 1.1, it can be expected for the PV penetration to keep on increasing in the following years to decades due to several favorable conditions, such as the continuous increase in cell efficiencies, decrease on the PV fabrication cost, scalability, no noise generation, and clean energy production. Although this technology has already reached a certain level of maturity where it is able to achieve similar (or lower) values for the cost of its electricity generation

4

1 Introduction

in certain countries, in comparison to non-renewable sources [12], it still has space for further improvements. Therefore, by continuously enhancing the PV properties, there will be more cases in which PV would not only be desired as a way to fight climate change, but also as an economical alternative to produce electricity. The overall objective of this work is then to study current limitations in the area of PV and propose strategies to address them by applying optimization approaches. The study can then be divided into three main sections, namely, the studies related to photovoltaic solar cells, modules, and systems. It is desired to fabricate solar cells with high electrical performance and low cost to later be integrated into solar modules which are expected to last for many years. Hence, in this work, the cell fabrication is examined up to a certain extent to optimize their fabrication steps, with the aim to enhance their electrical performance and reduce their fabrication cost. The fabrication of solar modules is also optimized considering not only standard test conditions, but also real weather conditions in different locations worldwide. At the system level, PV systems can be divided into grid-connected and off-grid systems. With respect to the former, the module orientation is optimized for monofacial and bifacial technologies, also studying their expected levelized cost of electricity to conclude, under which locations/conditions, a particular technology will be more effective. With respect to the second system type, off-grid PV hybrid systems (systems composed of solar panels, batteries, and diesel generators) are also studied. Here, a diesel replacement strategy (reduction of diesel consumption based on the progressive addition of PV and batteries) is proposed aiming to reduce the initial investment required to install solar panels and batteries, which is a typical barrier for financing these projects. In addition, the dispatch strategy for these systems is also optimized aiming to reduce the overall system costs in their daily operation. To conduct the optimization approaches for the different studies of this thesis, regardless of whether the optimization is desired to be implemented at the cell, module or system level, the following standard steps are followed: (1) Describe the problem to be examined; (2) analyze the approaches found in the literature to address the problem of interest; (3) discuss the disadvantages or gaps from the current approaches presented in the literature; (4) propose a new approach and indicate its theoretical advantages; (5) model the phenomenon to be studied (e.g. model of the electrical performance of a solar cell, module, or PV system) with a set of mathematical equations; (6) define the optimization problem, indicating the objective function (what it is desired to be achieved), the constraints (to ensure that the solutions can be implemented in real life), and the optimization variables (the variables desired to be optimized within the solution space); (7) describe the optimization algorithm to be applied together with its properties; and (8) generate and analyze the obtained results.

1.3 Author’s Original Contributions

5

1.3 Author’s Original Contributions The main contributions from the author’s work are listed below: (1) Proposed an advanced optimization approach to enhance the electrical performance and reduce the fabrication cost of monofacial and bifacial crystalline Si-based cells and modules. Although approaches can be found in the literature to enhance the metallization design of cells/modules, they only consist of taking one or two parameters to be increased linearly until the best result can be yielded. Nevertheless, there are more variables that can be taken into account to further enhance the optimization design. Moreover, an optimization approach based on a linear increase is not the most effective method to reach the optimal solution when there are multiple parameters to optimize. Therefore, the proposed approach optimizes multiple parameters in parallel (number and dimensions of fingers, busbars, and interconnector ribbons) to enhance the electrical performance and reduce the fabrication cost under standard test conditions and real world conditions. (2) With respect to grid connected PV systems, the expected extra energy gain when installing bifacial modules compared to the monofacial ones have been reported in the literature. Nevertheless, the main question that needs to be answered is: Are bifacial PV systems more cost-effective than their monofacial counterparts? In this work, the author evaluated and compared the levelized cost of electricity between monofacial and bifacial PV systems to conclude on the conditions in which bifacial PV systems are more cost-effective. A detailed analysis on the environmental influences as well as the local albedo was also performed together with the optimization of the module orientation for different scenarios, i.e. when any module orientation is allowed and when only vertical module orientations are allowed. (3) Although different works show that the addition of solar panels into off-grid systems to form PV hybrid systems can be cost-effective, a high investment is typically required. On the contrary, systems composed of diesel generators only require minimal initial investment, despite the risk of resulting in higher costs at the end of the system lifespan. This could then constitute a “deal breaker” for investors or local communities who might not be able, or are not willing to spend such large funds upfront to hybridize off-grid systems. Consequently, the author developed a strategy to reduce the required initial investment, while assuring high savings at the end of the project lifespan. The proposed approach led to an optimal process to add solar panels and batteries over time. This method is then beneficial to promote the hybridization of systems originally formed by diesel generators by requiring a low initial investment yet achieving considerable savings. (4) As off-grid PV hybrid systems are formed by multiple energy sources (in this work these systems are composed of solar panels, batteries, and diesel generators), it is then necessary to optimize their dispatch strategy (to set their optimal power production and control their ON/OFF state). Although scheduling algo-

6

1 Introduction

rithms have already been implemented in real systems (such as the DG backup based algorithm and the spinning reserve based algorithm), the author proposed an approach that incorporates load and irradiance forecasting to further enhance the system performance. The results revealed that, with an accurate enough forecasting approach, the system operation can be improved. This approach can then be applied in PV hybrid systems to further increase the overall savings.

1.4 Thesis Structure This thesis is comprised of seven chapters. In this chapter provides the motivation of this work indicating the concerns related to energy generation from non-renewable sources (limitation and generation of considerable GHG emissions) together with the potential of renewable sources, in particular the one from solar energy, to satisfy the increasing load demand. This chapter also shows the constant increase of the PV installed capacity over time and the potential to keep raising its penetration worldwide. The objectives from this thesis are then briefly discussed, i.e. to address technical gaps to further optimize performance parameters at the cell, module, and system levels. The original contributions from this work are then provided. Chapter 2 deals with the introduction of this research. The photovoltaic effect is explained in more detail together with the description and characteristics of solar cells, modules, and systems. A review on the optimization problems and methods to solve them is also provided as these will be applied in the following chapters. Chapter 3 proposes a methodology to optimize the grid metallization design of Si wafer-based solar cells and modules under standard test conditions and real world conditions. On the one hand, under standard test conditions, a multiobjective and robust optimization approach is implemented to optimize several parameters in parallel (number and dimensions of fingers, busbars, silver pads and ribbons) to enhance the efficiency and reduce the silver consumption at the cell and module levels. With the obtained pareto-optimal fronts, the minimum fabrication cost is estimated. On the other hand, under real world conditions, the typical meteorological year data of irradiance and temperature are estimated for different locations worldwide to optimize the grid metallization design of solar modules. Chapter 4 investigates whether it is more cost-effective to install PV systems using monofacial or bifacial modules (in grid-connected systems) for designs which allow any module orientation and those with vertical module orientations, considering a total of 55 locations worldwide. The cost-effectiveness of a PV system is defined based on its levelized cost of electricity (LCOE). In addition, the module orientation for each case study is optimized, discussing also the influence of conditions, such as weather and albedo, on its ideal design. Chapter 5 deals with the sizing optimization of PV hybrid system. In this chapter, a diesel replacement strategy is proposed by progressively adding solar panels and batteries in the off-grid systems originally composed of diesel generators. The strat-

1.4 Thesis Structure

7

egy defines an optimal process to add these distributed sources over time to take advantage of their expected price reduction in the future. A limited initial investment, financed partially by a bank loan, is taken into account to install solar panels and batteries at the beginning. For the subsequent years, further installations of solar panels and batteries are funded by the accumulated diesel savings. Chapter 6 also deals with PV hybrid system. Here, a dispatch strategy optimization algorithm is proposed for PV-battery-diesel hybrid system considering load and irradiance forecasting. The results from the proposed algorithm are compared with benchmark algorithms to analyze the advantages of the former. The simulations take place in a real time simulator in an effort to validate the accuracy of these results and evaluate the grid quality. Chapter 7 provides the main conclusions from this thesis, also indicating the proposed future work based on the findings and limitations from this thesis.

References 1. 2. 3. 4. 5. 6. 7.

8. 9. 10. 11. 12.

BP-Global (2018) BP statistical review of world energy United_Nations (2015) Paris agreement. Paris, France International_Energy_Agency_(IEA) (2018) IEA/IRENA joint policies and measured database Smil V (2017) Energy transitions: global and national perspectives, 2nd edn. Praeger, Santa Barbara Perez M, Perez R (2015) Update 2015—a fundamental look at supply side energy reserves for the planet. Nat Gas 2(9):215 Sivaram V, Kann S (2016) Solar power needs a more ambitious cost target. Nat Energy 1(4):16036 Smets A, Jäger K, Isabella O, Swaaij R, Zeman M (2016) Solar energy: the physics and engineering of photovoltaic conversion technologies and systems, 1st edn. UIT Cambridge, Cambridge PVinsights (2019) Solar PV module weekly spot price International_Energy_Agency_(IEA) (2019) 2019 snapshot of global PV markets. Technical report IEA PVPS T1-35:2019 International_Energy_Agency_(IEA) (2016). Trends 2016 in photovoltaic applications. Technical report IEA PVPS T1-30:2016 International_Energy_Agency_(IEA) (2018) 2018 snapshot of global photovoltaic markets. Technical report IEA PVPS T1-33:2018 Breyer C, Gerlach A (2013) Global overview on grid-parity. Prog Photovolt Res Appl 21(1):121–136

Chapter 2

Background and Literature Review

2.1 Review of the Photovoltaic Field 2.1.1 Solar Cells Solar cells correspond to the basic unit where the photovoltaic effect takes place. The photovoltaic effect, first discovered by Becquerel in 1839 [1], consists on the voltage formation in an element due to light absorption. At present, most of the solar cells in the market are made from crystalline silicon [2] due to their many advantages, namely, availability, chemical stability, industry experience with this semiconductor, band gap value, among others. The operational principle of a p-type Si-based solar cell is presented in Fig. 2.1a. Once a photon with enough energy is absorbed by the cell (step 1), an electron from the Si covalent bonds is released and an electron-hole pair is produced (step 2). The released electron and hole will then flow through the cell due to diffusion. If they reach the p-n junction, they will be separated due to the electric field present in this junction (step 3). Once separated, the electron flows through an external circuit (step 4), where electrical power can be delivered, before it recombines with a hole (step 5). The equivalent circuit of a solar cell can be represented based on the two-diode model [3], presented in Fig. 2.1b. This is composed of the photovoltaic current (Iph ) whose value increases based on the amount of light absorption, and two diodes (D1 and D2) to represent the recombination losses that occur at the base and emitter (D1), and the recombination losses at the depletion region (D2) [4]. In addition, the parallel resistance (Rp ) accounts for the losses due to internal shunts, e.g. free electrons located at the n region flowing directly to the p region at the edges of the cell due to inefficient edge isolation during the cell fabrication process. The variable,Rs is the series resistance and constitutes the resistive losses from charges traveling through the cell [5]. Finally, the variables, VL and IL are the load voltage and current, respectively. Subsequently, considering the two-diode model, the load voltage and current produced from a single solar cell can be estimated based on Eq. (2.1): © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7_2

9

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2 Background and Literature Review

 VL +Rs ·IL  VL +Rs ·IL   V +R ·I L s L IL = Iph − Io1 e n1 ·vt − 1 − Io2 e n2 ·vt − 1 − Rp

(2.1)

The second and third terms from the right side of Eq. (2.1) correspond to the current flowing through D1 and D2, respectively where the dark saturation currents (Io1 and Io2 ) and ideality numbers (n 1 and n 2 ) are considered together with the thermal voltage vt . The last term from this equation corresponds to the current flowing through the parallel resistance, Rp . Based on Eq. (2.1), the load current versus load voltage curve, as well as the load power versus load voltage curve for a typical Si-based solar cell can be estimated. These curves are presented in Fig. 2.1c for a fixed value of irradiance and temperature. As it can be understood, it is desired for solar cells to produce the maximum possible power and as such, to operate at their maximum power point (MPP) [6]. The operating point of a solar cell depends on the value of the external resistance. For example, for an external resistance equal to zero (short circuit condition), the output voltage is set to zero while the current is set to its maximum; for an external resistance equal to infinity (open circuit condition), the output voltage is set to its maximum while the current is set to zero. Under the two previous mentioned operational points, the electrical power generation is equal to zero, as seen in Fig. 2.1c. Nevertheless, by properly setting the value of the external resistance, the maximum power point can be reached. Within this work, two cell technologies are analyzed: (1) crystalline Si monofacial (only absorbs light from the front side) Aluminium Back Surface Field (Al-BSF) cells, which possess most of the market share [8]; and (2) crystalline Si bifacial (able to absorb light from the front and rear side) Passivated Emitter Rear Totally-diffused (PERT) cells. The bifacial technology is also investigated as it is expected to increase its market share in future [8].

2.1.2 Solar Modules Crystalline Si-based solar cells have a thickness of the order of the micrometers. Therefore, these cells are fragile and can be easily broken by external forces. In addition, they are susceptible to the environment and their performance can reduce significantly when exposed to elements such as oxygen and water vapor. Consequently, solar modules are introduced to protect the cells. Solar modules are composed of solar cells which are surrounded by an encapsulant (typically Ethyl Vinyl Acetate (EVA)). Glass is then placed on the top, and a backsheet is typically placed at the rear side when fabricating monofacial modules (for bifacial modules, glass is placed at the rear side instead of the backsheet, as light needs to be absorbed from the rear side as well).

2.1 Review of the Photovoltaic Field

11

Fig. 2.1 a Operational principle of a solar cell (adapted from [7]); b two-diode model of a solar cell; and c IV curve and power curve of a typical Si-based solar cell

12

2 Background and Literature Review

Solar modules are composed of many cells (typically 60 and 72 cells [8]). As can be seen from Fig. 2.1c, the external voltage from an individual cell is low and therefore, cells within a module are mostly connected in series to raise the overall voltage. The electrical properties of these modules can also be represented based on the two-diode model, as shown in Fig. 2.2a. The terms Ns and Np correspond to the number of solar cells connected in series and number of cell strings connected in parallel, respectively. For a typical 60 cell module for example, all the cells are in series connection, therefore, Ns =60 and Np =1. The load voltage and current from a solar module can then be estimated based on the following equation: ⎛ Np · VL + Ns · Rs · jL IL = Np · Iph − − Np · Io1 ⎝e N s · Rp

VL Rs ·IL Ns + Np n 1 ·vt

⎞

⎛

− 1⎠ − Np · Io2 ⎝e

VL Rs ·IL Ns + Np n 2 ·vt

⎞ − 1⎠

(2.2) The simulated current versus voltage and power versus voltage curves for a 60cell solar module is then presented in Fig. 2.2b. Due to the series connection of the cells, the overall voltage is considerably higher than the voltage from an individual cell, while its maximum current remains the same to the one of a single cell. The module constitutes the end product which can be directly commercialized and installed in real applications.

2.1.3 Photovoltaic Systems As the name suggests, photovoltaic systems are the final setup, where solar modules are used to generate electricity for a certain purpose or application. These can be classified into two categories, namely, “grid connected” and “off-grid systems”.

2.1.3.1

Grid Connected PV Systems

These systems are directly connected to the main electricity grid via power electronic converters. Grid connected PV systems account for most of the PV installation capacity worldwide (>95% [2]) and can be further subdivided into (1) residential systems, with a typical installed capacity of a few kWp; (2) commercial systems, with a typical installed capacity in the order of hundreds of kWp; and (3) utility scale systems, with an installed capacity in the order of tens or even hundreds MWp [9]. Residential and commercial PV installations are typically employed with the aim to energize a particular load, e.g. a house or a factory, and to only export the surplus energy to the utility grid. On the other hand, utility scale PV systems aim to directly export/sell their energy production to the grid. Since the power output produced from solar panels is DC, while the main grid is typically AC, an inverter is required to convert DC power into AC power [10]. Depending on the inverter chosen, different system architectures can be adopted

2.1 Review of the Photovoltaic Field

13

Fig. 2.2 a Two-diode model of a solar module; and b IV curve and power curve of a typical 60-cell Si-based module

[3]. Figure 2.3 shows the three commonly used designs. When micro inverters are employed (Fig. 2.3a), typically one module is connected per inverter. With respect to string inverters (Fig. 2.3b), as it’s name indicates, a string of panels is connected per inverter. For a central inverter, all panels are connected via a single inverter (the system is centralized). Under ideal conditions, the central inverter architecture achieves the highest overall efficiency and lowest inverter cost per Wp, followed by the string inverter and then the micro inverter. Nevertheless, the micro inverter can achieve a better performance over non-ideal conditions such as scenarios when there is a considerable amount of shading over a module, as with this configuration, only the power output from one module (the shaded one) is affected. If a module

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2 Background and Literature Review

Fig. 2.3 System architectures of PV installations based on the employed inverter: a micro inverters; b string inverters; and c central inverter

is heavily shaded in a string inverter configuration, the performance of the whole string would have been affected. A similar (but amplified) outcome would occur in a central inverter configuration. As described Sect. 2.1.1, it is desired for the PV devices to operate at their maximum power point. This is typically achieved by the inverters which have incorporated a maximum power point tracking (MPPT) algorithm. Different MPPT approaches are presented in the literature, which can be classified into indirect and direct MPPT. Indirect MPPT algorithms apply assumptions and sample measurements to find the MPP. For example, the fractional open circuit voltage method considers that the voltage at MPP corresponds to a fixed fraction of the open circuit voltage (for crystalline Si, the fraction value is typically set between 0.7 to 0.8 [3]). Therefore, it will set the panels voltage equal to a certain value. Although this method is simple to implement, it has disadvantages such as the requirement to fix the fraction value (depending on the technology this value will be different) and, as time passes, the panels start to degrade and the fraction value will change. On the other hand, direct MPPT algorithms measure electrical signals from the panels (such as current, voltage and power) to track the MPP. Two popular direct approaches are the perturb and observe (P&O) method and the incremental conductance method. The former one applies a small perturbation in the panel voltage and analyzes the increase/decrease on the power output. For example, assuming ideal conditions, if the voltage is slightly increased and the resulting output power is also increased, it means that the operational point is currently to the left side of the peak in the power versus voltage curve shown in Fig. 2.2b. Consequently, voltage increments are favorable and therefore, a second voltage increment will be applied as long as the power keeps on increasing (operation point still located to the left side of the peak in the power vs voltage curve). Once the power decreases due to a voltage increment, it means that the operational point is to the right side of the peak in the power versus voltage curve (increment

2.1 Review of the Photovoltaic Field

15

in voltage produces reduction in power). Therefore, the voltage will then be slightly decreased aiming to maximize the power output, and so on. The incremental conductance method compares the incremental conductance with respect to the negative instantaneous conductance, if the former is higher, it means that the current operation point is to the left side of the peak in the power versus voltage curve and therefore the voltage reference should increase (opposite action takes place if the incremental conductance is lower than the negative instantaneous conductance). Although the incremental conductance method is in general able to achieve a slightly better performance than the P&O method, it is also more complex as it requires for the incremental and instantaneous conductance to be calculated. More details on the MPPT methods can be found in [3].

2.1.3.2

Off-Grid PV Systems

Currently, about 14% of the world’s population does not have access to electricity, with 84% of this population located in rural areas [11]. Therefore, off-grid systems are helpful in these scenarios, as it minimizes or even removes the need to extend utility grids to the remote places. When these stand-alone systems include solar panels, they are known as off-grid PV systems. Different AC system designs can be implemented based on the requirements for particular case studies.1 Three of these designs are presented in Fig. 2.4 where the arrows represent the direction of power flow. The first system (Fig. 2.4a) shows a PV system connected to an inverter which is then connected to the load. In this system, the only energy source are the solar panels and no storage device is present. Therefore, electrical power is available only when there is irradiance, and the maximum available power will depend on the level of irradiance. Consequently, these systems are applied only when there is no need to have full control on the load schedule. A typical application of this system is water irrigation for agricultural crops. The second system presented in Fig. 2.4b incorporates batteries that store any surplus of power produced from the solar panels to be used at later times when required (e.g. during nighttime, when solar panels are not able to produce electrical power). This system typically employs a charge controller, connected between the solar panels and batteries. The main functions of the charge controller are to ensure for the panels to operate at MPP. While inverters are employed to convert DC power into AC power. For these off-grid systems, besides solar panels, other sources of energy can be incorporated. These systems are then called PV hybrid systems. For this thesis, PV hybrid systems composed of solar panels, batteries and diesel generators are investigated, as shown in Fig. 2.4c. These systems normally have a higher installed capacity than the previous ones. Therefore, solar panels can be assigned to their own inverter while the battery system can be assigned to its own bidirectional converter (which will control the discharging/charging power of the batteries). Diesel generators produce AC power, 1 Although

there are also DC off-grid systems, these are not considered in this work and therefore, will not be discussed.

16

2 Background and Literature Review

Fig. 2.4 a PV system without storage or other source of energy; b PV-battery systems; and c PV hybrid system composed of solar panels, batteries and diesel generators

2.1 Review of the Photovoltaic Field

17

consequently, no inverter is required for them. Due to extra equipment installed for the latter system, its optimal control is more complex and challenging. How to derive such control algorithms will be discussed later in this thesis.

2.2 Review of the Optimization Field 2.2.1 Optimization Problem An optimization problem can be defined as a problem where it is desired to find the best/optimal solution within a solution space. An optimization problem is composed of an objective function (what is desired to be achieved, e.g. maximize savings, minimize CO2 emissions), constraints (which define the solution space and are required so that the results can be implementable in real life), and optimization variables (variables whose value is required to be optimized within the solution space to obtain the optimal solution).

2.2.2 Optimization Algorithms Optimization algorithms are then applied to solve problems where their effectiveness can be deduced based on factors such as how fast and how close are the obtained results with respect to the optimal one. The optimization algorithms applied in this thesis correspond to the heuristic and meta-heuristic algorithms. These algorithms are employed when it is not imperative to find the optimal solution but a close approximation is good enough. Heuristic algorithms are designed to solve a particular problem (so-called problem-dependent algorithms). While the advantage of these approaches is that they aim to analyze the conditions of a particular problem, and to design a specific algorithm to solve it, they might not work well when applied to other optimization problems (or might not even be applicable for a different optimization problem). Therefore, a heuristic algorithm should only be used for the problem it was designed for. On the other hand, meta-heuristic algorithms employ techniques independent of the particular problem specifications. Consequently, although they do not take advantage of the specifics of a problem, they can be applied in multiple optimization problems. Literature presents different meta-heuristic algorithms. These can be divided into population-based and non-population-based algorithms. The former initially defines a population of candidate solutions within the solution space (these can be declared randomly or by applying principles such as the homogeneous distribution [12]) and calculates the fitness of the initial population. Based on their result, the position of the candidates solutions for the next iteration is defined following the principles of the employed algorithm. The search for the optimal solution within the solution space

18

2 Background and Literature Review

is based on a trial-and-error process. Yet, it is expected that, as the iteration number increases, candidate solutions will reach closer to the optimal solution. An example of population-based meta-heuristic algorithms is genetic algorithm [13], which emulates the natural selection process. At the beginning, an initial population is defined. Each individual of this population represents a chromosome which contains genes of different attributes. These attributes correspond to the values of the optimization variables. Based on these variables, the objective functions are calculated. The parents are then randomly selected to generate the offspring by applying operators such as crossover and mutation and then the process is iterated. Another population-based algorithm corresponds to the particle swarm optimization algorithm [14]. This algorithm is inspired by the movement in a bird flock where an initial population (bird flock) is defined at different positions (each position correspond to the values of the optimization variables within the solution space). The position from each member of the population is then evaluated storing the position with the best overall solution and the best individual position from each member. Based on these results, the new position from each member is estimated and then evaluated to repeat the previous process iteratively aiming to reach solutions closer to the optimal one. Non-population-based algorithms are also iterative algorithms, however they employ a single potential solution to travel through the solution space to find the optimal solution. An example of these algorithms is tabu search [15]. The tabu search algorithm applies a neighborhood search procedure which aims to move to an improved solution within its neighborhood after each iteration. To prevent the potential solution from exploring previously analyzed solutions, a tabu list is used. This list is a memory structure where the previous analyzed solutions are stored. More details on the different meta-heuristic algorithms can be found in [16–21]. While the previous algorithms are designed to solve a single objective function, other algorithms are also introduced to solve optimization problems which contain multiple objectives. When multiple objectives are present, not a single optimal solution but a set of optimal solutions are obtained (known as pareto-optimal solutions or pareto-optimal front). This outcome is because each solution from the same pareto front is non-dominated with respect to the others [22]. To further develop this idea, we can consider a multiobjective optimization problem defined as: maximi ze (z 1 )

(2.3)

minimi ze (z 2 )

(2.4)

from which all the possible solutions (optimal and non-optimal) are illustrated in Fig. 2.5. The set of pareto-optimal solutions is then presented. It can be appreciated that, if a particular solution s1 has a higher z 1 value than the one from another solution s2 , the latter will then have a lower z 2 value than the one from s1 so that it cannot be decided which solution is better.

2.2 Review of the Optimization Field

19

Fig. 2.5 Set of pareto-optimal solutions for a multiobjective optimization problem

Although the previous algorithms aim to find optimal solutions, depending on the particular case study, the solutions might be required to be robust. Robust solutions are the ones in which a slight change on the optimization variables will not lead to an abrupt change on the values of the objective functions [23–25]. To further develop this idea, let us assume the following optimization problem composed of a single optimization variable z 3 and a single objective function f (z 3 ), such as: minimi ze ( f (z 3 ))

(2.5)

The solution space is then provided in Fig. 2.6. It can be seen that two local minima are presented: s1 and s2 . As this is a minimization problem, s1 (the global minimum) could be considered as the best result. Nevertheless, this solution is not robust because slight changes in z 3 will generate abrupt changes on f (z 3 ). Hence, s1 should not be taken into account (unless its value can be precisely fixed in real life). When analyzing the second local minimum, s2 , it can be seen that slight variations in z 3 do not bring abrupt changes on f (z 3 ). As a result, s2 is a robust solution and could be considered as the final result (despite the fact that it is not the global minimum).

2.3 Summary This chapter provided the background and literature review which work as the starting point for the next chapters where the findings from this thesis are presented. Particular

20

2 Background and Literature Review

Fig. 2.6 Illustration of robust (s2 ) and non-robust (s1 ) solutions

emphasis was given to the photovoltaic and optimization fields as these will be discussed through the whole document.

References 1. Becquerel AE (1839) Recherches sur les effets de la radiation chimique de la lumiere solaire au moyen des courants electriques. CR Acad Sci 9(145):1 2. International_Energy_Agency_(IEA) (2016) Trends 2016 in photovoltaic applications. Technical report IEA PVPS T1-30:2016 3. Smets A, Jäger K, Isabella O, Swaaij R, Zeman M (2016) Solar energy: the physics and engineering of photovoltaic conversion technologies and systems, 1st edn. UIT Cambridge, Cambridge 4. Rodríguez C, Pospischil M, Padilla A, Kuchler M, Klawitter M, Geipel T, Padilla M, Fellmeth T, Brand A, Efinger R, Linse M, Gentischer H, König M, Hörteis M, Wende L, Doll O, Clement F, Biro D (2015) Analysis and performance of dispensed and screen printed front side contacts on cell and module level. In: Proceedings of 31th European PV solar energy conference and exhibition (EU PVSEC). Hamburg, pp 983–990 5. Mette A (2007) New concepts for front side metallization of industrial silicon solar cells. PhD thesis, Fraunhofer Institute for Solar Energy Systems ISE, Albert Ludwig University of Freiburg 6. Gallegos CDR, Alvarado MSA (2015) Homemade dye sensitized solar cell analysis: characterization techniques, modeling and simulation 7. Rodríguez-Gallegos CD (2014) Experimental evaluation and characterization of dispensed front side contacts on silicon solar cells during module integration. Msc thesis, Fraunhofer Institute for Solar Energy Systems ISE, Ulm University 8. Pujari NS et al (2018) International technology roadmap for photovoltaic (ITRPV): 2017 results. Technical report, ITRPV-VDMA 9. Fu R, Feldman DJ, Margolis RM, Woodhouse MA, Ardani KB (2017) US solar photovoltaic system cost benchmark: Q1 2017. Technical report NREL/TP-6A20-68925, National Renewable Energy Laboratory (NREL). Golden, USA 10. Gandhi O, Rodríguez-Gallegos C, Reindl T, Srinivasan D (2018) Competitiveness of PV inverter as a reactive power compensator considering inverter lifetime reduction. Energy Procedia 150:74–82

References

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11. International_Energy_Agency_(IEA) (2017) Energy access outlook 2017: from poverty to prosperity. IEA: Paris, France, p 144 12. Chelouah R, Siarry P (2000) A continuous genetic algorithm designed for the global optimization of multimodal functions. J Heuristics 6(2):191–213 13. Kantardzic M (2011) Genetic algorithms. In: Data mining: concepts, models, methods, and algorithms, chapter 13, 2nd edn. Wiley, New Jersey, pp 385–413 14. Parsopoulos KE, Vrahatis MN (2010) Particle swarm optimization and intelligence: advances and applications, 1st edn. Information Science Reference, Hershey 15. Glover F (1997) Tabu search and adaptive memory programming-advances, applications and challenges. In: Interfaces in computer science and operations research. Springer, pp 1–75 16. Beheshti Z, Shamsuddin SMH (2013) A review of population-based meta-heuristic algorithms. Int J Adv Soft Comput Appl 5(1):1–35 17. Yang XS (2010) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver press, Frome 18. Osman IH, Kelly JP (1996) Meta-heuristics: an overview. In: Meta-heuristics: theory and applications, chapter 1. Kluwer Academic Publishers, Boston, pp 1–21 19. Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Metaheuristic algorithms in modeling and optimization. In: Metaheuristic applications in structures and infrastructures, chapter 1. Elsevier, London, pp 1–24 20. Gandhi O, Rodríguez-Gallegos CD, Srinivasan D (2016) Review of optimization of power dispatch in renewable energy system. In: 2016 IEEE innovative smart grid technologies-Asia (ISGT-Asia). IEEE, Melbourne, pp 250–257 21. Rodríguez-Gallegos FL, Rodríguez-Gallegos CA, Rodríguez-Gallegos AA, RodríguezGallegos CD (2020) Natural reforestation optimization (NRO): a novel optimization algorithm inspired by the reforestation process. J Comput Sci 16(8):1172–1184 22. Gandhi O, Rodríguez-Gallegos CD, Zhang W, Srinivasan D, Reindl T (2018) Economic and technical analysis of reactive power provision from distributed energy resources in microgrids. Appl Energy 210:827–841 23. Hampel FR (1971) A general qualitative definition of robustness. Ann Math Stat 42(6):1887– 1896 24. Deb K, Gupta H (2006) Introducing robustness in multi-objective optimization. Evol Comput 14(4):463–494 25. Huber PJ (2011) Robust statistics. In: International encyclopedia of statistical science, 1st edn. Springer, Berlin, pp 1248–1251

Chapter 3

On the Optimization for the Grid Metallization Design of Si-Based Solar Cells and Modules

3.1 Introduction For solar cells and modules to collect the energized electrons and transfer them to an external circuit to deliver the energy, metallic contacts are necessary to be printed (fingers and busbars when fabricating the solar cells) and soldered (interconnector ribbons when fabricating the modules). The fingers are thin metallic structures which collect the energized electrons through the solar cell. After flowing through the fingers, these electrons are then gathered at the busbars to be transported outside of the cell. When dealing with solar modules, interconnector ribbons are soldered on top of the busbars so that electrons could flow through these and be released to an external circuit. These metallic contacts are presented in Fig. 3.1. The metallization design influences the electrical performance and manufacturing cost of solar cells and modules. Therefore, it is desired to find its optimal design— number and dimension of fingers, busbars, and interconnector ribbons—the common approach consists in taking one or two parameters and increase them linearly until the best result can be appreciated. As for example, Fig. 3.2a, b show the simulated efficiency of a solar cell (considering typical industrial parameters) based on a linear increase on the number of printed fingers and on the number of fingers/busbars, respectively. Literature presents different research which have been carried out to optimize the metallization design following the previous approach. This is summarized in Table 3.1, where variables such as: (a) width, height and number of front fingers (wfi_f , hfi_f and nfi_f , respectively); (b) width and number of front busbars (wBB_f and nBB , respectively); and (c) width of the interconnector ribbons (wir ), are optimized to enhance objective functions such as the cell/module efficiency, power, fabrication cost (η, P and cf , respectively), as well as the levelized cost of electricity (LCOE). It can be seen that a maximum of only two variables are optimized in parallel. Nevertheless, there are more variables that can be taken into account to further enhance the optimization design. Moreover, an optimization approach based on a linear increase is not the most effective method to reach the optimal solution when there are multiple parameters to optimize. In addition, regarding the possible © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7_3

23

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3 On the Optimization for the Grid Metallization …

Fig. 3.1 Solar cell (left) showing the printed fingers and busbars; and one-cell module (right) showing the printed fingers and soldered interconnector ribbons

a)

b)

Fig. 3.2 a Simulated cell efficiency based on the number of fingers; b simulated cell efficiency based on the number of fingers/busbars. The star shows the design with the highest efficiency

objective functions, only one is typically considered at a time. However, the two main objectives for the cell/module design are to maximize their electrical performance and to reduce their cost. As a result, either both of them should be optimized at the same time or they can be combined into one single variable such as cf or LCOE.

3.1 Introduction

25

Table 3.1 Review on the metallization design optimization Papers

Optimization variables wfi_f hfi_f

nfi_f

Objective functions

wBB_f nBB

wir

[1–3] x x

[6]

x

x

[6]

x

x

[3]

x

cf

cf

(βmod = 1)

(βcell = 1)

(βmod = 1)

LCOE

x x x x

[3]

x

[7]

x

x x

x

[3, 8– 17]

x

[13, 18, 19]

x

[13]

x

[13]

x

[13]

x

[5, 20]

x

[21]

x

x x

x

x x x x

x

x

x

x

x

x

[3, 22]

[24]

η, P

(βcell = 1)

x

[4–6] x

[3, 23]

η, P

x

x

x

x

Therefore, in this work, an approach to optimize several parameters in parallel is developed (these will be referred as optimization variables): the number and width of fingers, busbars (as well as their height), interconnectors and silver pads (which are printed at the rear side of the cell to solder the rear interconnector ribbons when rear busbars are not printed). The optimization of interconnectors is only considered when dealing with solar modules. The objectives are to enhance the efficiency and reduce the silver consumption (these will be referred as objective functions). Because these are conflicting objectives, a multiobjective optimization approach is required. The non-sorting genetic algorithm NSGA-II [25], a state-of-the-art- solver for multiobjective optimization problems, is employed. Furthermore, to apply this optimization approach in the production of solar cells and modules, it is necessary to ensure that small changes in the optimization and input variables would not considerably change the values of the objective functions. Therefore, robust conditions are considered. Based on the obtained results, the fabrication cost is estimated as well. In the present work, the manufacturing design for Cz-Si based p-type Al-BSF monofacial is optimized and PERT bifacial (full-cell and half-cell) solar cells and

26

3 On the Optimization for the Grid Metallization …

modules. The bifacial technology and half-cell are included in this study due to their expected increase in the future market share [26].

3.2 Modelling of Cell and Module Performance The two-diode model is applied to determine the performance of the solar cells and modules. Based on this model, the equivalent circuit for a solar module consisting of Ns solar cells connected in series and Np parallel strings of solar cells is shown in Fig. 3.3. Its electrical performance can then be expressed based on the following equation: ⎛ Np · VL + Ns · rs · jL ⎜ jL = Np · jph − − Np · jo1 ⎝e Ns · rp

VL rs ·jL Ns + Np n1 ·vt

⎞

⎛

⎜ ⎟ − 1⎠ − Np · jo2 ⎝e

VL rs ·jL Ns + Np n2 ·vt

⎞ ⎟ − 1⎠

(3.1) From Eq. 3.1, the voltage and current at which the PV device produces its maximum power (Pmpp = Vmpp · Impp , respectively) can be estimated from the IV characteristics. The efficiency, η [%], under STC can then be obtained as shown in Eq. 3.2. η=

1000

W m2

Vmpp · Impp · 100% · (1 + ab · αbi ) · Atotal

(3.2)

 being ab the albedo factor and Atotal m2 the total area of the PV device. To obtain the IV characteristics at the cell and module level, external contacts need to be applied to allow the flow of electrons. For solar cells, these contacts are located at the front side

Fig. 3.3 Equivalent circuit of a solar module based on the two-diode model (similar to [27, 28])

3.2 Modelling of Cell and Module Performance

27

Fig. 3.4 External contacts employed for solar cells to obtain the IV curve. The subscript x is replaced by f and r to represent the front and rear side parameters, respectively

(on top of the busbars) and at the rear side (in contact with the Aluminum layer or the rear busbars for the monofacial or bifacial technologies, respectively). Figure 3.4 shows the locations where the front and rear external contacts are located (one string of four contacts per busbar are assigned in this example) to estimate the IV curve [29]. At the module level, the external contacts are connected to the cells located at the beginning and at the end of the electrical connection, as shown in Fig. A.4c. The calculation of η takes into consideration the influence that the optimization variables have on jph , jo1 , jo2 and rs . The procedures to estimate these variables are presented in the Appendix Sect. A. It is assumed that rp is higher than 10 kΩcm2 so that its influence can be neglected [30].

3.3 Estimation of Silver Consumption  As the second objective is to reduce the total silver consumption, mAg g , it is necessary to estimate its value with respect to the grid design. Based on the manufacturing process, there will be a certain amount of silver contained at the fingers, busbars and silver pads (when silver paste is employed). The equations to obtain the silver consumption from each element are presented in Table 3.2. The total silver consumption can then be estimated by adding the kth individual contributions, mAg_x (k), from Table 3.2.

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3 On the Optimization for the Grid Metallization …

Table 3.2 Equations to estimate the silver consumption mAg term Silver consumption estimation Condition mAg_pads mAg_BB_r mAg_fi_r mAg_fi_f mAg_BB_f

DAg_pads · nBB · npads · wpads · lpads · hpads · Ns · Np DAg_r · nBB · wBB_r · lcell · hBB_r · Ns · Np 2 · DAg_r · nfi_r · ARel_fi_r · wfi_r wcell · Ns · Np 2 · DAg_f · nfi_f · ARel_fi_f · wfi_f wcell · Ns · Np DAg_f · nBB · wBB_f · lcell · hBB_f · Ns · Np

mAg =



αmo = 1 αbi = 1 αbi = 1 All cases All cases

mAg_x (k)

(3.3)

k=1

3.4 Estimation of the Fabrication Cost  The fabrication cost of solar cells and modules, cf USD/Wp , is defined as the relation between the total cost of production, Ct [USD], with respect to their maximum  electrical power under STC, P Wp . P is defined as: P = Vmpp · Impp cf is then: cf =

Ct P

(3.4)

(3.5)

3.5 Optimization Under Standard Test Conditions 3.5.1 Optimization Problem Based on the above sections, the optimization problem can now be defined. As previously indicated, the aim is to maximize the efficiency and minimize the silver consumption by optimizing the following variables: nfi_f , wfi_f , nfi_r , wfi_r , nBB , wBB_f , hBB_f , wBB_r , hBB_r , npads , wpads and wir . Constraints regarding the fabrication process must also be considered to ensure that the obtained solutions can be implemented in real life. The optimization problem is formulated as:

3.5 Optimization Under Standard Test Conditions

29

maximize (η)

(3.6)

 minimize mAg

(3.7)

subject to: x1_min ≤ x1 ≤ x1_max ,

η − η  x 1± Varunc

( 1 ( 100% ))

· 100% ≤ Objsen ,

η

mAg − mAg x 1± Varunc

( 1 ( 100% ))

· 100% ≤ Objsen ,

mAg

(3.8) (3.9)

(3.10)

  x1 = nfi_f , wfi_f , nBB , wBB_f , hBB_f nfi_f · wfi_f ≤ lcell

(3.11)

nBB · wBB_f ≤ wcell

(3.12)

if αmo = 1, then : x2_min ≤ x2 ≤ x2_max ,

(3.13)



η − η  x 1± Varunc

( 2 ( 100% ))

· 100% ≤ Objsen ,

η



mAg − mAg x 1± Varunc

( 2 ( 100% ))

· 100% ≤ Objsen ,

mAg   x2 = npads , wpads nBB · wpads ≤ wcell

(3.14)

(3.15)

(3.16)

if αmo = 1 & βmod = 1, then : wir ≥ wpads

(3.17)

30

3 On the Optimization for the Grid Metallization …

if αbi = 1, then : x3_min ≤ x3 ≤ x3_max ,

η − η  x 1± Varunc

( 3 ( 100% ))

· 100% ≤ Objsen ,

η

mAg − mAg x 1± Varunc

( 3 ( 100% ))

· 100% ≤ Objsen ,

mAg

(3.18)

(3.19)

(3.20)

  x3 = nfi_r , wfi_r , wBB_r , hBB_r nfi_r · wfi_r ≤ lcell

(3.21)

nBB · wBB_r ≤ wcell

(3.22)

if αbi = 1 & βmod = 1, then : wir ≥ wBB_r

(3.23)

if βmod = 1, then : x4_min ≤ x4 ≤ x4_max ,



η − η  x 1± Varunc ( 4 ( 100% ))

· 100% ≤ Objsen ,

η



mAg − mAg x 1± Varunc ( 4 ( 100% ))

· 100% ≤ Objsen ,

mAg

x4 = {wir } wir ≥ wBB_f

(3.24)

(3.25)

(3.26)

(3.27)

Equations 3.6 and 3.7 define the objective functions, i.e. maximize the electrical efficiency and minimize the silver consumption, respectively. Constraints with respect to the maximum and minimum values allowed for the optimization variables are defined in Eq. 3.8 (allowed range for the number and dimension of front fingers and busbars); Eq. 3.13 (allowed range for the number and dimension of silver pads); Eq. 3.18 (allowed range for the number and dimension of rear fingers and

3.5 Optimization Under Standard Test Conditions

31

busbars); and Eq. 3.24 (allowed range for the dimension of the interconnector ribbons). These constraints are applied to guarantee that the electrical yield and screen lifetime are not severely affected. Furthermore, it needs to be assured that the grid metallization design does not overcome the cell dimensions. This is achieved by implementing Eq. 3.11 (overall width from all front fingers does not overcome cell length); Eq. 3.12 (overall width from all front busbars does not overcome cell width); Eq. 3.16 (overall width from all silver pads does not overcome cell width); Eq. 3.21 (overall width from all rear fingers does not overcome cell length); and Eq. 3.22 (overall width from all rear busbars does not overcome cell length). Additionally, to maximize the contact area when soldering the interconnector ribbons during the fabrication of solar modules, their width shall be greater than or equal to the width of the silver pads (Eq. 3.17) and widths of the rear and front busbars (Eqs. 3.23 and 3.27, respectively). Finally, a set of constraints have been introduced to guarantee that the values from the objective functions (efficiency and silver consumption) are robust. In these constraints, η  x 1± Varunc [%] and mAg x 1± Varunc [mg] represent the efficiency and ( a ( 100% )) ( a ( 100% )) silver consumption values when a particular optimization variable, xa , is slightly increased (or decreased) by a defined uncertainty value, Varunc [%], respectively. Objsen [%] stands for the maximum allowed sensitivity of the objective function. These constraints are defined in Eqs. 3.9 and 3.10 (to analyze the variability influence of the number and dimension of front fingers and busbars); Eqs. 3.14 and 3.15 (to analyze the variability influence of the number and dimension of silver pads); Eqs. 3.19 and 3.20 (to analyze the variability influence of the number and dimension of rear fingers and busbars); and Eqs. 3.25 and 3.26 (to analyze the variability influence of the dimension of the interconnector ribbons). These conditions will be further discussed in Sect. 3.5.2.2.

3.5.2 Optimization Algorithms Considering that the current optimization problem cannot be analytically solved, optimization algorithms must be employed. The presented work is a a multiobjective optimization problem (maximization of the efficiency and minimization of the silver consumption) whose solutions are desired to be robust. Therefore, multiobjective optimization algorithms are applied with the addition of robust conditions. These are presented in the following subsections.

3.5.2.1

Multiobjective Optimization Algorithm

The multiobjective optimization algorithm that employed in this work correspond to the nondominated sorting genetic algorithm II (NSGA-II). This algorithm has, among others, the following common characteristics:

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3 On the Optimization for the Grid Metallization …

(1) Searching of the whole pareto-optimal solutions at once (do not search for an individual solution per simulation). (2) Diversity preservation, the obtained solutions should be spread among the pareto front. (3) The optimization variables can be continuous or discrete. The NSGA-II approach was proposed by Deb et al. [25]. Its principle is based on the Genetic Algorithm (GA) which is inspired by the biological evolution of the organisms (the strongest survive and are able to pass their genes to the off-spring) [31–34]. GA is based on randomized operators: selection, crossover and mutation. Each member of the population (chromosomes) is associated with defined values of the optimization variables (their genes), the better their value of the objective function, the stronger they are considered (by defining a fitness function) and the higher the probability to pass their genes to the off-spring. NSGA-II applies this principle to solve multiobjective optimization problems by searching the paretooptimal front.

3.5.2.2

Robust Condition

Even though the pareto-optimal solutions can be obtained from the NSGA-II, it may not be possible to exactly replicate the obtained values of the continuous optimization variables in real life. Therefore, it is necessary to ensure that a slight change on an optimization variable will not lead to an abrupt change on the values of the objective functions. Hence, robust solutions are desired [35–37]. For the optimization problem presented in this work, robust conditions were developed so that, for a solution to be taken into account, small changes on their individual optimization variables (i.e. number and width of fingers, busbars (as well as their height), interconnectors and silver pads), cannot bring abrupt changes on the values of the objective functions (i.e. efficiency and silver consumption). These constraints were presented in Sect. 3.5.1 when defining the objective problem (Eqs. 3.9, 3.10, 3.14, 3.15, 3.19, 3.20, 3.25 and 3.26).

3.5.3 Case Study In this investigation, the evaluated solar cells are industrial Cz-Si p-type Al-BSF monofacial and PERT bifacial with a metallization grid printed by employing the single screen printing technology. The proposed optimization approach will be applied to eight cases: monofacial solar cell/module, bifacial solar cell/module, all having full and half-cell cases. The parameters regarding the fabrication process, measurement conditions, costs and other properties were selected based on a literature review [6, 14, 38–44] together with experiments and simulations conducted at the Solar Energy Research Institute of

3.5 Optimization Under Standard Test Conditions

33

Singapore (SERIS). The maximum and minimum range of the optimization variables were defined so that their implementation in real life can be assured. Tables 3.3 and 3.4 present the specifications employed for the analyzed cases and the range of the optimization variables, respectively. Because hir , hbr and cs do not affect the silver consumption, they can be immediately defined to enhance the efficiency by setting a high value for hir and hbr (this will reduce rs ), and a low value for cs (this will reduce rs and will also decrease the area which is not occupied by the cells within the module). Furthermore, hpads and lpads can be set to a low value to reduce the silver consumption. Moreover, it can be understood that the grid design with the highest efficiency at the cell level will have the highest value of hBB_f (and hBB_r for the bifacial technology) while, with respect to the modules, hBB_f (and hBB_r for the bifacial technology) should be set to their minimum value to reduce the silver consumption without influencing the efficiency. It is considered that the solar modules formed by full-cell are composed of 60 solar cells connected in series forming a structure of 6 columns and 10 rows (Ns = 60, Np = 1, nc = 6, nr = 10). The modules formed by half-cells are composed of two groups connected in parallel, where each group contains  60 solar cells connected in series, forming a structure of 6 columns and 20 rows Ns = 60, Np = 2, nc = 6, nr = 20) so that both modules can also be compared based on their current and voltage ratings. To estimate the fabrication cost for all the scenarios, the bill of materials (BOM) for a standard Al-BSF p-type solar module with standard glass size (165.5 × 99.1 cm2 ), as shown in Table 3.5, is employed as a reference. This was obtained based on a market survey performed at SERIS which considered information gathered from different module manufactures. This module is composed of 60 solar cells (full-cell) each of which contains 82 fingers with a width of 55 µm and three busbars with a width of 1.5 mm. With respect to the cost associated to the glass, EVA and backsheet, they are assumed to be proportional to the area of the solar module while the cost of the frame is assumed to be proportional to the perimeter of the solar module and the cost of the ribbons are assumed to be proportional to the total amount of ribbon material used. Furthermore, the following values were obtained based on a cost analysis: • For Al-BSF p-type full-cells, the wafer and cell processing cost correspond to the 62 and 38% of the cell cost, respectively. These values were obtained following the approach presented in [43]. • The cell processing cost for half-cells is 51.3% the one of full-cells (value obtained by applying the approach from [43]). This is because of the extra process required to cut a full-cell into two half-cells, which is considered to be within the cell processing steps. • To fabricate a module composed with half-cells, the extra cost related to the stringer process corresponds to 0.7% of the cost of the standard module (value obtained following the approach from [43]).

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3 On the Optimization for the Grid Metallization …

Table 3.3 Parameters specifications for the case study General parameters Rear side metal layer #fc, #rc temp [K] ab lcell [cm] wcell [cm] ns np

nc nr

Varunc , Objsen [%] cs [mm] Reference cell jph_ref_f [mA/cm2 ] jph_ref_r [mA/cm2 ] Λref_f [%] Λref_r [%] n1 jo1_p_AlBSF [fA/cm2 ] jo1_n+ [fA/cm2 ] jo1_n+ _met [fA/cm2 ] jo1_p+ [fA/cm2 ] jo1_p+ _met [fA/cm2 ] n2 jo2_n+ [nA/cm2 ] jo2_f_met [nA/cm2 ] jo2_p+ [nA/cm2 ] jo2_r_met [nA/cm2 ] Silver pads hpads [¯m] lpads [mm]

16, full-cell 8, half-cell 298 0.2 15.6 15.6, full-cell 7.8, half-cell 1, βcell = 1 60, βmod = 1 2, βmod = 1 AND half-cell 1, rest 1, βcell = 1 6, βmod = 1 1, βcell = 1 10, βmod = 1, full-cell 20, βmod = 1, half-cell 5 1 38.2 30.8 6.0 5.0 1 300 250 1100 60 400 2 10 156 5 40 10 5, full-cell 2.5, half-cell

ρm_r [m] Thm_r [¯m] Base ρb [m] Thb [¯m] Emitter & p+ layer Rsh_e [/] Rsh_p+ [/] Contacts ρc_ge , ρc_gp+ [m2 ] Busbars ρBB_f [m] ρBB_r [m] EWBB_f , EWBB_r [%] Fingers ρfi_f [m] ρfi_r [m] ARel_fi_f , ARel_fi_r EWfi_f , EWfi_r [%] Interconnector ribbons ρir [m] EWir [%] hir [mm] Backsheet nair nglass lightsp , lightpp [%] Thglass [mm] ncs θrl [◦ ] nlb_max Rbs [%] Paste DAg_f [g/cm3 ] DAg_r [g/cm3 ] DAg_pads [g/cm3 ]

2.56 · 10−8 15 2 · 10−2 200 90 60 30 · 10−8

3 · 10−8 4 · 10−8 100 3 · 10−8 4 · 10−8 0.18 90, βcell = 1 60, βmod = 1 1.68 · 10−8 100 0.3 1 1.5 50 4 10 1 2 80 9.44 6.82 6.29

3.5 Optimization Under Standard Test Conditions Table 3.4 Searching range of the optimization variables Minimum nfi_fs , nfi_rs wfi_fs , wfi_rs [µm] nBB_ir wBB_fs , wBB_rs [mm] hBB_fs , hBB_rs [µm] npads wpads , wir [mm]

70, full-cell 35, half-cell 35 3 0.5 10 2 0.5

35

Maximum 250, full-cell 125, half-cell 100 7 5 50 8 5

Table 3.5 Component cost for a standard 60-cell Si solar module Components Cost contribution (%) Solar cells Glass EVA Backsheet Interconnector ribbons Bussing ribbons Frame Others

70.8 5.1 3.3 7.8 1.5 0.4 6.8 4.3

• By applying the analysis provided in [45] and considering the standard fabrication steps for PERT p-type bifacial cells[46], their cell processing cost is assumed to be 42.3% higher than the one of Al-BSF p-type solar cells. • With respect to the current market situation, the silver price is taken as 0.60 USD/g [44].

3.5.4 Results and Discussion The optimization designs for the eight analyzed cases are presented in Fig. 3.5. Here, the three particular operational points whichachieved the maximum efficiency, g , and minimum fabrication cost, minimum silver consumption, m ηmax [%], Ag_min  cf_min USD/Wp , are analyzed. The efficiency and silver consumption optimization results for monofacial solar cells (full-cells and half-cells) are presented in Fig. 3.5a. It is noted that the efficiency range for both of them is the same (ηmax = 19.85%) while the full-cell has roughly twice the silver consumption than the half-cell (as expected because of their dimen-

36

3 On the Optimization for the Grid Metallization …

sion difference). The corresponding cf values are then plotted in Fig. 3.5b. It can be noticed that the fabrication cost for full-cell (cf_min = 0.308 USD/Wp ) is lower than the one for half-cell (cf_min = 0.310 USD/Wp ). This is due to the extra step half-cells go through during the cell processing in order to cut a full-cell into two half-cells, as explained on the previous section. By analyzing the results for monofacial solar modules presented in Fig. 3.5c, a considerable advantage from the half-cell modules (ηmax = 19.67%) with respect to their full-cell counterparts (ηmax = 19.27%) is observed as they show a lower cell-to-module losses and hence a higher efficiency. This difference is also noted when calculating the cf values (cf_min = 0.433 USD/Wp for half-cell modules and cf_min = 0.442 USD/Wp for full-cell modules) shown in Fig. 3.5d. The reason for the superior results of the half-cell in comparison to its full-cell counterpart at the module level is because of its enhanced electrical performance, mainly due to its lower resistive losses in the front and rear side interconnector ribbons. At the module level, the generated current needs to flow through the whole interconnector ribbons. This means that the current flowing through the interconnector ribbons for the fullcell module will be, approximately, twice the one of the half-cell module. Since the power losses are a function of the square of the current, higher resistive losses occur for full-cell modules. This is evident from the equations of rir_f and rir_r (Table A.1) which are proportional to the square of the cell length. The previous statements can be corroborated by Fig. 3.6. Here, the contributions of each component of rs for the eight cases at the cf_min operational point are presented. Therefore, despite the higher cost (USD) to produce a half-cell module, its higher power rating achieves a lower fabrication cost. A similar trend is obtained by analyzing the bifacial solar cells and modules. Figure 3.5e provides the optimization results for bifacial solar cells. Once more, the efficiency range for both, full-cells and half-cells, is similar (ηmax = 19.08%) while the full-cells achieve a lower fabrication cost than the half-cells (cf_min = 0.314 USD/Wp and cf_min = 0.317 USD/Wp , respectively) as presented in Fig. 3.5f. For bifacial solar modules (Fig. 3.5g), the advantage of the half-cells (ηmax = 18.74%, cf_min = 0.418 USD/Wp ) with respect to the full-cells (ηmax = 18.40%, cf_min = 0.425 USD/Wp ) is also corroborated. This outcome is due to the resistive losses associated to rir_f and rir_r (previously discussed) which can also be seen in Fig. 3.6. Figure 3.5 also reveals the lower efficiency of bifacial solar cells and modules in comparison to their monofacial counterparts. This can be explained mainly by two factors associated to the rear side structure of bifacial cells: (1) The extra resistive losses for the bifacial technologies due to their rear grid metallization design [47], as seen in Fig. 3.6; (2) The rear side of bifacial cells is less efficient than its upper side [48], as shown by the jph_ref_fs and jph_ref_rs values from Table 3.3. Nevertheless, the power produced by a bifacial module can be higher than the one of the monofacial module as the former is also able to absorb light coming from its rear side. This is the case of the present analysis in which an albedo factor of 0.2 was

3.5 Optimization Under Standard Test Conditions

37

Fig. 3.5 Multiobjective optimization results (pareto-optimal solutions) and fabrication costs results for: monofacial solar cells (a & b), monofacial solar modules (c & d), bifacial solar cells (e & f) and bifacial solar modules (g & h)

Fig. 3.6 rs contributor values among all the studied cases for the cf_min operational points

considered. Based on Fig. 3.5, the output power of the optimal-pareto fronts for the monofacial and bifacial modules can be calculated. This is presented in Fig. 3.7. Regardless of the higher  power produced by the bifacial technology, it presents a higher fabrication cost USD/Wp than the monofacial technology at the cell level. This result is because of the considerable larger cost related to the cell processing of the former. Nevertheless, at the module level, the influence of this cost is reduced and, due to its higher output power, the bifacial modules reach a lower fabrication

38

3 On the Optimization for the Grid Metallization …

Fig. 3.7 Output power for a monofacial solar modules and b bifacial solar modules

cost than the monofacial ones. It is important to take into account that the albedo factor plays a critical role in this outcome. On the one hand, with the current optimalpareto solutions, if the albedo factor is set to zero, the fabrication cost for bifacial modules would be higher than the monofacial ones. On the other hand, an increase of the albedo factor will considerably decrease the fabrication cost for the bifacial technology so that even bifacial cells can reach a lower fabrication cost than their monofacial counterparts. This influence is summarized in Fig. 3.8. This graph also reveals that, in order to be more cost effective than the monofacial technology, bifacial modules require a lower albedo factor than the bifacial cells. The previous outcome is because the cost relation between both technologies is lower at the module level than at the cell level. Therefore, to achieve the same fabrication cost, the relation in power (between both technologies) at the module level should also be lower than at the cell level, i.e. lower albedo factor at the module level. The values of the optimization variables and electrical performance properties obtained for the cases of ηmax , mAg_min and cf_min are provided in Table A.2 at the Appendix Sect. A.4. Based on this table, the following observations can be made: (1) The optimum grid metallization design will depend on the particular case of interest (i.e. cell/module, monofacial/bifacial and full-cell/half-cell). (2) A general trend is noted: the higher the number of fingers, busbars and interconnector ribbons, and the lower their width, the better will be the efficiency and fabrication cost results (as seen for the cases related to ηmax and cf_min ). The reason is that, by raising their number, the metallization fraction increases so that the overall rs goes down. Consequently, the fill factor is enhanced. Their

3.5 Optimization Under Standard Test Conditions

39

Fig. 3.8 Influence of the albedo factor for a bifacial cells and b bifacial modules. The monofacial technology is also included to be used as a reference

width then needs to be reduced to assure a high photovoltaic current density and low dark saturation current densities. (3) For the bifacial technology, the number and width of the fingers at the rear side (nfi_r and wfi_r , respectively) are higher (or equal) to their front counterparts (nfi_f and wfi_f , respectively). Since the front side is more efficient and receives a higher irradiance than the rear side (due to the jph_ref_f , jph_ref_r and ab values defined in Table 3.3), it is desired to reduce the metallization fraction at the front side (to enhance the light collection) and to increase the metallization fraction at the rear side (to reduce the resistive losses) [49]. A sensitivity analysis based on the minimum fabrication cost cf_min is also conducted to investigate how the change in the parameter values will affect the results of this study (no sensitivity analysis is required for the efficiency vs silver consumption curves presented in Fig. 3.5 because these results are robust, as explained in Sect. 3.5.2.2). From Fig. 3.5, the grid design which generates the cf_min value (this will be referred as the original grid design) was obtained based on the BOM and silver price provided in Sect. 3.5.3. Nevertheless, as the cost of these materials can vary, it is necessary to analyze, by considering a change in the market, if the original grid design continues to generate the cf_min value or another design (this will be referred as the non-original grid design) will do it. Figure 3.9 shows the sensitivity analysis of cf_min with respect to variations of the BOM and silver price for six analyzed cases. A linear tendency is observed for changes on these values. It can also

40

3 On the Optimization for the Grid Metallization …

Fig. 3.9 Sensitivity analysis of cf_min based on cost variations for selected configurations. The cell processing cost does not include the silver cost

be noted that the wafer and cell processing cost have a considerable influence on cf_min due to their higher share of the cost, as indicated in Sect. 3.5.3. Under certain market conditions, the original grid design will not generate the cf_min value as other designs (the non-original grid designs, represented by “≡”) are more suitable. This shows the influence that the market has on the fabrication process.

3.5.5 Experimental Validation Our proposed approach to estimate the values of efficiency and silver consumption has been experimentally validated and the results are presented in this section. Due to lack of resources, it was not possible to fabricate the cells and modules with the optimal designs obtained from Sect. 3.5.4. Instead, the available screens were employed to print the fingers and busbars and compare the real results with the simulated cases. Although optimal designs were not printed, the credibility of the presented approach can be proven by showing its accuracy for the available samples. For the validation, Cz-Si based p-type Al-BSF monofacial full-cell samples have been used. Furthermore, some of the samples were utilized to manufacture onecell modules. The samples were categorized based on whether they are cells or modules, and based on the metallization printing design. Each group is labeled with the following format “XyBB−zf ” where “X ” denotes whether the sample is a cell or a one-cell module (C and M , respectively); y indicates the number of printed busbars; and z is the number of printed fingers. For example, group C3BB−83f refers to solar cells with three busbars and 83 fingers. Three groups of cells were fabricated with 18 samples per group, namely C3BB−83f , C4BB−87f , and C5BB−87f . Furthermore, six

3.5 Optimization Under Standard Test Conditions

41

Fig. 3.10 Percentage error between the measured and estimated values for the a efficiency and b silver consumption

cells from group C3BB−83f were selected randomly to be made into one-cell modules (M3BB−83f ). Figure 3.10 shows the percentage error of the efficiency, ηerror [%], and of the silver consumption, mAg_error [%], between the real results and the estimated ones. To measure the silver consumption, the cells were weighed before and after the printing process. In addition, the IV testers Wavelabs Sinus 220 and H.A.L.M. Sun Simulator (both Class AAA) were used to measure the efficiency of the cells and modules, respectively. Furthermore, reference cells were considered to obtain the properties of the analyzed batch while an optical microscope together with the Reflectometer software [38, 50] were employed to obtain the optical and geometric properties of the fingers and busbars. With respect to the percentage error of the efficiency, Fig. 3.10a shows that for the four analyzed groups, the mean and 75th percentile values are lower than 2%. Furthermore, for the percentage error of the silver consumption, given in Fig. 3.10b, mean values lower than 7.5% were reached together with 75th percentile values below 10%. Hence, the proposed approach is shown to posses a high level of accuracy.

3.5.6 Summary This work proposed a methodology to optimize the grid metallization design of Si wafer-based solar cells and modules under standard test conditions. A multiobjective and robust optimization approach was implemented to optimize several parameters in parallel (number and dimensions of fingers, busbars, silver pads and ribbons) in order to enhance the efficiency and reduce the silver consumption at the cell and module level. With the obtained pareto-optimal fronts, the minimum fabrication cost  USD/Wp was also estimated. Eight cases were analyzed for industrial Cz-Si based p-type Al-BSF monofacial and PERT bifacial, full-cell and half-cell, solar cells and modules. The results reveal

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3 On the Optimization for the Grid Metallization …

that at the cell level there is no considerable difference between the electrical performance between full-cells and half-cells (i.e. maximum efficiency of 19.85 and 19.08% for the monofacial and bifacial cells, respectively). Consequently, a higher fabrication cost for the latter one was obtained due to the extra cutting step halfcells go through. Nevertheless, at the module level, because of their lower resistive losses, half-cell modules reached higher efficiency values (i.e. maximum efficiency of 19.67 vs 19.27% for monofacial modules and 18.74 vs 18.40% for bifacial modules) and lower fabrication cost (i.e. minimum fabrication cost of 0.433 USD/Wp vs 0.442 USD/Wp for monofacial modules and 0.418 USD/Wp vs 0.425 USD/Wp for bifacial modules). The bifacial technology showed lower efficiency values than its monofacial counterpart (mainly because of the low efficiency at their rear side and higher resistive losses). Nonetheless, it has the potential to generate a higher output power as it can also absorb light from the rear side (i.e. for full-cell modules, a maximum power of 285 Wp and 327 Wp were obtained for the monofacial and bifacial technologies, respectively). As a result, for the analyzed cases in which an albedo factor of 0.2 was considered, the bifacial modules were more cost-effective than the monofacial ones.

3.6 Optimization Under Real-World Conditions Different to STC, real-world conditions present another level of complexity as the temperature and irradiance change in time and the effective irradiance reaching the module depends on the module orientation [51]. Therefore, the present work corresponds to the next stage, in which the grid metallization design optimization will be performed considering real-world conditions, as the final goal is for the modules to operate optimally at the locations they will be installed.

3.6.1 Approach We aim to optimize the grid metallization design for PV modules either to (1) maximize the average daily energy generation, max (Ed ); or (2) reduce the module fabri  cation cost per kWh, min Cf,Wh , defined as the relation between the cost to fabricate a module with respect to Ed . The average daily energy produced by a module can be estimated from the power produce by the module in real-world conditions, Preal [W], estimated as: Pmpp · (If + Ir · b) Preal = (3.28) [1 + γ · (Tc − 25)] 1000 where Pmpp [W] is the module power under STC (see Sect. 3.2), If [W/m2 ] and Ir [W/m2 ] are the overall irradiance reaching the module front and rear side, respectively, while b [%] is the bifaciality factor (b = 0 when dealing with monofacial mod-

3.6 Optimization Under Real-World Conditions

43

ules). The variable γ [%/◦ C] is the module temperature coefficient (set to −0.41%/◦ C [52]), and Tc [◦ C] is the cell temperature which can be estimated from the ambient temperature as shown in [52]. As the shading percentage produced by the fingers and interconnector ribbons will not be constant (due to the sun movement), it is necessary to estimate their shading influence based on the sun position. To estimate the amount of light been blocked by the fingers within the module, a total of 104 screen-printed fingers from 3 different cells batches (real samples described in Sect. 3.5.5) were analyzed. Figure 3.11a shows one representative finger sample. For each sample, the effective finger width (EWf ), defined as the percentage of light that the fingers are effectively blocking,1 has been estimated using the Reflectometer software based on the angle of incidence of light (AOI)2 and the cardinal location of the light source with respect to the fingers, as seen in Fig. 3.11a. The results present a similar EWf profile for the different finger samples and their average value is plotted in Fig. 3.11b. This figure shows that the EWf value does not change considerably regardless of the location of the light source. Yet, when the light source is in front or behind the fingers, i.e. 0◦ N and 180◦ S, respectively, the EWf value increases with the angle of incidence as the fingers start to shade unmetallized regions. Nevertheless, the shades do not propagate substantially due to the low finger electrical aspect ratio, and also because the refracted angle of light which enters the module reduces in comparison to the incident angle, as can be explained from Snell’s law. For example, incident light with AOI = 85◦ (from which a large shade will be expected from the fingers if light source is located at 0◦ N or 180◦ S) will be refracted at the air-glass interface with an angle of 42◦ . In addition, the EWf reduces when increasing the AOI value when the light source is at the same direction of the finger path, i.e. 90◦ E and 270◦ W. At these locations, no shadow is produced but, as the angle of incidence increases, the amount of light been internally reflected at the glass-air interface, after impacting the finger, also increases. The same approach was applied to estimate the EW of the interconnector ribbons, which, different to the fingers, have a rectangular shape with a width considerably higher than their thickness. Consequently, their EW can be directly estimated with respect to the angle of incidence of light.

3.6.2 Case Study A total of six locations worldwide have been analyzed, i.e. Singapore, Brazil, Saudi Arabia, China, USA, and Germany. The historical weather profiles (ambient temperature Ta , global horizontal irradiance GHI , direct normal irradiance DNI , and diffuse horizontal irradiance DHI ) were provided by the Solar Energy Research Institute of example, EWf = 30% means that 30% of the light impacting the finger is blocked and not absorbed by the cell. 2 Angle between the light source and the normal of the module surface, e.g. AOI = 0◦ when light is perpendicular to the module surface; AOI = 90◦ when light is parallel to the module surface. 1 For

44

3 On the Optimization for the Grid Metallization …

Fig. 3.11 a A sample of a screen-printed finger. b Polar contour plot of the average finger’s effective width within the module. The radius represents the angle of incidence of light (AOI) while the polar angle indicates the cardinal location of the light with respect to the fingers (shown in (a))

Fig. 3.12 Monthly albedo values for the six analyzed locations

Singapore (SERIS) for Singapore, and by the World Radiation Monitoring Center— Baseline Solar Radiation Network (WRMC-BSRN) for the rest of the locations [53]. The variables GHI , DNI , and DHI are employed to estimate the irradiance reaching the module (If and Ir ) following the approach presented in the Appendix Sect. C. Thereafter, the finger shading influence is considered. Furthermore, the monthly albedo values were obtained from the NASA’s Surface meteorology and Solar Energy (NASA-SSE) [54] and are presented in Fig. 3.12. The value of the other required parameters to estimate the module performance and cost, as well as the range of the optimization parameters, were previously provided in Sect. 3.5.3.

3.6 Optimization Under Real-World Conditions

45

3.6.3 Optimization Algorithm In order to find the optimum metallization design, considering the optimization of Ed or Cf,Wh , genetic algorithm (GA) is applied defining a population number and number of iterations of 500 and 100, respectively, with a mutation rate of 0.02. GA is a meta-heurisitc algorithm inspired by the natural selection process and has the following characteristics: able to handle discrete (number of fingers, busbars, and interconnector ribbons) and continuous variables (width and height of the fingers, as well as width of the busbars and interconnector ribbons); is robust; is unlikely to be trapped in a local minimum; among others [34, 55].

3.6.4 Results and Discussion Table 3.6 presents the results for the six analyzed locations concerning the optimum metallization designs for a monocrystalline p-type Si-based 60-cell module, for AlBSF monofacial and PERT bifacial technologies. Here, we take into account their optimum module azimuth (Az) and tilt angles, as given in [52]. The results presented in Table 3.6 are obtained considering the objective to be, either: (1) to maximize Ed  “max (Ed )”, or (2) to minimize Cf,Wh “min Cf,Wh ”. Table 3.6 provides the metallization designs, Ed and Cf,Wh values, as well as Ed [%]which indicates the difference of the Ed values obtained from the max (Ed ) the difference of the Cf,Wh and min Cf,Wh designs. Similarly, Cf,Wh [%]  indicates values obtained from the max (Ed ) and min Cf,Wh designs. With respect to the metallization designs, it can be noticed that the metallization fraction (based on the number and width of fingers and interconnector ribbons) is higher when optimizing Ed , in comparison to the designs when optimizing Cf,Wh . This is expected as higher metallization fraction increases the cost of the module, which reduces Cf,Wh . On the one hand, when the objective is to maximize Ed , Table 3.6 shows that the height of the fingers is set to their maximum as this will further reduce the finger resistance. On the other hand, when the objective is to minimize Cf,Wh , the finger height is reduced as the cost increase due to silver consumption needs to be considered. It can also be noticed that the height of the front fingers is higher than the rear ones. This outcome is justified because, as there are fewer fingers at the front side, their height should be enhanced to avoid a considerable increase on their resistance contribution. To get a better insight on the final results, the optimized values of Ed − Ed and Cf − Cf,Wh are plotted in Fig. 3.13a, b, respectively. With respect to Ed , the bifacial modules are able to produce more energy. However, their Cf,Wh values are higher due to the extra cost required to manufacture them. Among the analyzed locations, the one from Saudi Arabia has the highest irradiance contribution. Consequently, its Ed values are the highest and its Cf,Wh values are the lowest. Furthermore, as Saudi Arabia also

Technology

(85◦ ,21◦ )

monofacial

Brazil (BZ)

(174◦ ,34◦ )

monofacial

long: 46.410◦

China (CH)

monofacial

USA (US)

bifacial

monofacial

bifacial

(164◦ ,47◦ )

long: 14.122◦

(170◦ ,37◦ )

lat: 52.210◦

Germany (GM)

long: −105.237◦ (165◦ ,43◦ )

lat: 40.125◦

(182◦ ,43◦ )

long: 116.962◦

(167◦ ,37◦ )

bifacial

lat: 39.754◦

(182◦ ,36◦ )

bifacial

lat: 24.910◦

(175◦ ,26◦ )

Arabia monofacial

(15◦ ,30◦ )

long: −47.713◦

Saudi (SA)

bifacial

lat: −15.601◦

(12◦ ,22◦ )

bifacial

long: 103.772◦

(81◦ ,10◦ )

monofacial

(Az,tilt)

lat: 1.300◦

Singapore (SG)

Country

130

 min Cf,Wh

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

120

128

114

120

134

140

127

134

125

134

120

126

138

145

136

max (Ed )

max (Ed )  min Cf,Wh

125

133

119

125

120

128

116

121

nfi,f

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

max (Ed )  min Cf,Wh

Objective

209

250

–

–

250

250

–

–

225

250

–

–

250

250

–

–

236

250

–

–

227

250

–

–

nfi,r

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

35

–

–

35

35

–

–

35

35

–

–

35

38

–

–

35

35

–

–

35

35

–

–

(µm)

(µm) 35

wfi,r

wfi,f

5

6

4

6

6

7

5

6

5

6

5

6

6

7

5

7

5

6

5

6

5

6

4

6

nir

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

(mm)

wir

8

20

10

20

7

20

8

20

8

20

8

20

7

20

8

20

8

20

8

20

8

20

10

20

(µm)

hfi,f

7

20

–

–

5

20

–

–

6

20

–

–

5

20

–

–

6

20

–

–

6

20

–

–

(µm)

hfi,r

953

964

901

909

1491

1507

1424

1434

1303

1320

1245

1253

1888

1909

1760

1774

1374

1391

1328

1336

1181

1195

1145

1155

(Wh/day)

Ed

Ed

14.28

14.68

13.91

14.1

9.17

9.46

8.84

8.96

10.45

10.73

10.1

10.24

7.24

7.49

7.16

7.29

9.91

10.18

9.47

9.6

11.52

11.84

10.95

11.1

1.13

0.90

1.05

0.72

1.25

0.61

1.13

0.78

1.23

0.61

1.16

0.92

(USD (%) cents/Wh/day)

Cf,Wh

Table 3.6 Results of the optimization designs for monocrystalline p-type Si-based Al-BSF monofacial and PERT bifacial 60-cell modules

2.79

1.40

3.22

1.33

2.70

1.36

3.41

1.88

2.72

1.36

2.80

1.40

(%)

Cf,Wh

46 3 On the Optimization for the Grid Metallization …

3.6 Optimization Under Real-World Conditions

47

Fig. 3.13 a Optimized daily energy generation (bars) and Ed (markers). b Optimized fabrication cost per Wh (bars) and Cf,Wh (markers)

has the highest overall albedo (as seen from Fig. 3.12), the extra energy generation of the bifacial module with respect to its monofacial counterpart is the highest for this location. As a result, the difference between the bifacial and monofacial Cf,Wh values is the lowest for Saudi Arabia (with high enough albedo values, the bifacial Cf,Wh value could be lower than the one from its monofacial counterpart). This shows once more the considerable influence that the surface albedo has in particular on bifacial modules. Figure 3.13a shows values of Ed up to 1.3%, while for Cf,Wh , Fig. 3.13b illustrates how the variations are considerably larger for bifacial modules (up to 3.5%) in comparison to their monofacial counterparts (up to 1.9%). The high values of Cf,Wh when dealing with bifacial modules are due to the substantial reduction of the number and height of fingers at the rear side (see Table 3.6) when comparing the  min Cf,Wh design with respect to the max (Ed ) design. Fewer and smaller fingers reduce the silver consumption and hence reduce the value of Cf,Wh .

3.6.5 Summary This work proposed an approach to optimize the metallization design, i.e. number and dimension of fingers and interconnector ribbons, for Al-BSF monofacial and PERT bifacial modules by considering real-world conditions. The optimization was performed to either maximize the energy production from the modules or to minimize their fabrication cost per Wh. The results reveal that the optimal metallization design depends on the location where the modules will be installed (due to the local weather conditions) and the desired objective to be optimized. As the approach here presented only requires for the screen of the screen printing machine to be modified (not considerable cost is required), this optimization method can be easily applied by cell and module manufacturersto enhance their profitability. In addition, although only the metallization design was optimized, this type of approach can also be applied to optimize other steps related to the fabrication of solar cells and modules. As such, this work is also of interest for the PV community in general.

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Chapter 4

Optimization and Cost-Effectiveness Analysis Between Si-Based Monofacial and Bifacial Grid-Connected PV Systems

4.1 Introduction Among the different materials for solar cells, Si crystalline based are the ones that dominate the current market (>90% [1, 2]). This group can be further divided into specific technologies, from which the Al-BSF has the highest share (>70% in 2017 [3]), followed by the PERC/PERL/PERT technologies (≈20% in 2017 [3]). The former can only be used for monofacial modules while the latter technologies can also be applied for bifacial modules. Bifacial modules had less than 5% of the market share in 2017 [3] despite their evident advantage, namely, potential for higher power production as light absorption occurs at both sides of the module [4, 5]. This value is likely to increase as the gap between the manufacturing cost of bifacial and monofacial modules has decreased significantly [6] (the share of bifacial modules is expected to reach almost 40% by 2028 [3]). Nevertheless, more research is still necessary to successfully increase the bifacial module penetration in the market, as concluded by Guerrero-Lemus et al. [7] after reviewing over 400 papers related to the bifacial technology that have been published since 1979. It is still required to accurately calculate the energy generation potential from these modules when installed in different locations of the world so that it could then be analyzed whether the extra energy generation from these modules (if any) in comparison to the one from their monofacial counterparts, is high enough to compensate for their associated cost. In recent years, different studies have been done to compare the performance between monofacial and bifacial modules. Guo et al. [8] did a worldwide study regarding the performance of vertical mounted bifacial modules (VMBF), i.e. vertical modules facing East-West, and conventional mounted monofacial modules (CMMM), i.e. facing towards the equator with inclination equal to the latitude. Satellite-based weather data provided by NASA’s Surface Meteorology and Solar Energy (NASA-SSE) were used [9] and modules were considered to have the same constant efficiency value (16%). Furthermore, no degradation or temperature influence was assumed and the bifaciality was set to 1. Their work concluded that depend-

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7_4

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52

4 Optimization and Cost-Effectiveness Analysis …

ing on the latitude, diffuse fraction, and albedo, the VMBF could have a better performance than the CMMM in different locations. Ito and Gerritsen [10] also studied the performance of monofacial and bifacial modules worldwide considering satellite-based irradiance data provided by NASASSE [9]. Here, they estimated the irradiance that will fall on vertical bifacial modules (facing North-South and East-West) and tilted monofacial/bifacial modules facing the equator. Their results show that for latitudes higher than 40◦ as well as polar regions, the vertical bifacial modules get more irradiance than the tilted monofacial ones (from 10% up to 30% more). This conclusion was also obtained for vertical modules facing East-West in arid regions at latitudes lower than 20◦ due to high albedo values. In [11], Sun et al. proposed an empirical approach to optimize the orientation and elevation of bifacial modules worldwide. They estimated the global horizontal irradiance at different locations using the PV_LIB Toolbox [12] and then tune it using the data provided by NASA-SSE [9]. In this work they considered the temperature influence and a front/rear module efficiency (under standard test conditions) of 17.4 and 15.6%, respectively, producing a bifaciality of 0.9. Their results revealed that with an albedo value of 0.25, the bifacial gain for ground-mounted bifacial modules (module elevation of zero meters) was less than 10% (except for locations close to the poles). Nevertheless, with an albedo value of 0.5 and modules with an elevation of one meter, the bifacial gain can be increased to 30%. Works which focus on individual locations have also been presented, e.g. [13–18]. These works have also shown that for particular locations and orientations, bifacial modules can achieve a higher irradiance collection and energy generation. While previous research have tried to estimate the absorbed irradiance and power production of bifacial modules (in comparison to monofacial ones), this still does not answer the main question: Are bifacial PV systems more cost-effective than their monofacial counterparts? To try to answer this, on top of the electrical performance, the costs associated to these modules also need to be considered. Therefore, in this work the levelized cost of electricity (LCOE) from bifacial and monofacial PV systems for different locations is estimated. LCOE is defined as the relation between the overall cost of a system with respect to its overall energy produced during its lifetime Furthermore, although worldwide analyses have already been done to compare monofacial and bifacial modules, there are still limitations in the existing works. For example, in order to get the weather conditions for multiple places worldwide, satellite-based data are typically employed. Nevertheless, these data suffer from accuracy issues, e.g. NASA-SSE reported global root mean square errors of 10.25% for the global horizontal irradiance, 29.34% for the diffuse horizontal irradiance and 22.73% for the direct normal irradiance [9]. Consequently, ground weather stations would be beneficial as they can achieve higher accuracy (as long as their equipment is well maintained). Therefore, in the present investigation, the data provided by 55 weather stations which are distributed around the globe were employed, in order to be able to perform a comprehensive worldwide study, and simultaneously assuring high accuracy in the results.

4.1 Introduction

53

Finally, while previous works have shown irradiance/performance results for these modules under specific orientations, this work presents the expected irradiance collection, energy generation, and LCOE for monofacial and bifacial modules for all orientations. Therefore, the reader can have a better idea about how critical is the accuracy on the module orientation based on the location.

4.2 Data Processing In the current work, ground weather stations are employed to obtain all the required weather data (with one-minute resolution). These stations record the historical weather data, in the order of years, that have been measured at their particular location. Among the different weather parameters that they collect, this work considersthe ones  associated with the irradiance,namely,  global horizontal irradiance, 2 normal irradiance, DNI W/m , and diffuse horizontal irradiGHI W/m2 , direct  ance, DHI W/m2 , as well as the ambient temperature, Ta [◦ C]. These four parameters are gathered and then processed to estimate the typical meteorological year (TMY) data to subsequently calculate the energy generated by the PV systems. The collected data must first go through two processes, namely filtering and filling. Then, the TMY data can be estimated. These procedures are explained in detail in the Appendix B.

4.3 Irradiance Model The irradiance reaching the module will also depend on the orientation of the solar module, which is defined by its azimuth and tilted angles, Am [◦ ] and θm [◦ ], respectively. To allow for easy visualization, Fig. 4.1 shows the module and sun angles. The overall irradiance can be divided into the irradiance reaching the front surface, If [W/m2 ], (for both monofacial and bifacial modules) and rear surface, Ir [W/m2 ], (only for bifacial modules). The front surface irradiance is defined in Eq. (4.1): If = Idir,f + Ignd,f + Idiff,f

(4.1)

where Idir,f [W/m2 ] corresponds to the direct irradiance contribution, Ignd,f [W/m2 ] represents the irradiance contribution due to ground reflection, and Idiff,f [W/m2 ] is the diffuse irradiance contribution at the front side. The rear surface irradiance Ir is estimated similar to its front counterpart considering the rear irradiance components. A detailed explanation on the approaches to estimate these values can be found in the Appendix C. Once the irradiance reaching the module has been estimated, its power production can then be estimated.

54

4 Optimization and Cost-Effectiveness Analysis …

Fig. 4.1 Graphical illustration of the module and sun angles of interest (similar to [19]). The variables Am and θm are the module azimuth and tilt angles, respectively, while As and z are the sun azimuth and zenith angles, respectively

4.4 PV Energy Generation In this section, the calculation of the electrical power produced by the PV system and delivered to the grid, PPV [W], is presented. For this estimation, the equation proposed by Skoplaki and Palyvos [20] is employed considering additional loss factors: PPV =

PSTC,f · (If + Ir · b) · f1 · [1 + γ · (Tc − 25)] · ηPV,inv · (1 − β0 − y · β1 ) · (1 − l) 1000

(4.2)

where PSTC,f [Wp ] is the total DC power production of the installed solar panels when light reaches only their front side under standard test conditions (STC)1 ; b [%] is the bifaciality factor, which indicates the efficiency of light collection at the rear side of the module with respect to the front side (b = 0 when dealing with monofacial modules). The variable f1 constitutes the spectral irradiance contribution, γ [%/◦ C] is the power temperature coefficient, and Tc [◦ C] corresponds to the cell temperature. The losses due to the PV inverters (including both, conversion efficiency as well as the efficiency of the maximum power point tracking (MPPT) algorithm) are accounted in ηPV,inv [%], defined as the weighted average efficiency. To consider the degradation of the solar panels in time, the model presented in [21, 22] is applied (for simplicity, the random factor is neglected). Here, β0 [%] is the initial PV degradation (caused by early degradation mechanisms such as light induced degradation), β1 [%/year] 1 In this work, the unit W

p is used to represent the direct power production under STC when light is reaching only the front side of the modules (regardless of whether monofacial or bifacial modules are considered).

4.4 PV Energy Generation

55

is the yearly degradation rate, and y is the year being analyzed. The parameter l [%] combines all of the other losses, e.g. shading, module mismatch, ohmic wiring losses, among others. Regarding f1 , as the solar spectral irradiance distribution changes during the daytime, it influences the module performance (in particular for high band gap semiconductor materials [23, 24]). Its contribution is represented by an equation empirically defined in [23, 24]: f1 = a0 + a1 · AMa + a2 · (AMa )2 + a3 · (AMa )3 + a4 · (AMa )4

(4.3)

where a0 , a1 , a2 , a3 , and a4 are the equation coefficients and AMa is the absolute air mass whose value is approximated using the approach from King et al. [25]: AMa ≈ e(−0.0001184·El) · AM

(4.4)

where AM is the atmospheric mass, calculated based on Kasten and Young’s equation [26], which is able to provide accurate results even for zenith angles reaching 90◦ : AM =

1 cos (z) + 0.50572 · (96.07995◦ − z)−1.6364

(4.5)

The estimation of Tc is based on the approach presented in [20, 27–29]: Tc = Ta +

(If + Ir ) · (TINOCT − 20) 800

(4.6)

where Ta [◦ C] is the ambient temperature and TINOCT [◦ C] is the installed normal operating cell temperature. The rear irradiance term (Ir ) is only considered when dealing with bifacial modules. The variable TINOCT depends on the mounting structure, as this will influence the heat dissipation of the solar modules [30]: TINOCT = TNOCT + xmount

(4.7)

where TNOCT [◦ C] is the normal operating cell temperature and xmount [◦ C] is a coefficient whose value is based on the selected mounting structure. Based on the power production, the yearly energy produced by the PV system, (y) EPV [Wh], can then be calculated.

4.5 Cost and LCOE Estimations In this section, the cost associated with the installation and maintenance of a PV system is described. The initial investment cost, Cini,inv [USD], is defined as:

56

4 Optimization and Cost-Effectiveness Analysis …

  Cini,inv = PSTC,f · cPV + cPV,ins + cPV,ivt(0)

(4.8)

where cPV [USD/Wp ], cPV,ins [USD/Wp ], and cPV,ivt(0) [USD/Wp ] are the cost coefficients related to the acquisition of the solar panels, their installation, and acquisition of the inverter during the year of PV installation, respectively. The variable cPV,ins can then be subdivided into the material costs, cPV,ins,mat [USD/Wp ], (cost of mounting structures, cables, monitoring devices, etc.) and the labor cost, cPV,ins,lab [USD/Wp ]: cPV,ins = cPV,ins,mat + cPV,ins,lab

(4.9)

With respect to the PV inverter, besides its initial acquisition cost, warranty extension costs, Cwar [USD], are also present [31, 32]. The inverter warranty is assumed to have a period of wPV years. For the ith warranty extension, a percentage of the inverter cost (at the time of the warranty extension), πPV(i·wPV ) [%], needs to be covered. This is summarized in the following equation: lS /wPV 



Cwar =

i=1

PSTC,f · cPV,inv(i·wPV ) · πPV(i·wPV ) ·

(1 + IR)i·wPV (1 + DR)i·wPV

(4.10)

where cPV,inv(i·wPV ) [USD/Wp ] is the inverter cost at the year i · wPV . The expression lS /wPV  gives the total number of times the warranty needs to be extended assuming a system lifetime of lS years. The variables IR [%] and DR [%] are the inflation and discount rates, respectively; these are applied to get the net present value (NPV). The summation used in Eq. (4.10) accounts for all the costs related to extend the inverter warranty during the system lifetime. For PV installations, it is customary to get a bank loan to pay for a part of the investment costs. In this work, it is assumed that a bank loan has been obtained to cover a percentage of the initial investment, lBank [%], with a bank interest rate of IRBank [%] and a debt tenor of dtBank years. Consequently, the borrower needs to pay every year to the bank (for a total of dtBank years) the amounts corresponding to the interest, CBank,int [USD], and amortization, CBank,amor [USD]. These can be calculated as follows [33]: CBank,int =

dt Bank y=1

CBank,int =

  Cini,inv · lBank · IRBank · (1 + IRBank )dtBank +1 − (1 + IRBank )y   (1 + IRBank ) · (1 + IRBank )dtBank − 1 · (1 + DR)y

dt Bank y=1



  IRBank · Cini,inv · lBank · (1 + IRBank )dtBank − CBank,int   (1 + IRBank )dtBank − 1 · (1 + DR)y

(4.11)

(4.12)

The summations from Eqs. (4.11), (4.12) accounts for the total payment to the bank during the first dtBank years.

4.5 Cost and LCOE Estimations

57

The owner of the project has the obligation to pay for the remaining cost of the initial investment, Cown [USD], at the beginning of the project: Cown = Cini,inv · (1 − lBank )

(4.13)

A PV insurance cost is also associated with these systems to manage risks, Cinsu [USD]. This is calculated based on a certain percentage of the initial investment, cinsu [%]: S  (1 + IR)y Cini,inv · cinsu · (4.14) Cinsu = (1 + DR)y y=1 The summation in Eq. (4.14) adds all the yearly insurance costs (it is assumed that the insurance contract needs to be renewed every year). The total operation and maintenance (O&M) cost of the PV system, CPV,OM [USD], also needs to be considered: Cinsu =

S  (1 + IR)y PSTC,f · cPV,OM · (1 + DR)y y=1

(4.15)

where cPV,OM [USD/year/Wp ] is the O&M cost coefficient. The summation employed in Eq. (4.15) is used to add all the yearly O&M costs. Similar to cPV,ins , cPV,OM can also be subdivided into its material, cPV,OM,mat [USD/year/Wp ], and labor, cPV,OM,lab [USD/year/Wp ], related costs: cPV,OM = cPV,OM,mat + cPV,OM,lab

(4.16)

The total cost associated to the PV system during its lifetime can now be defined as: CPV = CBank,int + CBank,amor + Cown + Cwar + Cinsu + CPV,OM

(4.17)

In the present investigation, the levelized cost of electricity, LCOE [USD/kWh], is used as a guide to determine the cost-effectiveness of the PV installation. The LCOE is the relation between the total cost of the system and the total energy production during the system lifetime [34, 35]. As such, LCOE indicates the cost to produce electrical energy. This parameter helps investors to decide whether or not to support/participate in energy related projects. The LCOE can be expressed as: LCOE = S

CPV (y)

EPV y=1 (1+DR)y

(4.18)

Notice that while CPV was already calculated based on its net present value, the yearly energy has to be discounted to also have its proper representation [36].

58

4 Optimization and Cost-Effectiveness Analysis …

4.6 Case Study 4.6.1 Weather Parameters A total of 55 locations around the globe are considered to test the performance and cost-effectiveness of monofacial/bifacial modules. These locations have their corresponding ground weather station, which provides historical irradiance and temperature data with one-minute resolution. These are then processed to obtain the TMY data following the approach presented in Appendix B. The analyzed locations are summarized in Table 4.1. For Singapore, the weather data is provided by the Solar Energy Research Institute of Singapore (SERIS) for the time range of 2011–2017, while the data for the rest of the locations are provided by the World Radiation Monitoring Center—Baseline Solar Radiation Network (WRMC-BSRN)2 with a time range depending on the particular location (within the interval of 1992– 2017), the specific years per location are indicated in [38]. The data provided by these institutions are chosen because, among other reasons, they assign at least one data scientist per station to assure the proper maintenance of the sensors as well as the data collection quality. Figure 4.2 presents the geographic distribution of the locations of interest. These are assigned to a particular climate condition, namely, tropical (TR), temperate (TM), arid (AR), and high albedo (HA), similar to [39]. To have a general idea on the local irradiance, they are superimposed with the mean annual irradiance (provided by NASA-SSE [9]) falling on a surface with tilt angle equal to its latitude and facing the equator (to simulate the conventional rule of thumb when installing solar panels). The ground weather stations do not provide albedo values. Consequently, the monthly albedo values provided by the NASA-SSE [9] have been used in this work. The modules considered here are the standard 60-cell modules which have a module length (lm ) of 1.6 m, and are installed with a height between the module lowest edge and the ground (hmg ) of 0.6 m. With the previous values, the estimation of the front and rear irradiance falling on a solar module with respect to its orientation can be estimated based on the equations provided in Sect. 4.3.

4.6.2 Module Performance Parameters The monofacial and bifacial technologies to be considered are Al-BSF and PERT, respectively. Both technologies are Si p-type monocrystalline. Same wafer types are assigned to both to fairly compare the features of a module based on whether 2 For

some locations, temperature data were not available. Therefore, the TMY temperature data were estimated using the Meteonorm software (which has a root mean square error of 1.2 ◦ C when interpolating monthly temperature values [37]). These locations are marked with an “X” under the column “T-Met” in Table 4.1.

4.6 Case Study

59

Table 4.1 Description of the locations to be analyzed # ID Location Latitude Longitude Altitude (◦ ) (◦ ) (m) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

TAM GVN SYO SPO DOM ASP COC DAR SON BRB FLO PTR SMS ALE EUR REG XIA TOR CAR PAL LIN SBO FUA ISH MNM SAP TAT GOB NAU LAU

31 32 33

ILO NYA MAN

34

KWA

Algeria Antarctica Antarctica Antarctica Antarctica Australia Australia Australia Austria Brazil Brazil Brazil Brazil Canada Canada Canada China Estonia France France Germany Israel Japan Japan Japan Japan Japan Namibia Nauru New Zealand Nigeria Norway Papua New Guinea Republic of the Marshall Islands

Climate

T. Met

1385 42 18 2800 3233 547 6 30 3109 1023 11 387 489 127 85 578 32 70 100 156 125 500 3 6 7 17 25 407 7 350

AR HA HA HA HA AR TR TR HA TR TM TR TM HA HA TM TM TM TM TM TM AR TM TM TM TM TM AR TR TM

X

22.790 −70.650 −69.005 −89.983 −75.100 −23.798 −12.193 −12.425 47.054 −15.601 −27.605 −9.068 −29.443 82.490 79.989 50.205 39.754 58.254 44.083 48.713 52.210 30.860 33.582 24.337 24.288 43.060 36.058 −23.561 −0.521 −45.045

5.529 −8.250 39.589 −24.799 123.383 133.888 96.835 130.891 12.958 −47.713 −48.523 −40.319 −53.823 −62.420 −85.940 −104.713 116.962 26.462 5.059 2.208 14.122 34.779 130.376 124.164 153.983 141.329 140.126 15.042 166.917 169.689

8.533 78.925 −2.058

4.567 11.930 147.425

350 11 6

TR HA TR

8.720

167.731

10

TR

X X X

X X X

X

(continued)

60

4 Optimization and Cost-Effectiveness Analysis …

Table 4.1 (continued) # ID Location 35 36 37 38 39 40 41 42

TIK SOV SIN DAA CNR IZA PAY CAB

43

CAM

44

LER

45

BER

46 47 48 49 50 51 52 53 54 55

BAR BIL BON BOS CLH DRA FPE GCR PSU SXF

Russia Saudi Arabia Singapore South Africa Spain Spain Switzerland The Netherlands United Kingdom United Kingdom United Kingdom USA USA USA USA USA USA USA USA USA USA

Latitude (◦ )

Longitude Altitude (◦ ) (m)

Climate

T. Met

71.586 24.910 1.300 −30.667 42.816 28.309 46.815 51.971

128.919 46.410 103.772 23.993 −1.601 −16.499 6.944 4.927

48 650 36 1287 471 2373 491 0

HA AR TR AR TM AR TM TM

X

50.217

−5.317

88

TM

X

60.139

−1.185

80

TM

X

32.267

−64.667

8

TM

71.323 36.605 40.067 40.125 36.905 36.626 48.317 34.255 40.720 43.730

−156.607 8 −97.516 317 −88.367 213 −105.237 1689 −75.713 37 −116.018 1007 −105.100 634 −89.873 98 −77.933 376 −96.620 473

HA TM TM TM TM AR TM TM TM TM

it is monofacial or bifacial. On the one hand, with respect to the monofacial modules considered here, the module datasheets from more than 30 manufacturers were investigated. Although not all the module parameters are the same among the different companies, most of them were found to have a value equal (or similar) to γ = −0.41%/◦ C, β0 = 3%, β1 = 0.7%/year, TNOCT = 45◦ . Consequently, these will be considered for monofacial modules. On the other hand, with respect to bifacial modules, the products from more than 15 manufacturers which provide both, monofacial and bifacial modules, were investigated. This search showed that in most of the cases, when the supplier’s monofacial/bifacial modules are from the same wafer type, the values in the datasheet for γ, β0 , and β1 are the same. Therefore, the values previously assigned to the monofacial modules are also used for the bifacial ones.

4.6 Case Study

61

Fig. 4.2 Locations of the weather stations on the world map superimposed with the average annual irradiance falling on a surface with tilt angle equal to its latitude and facing the equator. Each location of interest is distinguished based on its climate condition

With respect to TNOCT , there is no general agreement on which module technology achieves a higher temperature under the same weather conditions. Some works claim that bifacial modules reach higher temperature values as they usually consider that a glass/glass module has a lower thermal conductivity than a glass/backsheet module [14, 16, 24, 40–42]. Other researchers consider that monofacial modules get hotter (this outcome is typically attributed as infrared light is almost invisible to bifacial cells due to the lack of an Al rear layer, consequently, less heat will be produced) [7, 43–47]. Finally, there are other publications which indicate that the temperature from both modules is similar [48–51]. In this work, the last statement was applied as this also agrees with most of the analyzed datasheets. Therefore, monofacial and bifacial modules have the same TNOCT value. Furthermore, the suppliers typically guarantee in their datasheets a lifetime for their monofacial solar modules of at least 25 years. For the bifacial modules, some suppliers guarantee a lifetime of at least 25 years while others 30 years at least. Based on these findings, it was decided to also set the bifacial module lifetime to 25 years. Consequently, the system lifetime (lS ) for all of our calculations is set to 25 years. At this point, the reader needs to keep in mind that the values presented here correspond to the ones that the module suppliers typically give as a warranty in their datasheets. Nevertheless, the solar modules may actually perform better and have longer lifetime, as was shown in [52–55]. With respect to the coefficients to estimate the spectral irradiance contribution (f1 ), Fanney et al. [23] empirically determined their values for crystalline based modules: a0 = 0.935823, a1 = 0.054289, a2 = −0.008677, a3 = 0.000527, a4 = −0.000011. These will be considered in the present work.

62

4 Optimization and Cost-Effectiveness Analysis …

Based on a literature review, e.g. [14, 15], and suppliers’ datasheets, the bifaciality factor (b) is set to 80% when dealing with bifacial modules. PV installations with a capacity (PSTC,f ) of 1 MWp are considered for both, monofacial and bifacial module technologies. Furthermore, rack mounting structures are assumed (xmount = −3◦ [30]). With respect to the inverter, a central inverter is considered for these systems. These inverters have a higher weighted efficiency (ηPV,inv ) in comparison to others and is set to 96%. This value is chosen after revising the datasheet of central inverters from different suppliers (recall that ηPV,inv not only considers the conversion efficiency but also the MPPT algorithm efficiency). For the extra losses of the PV system (l), a value of 3% is empirically defined. With the previous values, the electricity generation for monofacial/bifacial based PV systems can be estimated from the equations presented in Sect. 4.4.

4.6.3 Cost Parameters The values provided in this section are estimated considering PV systems with an installed capacity of 1 MWp (as indicated in the previous subsection). The parameters related to the costs can be divided into two groups, namely, the ones whose value can be considered to be constant worldwide (up to a certain extent) and the ones that highly depend on the particular location. The variables considered to be constant worldwide are the ones associated with the inverters, the material cost for the PV installation and O&M, and the yearly insurance. With respect to the inverters, their present and future acquisition values (cPV,inv(0) and cPV,inv(i·wPV ) , respectively), together with the percentage of warranty extension cost (πPV ) for the years of interest (considering a warranty period (wPV ) of five years), are presented in Fig. 4.3 for the case of monofacial PV systems. These were obtained based on an internal analysis performed at SERIS (previously presented in [31, 32]) after analyzing different PV inverter suppliers. When bifacial modules are used, these inverters are recommended to be oversized so that they can handle the extra power produced at their rear side. In [56], it was recommended to oversize the inverter by at least 20% (with respect to its monofacial counterpart); this suggestion has been applied in the present work so that the inverter cost for bifacial modules is 1.2 times the one for monofacial modules (a linear cost relation is assumed for simplicity). To estimate the material cost related to the PV installations and O&M (cPV,ins,mat and cPV,OM,mat , respectively), Singapore is taken as a reference due to the good amount of information that SERIS has on its host country. In Singapore, cPV,ins,mat is estimated to be 0.28 USD/Wp (this includes the racking/substructures, cables, monitoring devices, among others). Furthermore, the yearly O&M cost is estimated to be 0.0076 USD/year/Wp ; from which half of its value is typically for the cPV,OM,mat cost. Although the previous values were estimated for Singapore, these are material costs that can, and are assumed to be constant worldwide.

4.6 Case Study

63

Fig. 4.3 PV inverter acquisition cost and warranty extension cost predictions

With respect to the yearly insurance, the percentage of the initial investment to be covered (cinsu ) is set to 0.3% (typical value for real PV systems). The variables which are highly dependent on the location are the ones related to the acquisition of the solar panels, labor, bank loans, and inflation/discount rates. The acquisition cost of monofacial solar panels (cPV ) is obtained from the weekly publication report provided by Singapore Solar Exchange [57]. This report provides updates on the module prices worldwide. With respect to the bifacial panels, a previous work [58] showed that their fabrication cost is about 11.2% higher than the one of their monofacial counterparts; this consideration is applied in this work. The labor costs for the PV installation and O&M (cPV,ins,lab and cPV,OM,lab , respectively) are estimated by taking their costs in Singapore as a reference (cPV,ins,lab = 0.22 USD/Wp and cPV,OM,lab = 0.0038 USD/year/Wp , for a monofacial PV system) and then scaling it to the labor cost from the country of interest, provided in [59–63]. Based on the results presented in [58], the costs of bifacial PV systems related to the PV installation and O&M are estimated to be 0.92% higher than the ones of their monofacial counterparts (as more bifacial modules would be required to achieve the installation capacity of 1 MWp ). In this work, special effort was taken to define the bank loan conditions to be as close as the ones from real PV projects. Nevertheless, these are highly dependent on the specifics of the project as they will be defined by factors related to the client and the bank policies, among others. For the current work, regardless of the location, a bank loan (lBank ) of 60% of the initial investment is considered (the project owner must pay the rest) with a debt tenor (dtBank ) of 10 years. The bank interest rate (IRBank ) was estimated by adding the debt premium (considered to be 2%) to the 10-year bond yield of the location, provided in [63]. The inflation and discount rates (IR and DR, respectively) are variables whose values are not only expected to depend on the location, but are also time dependent. Nevertheless, due to the limited available data to forecast their values for the next 25 years, the inflation rates estimated for the year 2022 for the different locations will be considered constant in time for this analysis, these are provided in [64]. Furthermore, the discount rate is calculated considering the previous parameters together with the corporate income tax (Cortax ) given in [65] and equity cost (Eqc ), as shown: DR = (1 − lBank ) · Eqc + lBank · IRBank · (1 − Cortax )

(4.19)

where Eqc is calculated based on the 20-year bond yield (Bond20y ) [63], Market risk premium (Mrp ) [66], and beta factor (set to 1), as shown:

64

4 Optimization and Cost-Effectiveness Analysis …

Table 4.2 Location-dependent cost variables Location

  cPV USD/Wp monofacial

Algeria Antarctica

IRBank (%)

IR (%)

c PV,ins,lab  USD/Wp monofacial

c PV,OM,lab  USD/year/Wp monofacial

0.444

0.01

0.0001

5.24

4.0

0.433

0.23

0.0039

5.53

3.2

DR (%)

8.74 7.32

Australia

0.375

0.32

0.0054

4.74

2.5

5.65

Austria

0.444

0.33

0.0056

2.88

2.2

3.96

Brazil

0.368

0.06

0.0011

11.47

4.0

12.10

Canada

0.470

0.25

0.0042

4.20

1.9

4.95

China

0.430

0.08

0.0014

5.87

2.6

7.62

Estonia

0.444

0.10

0.0017

2.00

2.5

3.32

France

0.444

0.31

0.0053

2.90

1.8

4.05

Germany

0.444

0.36

0.0061

2.62

2.5

3.74

Israel

0.444

0.19

0.0032

3.77

2.0

5.26

Japan

0.378

0.22

0.0037

2.04

1.6

3.23

Namibia

0.444

0.01

0.0001

12.00

5.8

12.31

Nauru

0.375

0.32

0.0054

4.74

2.0

5.65

New Zealand

0.375

0.20

0.0034

4.95

2.0

5.88

Nigeria

0.444

0.01

0.0001

15.71

14.5

16.35

Norway

0.444

0.40

0.0069

3.95

2.5

4.88

Papua New Guinea

0.410

0.28

0.0047

4.11

5.0

7.30

Republic of the Mar- 0.470 shall Islands

0.32

0.0055

4.82

2.1

6.28

Russia

0.444

0.04

0.0006

9.08

4.0

10.48

Saudi Arabia

0.371

0.13

0.0022

5.63

2.0

7.19

Singapore

0.371

0.22

0.0038

4.34

1.9

5.62

South Africa

0.444

0.07

0.0012

10.20

5.5

10.58

Spain

0.444

0.19

0.0033

3.56

1.9

4.88

Switzerland

0.444

0.50

0.0085

2.08

1.0

3.26

The Netherlands

0.444

0.29

0.0049

2.48

1.6

3.56

United Kingdom

0.444

0.24

0.0040

3.47

2.0

4.56

USA

0.470

0.32

0.0055

4.82

2.3

5.68

  Eqc = Bond20y + Mrp · beta

(4.20)

It is worth mentioning that, due to the special conditions of the Antarctica, it was not possible to find its cost data. Consequently, they are estimated by averaging the cost data from four countries, out of the 12, which originally signed the Antarctica Treaty and were actively participating during the International Geophysical Year, namely, Russia, United Kingdom, USA, and Australia. Table 4.2 then summarizes the location-dependent cost variables, discussed in the previous paragraphs, for the sites of interest. With the previous data, the overall costs related to the PV systems can be calculated and then, the LCOE can be estimated based on the equation from Sect. 4.5. In the following, the generated results will be presented and analyzed.

4.7 Results and Discussion

65

4.7 Results and Discussion The results obtained for each of the locations of interest are provided in Table 4.3, for the monofacial PV systems, and Table 4.4, for the bifacial PV systems. These tables show the results for the optimized module orientation designs which achieved the lowest LCOE (obtained after considering all possible Am and θm values with a one degree resolution) for the cases when any module orientation (AMO) is allowed, i.e. any value of Am and θm is permitted; and for the cases when only vertical module orientations (VMO) are allowed for bifacial PV systems, i.e. θm is fixed to 90◦ and any value of Am is permitted. These tables show: • CPV,Wp [USD/Wp ]: overall costs per Wp of the PV systems, i.e. CPV,Wp = CPV /PSTC,f . The variable CPV,Wp has the same value for AMO and VMO configurations; • Am , θm [◦ ]: module orientation which achieve the lowest LCOE. These will be referred as optimum orientation; • Id [Wh/m2 /day]: daily average effective irradiation for optimum module orientation, i.e., Id = (If + Ir · b) · f1 ; • Ed [Wh/Wp /day]: daily average energy production of the PV system per Wp for (y) S EPV ; optimum module orientation, i.e. Ed = y=1 PSTC,f ·S ·365 • LCOE [USD/Wh]: levelized cost of electricity for optimum module orientation; and • LCOEip [%]: LCOE improvement. The variable LCOEip is the comparison between the LCOE from the optimized design (shown in these tables) and the design applying the conventional rule of thumb, i.e. module tilt angle equal to the latitude and facing the equator. As for example, LCOEip = 4% means that the LCOE value with the conventional orientation design is 4% higher than the one from the optimized orientation. The variable LCOEip is a measure on how optimal is the traditional orientation design. As VMO designs are a niche in the current market, due to space limitations, only their module orientation and LCOE values are provided for bifacial modules. Furthermore, Table 4.4 also indicates how much should the cost of bifacial modules be with respect to their monofacial counterparts (for AMO designs) in order for them to reach the same LCOE (when optimized orientations are considered). This is referred as cmb . As for example, cmb = 120% means that for the bifacial PV system to reach the same LCOE value as the one from the monofacial PV system, the cost of the bifacial module (in USD/Wp ) should be 1.2 times the one of the monofacial module. The parameter cmb is important to appreciate the potential of the bifacial technology. In order to better interpret the results provided in Tables 4.3 and 4.4, trends obtained from them are presented and discussed in the following subsections.

ID

TAM GVN SYO SPO DOM ASP COC DAR SON BRB FLO PTR SMS ALE EUR REG XIA TOR CAR PAL

#

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Algeria Antarctica Antarctica Antarctica Antarctica Australia Australia Australia Austria Brazil Brazil Brazil Brazil Canada Canada Canada China Estonia France France

Location

Table 4.3 Monofacial PV systems results

0.87 1.18 1.18 1.18 1.18 1.28 1.28 1.28 1.41 0.88 0.89 0.89 0.89 1.29 1.29 1.29 0.97 1.11 1.37 1.37

167 355 357 146 355 2 9 5 171 12 2 330 9 180 193 178 182 179 179 175

27 49 58 79 68 26 12 18 42 22 25 12 27 59 55 42 36 39 38 36

Monofacial PV systems AMO designs CPV,Wp Am θm (USD/Wp ) (◦ ) (◦ ) 6407 3676 3915 3738 5442 6482 5580 5651 4462 4936 4243 5694 5566 2745 2851 4592 4696 3152 5112 3671

Id (Wh/m2 /day) 4.87 3.25 3.39 3.64 4.93 5.10 4.26 4.22 3.86 3.80 3.26 4.27 4.34 2.43 2.51 3.76 3.85 2.58 4.01 2.95

4.72 8.54 8.19 7.64 5.63 5.10 6.10 6.16 6.27 7.82 8.97 6.84 6.74 10.12 9.81 6.55 6.11 6.94 5.92 8.05

Ed LCOE (Wh/Wp /day) (USD cents/kWh)

(continued)

0.53 4.99 1.04 2.23 0.52 0.05 0.04 0.45 0.67 0.63 0.12 0.37 0.23 4.21 7.04 0.76 0.18 4.26 0.50 2.09

LCOEip (%)

66 4 Optimization and Cost-Effectiveness Analysis …

ID

LIN SBO FUA ISH MNM SAP TAT GOB NAU LAU ILO NYA MAN

KWA

TIK SOV SIN DAA CNR

#

21 22 23 24 25 26 27 28 29 30 31 32 33

34

35 36 37 38 39

Table 4.3 (continued)

Germany Israel Japan Japan Japan Japan Japan Namibia Nauru New Zealand Nigeria Norway Papua New Guinea Republic of the Marshall Islands Russia Saudi Arabia Singapore South Africa Spain

Location

0.92 0.97 1.12 1.01 1.18

1.34

1.47 1.16 1.19 1.19 1.19 1.19 1.19 0.91 1.26 1.10 0.99 1.49 1.23

178 175 81 8 181

167

170 176 179 178 180 175 179 350 49 356 193 179 72

50 26 10 31 34

9

37 29 27 16 21 32 35 25 3 37 12 44 7

Monofacial PV systems AMO designs CPV,Wp Am θm (USD/Wp ) (◦ ) (◦ )

2611 6527 4291 6293 4524

5294

3429 6179 3964 4228 5504 3801 4310 7020 5541 4531 4790 2062 4846

Id (Wh/m2 /day)

2.32 4.85 3.24 4.88 3.57

3.99

2.77 4.73 3.12 3.23 4.18 3.09 3.44 5.28 4.15 3.72 3.63 1.80 3.65

12.04 4.68 7.04 6.32 6.25

7.23

8.95 4.80 6.10 5.88 4.55 6.16 5.53 5.92 6.19 6.16 11.89 15.68 7.93

Ed LCOE (Wh/Wp /day) (USD cents/kWh)

(continued)

4.70 0.05 0.90 0.19 0.86

0.05

3.13 0.08 0.62 0.71 0.15 1.46 0.02 0.20 0.07 0.80 0.12 14.57 0.44

LCOEip (%)

4.7 Results and Discussion 67

ID

IZA PAY CAB

CAM

LER

BER

BAR BIL BON BOS CLH DRA FPE GCR PSU SXF

#

40 41 42

43

44

45

46 47 48 49 50 51 52 53 54 55

Table 4.3 (continued)

Spain Switzerland The Netherlands United Kingdom United Kingdom United Kingdom USA USA USA USA USA USA USA USA USA USA

Location

1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38

1.26

1.26

1.26

1.18 1.62 1.34

182 183 175 167 180 176 178 178 181 182

179

178

183

176 179 181

50 32 32 37 32 33 39 29 31 37

25

36

34

25 35 37

Monofacial PV systems AMO designs CPV,Wp Am θm (USD/Wp ) (◦ ) (◦ )

2691 4957 4510 5295 4991 6407 4508 4777 4117 4665

4847

2461

3351

7107 3973 3394

Id (Wh/m2 /day)

2.38 3.90 3.61 4.20 3.97 4.91 3.66 3.73 3.30 3.75

3.73

2.04

2.72

5.64 3.19 2.73

11.81 7.21 7.80 6.69 7.09 5.73 7.68 7.54 8.53 7.50

6.15

11.26

8.43

3.95 8.11 8.12

Ed LCOE (Wh/Wp /day) (USD cents/kWh)

3.77 0.37 0.77 0.82 0.38 0.21 0.94 0.26 1.13 0.62

0.66

6.56

3.18

0.17 1.58 2.64

LCOEip (%)

68 4 Optimization and Cost-Effectiveness Analysis …

ID

TAM

GVN

SYO

SPO

DOM

ASP

COC

DAR

SON

BRB

FLO

PTR

SMS

ALE

EUR

REG

XIA

TOR

CAR

PAL

#

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

France

France

Estonia

China

Canada

Canada

Canada

Brazil

Brazil

Brazil

Brazil

Austria

Australia

Australia

Australia

Antarctica

Antarctica

Antarctica

Antarctica

Algeria

Location

1.45

1.45

1.20

1.05

1.38

1.38

1.38

0.96

0.96

0.96

0.94

1.49

1.35

1.35

1.35

1.25

1.25

1.25

1.25

172

178

173

182

177

191

227

13

310

3

15

169

5

12

2

276

125

283

348

163

46

43

49

43

49

75

84

33

19

31

30

52

22

16

31

90

90

88

64

35

(◦ )

(◦ )

(USD/Wp )

0.94

θm

Am

CPV,Wp

AMO designs

Bifacial PV systems

Table 4.4 Bifacial PV systems results

4015

5494

3449

5051

5052

3836

3932

5888

5974

4416

5245

5012

5792

5682

6872

7505

6434

5079

4387

6986

(Wh/m2 /day)

Id

3.22

4.29

2.82

4.13

4.12

3.37

3.47

4.57

4.46

3.38

4.02

4.31

4.32

4.34

5.38

6.75

6.18

4.38

3.85

5.27

(Wh/Wp /day)

Ed

LCOEip

7.84

5.88

6.85

6.13

6.37

7.79

7.57

6.87

7.04

9.28

7.94

5.96

6.37

6.35

5.11

4.38

4.78

6.75

7.68

4.72

0.23

0.01

0.90

0.13

0.04

0.35

0.49

0.42

1.66

0.10

2.27

0.54

1.19

0.23

0.56

1.15

0.46

1.11

0.62

1.78

(USD (%) cents/kWh)

LCOE

119

114

115

110

119

185

207

106

104

103

107

128

99

97

110

194

284

173

144

111

(%)

cmb

111

105

109

201

131

199

245

79

272

83

83

152

87

87

86

276

125

280

296

97

(◦ )

(continued)

9.01

7.00

7.43

7.75

7.35

7.95

7.58

8.25

8.31

12.36

9.43

6.74

8.16

8.14

6.15

4.38

4.78

6.75

8.01

5.49

(USD cents/kWh)

LCOE

VMO designs Am

4.7 Results and Discussion 69

ID

LIN

SBO

FUA

ISH

MNM

SAP

TAT

GOB

NAU

LAU

ILO

NYA

MAN

KWA

TIK

SOV

SIN

DAA

CNR

IZA

#

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

Table 4.4 (continued)

1.58

1.07

1.18

1.34

0.99

1.27

1.27

1.27

1.27

1.27

1.24

Spain

Spain

South Africa

Singapore

Saudi Arabia

Russia

1.26

1.26

1.09

1.20

1.04

1.00

Republic of 1.42 the Marshall Islands

174

181

11

85

174

174

160

78

170

200

355

74

347

179

174

180

178

179

173

164

28

42

36

21

34

65

13

12

67

22

44

7

31

42

40

25

22

34

37

47

(◦ )

(◦ )

(USD/Wp )

1.56

θm

AMO designs Am

CPV,Wp

Papua New 1.31 Guinea

Norway

Nigeria

New Zealand

Nauru

Namibia

Japan

Japan

Japan

Japan

Japan

Israel

Germany

Location

Bifacial PV systems

7279

4909

6750

4530

7170

3174

5385

4948

2485

5081

4866

5631

7588

4612

3995

5653

4332

4145

6839

3721

(Wh/m2 /day)

Id

5.77

3.85

5.20

3.41

5.29

2.80

4.05

3.72

2.16

3.84

3.98

4.21

5.67

3.67

3.24

4.28

3.31

3.26

5.20

2.99

(Wh/Wp /day)

Ed

LCOEip

4.13

6.18

6.38

7.11

4.60

10.77

7.55

8.27

13.80

12.21

6.13

6.46

5.97

5.53

6.25

4.73

6.12

6.22

4.68

8.77

0.05

0.01

0.54

3.73

0.85

0.44

0.26

1.33

1.32

1.60

0.06

0.65

0.81

0.40

0.17

0.01

0.05

0.00

0.42

0.86

(USD (%) cents/kWh)

LCOE

99

114

109

108

117

138

98

98

158

105

112

97

109

112

106

99

98

105

119

118

(%)

cmb

96

257

83

91

94

138

91

90

129

268

293

89

273

109

124

265

94

101

98

121

(◦ )

(continued)

5.05

7.20

7.55

8.34

5.31

11.28

9.74

10.19

14.35

14.87

7.39

7.97

6.94

6.95

7.78

6.05

7.66

7.85

5.40

10.00

(USD cents/kWh)

LCOE

VMO designs Am

70 4 Optimization and Cost-Effectiveness Analysis …

ID

PAY

CAB

CAM

LER

BER

BAR

BIL

BON

BOS

CLH

DRA

FPE

GCR

PSU

SXF

#

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

Table 4.4 (continued)

USA

USA

USA

USA

USA

USA

USA

USA

USA

USA

United Kingdom

United Kingdom

United Kingdom

The Netherlands

1.47

1.47

1.47

1.47

1.47

1.47

1.47

1.47

1.47

1.47

1.34

1.34

1.34

1.43

182

181

177

177

175

180

165

174

184

185

179

178

183

181

43

39

36

46

38

37

43

39

38

66

30

48

43

47

43

(◦ )

(◦ )

(USD/Wp ) 179

θm

AMO designs Am

CPV,Wp

Switzerland 1.70

Location

Bifacial PV systems

5043

4385

5056

4907

6830

5199

5679

4823

5280

3340

5004

2644

3545

3690

4323

(Wh/m2 /day)

Id

4.04

3.50

3.94

3.97

5.21

4.12

4.49

3.84

4.14

2.93

3.85

2.19

2.87

2.96

3.45

(Wh/Wp /day)

Ed

LCOEip

7.40

8.53

7.59

7.52

5.73

7.24

6.65

7.77

7.21

10.18

6.36

11.20

8.52

7.97

7.89

0.02

0.05

0.05

0.06

0.07

0.00

0.80

0.09

0.05

0.20

0.04

1.13

0.50

0.25

0.13

(USD (%) cents/kWh)

LCOE

116

111

109

118

111

105

113

112

111

160

101

113

108

117

122

(%)

cmb

246

256

99

125

101

259

121

109

259

195

96

174

241

124

252

(◦ )

9.06

10.47

9.45

8.87

7.05

9.31

8.24

9.46

8.93

10.59

8.16

13.00

10.37

9.26

9.42

(USD cents/kWh)

LCOE

VMO designs Am

4.7 Results and Discussion 71

72

4 Optimization and Cost-Effectiveness Analysis …

4.7.1 Monofacial AMO Versus Bifacial AMO The results of the monofacial and bifacial technologies when any module orientation is allowed are discussed in this section. Figure 4.4a presents the LCOEip values for the AMO designs for monofacial and bifacial systems with respect to their location latitude. On the one hand, with respect to the monofacial systems, it can be appreciated that for all the locations with latitudes lower than 60◦ , the LCOEip value is lower than 5%. Only when reaching higher latitudes, values beyond 5% were obtained for some locations (with a maximum value close to 15%). On the other hand, for bifacial systems, regardless of the geographical position, LCOEip is always below 5%. Figure 4.4b then presents the extra energy delivered to the grid from the bifacial PV systems, with respect to the one from the monofacial PV systems for the AMO designs. An exponential tendency can be appreciated in which the relative energy generated from the bifacial systems increase as the latitude gets closer to the poles. For latitude values of up to 65◦ , the bifacial energy increase is within 1% to 12%. Beyond this latitude range, the energy increase from the bifacial systems rises considerably, reaching values of up to 71%. The LCOE results for the AMO designs are then presented in Fig. 4.4c. For latitudes lower than 40◦ , monofacial systems are in general more cost-effective than their bifacial counterparts. Beyond this range, the tendency is reversed and the bifacial systems are in general more cost-effective. Another point to note is that only for latitudes above 65◦ , the LCOE difference between bifacial/monofacial systems is considerable (between 0.8 to 2.9 USD cents/kWh). Finally, Fig. 4.4 d presents the percentage of the bifacial panel cost in comparison to the monofacial one to get the same LCOE for AMO designs. Recall that, as mentioned in Sect. 4.6.3, in the present work it is considered that the cost of the bifacial module is 11.2% higher than the monofacial one (cmb =111.2%). A total of 27 locations reach cmb > 111.2%. These are the ones that achieved a lower LCOE for

Fig. 4.4 Trends from the case studies: monofacial AMO versus bifacial AMO

4.7 Results and Discussion

73

bifacial systems previously presented in Fig. 4.4c. Similar to the trend from Fig. 4.4b, cmb reaches its highest values close to the poles. For the location closest to the pole, SPO, the cost of the bifacial modules can even be equal to 2.84 times that of the monofacial module and still reach the same LCOE value. It is interesting to analyze the cases which are in the range of 100% to 111.2% (20 in total). This range indicates that, although with the current module price the monofacial systems reached lower LCOE values, if the gap between the bifacial/monofacial module costs keeps decreasing in time (which is an expected trend), bifacial systems can also become more cost-effective for these locations. In addition, 8 locations (close to the equator) are found to have cmb values below 100%. For these locations, even if the module cost from bifacial and monofacial technologies were to be the same, the monofacial systems will still be more cost-effective. Some of the alternatives to turn this around would be for bifacial modules to actually be cheaper than the monofacial ones (which even in the future would be very difficult to achieve), or to enhance the front efficiency as well as the rear efficiency (linked to the bifaciality factor) of the bifacial modules (this is a more reliable approach for future scenarios).

4.7.2 Monofacial AMO Versus Bifacial VMO For niche applications in which VMO designs are desired, the energy/cost between bifacial VMO and monofacial AMO designs is compared to quantify the sacrifices (if any) that the former faces. Based on the energy production, Fig. 4.5a reveals that for latitude values up to 65◦ , bifacial VMO designs produce lower energy than the monofacial AMO systems for almost all the locations (reaching values down to −23%). Beyond this range, the former is able to produce higher amount of energy (up to 71%). For latitudes below 65◦ , the monofacial AMO designs reach lower LCOE values than the bifacial VMO ones, as seen in Fig. 4.5b. This figure also reveals that the bifacial VMO designs have a considerable disadvantage at places close to the equator and a considerable advantage at places close to the poles. To better comprehend the influence of the module orientation, the polar contour plot of the Id , Ed , and LCOE values are presented at the Appendix D. These plots show that, except for the location closest to the pole, i.e. SPO, the LCOE range of values for the bifacial systems is smaller than that for the monofacial systems. This suggests that the decision for the bifacial module orientation is less critical than for the monofacial one. It can also be seen that the optimal orientations of bifacial systems require the module to have a higher tilt angle, an expected trend as this will enhance the irradiance collection at the rear side. For locations that are not that close to the equator, the best results require for the modules to practically face the equator.

74

4 Optimization and Cost-Effectiveness Analysis …

Fig. 4.5 Trends from the case studies: monofacial AMO versus bifacial VMO

4.7.3 Sensitivity Analysis Although the variables considered here were estimated in an effort to represent the different situations worldwide, these can change for particular case studies. Consequently, a sensitivity analysis is necessary to have an idea on the LCOE variability. Thus, different variables of interest were modified within ±20% of their original value (given in Sect. 4.6) and then the LCOE (with the optimized module orientation previously defined in Tables 4.3 and 4.4) is calculated. This analysis is only presented for the AMO designs for six locations. These results are shown in Fig. 4.6 in which the original LCOE values are also provided. The selected variables correspond to the inflation rate (IR), discount rate (DR), bank interest rate (IRBank ), cost of solar panels (cPV ), installation cost (cPV,ins ), system lifetime (S ), power temperature coefficient (γ), yearly module degradation (β1 ), albedo (ρ), and bifaciality factor (b). All of these variables tend to have a linear trend except for S owing to the following reasons. Firstly, as indicated in Sect. 4.6.3, the inverter has a warranty period of five years, and as such, it needs to be paid during years 6, 11, 16, 21, 26 and so on. Therefore, a low reduction on the LCOE is appreciated when S varies from 20 years to 21 years (parameter variation from 80% to 84%, as seen in Fig. 4.6) and from 25 years to 26 years (parameter variation from 100% to 104%, as seen in Fig. 4.6). Secondly, because the effective yearly energy is reduced due to the discount rate DR (as seen in Eq. (3.21)), the LCOE approaches a saturation value as S increases. For these scenarios, the variables that showed a high influence on the LCOE are DR, cPV , cPV,ins , S , and b. These reached a maximum LCOE deviation of 6.9%, 8.8%, 9.6%, 8.5%, and 8.7%, respectively. The rest of the analyzed variables reached a maximum deviation below 5%.

4.7 Results and Discussion

75

Fig. 4.6 Sensitivity analysis for selected parameters and locations for monofacial and bifacial PV systems with AMO designs

76

4.7.3.1

4 Optimization and Cost-Effectiveness Analysis …

Albedo Influence

The results discussed so far were obtained by considering monthly albedo values provided by the NASA-SSE [9]. Although these are estimations based on satellite data for those particular locations, they do not consider how the ground conditions would change due to ground preparation for mounting the PV structures [67]. Consequently, in this section we analyze the LCOE dependence on the albedo factor. Figure 4.7 presents the variations on the LCOE values for monofacial and bifacial AMO, and bifacial VMO designs with respect to the albedo for six locations. The optimum module orientation (Am , θm ) is also provided for albedo values of 0, 0.5, and 1 to observe how big their variation is. It can be noticed that, as the albedo value increases, the optimal module tilt angle will also tend to increase. For the case of Antarctica (SPO station), regardless of the albedo value, the bifacial systems are more cost-effective than the monofacial ones (as previously discussed, the bifacial technology have a higher performance close to the poles). Nevertheless, for the other five locations, monofacial AMO systems are more cost-effective than bifacial AMO and VMO designs when the albedo value is set to 0. Nonetheless, as the albedo value increases, the bifacial systems considerably reduce their LCOE values (due to the fact that, as the albedo value increases, the bifaciality gain also increases). The minimum albedo value at which bifacial AMO systems are more cost-effective than the monofacial AMO ones will be known as ρAA . In a similar way, the variable

Fig. 4.7 LCOE estimations for optimum module orientation based on the albedo value for six selected locations for monofacial AMO, bifacial AMO, and bifacial VMO designs. The values in parentheses correspond to the optimum module orientation (Am , θm ) and are provided for albedo values of 0, 0.5, and 1

4.7 Results and Discussion

77

Fig. 4.8 Values of ρAA and ρAV with respect to their latitude. The albedo range of values for typical surfaces, obtained from [68, 69], are also provided

ρAV represents the minimum albedo value at which bifacial VMO designs are more cost-effective than the monofacial AMO ones. Based on the values from ρAA and ρAV , the ground conditions which assure the effectiveness of bifacial PV installations can be defined. The values of ρAA and ρAV are presented in Fig. 4.8 with respect to their latitudes. Concerning the AMO designs, the highest albedo values are required for locations close to the equator in order for bifacial systems to be more cost-effective than the monofacial ones (albedo up to 0.30). As seen from this figure, many surfaces are able to fulfill this condition. As the locations get closer to the poles, the ρAA value decreases down to zero at which, regardless of the albedo value, the bifacial technology is more cost-effective than its monofacial counterpart. With respect to the ρAV values, as expected, the albedo requirement is stricter for bifacial VMO systems to be more cost-effective than the monofacial AMO designs (reaching values of up to 0.57). Consequently, fewer surface types are able to fulfill this condition.

4.8 Summary This work has investigated whether it is more cost-effective to install PV systems using monofacial or bifacial modules for designs which allow any module orientation (AMO) and designs with vertical module orientation (VMO). A total of 55 locations worldwide were analyzed. The cost-effectiveness of a system was defined by its levelized cost of electricity (LCOE). To estimate the LCOE value, first, historical oneminute resolution weather data provided by different weather stations were obtained. Subsequently, filtering and filling processes were used to determine their typical

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meteorological year (TMY) data. With the TMY data, the irradiance at the front/rear sides of the modules were estimated. Afterwards, the energy generation of the PV systems and the total system cost during their lifetime (assumed to be 25 years) were calculated. At this point the LCOE was estimated for systems of 1 MWp . The main conclusions of this work are: 1 For latitudes above 40◦ , bifacial AMO designs are in general more cost-effective than monofacial AMO systems. This tendency is reversed, however, for latitudes below 40◦ with low albedo values. Nevertheless, if the albedo value is kept to a minimum between 0.12 to 0.30 (depending on the location), bifacial AMO designs can be more cost-effective. 2 When comparing monofacial AMO against bifacial VMO, the latter is more cost-effective only for locations close to the poles, i.e. latitudes higher than 65◦ . Nonetheless, bifacial VMO designs could even reach a lower LCOE than monofacial AMO systems at latitudes below 65◦ if the albedo value can be maintained between 0.29 to 0.57 (depending on the location). 3 The LCOE difference between the one obtained from the optimized module orientation and the one with module orientation based on the conventional approach (module facing the equator with tilt angle equal to its latitude) is less than 5% for the bifacial PV systems for any location and for monofacial PV systems when located at latitudes below 60◦ .

References 1. International_Energy_Agency_(IEA) (2016) Trends 2016 in photovoltaic applications. Technical report IEA PVPS T1–30:2016 2. Rajput AS, Zhang Y, Rodríguez-Gallegos CD, Khanna A, Basu PK, Nalluri S, Singh JP (2020) Comparative study of the electrical parameters of individual solar cells in a c-si module extracted using indoor and outdoor electroluminescence imaging. IEEE J Photovolt 10(5):1396–1402 3. Pujari NS et al (2018) International technology roadmap for photovoltaic (ITRPV): 2017 results. Technical report, ITRPV-VDMA 4. Rodríguez-Gallegos CD, Gandhi O, Panda SK, Reindl T (2020) On the PV tracker performance: tracking the sun versus tracking the best orientation. IEEE J Photovolt 10(5):1474–1480 5. Rodríguez-Gallegos CD, Liu H, Gandhi O, Singh JP, Krishnamurthy V, Kumar A, Stein JS, Wang S, Li L, Reindl T et al (2020) Global techno-economic performance of bifacial and tracking photovoltaic systems. Joule 6. Marion B, MacAlpine S, Deline C, Asgharzadeh A, Toor F, Riley D, Stein J, Hansen C (2017) A practical irradiance model for bifacial PV modules: preprint. Technical report NREL/CP5J00-67847, National Renewable Energy Laboratory (NREL), Golden, USA 7. Guerrero-Lemus R, Vega R, Kim T, Kimm A, Shephard LE (2016) Bifacial solar photovoltaics– a technology review. Renew Sustain Energy Rev 60:1533–1549 8. Guo S, Walsh TM, Peters M (2013) Vertically mounted bifacial photovoltaic modules: a global analysis. Energy 61:447–454 9. NASA (2018) Surface meteorology and solar energy 10. Ito M, Gerritsen E (2016) Geographical mapping of the performance of vertically installed bifacial modules. In: Proceedings of 32nd European PV solar energy conference and exhibition (EU PVSEC). Munich, pp 1603–1609

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Chapter 5

Optimal Diesel Replacement Strategy for the Progressive Introduction of PV and Batteries

5.1 Introduction Many places around the globe are not connected to the mains utility grid as it may not be cost effective due to several factors, such as geographical conditions and low load demand, among others. Consequently, off-grid systems are typically employed to energize these loads. Traditional off-grid systems are typically energized by nonrenewable energy sources like diesel generators (DGs). Despite advantages of using DGs, e.g. precise control on power generation, they suffer from several drawbacks, such as high associated cost from diesel, as well as CO2 emissions. As a result, addition of renewable energy sources into these systems can alleviate fuel price uncertainties and environmental concerns. Recently, use of photovoltaic solar panels (PV) has become a viable solution in many regions with a decent level of solar irradiance. This is mainly because of reasons such as their continuous price reduction, scalability, and simple installation process. Furthermore, addition of batteries (BAT) is also of interest as they can store any extra energy generated by the PV, as well as improve the ON/OFF operation of DGs [1]. Even though addition of PV and batteries could be beneficial, an optimal design process is necessary to avoid undersized/oversized systems and to achieve the lowest life-cycle cost. Currently, there are several approaches available in literature that have been proposed to tackle this challenge by focusing on particular objectives, e.g. cost reduction and CO2 emission reduction. Nevertheless, most works tend to assume that there is unlimited amount of capital available so that the optimum number of PV panels and batteries can be installed at the beginning. Despite promising theoretical results that could be achieved with this assumption, this might not be a realistic approach. For example, Roberts et al. [2] developed a probabilistic simulationbased optimization approach which incorporated three modules, namely: optimization module, based on the non-dominated sorting genetic algorithm II (NSGA-II); uncertainty module, which considers probability distribution functions to simulate variations on the weather conditions, load, and failure probability of the system’s components; and the simulation module. Their case study considered the optimiza© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7_5

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tion design for a PV+BAT+DG system for a rural community located at the Amazonian region of Brazil. The optimal solution found (based on the net present value and power supply probability) required an initial investment, to install solar panels and batteries, of 65% of the life-cycle cost. In another study, Ogunjuyigbe et al. [3] used the genetic algorithm (GA) to optimize the sizing design for a residential building considering the addition of solar panels, batteries, diesel generators, and wind turbines (WT). They focused on the reduction of total costs, dump energy, as well as CO2 emissions. The optimal design required an initial investment of 32% of the life-cycle cost for the installation of PV panels (16%), batteries (8%), and wind turbines (8%). For a microgrid located at the Dongfushan Island in China, Zhao et al. [4] analyzed whether a hybrid system composed of PV+BAT+WT+DG could be advantageous based on the reduction of the life-cycle cost, pollutant emissions, as well as increase of the renewable penetration, by also applying GA together with weighting factors. Their work concluded that this type of hybrid design would be beneficial, however, about 1/3 of the total cost would be required for the initial investment. The benefits on the system hybridization has also been shown in case studies from Europe, as for example, Soshinskaya et al. [5] used the software hybrid optimization of multiple energy resources (HOMER) to optimize the design for an industrial sized water treatment plant in the Netherlands by the addition of PV+BAT+WT+DG. The work summarized that in order to get the lowest life-cycle cost, more than 50% of this cost was necessary to be provided at the beginning to install the solar panels, batteries, and wind turbines. With respect to the Southeast Asian region, Halabi et al. [6] also employed HOMER to design PV+BAT+DG systems for two decentralized power stations in Malaysian islands. Their findings showed that the design with the lowest life-cycle cost required about 1/4 of its cost for the initial installation. In [7], Yilmaz and Dincer also used HOMER to optimize the sizing design for a PV+BAT+DG system in Kilis, Turkey. Among the different designs, the one which presented the lowest initial investment reached a value of 25% of the life-cycle cost, while the design with the lowest life-cycle cost required an initial investment of 85% of the total costs. For rural electrification in remote areas in Algeria, Kaabeche and Ibtiouen [8] presented a basic optimization algorithm, based on the linear increase of employed solar panels and wind turbines, to reduce the total costs by installing a PV+BAT+WT+DG system. Here, their optimal result required an initial investment of about 30% of the total life-cycle cost. Yahiaoui et al. [9] also examined another rural village from Algeria (Ilamane) and proposed a particle swarm optimization (PSO) algorithm for optimization of the life-cycle costs for a PV+BAT+DG system by keeping the loss of load probability and CO2 emissions as constraints. Their optimum result required an initial investment of 60% of the total costs. Yahiaoui et al. also employed HOMER to optimize the system design from which an initial investment of 90% of the total costs was required. Remote areas in Iran have been investigated by Maleki and Askarzadeh [10] where the optimization design of PV+BAT+DG systems took place by applying a discrete version of the harmony search algorithm (DHS). Their results showed

5.1 Introduction

85

that the design with the lowest life-cycle cost required an initial investment of 44% of this value for the installation of solar panels (37%) and batteries (7%). On top of the many works mentioned above, the author has also carried out a previous study to hybridize a DG-only system (in Indonesian islands) by the addition of solar panels and batteries using the optimization algorithm NSGA-III to minimize the life-cycle cost, CO2 equivalent emissions, and grid voltage deviations [1]. The optimal design generated a total life-cycle cost equal to 77% of the benchmark scenario, i.e. DG-only system. However, the required initial investment corresponded to 16% of the total life-cycle cost. The aforementioned discussions present multiple case studies with optimized hybridization of different off-grid systems worldwide. Although they all show that the addition of renewable energy sources could be cost effective in the long term, they all have the requirement for a high initial investment (reaching values from 16% up to 90% of the total life-cycle cost). On the contrary, systems composed of DGs only require minimal initial investment, despite the risk of yielding higher costs at the end of the system lifespan [1, 11]. This could then constitute a deal breaker for investors or local communities who might not be able, or are not willing to spend such large funds upfront to hybridize off-grid systems. Consequently, a strategy to reduce the initial investment, while assuring high savings at the end of the project lifespan, is desirable. In addition, when optimizing the sizing design of these hybrid systems, the lifespan of the system is typically assumed to be within the range of 20 years up to 30 years. Nonetheless, to estimate the system performance under different designs, only one year is typically simulated. The subsequent years are assumed to be the same and are only influenced by factors such as interest, discount, and inflation rates. Nevertheless, within this long time horizon, the price and performance of many elements are expected to change in time. In order to tackle this issue, it is common to apply sensitivity analyses which change the price of critical elements but keep them constant within the system lifespan [2, 3]. Yet, this approach still has limitations as no time variations of costs are considered within the simulation time frame. Consequently, to properly estimate the system performance in the long term, the simulation should be carried out over the system lifetime so that time dependent variables can be considered. This work aims to tackle the previous challenges by optimizing the number of solar panels and batteries that should be progressively installed, year after year, in systems which are originally energized only by DGs. This is carried out to keep the initial investment as low as possible, and to avoid large interest and amortization repayments to service the bank loan. The yearly savings from lower diesel consumption is first used to service the bank loan and any left-overs are then gradually re-invested to install more solar panels and batteries in the subsequent years. Through this approach, it is aimed to provide a diesel replacement strategy for off-grid systems, which lowers the burden derived from the initial investment requirement. Moreover, the system performance is fully simulated for all the years of the system lifespan. Therefore, time dependent variables can be considered, such as

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5 Optimal Diesel Replacement Strategy for the Progressive …

price variations of solar panels, batteries, inverters, and diesel, as well as performance degradation of solar panels and batteries, among others. In addition, the influence of these systems on the environment is also studied based on the CO2 equivalent life-cycle emissions, CO2e [mil. kgCO2 ]. The parameter CO2e does not only consider the CO2 emissions related to direct burning of fuel and life cycle emissions of each component (from extraction of raw materials to final disposal), but also considers the influence of the other greenhouse gases (which are expressed based on their CO2 equivalence [12]). Therefore, an accurate representation of the environmental impact can be performed.

5.2 Modelling of PV Hybrid Systems In the present work, off-grid systems which are initially energized only by DGs are considered. They can then be hybridized by adding solar panels (PV) and batteries (BAT). A basic representation of these systems is presented in Fig. 5.1. The main grid is an AC grid where the loads are connected. To transfer the power produced by the PV to the loads, inverters are used. They control the solar panels to operate at maximum power point. Furthermore, bidirectional converters are used for batteries in order to transfer power to/from the grid (discharging/charging operation). In addition, a dump load is assumed to have been installed to consume any surplus power. In the following subsections, the mathematical formulation of cost and electrical performance associated to the three elements of interest (DGs, PV, and batteries) is presented. To carry out the modelling, the time is discretized by applying a timeslotted system. This is indexed by t, 1 ≤ t ≤ T , where T is the total number of time slots and t represents the slot size which is set to one hour to keep a balance between simulation accuracy and computational burden.

Fig. 5.1 Off-grid system, originally composed of diesel generators, in which solar panels and batteries have been added

5.2 Modelling of PV Hybrid Systems

87

5.2.1 Diesel Generators 5.2.1.1

Cost

The variable CDG [USD] considers the total expenses to buy the DGs within the system lifetime, S [year]. Even though these are originally installed, they have a limited lifetime, DG [year], so new DGs might need to be purchased in the future years. This is presented in Eq. (5.1): S /DG  n DG

 

CDG =

i=1

· cDG(i) · PDG,nominal( j) ·

j=1

(1 + I R)i·DG −1 , (1 + D R)i·DG −1

(5.1)

where n DG is the number of DGs, cDG(i) [USD/kW] is their specific cost during the ith replacement period and PDG,nominal( j) [W] corresponds to the nominal power of the jth diesel generator. Furthermore, the inflation rate, I R[%], is taken into account to include cost of inflation. In addition, a discount rate, D R[%], is needed as the life-cycle cost is calculated in net present value terms. The total cost associated with the diesel consumption, Cdiesel [USD], is calculated by estimating the amount of diesel used at each time slot t, namely, κdiesel(t) [l]. Only the DGs that are operating, i.e. ON-mode, are considered. The diesel consumption is calculated as [13]: κdiesel(t) =

n DG  (aDG · PDG( j,t) + bDG · PDG,nominal( j) ) · u ( j,t) · t,

(5.2)

j=1

where PDG( j,t) [W] is the power produced by the jth DG that is ON at the time slot t; u ( j,t) indicates the status of the jth DG at time slot t, i.e. u ( j,t) = 0 if DG is OFF, otherwise u ( j,t) = 1. The values of the coefficients aDG [l/kWh] and bDG [l/kWh] depend on the quality of the DGs (the lower they are, the less diesel is consumed to generate a specific power). The total cost of diesel can then be calculated: Cdiesel =

T  cdiesel(t) · κdiesel(t) ,

(5.3)

t=1

where cdiesel(t) [USD/l] corresponds to the diesel price. The summation of this equation accounts for all time slots. Finally, the total cost due to operation and maintenance (O&M) associated to the DGs, CDG,OM [USD], is obtained by adding the O&M cost for each year y: CDG,OM

S  n DG  (1 + I R) y−1 = cDG,OM · PDG,nominal( j) · , (1 + D R) y−1 y=1 j=1

(5.4)

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where cDG,OM [USD/year/kW] is the O&M cost factor for DGs. Other costs such as start-up/shutdown costs are not considered as they tend to be low for DGs of small size [14].

5.2.1.2

Electrical Performance

To avoid issues related to the proper operations of the DGs (such as oiling up of the silencer, bore glazing, and high temperature), their operation is typically limited within their nominal power and a minimum value [15, 16]: PDG,min( j) ≤ PDG( j,t) ≤ PDG,nominal( j) ,

∀t ∈ {1, . . . , T }, u ( j,t) ∈ {1},

(5.5)

where PDG,min( j) [W] corresponds to the minimum allowed power produced by the jth diesel generator that is operating.

5.2.1.3

CO2e Emissions

The CO2e emissions, due to the of DGs and consumption of diesel, are defined in Eqs. (5.6) and (5.7), respectively: S /DG  n DG DG C O2e =

  δDG(i) · PDG,nominal( j) , i=1

diesel C O2e =

(5.6)

j=1 T  δdiesel · κdiesel(t) ,

(5.7)

t=1

with δDG(i) [g/kW] being the CO2e emission coefficient associated to the installed DGs at the ith replacement, and δdiesel [g/l] being the CO2e emissions per liter of diesel.

5.2.2 Solar Panels 5.2.2.1

Cost

When it comes to solar panels, capital investment consists of buying the panels, cPV(y) [USD/Wp], and their installation, cPV,ins [USD/Wp].1 Solar panels can be 1 cPV,ins

others.

considers the cost related to the module installation labor, racking/sub-structures, among

5.2 Modelling of PV Hybrid Systems

89

installed at any time, hence, their cost addition during the off-grid system’s lifetime is: CPV + CPV,ins =

S 

 (1 + I R) y−1  n PV(y) · PPV,STC · cPV(y) + cPV,ins . , (1 + D R) y−1 y=1

(5.8)

where CPV [USD] and CPV,ins [USD] represent the total acquisition and installation cost, respectively. The variable n PV(y) is the number of solar panels installed at the yth year and PPV,STC [Wp] is the power output of a single module under standard test conditions (STC). When the installation of solar panels takes place, their required inverters must also be purchased. Furthermore, inverter warranties are usually purchased as well. The total cost related to the PV inverters can then be defined as: CPV,inv = ⎛

S  n PV(y) · PPV,STC · y=1

y−1 ⎝cPV,inv(y) · (1 + I R) + (1 + D R) y−1

(S −y)/w  PV  l=1

⎞ (1 + I R) y+l·wPV −1 ⎠ cPV,inv(y+l·wPV ) · πPV(l) · . (1 + D R) y+l·wPV −1

(5.9) In Eq. (5.9), the first summation accounts for the PV inverters that are purchased each year (if any). The variable cPV,inv(y) [USD/Wp] is the inverter cost at the yth year (the year in which the associated solar panels are installed). The second summation is used to consider the cost that needs to be covered for the years in which the inverter warranties are extended.2 The total O&M cost associated to the solar arrays, CPV,OM [USD], needs to be calculated by considering the increase in the number of solar panels over time (solar panels can be added in different years). The total number of solar panels installed until year y is defined as: y  n PV(k) . (5.10) NPV(y) = k=1

The variable CPV,OM can then be calculated as: CPV,OM =

S  y=1

cPV,OM · NPV(y) · PPV,STC ·

(1 + I R) y−1 , (1 + D R) y−1

(5.11)

where cPV,OM [USD/year/Wp] is the yearly O&M cost associated to the solar panels. warranties have a limited active time of wPV years. After this time has passed, a renewal is necessary. The cost due to the lth warranty renewal is calculated as a percentage πPV(l) [%] of the inverter cost at the year in which the renewal is taking place, cPV,inv( y+l·wPV ) .

2 These

90

5.2.2.2

5 Optimal Diesel Replacement Strategy for the Progressive …

Electrical Performance

The power generated by the solar panels at time slot t, PPV(t) [W], is in principle estimated based on the equation proposed in [17]. In addition, a degradation term is included here: 

 NPV(y) · PPV,STC · I(t) · 1 + γ · Tc(t) − 25 · ηPV,inv · (1 − β0 − y · β1 ) , 1000 (5.12) where y is the year in which the current power is calculated, I(t) [W/m2 ] is the solar irradiance, γ[%/◦ C] is the power temperature coefficient of the solar module, Tc(t) [◦ C] is the temperature of the solar cells, and ηPV,inv [%] is the weighted average efficiency of their inverters. As discussed in [18], solar panels suffer from a performance degradation over time. Hence, a degradation factor is added in which β0 [%] accounts for the initial degradation while β1 [%/year] is the annual degradation rate [18]. Furthermore, the equation from [17] is used to estimate the value of Tc(t) based on the ambient temperature, Ta(t) [◦ C], and the normal operating cell temperature TNOCT [◦ C] [19]: I(t) (5.13) Tc(t) = Ta(t) + (TNOCT − 20) . 800 PPV(t) =

5.2.2.3

CO2e Emissions

PV ), the The CO2e emissions associated in this section are due to solar panels (C O2e PV,ins PV,inv array support for their installation (C O2e ) and the PV inverters (C O2e ), with emission coefficients of δPV [g/Wp ], δPV,ins [g/Wp ], and δPV,inv [g/Wp ], respectively. This can be calculated as:

PV = C O2e

S  n PV(y) · PPV,STC · δPV ,

(5.14)

y=1

PV,ins C O2e =

S  n PV(y) · PPV,STC · δPV,ins ,

(5.15)

y=1

PV,inv C O2e

=

S 

n PV(y) · PPV,STC · n PV,inv,rep(y) · δPV,inv ,

(5.16)

y=1

where n PV,inv,rep(y) is the number of times a new inverter is installed for the PV installation at year y. The term n PV,inv,rep(y) · δPV,inv accounts for all inverters that are installed through the lifetime of the system.

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91

5.2.3 Batteries 5.2.3.1

Cost

The total acquisition cost of the batteries, CBAT [USD], is defined as: CBAT

S  (1 + I R) y−1 = n BAT(y) · S0 · cBAT(y) · , (1 + D R) y−1 y=1

(5.17)

where n BAT(y) is the number of batteries installed at year y, S0 [kWh] is the battery initial capacity, and cBAT(y) [USD/kWh] is the battery cost per unit energy at the yth year. The calculation of the total cost associated to the battery inverters is performed by employing the same principle used in Eq. (5.9) (the superscript BAT is applied to denote the battery parameters), which gives: CBAT,inv =

S    n BAT(y) · max Pc,max , Pd,max · y=1

⎛

y−1 ⎝cBAT,inv(y) · (1 + I R) + (1 + D R) y−1

(S −y)/w  BAT  l=1

⎞ (1 + I R) y+l·wBAT −1 ⎠ cBAT,inv( y+l·wBAT ) · πBAT(l) · . (1 + D R) y+l·wBAT −1

(5.18) The variables Pc,max [W] and Pd,max [W] correspond to the maximum charging/discharging power from a singlebattery, respectively. The maximum operator in Eq. (5.18), i.e. max Pc,max , Pd,max , is required as these inverters must be able to handle the maximum charging/discharging power from the battery banks. The battery systems also have an associated O&M cost. Its total cost, CBAT,OM [USD], is defined as: CBAT,OM =

S 

 (1 + I R) y−1  cBAT,OM · NBAT(y) · max Pc,max , Pd,max · , (1 + D R) y−1 y=1

(5.19)

where cBAT,OM [USD/year/kW] is the yearly O&M cost and NBAT(y) corresponds to the total number of batteries at year y. The variable NBAT(y) is calculated in a similar way as NPV(y) .

5.2.3.2

Electrical Performance

Because batteries degrade over time, they have a finite lifetime and need to be replaced. In this work, two lifetime estimations are taken into account: 1. the float lifetime float , which is the battery lifetime when it has not been used at all [20];

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5 Optimal Diesel Replacement Strategy for the Progressive …

and 2. the charging/discharging lifetime, which represents the battery degradation due to charging/discharging processes [21]. With respect to the charging/discharging lifetime, the approach presented by [21] is used, i.e. lifetime estimation based on the calculation of the total energy that a single battery will discharge during its lifetime, E [kWh]. In this work, it is assumed that when one of the two lifetimes is reached, the batteries must be replaced. The charging/discharging lifetime can be used to define the battery replacement cost, CBAT,rep(t) [USD][22]. The variable CBAT,rep(t) represents the cost of the battery to deliver energy at time slot t (the more energy it discharges, the sooner it is required to be replaced): S0 · cBAT(y) Pd(t) · t , (5.20) CBAT,rep(t) = · E ηBAT,inv where Pd(t) [kW] corresponds to the total discharging power from the battery inverters at the AC side (see Fig. 5.1). The variable ηBAT,inv [%] is the average weighted efficiency of these inverters. The maximum charging/discharging power of the batteries needs to be controlled to avoid the acceleration of degradation processes: 0 ≤ Pc(t) ≤

NBAT(t) · Pc,max , ηBAT,inv

∀t ∈ {1, . . . , T },

0 ≤ Pd(t) ≤ NBAT(t) · Pd,max · ηBAT,inv ,

∀t ∈ {1, . . . , T },

(5.21)

(5.22)

where Pc(t) [kW] is the total charging power at the AC side. A reduction on the battery capacity is associated with their degradation. Here, the cycle-based capacity loss presented in [23] is taken into account to estimate the capacity curtailment. This reduction is associated with the charging/discharging lifetime, previously explained. It is assumed that the battery needs to be replaced when its capacity is reduced to 80% of its original value [23]. The new battery capacity at time slot t, S(t) [kWh], can then be calculated as: S(t) = S(t−1) −

Pd(t) · t · S0 · (1 − 0.8) . ηBAT,inv · NBAT(t) · E

(5.23)

In Eq. (5.23), the first term is the battery capacity at a time slot t − 1, while the second term corresponds to the capacity reduction in case it discharges at the current time slot. The battery state of charge, S OC(t) [%], is calculated based on its charging/ discharging operation:  = S OC(t−1) · σ + ηc · ηBAT,inv · Pc(t) −



t , NBAT(t) · S0 (5.24) where σ[%/month] represents the battery self-discharge. The variables ηc [%] and ηd [%] are the battery charging/discharging efficiencies, respectively. S OC(t)

Pd(t) ηd · ηBAT,inv

·

5.2 Modelling of PV Hybrid Systems

93

Furthermore, the S OC value also needs to be kept within a safety boundary by defining its maximum and minimum limits (S OCmax and S OCmin , respectively) [24, 25]: ∀t ∈ {1, . . . , T }. (5.25) S OCmin ≤ S OC(t) ≤ S OCmax ,

5.2.3.3

CO2e Emissions

  BAT Here, the CO

 2e emissions are associated to the batteries C O2e and their inverters BAT,inv C O2e : BAT C O2e

S  = n BAT(y) · δBAT ,

(5.26)

y=1

BAT,inv C O2e =

S 

  n BAT(y) · max Pc,max , Pd,max · n BAT,inv,rep(y) · δBAT,inv ,

(5.27)

y=1

where δBAT [g/kWh] is the CO2e emission coefficient of batteries and δBAT,inv [g/kW] is the CO2e emission coefficient associated to their inverters. Equation (5.27) is the analogy of Eq. (5.16) for battery inverter. Furthermore, similar to Eq. (5.18), the maximum operator is used as these inverters need to cater for the maximum charging/discharging power of the batteries.

5.2.4 Spinning Reserve The spinning reserve, S R [W], is required to overcome unexpected scenarios in which the load demand is suddenly increased or the PV power is suddenly decreased. Only the DGs and batteries can contribute to this reserve (S RDG [W] and S RBAT [W], respectively): (5.28) S R(t) = S RDG(t) + S RBAT(t) . For the case of the DGs, only the ones that are in ON state can be considered (because extra time would be required for DGs that are currently OFF to produce power). The extra power that they would be able to supply, if necessary, is equal to the difference between their nominal power (PDG,nominal( j) ) and the power they are currently generating (PDG( j,t) ): S RDG(t) =

n DG  

 PDG,nominal( j) − PDG( j,t) · u ( j,t) .

(5.29)

j=1

For batteries, the extra power they can deliver to the AC grid is calculated considering the maximum power they can deliver to the grid (NBAT(t) · Pd,max · ηBAT,inv )

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5 Optimal Diesel Replacement Strategy for the Progressive …

and the power they are currently delivering into the grid (Pd(t) ): S RBAT(t) = NBAT(t) · Pd,max · ηBAT,inv − Pd(t) .

(5.30)

The S R condition is defined in terms of the current load demand and PV power (which are the ones that can unexpectedly change). This is achieved with the addition of the εload (0 ≤ εload ≤ 1) and εPV (0 ≤ εPV ≤ 1) coefficients. Their values are defined based on the uncertainty level (the higher the uncertainty, the higher should be the coefficient value). The spinning reserve condition can then be defined as: S R(t) ≥ Pload(t) · εload + PPV(t) · εPV ,

∀t ∈ {1, . . . , T }.

(5.31)

5.3 Problem Formulation In this work, two optimization problems are formulated. The first one employs the traditional approach to perform a sizing design optimization while the second one optimizes the number of solar panels, n PV , and batteries, n BAT , to be installed to hybridize a DG-only off-grid system. The goal is to show the limitations of the traditional approach and the advantages of the proposed replacement strategy over time.

5.3.1 Traditional Problem Formulation In the current section, the problem is defined to optimize the sizing design of solar panels and batteries to reduce the accumulated cost throughout the system lifetime. This is based on the standard approach adopted by multiple research papers that study the sizing optimization of PV hybrid systems, previously described in Sect. 5.1, including its limitations: • Unlimited initial investment, Iin [USD], is available, i.e. regardless of the required number of solar panels and batteries to be installed, it is assumed that the investor has enough capital available. • Solar panels and batteries can only be installed in the beginning (except when replacements are required, i.e. inverters and batteries). • No bank loan considerations, i.e. the investors fully pays with their own capital. For the following, the accumulated cost during the system lifetime, CT,P1 [USD], is defined as: CT,P1 = CDG + Cdiesel + CDG,OM + CPV + CPV,ins + CPV,inv + CPV,OM + CBAT + CBAT,inv + CBAT,OM .

(5.32)

5.3 Problem Formulation

95

In order to show the relation between the accumulated cost during the system lifetime, CT,P1 , and the required initial investment, Iin , a multi-objective optimization problem is defined:   CT,P1 (P1) minimize Iin subject to : n DG 

PDG( j,t) · u ( j,t) + PPV(t) + Pd(t) − Pc(t) ≥ Pload(t) ,

∀t ∈ {1, . . . , T },

(5.33)

j=1

(A.3) , (3.4) , (3.5) , (3.8) , (3.12) , n PV ≥ 0,

(5.34)

n BAT ≥ 0.

(5.35)

Equation (5.33) is applied so that the loads are always satisfied. Any extra energy generated by the distributed sources is consumed by the dump load (see Fig. 5.1).

5.3.2 Diesel Replacement Formulation For the proposed optimization problem, the objective remains the same, to reduce the accumulated cost during the system’s lifetime. Nevertheless, a more realistic scenario is considered with the following properties: • Limited initial investment: the investor has limited amount of capital available to install solar panels and batteries. • Solar panels and batteries can be installed at different points in time with different scale: this takes into account the scalability properties of PV and batteries. • Bank loan considerations: due to the high initial investment typically required for the design of these systems, a bank loan is desired to lower the equity investment. Based on the economic viability and riskiness of the project, the bank decides on the following parameters: – The amount of the loan, lBank [%], which is the percentage of the initial investment that the bank covers (the owner of the project is required to pay the rest). – The bank interest rate, I RBank [%]. – Debt tenor, dtBank [year], the time required for the borrower to repay the loan. Consequently, the borrower is required to pay every year to the bank a fixed amount divided into amortization, CBank,amor [USD], and interest, CBank,int [USD], until the

96

5 Optimal Diesel Replacement Strategy for the Progressive …

debt is repaid, i.e. after dtBank years have passed. The values of CBank,int and CBank,amor can be obtained from Eqs. (4.11) and (4.12), respectively. In this scenario, only a certain number of solar panels and batteries can be installed in the beginning, limited by the allowed initial capital investment. Further installations are undertaken in subsequent years without the need for fresh capital as the savings from the reduced diesel consumption is used. This strategy is explained as follows: In the original DG-only off-grid system, diesel consumption and associated diesel fuel purchases are relatively high. The addition of solar panels and batteries will lower this diesel fuel consumption. The difference in the overall yearly cost from the original DG-only system (which considers the diesel consumption and O&M of the DGs) with respect to the one from the proposed system (which considers the cost to install solar panels and batteries, bank debt if any, diesel consumption and O&M of solar panels, batteries and DGs) translates into savings to the owner of the system and are defined as S ydiesel [USD]. These savings can then be used to buy more solar panels and batteries for future years allowing further diesel consumption reductions. This cycle is repeated for the future years until the optimum hybridization is achieved. Consequently, an initial balance, Balini(y) [USD], at each year can be defined. This balance corresponds to the amount of money the owner has at the beginning of year y in order to buy additional solar panels and batteries (if required). The Balini(y) for a year y is calculated based on the balance from the previous year Balini(y−1) , deducting the cost from installing PV, CostPV(y−1) [USD], (includes capital expenditure, installation, inverter, O&M, and replacement costs) and batteries, CostBAT(y−1) [USD], (includes capital expenditure, inverter, O&M, and replacement costs) in the previous year, as well as deducting the bank amortization and interest payments, and adding the savings from lower diesel consumption: Balini(y) = Balini(y−1) − CostPV(y−1) − CostBAT(y−1) − CBank,amor(y) − CBank,int(y) + Sdiesel(y−1) .

(5.36)

It can be understood that the initial balance for the first year is equal to the initial investment Iin (the bank amortization and interest are assumed to be paid at the end of the respective years). For the current study, sequential optimization problems are solved: (1) During the first year, the number of PV, n PV(1) , and batteries, n BAT(1) , to be installed are estimated by solving an optimization problem to reduce the lifecycle cost for the off-grid system (S years). (2) With the values of n PV(1) and n BAT(1) , the balance for the second year (Balini(2) ) is obtained. Thereafter, a second optimization problem is defined to find the number of PV and batteries that should be installed in this year (n PV(2) and n BAT(2) , respectively) to reduce the total accumulated cost during the rest of the system lifetime (S − 1 years).

5.3 Problem Formulation

97

(3) The previous step is then repeated for the subsequent years until y = S , i.e. if the lifetime was defined at 25 years, a total of 25 optimization problems will be solved.3 For this problem, the life-cycle cost for the off-grid system, CT,P2 [USD], is defined as: CT,P2 = CBank,amor + CBank,int + CDG + Cdiesel + CDG,OM + CPV + CPV,ins + CPV,inv + CPV,OM + CBAT + CBAT,inv + CBAT,OM .

(5.37)

The optimization problem can then be defined for a particular year y as:   (P2) minimize CT,P2 subject to : n DG 

PDG( j,t) · u ( j,t) + PPV(t) + Pd(t) − Pc(t) ≥ Pload(t) ,

∀t ∈ {1, . . . , T },

(5.38)

j=1

Balini(y) ≥ CPV(y) + CPV,ins(y) + CPV,inv(y) + CBAT(y) + CBAT,inv(y) ,

∀y ∈ {1, . . . , S },

(5.39) (A.3) , (3.4) , (3.5) , (3.8) , (3.12) , n PV(y) ≥ 0,

(5.40)

n BAT(y) ≥ 0.

(5.41)

Equation (5.39) is added in order to constrain the system so that the total cost associated to acquire and install the n PV(y) solar panels and n BAT(y) batteries, as well as their required inverters during the analyzed year y, does not exceed the yearly available balance.

5.4 Algorithms Due to the discontinuous states of the DGs, i.e. ON/OFF states, these optimization problems cannot be solved using exact optimization methods. As a result, metaheuristic approaches are employed. Even though there is no guarantee to find the global optimum, if well designed, they can obtain a sufficiently good solution. 3 It

is necessary to notice that the optimization problem is not designed to reduce the accumulated cost for the next S years but only for the remaining years within the system lifetime. As for example, if S is set to 25 years and we are optimizing the number of PV and batteries to be installed during the 5th year, the optimization problem will aim to reduce the accumulated cost from year 5 till year 25.

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5.4.1 Sizing Algorithm To solve the multi-objective optimization problem (P1), the current state-of-the-art algorithm is used, namely, the non-dominated sorting genetic algorithm III (NSGAIII) [26]. NSGA-III is chosen due to its desirable properties: able to handle discrete optimization variables (such as n PV and n BAT ), diversity preservation, good convergence, simplicity, and computational efficiency, among others [26]. Furthermore, as (P2) corresponds to a single-objective optimization problem, the well-established genetic algorithm (GA) is used. GA is a population-based approach that imitates the natural selection process, and has the following qualities: is able to handle discrete variables, is less likely to get trapped in a local minimum, and is a robust algorithm, among others [27].

5.4.2 Scheduling Algorithm For any of the sizing problems, a dispatch strategy is needed to define how the different energy sources will operate together. Therefore, a centralized controller is applied to control the power output from the DGs (as well as their ON/OFF state) and batteries (PV are always working at maximum power point). A rule-based approach is designed based on the following priority criteria: (1) Fulfillment of the load demand. (2) Fulfillment of the spinning reserve constraint, i.e. Eq. (3.12). (3) Fulfillment of the constraint regarding the minimum/maximum power output from DGs, i.e. Eq. (A.3). (4) Minimization of the life-cycle cost. (5) Charging of the batteries. This scheduling algorithm is described in detail in the Appendix E. Flow charts corresponding to the computation of (P1) and (P2) are presented in Fig. 5.2.

5.5 Case Study A case study is defined to visualize how the hybridization process can be achieved. This takes place on an Indonesian island which has an off-grid fully operated by only DGs. The total load demand was measured for a full year (2016) and its normalized profile is presented in Fig. 5.3a. This profile is used as the basis with a peak demand of 200 kW during the first year, increasing annually by 5% thereafter. Four DGs with a nominal capacity of 125 kW each are assumed to be previously installed. The irradiance and ambient temperature parameters correspond to the typical meteorological

5.5 Case Study

99

Fig. 5.2 Flowchart to solve a the multi-objective optimization problem (P1); and b the proposed optimization problem (P2)

year (TMY) based on five years historical data (1 January 2012–31 December 2016). These data, collected by the Solar Energy Research Institute of Singapore (SERIS), were measured in Singapore (latitude of 1.3026◦ , longitude of 103.7729◦ , tilted angle of 10◦ , and azimuth angle of 180◦ ). These are presented in Fig. 5.3b, c, respectively, and are used as a proxy for this case study as many Indonesian islands are located close to Singapore. Based on a thorough literature review ([28] for the IR and DR, [10, 15, 29, 30] for the DGs, [31–33] for PV, and [32, 34–37] for batteries) and an internal analysis performed at SERIS, the rest of the required input parameters are presented in Table 5.1.

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Fig. 5.3 3-D time-plot considering the “day” and “hour” axes of the normalized load demand a TMY data set of the solar irradiance b respectively and TMY data set of the ambient temperature c Table 5.1 Parameter values for the case study System properties S 25 years DR 11.1% I RBank 10.5% Diesel generators n DG 4 PDG,nominal 125 kW aDG 0.246 l/kWh cDG,OM 0.14 USD/year/kW Solar panels (multicrystalline) PPV,STC 325 Wp wPV 5 years γ −0.4%/◦ C β1 0.7%/year ηPV,inv 98% Batteries (LiFePO4 ) S0 3.84 kWh Pd,max 3.84 kW wBAT 5 years ηBAT,inv 94% ηd 96% S OCmax 95% float 15 years Spinning reserve εload 0.1

IR lBank dtBank

3.8% 60% 10 years

cDG PDG,min bDG DG

500 USD/kW 0.3 · PDG,nominal 0.084 l/kWh 15 years

cPV,ins cPV,OM β0 TNOCT PV

0.45 USD/Wp 7.1 USD/year/kWp 3% 46.6◦ C 25 years

Pc,max cBAT,OM E ηc σ S OCmin

3.84 kW 7 USD/year/kWh 8832 kWh 96% 1%/month 20%

εPV

0.2

5.5 Case Study

101

Fig. 5.4 Estimated costs of: a diesel (cdiesel ); b solar panels and batteries (cPV and cBAT , respectively); and c solar inverters (cPV,inv )

The estimated diesel price for the subsequent years (cdiesel ) is presented in Fig. 5.4a. This graph was plotted by considering the reference case for future oil prices described in [38] and by setting the average diesel price in Indonesia equal to 0.645 USD/l in 2016 [39]. With respect to the PV panels and LiFePO4 batteries, their costs are expected to reduce in time. These are presented in Fig. 5.4b. To estimate the future cost of the solar panels (cPV ), the module price trend shown in [40] and a cost for multicrystalline panels equal to 0.354 USD/Wp in 2017 [41] are considered. Nevertheless, the cost trend presented in [40] was executed till the year 2027. As a result, a conservative case was adopted in this work by keeping a constant cost after this year. The expected cost for batteries (cBAT ) was estimated by digitizing a graph from [34]. Based on an internal investigation performed at SERIS, the estimated cost for the PV inverters (cPV,inv ) is presented in Fig. 5.4c, while the cost that needs to be paid to extend the inverter warranty (πPV ) is set to 25% (first warranty extension, after wPV years), 45% (second warranty extension, after 2 · wPV years), 60% (third warranty extension, after 3 · wPV years), and 60% (fourth warranty extension, after 4 · wPV years) of the inverter cost at that particular year. Furthermore, based on a cost comparison from inverters in the market, the cost of battery inverters (cBAT,inv ) is assumed to be 1.5 times the one of PV inverters. For simplicity, the warranty percentage cost of the battery inverters (πBAT ) is assumed to be the same as the one for PV inverters. With respect to the optimization algorithms, the parameters for the NSGA-III algorithm (to solve problem (P1)) were designed with a population number and a total number of iterations equal to 500 for both. For the GA algorithm (to solve (P2)), the population number and number of iterations were set to and 50 and 30, respectively. Furthermore, for both algorithms, the mutation rate was set to 0.02. These values were selected based on an empirical analysis.

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5.6 Results and Discussion This section is split into two parts. The first part corresponds to the results and analysis obtained from the optimization problem (P1), while the second part deals with the optimization problem (P2).

5.6.1 Results from (P1) The obtained pareto front after solving (P1) is presented in Fig. 5.5. Two points are highlighted based on the different configurations: the lowest initial investment (green triangle); and the lowest life-cycle cost (blue triangle). The configuration with zero initial investment refers to the case when no solar panels or batteries are added at all to the current DG-only off-grid system. It reflects the life-cycle cost in case the off-grid system will continue to run purely on DGs which was calculated at 10.53 mil. USD. This includes the diesel consumption and replacement costs during a 25 years lifetime. By adding different numbers and combinations of solar panels and batteries, the life-cycle cost could be reduced to a minimum of 7.06 mil. USD, thanks to diesel consumption savings. Albeit this only can be achieved with an initial investment of 3.47 mil. USD. The figure visualizes that without any restriction in capital, the faster the optimum hybridization is funded, the lower is the life-cycle cost of the entire off-grid system. However, as mentioned previously, this requires a large upfront investment which might not be available and is a barrier for a wider adoption of renewable energies. Therefore, the next section tries to provide an alternative

Fig. 5.5 Pareto front solution from the traditional problem formulation

5.6 Results and Discussion

103

approach to successfully develop these renewable systems, while at the same time showing that larger initial investment does not necessarily yield lower life-cycle cost.

5.6.2 Results from (P2) 5.6.2.1

Cost Analysis

In order to lower the initial investment burden, a new approach was proposed in (P2) that considers a limited initial investment, bank loans and searches for an optimum diesel replacement strategy. Figure 5.6 shows the life-cycle cost of the off-grid system obtained after solving (P2). The white area on the top of the figure can be described as the total savings with respect to the DG-only off-grid system (zero initial investment, highlighted with a black circle in this figure). For this graph, a wide range of initial investment scenarios were analyzed ranging from 0 to 3.5 mil. USD with a step increase of 0.01 mil. USD. If the off-grid system remains fully powered by DGs, the life-cycle cost is 10.53 mil. USD. However, as the initial investment increases, the diesel cost share is reduced and the cost associated to the PV and batteries becomes more dominant. It can also be observed that with increasing initial investment up to ≈0.15 mil. USD, the overall cost is significantly reduced, showing that even with a small initial investment, costs can be considerably reduced. The design that achieved the lowest life-cycle cost (6.62 mil. USD) is highlighted with a red circle, for which an initial investment of 0.25 mil. USD was required. This design is referred as plow,cost . Under the possibility to gradually add PV and batteries over time, a higher initial

Fig. 5.6 Life-cycle cost breakdown based on the different amounts of initial investment. The black circle highlights the result of the DG-only case while the red circle denotes the design which achieves the lowest life-cycle cost

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Fig. 5.7 Sizing strategy for the lowest life-cycle cost design, plow,cost , which was achieved with an initial investment of 0.25 mil. USD

investment does not necessarily lead to a lower life-cycle cost (contrary to the message inferred from Fig. 5.5). This observation is mainly because: (1) by considering bank loans to finance part of the initial capital expenditure, a high initial investment translates to higher amortization/interest costs, elevating the life-cycle cost; (2) high initial investment is fully weighted in a discounted cash flow model, while funding with accumulated savings on a later stage benefits from the higher discount factor; and (3) by postponing additional investments on solar panels and batteries, the investor can benefit from expected lower prices in the future, as seen from Fig. 5.4b, c. The sizing strategy for plow,cost is shown in Fig. 5.7. The figure presents the number of solar panels and batteries that are installed every year as well as the yearly initial balance (Balini(y) , as explained in Sect. 5.3.2). Here, it can be appreciated that the initial investment (0.25 mil. USD) is used in the first year to buy a total of 879 solar panels (286 kWp ). With the diesel savings, more solar panels are then bought in the subsequent years based on the available amount of Balini(y) . At the fourth year, batteries are also added into the system. From then onwards, both, solar panels and batteries are gradually added until the eighteenth year. In the following years, no further investments are carried out. The investment pattern can be split into three stages: (1) PV installation only [1–3 years]: during the first three years, only solar panels are added into the off-grid system. Due to a limited amount of available capital, the highest installation priority is given to the solar panels as they can directly reduce the diesel consumption during the daytime.

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Fig. 5.8 Total CO2e emissions during the system lifetime. The result for the DG-only case is highlighted with a black circle, while the design that produced the lowest life-cycle cost is highlighted with a red circle. The superscript employed in this figure denotes the contribution of a particular PV,inv element/process. As for example, CO2e denotes the total CO2e emissions with respect to the PV inverters

(2) PV + Battery installation [4–18 years]: Once a certain amount of solar panels have been installed, batteries can then be added as well to store any amount of extra energy produced by the PV. As the number of installed solar panels increases, so does the batteries in order to continue storing any extra energy generated. (3) No installation [19–25 years]: A point is reached in which it is not cost effective anymore to install more solar panels/batteries, i.e. there is not enough time to pay back the invested money within the remaining system lifetime.4 At this point, the balance keeps on increasing due to the diesel savings Sdiesel .

5.6.2.2

Emission Analysis

Figure 5.8 shows the CO2 equivalent life-cycle emissions, CO2e [mil. kgCO2 ], from all the generation sources.A general trend can be seen: the higher the initial investment, the lower the total CO2e emissions. This is an expected result because, with a higher initial investment, more solar panels and batteries can be installed since the beginning. Consequently, the total diesel consumption is significantly reduced (see Fig. 5.6). Nevertheless, as the initial investment increases, so do the CO2e emissions shares associated to the solar panels and batteries, e.g. for an initial investment of 4 As

explained in Sect. 5.3.2, the optimization algorithm does not aim to reduce the accumulated cost for the next S years but only for the remaining years within the system lifetime.

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Fig. 5.9 Percentage of diesel consumption of the hybrid system for the plow,cost design (initial investment of 0.25 mil. USD) with respect to the DG-only system

3.5 mil. USD, these distributed sources, together, generate more CO2e emissions than the ones associated to diesel. Nonetheless, the total number of installed solar panels and batteries does not significantly change with respect to the variation of the initial investment amounts, e.g. the accumulated number of installed solar panels and batteries are 8446 (≈2.7 MWp ) and 1585 (≈6.1 MWh), respectively, for an initial investment of 0.25 mil. USD; and 8277 (≈2.7 MWp ) and 1581 (≈6.1 MWh), respectively, for an initial investment of 3.5 mil. USD. This can be appreciated in Fig. 5.8, where the heights of the areas related to the solar panels and batteries do not considerably change for most of the initial investment values. It is also noteworthy that, with respect to the CO2e emissions, an exponential reduction region is observed when initial investments are low, followed by a lineal reduction region and ending with a plateau region when initial investments are high. As such, even with a low initial investment, the CO2e emissions can already be considerably reduced. To show the dependence on the diesel generators, Fig. 5.9 presents the percentage of diesel consumption for the hybrid system for the plow,cost design, i.e. initial investment of 0.25 mil. USD, with respect to the consumption for the DG-only system. It can be seen that the percentage of diesel consumption is reduced in time during the first years, as numerous solar panels and batteries are installed at this period (see Fig. 5.7), reaching a minimum of 2.8% for the year 12. For the subsequent years, this percentage rises because no more solar panels and batteries are added (as it was not cost effective, as explained in Sect. 5.6.2.1) while the yearly load demand keeps increasing. The diesel consumption for the final year is 14.6%, showing by this the shift towards a hybrid system which highly relies on the power production from the solar panels.

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Fig. 5.10 Sensitivity analysis showing the life-cycle cost with respect to variations of the cost of solar panels, batteries, and diesel for an initial investment of 0.25 mil. USD

5.6.2.3

Sensitivity Analysis

Because the sizing design of these electrical systems takes place considering the conditions for the future years (25 years in this study), there is an associated risk based on how accurate the predictions are for the future cost of solar panels, batteries, and diesel price, among other variables. One advantage of the presented method is that, as the installations occur progressively, this approach can be applied at the end of each year by updating the forecast estimations of the different parameters and hence giving the opportunity to adjust the system design based on these changes (different to traditional approaches which try to install the whole system only during the first year). Furthermore, to show the impact that changes on the cost of solar panels, batteries, and diesel have on the overall costs, a sensitivity analysis was performed by changing their values from 80 to 120% of the original values, when the initial investment is 0.25 mil. USD. These results are presented in Fig. 5.10. Here, an expected trend is observed in which, as the cost of any of these parameters increases, the overall life-cycle cost also increases. In addition, it can be appreciated that the diesel price has the highest influence followed by the batteries and the solar panels producing life-cycle cost variations within the range of ±10, ±5, and ±3%, respectively, when the aforementioned parameters experience variations within a range of ±20%.

5.7 Summary In this work, a diesel replacement strategy is proposed by progressively adding solar panels and batteries in the off-grid systems originally composed of diesel generators (DG-only systems). The strategy defines an optimal process to add these distributed sources over time to take advantage of their expected price reduction in the future.

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A limited initial investment, financed partially by a bank loan, is taken into account to install solar panels and batteries at the beginning. For the subsequent years, further installations of solar panels and batteries are funded by the accumulated diesel savings. An Indonesian island is used for the case study, assuming an off-grid system lifetime of 25 years. When no solar panels or batteries are added (DG-only system), a life-cycle cost of 10.53 mil. USD is obtained. The results generated from this work show that the highest initial investment does not necessarily yield the lowest life-cycle cost. On the contrary, only a relatively low investment, i.e. 0.25 mil. USD, is required to achieve the lowest life-cycle cost, i.e. 6.62 mil. USD (the initial investment is only 3.8% of this value). In this scenario, only solar panels are installed during the first few years with batteries added in future years when they are considered cost-effective. No additions are done in the final years approaching the end of the off-grid system lifetime due to the lack of economic viability. The obtained results also show that even if lower initial investments are available, the overall costs can still be drastically reduced, as there is an exponential decay of the life-cycle costs with respect to the increase of initial investments until around 0.15 mil. USD. This trend is a positive outcome to promote the hybridization of DG-only systems.

References 1. Rodríguez-Gallegos CD, Yang D, Gandhi O, Bieri M, Reindl T, Panda SK (2018) A multiobjective and robust optimization approach for sizing andplacement of PV and batteries in offgrid systems fully operated by dieselgenerators: an Indonesian case study. Energy 160:410–429 2. Roberts JJ, Cassula AM, Silveira JL, da Bortoni EC, Mendiburu AZ (2018) Robust multiobjective optimization of a renewable based hybrid power system. Appl Energy 223:52–68 3. Ogunjuyigbe ASO, Ayodele TR, Akinola OA (2016) Optimal allocation and sizing of PV/wind/split-diesel/battery hybrid energy system for minimizing life cycle cost, carbon emission and dump energy of remote residential building. Appl Energy 171:153–171 4. Zhao B, Zhang X, Li P, Wang K, Xue M, Wang C (2014) Optimal sizing, operating strategy and operational experience of a stand-alone microgrid on Dongfushan island. Appl Energy 113:1656–1666 5. Soshinskaya M, Crijns-Graus WHJ, van der Meer J, Guerrero JM (2014) Application of a microgrid with renewables for a water treatment plant. Appl Energy 134:20–34 6. Halabi LM, Mekhilef S, Olatomiwa L, Hazelton J (2017) Performance analysis of hybrid PV/diesel/battery system using HOMER: a case study Sabah, Malaysia. Energy Convers Manag 144:322–339 7. Yilmaz S, Dincer F (2017) Optimal design of hybrid PV-diesel-battery systems for isolated lands: a case study for Kilis, Turkey. Renew Sustain Energy Rev 77:344–352 8. Kaabeche A, Ibtiouen R (2014) Techno-economic optimization of hybrid photovoltaic/wind/diesel/battery generation in a stand-alone power system. Sol Energy 103:171–182 9. Yahiaoui A, Benmansour K, Tadjine M (2016) Control, analysis and optimization of hybrid PV-diesel-battery systems for isolated rural city in Algeria. Sol Energy 137:1–10 10. Maleki A, Askarzadeh A (2014) Optimal sizing of a PV/wind/diesel system with battery storage for electrification to an off-grid remote region: a case study of Rafsanjan, Iran. Sustain Energy Technol Assess 7:147–153

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11. Rodríguez-Gallegos CD, Gandhi O, Yang D, Alvarez-Alvarado MS, Zhang W, Reindl T, Panda SK (2018) A siting and sizing optimization approach for PV-battery-diesel hybrid systems. IEEE Trans Ind Appl 54(3):2637–2645 12. Houghton JT (1996) Climate change 1995: the science of climate change: contribution of working group I to the second assessment report of the intergovernmental panel on climate change, 2nd edn. Cambridge University Press, Cambridge 13. Rodríguez-Gallegos CD, Rahbar K, Bieri M, Gandhi O, Reindl T, Panda SK (2016) Optimal PV and storage sizing for PV-battery-diesel hybrid systems. In: IECON 2016-42nd annual conference of the IEEE industrial electronics society. IEEE, pp 3080–3086 14. Olsina F, Larisson C (2010) Optimization of spinning reserve in stand-alone wind-diesel power systems. In: Wind power, chapter 19, 1st edn. INTECH, Croatia, pp 437–464 15. Nacfaire H (1989) Wind-diesel and wind autonomous energy systems, 1st edn. Elsevier Applied Science, New York 16. Rodríguez-Gallegos CD, Gandhi O, Reindl T, Panda SK (2017) PHSO: a graphic user interface optimizer for the sizing design of the PV hybrid systems. In: 33rd European photovoltaic solar energy conference and exhibition (EUPVSEC), pp 2375–2379 17. Skoplaki E, Palyvos JA (2009) On the temperature dependence of photovoltaic module electrical performance: a review of efficiency/power correlations. Sol Energy 83(5):614–624 18. Yang D, Liu L, Rodríguez-Gallegos CD, Idris LH, Ye Z (2017) Statistical modeling, parameter estimation and measurement planning for PV degradation. In: Carter JG (ed) Solar energy and solar panels: systems, performance and recent developments, chapter 3, 1 edn. Nova Science Publishers, Inc, New York, pp 123–150 19. Gandhi O, Rodríguez-Gallegos CD, Gorla NB, Bieri M, Reindl T, Srinivasan D (2018) Reactive power cost from PV inverters considering inverter lifetime assessment. IEEE Trans Sustain Energy 10(2):738–747 20. Yang H, Zhou W, Lin L, Fang Z (2008) Optimal sizing method for stand-alone hybrid solar-wind system with LPSP technology by using genetic algorithm. Sol Energy 82(4):354–367 21. Lambert T, Gilman P, Lilienthal P (2006) Micropower system modeling with homer. Integr Altern Sources Energy 1(15):379–418 22. Rodríguez-Gallegos CD, Alvarez-Alvarado MS, Gandhi O, Yang D, Zhang W, Reindl T, Panda SK (2016) Placement and sizing optimization for PV-battery-diesel hybrid systems. In: The 4th IEEE international conference on sustainable energy technologies (ICSET). IEEE, Hanoi, Vietnam, pp 83–89 23. Yang Y, Li H, Aichhorn A, Zheng J, Greenleaf M (2014) Sizing strategy of distributed battery storage system with high penetration of photovoltaic for voltage regulation and peak load shaving. IEEE Trans Smart Grid 5(2):982–991 24. Gandhi O, Zhang W, Rodríguez-Gallegos CD, Bieri M, Reindl T, Srinivasan D (2018) Analytical approach to reactive power dispatch and energy arbitrage in distribution systems with DERs. IEEE Trans Power Syst 33(6):6522–6533 25. Gandhi O, Rodríguez-Gallegos CD, Zhang W, Srinivasan D, Reindl T (2018) Economic and technical analysis of reactive power provision from distributed energy resources in microgrids. Appl Energy 210:827–841 26. Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using referencepoint-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601 27. Kantardzic M (2011) Genetic algorithms. In: Data mining: concepts, models, methods, and algorithms, chapter 13, 2nd edn. Wiley, New Jersey, pp 385–413 28. Bieri M, Winter K, Tay S, Chua A, Reindl T (2017) An irradiance-neutral view on the competitiveness of life-cycle cost of PV rooftop systems across cities. Energy Procedia 1–8 29. Tsuanyo D, Azoumah Y, Aussel D, Neveu P (2015) Modeling and optimization of batteryless hybrid PV (photovoltaic)/diesel systems for off-grid applications. Energy 86:152–163 30. Agarwal N, Kumar A et al (2013) Optimization of grid independent hybrid PV-diesel-battery system for power generation in remote villages of Uttar pradesh, India. Energy Sustain Dev 17(3):210–219

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31. REC (2017) High performance solar panels: REC peak energy 72 series 32. SMA (2017) Solar inverters - battery inverters 33. Bieri M (2018) Solar economics handbook. Technical report, Solar Energy Research Institute of Singapore (SERIS) 34. Bronski P, Creyts J, Guccione L, Madrazo M, Mandel J, Rader B, Seif D, Lilienthal P, Glassmire J, Abromowitz J et al (2014) The economics of grid defection: when and where distributed solar generation plus storage competes with traditional utility service. Technical report, Rocky Mountain Institute 35. Victron-Energy (2017) 12,8 Volt Lithium-Iron-Phosphate batteries 36. Wang X, Adelmann P, Reindl T (2012) Use of LiFePO4 batteries in stand-alone solar system. Energy Procedia 25:135–140 37. Zakeri B, Syri S (2015) Electrical energy storage systems: a comparative life cycle cost analysis. Renew Sustain Energy Rev 42:569–596 38. U.S._Energy_Information_Administration (2017) Real petroleum crisis: crude oil: Brent spot 39. GlobalPetrolPrices.com (2017) Data services 40. Cellere G et al (2017) International technology roadmap for photovoltaic (ITRPV): 2016 results including maturity reports. Technical report, ITRPV-VDMA 41. PVinsights (2017) Solar PV module weekly spot price

Chapter 6

On the Dispatch Strategy Optimization for PV Hybrid Systems in Real Time

6.1 Introduction Dispatch strategy (also known as scheduling) refers to the operation and power control of the different energy sources in a system. In this study, the sources correspond to the PV system, battery system and diesel generators. It is therefore desired to control these sources to satisfy defined constraints, such as the fulfillment of the load demand, and to enhance their operation to achieve a reduction of the overall costs and CO2 emissions, for example. Different to sizing optimization problems whose aim is to set the ideal number of installed energy sources (such as the one described in Sect. 5), scheduling optimization problems assume that the required sources have been previously installed, and only focus on the optimization of their daily operation. With respect to PV-battery-diesel hybrid systems, the literature presents different works to optimize their dispatch strategy for one or a few days. However, the modeling of systems for scheduling algorithms are typically based on step sizes of 60 min or below, e.g. [1–7]. Therefore, factors such as grid quality [8, 9] cannot be properly assessed (will not be able to properly study the frequency and voltage deviations, as well as harmonic levels). Furthermore, while these optimization problems provide the desired state (ON/OFF) and power output from the different energy sources, if applied in real systems, these values would correspond to the set points of the real controllers (e.g. PV inverter, battery inverter, DG controller) which require some time to reach the defined set point. It is then necessary to also analyze if the set points provided by the optimization algorithm can properly be executed by the controllers in real time. Hence, any proposed dispatch strategy algorithm would be desired to be implemented in a real PV-hybrid system to confirm its validity. Nevertheless, due to the required investment to build a real system, another option would be to employ real time simulators. These simulators receive this name due the small time step by which the simulations are carried out. Therefore, the operation of a system can be assessed with a high level of accuracy.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7_6

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As PV hybrid systems have been installed in real life, real dispatch strategies have already been implemented. Two of these strategies, referred in this work as the diesel backup, and spinning reserve strategies, will be used as the benchmark to compare the performance of the proposed algorithm. The latter aims to apply forecasting approaches on the load and irradiance to consider their future profiles to better optimize the scheduling of the different energy sources. Therefore, in this work a dispatch strategy optimization algorithm is proposed for off-grid PV-battery-diesel hybrid systems. The results from the proposed and benchmark algorithms, obtained from a real time simulator, will then be presented and discussed.

6.2 Real Time Simulator The employed real time simulator corresponds to the Typhoon Hardware in Loop 604 (HIL604). This device can simulate systems with a time step in the range of 0.5–20 µs (time step of 2 µs was set in this work) and was designed to simulate, among others, microgrids (such as the one in this chapter). Figure 6.1a presents the discussed hardware as well as the Typhoon SCADA interface for a diesel generator. Figure 6.1b shows an example of a PV hybrid system in the Typhoon Schematic Editor. The “PV system” block contains the solar array as well as the PV inverter and filters. In a similar way, the “Battery system” block contains the battery bank model together with its converter and required filters while the “Diesel generator” block contains the model of diesel generators together with their voltage/frequency controller and synchronism blocks (to assure for diesel generators to be connected to the grid only if they are in synchronism with it). The “load” block contains the overall load demand of the system. Finally, the “scheduling algorithm” block corresponds to the main controller which sets the power and state of the energy sources of interest based on the applied algorithm (see Sect. 6.3).

Fig. 6.1 a Typhoon HIL604 hardware and SCADA; b PV hybrid system in the Typhoon Schematic Editor

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6.3 Algorithms As mentioned in Sect. 6.1, besides the proposed scheduling algorithm, two algorithms which are applied in real systems are also simulated and act as the benchmark. Although these algorithms follow different principles, they can control the same state and set points of the equipment of interest, which are: (1) state of the PV array (connected or disconnected), (2) state of the diesel generators (ON/OFF), and (3) set points of the desired power output of the diesel generators. Other signals which could be thought to be controlled but are not are: (1) power output from the PV array: PV systems are usually operated at their maximum power point, as is the case of this study; (2) battery system state: in this work, the battery system is the grid forming component (controls the grid voltage and frequency), therefore, it should not be disconnected; and (3) battery system power: as the PV array operates at its maximum power point, and the “scheduling algorithm” block sets the desired power output from the diesel generators, the power of the battery system will be one to assure that the power generated is equal to the power demanded. Therefore, by knowing the power from the PV system, load demand, and controlling the power from the diesel generators, the power from the battery system can be indirectly controlled to a certain extent. The discussed scheduling algorithms present three stages in their operation. These are shown in Fig. 6.2, and are ordered based on their priority: (1) battery safety; (2) ON/OFF state of diesel generators (define the ON/OFF state of diesel generators under normal operation, i.e. when the battery safety stage has not been activated); and (3) power set of diesel generators (controls the power of diesel generators under normal operation, i.e. when the battery safety stage has not been activated). The stage with the highest priority corresponds to the battery safety and aims to keep the battery state of charge (S OC) between a minimum S OCmin and maximum S OCmax defined. On the one hand, if at any given time the battery S OC is below S OCmin , the required generators will be turned ON to contribute to the load demand and charge the batteries (the power output from these generators will be limited based on the maximum charging power from the batteries). Once the battery S OC has increased to a level S OCbsmin , the DGs will return to their original ON/OFF state. On the other hand, if at any given time the battery S OC is above S OCmax , all diesel generators will be turned OFF and the PV array will be disconnected from the grid until the battery S OC has decreased to a level S OCbsmax . Afterwards, the DGs will return to their original ON/OFF state and the PV array will be connected back to the grid. The battery safety stage algorithm is the same for all the studied scheduling algorithms. Nevertheless, each algorithm implements different principles for the DG ON/OFF state stage and DG power stage. These stages will be described in the next subsections for the two benchmark algorithms and the proposed one.

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Fig. 6.2 Stages of the scheduling algorithms

6.3.1 Benchmark Algorithm 1: DG Backup Based This algorithm gives priority for the PV array and batteries to provide the required power to satisfy the load demand while the diesel generators are kept as a backup (they are not operating during normal operation). Only when the batteries have reached the minimum state of charge (S OCmin ), the backup diesel generators are turned ON and their power is set to contribute to the load demand and to charge the batteries as much as possible (considering their maximum allowed charging power). Once the batteries have been charged to a defined state of charge S OCbench , the diesel generators are turned OFF.

6.3.2 Benchmark Algorithm 2: Spinning Reserve Based With respect to the DG ON/OFF state stage (see Fig. 6.2), the state of the DGs is controlled based on the spinning reserve condition. This condition requires the system to have enough available power to be delivered in case there is a sudden change in the load or irradiance. The spinning reserve condition was previously defined in Sect. 5.2.4 with the following equation: S R ≥ Pload · εload + PPV · εPV

(6.1)

where S R [W] corresponds to the present spinning reserve while Pload [W] is the load power and PPV [W] is the power from the PV system (with coefficients εload and

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εPV , respectively). When the spinning reserve condition is not fulfilled, an adequate number of diesel generators are turned ON until the condition has been fulfilled. Subsequently, to analyze whether DGs can be turned OFF, it is required for them to be ON for at least a minimum time TON−OFF , as it is not recommended for DGs to be turned OFF shortly after they have been turned ON (and vice-versa). Once this time has passed, the DGs can be turned OFF as long as the spinning reserve condition is still fulfilled when a higher load coefficient (εload,2 instead of εload ) and PV coefficient (εPV,2 instead of εPV ) are applied in Eq. (6.1). These coefficients are increased at this stage in an effort to avoid the spinning reserve condition to be unfulfilled after a short time. With respect to the DG power stage (see Fig. 6.2), the power produced by the DGs which are ON is estimated by applying a similar approach as the one shown in Sect. E: (1) If the power produced from the PV system is higher than the load demand, it means that the PV system alone can satisfy the load demand. Therefore, the power output from DGs is set to their PDG,min (due to their constraint previously presented in Eq. (5.5)). (2) If the power produced from the PV system is lower than the load demand, batteries and/or diesel generators must also generate power based on the following criteria: (a) If the cost per kWh to discharge the batteries (see Sect. 5.2.3.2) is lower than the one from the diesel generators, the former, together with the PV system, are used to satisfy the load demand. If batteries cannot provide all the required power (due to their discharging power constraint, as shown in Eq. (5.22)), the DGs which are ON will then be employed as well. (b) If the cost per kWh to discharge the batteries is higher than the one from the diesel generators, the DGs which are ON, together with the PV system, are used to satisfy the load demand. If DGs cannot provide all the required power (as they are limited by their nominal power, as shown in Eq. (5.5)), batteries will then be employed as well. (3) If the power from a DG is below PDG,min , it will then be set to PDG,min .

6.3.3 Proposed Algorithm: Forecast Based The DG ON/OFF state stage (see Fig. 6.2) of the proposed forecast based algorithm is only applied after the DGs have maintained a fixed state for at least TON−OFF minutes (similar to the norm applied in Sect. 6.3.2). Once this time have passed, the load and irradiance forecast for the next TON−OFF minutes is obtained to estimate which ON/OFF combination of the DGs is able to produce the lowest cost during this forecasted time range (and is also able to satisfy the load demand). For each ON/OFF combination of the DGs, their power (as well as the battery power) is estimated

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following the DG power stage approach presented in Sect. 6.3.2. The ON/OFF combination of DGs which, been able to satisfy the load demand, produced the lowest cost, will then be applied. This approach will later be repeated after the DGs have kept a fixed state for at least TON−OFF minutes. The power of the DGs is set applying the same approach for the DG power stage presented in Sect. 6.3.2.

6.4 Case Study The case study considers load and irradiance profiles for a particular day of the yearly data previously shown in Fig. 5.3. These profiles are presented in Fig. 6.3 (peak load set to 800 kW) together with the forecasting estimations obtained by applying the TBATS model [10] which generated a normalized root mean square error of 6.6% for the load estimation and 31.6% for the irradiance estimation. The analyzed PV hybrid system is composed of a PV system with an installed capacity of 200 kWp , a battery system with a capacity of 1.5 MWh with maximum charging/discharging power of 250 kW and discharging cost per kWh of 0.2 USD/kWh (see Sect. 5.2.3.2). Furthermore, the maximum (S OCmax ) and minimum (S OCmin ) states of charge of the batteries are set to 95 and 20%, respectively, with the parameters S OCbsmin , S OCbsmax , and S OCbench set to 40, 75, and 90%, respectively. Two diesel generators of 500 kW each are considered in this work. These generators have diesel coefficients of aDG = 0.246 l/kWh and bDG = 0.084 l/kWh (see Eq. (5.2)), with a diesel price set to 1 USD/l. The minimum ON/OFF time of

Fig. 6.3 Real and forecasted profiles for a load and b irradiance

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the diesel generators (TON−OFF ) is set to 60 min. With respect to the spinning reserve condition, the εload and εPV coefficients are set to 0.20 and 0.25, respectively, while the εload,2 and εPV,2 coefficients are set to 0.30 and 0.35, respectively. In addition, the grid voltage and frequency are set to 230 V and 50 Hz, respectively. The grid quality is evaluated based on the allowed ranges, i.e. frequency range between 49.5–50.5 Hz [11], voltage range between 0.95–1.05 p.u. [12], and total harmonic distortion (THD) below 8% [13].

6.5 Results and Discussion This section presents the simulation results from the previous specified system, obtained from the real time simulator Typhoon HIL604. Figure 6.4 shows the preliminary results from the benchmark and proposed algorithms. With respect to the DG backup approach, as expected, diesel generators only operate (DG state = 1) when batteries reach their minimum state of charge (20%) and stop their operation (DG state = 0) once the batteries have been charged till 90%. When DGs are not operating, the power from the solar panels and batteries is applied to satisfy the load demand. With respect to the other algorithms, when comparing the power profiles from the spinning reserve based (Fig. 6.4d) and forecast based (Fig. 6.4g) results, similar values are obtained. In addition, for both cases, the first diesel generator (DG1) is ON during the whole day while the second diesel generator (DG2) has the same operation state for both algorithms till 8:20 AM (see Fig. 6.4e, h). Till this time, it can be noticed that DG2 is turned on when batteries reached their minimum SOC and therefore, DG2 is turned ON to help charge battery till it reaches the defined

Fig. 6.4 Power profiles, DG ON/OF state, battery SOC and accumulated costs results obtained from the DG backup based approach; spinning reserve based approach, and forecast based approach

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S OCbsmin value (40%). For the case of the spinning reserve based approach, after 8:20 AM, DG2 remains operating till the end of the day while its operation for the forecast based approach is only regulated by the battery SOC safety mechanism (previously explained). DG2 remains ON for the SR based approach after 8:20 AM because, by that time, the load has increased to a value in which a single DG will not be able to satisfy the SR condition, therefore, a second DG needs to be turned ON. With the forecast based approach, however, based on the forecasted results, it was concluded that a single DG will be able to handle the power required by the load in the future hours. Figure 6.4c, f, i present the accumulated costs produced from the batteries, DGs (diesel consumption), and the total (battery cost + diesel cost) for the three analyzed approaches. For all the algorithms, batteries generated the lowest cost. In addition, the total cost at the end of the day was similar when using the benchmark algorithms (5967 USD for the DG backup based approach and 5989 USD for the SR based approach) while the minimum cost was achieved with the proposed one (5678 USD) generating 5% savings. Figure 6.5 presents a closer view to the overall costs. It can be noticed that, as the DG backup based approach employed only the batteries till 1:00 AM, while the other algorithms also use their DG (see Fig. 6.4b, e, h), the former produces a lower cost. However, after 1:00 AM, the battery SOC for the DG backup based approach has reached its minimum, therefore, the two DGs start to operate. Consequently, due to the high diesel consumption, the overall cost from this algorithm becomes the highest after a short time. It can also be noted that the total costs produced from the SR and forecast based approaches are similar till 8:20 AM as the power profiles and the operation states of their DGs is the same (as previously explained). However, after this time, the SR based approach turns ON the second DG and, although the power profiles keep been similar, the SR based approach starts to produce higher cost than the forecast based approach. This is a consequence of the diesel consumption required to keep a DG in ON state (see Eq. (5.2)). As for example, although the power required to be produced by the DGs is similar, during 11:00 AM, there is only one operating DG when using the forecast based approach (see Fig. 6.4h) while the two DGs are operating during this time for the SR based approach (see Fig. 6.4e). Therefore, the latter will consume extra diesel to keep the second DG in ON state. This shows the advantage from the forecast based approach to better decide on the ON/OFF state of DGs to reduce the diesel consumption and consequently the overall cost (Fig. 6.5). With respect to the grid quality, Fig. 6.6 presents the grid frequency, voltage and the total harmonic distortion, measured for all the approaches. The safety ranges defined in Sect. 6.4 have not been violated giving more confidence to apply the proposed algorithm in a real application.

6.6 Summary

119

Fig. 6.5 Total accumulated cost for the analyzed case study obtained from the benchmark and proposed algorithms

Fig. 6.6 Measured grid parameters, i.e. frequency, line-line voltage and their total harmonic distortion, from the benchmark and proposed algorithms

6.6 Summary In this work, a scheduling optimization algorithm was proposed. This algorithm considers the future load and irradiance conditions (employing forecasting methods) to set the optimal power outputs of the energy sources and to control their operation state, e.g. when to turn ON/OFF the diesel generators. As a benchmark, two

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6 On the Dispatch Strategy Optimization for PV Hybrid Systems in Real Time

algorithms which are typically used in real PV hybrid systems were considered: (1) the DG backup based algorithm which only employs the DGs when the battery has achieved a minimum state of charge; and (2) the spinning reserved based algorithm which evaluates whether there is enough spinning reserve to decide on the ON/OFF state of the DGs. In an effort to validate the results generated from this chapter, a real-time simulator (Typhoon Hardware in Loop 604—HIL604) was used to test the effectiveness of the applied optimization algorithms. For the analyzed case study, the results revealed that the proposed algorithm (forecasting based) is able to achieve a lower cost in comparison to the others (5%). This outcome was produced because the forecasting estimations were accurate enough to make good decisions on the scheduling. Therefore, it can be concluded that the application of forecasting approaches can be beneficial to optimize the performance of PV hybrid systems. Nevertheless, special care should be taken to the forecasting accuracy as high forecasting errors could reduce the system performance. In addition, the grid quality was evaluated for all the analyzed optimization algorithms. The results showed that the frequency, voltage, and total harmonic distortion were kept within the allowed limit. This outcome suggests that the proposed algorithm could be applied in a real system without seriously affecting the grid quality.

References 1. Jiang T, Yu L, Cao Y (2015) Energy management of internet data centers in smart grid, 1st edn. Springer, Heidelberg 2. Savi´c A, -Duriši´c Ž (2014) Optimal sizing and location of SVC devices for improvement of voltage profile in distribution network with dispersed photovoltaic and wind power plants. Appl Energy 134:114–124 3. Shang C, Srinivasan D, Reindl T (2016) Economic and environmental generation and voyage scheduling of all-electric ships. IEEE Trans Power Syst 31(5):4087–4096 4. Riffonneau Y, Bacha S, Barruel F, Ploix S et al (2011) Optimal power flow management for grid connected PV systems with batteries. IEEE Trans Sustain Energy 2(3):309–320 5. Gupta A, Saini RP, Sharma MP (2011) Modelling of hybrid energy system-part II: combined dispatch strategies and solution algorithm. Renew Energy 36(2):466–473 6. Kahrobaee S, Asgarpoor S, Kahrobaee M (2014) Optimum renewable generation capacities in a microgrid using generation adequacy study. In: Proceedings of 2014 IEEE/PES transmission and distribution conference and exposition. Chicago, USA. IEEE, pp 1–5 7. Rahbar K, Xu J, Zhang R (2015) Real-time energy storage management for renewable integration in microgrid: an off-line optimization approach. IEEE Trans Smart Grid 6(1):124–134 8. Gandhi O, Kumar DS, Rodríguez-Gallegos CD, Srinivasan D (2020) Review of power system impacts at high PV penetration part I: factors limiting PV penetration. Sol Energy 210:181–201 9. Kumar DS, Gandhi O, Rodríguez-Gallegos CD, Srinivasan D (2020) Review of power system impacts at high PV penetration part II: potential solutions and the way forward. Sol Energy 10. De Livera AM, Hyndman RJ, Snyder RD (2011) Forecasting time series with complex seasonal patterns using exponential smoothing. J Am Stat Assoc 106(496):1513–1527 11. Markiewicz H, Klajn A (2004) Voltage disturbances standard EN 50160-voltage characteristics in public distribution systems. Wroclaw Univ Technol 21:215–224

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12. Masri et al K (2016) American national standard for electric power systems and equipmentvoltage ratings (60 Hz). Technical report ANSI C84.1-2016, National Electrical Manufacturers Association, Virginia, USA 13. Halpin et al M (2014) IEEE recommended practice and requirements for harmonic control in electric power systems. Technical report IEEE Std 519-2014, New York, USA

Chapter 7

Conclusions and Proposed Future Works

7.1 Conclusions This work discusses some of the current limitations in the PV field and proposes strategies to address them by applying optimization approaches. Different studies were performed to enhance the performance at the cell, module, and system levels. These were detailed in the Chaps. 3–6 of this work. In Chap. 3, the grid metallization design (number and dimension of fingers, busbars, and interconnector ribbons) of crystalline Si-based solar cell (full size and halfcut cells) and modules (for monofacial Aluminium Back Surface Field (Al-BSF) and bifacial Passivated Emitter Rear Totally-diffused (PERT) technologies) were optimized by applying a multi-objective and robust optimization approach focused on the enhancement of electrical performance under standard test conditions (STC) and reduction of fabrication cost. Based on the optimal metallization designs, it can be concluded that the higher the number of fingers, busbars and interconnector ribbons, and the lower their width, the better will be the efficiency and fabrication cost results. The reason is that, by raising their number, the metallization fraction increases so that the overall series resistance goes down. Consequently, the fill factor is enhanced. Their width then needs to be reduced to assure a high photovoltaic current density and low dark saturation current densities. At the cell level, there was no considerable difference in electrical performance between full-cells and half-cells (maximum efficiency of 19.85 and 19.08% were obtained for monofacial and bifacial cells, respectively). Nevertheless, at the module level, because of their lower resistive losses, half-cell modules reached higher efficiency values (maximum efficiency of 19.67 vs 19.27% for monofacial modules and 18.74 vs 18.40% for bifacial modules), and lower fabrication cost (minimum fabrication cost of 0.433 USD/Wp vs 0.442 USD/Wp for monofacial modules and 0.418 USD/Wp vs 0.425 USD/Wp for bifacial modules).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7_7

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7 Conclusions and Proposed Future Works

When optimizing monofacial and bifacial cells/modules, the latter showed lower efficiency values (mainly because of the low efficiency at their rear side and higher resistive losses). Nonetheless, bifacial modules have the potential to generate higher output power as they can also absorb light from the rear side (for full-cell modules, a maximum power of 285 Wp and 327 Wp were obtained for the monofacial and bifacial technologies, respectively, when the albedo value was set to 0.2). In addition, when comparing the optimization designs between monofacial and bifacial technologies, it can be concluded that, in general, the number and width of the fingers at the rear side have a higher value than the ones at the front side. The previous outcome can be attributed to the fact that the front side of a bifacial cell/module is more efficient than its rear side, and as such the front side should receive higher irradiance. Therefore, it is desired to reduce the metallization fraction at the front side to enhance light collection. Consequently, the metallization fraction at the rear side should increase to reduce the resistive losses. The metallization design was also performed under real world conditions considering six locations worldwide. The results revealed the dependence of the metallization design based on the particular environmental conditions. Hence, if the module manufacturer is aware of the locations the modules will be installed, the module fabrication can be optimized for particular clients. In Chap. 4, the module orientation for grid-connected systems was optimized for installations in which (1) any module orientation is allowed (AMO); or (2) only vertical module orientations (VMO) are allowed. Monofacial Al-BSF and bifacial PERT modules were examined in this study. Their cost-effectiveness, based on the levelized cost of electricity (LCOE), was also compared considering weather profiles from 55 locations worldwide. The results reveal that for latitudes above 40◦ , bifacial AMO designs are in general more cost-effective than monofacial AMO systems as for locations with higher latitudes, the overall rear irradiance increases. This tendency is reversed, however, for latitudes below 40◦ with low albedo values. Nevertheless, if the albedo value is kept to a minimum between 0.12 to 0.30 (depending on the location), bifacial AMO designs can also be more cost-effective. When comparing monofacial AMO against bifacial VMO, the latter is more costeffective only for locations close to the poles, i.e. latitudes higher than 65◦ . Nonetheless, bifacial VMO designs could even reach a lower LC O E than monofacial AMO systems at latitudes below 65◦ , if the albedo value is maintained between 0.29 to 0.57 (depending on the location). The albedo value is particular influential for bifacial modules as it can considerably enhance the light collected at the module rear side. The LC O E values obtained from the optimal module orientation have also been compared with those obtained from the orientation defined in the conventional approach (module facing the equator with tilt angle equal to its latitude). The reduction in LC O E achieves values below 5% for the bifacial PV systems for any location and for monofacial PV systems when located at latitudes below 60◦ . Above 60◦ , the improvement in LCOE for monofacial PV systems can reach up to 15%. Hence, bifacial installations are not as sensitive to the module orientation as their monofacial counterparts.

7.1 Conclusions

125

In Chap. 5, a diesel replacement strategy was proposed by progressively adding solar panels and batteries in off-grid systems originally composed of diesel generators (DG-only system) to form PV hybrid systems. The aim of the proposed approach was to reduce the required initial investment (which tends to be high for PV systems) and yet to achieve considerable savings by installing solar panels at these off-grid systems. This in addition to considerable CO2 emission reductions. The strategy defined an optimal process to add these distributed sources over time to take advantage of their expected price reduction in the future. A limited initial investment, financed partially by a bank loan, is considered to install solar panels and batteries at the beginning. For the subsequent years, further installations of solar panels and batteries are funded by the accumulated diesel savings. In this work, an Indonesian island was used for the case study, assuming an off-grid system lifetime of 25 years. When no solar panels or batteries were added (DG-only system), a life-cycle cost of 10.53 mil. USD was obtained. The results generated from this work show that the highest initial investment does not necessarily yield the lowest life-cycle cost. On the contrary, only a relatively low investment, i.e. 0.25 mil. USD, is required to achieve the lowest life-cycle cost, i.e. 6.62 mil. USD (the initial investment is only 3.8% of this value). In this scenario, only solar panels are installed during the first years with batteries added in future years when they are considered cost-effective. Based on the performed study, it can be concluded that even if a low initial investment is available to hybridize a DG-only system, the overall cost can still be drastically reduced. While Chap. 5 aimed to optimize the sizing strategy for PV hybrid systems, Chap. 6 focused on the dispatch strategy optimization of these systems once installed. In an effort to validate the results generated from this chapter, a real-time simulator (Typhoon Hardware in Loop 604—HIL604) was used to test the effectiveness of the applied optimization algorithms. In this work, a scheduling optimization algorithm was proposed, which considers the future load and irradiance conditions (employing forecasting methods) to set the optimal power outputs of the energy sources and to control their operation state, e.g. when to turn ON/OFF the diesel generators. As a benchmark, two algorithms which are typically used in real PV hybrid systems were considered: (1) the DG backup based algorithm which only employs the DGs when the battery has achieved a minimum state of charge; and (2) the spinning reserve based algorithm which evaluates whether there is enough spinning reserve to decide the ON/OFF state of the DGs. For the analyzed case study, the results revealed that the proposed algorithm (forecasting based) is able to achieve a lower cost in comparison to the others (−5%). The previous outcome was because the forecasting estimations were accurate enough to make economical decisions on the scheduling. Therefore, it can be concluded that applying forecasting approaches can be beneficial to optimize the performance of PV hybrid systems. Nevertheless, special care should be taken to the forecasting accuracy as high forecasting errors could reduce the system performance.

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7 Conclusions and Proposed Future Works

In addition, the grid quality was evaluated for all the analyzed optimization algorithms. The results show that the frequency, voltage, and total harmonic distortion were kept within the permisible limits. This outcome suggests that the proposed algorithm could be applied in a real system without affecting the grid quality.

7.2 Proposed Future Work Even though the work from this thesis addressed a number of different technical gaps at the cell, module and system level, future work is proposed here, based on the findings and limitations from this investigation. The proposed future works are listed below: (1) In Chap. 3, the metallization design for the fabrication of cells and modules was optimized. However, this design corresponds to one step out of many required to fabricate solar cells and modules. Although it is normal to optimize the fabrication steps independently, there is dependence between these. Therefore, it would be desired to develop an overall optimization platform to control in parallel all the recipes related to the fabrication steps. If this platform is properly developed, the cell/module performance is expected to be enhanced. However, extra challenges will be present when developing the overall model due to the particular complexities of each process step. (2) While the work done in Chap. 4 improves the understanding on the conditions for bifacial PV installations to be more cost effective than the monofacial ones, the analyzed systems where fixed-tilt systems, i.e. module orientation is fixed. Due to the continuous decrease on the PV system cost, bifacial tracking installations are becoming a hot topic and therefore, the analysis on the cost-effectiveness of these systems would be of interest. To properly analyze bifacial tracking systems, extra knowledge on the tracking algorithms and structures would be required. (3) Chapter 5 provided a diesel replacement strategy to hybridize off-grid systems originally composed of diesel generators by progressively adding solar panels and batteries. Nevertheless, based on the location for a particular case study, the addition of other renewable sources could be desired. Therefore, a future work would be to provide an approach to optimize the system hybridization considering other renewable sources (e.g. wind power) as well. (4) Although the proposed dispatch strategy presented in Chap. 6 proved to be superior than the benchmark for the analyzed case study, these results were obtained from a real time simulator. Even though by working on a real time simulator, the validity of the obtained results increases because factors such as the grid quality can also be analyzed, final validation should be performed in a real system. Hence, the next stage for this work would be to implement the developed optimization algorithm in a real PV-hybrid system and analyze its performance.

Appendix A

Influence of Grid Metallization Design in Cell/Module

A.1

Photovoltaic Current Density Estimation

 mA  For a solar cell, the value of jph cm can be assumed to have a linear relation with 2 respect to the amount of light it absorbs. In this investigation, three main components for the estimation of jph are considered, namely: the contribution due to direct light incident on front side of the solar cell (light reflected from the backsheet,  mA  mA  if , due to the backsheet influence j any, is not included) jph_di_f cm ph_bs cm2 (for 2  mA  glass/backsheet modules) and due to the albedo component jph_ab cm (for the 2 bifacial technology), so that: jph = jph_di_f + jph_bs · αmo · βmod + jph_ab · αbi

A.1.1

(A.1)

Direct Impact Contribution

The higher the shading percentage of the front grid metallization, Λcell_f [%], the lower will be its jph_di_f value. Therefore, the value of jph_di_f for a particular solar cell with front shading percentage Λcell_f can be estimated from a reference solar cell with known photovoltaic current density of jph_ref_f and front shading percentage of Λref_f , as shown in Eq. A.2. All the properties from the reference and evaluated solar cell, except for the ones related to the grid metallization design, are assumed to be the same, e.g. doping level, cell dimensions, among others. jph_di_f =

100% − Λcell_f · jph_ref_f 100% − Λref_f

(A.2)

To estimate the value of Λcell_f for a particular solar cell, the effective width of its fingers, E Wfi_f [%], busbars, E WBB_f [%], (or interconnectors ribbons, E Wir [%], when the solar cell is a within a solar module) should be considered. The effective © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7

127

128

Appendix A: Influence of Grid Metallization Design in Cell/Module

Fig. A.1 Illustration of the influence that the grid geometry has regarding light absorption

width, E W [%], is defined as the percentage of light that is being blocked by the metallization grid and is dependent on its geometry [1, 2]. Figure A.1 (left image) shows a finger shape from which light can be reflected outside or towards the cell, so that 0% < E Wfi_f < 100%. The influence that the glass-air layer has on the E Wfi_f at the module level is also presented in Fig. A.1 (right image). Here, it can be noticed that even if light is reflected back from the solar cell (after impacting the finger) it can still be partially or fully internally reflected based on the angle of incidence of light at the glass-air interface. The influence of the EVA-glass layer is neglected as they have a similar refractive index [3–6]. A full description regarding the approaches to estimate the E W from real experiments and simulations are provided in [2, 7]. The shading percentage Λcell_f for a single solar cell and for a solar cell within a module can then be defined as follows:  n ·w ·E W ·w +n ·w ·E W · l −n ·w ·E W /100% ) , cell fi_f fi_f fi_f cell BB BB_f BB_f ( cell fi_f fi_f fi_f Λcell_f = n fi_f ·wfi_f ·E Wfi_f ·wcell +n BB ·wir ·E WAircell ·(lcell −n fi_f ·wfi_f ·E Wfi_f /100%) , cell in module Acell

A.1.2

(A.3)

Backsheet Influence

In the case of monofacial solar cells within a module, a backsheet layer is assumed to be placed behind the cells. As a result, light incident on the backsheet at the cell spacing can be internally reflected towards the solar cell at the glass-air interface (light absorption at the glass and EVA layers are considered to be minimum, hence, are neglected [8]), as shown in Fig. A.2. To estimate the jph_bs value, the following procedure takes place: 1 Split the cell spacing into n cs subdivisions, as shown in Fig. A.2. 2 Initialize the analysis (i = 1). 3 For the ith subdivision:

Appendix A: Influence of Grid Metallization Design in Cell/Module

129

Fig. A.2 Internal reflection of light due to the backsheet influence

(a) Assume light impacts the center point of the current subdivision. (b) Light is reflected following the lambertian reflectance distribution (similar to [9–12], the backsheet is considered to be a lambertian surface. Its weighted average reflectance is defined as Rbs ). (c) Split the reflected light into a fixed angle θrl , as shown in Fig. A.2. (d) For each segment of the reflected light, the employment of the Snell’s law, the law of reflection and the Fresnel equations take place to determine the percentage of light that is internally reflected at the glass-air interface. (e) Evaluate if the internally reflected light from the previous step reaches the solar cell (absorption is assumed) or impacts a subdivision of the cell spacing (light reflection is assumed). For the latter, if the number of times that light has bounced from the backsheet has not reached the maximum defined, n lb_max , steps 3a till 3d are then repeated, taking into account the current internally reflected light and the subdivision it impacted. If the value of n lb_max has been reached, the analyzed light portion is neglected as it is expected to have a very low irradiance value [13]. 4 If i < n cs , move to the next subdivision (i = i + 1) and repeat step 3. 5 Once the whole subdivisions have been analyzed (i = n cs ), the value of jph_bs can be estimated based on the total absorbed light at the solar cell (obtained from step 3e).

A.1.3

Albedo Influence

In this work, the albedo influence is considered as the proportion of light that, after impacting the surroundings, is reflected towards the rear side of the cell/module [13, 14]. Under STC, this will only be assumed to influence the bifacial technology in an effort to consider the bifacial module properties to absorb light from the module rear side (glass/glass modules are assumed for this technology [13]). To calculate the  mA albedo contribution, jph_ab cm 2 , it is necessary to obtain the photovoltaic current  mA  density at the rear side of the cell, jph_di_r cm 2 , which can be estimated similar to Eq. A.2:

130

Appendix A: Influence of Grid Metallization Design in Cell/Module

jph_di_r =

100% − Λcell_r · jph_ref_r 100% − Λref_r

(A.4)

Equation A.3 can then be used to calculate Λcell_r by considering rear fingers, busbars and interconnectors instead of their front counterparts. The albedo contribution can now be obtained: (A.5) jph_ab = ab · jph_di_r where ab is the albedo factor. The higher it is, the more light is reflected from surfaces towards the rear side of the bifacial cell.

A.2

Dark Saturation Current Densities Estimation

 mA  The dark saturation current density from diode 1, jo1 cm 2 , represents the electronhole recombination produced at the emitter, bulk and rear regions of the solar cell. Thus, it can be defined by Eq. A.6 in which the metallization influence is taken into account (similar to [15]): jo1 = (1 − FM_f ) · jo1_n+ + FM_f · jo1_n+ _met + jo1_b + jo1_r

(A.6)

where FM_f is the metallization fraction at the front side of the solar cell due to mA is the front fingers and front busbars (contacting busbars are assumed). jo1_n+ cm 2  mA  the jo1 contribution from the emitter, jo1_n+ _met cm2 is the jo1 contribution at the  mA  emitter-metal interface, jo1_b cm is the jo1 contribution from the base (due to its 2  mA  low value, the jo1_b term will be neglected in this paper) and jo1_r cm is the jo1 2  mA  contribution from the rear side. To calculate jo1_r cm2 , it is necessary to specify whether the analyzed solar cell is monofacial (which has an Al-BSF layer at the rear side) or bifacial (which has fingers and busbars at the rear side):  jo1_r =

jo1_p_AlBSF , αmo = 1 (1 − FM_r ) · jo1_p+ + FM_r · jo1_p+ _met , αbi = 1

(A.7)

 mA  stands for the jo1 contribution at the base-Al-BSF interface. where jo1_p_AlBSF cm 2 due FM_r corresponds to the metallization fraction  at the rear side of the solar cell mA is the jo1 contribution from the p + rear to rear fingers and rear busbars, jo1_p+ cm 2  mA  layer and jo1_p+ _met cm is the jo1 contribution at the rear p + -metal interface. The 2 contributions for jo1 are represented in Fig. A.3. With respect to the the dark saturation current from diode 2 (two-diode model), jo2 represents the recombination losses that occur at the depletion region and can be estimated in a similar way as done for jo1 (similar to [15]):

Appendix A: Influence of Grid Metallization Design in Cell/Module

131

Fig. A.3 Schematic of the jo1 contributions for a monofacial and b bifacial technologies

jo2 = (1 − FM_f ) · jo2_n+ + FM_f · jo2_f_met + (1 − FM_r ) · jo2_p+ · αbi + FM_r · jo2_r_met · αbi

 mA 

 mA 

(A.8)

being jo2_n+ cm2 the jo2 contribution from the emitter, jo2_f_met cm2 the jo2 con mA  tribution from the front metal contacts, jo2_p+ cm the jo2 contribution from the 2  mA  + rear p layer and jo2_f_met cm2 the jo2 contribution from the rear metal contacts. jo2_p+ and jo2_f_met are only considered when dealing with the bifacial technology.

A.3

Area Weighted Series Resistance Estimation

To estimate the total area weighted series resistance, rs [Ωcm2 ], the lumped series resistance model [2, 15–18] is applied. It consists of calculating the individual rs contributors by weighting them to their respective unit cell area (the obtained values can be extended to the whole cell because of the unit cell periodicity). Therefore, rs will be equal to the addition of all the area weighted series resistance contributors. The calculation process for rs is as follows [2, 17]: 1 Select the series resistance contributor of interest ( jth contributor, j = 1, 2, ...). 2 Define its unit cell with area Auc ( j) [cm2 ]. 3 Calculate the effective resistance, Reff ( j) [Ω], based on the total power losses (due to the resistance of interest), Ploss ( j) [W], and total current generated in the unit cell, Iuc ( j) [A]: Ploss ( j) (A.9) Reff ( j) = 2 Iuc ( j) 4 Estimate the area weighted series resistance of the contributor of interest, r ( j) [Ωcm2 ], by weighting its Reff ( j) value to Auc ( j): r ( j) = Reff ( j) · Auc ( j)

(A.10)

5 The previous steps are repeated to obtain the area weighted series resistance of all the contributors. By adding them all, rs can be obtained:

132

Appendix A: Influence of Grid Metallization Design in Cell/Module

Fig. A.4 Area weighted series resistance contributions for a monofacial cells, b bifacial cells and c modules

rs =

 r ( j)

(A.11)

j=1

At the cell level, the contributors for rs [Ωcm2 ] are: the area weighted series resistance of the rear side metal layer rm_r [Ωcm2 ] (αmo = 1), rear busbar rBB_r [Ωcm2 ] (αbi = 1), rear finger rfi_r [Ωcm2 ] (αbi = 1), contact of rear grid to p + layer rc_gp+ [Ωcm2 ] (αbi = 1), p + layer rp+ [Ωcm2 ] (αbi = 1), base rb [Ωcm2 ], emitter re [Ωcm2 ], contact of front grid to emitter rc_ge [Ωcm2 ], front finger rfi_f [Ωcm2 ] and front busbar rBB_f [Ωcm2 ]. These contributions for monofacial and bifacial solar cells are presented in Fig. A.4a, b, respectively. To estimate the rs value of a cell within a module, extra terms need to be considered as ribbons will be added to interconnect the cells. These extra contributions are: the area weighted series resistance of the front side interconnector ribbon, rir_f [Ωcm2 ], rear side interconnector ribbon, rir_r [Ωcm2 ], cell spacing interconnector ribbon, rir_cs [Ωcm2 ] and bussing ribbon, rbr [Ωcm2 ], as shown in Fig. A.4c (rir_r is not shown in this figure as it is located at

Appendix A: Influence of Grid Metallization Design in Cell/Module

133

Table A.1 Equations to estimate value of the rs contributors rs term rs Contributor estimation Condition rm_r rBB_r rfi_r rc_gp+

ρm_r ·lf_f ·a 3·T h m_r [17]  2 a·ρBB_r · 2·br2 +sf_r

rb re rc_ge

βcell = 1, αbi = 1

3·h BB_r ·wBB_r ρfi_r ·lf_r ·a sf_r 2 3·A Rel_fi_r ·wfi_r √ a·sf_r · Rsh_p+ ·ρc_gp+ 2·lf_r



coth r p+

αmo = 1

wfi_r 2



αbi = 1

Rsh_p+ ρc_gp+

·

αbi = 1 [17]

Rsh_p+ ·(sf_r −wfi_r )·a·sf_r 12·lf_r ρb ·T h b ·Acell [2] Ac_nm Rsh_e ·(sf_f −wfi_f )·a·sf_f [17] √ 12·lf_f  a·sf_f · Rsh_e ·ρc_ge w · coth 2fi_f 2·lfi_f

αbi = 1 All cases 

Rsh_e ρc_ge



All cases All cases

[17] rfi_f rBB_f rir_f

ρfi_f ·lf_f ·a·sf_f [17] 2 3·A Rel_fi_f ·wfi_f   2 a·ρBB_f · 2·bf2 +sf_f 3·h BB_f ·wBB_f 2 2·n 2f_f +1 a·ρir ·lcell 3·h ir ·wir · n2

[2]

βcell

[2]

βmod = 1

f_f

rir_r

rir_cs

2 a·ρir ·lcell 3·h ir ·wir 2 a·ρir ·lcell 3·h ir ·wir

· ·

ρir ·cs·Acell h ir ·wir ·n BB

All cases

2·n 2ag +1 [2] n 2ag 2·n 2fi_r +1 n 2fi_r

βmod = 1, αmo = 1 βmod = 1, αbi = 1 βmod = 1

the rear side of the cell). Due to their low value, other resistance contributors such as the contact resistance between the base and the rear side metal (αmo = 1) and the contact resistance of the soldering joint (βmod = 1) between busbars (or silver pads) and the interconnector ribbons, among others, are neglected. The equations of the area weighted series resistance contributors are presented in Table A.1.1

A.4

Table of Results Under STC

See Table A.2.

1 Unless

assigned with a citation, the expressions for the rs contributors were determined in this work. To estimate rir_fs and rir_fs , it is assumed that the whole busbars (or rear silver pads) are soldered to the interconnector ribbons. The value of rbr will depend on the specific module design, i.e., position of the bypass diodes and output terminals.

Appendix A: Influence of Grid Metallization Design in Cell/Module

Table A.2 Parameters of the grid designs of interest

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Appendix A: Influence of Grid Metallization Design in Cell/Module

135

Bibliography 1 Pospischil M, Kuchler M, Klawitter M, Rodríguez C, Padilla M, Efinger R, Linse M, Padilla A, Gentischer H, König M (2015) Dispensing technology on the route to an industrial metallization process. Ener Procedia 67:138–146 2 Rodríguez C, Pospischil M, Padilla A, Kuchler M, Klawitter M, Geipel T, Padilla M, Fellmeth T, Brand A, Efinger R, Linse M, Gentischer H, König M, Hörteis M, Wende L, Doll O, Clement F, Biro D (2015) Analysis and performance of dispensed and screen printed front side contacts on cell and module level. In: Proceedings of the 31th European PV Solar Energy Conference and Exhibition (EU PVSEC), pp 983–990, Hamburg, Germany, 2015. 3 McIntosh KR, Cotsell JN, Cumpston JS, Norris AW, Powell NE, Ketola BM (2009) An optical comparison of silicone and EVA encapsulants for conventional silicon PV modules: A ray-tracing study. In 34th IEEE Photovoltaic Specialists Conference (PVSC), pp 544–549, Philadelphia, USA, 2009. 4 Dupeyrat P, Ménézo C, Wirth H, Rommel M (2011) Improvement of PV module optical properties for PV-thermal hybrid collector application. Solar Energy Mater Solar Cells 95(8):2028–2036 5 Baker-Finch SC, McIntosh KR, Terry ML (2012) Isotextured silicon solar cell analysis and modeling 1: Optics. IEEE J Photovoltaics 2(4):457–464 6 Alonso-Álvarez D, Ross D, Klampaftis E, McIntosh KR, Jia S, Storiz P, Stolz T, Richards BS (2015) Luminescent down-shifting experiment and modelling with multiple photovoltaic technologies. Progress Photovoltaics: Res Appl 23(4):479–497 7 Rodríguez-Gallegos CD (2014) Experimental evaluation and characterization of dispensed front side contacts on silicon solar cells during module integration. Msc thesis, Fraunhofer Institute for Solar Energy Systems ISE, Ulm University 8 Tao W, Du Y (2015) The optical properties of solar cells before and after encapsulation. Solar Energy 122:718–726 9 McIntosh KR, Swanson RM, Cotter JE (2006) A simple ray tracer to compute the optical concentration of photovoltaic modules. Progress Photovoltaics: Res Appl 14(2):167–177 10 Peters M, Guo S, Liu Z (2015) Full loss analysis for a multicrystalline silicon wafer solar cell PV module at short-circuit conditions. Progress Photovoltaics: Res Appl, 24:560,569, 2015 11 Vogt MR (2015) Development of physical models for the simulation of optical properties of solar cell modules. PhD thesis, Leibniz University of Hannover, 2015 12 Winter M, Vogt MR, Holst H, Altermatt PP (2015) Combining structures on different length scales in ray tracing: Analysis of optical losses in solar cell modules. Optic Quant Electron 47(6):1373–1379 13 Singh JP, Guo S, Peters IM, Aberle AG, Walsh TM (2015) Comparison of glass/glass and glass/backsheet PV modules using bifacial silicon solar cells. IEEE JPhotovoltaics 5(3):783–791

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14 Singh JP, Walsh TM, Aberle AG (2014) A new method to characterize bifacial solar cells. Progress Photovoltaics: Res Appl 22(8):903–909 15 Fellmeth T, Clement F, Biro D (2014) Analytical modeling of industrial-related silicon solar cells. IEEE J Photovoltaics 4(1):504–513 16 Goetzberger A, Knobloch J, Voss B (1998) Crystalline silicon solar cells. John Wiley & Sons, Chichester, UK, 1st edition 17 Mette A (2007) New concepts for front side metallization of industrial silicon solar cells. Phd thesis, Fraunhofer Institute for Solar Energy Systems ISE, Albert Ludwig University of Freiburg 18 Rajput AM, Rodríguez-Gallegos CD, Ho JW, Nalluri S, Raj S, Aberle AG, Singh JP (2019) Fast extraction of front ribbon resistance of silicon photovoltaic modules using electroluminescence imaging. Solar Energy 194:688–695

Appendix B

Weather Data Processing

B.1

Data Filtering

The filtering process consists of applying quality controls to assure the accuracy of the recorded data by removing data points which do not satisfy certain conditions. At present, there is no general agreement on the conditions to be applied to filter the data. Nonetheless, Gueymard and Ruiz-Arias [1] introduced a set of nine comprehensive conditions to filter out irradiance data based on their low accuracy. Eight of these conditions are first applied while the remaining one will be used later (see Appendix B.3): GHI > 0, DHI > 0, DNI  0 DNI < 1100 + 0.03 · El DNI < I0 DHI < 0.95 · I0 · cos1.2 (z) + 50 GHI < 1.5 · I0 · cos1.2 (z) + 100 |100 · (DNI · cos (z) + DHI − GHI) /GHI| < 5% DHI/GHI < 1.05 for GHI > 50 and z < 75◦ DHI/GHI < 1.10 for GHI > 50 and z > 75◦   where El m2 is the surface elevation, I0 [W/m2 ] is the extraterrestrial irradiance normal to a surface2 and z [◦ ] is zenith angle of the sun.3 1 2 3 4 5 6 7 7

0 is calculated based on the model proposed by Spencer [2], which has an accuracy of ±0.01% [3]. The solar constant is set to 1367 W/m2 [4]. 3 The current state-of-the-art algorithm to estimate the position of the sun (zenith and azimuth values, z [◦ ] and As [◦ ], respectively), namely, solar position algorithm (SPA), is used. The SPA, first introduced in [5] and later revised in [6], achieves uncertainties in the range of ±0.0003◦ [6]. 2I

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7

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138

B.2

Appendix B: Weather Data Processing

Data Filling

Due to the previous filtering or for circumstances in which the sensors were not able to record the data, such as maintenance routines or sudden shut downs, there may be missing data at certain time periods. To overcome this issue, the employed approach to fill missing data is based on the method presented by the National Renewable Energy Laboratory [7]. Here, the applied filling approach depends on the length of the missing consecutive data. This approach is summarized in the following: • Up to 5 h data gaps: filling process based on a linear interpolation using the known data located before/after the current gap. • Up to 24 h data gaps: filling procedure takes place by generating the average profile from the same minutes that belong to this time gap considering the previous/following days. • Up to 1 year data gaps: the missing data is replaced with the data of the same time interval from the year which is most similar to the one been analyzed. Furthermore, as the irradiance variables are related as shown in Eq. (B.1), the value of a missing irradiance variable can be calculated when the other two are known. This is applied except for cases when the D N I is missing and z ≥ 75◦ to avoid large errors being generated by the “cos (z)” term. G H I = D N I · cos (z) + D H I

B.3

(B.1)

Typical Meteorological Year Data Estimation

A TMY dataset typifies the weather condition of a location; it contains 12 months (from different years) selected based on a defined criteria. The TMY data can be used to estimate the performance of PV devices in the long term, as will be the case for this study. The literature presents different approaches to estimate the TMY data, e.g., [8–16]. Among these, the one proposed by SolarGIS [16] will be employed as this has been developed specifically for PV applications. Based on the yearly recorded data, the SolarGIS method chooses the 12 months that form the TMY data by taking into account their similarity index. This is calculated considering two criteria, namely, the similarity of monthly averages and the similarity of the cumulative distribution function from time series; the importance from each criteria is set by weighting indices. The G H I , D N I , D H I , and Ta data are evaluated based on the two previous criteria. These weather parameters also have an associated weighted index. When the 12 months have been selected, their G H I and D N I values are scaled so that their average value is equal to the ones from the multiyear time series. A more detailed explanation of this approach can be found in [16]. At this point the TMY data have been generated. The remaining filtering condition, namely, z < 85◦ [1], is now applied on this dataset to remove data which

Appendix B: Weather Data Processing

139

have negligible (or any) influence on the estimation of the PV performance as this corresponds to the nighttime period [1, 17]. Thus, the computational burden for the future calculations has been reduced as this condition eliminates about half of the data. The resulting dataset will be referred as the TMY data for the other sections.

Bibliography 1 Gueymard CA Ruiz-Arias JA (2016) Extensive worldwide validation and climate sensitivity analysis of direct irradiance predictions from 1-min global irradiance. Solar Energy 128:1–30 2 Spencer JW (1971) Fourier series representation of the position of the sun. Search 2(5):172–172 3 Iqbal M (1993) An introduction to solar radiation. Academic Press Canada, Ontario, Canada, 1st edition 4 Duffie JA, Beckman WA (2013) Solar engineering of thermal processes. John Wiley & Sons, New Jersey, USA, 4th edition 5 Meeus J (1998) Astronomical Algorithms. Willmann-Bell, Richmond, USA, 2nd edition 6 Reda I, Andreas A (2004) Solar position algorithm for solar radiation applications. Solar Energy 76(5):577–589 7 Wilcox S (2007) National solar radiation database 1991-2005 update: User’s manual. Technical Report NREL/TP-581-41364, National Renewable Energy Laboratory (NREL), Golden, USA, 2007 8 Hall L, Prairie R, Anderson H, Boes E (1978) Generation of typical meteorological years for 26 SOLMET stations. Technical report, Sandia National Laboratories, Albuquerque, USA, 1978 9 Festa R, Ratto CF (1993) Proposal of a numerical procedure to select reference years. Solar Energy 50(1):9–17 10 Marion W, Urban K (1995) Users manual for TMY2s: Derived from the 1961–1990 national solar radiation data base. Technical Report DE-AC3683CH10093, National Renewable Energy Laboratory (NREL), Golden, USA, 1995 11 Kalogirou SA (2003) Generation of typical meteorological year (TMY-2) for Nicosia, Cyprus. Renew Energy 28(15):2317–2334 12 Faiman, Feuermann D, Ibbetson P, Medwed B, Zemel A, Ianetz A, Liubansky V, Setter I, Suraqui S (2004) The negev radiation survey. J Solar Energy Eng 126(3):906–914 13 Wilcox S, Marion W (2008) Users manual for TMY3 data sets. Technical Report NREL/TP-581-43156, National Renewable Energy Laboratory (NREL), Golden, USA 14 Hoyer-Klick C, Hustig F, Schwandt M, Meyer R (2009) Characteristic meteorological years from ground and satellite data. In: Proceedings of the 15th solarPACES symposium, pp 1–8, Berlin, Germany

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Appendix B: Weather Data Processing

15 Wey E, Thomas C, Blanc P, Espinar B, Mouadine M, Bouhamidi MH, Belkabir Y (2012) A fusion method for creating sub-hourly dni-based tmy from long-term satellite-based and short-term ground-based irradiation data. In: SolarPACES 2012, pp 1–7, Marrakech, Morocco, 2012. PSE AG 16 Cebecauer T, Suri M (2015) Typical meteorological year data: SolarGIS approach. Energy Procedia 69:1958–1969 17 Yang D (2016) Solar radiation on inclined surfaces: Corrections and benchmarks. Solar Energy 136:288–302

Appendix C

Approaches to Estimate the Front and Rear Irradiance Reaching the Module

C.1

Front Surface Irradiance

As previously indicated in Sect. 4.3, the front surface irradiance is defined as: If = Idir,f + Ignd,f + Idiff,f

(C.1)

where Idir,f [W/m2 ] corresponds to the direct irradiance contribution, Ignd,f [W/m2 ] represents the irradiance contribution due to ground reflection, and Idiff,f [W/m2 ] is the diffuse irradiance contribution at the front side. The direct irradiance contribution at the front side is calculated as follows: Idir,f = D N I · cos (AO If ) · rldir,f

(C.2)

where AO If [◦ ] is the angle of incidence between the D N I radiation and the normal of the front surface of the module, defined as: cos (AO If ) = max (cos (z) · cos (θ m ) + sin (z) · sin (θ m ) · cos (As − Am ) , 0) (C.3) The maximum operator in Eq. (C.3) accounts for the cases when the D N I of the sun does not reach the module front surface, i.e., sun is no longer on the horizon or is behind the module. The variable rldir,f corresponds to the reflection losses of light reaching the front surface for the Idir,f irradiance. To quantify it, the well established equation proposed by Martin and Ruiz is used [1]: rldir,f =

1 − exp (− cos (AO If ) /ar ) 1 − exp (−1/ar )

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7

(C.4)

141

142

Appendix C: Approaches to Estimate the Front and Rear Irradiance …

where ar is the angular loss coefficient empirically determined. In this work, ar is set to 0.16, value within the range for commercial clean crystalline Si modules [2]. Fig. C.1a shows the relation between rldir,f and AO If . The calculation of Ignd, f is presented in Eq. (C.6): Ignd,f = G H I · ρ · gv f · rlgnd,f

(C.5)

where ρ is the albedo from the ground and gv f is the ground view factor which is commonly calculated assuming an isotropic model [3]: gv f =

1 − cos (θ m ) 2

(C.6)

The variable rlgnd,f represents the reflection losses of light reaching the front surface for the Ignd,f irradiance. In a recent publication, Marion [4] proposed an analytical approach to estimate the reflection losses for the diffuse radiation components, namely, sky, circumsolar, horizon, and ground-reflected. This approach consists of subdividing the light emitting area and obtaining the reflection losses from each of these (the Martin and Ruiz loss model [1] was used in our work). The contribution from each division is then weighted and added to get the total reflection losses. The value of rlgnd,f depends on the module tilt angle, and their relation is presented in Fig. C.1 b). The diffuse radiation contribution at the front side is defined as: Idiff,f = D H I · sv f

(C.7)

where sv f is the sky view factor. Different approaches are proposed to estimate sv f . In a recent work, Yang [8] presented a comprehensive evaluation of 26 of these models and evaluated their accuracy against 18 datasets from locations worldwide. Although he concluded that there is no universal method, the so called Perez4 model achieved a considerably good performance, and as such will be used in this work. The Perez models divide the sky hemisphere into three regions, namely, sky, circumsolar, and horizon. Eq. (C.8) presents the calculation of sv f based on the Perez4 model; light reflection losses have also been included: a 1 + cos (θ m ) · rlsky,f + F1 ·  · rlcir,f + F2 · sin (θ m ) · rlhor,f 2 c (C.8) where F1 , F2 , a  , and c are coefficients defined in [8]. To estimate the reflection losses from the sky and horizon components of light reaching the front surface (rlsky,f and rlhor,f , respectively), the approach presented by Marion is applied once more [4]. Here, rlsky,f and rlhor,f are also dependent of the module tilt angle, as shown in Fig. C.1b. The circumsolar component is typically considered to have the same AO I value as the one from Idir,f [4], as such, rlcir,f = rldir,f (see Fig. C.1a). sv f = (1 − F1 ) ·

Appendix C: Approaches to Estimate the Front and Rear Irradiance …

C.2

143

Rear Surface Irradiance

The rear surface irradiance, Ir [W/m2 ], is defined similarly to its front counterpart (see Eq. (C.1)): (C.9) Ir = Idir,r + Ignd,r + Idiff,r where the direct and diffuse components, namely, Idir,r [W/m2 ] and Idiff,r [W/m2 ], respectively, can be calculated following the same approaches as the ones previously introduced for their front counterparts, by considering the appropriate tilt angle, i.e., replacing θ m for θ m + 180◦ . With respect to the ground-reflected irradiance at the module rear side, Ignd,r [W/m2 ], the complexity of its calculation increases because the isotropic behavior that was assumed for its front counterpart should not be applied anymore. This is in view of the fact that the shadow the module produces on the ground will now have a big influence on Ignd,r and as such, a non-uniform irradiance distribution on the ground needs to be considered [5, 7]. Recently, Marion et al. [7] presented a practical and fast approach to estimate the Ignd,r contribution. This method does not estimate the irradiance per solar cell but the one along the row’s length of the solar panels, allowing a fast simulation. For this method, it is assumed that the PV rows are composed of at least 12 solar modules, otherwise, other methods are recommended, i.e., [5]. In the following, we present Marion’s method with certain modifications based on the assumption that the space between the module rows is large enough and as such, the influence and shading produced from neighboring module rows are neglected. For simplicity, the ground reflected irradiance reaching the middle point of the module rows will be considered as Ignd,r . Marion’s method divides the fieldof-view into 180 one-degree regions, i (see Fig. C.1c). The parameter Ignd,r is then defined as: ◦ −θ m 180  (i) Ignd,r ρ · G R I (i) · C F (i) · rlgnd,r (C.10) i=1◦

The summation used in Eq. (C.10) adds all the ground contributions. For each ith region, the irradiance that is emanating from the ground, G R I (i) [W/m2 ], is considered. This is defined as:  G R I (i) =

 D N I · cos (z) + D H I · F1 · ac + C Fsky · D H I · (1 − F1 ) , if ground is unshaded

, if ground is shaded

C Fsky · D H I · (1 − F1 )

(C.11) where C Fsky = 1/2 · (1 − cos (σ ))  σ =

, >0 + 180◦ , otherwise

(C.12)

(C.13)

144

Appendix C: Approaches to Estimate the Front and Rear Irradiance …

Fig. C.1 a Reflection losses for DNI and circumsolar contributions at the front side (rldir,f and rlcir,f , respectively) versus the angle of incidence; b Reflection losses for ground, sky, and horizon contributions at the front side (rlgnd,f , rlsky,f , and rlhor,f , respectively) versus the module tilt angle; c Field of view for the ith one degree segment; d Reflection losses for ground contribution at the rear side versus the ith one degree segment

⎛

⎞ h mg + lm · sin (θ m ) ⎠  = atan ⎝  h mg (i) · cos + l − x (θ ) m m sin(θ m )

x (i) =

sin (i) ·



h mg sin(θ m )

+

lm 2

(C.14)



sin (180◦ − i − θ m )

(C.15)

where lm [m] is the module length and h mg [m] is the module height measured between the module lowest edge and the ground. The parameter C F (i) is the configuration factor for the ith segment: C F (i) = 1/2 · (cos (i − 1) − cos (i))

(C.16)

(i) represents the reflection losses of light reaching the rear modThe variable rlgnd,r ule surface for the Ignd,r contribution. This is also calculated based on Marion’s (i) method [4]. The variable rlgnd,r is dependent on the ith one-degree segment, as shown in Fig. C.1d.

Appendix C: Approaches to Estimate the Front and Rear Irradiance …

145

Bibliography 1 Martin N, Ruiz JM (2001) Calculation of the PV modules angular losses under field conditions by means of an analytical model. Solar Energy Mater Solar Cells 70(1):25–38 2 Martín N, Ruiz JM (2005) Annual angular reflection losses in PV modules. Progress Photovoltaics: Res Appl, 13(1):75–84 3 Gueymard CA (2009) Direct and indirect uncertainties in the prediction of tilted irradiance for solar engineering applications. Solar Energy 83(3):432–444 4 Marion B (2017) Numerical method for angle-of-incidence correction factors for diffuse radiation incident photovoltaic modules. Solar Energy 147:344–348 5 Yusufoglu UA, Pletzer TM, Koduvelikulathu LJ, Comparotto C, Kopecek R, Kurz H (2015) Analysis of the annual performance of bifacial modules and optimization methods. IEEE J Photovoltaics 5(1):320–328 6 Shoukry I, Libal J, Kopecek R, Wefringhaus E, Werner J (2016) Modelling of bifacial gain for stand-alone and in-field installed bifacial PV modules. Energy Procedia 92:600–608 7 Marion B, MacAlpine S, Deline C, Asgharzadeh A, Toor F, Riley D, Stein J, Hansen C (2017) A practical irradiance model for bifacial PV modules: Preprint. Technical Report NREL/CP-5J00-67847, National Renewable Energy Laboratory (NREL), Golden, USA 8 Yang D (2016) Solar radiation on inclined surfaces: Corrections and benchmarks. Solar Energy 136:288–302

Appendix D

Polar Contour Plots

See Fig. D.1.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7

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Appendix D: Polar Contour Plots

Fig. D.1 Polar contour plots of the Id , E d , and LC O E values for the monofacial and bifacial systems for selected locations. The “x” indicates the orientations which achieved the lowest LC O E for AMO and VMO designs

Appendix D: Polar Contour Plots

Fig. D.1 (continued)

149

150

Fig. D.1 (continued)

Appendix D: Polar Contour Plots

Appendix D: Polar Contour Plots

Fig. D.1 (continued)

151

Appendix E

Scheduling Algorithm Applied for PV Hybrid Systems

The applied scheduling algorithm for Chap. 5 is based on a centralized controller used to control the power output from DGs (as well as their ON/OFF state) and batteries at every time step based on the following priority: 1 The loads must always be satisfied. 2 The spinning reserve constraint, i.e., Eq. (5.31), should be satisfied. If it is not possible, it should be fulfilled as much as possible. 3 The minimum power condition from DGs, i.e., Eq. (5.5), should be satisfied. If it is not possible, it should be fulfilled as much as possible. 4 The total cost should be minimized as much as possible. 5 Charge the batteries. The priority list is designed to give the prime concern to the fulfillment of the load demand. Consequently, the spinning reserve condition is set as the second priority to assure that the system is fast enough to respond and fulfill the load demand, i.e., when the load and/or solar output change suddenly. Due to the spinning reserve constraint, there might be cases when the DGs are required to operate at power levels lower than their defined minimum, which motivates the third priority. The fourth priority is to reduce the total cost during the system lifetime. Finally, the fifth priority is established to charge the batteries with any energy surplus. The employed scheduling algorithm is presented in Fig. E.1. To represent all possible combinations of ON/OFF states of DGs, a (2n DG − 1) × n DG matrix, G, is constructed. The rows of G contains binary numbers of length n DG , e.g, (0, 1, 0) means the second DG is ON while the other two are OFF, when n DG = 3; the row (0, 0, 0) is not allowed as at least one DG must remain ON. The combinations are arranged in ascending order of total generating power of the DGs. The variable G(i) is used to represent the ith row of G. Similarly, a matrix B is constructed to represent all combinations of DGs arranged in ascending order based on operational cost, which includes the operational cost of DGs and batteries. The variable B(i) is used to represent the ith row of B. These matrices are employed to choose the best combination of operating DGs that, after fulfilling all previous priorities, achieve the lowest cost at a particular time. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. D. Rodríguez Gallegos, Modelling and Optimization of Photovoltaic Cells, Modules, and Systems, Springer Theses, https://doi.org/10.1007/978-981-16-1111-7

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154

Appendix E: Scheduling Algorithm Applied for PV Hybrid Systems

Fig. E.1 Flow chart diagram of the employed scheduling algorithm. The variable n DG,on(t) corresponds to the number of DGs that are ON at time t and is used when considering only the DGs that are operating

The scheduling algorithm starts by calculating, for the current time step, the power output delivered from the solar panels to the grid, as well as the maximum possible discharging and charging power that batteries can deliver or take from the grid (Pdis,max(t) and Pch,max(t) , respectively). Once this step is completed, the algorithm analyzes whether the power produced from the solar panels is enough to fulfill the load demand: On the one hand, if the power from the solar panels fulfills the load demand, it means that the batteries do not need to be discharged (Pd(t) = 0), instead, they can be charged (Pc(t) ≥ 0). To obtain the value of Pc(t) , the ON/OFF combinations of DGs are evaluated from lower to higher accumulated capacity (by using the G(i) vector). For any combination, the DGs are set to operate at their minimum power PDG,min( j) , as the PV can satisfy the load demand. The batteries can then be charged with the remaining power, provided the charging power does not exceed Pch,max .

Appendix E: Scheduling Algorithm Applied for PV Hybrid Systems

155

Any extra generated power is assumed to be consumed by the dump loads. With the current power values, the spinning reserve condition is evaluated. If this condition is satisfied, the current power dispatch is considered to be the most cost effective. If this condition is not fulfilled, the next ON/OFF combination of DGs is evaluated. In case when none of the combinations defined in the G matrix was able to fulfill the spinning reserve condition, the charging power of batteries is set to zero. On the other hand, if the power from the solar panels are not enough to fulfill the load demand, it means that the DGs or batteries need to deliver power. Each ON/OFF combination of DGs is evaluated (arranged from lower to higher operational cost of DGs & batteries) to obtain the vector B(i) . Based on B(i) , the ON/OFF combinations of DGs are analyzed. For a defined combination, it is first evaluated whether it is possible to satisfy the load demand. If this condition is not achieved, the current combination is discarded, and the next one is evaluated. If the load can be satisfied, the operation priority between the DGs and batteries is compared. This is achieved by comparing the cost per energy production from DGs, aDG · cdiesel(t) , and batteries, S0 · cBAT(t) /E. If it is more cost effective to deliver power from the DGs, the discharging power from batteries will be decreased as much as possible. If it is more cost effective to deliver power from the batteries, they will be discharged as much as possible (by considering the minimum required power needed to be generated by the DGs and their maximum possible discharging power). After fulfilling the PDG,min(k) condition, the spinning reserve condition is evaluated. If this condition is not fulfilled, the next ON/OFF combination of DGs is evaluated. In the case when none of the combinations defined by the G matrix fulfills the spinning reserve condition, the charging power of batteries is set to zero. At this point the desired power output from diesel generators (as well as their ON/OFF state) and batteries has been obtained for the current time step. Therefore, the next time step is evaluated and so on until all required time steps are analyzed.