OWC-Based Ocean Wave Energy Plants: Modeling and Control [1st ed.] 9789811598487, 9789811598494

Table of contents :
Front Matter ....Pages i-viii
Introduction (Sunil Kumar Mishra, Dusmanta Kumar Mohanta, Bhargav Appasani, Ersan Kabalcı)....Pages 1-14
Overview of OWC Mathematical Model (Sunil Kumar Mishra, Dusmanta Kumar Mohanta, Bhargav Appasani, Ersan Kabalcı)....Pages 15-27
Control Challenges of OWC (Sunil Kumar Mishra, Dusmanta Kumar Mohanta, Bhargav Appasani, Ersan Kabalcı)....Pages 29-37
Power Generation Control of OWC Using Airflow Control (Sunil Kumar Mishra, Dusmanta Kumar Mohanta, Bhargav Appasani, Ersan Kabalcı)....Pages 39-53
Maximum Power Point Tracking of OWC Using Rotational Speed Control (Sunil Kumar Mishra, Dusmanta Kumar Mohanta, Bhargav Appasani, Ersan Kabalcı)....Pages 55-81
Conclusion (Sunil Kumar Mishra, Dusmanta Kumar Mohanta, Bhargav Appasani, Ersan Kabalcı)....Pages 83-84

Citation preview

Energy Systems in Electrical Engineering

Sunil Kumar Mishra Dusmanta Kumar Mohanta Bhargav Appasani Ersan Kabalcı

OWC-Based Ocean Wave Energy Plants Modeling and Control

123

Energy Systems in Electrical Engineering Series Editor Muhammad H. Rashid, Florida Polytechnic University, Lakeland, USA

More information about this series at http://www.springer.com/series/13509

Sunil Kumar Mishra · Dusmanta Kumar Mohanta · Bhargav Appasani · Ersan Kabalcı

OWC-Based Ocean Wave Energy Plants Modeling and Control

Sunil Kumar Mishra School of Electronics Engineering Kalinga Institute of Industrial Technology Bhubaneswar, India Bhargav Appasani School of Electronics Engineering Kalinga Institute of Industrial Technology Bhubaneswar, India

Dusmanta Kumar Mohanta Department of Electrical and Electronics Engineering Birla Institute of Technology Mesra, Ranchi, India Ersan Kabalcı Department of Electrical and Electronics Engineering Nevsehir Haci Bektas Veli University Nevsehir, Turkey

ISSN 2199-8582 ISSN 2199-8590 (electronic) Energy Systems in Electrical Engineering ISBN 978-981-15-9848-7 ISBN 978-981-15-9849-4 (eBook) https://doi.org/10.1007/978-981-15-9849-4 © 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

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Significance of Ocean Wave Energy . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Historical Development of OWC Control Systems . . . . . . . . . . . . . . . . 2 1.3 Summary of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Overview of OWC Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Ocean Wave Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 OWC Chamber Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Wells Turbine Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 DFIG Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Wells Turbine-DFIG Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 15 18 18 23 25 25

3 Control Challenges of OWC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Simulation of Open Loop/Uncontrolled OWC . . . . . . . . . . . . . . . . . . . 3.2 Classification of Control Techniques for OWC . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29 29 30 37

4 Power Generation Control of OWC Using Airflow Control . . . . . . . . . . 4.1 PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Fractional Order PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Optimally Tuned PID and FOPID Control . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39 39 43 48 52

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 MPPT Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 PI Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Backstepping Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Sliding Mode Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55 55 56 57 71 81

6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 v

About the Authors

Sunil Kumar Mishra received PhD degree in Electrical Engineering from Motilal Nehru National Institute of Technology (MNNIT) Allahabad, India. He is presently working as Assistant Professor in the School of Electronics Engineering, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha, India. He previously worked as the Assistant Professor in the Department of Electrical and Electronics Engineering, Ajay Kumar Garg Engineering College Ghaziabad, India. His research areas are ocean wave energy (control perspectives) and nonlinear controller design. He has teaching experience of more than one year and has published more than 10 research papers in reputed international journals and renowned conferences. He is also the reviewer of Transactions of Institute of Measurement and Control (TIMC) Journal. Dusmanta Kumar Mohanta received the Ph.D. (Engg.) degree from Jadavpur University, Kolkata, India. He was an Electrical Engineer with the Captive Power Plant, National Aluminium Company (NALCO), Angul, India, from 1991-1998. He is currently a Professor with the Department of Electrical and Electronics Engineering at BIT, Mesra, Ranchi. He has more than 20 years of teaching experience in addition to his industrial experience of 8 years. He has been a Senior Member of IEEE (USA), Member of IEEE PES RRPA subcommittee, Life Member of ISTE and a Fellow of Institutions of Engineers (India). He is an Editor of Power Components & Systems (Taylor & Francis Publications); Subject Editor of IET Generation, Transmission & Distribution; Associate Editor of IEEE Access as well as of Electrical Engineering (Springer Nature). Bhargav Appasani received the Ph.D. (Engg.) degree from Birla Institute of Technology, Mesra, India. He is currently an Assistant Professor with the School of Electronics Engineering, KIIT Deemed University, Bhubaneswar, India. He has published more than 40 papers in international journals and conference proceedings. He has also published 4 book chapters with Springer and Elsevier. He is the reviewer for IEEE Transactions on Smart Grid, IEEE Transactions on Antennas and Propagation, IEEE Access, etc. He also has a patent filed to his credit. vii

viii

About the Authors

Ersan Kabalcı received B.S. and M.Sc. degrees in Electronics and Computer Education from Gazi University, Ankara, Turkey, in 2003 and in 2006 respectively. He received the Ph.D. degree from Gazi University, Ankara, Turkey, in 2010 with the thesis on implementing an enhanced modulation scheme for multilevel inverters. From 2005 to 2007, he was with Gazi University as a lecturer. He is currently with the Department of Electrical and Electronics Engineering Department since 2010, Nevsehir HBV University, where he became an Assistant Professor in 2011; an Associate Professor in 2013, and full Professor in 2019 on power plants and power electronics-drives; and is Head of Department. Dr. Kabalcı is an Associate Editor of several international indexed journal on Power Electronics and Renewable energy sources. His current research interests include power electronic applications and drives for renewable energy sources, microgrids, distributed generation, power line communication, and smart grid applications. He is IEEE Member since 2009, and senior-member since 2018.

Chapter 1

Introduction

1.1 The Significance of Ocean Wave Energy It has become indispensable to explore clean and renewable energy resources, as carbon-dioxide emissions pose severe environmental dangers. A very troubled weather pattern and global warming issues seen in the last couple of years are proof of vulnerabilities that could get worse in the near future. Therefore, many clean and renewable energy resources such as hydro, solar and wind power are being used on a big scale to tackle these challenging circumstances. Another promising source of sustainable energy to generate electricity is the ocean wave energy (Clement et al. 2002a; Zhang et al. 2009h; Brekken et al. 2011e). It was first realized in the form of tsunamis and cyclones as damaging in nature. Still, nowadays, its enormous energy potential is being used for beneficial reasons such as electric power generation (Parkinson et al. 2015e; Rusu and Onea 2016o). The potential of wave energy is estimated at around 2,000 TWh/year for the electricity generation. This share roughly comprises 10% of total global electricity demand (Rodrigues 2008; Gunn and Williams 2012c; Kumar and Anoop 2015d). Ocean wave energy has seen slower progress over many years due to a wider tendency toward other resources and insufficient research funding. Still, the amount of research funding has increased over the past few years. It has given a strong momentum for wave energy technology growth. As a consequence, many prototypes were effectively created, and some of them also achieved pre-commercial level, such as oscillating water column (OWC), Archimedes wave swing, Pelamis, Wave dragon, etc. (Bjarte-Larsson and Falnes 2006a; Valério et al. 2007b; Falnes 2007a; Burman and Walker 2009e; Falcão 2010e; Portillo 2020; Polinder et al. 2005c; Das and Pal 2006b). The OWC technique (Falcão and Henriques 2016d) is one of the most commonly regarded techniques by wave power researchers. Many OWC studies have been published recently covering several aspects related to OWC (Kelly et al. 2016j; Delmonte et al. 2016c; Liu et al. 2016l; Bailey et al. 2016a; Torres et al. 2016q). The simplicity is the outstanding benefit of OWC since the only moving part of the system © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 S. K. Mishra et al., OWC-Based Ocean Wave Energy Plants, Energy Systems in Electrical Engineering, https://doi.org/10.1007/978-981-15-9849-4_1

1

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1 Introduction

for energy conversion is the rotor of a turbine that directly drives an electrical generator. In an OWC, an alternating air flows between the chamber and the atmosphere. The air turbines installed at OWC are, therefore, fundamentally the self-rectifying type, i.e., their rotational direction remains unchanged regardless of the direction of airflow. The Wells Axial Flow Turbine has been introduced at most of the OWC plants installed (Gato et al. 1991a, 1996; Raghunathan 1995; Setoguchi et al. 2003b; Falcão et al. 2014a; Shehata et al. 2016p) and is a very common self-rectifying air turbine. Consequently, an OWC plant fitted with a Wells turbine and a doubly-fed induction generator (DFIG) was considered to derive electrical energy from ocean waves.

1.2 Historical Development of OWC Control Systems Researches into wave energy converters have begun as an instant response to the 1970s petroleum crisis. Since then, several nations have conducted research projects, but the majority of ocean wave power studies and development has been focused in Europe. Several state and personal aid study programmes, primarily in the UK, Portugal, Ireland, Norway, Sweden and Denmark, were then initiated. The study was directed at designing intermediate and long-term techniques for industrial wave power conversion. The European Commission endorsed these nations and organized various meetings on ocean energy. The cooperation between the different organizations and universities around the world was improved. Furthermore, wave energy projects have been started by other states, such as India, Australia, Canada, China, Sri Lanka, USA, Israel and Japan (Clement et al. 2002a; Brekken et al. 2011e; Rusu and Onea 2016o; Rodrigues 2008; Gunn and Williams 2012c; Kumar and Anoop 2015d; Falcão and Henriques 2016d). While the focus of this work is on controlling OWC plants, a short review of the worldwide construction of important OWC plants is discussed first followed by an exhaustive review of existing control strategies for OWC installations. The seminal work on OWC is attributed to the Japanese navy officer, Yoshio Masuda, who created a navigation buoy that was attached to a unidirectional air turbine that further needed valve rectification (Masuda 1986f; Masuda and McCormick 1986e). Since 1965, these buoys had become commercial and later had been renamed as OWC. The Kaimei, composed of 13 OWC chambers, was implemented in 1978– 1980 on the west coast of Japan following the development of OWC by Masuda. Most OWC plants have been installed with Wells turbine while some of the major plants were constructed at distinct places in the following years (Zhang et al. 2009h; Falcão and Henriques 2016d; Ohneda et al. 1991c; Suzuki et al. 2004; Ravindran and Koola 1991d; Mala et al. 2009f; Whittaker et al. 1993; Falcão 2000a; Heath et al. 2000b; Torre-Enciso et al. 2009g), e.g. (i) 60 kW OWC plant installed in a breakwater in the port of Sakata, Japan, 1990, (Ohneda et al. 1991c; Suzuki et al. 2004); (ii) 125 kW Bottom-standing OWC at Trivandrum, India, 1991 (Ravindran and Koola 1991d; Mala et al. 2009f); (iii) 75 kW Coastline OWC in Islay, Scotland,

1.2 Historical Development of OWC Control Systems

3

United kingdom, 1991 (Whittaker et al. 1993); (iv) 400 kW OWC plant (Fig. 1.1) in Pico, Azores, Portugal, 1999 (Falcão 2000a); (v) 500 kW LIMPET OWC plant on the island of Islay, Scotland, UK, 2000 (Heath et al. 2000b); (vi) 100 kW Shoreline OWC, Guangdong Province, China, 2001 (Zhang et al. 2009h); (vii) 300 kW Multichamber OWC plant (Fig. 1.2) integrated into a breakwater, Mutriku harbour, Basque Country, Spain, 2008 (Torre-Enciso et al. 2009g); (viii) Backward-Bent-Duct-Buoy

Fig. 1.1 400 kW OWC plant in Pico, Azores, Portugal (Portillo 2020)

Fig. 1.2 The biradial turbine testing at Mutriku wave power plant, Spain (Portillo 2020)

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1 Introduction

Fig. 1.3 The Backward-Bent-Duct-Buoy at the Galway Bay, Ireland (Portillo 2020)

(Fig. 1.3) at the Galway Bay, Ireland, 2008; (ix) 1 MW Oceanlinx greenWAVE at Port MacDonnell Australia, 2014 (Falcão and Henriques 2016d); (x) 500 kW OWC plant at Yongsoo, Jeju Island, South Korea, 2015 (Falcão and Henriques 2016d). A few of these OWCs are illustrated in Figs. 1.1–1.3. For the images of the remaining OWCs, please refer to (Falcão and Henriques 2016d). The extremely uncertain ocean wave energy behaviour resulted in a massive power variance at the generator output, which was not suitable for the grid. Another significant problem was the efficiency of energy conversion to create different types of OWC designs and turbines. Practical and robust control systems were needed to enhance the efficiency of the OWC plants. In the last three decades (Evans and Falcão 1986a; Hoskin et al. 1986b; Hotta et al. 1986c; Oltedal 1986g; Jefferys and Whittaker 1986d; Sarment et al. 1987; Gato and Falcáo 1989; Sarmento et al. 1990; Korde 1991b, 1999d, 2000d; Falcáo and Justino 1999b; Justino and Falcáo 1999c; Chatry et al. 1999a; Falcáo and Rodrigues 2002d; Falcáo 2002b; Falcáo 2002c; Falcáo et al. 2003a; Justino 2006c; Jayashankar et al. 2000c; Rao and Murthy 2005d; Muthukumar et al. 2005b; Murthy and Rao 2005a; Amundarain et al. 2009b, c, d, 2010c, d, 2011c, d; Alberdi et al. 2009a, 2010a, b, 2011a, b, 2012a; Garrido et al. 2012b, 2013b, c, 2016e, f; Barambones and Durana 2015a; Lekube et al. 2016k; Mishra et al. 2016; Mishra et al. 2016, 2018c; Lekube et al. 2018a; M’zoughi et al. 2018b; Arenas et al. 2019; Ceballos et al. 2013a, 2015b; Samrata et al. 2015g; Ramirez et al. 2015f; Colak and Kocabas 2015c, 2016b; Henriques et al. 2016g), many control systems that have been introduced in the remainder were proposed.

1.2 Historical Development of OWC Control Systems

5

Initial contributions to OWC plant control emerged in Evans and Falcão (1986a) in which two control approaches, phase control (Hoskin et al. 1986b; Hotta et al. 1986c; Oltedal 1986g) and latching control (Jefferys and Whittaker 1986d), were suggested to improve the overall energy harvested from OWC plant. By matching the phase between incident wave force and column velocity, the OWC energy captured was maximized. In Hoskin et al. (1986b), the air valves were used to suppress the column velocity under periodic and irregular waves to match the phase of incident wave force and column velocity. The approach to phase control was applied in Hotta et al. (1986c) to an OWC wave tank. This research also included the air turbine (Wells turbine), model. A cylindrical OWC power buoy was simulated in Oltedal (1986g) using phase control where the air valves were used to rectify airflow and improve the energy captured. In Jefferys and Whittaker (1986d), an OWC plant latching control was suggested to optimize output power by stopping airflow during a part of the incident wave cycle. The phase control was suggested in Sarment et al. (1987) by changing the Wells turbine blade angle. This research was further conducted on test rig experiments (Gato and Falcáo 1989). A similar strategy was presented in Sarmento et al. (1990) for phase control of the OWC plant. In Korde (1991b), a passive OWC phase control was suggested to maximize the extraction of wave energy. The controller was built on an analog control circuit and periodic wave conditions were tested. The energy absorption was increased by changing the relative phase difference between pressure and velocity. In Korde (1999d), a time history of past velocities measurement for reactive phase control of OWC was used to estimate future velocity. In Falcáo and Justino (1999b), the airflow control was suggested for OWC plant fitted with a Wells turbine using two forms of air valves: (i) bypass valve and (ii) throttle valve. The Wells turbine suffers from the stagnation problem because of excess airflow over the turbine conduit. The air valves were therefore used to discharge the surplus air via valves to prevent stalling of the Wells turbine. In Justino and Falcáo (1999c), the rotational speed controller was suggested for an OWC plant with a variable speed Wells turbine to extract maximum energy from incident waves. Three different approaches were proposed: (i) keeping the electric torque constant over intervals of a few wave periods; (ii) adjusting the rotor speed around the reference speed (the reference must be in accordance with sea states); (iii) maintaining the reference to the torque in proportion to the squared value of the rotor speed. The latter was proposed rather than the first two approaches for better results. For OWC plants using a non-linear wave tank, a self-adaptive feedback-feed forward control was suggested in Chatry et al. (1999a). It was intended that the airflow speed in the OWC chamber should be controlled. Air pressure and its derivative as feedback elements and airflow rate as a feed-forward element were the inputs to the control unit. The controller output was the airflow rate within the OWC chamber. A review of applications for control systems at OWC plants has been reported in Korde (2000d). Much of the innovations in wave energy conversion devices were restricted to ideas, designs and laboratory tests prior to this review. At that moment, most control studies (Evans and Falcão 1986a; Hoskin et al. 1986b; Hotta et al. 1986c; Oltedal 1986g; Jefferys and Whittaker 1986d; Sarment et al. 1987; Gato and Falcáo

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1 Introduction

1989; Sarmento et al. 1990; Korde 1991b, 1999d, 2000d; Falcáo and Justino 1999b; Justino and Falcáo 1999c; Chatry et al. 1999a) did not recognize the dynamics of turbo-generators and their control problems. Research works undertaken in Falcáo and Justino (1999b) and Justino and Falcáo (1999c) were extended with different goals in Falcáo and Rodrigues (2002d), Falcáo (2002b), Falcáo (2002c), Falcáo et al. (2003a), Justino (2006c). The efficiency of a Wells turbine-mounted OWC was analysed in Falcáo and Rodrigues (2002d). Sea states were characterized by their spectra of power in which sea wave height was assumed to be a Gaussian probability density function. Using numerical illustrations, it has been shown that the dimensions of the turbine and the speed of the rotor can be adjusted for maximum energy generation. Control of turbine flow and the controllable rotational speed was also taken into account. In Falcáo (2002b), an optimal algorithm for the rotational speed control was proposed to regulate the maximum extraction of power at the OWC plant. It was focused on linear control theory, as explained in Falcáo and Rodrigues (2002d), of a stochastic process. A phase-controlled absorption by the linear array of OWC units of ocean-wave energy was suggested in Falcáo (2002c). In Sarmento et al. (1990), an approach for controlling bypass air valves was developed to restrict excess flow. In Justino (2006c), the maximum latching control law based on a Pontryagin principle was proposed for driving the throttle valve of the OWC plant to achieve maximum energy extraction. In Jayashankar et al. (2000c), the OWC was likely researched for the first time with a DFIG and a Wells turbine. To change the rotor slip according to changes in chamber pressure, an external rotor resistance is attached to the rotor part of the DFIG. This research focused primarily on enhancing the efficiency of the OWC plant in Trivandrum, India, Ravindran and Koola (1991d), Mala et al. (2009f). The problem of Wells turbine stalling was solved by regulating the rotor speed to reduce the coefficient of turbine flow below certain threshold values. The two resistance switches and continuous resistance switching strategies have been proposed for rotational speed control. The control block was based on a look-up-table (LUT) table with the input of the chamber pressure and the output of the external rotor resistance. The evolved variants of Jayashankar et al. (2000c) can be found in Rao and Murthy (2005d), Muthukumar et al. (2005b), Murthy and Rao (2005a) depending on various control provisions for power electronic converters. However, these findings have completely side-stepped the mathematical analysis of control systems. The research performed in Jayashankar et al. (2000c) was also used to resolve the control problems of the Mutriku harbour OWC plant, Basque Country, Spain (TorreEnciso et al. 2009g). The methods for changing the external rotor resistance were suggested in Amundarain et al. (2009b, d), Alberdi et al. (2009a), Amundarain et al. (2009c). The primary purpose of this work was to avoid the Wells turbine’s stalling behaviour. In modelling and control method aspects, Amundarain et al. (2009b, 2009c), Alberdi et al. (2009a) studies were quite close to Jayashankar et al. (2000c) while (Amundarain et al. 2009c) suggested rotational speed control using neural network (NN). Based on chamber pressure and internal rotor resistance as the input and output data, the NN method was applied to train the LUT.

1.2 Historical Development of OWC Control Systems

7

During the latest stage of OWC plant research, the primary attention was on control of the doubly-fed induction generator (DFIG). In Amundarain et al. (2010c), an OWC with a wells Turbine-DFIG module was suggested to regulate airflows and rotational speed control strategies. For airflow control, a proportional-integralderivative controller (PID) was proposed. The parameters of PID were adjusted using the standard tuning technique of Ziegler-Nichols (ZN). A PI control system was implemented again for rotational speed control. The control inputs acquired from the PI controller were given to the pulse-width-modulation (PWM) device that supplied the DFIG rotor side converter with gate pulses. The amount of flux which in turn regulated the speed of the rotor was controlled. However, for acquiring the optimum reference point, no definite approach was developed. The LUT was designed to select the target speed between chamber pressure and reference speed. In Amundarain et al. (2010d), there was a more detailed analysis of Amundarain et al. (2010c). Studies in Amundarain et al. (2010c, d) have been expanded further to laboratory testing in Amundarain et al. (2011c). Rotational speed control strategies focusing on NN were designed in Alberdi et al. (2010a) and Amundarain et al. (2011d). Chamber pressure and reference speed were used to prepare the input–output information to acquire the maximized power. The NN-based strategy substituted the Amundarain et al. (2010c, 2011c), standard LUT, but the controller was still the PI. The strategy relying on NN includes intense training. Also, if not correctly configured, the PI control system for DFIG’s rotational speed control may contribute to instability. How the parameters of the PI were chosen was not indicated. By suggesting a sliding mode control (SMC) system for DFIG rotational speed control in Garrido et al. (2012b, 2013b), Barambones and Durana (2015a), this issue has been fixed to some point. The SMC law was formed on the Lyapunov stability principle that guarantees the asymptotic stability to a closed-loop system. The SMC scheme works on the sliding surface principle where the control signal toggles continuously between two levels. This concept is also referred to as a chattering effect. While the SMC provides the closed-loop system with stability, it is not suitable due to the chattering effect that can compromise system performance. Airflow control and rotational speed control strategies have also been widened in Alberdi et al. (2010b, 2011a, b, 2012a) to grid side controls. These studies were basically intended at testing the fault-ride through capabilities of DFIG driven by OWC turbine. OWC plant behaviour fitted with Wells turbine-DFIG scheme was examined under faulty circumstances and airflow control and rotational speed control systems. Some techniques of fault security have also been suggested. In Garrido et al. (2013c), the system states for the reduction of the size of the measurement were implemented as an observer-oriented control. The PI controller was still the rotational speed regulator of DFIG. A sensor-free control strategy was again implemented in Garrido et al. (2016e). In this study, the issue of control has been split into small and elevated climatic regions. For poor climatic circumstances, the aim was to harness as much energy from ocean waves as appropriate but to reduce the use of energy by implementing airflow control in elevated climatic circumstances. For airflow command via the throttle valves, a PID controller was used. The OWC design was built in Garrido et al. (2016f) using a tracking function curve to optimize

8

1 Introduction

the energy of the ocean wave. To evaluate the plant efficiency, the real-time data from Mutriku OWC (Torre-Enciso et al. 2009g) was selected. Rotational speed optimization for the MPPT of OWC installation integrated with a Wells turbine-DFIG was suggested as a follow-up to previous work (Lekube et al. 2016k). An analysis was performed in this study between the Wells turbine flow coefficient and rotor speed to obtain the optimum rotor speed points for different climatic conditions at the ocean. In order to realize MPPT, these optimum points were then used to regulate rotor speed. An optimal speed controller based on the fuzzy-backstepping method was designed in Mishra et al. (2016m). Three Lyapunov-based non-linear controllers were proposed in Mishra et al. (2016n) for OWC plant emulation, rotational speed control and DC link voltage control of DFIG’s grid side converter (GSC), respectively. Flow controller was designed in Lekube et al. (2018a) for Wells turbines for harnessing maximum wave power using OWC. An event-triggered controller for the OWC energy plant was presented in Mishra et al. (2018c) wherein the main objective was to minimize control updates when controller and plant interact with others via a communication channel. In M’zoughi et al. (2018b), a fuzzy gain scheduled and PI-type airflow controller for an OWC, which was an advanced version of the airflow controller presented earlier in Amundarain et al. (2010c, 2011c), Amundarain et al. (2010d). For more details on the control of OWC plants, please refer (Arenas et al. 2019). In addition, some previous control systems implemented for OWCs fitted with a permanent synchronous magnet (PMSG) system would be discussed (Ceballos et al. 2013a, 2015b; Samrata et al. 2015g; Ramirez et al. 2015f; Colak and Kocabas 2015c, 2016b; Henriques et al. 2016g, h, i). An approach for MPPT was formulated in Ceballos et al. (2013a) by obtaining the best possible rotor speed levels with an assessment of pneumatic power and rotor speed under various weather circumstances. By restricting the flow coefficient below the permissible range, the behaviour of the small inertia Wells turbine was optimized with these optimum values. A standalone off-grid OWC plant with a Darrieus turbine-PMSG scheme was investigated in Samrata et al. (2015g). Its goal was to develop an MPPT system for the use of green energy in Malaysia. The curve of MPPT was drawn between mechanical power and speed of the rotor. Optimum speed levels were calculated based on this curve. The PI controller was then used to regulate the speed of the rotor. An expanded variant of Ceballos et al. (2013a) was suggested in Ceballos et al. (2015b), where three control systems with Wells turbine-PMSG devices were suggested for the OWC plant. In the first strategy, two back-to-back AC/DC/AC converters for injecting smooth power into the grid included an ultra-capacitor in the DC link. In the second approach, a PI control was applied for maintaining the rotor speed constant. However, it was emphasized that this approach was only appropriate for the OWC prototype level and, from a practical point of view; the variation in the speed of the rotor according to the sea wave scenario was suggested as a necessary measure. As a result, an optimum speed control law was created in the third strategy to extract peak energy from ocean waves. The emulation of Wells turbine features in a DC motor combined with a PMSG was discussed in Ramirez et al. (2015f). It was mainly the design of an experimental laboratory set-up. This model was tested in irregular wave

1.2 Historical Development of OWC Control Systems

9

patterns. It has been suggested that this configuration of the emulator can be used for further OWC plant research. However, this research did not raise the comprehensive layout and stabilization problems of the suggested experimental configuration. A nearest-three-vector space-vector pulse-width-modulation method was designed in Colak and Kocabas (2015c) and Colak and Kocabas (2016b) to maintain DC link voltage steady and extract peak energy from ocean waves. In Henriques et al. (2016g), an OWC floating plant latching control technique was suggested to increase the Wells turbine’s power output. In Henriques et al. (2016h), the regulation of a biradial air turbine-PMSG system under elevated sea-wave weather circumstances was investigated by experiments conducted in a test facility. A receding horizon latching control approach was formulated in Henriques et al. (2016i), an expansion of Henriques et al. (2016g, h). The objective of the receding lateral control was to operate a high-speed valve to remove the surplus air supply by closing the valve at a suitable point. To achieve the required response, the ocean wave forecast was regarded as essential with a sea wave forecasting model such as receding horizontal control. Some review documents on the control of OWC plants have also been reported in previous years (Falcão and Henriques 2016d; Xie and Zuo 2013d; Hong et al. 2014c; Freeman et al. 2014b). Various ocean waves energy transformation techniques and their control practices were discussed in Xie and Zuo (2013d). It included the floating oscillating object, the OWC and the wave overtopping transformation techniques. Electrical control methods for ocean wave power converters were discussed in a comprehensive way in Hong et al. (2014c). The review of control policies for OWC plants was discussed in Freeman et al. (2014b). Some control schemes, such as frequency-domain control, latching control, time-domain control, and modern neural network design techniques, fuzzy logic and model predictive control have been evaluated. Next, an extensive analysis of OWC plants and air turbines was provided in Falcão and Henriques (2016d). This review included the overall growth of OWC plants constructed to date in separate places around the world, distinct turbines used in OWC and some associated control techniques.

1.3 Summary of the Book The primary aim of this book is to provide a detailed strategy for modelling and controller design for the OWC wave power plant. The organization of the book is as follows: Chapter 2 deals with the mathematical modelling of OWC plant. The plant consists of (1) ocean waves as input source, (2) OWC chamber, (3) turbine and (4) generator model. The modelling of each section is discussed in detail. Chapter 3 deals with the identification of control challenges of OWC plant. This is done by performing simulation on uncontrolled or open-loop OWC plant. Chapter 4 deals with the development of the OWC plant airflow control. This control approach is applied to achieve the desired power generation from OWC plant.

10

1 Introduction

Two types of airflow controllers, (1) PID controller and (2) FOPID controller, are designed using manual tuning as well as optimal tuning methods. Chapter 5 deals with the design of OWC rotational speed regulation. The goal in this section is to optimize OWC power generation. The design of three control schemes, (1) PI control, (2) backstepping control and (3) sliding mode control, are discussed. Chapter 6 summarizes the main contribution of the book and makes mention of some scopes of the work for possible future investigations.

References Alberdi M, Amundarain M, Maseda FJ, Barambones O (2009a) Stalling behaviour improvement by appropriately choosing the rotor resistance value in wave power generation plants. In: 2nd international conference on clean electrical power. Italy, pp 64–67 Alberdi M, Amundarain M, Garrido AJ, Garrido I (2010a) Neural control of OWC-based wave power generation plant. In: 3rd international conference on ocean energy. Spain, pp 1–6 Alberdi M, Amundarain M, Garrido AJ, Garrido I (2010b) Ride through of OWC-based wave power generation plant with air flow control under symmetrical voltage dips. In: 18th mediterranean conference on control and automation. Morocco, pp 1271–1277 Alberdi M, Amundarain M, Garrido AJ, Garrido I, Casquero O, Sen MD (2011a) Complementary control of oscillating water column-based wave energy conversion plants to improve the instantaneous power output. IEEE Trans Energy Convers 26(4):1021–1032 Alberdi M, Amundarain M, Garrido AJ, Garrido I, Maseda FJ (2011b) Fault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped with doubly fed induction generator and airflow control. IEEE Trans Industr Electron 58(5):1501–1517 Alberdi M, Amundarain M, Garrido AJ, Garrido I, Sainz FJ (2012a) Control of oscillating water column-based wave power generation plants for grid connection. In: 20th mediterranean conference on control and automation. Spain, pp 1485–1490 Amundarain M, Alberdi M, Garrido A, Garrido I (2009b) Control of the stalling behaviour in wave power generation plants. In: 6th international conference-workshop on compatibility and power electronics. Spain, pp 117–122 Amundarain M, Alberdi M, Garrido I, Garrido A (2009c) Wells turbine Control in wave power generation plants. In: IEEE international electric machines and drives conference. USA, pp 177– 182 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2009d) Neural control of the Wells turbinegenerator module. In: Joint 48th IEEE conference on decision and control and 28th Chinese control conference. P.R. China, pp 7315–7320 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2010c) Control strategies for OWC wave power plants. In: American control conference. USA, pp 4319–4324 Amundarain M, Alberdi M, Garrido AJ, Garrido I, Maseda J (2010d) Wave energy plants: Control strategies for avoiding the stalling behaviour in the Wells turbine. Renew Energy 35:2639–2648 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011c) Modeling and simulation of wave energy generation plants: Output power control. IEEE Trans Industr Electron 58(1):105–117 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011d) Neural rotational speed control for wave energy converters. Int J Control 84(2):293–309 Arenas AM, Garrido AJ, Rusu E, Garrido I (2019) Control strategies applied to wave energy converters: state of the art. Energies 12:3115 Bailey H, Robertson BRD, Buckham BJ (2016a) Wave-to-wire simulation of a floating oscillating water column wave energy converter. Ocean Eng 125:248–260

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Barambones O, Durana JMG (2015a) Sliding mode control for power output maximization in a wave energy systems. Energy Procedia 75:265–270 Bjarte-Larsson T, Falnes J (2006a) Laboratory experiment on heaving body with hydraulic power take-off and latching control. Ocean Eng 33:847–877 Brekken T, Batten B, Amon E (2011e) From blue to green. IEEE Control Syst Mag 31(5):18–24 Burman K, Walker A (2009e) Ocean energy technology overview. In: The U.S. department of energy and the office of energy efficiency and renewable energy, pp 1–30 Ceballos S, Rea J, Lopez I, Pou J, Robles E, O’Sullivan DL (2013a) Efficiency optimization in low inertia Wells turbine-oscillating water column devices. IEEE Trans Energy Convers 28(3):553– 564 Ceballos S, Rea J, Robles E, Lopez I, Pou J, O’Sullivan DL (2015b) Control strategies for combining local energy storage with wells turbine oscillating water column devices. Renew Energy 83:1097– 1109 Chatry G, Clément AH, Sarmento A (1999a) Simulation of a self-adaptively controlled OWC in a nonlinear numerical wave tank. In: Proceedings of the 9th international offshore and polar engineering conference. France, pp. 290–296 Clement A, McCullen P, Falcao A et al (2002a) Wave energy in Europe: current status and perspectives. Renew Sustain Energy Rev 6:405–431 Colak I, Kocabas AD (2015c) NTV-SV-PWM controlled three-level converter for ocean wave energy conversion. In: 56th international scientific conference on power and electrical engineering of riga technical university. Latvia, pp 1–5 Colak I, Kocabas DA (2016b) DC link balancing of space vector modulation controlled three-level converter for ocean wave energy conversion. In: 57th international scientific conference on power and electrical engineering of riga technical university. Latvia, pp 1–7 Das B, Pal BC (2006b) Voltage control performance of AWS connected for grid operation. IEEE Trans Energy Convers 21(2):353–361 Delmonte N, Barater D, Giuliani F (2016c) Review of oscillating water column converters. IEEE Trans Ind Appl 52(2):1698–1710 Evans DV, Falcão AFO (1986a) Hydrodynamics of ocean wave-energy utilization. In: IUTAM symposium Lisbon/Portugal. Springer, Berlin Falcão AFO (2000a) The shoreline OWC wave power plant at the Azores. In: Proceedings of 4th European wave energy conference. Aalborg, Denmark, pp 42–47 Falcáo AFO (2002b) Control of an oscillating-water-column wave power plant for maximum energy production. Appl Ocean Res 24:73–82 Falcáo AFO (2002c) Wave-power absorption by a periodic linear array of oscillating water columns. Ocean Eng 29:1163–1186 Falcão AFO (2010e) Wave energy utilization: A review of the technologies. Renew Sustain Energy Rev 14:899–918 Falcão AFO, Henriques JCC (2016d) Oscillating-water-column wave energy converters and air turbines: A review. Renew Energy 85:1391–1424 Falcáo AFO, Justino PAP (1999b) OWC wave energy devices with air flow control. Ocean Eng 26:1275–1295 Falcáo AFO, Rodrigues RJA (2002d) Stochastic modelling of OWC wave power plant performance. Appl Ocean Res 24:59–71 Falcáo AFO, Vieira LC, Justino PAP, André JMCS (2003a) By-pass air-valve control of an OWC wave power plant. J Offshore Mech Arct Eng 125:205–210 Falcão AFO, Henriques JCC, Gato LMC et al (2014a) Air turbine choice and optimization for floating oscillating-water-column wave energy converter. Ocean Eng 75:148–156 Falnes J (2007a) A review of wave-energy extraction. Marine Struct 20:185–201 Freeman K, Dai M, Sutton R (2014b) Control strategies for oscillating water column wave energy converters. Underwater Technol 32(1):3–13 Garrido AJ, Garrido I, Amundarain M, Alberdi M, Sen MD (2012b) Sliding-mode control of wave power generation plants. IEEE Trans Ind Appl 48(6):2371–2381

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Garrido AJ, Garrido I, Alberdi M, Amundarain M, Barambones O, Romero JA (2013b) Robust control of oscillating water column (OWC) devices: power generation improvement. In: OCEANS. San Diego, pp 1–4 Garrido AJ, Garrido I, Alberdi M, Amundarain M, Sen MD (2013c) Sensorless control for an oscillating water column plant. In: World congress on sustainable technologies. United Kingdom, pp 1−4 Garrido AJ, Garrido I, Lekube J, Otaola E, Carrascal E (2016e) Oscillating water column control and monitoring. In: OCEANS. USA, pp 1–6 Garrido AJ, Garrido I, Lekube J, Sen MD (2016f) OWC on-shore wave power plants modeling and simulation. In: IEEE international conference on emerging technologies and innovative business practices for the transformation of societies. Mauritius, pp 43–49 Gato LMC, Falcáo AFO (1989) Aerodynamics of the wells turbine: Control by swinging rotorblades. Int J Mech Sci 31(6):425–434 Gato LMC, Eça LRC, Falcão AFO (1991a) Performance of the Wells turbine with variable pitch rotor blades. J Energy Res Technol 113:141–146 Gato LMC, Warfield V, Thakker A (1996) Performance of a high-solidity Wells turbine for an OWC wave power plant. J Energy Res Technol 118:263–268 Gunn K, Williams CS (2012c) Quantifying the global wave power resource. Renew Energy 44:296– 304 Heath T, Whittaker TJT, Boake CB (2000b) The design, construction and operation of the LIMPET wave energy converter (Islay, Scotland). In: Proceedings of 4th European wave energy conference. Aalborg, Denmark, pp 49–55 Henriques JCC, Gato LMC, Falcão AFO, Robles E, Faÿ FX (2016g) Latching control of a floating oscillating-water-column wave energy converter. Renew Energy 90:229–241 Henriques JCC, Gomes RPF, Gato LMC, Falcão AFO, Robles E, Ceballos S (2016h) Testing and control of a power take-off system for an oscillating water- column wave energy converter. Renew Energy 85:714–724 Henriques JCC, Gato LMC, Lemos JM, Gomes RPF, Falcão AFO (2016i) Peak-power control of a grid-integrated oscillating water column wave energy converter. Energy 109:378–390 Hong Y, Waters R, Boström C et al (2014c) Review on electrical control strategies for wave energy converting systems. Renew Sustain Energy Rev 31:329–342 Hoskin RE, Count BM, Nichols NK, Nicol DAC (1986b) Phase control for the oscillating water column. In: Hydrodynamics of ocean wave-energy utilization, pp 257–268 Hotta H, Miyazaki T, Washio Y (1986c) Increase in absorbed wave energy by the phase control for air flow on OWC wave power device. In: Hydrodynamics of ocean wave-energy utilization, pp 293–302 Jayashankar V, Udayakumar K, Karthikeyan B, Manivannan K, Venkatraman N, Rangaprasad S (2000c) Maximizing power output from a wave energy plan. In: IEEE power engineering society winter meeting, vol 3. Singapore, pp. 1796–1801 Jefferys R, Whittaker T (1986d) Latching control of an oscillating water column device with air compressibility. In: Hydrodynamics of ocean wave-energy utilization, pp 281–291 Justino PAP (2006c) Pontryagin maximum principle and control of a OWC power plant. In: 25th international conference on offshore mechanics and arctic engineering. Germany, pp 1–9 Justino PAP, Falcáo AFO (1999c) Rotational speed control of an OWC wave power plant. J Offshore Mech Arct Eng 121:65–70 Kelly JF, Wright WMD, Sheng W (2016j) Implementation and verification of a wave-to-wire model of an oscillating water column with impulse turbine. IEEE Trans Sustain Energy 7(2):546–553 Korde UA (1999d) Efficient primary energy conversion in irregular waves. Ocean Eng 26:625–651 Korde UA (2000d) Control system applications in wave energy conversion. In: MTS/IEEE conference and exhibition oceans. USA, pp 1817–1824 Korde UA (1991b) Development of a reactive control apparatus for a fixed two-dimensional oscillating water column wave energy device. Ocean Eng 18(5):465–483

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Kumar VS, Anoop TR (2015d) Wave energy resource assessment for the Indian shelf seas. Renew Energy 76:212–219 Lekube J, Garrido AJ, Garrido I (2016k) Rotational speed optimization in oscillating water column wave power plants based on maximum power point tracking. IEEE Trans Autom Sci Eng 99:1–11 Lekube J, Garrido AJ, Garrido I, Otaola E, Maseda J (2018a) Flow control in wells turbines for harnessing maximum wave power. Sensors 18:535 Liu Z, Cui Y, Kim KW, Shi HD (2016l) Numerical study on a modified impulse turbine for OWC wave energy conversion. Ocean Eng 111:533–542 M’zoughi F, Bouall‘egue S, Garrido AJ, Garrido I, Ayadi M (2018b) Fuzzy gain scheduled pi-based airflow control of an oscillating water column in wave power generation plants. IEEE J. Oceanic Eng 44(4):1058–1076 Mala K, Badrinath SN, Chidanand S, Kailash G, Jayashankar V (2009f) Analysis of power modules in the Indian wave energy plant. In: Proceedings of annual IEEE india conference (INDICON), pp 95–98 Masuda Y, McCormick ME (1986e) Experiences in pneumatic wave energy conversion in Japan. In: Utilization of ocean waves: wave to energy conversion. American Society of Civil Engineering, New York, pp 1–33 Masuda Y (1986f) An experience of wave power generator through tests and improvement. In: Hydrodynamics of ocean wave-energy utilization. Springer, Berlin, pp 445-452 Mishra SK, Purwar S, Kishor N (2016m) An optimal and non-linear speed control of oscillating water column wave energy plant with wells turbine and DFIG. Int J Renew Energy Res 6(3) Mishra SK, Purwar S, Kishor N (2016n) Design of non-linear controller for ocean wave energy plant. Control Eng Practice 56(3):111–122 Mishra SK, Purwar S, Kishor N (2018c) Event-triggered nonlinear control of owc ocean wave energy plant. IEEE Trans Sustain Energy 9(4):1750–1760 Murthy BK, Rao SS (2005a) Rotor side control of Wells turbine driven variable speed constant frequency induction generator. Electr Power Components Syst 33:587–596 Muthukumar S, Desai R, Jayashankar V, Santhakumar S, Setoguchi T (2005b) Design of a standalone wave energy plant. In: Proceedings of the 15th international offshore and polar engineering conference. South Korea, pp 497–502 Ohneda H, Igarashi S, Shinbo O et al (1991c) Construction procedure of a wave power extracting caisson breakwater. In: Proceedings of 3rd symposium on ocean energy utilization. Tokyo, pp 171–179 Oltedal G (1986g) Simulation of a pneumatic wave-power buoy with phase control. In: Hydrodynamics of ocean wave-energy utilization, pp 303–313 Parkinson SC, Dragoon K, Reikard G et al (2015e) Integrating ocean wave energy at large-scales: A study of the US Pacific Northwest. Renew Energy 76:551–559 Polinder H, Mecrow BC, Jack AG, Dickinson PG, Mueller MA (2005c) Conventional and TFPM linear generators for direct-drive wave energy conversion. IEEE Trans Energy Convers 20(2):260– 267 Portillo JCC et al (2020) Wave energy converter physical model design and testing: The case of floating oscillating-water-columns. Appl Energy 278 Raghunathan S (1995) The Wells air turbine for wave energy conversion. Progressn Aerosp Sci 31:335–386 Ramirez D, Bartolome JP, Martinez S, Herrero LC, Blanco M (2015f) Emulation of an OWC ocean energy plant with PMSG and irregular wave model. IEEE Trans Sustain Energy 6(4):1515–1523 Rao SS, Murthy BK (2005d) Control of induction generator in a Wells Turbine based wave energy system. In: IEEE International Conference on Power Electronics and Drives Systems, vol 2. Malaysia, pp 1590–1594 Ravindran M, Koola PM (1991d) Energy from sea waves-the Indian wave energy program. Curr Sci 60:676–680 Rodrigues L (2008) Wave power conversion systems for electrical energy production. In: International conference on renewable energies and power quality (iCREPQ’08). Santander

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Rusu E, Onea F (2016o) Estimation of the wave energy conversion efficiency in the Atlantic Ocean close to the European islands. Renew Energy 85:687–703 Samrata NH, Ahmada N, Choudhurya IA, Tahab Z (2015g) An off-grid stand-alone wave energy supply system with maximum power extraction scheme for green energy utilization in Malaysian Island. Desalination Water Treatment 57(1):58–74 Sarmento A, Gato LMC, Falcáo AFO (1990) Turbine-controlled wave energy absorption by oscillating water column devices. Ocean Eng 17(5):481–497 Sarment A, Gato LMC, Falcáo AFO (1987) Wave-energy absorption by an OWC device with bladepitch-controlled air-turbine. In: Proceedings of 6th international offshore mechanics and arctic engineering symposium, vol 2, pp 465–473 Setoguchi T, Santhakumar S, Takao M et al (2003b) A modified Wells turbine for wave energy conversion. Renew Energy 28:79–91 Shehata AS, Saqr KM, Xiao Q et al (2016p) Performance analysis of wells turbine blades using the entropy generation minimization method. Renew Energy 86:1123–1133 Suzuki M, Arakawa C, Takahashi S (2004) Performance of a wave power generating system installed in breakwater at Sakata port in Japan. In: Proceedings of 14th international offshore polar engineering conference. Toulon, France Torre-Enciso Y, Ortubia I, Aguileta LIL, MarquesJ (2009g) Mutriku wave power plant: from the thinking out to the reality. In: Proceedings of 8th European wave tidal energy conference. Uppsala, Sweden, pp 319–329 Torres FR, Teixeira PRF, Didier E (2016q) Study of the turbine power output of an oscillating water column device by using a hydrodynamic – Aerodynamic coupled model. Ocean Eng 125:147–154 Valério D, Beirão P, Costa JS (2007b) Optimisation of wave energy extraction with the Archimedes wave swing. Ocean Eng 34:2330–2344 Whittaker TJT, McIlwaine SJ, Raghunathan S (1993) A review of the Islay shoreline wave power station. In: Proceedings of 1st European wave energy symposium. Edinburgh, pp 283–286 Xie J, Zuo L (2013d) Ocean wave energy converters and control methodologies. In: Proceedings of the dynamic systems and control conference. USA, pp 1–10 Zhang D, Li W, Lin Y (2009h) Wave energy in China: Current status and perspectives. Renew Energy 34:2089–2092

Chapter 2

Overview of OWC Mathematical Model

The OWC system is usually constructed on the shoreline of the ocean, as shown in Fig. 2.1 (Mishra et al. 2016d). The OWC consists of four walls. It is open at the bottom where the ocean waves hit. The OWC chamber is partly watered, while the top part of the column is filled with air. The Wells turbine is installed in a circular cabinet at the top of the chamber and is driven by a DFIG connected to it. Based on rising and falling levels of seawater, the air in the chamber is compressed and decompressed. As a consequence, the oscillatory movement of the water causes the bidirectional airflow. Notwithstanding the alternating path of the airflow, the Wells turbine is constructed in such a manner that its rotation is always one-way. Next, mathematical models of ocean waves, OWC chamber, Wells turbine and DFIG are described.

2.1 Ocean Wave Modelling Ocean waves are created by winds or storms or by regional winds reaching the coastline of the ocean. The wind produces swells of water that touch the shoreline in the shape of waves. Modelling ocean waves has been a difficult job, as these waves are extremely uneven in nature. A number of ocean wave concepts have been suggested to explore the features of ocean waves (Young 1999b; Bhattacharyya and McCormick 2003a; Pierson and Moskowitz 1964; Hasselmann et al. 1973; Torsethaugen 1996; McCormick 1999a; Brodtkorb et al. 2000). Some theories are focused on the linear design of ocean waves (Young 1999b; Bhattacharyya and McCormick 2003a), while many wave models are focused on the stochastic model of ocean waves (Pierson and Moskowitz 1964; Hasselmann et al. 1973; Torsethaugen 1996; McCormick 1999a; Brodtkorb et al. 2000). The simple linear shape of the ocean wave is shown in Fig. 2.2. The peak of the wave is the crest, while the bottom of the wave is considered as a trough. The wave height (h) is the difference between the crest and the trough. The range between two © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 S. K. Mishra et al., OWC-Based Ocean Wave Energy Plants, Energy Systems in Electrical Engineering, https://doi.org/10.1007/978-981-15-9849-4_2

15

16

Fig. 2.1 Schematic representation of OWC plant

Fig. 2.2 Ocean wave

2 Overview of OWC Mathematical Model

2.1 Ocean Wave Modelling

17

consecutive troughs or crests shall be the ocean wave wavelength (λ), whereas the sea depth (d) is called the distance between the ocean bottom and the still water (SWL) level. The wave energy per unit length of the crust is determined by Young (1999b): E=

ρw gh 2 λ 8

(2.1)

The wave energy can therefore be assigned per unit area (also known as specific wave energy) as: E=

E ρw gh 2 = λ 8

(2.2)

where, ρ w is the water density (Kg/m3 ), g is the gravitational constant (9.81 m/s2 ). The propagation speed or celerity of a wave is defined as: C=

λ T

(2.3)

where, T is the wave period (s). The rate of propagation of wave energy is directly dependent on the velocity of the wave group and is given as: C g = nC (m/s)

(2.4)

where, C g is the celerity (wavefront velocity) (m/s), n is the constant determined by:   4π d/λ 1 1+ n= 2 sinh(4π d/λ)

(2.5)

The wave resources are generally defined by the wave power stored in per meter of the wavefront. Therefore, the wavefront power can be described as: Pwavefront = nC E = C g E

(2.6)

After substituting the value of n in Eq. (2.6), we obtain wavefront power as: Pwavefront

  4π d/λ ρw gh 2 λ 1+ (W/m) = 16T sinh(4π d/λ)

(2.7)

18

2 Overview of OWC Mathematical Model

2.2 OWC Chamber Modelling Upon hitting the column, the incoming waves produce alternating airflow through the turbine duct. If the wave height is presumed to be the same outside and inside the chamber, the following expression will give the airflow velocity (Ramirez et al. 2015b):  Vx =

AOW C Aduct



∂h(t) ∂t

(2.8)

where, V x is the air velocity (m/s), AOWC is the chamber cross-sectional area (m2 ), Aduct is the duct cross-sectional area (m2 ) and h(t) is the wave amplitude (m) inside the OWC. The air losses within the column are ignored. The expression for differential OWC chamber pressure (Pa) across the turbine duct is given as: dP =

 Ca kt  2 V + (r ωr )2 Aduct x

(2.9)

Also, the input wave power available for airflow at the turbine duct is given as: Pin = (d P + ρVx2 /2)Vx Aduct

(2.10)

The OWC chamber pressure is considered as the input to the Well turbine. The regular and irregular form of OWC chamber pressures has been considered in this book for the study of OWC control. Next, the MATLAB/SIMULINK model of OWC chamber pressure is shown in Fig. 2.3. The manual switch is used to switch between regular and irregular pressure waveforms.

2.3 Wells Turbine Modelling Dr. Alan Arthur Wells invented the Wells turbine at Queen’s University in Belfast, UK in 1976 (Raghunathan 1995). Its input is the airflow inside the OWC chamber, which creates a drop in oscillatory pressure across the turbine rotor, as shown in Fig. 2.4. The Wells turbine has been designed to transform bidirectional airflow into a unidirectional rotating motion that drives the generator (Amundarain et al. 2009b, c, d, 2010b, c, d, 2011a, b, c, d; Alberdi et al. 2009a, 2010a, 2012a; Garrido et al. 2012b, 2013a, b, 2016a, b; Barambones and Durana 2015a; Lekube et al. 2016c, 2018a; Mishra et al. 2016e, 2018c; M’zoughi et al. 2018b; Arenas et al. 2019). The mathematical equation of the Wells turbine torque (T t ) is given as Amundarain et al. (2010d):

2.3 Wells Turbine Modelling

19

Fig. 2.3 MATLAB/SIMULINK model of OWC chamber pressure

  Tt = Ct kt r Vx2 + (r ωr )2

(2.11)

where, k t is the turbine constant (kg/m) and given as: kt = 0.5ρa bt n t lt

(2.12)

The Wells turbine flow coefficient is expressed as: φ=

Vx r ωr

(2.13)

Next, Wells turbine output power is given by the expression: Pt = Tt ωr

(2.14)

Finally, the Wells turbine efficiency is represented as:   Tt ωr 1 Ct = ηt = d P Qx φ Ca

(2.15)

where, Qx is the air flow rate (m3 /s) and given by the expression: Q x = Vx Aduct

(2.16)

20

2 Overview of OWC Mathematical Model

Fig. 2.4 Schematic representation of Wells turbine

where, C a is the power coefficient, C t is the torque coefficient, T t is turbine-generated torque (Nm), φ is the flow coefficient, ωr is the turbine rotor speed (rad/s), ηt is the efficiency of the turbine, r is the mean radius (m), lt is the blade chord length, bt is the blade height, nt is the number of blades, ρ a is the air density (Kg/m3 ). Equation (2.14) suggests that the performance of the Wells turbine depends on the coefficients of power, torque and flow. Variation of the coefficient of power and the coefficient of torque against the flow coefficient for the typical Wells turbine is shown in Fig. 2.5. The coefficient of flow is directly proportional to the velocity of the airflow in Eq. (2.11). As the velocity of airflow increases, the flow coefficient also increases, resulting in higher torque coefficient (C t ). This rise, however, is limited to a critical flow coefficient of 0.3 (Amundarain et al. 2010d), which is seen in Fig. 2.5b. The turbine efficiency subsequently drops significantly due to the stalling phenomenon. The Wells turbine performance study will be addressed in Chap. 3.

2.3 Wells Turbine Modelling

21

(a) Power coefficient versus flow coefficient

(b) Torque coefficient versus flow coefficient Fig. 2.5 Wells turbine characteristics (Falcáo et al. 2003b)

The MATLAB/SIMULINK diagram of Wells turbine is shown in Fig. 2.6. There are three inputs exist as differential pressure, rotor speed and control input to manipulate differential pressure at turbine duct. The output variables are: turbine flow coefficient, turbine torque and its mean value, turbine power and its mean value, input power available at turbine duct and its mean value. The nonlinear characteristics of Wells turbine (in Fig. 2.5) have been designed using truth tables.

Fig. 2.6 MATLAB/SIMULINK diagram of Wells Turbine

22 2 Overview of OWC Mathematical Model

2.4 DFIG Modelling

23

2.4 DFIG Modelling The dq equivalent dynamic model of the DFIG has been considered (Amundarain et al. 2010d; Bose 2002; Wilamowski and Irwin 2011e). The mathematical equations of the stator and rotor voltages for d and q-axis are respectively given as: dψds dψ Rs L m Rs L m Rs L r Rs L r =− ψds + ωe ψqs + ψdr + v _ ds ds = − ψds + ωe ψqs + ψdr + vds dt K K dt K K

(2.17)

dψqs Rs L r Rs L m = −ωe ψds − ψqs + + ψqr + vqs dt K K

(2.18)

Rr L m dψdr Rr L s = ψds − ψdr − (ωr − ωe )ψqr + vdr dt K K

(2.19)

dψqr Rr L m = ψqs + (ωr − ωe )ψdr + vqr dt K

(2.20)

where, K = L s L r − L 2m . ψds , ψqs , ψdr and ψqr are stator and rotor dq flux quantities. Rs and Rr are stator and rotor resistances whereas L s , L r and L m are the stator, rotor and mutual inductances respectively. The ωe is the stator supply frequency while vds , vqs , vdr and vqr denotes the stator and rotor dq voltages. The flux states ψ ds , ψ qs , ψ dr and ψ qr are subjected to initial conditions ψ ds0 , ψ qs0 , ψ dr0 and ψ qr0 respectively. The electromagnetic torque and output power expressions are:  Te = −M ψqs ψdr − ψds ψqr

(2.21)

Pg = Te ωr

(2.22)

   where, M = − 23 2p LKm . p is number of pole of DFIG. The relationship between the different currents and the DFIG flux linkages is defined by: ⎫ ψqs = L s i qs + L m i qr ; ψds = L s i ds + L m i dr ⎬ ψqr = L r i qr + L m i qs ; ψdr = L r i dr + L m i ds ⎭ L s = L ls + L m ; L r = L lr + L m

(2.23)

where, iqs , and iqr are the q-axis stator and rotor currents (A); ids , and idr are the d-axis stator and rotor currents (A). Next, the MATLAB/SIMULINK diagram of DFIG is shown in Fig. 2.7. Design of DFIG has three stages: rotor and stator flux calculation, rotor and stator currents, and power and torque calculation. The input variables are stator and rotor voltages

Fig. 2.7 MATLAB Simulink diagram of DFIG

24 2 Overview of OWC Mathematical Model

2.4 DFIG Modelling

25

Fig. 2.8 MATLAB/SIMULINK diagram of Wells Turbine-DFIG Coupling

whereas output variables are DFIG torque, power generated, rotor and stator flux, and stator and rotor currents.

2.5 Wells Turbine-DFIG Coupling The coupling relation between the Wells turbine-DFIG is given by J

dωr = Tt − Te − Fωr dt

(2.24)

where, J is the moment of inertia of turbo-generator system (kg m2 ) and F is the friction constant (kg m2 s−1 ). The MATLAB/SIMULINK diagram for Wells turbine-DFIG coupling is presented in Fig. 2.8 which is comprised regarding to Eq. (2.24).

References Alberdi M, Amundarain M, Maseda FJ, Barambones O (2009a) Stalling behaviour improvement by appropriately choosing the rotor resistance value in wave power generation plants. In: 2nd international conference on clean electrical power. Italy, pp 64–67 Alberdi M, Amundarain M, Garrido AJ, Garrido I (2010a) Neural control of OWC-based wave power generation plant. In: 3rd international conference on ocean energy. Spain, pp 1–6 Alberdi M, Amundarain M, Garrido AJ, Garrido I (2010b) Ride through of OWC-based wave power generation plant with air flow control under symmetrical voltage dips. In: 18th mediterranean conference on control and automation. Morocco, pp 1271–1277 Alberdi M, Amundarain M, Garrido AJ, Garrido I, Casquero O, Sen MD (2011a) Complementary control of oscillating water column-based wave energy conversion plants to improve the instantaneous power output. IEEE Trans Energy Convers 26(4):1021–1032

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2 Overview of OWC Mathematical Model

Alberdi M, Amundarain M, Garrido AJ, Garrido I, Maseda FJ (2011b) Fault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped with doubly fed induction generator and airflow control. IEEE Trans Industr Electron 58(5):1501–1517 Alberdi M, Amundarain M, Garrido AJ, Garrido I, Sainz FJ (2012a) Control of oscillating water column-based wave power generation plants for grid connection. In: 20th mediterranean conference on control and automation. Spain, pp 1485–1490 Amundarain M, Alberdi M, Garrido A, Garrido I (2009b) Control of the stalling behaviour in wave power generation plants. In: 6th international conference-workshop on compatibility and power electronics. Spain, pp 117–122 Amundarain M, Alberdi M, Garrido I, Garrido A (2009c) Wells turbine control in wave power generation plants. In: IEEE international electric machines and drives conference. USA, pp 177– 182 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2009d) Neural control of the Wells turbinegenerator module. In: Joint 48th IEEE conference on decision and control and 28th chinese control conference. P.R. China, pp 7315–7320 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2010c) Control strategies for OWC wave power plants. In: American Control conference. USA, pp 4319–4324 Amundarain M, Alberdi M, Garrido AJ, Garrido I, Maseda J (2010d) Wave energy plants: Control strategies for avoiding the stalling behaviour in the Wells turbine. Renew Energy 35:2639–2648 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011c) Modeling and simulation of wave energy generation plants: Output power control. IEEE Trans Industr Electron 58(1):105–117 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011d) Neural rotational speed control for wave energy converters. Int J Control 84(2):293–309 Arenas AM, Garrido AJ, Rusu E, Garrido I (2019) Control strategies applied to wave energy converters: state of the art. Energies 12:3115 Barambones O, Durana JMG (2015a) Sliding mode control for power output maximization in a wave energy systems. Energy Procedia 75:265–270 Bhattacharyya R, McCormick ME (2003a) Wave energy conversion. Ocean Eng 6(1):1–187 Bose BK (2002) Modern power electronics and AC drives. Prentice Hall Brodtkorb PA, Lindgren G, Rychlik I et al (2000) WAFO-a Matlab toolbox for analysis of random waves and loads. In: The 10th international offshore and polar engineering conference. USA Falcáo AFO, Vieira LC, Justino PAP, André JMCS (2003b) By-pass air-valve control of an OWC wave power plant. J Offshore Mech Arct Eng 125:205–210 Garrido I, Garrido AJ, Alberdi M, Amundarain M, Sen MD (2013a) Sensorless control for an oscillating water column plant. United Kingdom, World Congress on Sustainable Technologies, pp 1–4 Garrido AJ, Garrido I, Amundarain M, Alberdi M, Sen MD (2012b) Sliding-mode control of wave power generation plants. IEEE Trans Ind Appl 48(6):2371–2381 Garrido AJ, Garrido I, Alberdi M, Amundarain M, Barambones O, Romero JA (2013b) Robust control of oscillating water column (OWC) devices: Power generation improvement. San Diego, Oceans, pp 1–4 Garrido I, Garrido AJ, Lekube J, Otaola E, Carrascal E (2016a) Oscillating water column control and monitoring. Oceans, USA, pp 1–6 Garrido AJ, Garrido I, Lekube J, Sen MD (2016b) OWC on-shore wave power plants modeling and simulation. In: IEEE international conference on emerging technologies and innovative business practices for the transformation of societies. Mauritius, pp 43–49 Hasselmann K, Bernett TP, Bouws E et al (1973) Measurements of wind-wave growth and swell decay during the joint North Sea Wave Project (JONSWAP). Deutschen Hydrografischen Zeitschrift 12:31–55 Lekube J, Garrido AJ, GarridoI I (2016c) Rotational speed optimization in oscillating water column wave power plants based on maximum power point tracking. IEEE Trans Autom Sci Eng (99):1– 11

References

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Lekube J, Garrido AJ, Garrido I, Otaola E, Maseda J (2018a) Flow control in wells turbines for harnessing maximum wave power. Sensors 18:535 M’zoughi F, Bouall‘egue S, Garrido AJ, Garrido I, Ayadi M (2018b) Fuzzy gain scheduled pi-based airflow control of an oscillating water column in wave power generation plants. IEEE J Oceanic Eng 44(4):1058–1076 McCormick ME (1999a) Application of the generic spectral formula to fetch limited seas. Marine Technol Soc J 33(3):27–32 Mishra SK, Purwar S, Kishor N (2016d) Design of non-linear controller for ocean wave energy plant. Control Eng Practice 56(3):111–122 Mishra SK, Purwar S, Kishor N (2016e) An optimal and non-linear speed control of oscillating water column wave energy plant with wells turbine and DFIG. Int J Renew Energy Res 6(3) Mishra SK, Purwar S, Kishor N (2018c) Event-triggered nonlinear control of owc ocean wave energy plant. IEEE Trans Sustain Energy 9(4):1750–1760. Pierson WJ, Moskowitz L (1964) A proposed spectral form for fully developed wind seas based on the similarity theory of S.A. Kitaigorodskii. J Geophys Res 69:5181–5190 Raghunathan S (1995) The Wells air turbine for wave energy conversion. Progress Aerosp Sci 31:335–386 Ramirez D, Bartolome JP, Martinez S, Herrero LC, Blanco M (2015b) Emulation of an OWC ocean energy plant with PMSG and irregular wave model. IEEE Trans Sustain Energy 6(4):1515–1523 Torsethaugen K (1996) Model for doubly peaked wave spectrum. Technical Report No. STF22 A96204, SINTEF Civil and Environment Engineering, Trondheim, Norway Wilamowski BM, Irwin JD (2011e) Power electronics and motor drives. CRC Press Young IR (1999b) Wind generated ocean waves. Ocean Eng 2:1–288

Chapter 3

Control Challenges of OWC

3.1 Simulation of Open Loop/Uncontrolled OWC The section presents the numerical simulations of the open-loop OWC plant to identify the control problems associated with OWC plants. Table 3.1 shows the data used for modelling the OWC in MATLAB/SIMULINK. The open-loop/uncontrolled OWC model is simulated for a duration of 100 s with regular and irregular pressure conditions. The MATLAB/SIMULINK diagram of overall OWC plant without any control scheme is shown in Fig. 3.1. For normal sea wave conditions, the turbine duct pressure difference is considered as dP = |7000 sin (0.1 π t)| Pa (Amundarain et al. 2011) and is shown in Fig. 3.2, where normal and irregular wave conditions are illustrated in Fig. 3.2a, and Fig. 3.2b respectively. After running the MATLAB simulation for 100 s, the time-varying waveforms of OWC plant parameters are obtained including turbine flow coefficient, turbine strength, electrical power and rotor speed which are represented by Fig. 3.3. It is observed that for dP = |7000 sin (0.1 π t)| Pa, turbine flow coefficient breaches the limit of 0.3 (Fig. 3.3a). The value of mean turbine power is obtained as 26.93 kW (Fig. 3.3a) whereas the mean power generated is −26.41 kW (Fig. 3.3a). Table 3.2 provides study of the open-loop/uncontrolled process for the coefficient of turbine flow and mean output power. The analysis has taken into a wide range of input pressure amplitudes (dPmax ) from 5000 to 8000 Pa. It is observed that the flow coefficient increases with the rise in pressure amplitude. As per Table 3.2 data, for dP = |6000 sin (0.1 π t)| Pa, mean output power touches the highest value of − 29.86 kW. On the further increase of dP, the mean output power starts decreasing because of the stalling phenomenon of Wells turbine (as discussed in Sect. 2.3).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 S. K. Mishra et al., OWC-Based Ocean Wave Energy Plants, Energy Systems in Electrical Engineering, https://doi.org/10.1007/978-981-15-9849-4_3

29

30 Table. 3.1 OWC chamber, Wells turbine and DFIG parameters

3 Control Challenges of OWC OWC chamber

DFIG

AOWC = 7.5

p=4

m2

Aduct = 1.1763 m2

Rs = 0.0181

Wells Turbine

L ls = 0.13

nt = 8; k t = 0.7079

L m = 7.413

r = 0.3643

Rr = 0.0334

bt = 0.4; l t = 0.38

L lr = 0.16

F = 0.02; J = 50

ωe = 100π rad/s

The irregular wave scenario is shown in Fig. 3.4 wherein the drop of peak pressure fluctuates between 5150 to 7150 Pa. As observed in the figure, there is no stalling the turbine for a lower pressure drop of 5150 Pa whereas, for a higher pressure drop of 7150 Pa, there is a stalling effect which is caused by the flow coefficient in Fig. 3.4a. The flow coefficient remains below 0.3 for 5150 Pa peak pressure drop whereas it exceeds 0.3 limit for 7150 Pa peak pressure drop. The turbine power is reduced in its stalling zones, as depicted in Fig. 3.4b This is further transferred to electrical power generated (in Fig. 3.4c). It is observed that the power generated is significantly reduced in the stalling regions as compared to no stall zones. Figure 3.4d represents the stalling effect in rotor speed.

3.2 Classification of Control Techniques for OWC From the simulation results of the previous section, it is evident that the stalling of Wells turbine is the main control challenge and must be avoided to attain the maximum possible output power and also to maintain the mean output power at the desired level. From the literature survey, it is observed that the airflow control and rotational speed control are the two most important control techniques which have been applied to OWC plants in the past. The schematic of the controlled OWC plant is shown in Fig. 3.5. The airflow control is implemented using flow control valves. The valve is used to bypass excess pressure from the OWC chamber, and thus the turbine can rotate freely without any stalling issue.

Fig. 3.1 MATLAB/SIMULINK diagram of overall OWC plant with no control schemes

3.2 Classification of Control Techniques for OWC 31

32

3 Control Challenges of OWC

(a) Input pressure for dP=|7000 sin (0.1 π t)| Pa

(b) Irregular wave conditions Fig. 3.2 Input pressure for regular and irregular wave scenarios. a Turbine flow coefficient, b Turbine power, c Power generated, d Rotor speed

3.2 Classification of Control Techniques for OWC

(a) Turbine flow coefficient

(b) Turbine power Fig. 3.3 Performance of open-loop/uncontrolled OWC plant for regular wave scenario

33

34

3 Control Challenges of OWC

(c) Power generated

(d) Rotor speed Fig. 3.3 (continued) Table. 3.2 Performance of open loop/uncontrolled OWC

−

dPmax (Pa)

ϕ

5000

0−0.27

−22.66

5500

0−0.29

−27.06

6000

0−0.31

−29.86

6500

0−0.34

−29.06

6800

0−0.35

−27.62

7000

0−0.36

−26.41

7300

0−0.38

−24.26

7500

0−0.39

−22.65

7800

0−0.41

−20.39

8000

0−0.42

−19.33

P g (kW)

3.2 Classification of Control Techniques for OWC

35

(a) Turbine flow coefficient

(b) Turbine power Fig. 3.4 Performance of open-loop/uncontrolled OWC plant for irregular wave scenario. a Turbine flow coefficient, b Turbine power, c Power generated, d Rotor speed

36

3 Control Challenges of OWC

(c) Power generated

(d) Rotor speed Fig. 3.4 (continued)

3.2 Classification of Control Techniques for OWC

37

Fig. 3.5 Controlled OWC plant

Another prevalent technique is rotational speed control which is implemented using power electronics at the generator side of the OWC plant. In case of DFIG type generator, two back to back AC/DC/AC converters that are defined as rotor side converter (RSC) and grid side converter (GSC) are used to convert the slip power around 30% of the generated power to the rotor side of the DFIG. These converters control the current supply given to the rotor, which in turn helps in achieving the variable speed operation of DFIG. The variable-speed operation of Wells turbineDFIG setup avoids the turbine stalling, and the mean output power is maximised with appropriate MPPT algorithm. In the next two chapters, the recently developed airflow control and rotational speed control techniques will be discussed.

Reference Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011) Modeling and simulation of wave energy generation plants: Output power control. IEEE Trans Industr Electron 58(1):105–117

Chapter 4

Power Generation Control of OWC Using Airflow Control

In this chapter, the airflow control scheme for output power control of the OWC plant is presented. The control valves are used to regulate the airflow inside the OWC chamber. Several studies have discussed the airflow control techniques in the past three decades, e.g. Falcáo and Justino (1999a), Falcáo et al. (2003, 2010a), Amundarain et al. (2010b, 2011c), Alberdi et al. (2011a, b), Mishra et al. (2015). However, the anti-windup type PID and FOPID controllers are very simple to design and very effective in terms of OWC performance. Therefore, anti-windup PID and FOPID controllers have been designed with manual as well as optimal tuning approaches.

4.1 PID Control The controller structure is shown in Fig. 4.1. The output power from the OWC plant is transferred to a mean block. Then, the mean power is compared with the desired output power. The comparison error is sent to the PID controller, which is the antiwindup valve controller. The structure of the anti-windup PID controller is shown in Fig. 4.2. The purpose of PID is to control the excessive airflow across the turbine duct so that the error between the average output power and reference power is minimized. Also, the stalling behaviour of the Wells turbine is avoided by limiting the airflow rate. The error signal fed to PID controller is given as: e(t) = P ref − P g

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 S. K. Mishra et al., OWC-Based Ocean Wave Energy Plants, Energy Systems in Electrical Engineering, https://doi.org/10.1007/978-981-15-9849-4_4

(4.1)

39

40

4 Power Generation Control of OWC Using Airflow Control

Fig. 4.1 Anti-windup PID-based airflow control of OWC plant

Fig. 4.2 The structure of anti-windup PID controller

where, P ref is the reference or desired average output power; P g is the measured average output power. The basic equation for PID controller is given by:    1 d e(t)dt + Td e(t) u(t) = K p e(t) + Ti dt

(4.2)

The Laplace transform gives:   1 U (s) = Kp 1 + + Td s E(s) Ti s

(4.3)

where, U(s) and E(s) are the Laplace transforms of u(t) and e(t), respectively; K p , T i , and T d are the proportional, integral and differential gains terms, respectively.

4.1 PID Control

41

The output of the PID controller represents the effective area of the valve to be maintained, which is further subtracted from the total area of the turbine duct. Hence, the effective area of the turbine duct varies in line with the changes in the valve area, and the desired output power is obtained by controlling the airflow rate. The transfer ratio between the valve input (control signal) and valve output has been taken as unity for simplicity. The detailed analysis of air valves can be found in Falcáo and Justino (1999a), Justino and Falcáo (1999b), Falcáo et al. (2003). The valve, which works as the final control actuator, has a saturation effect. Thus, the FOPID output should be restricted so that the saturation effect is avoided. When the valve gets saturated, the output feedback does not affect the valve response. The valve goes to steady-state, and the closed-loop system becomes an open-loop. The error between the actual and desired value persists, which causes the integral values of PID to increase. This may increase the control effort, which has to be reduced. When high flow rate has to pass through the turbine duct, the valve position will not change to reduce the effective area of the valve because of very high values of the integral term of the PID controller. Thus, we have considered the anti-windup type PID control (Amundarain et al. 2010a, b, 2011c), which is an extension of PID control. Next, the MATLAB/SIMULINK diagram of closed-loop OWC plant control system using anti-windup PID controller is shown in Fig. 4.3. The control input to the OWC plant is Avalve that is the effective area covered by the valve to manipulate the differential pressure at the turbine duct. The internal MATLAB/SIMULINK view of anti-windup PID controller is shown in Fig. 4.4. The simulation results were obtained for regular and irregular wave conditions. The performance of the antiwindup PID controller has been assessed for K p = 20, Ti = 10 and Td = 1. The

Fig. 4.3 The MATLAB/SIMULINK diagram of anti-windup PID controller

42

4 Power Generation Control of OWC Using Airflow Control

Fig. 4.4 The MATLAB/SIMULINK diagram of anti-windup PID controller

reference output power is P r e f = −23kW . The controlled output power waveform and control efforts are shown in Fig. 4.5 for normal wave conditions. The mean output power (in Fig. 4.5a) successfully tracks the reference power where the power waveform gets settled in 90 s approximately. This is due to the manual tuning of the anti-windup PID parameters. Similarly, control effort signals (in Fig. 4.5b) have initial transients which die out after 100 s of time duration. This could be further improved by fine-tuning the controller parameters. The other OWC relevant parameters such as turbine flow coefficient, turbine power and rotor speed are shown in Fig. 4.6 for regular wave conditions. The flow coefficient (in Fig. 4.6a) is always maintained with its threshold limit that shows the efficacy of the control scheme. Also, as observed in the turbine power waveform in the (in Fig. 4.6b), there is no sign of turbine stalling and mean turbine power is forced to track the referencce value of 23 kW. Similarly, the rotor speed signal (in Fig. 4.6c) is smooth for whole time duration except for few initial seconds. Next, the performance of the anti-windup PID controller with irregular wave conditions is shown in Figs. 4.7 and 4.8. As shown in Fig. 4.7a, the mean electrical output power successfully tracks the reference power. However, there are small transients persistent due to uncertainty added in the pressure waveform. It is more visible in the control effort waveform in Fig. 4.7b that has a high variation to mitigate the effect of irregular waves in output power. The flow coefficient variation is not affected by the regular wave conditions, as shown in Fig. 4.8a. Next, turbine power and rotor speed waveforms (in Fig. 4.8b, c) are also stalling free. However, there is a stalling effect in the initial transient phase, as this is the time that OWC plant needs to be fully operated in generator mode.

4.2 Fractional Order PID Control

43

(a) Power generated

(b) Valve control effort Fig. 4.5 The performance of anti-windup PID controller for airflow control of OWC plant with regular wave conditions

4.2 Fractional Order PID Control In this section, we discuss the implementation of FOPID controller, which is an advanced form of PID controller. The FOPID has many advantages over the conventional PID controller (Mishra et al. 2015; Das et al. 2011; Duma et al. 2012; Mishra and Purwar 2014). Many studies have revealed that by tuning fractional parameters appropriately, the FOPID controller performs better than the PID controller (Hamamci 2007; Yeroglu and Tan 2011). In FOPID, the integrator and differentiator terms are of fractional nature that is based on the fractional calculus branch of mathematics (Ortigueira 2011). The fractional order differentiation and integration had originated from fractional calculus. Recently some MATLAB toolboxes and

44

4 Power Generation Control of OWC Using Airflow Control

(a) Flow coefficient

(b) Turbine power

(c) Rotor speed Fig. 4.6 The performance of OWC with anti-windup PID-based airflow controller under regular wave conditions

4.2 Fractional Order PID Control

45

(a) Power generated

(b) Valve control effort Fig. 4.7 The performance of anti-windup PID controller for airflow control of OWC plant with irregular wave conditions

methods to work with fractional order operator have been developed (Oustaloup et al. 2000; Xue and Chen 2002; Valério 2005; Tepljakov et al. 2011). These developments have made it easy to work with fractional calculus and to design FOPID. The basic equation for FOPID controller is given by:   1 u(t) = K p e(t) + D −λ e(t) + Td D μ e(t) Ti

(4.4)

The Laplace transform gives:   1 U (s) μ = Kp 1 + + T s d E(s) Ti s λ

(4.5)

46

4 Power Generation Control of OWC Using Airflow Control

(a) Flow coefficient

(b) Turbine power

(c) Rotor speed Fig. 4.8 The performance of turbine flow coefficient, turbine power and rotor speed with antiwindup PID-based airflow controller under irregular wave conditions

4.2 Fractional Order PID Control

47

Fig. 4.9 The structure of anti-windup FOPID controller

where, D ≡ dtd ; U(s) and E(s) are the Laplace transforms of u(t) and e(t) respectively; K p , T i , and T d are the proportional, integral and differential gains terms respectively; λ and μ are the fractional orders of differential and integral part of the FOPID, respectively. Next, the basic structure of FOPID controller with anti-windup scheme is shown in Fig. 4.9. Two additional parameters λ and μ are included in the expression of FOPID controller which makes it design more challenging as compared to the PID controller. So, we take the values of three main parameters same as that of anti-windup PID controller and vary the additional parameters λ and μ to obtain the improved results. As far as MATLAB/SIMULINK model of anti-windup FOPID is concerned, we have replaced the integer-order integral and derivative blocks with the fractional integral and derivative blocks. These blocks were built using a very popular MATLAB toolbox called as FOMCON (Oustaloup 2000; Xue and Chen 2002; Valério 2005; Tepljakov et al. 2011). So, the MATLAB/SIMULINK diagram of anti-windup FOPID controller is the same in all respects except for integral and derivative blocks. Next, the simulation results are obtained with three sets of the following control parameters of FOPID: (i) K p = 20, Ti = 10, Td = 1 and λ = μ = 0.5, (ii) K p = 20, Ti = 10, Td = 1 and λ = μ = 1.0 and (iii) K p = 20, Ti = 10, Td = 1 and λ = μ = 1.5. The performance of FOPID controller has been evaluated with regular and irregular wave conditions and is shown in Figs. 4.10 and 4.11, respectively. It is observed that the FOPID performance is very much dependent upon the selection of fractional parameters λ and μ. The λ and μ are varied from 0.5 to 1.5 and the responses are shown in the figure. For λ = μ = 0.5, the oscillations in output power response are smaller as compared to that for λ = μ = 1.5. The best response is achieved with λ = μ = 1.0 wherein trajectory settles earlier than for other cases. However, there is still scope of improving the performance by optimising the FOPID parameters.

48

4 Power Generation Control of OWC Using Airflow Control

(a) Mean power generated

(b) Valve control effort Fig. 4.10 The performance of anti-windup FOPID controller for airflow control of OWC plant with regular wave conditions

4.3 Optimally Tuned PID and FOPID Control In this section, the anti-windup PID and FOPID controller parameters have been optimized to achieve the best possible performance of the OWC plant. Also, a comparative study has been carried out between PID and FOPID-based airflow control schemes. The PID and FOPID parameters have been chosen on a trial and error basis in the previous section. To tune the control parameters, an integral time absolute error (ITAE) type objective function has been considered. The mathematical expression for ITAE can be given as:

4.3 Optimally Tuned PID and FOPID Control

49

(a) Mean power generated

(b) Valve control effort Fig. 4.11 The performance of anti-windup PID controller for airflow control of OWC plant with irregular wave conditions

Ts I T AE =

t|e(t)|dt

(4.6)

0

where, T s is the simulation runtime for OWC model. Substituting the value of e(t) in the above equation, the ITAE expression can be written as: Ts I T AE = 0

  t  P r e f − P g dt

(4.7)

50

4 Power Generation Control of OWC Using Airflow Control

The ITAE was minimized using PSO, a population-based optimisation method and the details of the same can be seen in Kennedy and Eberhart (1995), Clerc (2006), Poli et al. (2007). The steps of the PSO algorithm are given as: Step 1: Initialize particles with random position and velocity vectors. Evaluate the fitness value of each particle. Step 2: Update individual best positions (pbest ) and global best positions (gbest ) according to best or minimum fitness values. Step 3: Update velocity and position of each particle in each iteration given as:     k+1 k + c × rand(.) × p k k dvid = w × vid 1 best,id − xid + c2 × rand(.) × gbest,id − xid

k+1 k xidk+1 = xid + vid

(4.8)

(4.9)

where, i = 1, 2, 3, . . . . . . N ; d = 1, 2, 3, . . . . . . M; k is the pointer of iterations k (generations); vid is the velocity of the ith particle at iteration k; w is the inertia weight factor and w = wmax -[(wmax -wmin )/k max ]*k; wmax and wmin are the maximum and minimum values of w respectively; k max is the maximum number of iterations; c1 and c2 are the cognitive and social acceleration factors respectively; rand () represents the random numbers uniformly distributed in the range (0, 1); xidk is the position of ith particle at iteration k; d is the dimension of the search space; N is the number of iterations; M is the number of dimensions. Repeat step 2 and step 3 until maximum numbers of iterations or error criteria are reached. The performance of optimally tuned airflow controllers is shown in Fig. 4.12. The mean output power waveforms for manually tuned PID and FOIPD, PSO-PID and PSO-FOPID are compared in Fig. 4.12a. The zoomed version of Fig. 4.12a is depicted in Fig. 4.12b. It is observed that PSO-PID and PSO-FOPID performances are much better as compared to the manually tuned controllers. Next, valve control efforts are shown in Fig. 4.12c wherein the minimized efforts are obtained for optimally tuned controllers. A comparison of the different controllers is also provided in Table 4.1. The ITAE values for all controllers are obtained. PSO-FOPID has the lowest ITAE value. However, the PSO-PID value is also very close to the PSO-FOPID.

4.3 Optimally Tuned PID and FOPID Control

51

(a) Mean power generated

(b) Mean power generated zoomed version

(c) Valve control effort Fig. 4.12 The performance of anti-windup PSO-PID and PSO-FOPID controller for airflow control of OWC plant

52

4 Power Generation Control of OWC Using Airflow Control

Table 4.1 Performance of controlled OWC with anti-windup PID and FOPID controllers under regular wave conditions Controller

Kp

Ti

Td

λ

μ

ITAE

PID

20

1.0

10.0

–

–

2.5 × 107

FOPID

20

1.0

10.0

0.5

0.5

9.4 × 107

20

1.0

10.0

1.5

1.5

6.2 × 108

PSO-PID

8.2

9.6

1.8

–

–

7.8 × 106

PSO-FOPID

15.5

5.2

3.3

0.97

1.93

7.5 × 106

References Alberdi M, Amundarain M, Garrido AJ, Garrido I, Casquero O, Sen MD (2011a) Complementary control of oscillating water column-based wave energy conversion plants to improve the instantaneous power output. IEEE Trans Energy Convers 26(4):1021–1032 Alberdi M, Amundarain M, Garrido AJ, Garrido I, Maseda FJ (2011b) Fault-ride-through capability of oscillating-water-column-based wave-power-generation plants equipped with doubly fed induction generator and airflow control. IEEE Trans Industr Electron 58(5):1501–1517 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2010a) Control strategies for OWC wave power plants. In: American control conference. USA, pp 4319–4324 Amundarain M, Alberdi M, Garrido AJ, Garrido I, Maseda J (2010b) Wave energy plants: Control strategies for avoiding the stalling behaviour in the Wells turbine. Renew Energy 35:2639–2648 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011c) Modeling and simulation of wave energy generation plants: Output power control. IEEE Trans Ind Electron 58(1):105–117 Clerc M (2006) Particle swarm optimization, ISTE Ltd. UK. Das S, Das S, Gupta A (2011) Fractional order modeling of a PHWR under step-back condition and control of its global power with a robust PIλDμ controller. IEEE Trans Nucl Sci 58(5):2431–2441 Duma R, Dobra P, Trusca M (2012) Embedded application of fractional order control. IET Electron Lett 48(24):1526–1528 Falcáo AFO, Justino PAP (1999a) OWC wave energy devices with air flow control. Ocean Eng 26:1275–1295 Falcáo AFO, Vieira LC, Justino PAP, André JMCS (2003) By-pass air-valve control of an OWC wave power plant. J Offshore Mech Arct Eng 125:205–210 Hamamci SE (2007) An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers. IEEE Trans Autom Control 52:1964–1969 Justino PAP, Falcáo AFO (1999b) Rotational speed control of an OWC wave power plant. J Offshore Mech Arct Eng 121:65–70 Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, pp. 1942–1948. Mishra SK, Purwar S (2014) To design optimally tuned FOPID controller for twin rotor MIMO system. In: 3rd students conference on engineering and systems. India, pp 1–6 Mishra SK, Purwar S, Kishor N (2015) Air flow control of OWC Wave Power Plants using FOPID controller. In: IEEE Multi-conference on systems and control. Sydney, Australia Ortigueira MD (2011) Fractional calculus for scientists and engineers. Springer. Oustaloup A, Levron F, Mathieu B, Nanot FM (2000) Frequency-band complex noninteger differentiator: characterization and synbook. In: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(1):25–39. Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intelligence, 1(1):33– 57.

References

53

Tepljakov A, Petlenkov E, Belikov J (2011) FOMCON: Fractional-order modeling and control toolbox for Matlab. In: Proceedings of the 18th international conference on mixed design of integrated circuits and systems (MIXDES), pp. 684–689. Valério D (2005) Ninteger v. 2.3 fractional control toolbox for Matlab, http://web.ist.utl.pt/~duarte. valerio. Xue D, Chen YQ (2002) A comparative introduction of four fractional order controllers. In: Proceedings of the fourth world congress, intelligent control and automation, 4:3228–3235. Yeroglu C, Tan N (2011) Note on fractional-order proportional–integral–differential controller design. IET Control Theory Appl 5(17):1978–1989

Chapter 5

Maximum Power Point Tracking of OWC Using Rotational Speed Control

This chapter deals with the MPPT control of OWC plant using rotational speed control. It is a very highly researched topic in OWC control. A large number of research papers have published in past three decades for rotational speed control of OWC plant, e.g. Justino and Falcáo (1999), Falcáo (2002), Justino (2006), Jayashankar et al. (2000), Murthy and Rao (2005), Amundarain et al. (2009, 2010a, b, 2011a), Amundarain et al. (2011b), Garrido et al. (2012), Garrido (2013), Barambones and Durana (2015), Lekube et al. (2016a, 2018a), Mishra et al. (2016b, c). The MPPT control consists of two parts: (i) MPPT reference and (ii) rotor speed controller. The MPPT reference is generated using the input–output analysis of the OWC plant. Then, three control schemes, PI control (Amundarain et al. 2011a), backstepping control (Mishra et al. 2016b; Lekube et al. 2018a), and sliding mode control (Garrido et al. 2012; Lekube et al. 2018a) are designed for controlling the rotor speed according to MPPT reference. Also, a detailed comparison of these schemes is carried out in this chapter.

5.1 MPPT Reference A relationship between OWC chamber pressure dP and reference rotor speed ωref is established in such a way that the controlled OWC plant always delivers maximized output power. Here, in Table 5.1, the relationship between dP and ωref is provided to change the ωref when there is a change in dP. As given in the table, the ωref from dP = |5000sin(0.1π t)|Pa to dP = |5000sin(0.1π t)|Pa, is constant around the synchronous speed of the DFIG, whereas, for higher values of dP, it starts increasing in a proportional manner. The values of ωref given in the table correspond to the maximized output power of the OWC plant.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 S. K. Mishra et al., OWC-Based Ocean Wave Energy Plants, Energy Systems in Electrical Engineering, https://doi.org/10.1007/978-981-15-9849-4_5

55

56

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

Table 5.1 The relationship between dP and ωref dP (Pa)

ωref (rad/s)

|5000sin(0.1π t)|

158.00

|5500sin(0.1π t)|

162.00

|6000sin(0.1π t)|

169.00

|6500sin(0.1π t)|

176.00

|6800sin(0.1π t)|

180.00

|7000sin(0.1π t)|

182.50

|7300sin(0.1π t)|

186.50

|7500sin(0.1π t)|

189.00

|7800sin(0.1π t)|

192.50

|8000sin(0.1π t)|

195.50

5.2 PI Control PI control is one of the simplest controllers available in the literature. It is still very popular due to its simple structure. A detailed discussion on its mathematical expression and structure are already discussed in Chapter 4. The PI control for rotational speed control of OWC plant was discussed previously in Amundarain et al. (2010a, 2011a). The Fig. 5.1 presents the MATLAB/SIMULINK block diagram of PI-based rotational speed control of OWC plant which aimed to attain the maximized output power. The rotor speed is taken as the OWC plant output and is given as feedback to the controller. Before feeding to the controller, the rotor speed is compared with the reference rotor speed, and then the error is transmitted to the PI controller. The reference rotor speed is decided by the relationship between dP and ωref as given in Table 5.1. A manual switch has been used to toggle the OWC plant in uncontrolled

Fig. 5.1 MATLAB/SIMULINK block diagram of PI-based rotational speed control of OWC plant

5.2 PI Control

57

and controlled modes. The output of the controller is the q-axis rotor voltage that manipulates the rotor speed of the Wells turbine-DFIG module of OWC plant. Next, the simulations are performed PI proportional and integral gains as −10 and −1, respectively. All other simulation parameters are chosen to be same as with the airflow control simulations of OWC plant. The results were obtained for all values of dP provided in Table 5.1, but for demonstration purpose, three cases of dP are taken into account. These are: (i) dP = |6000sin(0.1π t)|Pa, (ii) dP = |7000sin(0.1π t)|Pa and (iii) dP = |8000sin(0.1π t)|Pa. The corresponding ωref values are 158.00, 182.50 and 195.50 rad/s. The PI controlled rotor speed (in Fig. 5.2) tracks the reference rotor speed for the cases of chamber pressures mentioned above. However, due to the manual selection of PI parameters, some oscillations are observed in the waveforms. These can be removed by auto-tuning of the PI controller. The same process of tuning can be applied as it was for airflow control. Another observation made in Fig. 5.2 is the increase in the speed reference for increasing pressure in the OWC chamber. Next, the rotor control voltage effort also enhances with increased OWC chamber pressure (Fig. 5.3). The PI controller successfully follows the desired trajectory, which in turn forces the turbine flow coefficients to remain below the permissible limit, and turbine stalling is avoided, as shown in Fig. 5.4. As observed in the figure, the turbine flow coefficient increases with an increase in OWC chamber pressure in the uncontrolled case, whereas in PI controlled cases, it always remains below 0.3 threshold limit. This also reflects in electrical output power generated from OWC plant (in Fig. 5.5) wherein uncontrolled output power decreases with increasing chamber pressure from dP = |6000sin(0.1π t)|Pa to |8000sin(0.1π t)|Pa. In the PI controlled case, the output power is maximized in each case shown in Fig. 5.5a–c. For dP = |6000sin(0.1π t)|Pa, the uncontrolled mean output power is −29.86 kW whereas, for PI controlled OWC plant, the means output power gets maximized to −30.90 kW. Similarly, for dP = |7000sin(0.1π t)|Pa and |8000sin(0.1π t)|Pa also, the mean output power from the OWC plant is maximized to −38.99 kW and −47.61 kW, respectively.

5.3 Backstepping Control The overall dynamics of the OWC plant are highly nonlinear, and it is a very tedious task to design the controller using linear control theory. The guaranteeing stability of a control system in all conditions is always needed. So, it is required to linearize the plant and then design the linear controllers (e.g. PI control) by satisfying the stability of the closed-loop system. However, it compromises the actual characteristics of key plant parameters. So, it is advised to directly design the nonlinear controller by taking into account the actual dynamics of any control system. The two most popular nonlinear controllers are the backstepping controller (Mishra et al. 2016c) and sliding

58

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

(a) Rotor speed with

(b) Rotor speed with

(c) Rotor speed with Fig. 5.2 The rotor speed performance due to PI-based rotational speed control OWC plant

5.3 Backstepping Control

59

(a) Rotor control voltage with

(b) Rotor control voltage with

(c) Rotor control voltage with Fig. 5.3 The performance of rotor control voltage due to PI-based rotational speed control OWC plant

60

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

(a) Turbine flow coefficient with

(b) Turbine flow coefficient with

(c) Turbine flow coefficient with Fig. 5.4 The performance of turbine flow coefficient due to PI-based rotational speed control OWC plant

5.3 Backstepping Control

61

(a) Output power with

(b) Output power with

(c) Output power with Fig. 5.5 The performance of output power due to PI-based rotational speed control OWC plant

62

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

mode controllers (Garrido et al. 2012). These techniques do consider the nonlinear terms present in the plant dynamics and closed-loop system stability is guaranteed. In this section, the backstepping controller design would be discussed. The backstepping control scheme is based on a step-by-step design wherein the plant dynamics must be in strict-feedback-form. To design backstepping control, we recall the OWC plant modeling equations from Chap. 2. The turbine-generator coupling equation is: J

dωr = Tt − Te − Fωr dt

(5.1)

Next, the DFIG equations are: dψds Rs L r Rs L m =− ψds + ωe ψqs + ψdr + vds dt K K

(5.2)

dψqs Rs L r Rs L m = −ωe ψds − ψqs + ψqr + vqs dt K K

(5.3)

Rr L m dψdr Rr L s = ψds − ψdr − (ωr − ωe )ψqr + vdr dt K K

(5.4)

dψqr Rr L m = ψqs + (ωr − ωe )ψdr + vqr dt K

(5.5)

It is first required to convert the above equations into strict-feedback-form. To achieve this, the DFIG stator flux is completely aligned to d-axis, also known as flux-oriented control (Mishra et al. 2018b). Hence, ψ ds = ψ s and ψ qs = 0. With stator flux orientation towards d-axis, the stator supply voltage in a synchronous rotating frame is aligned towards q-axis, i.e. vds = 0 and vqs = V s . Here, the stator supply voltage V s is a dc quantity in the synchronous rotating frame. Therefore, the Eq. (5.1) an Eq. (5.2) can now be expressed as: Rs L r Rs L m dψs =− ψs + ψdr dt K K

(5.6)

Rs L m ψqr + Vs K

(5.7)

0 = −ωe ψs +

As the stator is connected to grid network, the stator resistance has very small influence. Hence, from Eq. (5.7), we obtain: Vs = ωe ψs ⇒ ψs =

Vs = constant ωe

(5.8)

It means that the time derivative of ψ s will be zero. Hence, from Eq. (5.6), the d-axis rotor flux can now be written as:

5.3 Backstepping Control

63

ψdr = L r L −1 m ψs

(5.9)

With ψ ds = ψ s and ψ qs = 0, the electro-magnetic torque T e of DFIG can be expressed as: Te = Mψs ψqr

(5.10)

Substituting the values of T e , ψ dr and ψ qs into Eqs. (5.10) and (5.1) respectively, we obtain:  dωr 1 Tt − Fωr − Mψs ψqr = dt J

(5.11)

dψqr = L r L −1 m ψs (ωr − ωe )ψdr + vqr dt

(5.12)

It is observed in Eqs. (5.11) and (5.12) that the rotor speed can be controlled by using vqr variable only. Hence, vqr is chosen as the control signal, u r , for rotational speed control and vdr = 0. The state-space model from Eqs. (5.11) and (5.12) is given below: z˙ 1 = k1 z 1 + k2 z 2 + D

(5.13)

z˙ 2 = k3 (z 1 − ωe ) + k4 z 2 + u r

(5.14)

where, k1 = − FJ ; k2 = − MJ ; k3 = LLmr ψ S ; k4 = − RrKL s ; u r = controlsignal = vqr ; D = TJt ; z 1 = ωr and z 2 = ψqr . Further, simplifying the above equation, we have: z˙ 1 = f 1 (z 1 , D) + k2 z 2

(5.15)

z˙ 2 = f 2 (z 1 , z 2 ) + u r

(5.16)

where, f 1 (z 1 , D) = k1 z 1 + D; and f 2 (z 1 , z 2 ) = k3 (z 1 − ωe ) + k4 z 2 . A step by step design approach is applied for the backstepping controller. For a second second-order system expressed by Eqs. (5.15) and (5.16), the controller is designed in two stages. First, a virtual controller, z 2d , is to be designed. Then, z 2d would be used for designing final control law u r . For designing the virtual control law, z 2d , if we choose the error component as: z˜ 1 = z 1d − z 1 Next, the first-order derivative of Eq. (5.17) is written as:

(5.17)

64

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

z˙˜ 1 = z˙ 1d − z˙ 1 = z˙ 1d − f 1 (z 1 , D) − k2 z 2

(5.18)

Further, by adding and subtracting k2 z 2d term, Eq. (5.18) becomes: z˙˜ 1 = z˙ 1d − f 1 (z 1 , D) − k2 z 2 + k2 z 2d − k2 z 2d

(5.19)

The virtual control law z 2d is chosen as: z 2d = k2−1 (˙z 1d − f 1 (z 1 , D) + σ1 z˜ 1 )

(5.20)

z˜ 2 = z 2d − z 2

(5.21)

where, σ1 > 0, Define:

Substituting Eqs. (5.20) and (5.21), the Eq. (5.19) can be expressed as: z˙˜ 1 = −σ1 z˜ 1 + k2 z˜ 2

(5.22)

Next, the derivative of Eq. (5.21) is given by: z˙˜ 2 = z˙ 2d − z˙ 2 = z˙ 2d − f 2 (z 1 , z 2 ) − u r

(5.23)

For designing the control law which ensures the closed-loop stability of the system (Eqs. (5.15) and (5.16)), a Lyapunov function candidate, Vlp f , is chosen as: Vlp f =

 1 2 z˜ 1 + z˜ 22 2

(5.24)

The first order time derivative of Eq. (5.24) is expressed as: V˙lp f = z˜ 1 z˙˜ 1 + z˜ 2 z˙˜ 2

(5.25)

⇒ V˙lp f = z˜ 1 (−σ1 z˜ 1 + k2 z˜ 2 ) + z˜ 2 (˙z 2d − f 2 (z 1 , z 2 ) − u r )

(5.26)

⇒ V˙lp f = −σ1 z˜ 12 + z˜ 2 {˙z 2d − f 2 (z 1 , z 2 ) + k2 z˜ 1 − u r }

(5.27)

The control law u r : u r = z˙ 2d − f 2 (z 1 , z 2 ) + k2 z˜ 1 + σ2 z˜ 2 gives:

(5.28)

5.3 Backstepping Control

65

Fig. 5.6 MATLAB/SIMULINK block diagram of backstepping-based rotational speed control of OWC plant

V˙lp f = −σ1 z˜ 12 − σ2 z˜ 22 ≤ 0

(5.29)

where, σ2 > 0. Here, Eq. (29) becomes negative semi-definite and V˙lp f does not contain any ∼ ∼ ∼ ∼ trajectories of error states z 1 and z 2 other than the trivial trajectory z 1 = z 2 = 0. ∼ ∼ Then, error states z 1 and z 2 converge asymptotically to zero. Hence, the system with the control law u r given in Eq. (28) is asymptotically stable. To obtain the simulation results with backstepping control, the MATLAB/SIMULINK model has been developed, as shown in Fig. 5.6. The OWC plant model is the same as it was for the PI control scheme discussed in the previous section. The backstepping control block has replaced the PI control block in Fig. 5.6. This block has been designed using MATLAB function, which is based on the Eqns.(5.15)–(5.29). The MATLAB codes are given in Table 5.2. Next, the performance of backstepping controller was re-evaluated with three cases of OWC chamber pressure as (i) d P = |6000sin(0.1π t)|Pa, (ii) d P = |7000sin(0.1π t)|Pa and (iii) d P = |8000sin(0.1π t)|Pa. The corresponding ωr e f values are 158.00, 182.50 and 195.50 rad/s. The rotor speed performance is displayed in Fig. 5.7 wherein the actual rotor speed very efficiently tracks the reference speed in all three cases, as shown in Fig. 5.7a–c. the magnified portion of rotor speed for the initial 0.5 s suggests that rise time and settling are significantly lower as compared to that of PI control in Fig. 5.2. There is peak overshoot, which is within the range of 10 rad/s for a short duration of about 0.1 s. The corresponding rotor control voltage efforts are shown in Fig. 5.8. For d P = |6000sin(0.1π t)|Pa, the rotor control voltage lies in the range 0–20 V. For d P = |7000sin(0.1π t)|Pa, it lies

66

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

Table 5.2 The backstepping control MATLAB code

within 20–40 V whereas for d P = |8000sin(0.1π t)|Pa it is within 30–60 V. It can be concluded that rotor control effort increases for increased chamber pressure. The backstepping controller, like the PI controller, successfully follows the desired trajectory and forces the turbine flow coefficients to remain below 0.3 value. This avoids Wells turbine stalling (in Fig. 5.9). The turbine flow coefficient increases with a corresponding rise in OWC chamber pressure in the uncontrolled case, whereas in the backstepping controlled OWC plant, the flow coefficient always remains below 0.3 threshold limit. The electrical output power generated from OWC plant (in Fig. 5.10) reaches to a maximum level wherein uncontrolled output power decreases with increasing chamber pressure from d P = |6000sin(0.1π t)|Pa to |8000sin(0.1π t)|Pa. In the backstepping controlled case, the output power is maximized in each case, as shown in Figs. 5.10a–c. For d P = |6000sin(0.1π t)|Pa, the uncontrolled mean output power is −29.86 kW, whereas, for backstepping controlled OWC plant, the mean output power gets maximized to −30.90 kW. Similarly, for d P = |7000sin(0.1π t)|Pa and |8000sin(0.1π t)|Pa also, the mean output power from the OWC plant is maximized to −38.99 kW and −47.61 kW, respectively. So, in terms of output power maximization, the backstepping control scheme is quite similar to that of PI control. However,

5.3 Backstepping Control

67

(a) Rotor speed with

(b) Rotor speed with

(c) Rotor speed with Fig. 5.7 The rotor speed performance due to backstepping-based rotational speed control OWC plant

68

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

(a) Rotor control voltage with

(b) Rotor control voltage with

(c) Rotor control voltage with Fig. 5.8 The performance of rotor control voltage due to backstepping-based rotational speed control OWC plant

5.3 Backstepping Control

69

(a) Turbine flow coefficient with

(b) Turbine flow coefficient with

(c) Turbine flow coefficient with Fig. 5.9 The performance of turbine flow coefficient due to backstepping-based rotational speed control OWC plant

70

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

(a) Output power with

(b) Output power with

(c) Output power with Fig. 5.10 The performance of output power due to backstepping-based rotational speed control OWC plant

5.3 Backstepping Control

71

the backstepping controller guarantees closed system stability, whereas it is not so in the case of PI control.

5.4 Sliding Mode Control Another technique that is very popular among the research community is sliding mode control. This technique is based on a sliding surface that is followed by the state trajectories of the system. For designing sliding mode control law, the tracking problem is given by Eqs. (5.15) and (5.16) is converted into the regulator problem to make the sliding surface s(t) = 0. Recalling Eq. (5.19) as: z˙˜ 1 = {˙z 1d − f 1 (z 1 , D) − k2 z 2d } + k2 z˜ 2

(5.30)

To covert the system dynamics into error dynamics, we choose: z 2d = k2−1 {˙z 1d − f 1 (z 1 , D)}

(5.31)

⇒ z 2d = k2−1 {˙z 1d − k1 z 1 − D}

(5.32)

⇒ z 2d = k2−1 {˙z 1d − k1 z 1d − D} + k2−1 k1 z˜ 1

(5.33)

Therefore, Eq. (5.30) becomes: z˙˜ 1 = k2 z˜ 2

(5.34)

The first derivative of Eq. (5.33) can be given by:   z˙ 2d = k2−1 z¨ 1d − k1 z˙ 1d − D˙ + k2−1 k1 z˜

(5.35)

1

Substituting Eq. (5.34) into Eq. (5.35) we have:   z˙ 2d = k2−1 z¨ 1d − k1 z˙ 1d − D˙ + k2−1 k1 k2 z˜ 2

(5.36)

  ⇒ z˙ 2d = k2−1 z¨ 1d − k1 z˙ 1d − D˙ + k1 z˜ 2

(5.37)

Putting the derivative of Eq. (5.37) in Eq. (5.23) we obtain:   z˙˜ →2 = k2−1 z¨ 1d − k1 z˙ 1d − D˙ + k1 z˜ 2 − f 2 (z 1 , z 2 ) − u r After solving Eq. (5.38), the following expression is obtained:

(5.38)

72

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

  z˙˜ 2 = k3 − k4 k2−1 k1 z˜ 1 + (k1 + k4 )˜z 2 − u r + f d

(5.39)

where, fd =

k2−1



 ˙ z −k1 z˙ 1d − D − k3 (z 1d − ωe ) − k4 k2−1 {˙z 1d − k1 z 1d − D}

(5.40)

1d

Now, the Eqs. (5.34) and (5.39) can be written in the state space form as: z˙˜ = A˜z + Bu r + E f d

(5.41)

   0 0 k2 0 ˙ z˜ ;B = where, A = ;E = ; z˜ = 1 k3 − k4 k2−1 k1 k1 + k4 z˜ 2 −1 1 Next, the sliding surface ξ can be chosen as: 

ξ = δ T z˜

(5.42)

 −1  T  δ A˜z + βsign(ξ ) ur = − δ T B

(5.43)



where, δ T = δ1T δ2 . The SMC law is chosen as:

where, β > 0. To prove that the system in Eq. (5.41) with SMC control law in Eq. (5.44) is asymptotically stable, we choose a Lyapunov function candidate as: Wlp f =

1 2 ξ 2

(5.44)

The first-order time derivative of Eq. (5.45) is: W˙ lp f = ξ ξ˙ = ξ δ T z˜ = ξ δ T (A˜z + Bu r + E f d )

(5.45)

  ⇒ W˙ lp f = ξ δ T A˜z + δ T Bu r + δ T E f d

(5.46)

After substituting the SMC control law u from Eq. (5.43) into Eq. (5.46), we obtain:

 −1  T  (5.47) δ A˜z + βsign(ξ ) + δ T E f d W˙ lp f = ξ δ T A˜z + δ T B − δ T B   ⇒ W˙ lp f = ξ δ T A˜z − δ T A˜z − βsign(ξ ) + δ T E f d

(5.48)

5.4 Sliding Mode Control

73

⇒ W˙ lp f = −βξ sign(ξ ) + ξ δ T E f d

(5.49)

⇒ W˙ lp f ≤ −β|ξ | + |ξ |δ T E f d

(5.50)

  ⇒ W˙ lp f ≤ − β − δ T E f d |ξ |

(5.51)

For the condition given below: β > δ T E fd + η

(5.52)

the Eq. (5.52) can be written as: W˙ lp f ≤ −η|ξ | ≤ 0

(5.53)

where, η > 0. Here, Eq. (5.53) becomes negative semi-definite and W˙ lp f = 0 does not contain any trajectory of sliding surface ξ other than trivial trajectory ξ = 0. Then, ξ converges asymptotically to zero. Hence, the system given by Eq. (5.41) with control law u given in Eq. (5.43) is asymptotically stable. For assessing the performance of the sliding mode control, the simulation model in MATLAB/SIMULINK, as shown in Fig. 5.11. Only the controller section is replaced in the model. All other blocks are the same as it was for PI and backstepping control schemes in Figs. 5.1 and 5.6, respectively. The sliding mode controller was

Fig. 5.11 MATLAB/SIMULINK block diagram of sliding mode-based rotational speed control of OWC plant

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5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

Table 5.3 The sliding mode control MATLAB code

designed using MATLAB function block. The codes for the sliding mode controller are provided in Table 5.3. Like PI and backstepping control, the performance of the sliding mode controller has been evaluated in terms of rotor speed, rotor control voltage, turbine flow coefficient, and output power. However, an additional waveform of sliding surface that is unique to sliding mode control has been included in simulation results discussions. A very fast-tracking of reference speed by actual rotor speed is achieved with sliding mode control, as shown in Fig. 5.12 for all three cases of OWC chamber pressures. However, a unique concept of chattering is present in sliding mode control due to switching between two levels. This can be observed in Fig. 5.13 as well in sliding surface waveforms. The system states reach to zero within 5 s and then toggle between two levels of −1 and + 1.

5.4 Sliding Mode Control

75

(a) Rotor speed with

(b) Rotor speed with

(c) Rotor speed with Fig. 5.12 The rotor speed performance due to sliding mode-based rotational speed control OWC plant

76

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

(a) Sliding surface with

(b) Sliding surface with

(c) Sliding surface with Fig. 5.13 The sliding surface variation in a sliding mode-based rotational speed control OWC plant

5.4 Sliding Mode Control

77

The rotor control voltage effort for sliding mode control is shown in Fig. 5.14. In all cases of OWC chamber pressure, the control cost is higher than the previous

(a) Rotor control voltage with

(b) Rotor control voltage with

(c) Rotor control voltage with Fig. 5.14 The performance of rotor control voltage due to sliding mode-based rotational speed control OWC plant

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5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

two control schemes, PI and backstepping control. The rotor control voltage toggles continuously between −170 V and +170 V. However, despite the chattering effect, the sliding mode controller is superior in terms of handling disturbances. Next, the turbine flow coefficient (in Fig. 5.15) remains below the threshold value in the sliding mode controlled OWC plant as well. The output power is maximised in all cases of OWC chamber pressure waveforms. However, due to huge chattering present in rotor control voltage, the output power waveform has high-frequency harmonics. Hence, the DFIG stator current waveforms are passed through a current filter which removes the high-frequency harmonics. The output power waveform with current filter is shown in Fig. 5.16. For d P = |6000sin(0.1π t)|Pa, |7000sin(0.1π t)|Pa and |8000sin(0.1π t)|Pa, the mean output power obtained are -30.85 kW, −39.00 kW and −47.00 kW, respectively. Three control schemes, namely, PI control, backstepping control and sliding mode control have presented in this chapter. All of them have some merits and demerits. The following points represent the comparison between them: • The design and implementation of the PI control scheme are very simple, whereas the design procedure for backstepping and sliding mode control is relatively complex. • It is not possible to guarantee complete stability of OWC with PI control as the original system is nonlinear in nature, whereas the controller is linear. However, with backstepping and sliding mode control, the stability of the closed-loop system is guaranteed because the design process involves the nonlinear dynamics of the plant. • In terms of the overall performance of the OWC plant, e.g. output power and turbine flow coefficient, all control schemes have delivered a satisfactory response. • In terms of rotor speed response, the backstepping controller performed better than the other two control schemes. • In terms of mitigating disturbances, the sliding mode control is preferred as compared to backstepping and sliding mode control schemes.

5.4 Sliding Mode Control

79

(a) Turbine flow coefficient with

(b) Turbine flow coefficient with

(c) Turbine flow coefficient with Fig. 5.15 The performance of turbine flow coefficient due to sliding mode-based rotational speed control OWC plant

80

5 Maximum Power Point Tracking of OWC Using Rotational Speed Control

(a) Output power with

(b) Output power with

(c) Output power with Fig. 5.16 The performance of output power due to sliding mode-based rotational speed control OWC plant

References

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References Amundarain M, Alberdi M, Garrido AJ, Garrido I (2009) Neural control of the Wells turbinegenerator module. In: Joint 48th IEEE conference on decision and control and 28th Chinese control conference. P.R. China, pp 7315–7320 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2010a) Control strategies for OWC wave power plants. In: American control conference. USA, pp 4319–4324 Amundarain M, Alberdi M, Garrido AJ, Garrido I, Maseda J (2010b) Wave energy plants: Control strategies for avoiding the stalling behaviour in the Wells turbine. Renew Energy 35:2639–2648 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011a) Modeling and simulation of wave energy generation plants: Output power control. IEEE Trans Ind Electron 58(1):105–117 Amundarain M, Alberdi M, Garrido AJ, Garrido I (2011b) Neural rotational speed control for wave energy converters. Int J Control 84(2):293–309 Barambones O, Durana JMG (2015) Sliding mode control for power output maximization in a wave energy systems. Energy Procedia 75:265–270 Falcáo AFO (2002) Control of an oscillating-water-column wave power plant for maximum energy production. Appl Ocean Res 24:73–82 Garrido AJ, Garrido I, Amundarain M, Alberdi M, Sen MD (2012) Sliding-mode control of wave power generation plants. IEEE Trans Ind Appl 48(6):2371–2381 Garrido AJ, Garrido I, Alberdi M, Amundarain M, Barambones O, Romero JA (2013) Robust control of oscillating water column (OWC) devices: Power generation improvement. San Diego, OCEANS, pp 1–4 Jayashankar V, Udayakumar K, Karthikeyan B, Manivannan K, Venkatraman N, Rangaprasad S (2000) Maximizing power output from a wave energy plant. IEEE Power Eng Soc Winter Meeting 3:1796–1801. Singapore Justino PAP (2006) Pontryagin maximum principle and control of a OWC power plant. In: 25th international conference on offshore mechanics and arctic engineering. Germany, pp 1–9 Justino PAP, Falcáo AFO (1999) Rotational speed control of an OWC wave power plant. J Offshore Mech Arct Eng 121:65–70 Lekube J, Garrido AJ, Garrido I (2016a) Rotational speed optimization in oscillating water column wave power plants based on maximum power point tracking. IEEE Trans Autom Sci Eng (99): 1–116 Lekube J, Garrido AJ, Garrido I, Otaola E, Maseda J (2018a) Flow control in wells turbines for harnessing maximum wave power. Sensors 18:535 Mishra SK, Purwar S, Kishor N (2016b) An optimal and non-linear speed control of oscillating water column wave energy plant with wells turbine and DFIG. Int J Renew Energy Res 6(3) Mishra SK, Purwar S, Kishor N (2016c) Design of non-linear controller for ocean wave energy plant. Control Eng Practice 56(3):111–122 Mishra SK, Purwar S, Kishor N (2018b) Event-triggered nonlinear control of owc ocean wave energy plant. IEEE Trans Sustain Energy 9(4):1750–1760 Murthy BK, Rao SS (2005) Rotor side control of Wells turbine driven variable speed constant frequency induction generator. Electric Power Components Syst 33:587–596

Chapter 6

Conclusion

In this book, modeling of the OWC plant and control schemes were discussed in detail. The simulation models of OWC plant and controllers were developed on MATLAB/SIMULINK platform. The subject matter has presented in such a way that the readers would find it easy to understand the concepts about the modeling and control of an OWC plant. A detailed account of recently developed OWC devices and their control techniques were presented in Chap. 1. The mathematical expressions for different segments of the OWC plant were discussed in Chap. 2, which include the descriptions of ocean waves, OWC chamber, Wells turbine, and DFIG. It was followed by the design of MATLAB/SIMULINK diagrams of each section of the OWC plant model. In Chap. 3, simulation results of the uncontrolled OWC plant were obtained on the OWC MATLAB/SIMULINK model that was developed in Chap. 2. Then, the Wells turbine stalling problem of the OWC plant was analyzed in detail for regular and irregular pressure conditions. To avoid turbine stalling, the two most important control schemes, airflow control and rotational speed control were introduced. The airflow control limits the flow of air turbine duct, which in turn avoids the stalling issue of the Wells turbine. Airflow control also very useful in controlling output power generated. Similarly, the rotational speed control is also helpful in avoiding turbine stalling by controlling the flux fed to the rotor of DFIG. The rotational speed controller is implemented, which aims to maximize the output power generated from the OWC plant. The PID and FOPID controllers were designed in Chap. 4 for regulating the airflow in the turbine duct of the OWC plant. The anti-windup form of PID and FOPID controllers were implemented, which was followed by the design of MATLAB/SIMULINK models of anti-windup PID and FOPID controllers. It is well known that control valves have a saturation effect, and the anti-windup approach helps in avoiding it. It was also found that FOPID is more flexible than the conventional PID controller. Later, optimally tuned PID and FOPID controllers were proposed for improving airflow controller performance. The ITAE type performance index was defined to measure the performance of the proposed PID and FOPID controllers. As © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 S. K. Mishra et al., OWC-Based Ocean Wave Energy Plants, Energy Systems in Electrical Engineering, https://doi.org/10.1007/978-981-15-9849-4_6

83

84

6 Conclusion

per the simulation analysis, the tuned controllers performed relatively better than the manually tuned controllers in terms of ITAE. The airflow control is used when it is required to control the electrical delivered to the grid. However, for maximizing the output power of the OWC plant, it is advised to go for rotational speed controllers. Finally, three rotational speed control schemes were designed in Chap. 5. These are PI, backstepping, and sliding mode control. The PI-based rotational speed control is one of the simplest controllers to design. However, it is not possible to guarantee stability without linearizing the OWC plant. In the linearized OWC plant, many key parameters might get compromised. So, it would be better to directly design the nonlinear controllers, which can also guarantee system stability. Therefore, backstepping control and sliding mode control techniques were proposed. The backstepping control is based on a step-by-step design approach that requires the system to be in strict-feedback-form. First, the OWC dynamics were converted in strict-feedbackform, and then the backstepping control law was designed. The backstepping control law satisfied the closed-loop stability of the OWC plant using the Lyapunov stability criterion. Next, in order to design the sliding mode controller, the OWC dynamics were converted in the form of error dynamics. Then, a sliding surface was chosen, followed by the design of the sliding mode control law. The sliding mode control law was again derived by satisfying the stability condition using the Lyapunov stability criterion. Again, the MATLAB/SIMULINK models of the PI, backstepping, and sliding mode controller were designed. Finally, a detailed discussion on simulation results was presented for each rotational speed controller. The modeling and control of OWC devices are evolving on each passing day. Many novel approaches are being proposed by researchers to improve the performance of the OWC devices. In this regard, this book provides a primary platform for postgraduate and doctoral level research scholars to start the research in this area.