Hydropower Plants and Power Systems -- Dynamic Processes and Control for Stable and Efficient Operation 978-3-030-17241-1

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Springer Theses Recognizing Outstanding Ph.D. Research

Weijia Yang

Hydropower Plants and Power Systems Dynamic Processes and Control for Stable and Efficient Operation

Springer Theses Recognizing Outstanding Ph.D. Research

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

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Weijia Yang

Hydropower Plants and Power Systems Dynamic Processes and Control for Stable and Efficient Operation Doctoral Thesis accepted by Uppsala University, Sweden

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Author Dr. Weijia Yang Division of Electricity Department of Engineering Sciences Uppsala University Uppsala, Sweden

Supervisor Dr. Per Norrlund Division of Electricity Department of Engineering Sciences Uppsala University Uppsala, Sweden

School of Water Resources and Hydropower Engineering Wuhan University Wuhan, China

Vattenfall AB Älvkarleby, Sweden

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-030-17241-1 ISBN 978-3-030-17242-8 (eBook) https://doi.org/10.1007/978-3-030-17242-8 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

There is no elevator to success. You have to take stairs.

Dedicated to my parents and my love

Supervisor’s Foreword

Hydropower will most likely continue to be a vital part of regulating capacity in many power systems worldwide, i.e. an important resource for balancing variations in both electricity demand and production. The unintentional variability of new renewable sources is a challenge to power systems, both due to larger amplitude in variations and due to characteristic timescales that old systems are not designed for. The ability of hydropower to adjust output power and delivering energy on a wide range of time scales is yet unparalleled. In the changing environment represented by electrical power systems transitioning to higher penetration of intermittent renewable sources, there is a need for predictions regarding the ability of existing and planned hydropower installations to provide system services. There is also a need to determine the operational costs related to these services. The thesis provides tools and insights into both these areas, treating, e.g. response time of hydropower units with complex waterways after major frequency disturbances, frequency control contribution during normal operation and relations between the quality of frequency control work and wear and fatigue indicators relevant for hydro power owners. The thesis shows an exceptional width in several dimensions, with modelling ranging from mechanical construction details via control systems, hydraulics and electrical phenomena, up to market conditions and incentives; with tools including mathematical analysis, numerical simulation, and on-site measurements; with results ranging from factors influencing generating equipment lifetime to electrical grid frequency quality and compliance with regulations. During his time as a Ph.D. student, Dr. Yang first developed tools, e.g. adding turbine controller capabilities to an existing computational framework for hydraulic computations (TOPSYS), and by that greatly expanding the set of applications possible to examine. He also wrote a description of the framework, making it more available to a wider academic audience. The validity of the framework was examined by comparisons to measurements from both Chinese and Swedish power plants, and performance measures such as response time were studied. These are only a few of the building blocks obtained by Dr. Yang, that eventually permitted him to evaluate cross-couplings between power plant dynamics and power system ix

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Supervisor’s Foreword

behaviour, under the different incentive structures valid in China, Sweden and the USA. The result is a work with international relevance, to a great extent thanks to the willingness of Dr. Yang to incorporate opinions from others, such as the Swedish industrial reference group and from academic contacts obtained at his visits abroad. Uppsala, Sweden November 2018

Dr. Per Norrlund

Parts of this thesis have been published in the following articles: • Stable Operation Regarding Frequency Stability: Weijia Yang, Jiandong Yang, Wencheng Guo, Wei Zeng, Chao Wang, Linn Saarinen, Per Norrlund. A mathematical model and its application for hydro power units under different operating conditions, Energies, 2015, 8(9), 10260–10275. Weijia Yang, Jiandong Yang, Wencheng Guo, Per Norrlund. Response time for primary frequency control of hydroelectric generating unit, International Journal of Electrical Power and Energy Systems, 74(2016):16–24. Weijia Yang, Jiandong Yang, Wencheng Guo, Per Norrlund. Frequency stability of isolated hydropower plant with surge tank under different turbine control modes, Electric Power Components and Systems, 43(15): 1707–1716. Wencheng Guo, Jiandong Yang, Weijia Yang, Jieping Chen, Yi Teng. Regulation quality for frequency response of turbine regulating system of isolated hydroelectric power plant with surge tank. International Journal of Electrical Power & Energy Systems, 2015, 73: 528–538. Wencheng Guo, Jiandong Yang, Jieping Chen, Weijia Yang, Yi Teng, Wei Zeng. Time response of the frequency of hydroelectric generator unit with surge tank under isolated operation based on turbine regulating modes. Electric Power Components and Systems, 2015, 43(20), 2341–2355. Wei Zeng, Jiandong Yang, Weijia Yang. Instability analysis of pumped-storage stations at no-load conditions using a parameter-varying model. Renewable Energy, 90 (2016): 420–429. Wei Zeng, Jiandong Yang, Renbo Tang, Weijia Yang. Extreme water-hammer pressure during one-after-another load shedding in pumped-storage stations. Renewable Energy, 99 (2016): 35–44. Jiandong Yang, Huang Wang, Wencheng Guo, Weijia Yang, Wei Zeng. Simulation of wind speed in the ventilation tunnel for surge tank in transient process. Energies, 9.2 (2016): 95. • Stable Operation Regarding Rotor Angle Stability: Weijia Yang, Per Norrlund, Chi Yung Chung, Jiandong Yang, Urban Lundin. Eigen-analysis of hydraulic-mechanical-electrical coupling mechanism for small signal stability of hydropower plant, Renewable energy, 115 (2018): 1014–1025. Weijia Yang, Per Norrlund, Johan Bladh, Jiandong Yang, Urban Lundin. Hydraulic damping mechanism of low frequency oscillations in power systems: Quantitative analysis using a nonlinear model of hydropower plants. Applied Energy 212 (2018): 1138–1152. • Efficient Operation and Balancing Renewable Power Systems: Weijia Yang, Per Norrlund, Linn Saarinen, Jiandong Yang, Wencheng Guo, Wei Zeng. Wear and tear on hydro power turbines – influence from primary frequency control, Renewable Energy, 87(2015) 88–95.

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Parts of this thesis have been published in the following articles

Weijia Yang, Per Norrlund, Linn Saarinen, Jiandong Yang, Wei Zeng, Urban Lundin. Wear reduction for hydropower turbines considering frequency quality of power systems: a study on controller filters. IEEE Transactions on Power Systems 32, (2017): 1191–1201. Weijia Yang, Per Norrlund, Jiandong Yang. Analysis on regulation strategies for extending service life of hydro power turbines, IOP Conference Series: Earth and Environmental Science. Vol. 49. No. 5. IOP Publishing, 2016. Weijia Yang, Per Norrlund, Linn Saarinen, Adam Witt, Brennan Smith, Jiandong Yang, and Urban Lundin. Burden on hydropower units for short-term balancing of renewable power systems. Nature communications 9, (2018): 2633. Linn Saarinen, Per Norrlund, Weijia Yang, Urban Lundin. Allocation of frequency control reserves and its impact on wear on a hydropower fleet, IEEE Transactions on Power Systems 33.1 (2018): 430–439. Linn Saarinen, Per Norrlund, Weijia Yang, Urban Lundin. Linear synthetic inertia for improved frequency quality and reduced hydropower wear and tear, International Journal of Electrical Power & Energy Systems 98 (2018): 488–495.

Acknowledgements

Many people said that an introduction section might be the most difficult part to write in a thesis, and I also agreed until I came to this very special section, just because I have so much gratitude to express, and I will feel guilty if I use any casual word for any one of them… Here I really would like to add the “Prof.” or “Dr.” title when I mention someone, as a Chinese tradition; but please allow me to neglect the title as a Swedish style, also because there will be too many titles in the text otherwise… The thesis was carried out as a part of “Swedish Hydropower Centre—SVC”. I thank the China Scholarship Council (CSC), StandUp for Energy, and I appreciate the scholarships and travel grants from the Anna Maria Lundin’s scholarship committee (twice), the Wallenberg, the ÅForsk, the Liljewalch and the Sederholm foundations! For my supervisors Per Norrlund and Urban Lundin, I think I can write a whole acknowledgement section just for you! To my main supervisor Per, I would like to express my sincere gratitude for your great guidance, your super nice character and your rigorous working attitude as a doctor in the field of numerical analysis! To my second supervisor Urban, thank you so much for your guidance, support and influence! In my mind, what you do is far more beyond a standard duty of a second supervisor. In many Chinese universities, there is a common prize similar to “Top 10 of the nicest supervisors”; I think that both of you will be winners if Uppsala University initiates this kind of award! To the head of our Division of Electricity, Mats Leijon, thank you for accepting me as a Ph.D. student and helping me to get my Ph.D. scholarship! Dear hydropower group members in Uppsala: Niklas Dahlbäck, Johan Abrahamsson, Birger Marcusson, Jose Perez, Jonas Noland, Fredrik Evestedt, thank you for your support and inspirations to my research. Especially to my co-authors and office-mates Linn Saarinen and Johan Bladh: thank you a lot for your comments and discussion on my works, and teaching me much knowledge and experience; I really appreciate and learned a lot from your professional and efficient way of working! To all the members of SVC reference group, thank you for your comments and supports to my project.

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Acknowledgements

I would like to thank my collaborators at Wuhan University in China. Thank you very much Jiandong Yang, you are like my “third supervisor” and I really appreciate your support and guidance! To all my co-authors and members in the hydropower group in Wuhan, especially Wencheng Guo, Chao Wang, Wei Zeng and Jiebin Yang, thank you for your discussion and help on my research, and the happy time we spent together! To all my friends in Wuhan and Changsha, thank you for companying, supporting and the happy hours we had together in my vacations! To the Energy-Water Resource Systems Team in the Oak Ridge National Laboratory in the USA: thank you Brennan Smith, Boualem Hadjerioua, Adam Witt and Stephen Signore for your wonderful cooperation and discussion. I will always keep in mind the hot but exciting days in Oak Ridge! To the SMart grid And Renewable energy Technology (SMART) Laboratory in the University of Saskatchewan in Canada: thank you C. Y. Chung for your great cooperation and insightful guidance! I also thank all the laboratory members, I indeed appreciate and enjoyed the atmosphere of your laboratory. My sincere thanks also go to all my teachers of the courses in Uppsala, KTH and Luleå: I not only gained the knowledge, but also had deep feelings on the high-quality Swedish education. I heartily thank the organizers, speakers and all fellow attendants of the UK Energy Research Centre Energy Summer School and the Energy Summer School in University of Groningen: the two summer schools really had a profound influence on my mind, much more than I thought before I attended! To Thomas Götschl, thank you for your support on my computer. Thank you, Maria Nordengren, Gunnel Ivarsson, Ingrid Ringård, Anna Wiström and Emma Holmberg, for the really helpful administrative works. Thank you Rafael Waters, Liguo Wang, Liselotte Ulvgård, Nattakarn Suntornwipat and all the student assistants, my teaching experience with you was great and smooth! Thank you Nicole Carpman for your help on ordering circuit components for the teaching! Thank all my friends, lunch-mates and colleagues in the Division of Electricity: André L., Anke B., Arvind P., Aya A., Eduard D., Flore R., Francisco F., Johan F., Juan de S., Kaspars S., Maria A. C., Minh Thao N., Pauline E., Per R., Tatiana P., Tobias K. and Victor M., thank you for the great time we had together in Angstrom, in nations and parties! To Anders G., Dalina J., Dana S., Irina D., Jennifer L., Jon O., Linnea S., Magnus H., Malin G., Marianna G., Markus G., Morgan R., Muzafar I., Petter E., Saman M., Simon T., Valeria C. and all other colleagues, thank you for sharing your interesting life and diverse knowledge from all over the world! To my new office-mates Anna F. and Jonathan S., thank you for companying for the last months of my Ph.D. study! Especially thank all my Mandarin-speaking colleges in the division, Wei L., Ling H., Yue H., Liguo W., Xiao Z., Wenchuang C., Jinming W., Qiulin L., Wooi Chin L., Lai Mun O., it is my great fortune to meet you! I give my great gratitude to my landlords Shuxi Z. and Guihua L., you are like my family in Uppsala! To my previous and current flat-mates, Shunguo W.,

Acknowledgements

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Yongmei G., Keqiang G., Xiaoyang S. and Huiying Q., thank you for all the wonderful days we had and all the ups and downs we went through together! To my pals, Changqing R., Feiyan L., Fengzhen S., Jiajie Y., Lichuan W., Meiyuan G. and Yi R., thank you for being by my side from the beginning till the end of my Ph.D. period! Thank you Hao C., Xiaoting Z., and Yanran Z., being together with you is always so nice and relaxing! To my dear Chinese friends, Chenjuan L., Chunling S., Cong S., Dan W., Fei H., Fengjiao Z., Haoyu L., Huimin Z., Jingyi H., Le F., Le G., Lei T., Lei Z., Lin S., Ling X., Liyang S., Mingzhi J., Na X., Ping Y., Qifan X., Rui S., Shihuai W., Song C., Teng Z., Tianyi S., Wen H., Wenxing Y., Xiaoliang L., Xiaowen L., Yuan T., Yuanyuan H., Zhibing Y., and Zhen Q., for all the happiness we shared and all the delicious Chinese food we had together! Really thank you Weiwei S., especially for your help and driving in Oak Ridge! I give unique thanks to unique groups: my football-mates from all over the world in Campus 1477, Flogsta fotboll, our division team, the Angstrom group and Barbafarsorna United, as well as Jiangtao C. and other Chinese teammates! Now I am proud to say that I achieved two goals of coming to Sweden: having a doctoral study and improving my football skill! Finally, to my family, especially to my parents and my love: any words here are pale and I will express my deepest gratitude with action! Wuhan, China

Dr. Weijia Yang

Contents

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1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Power System Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Features of Hydropower Generating Systems . . . . . . . . . . . . 1.2.1 Hydraulic—Mechanical—Electrical Coupling System 1.2.2 Problems of Oscillations . . . . . . . . . . . . . . . . . . . . . 1.3 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Dynamic Processes and Modelling of Hydropower Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Regulation Quality and Operating Stability . . . . . . . . 1.3.3 Efficient Operation: Wear, Efficiency and Financial Impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Hydropower Research at Uppsala University . . . . . . . . . . . . 1.5 Scope of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Outline of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Methods and Theory . . . . . . . . . . . . . . . . . . . . . . . 2.1 Principles of Methods . . . . . . . . . . . . . . . . . . . 2.1.1 Numerical Simulation . . . . . . . . . . . . . 2.1.2 On-Site Measurement . . . . . . . . . . . . . . 2.1.3 Theoretical Derivation . . . . . . . . . . . . . 2.2 Engineering Cases: HPPs in Sweden and China References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Various Hydropower Plant Models . 3.1 Numerical Models in TOPSYS . 3.1.1 Model 1 . . . . . . . . . . . . 3.1.2 Model 4 and 4-S . . . . . . 3.2 Numerical Models in MATLAB

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3.2.1 Model 2-L (in Simulink) . . . . . . . . . . . . . . . . . 3.2.2 Model 5 and 5-S (in SPS) . . . . . . . . . . . . . . . . 3.3 Models for Theoretical Derivation . . . . . . . . . . . . . . . . 3.3.1 Model 3-F . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Model 3-L . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Model 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Numerical Models in MATLAB for HPPs with Kaplan Turbines (Model 2-K) . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 System Components . . . . . . . . . . . . . . . . . . . . 3.4.2 Turbine Characteristic from Measurements . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Stable Operation Regarding Frequency Stability . . . . . . . . 4.1 Case Studies on Different Operating Conditions . . . . . . . 4.1.1 Comparison of Simulations and Measurements . . 4.1.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Response Time for Primary Frequency Control . . . . . . . 4.2.1 Specifications of Response of PFC . . . . . . . . . . . 4.2.2 Formula and Simulation of Response Time . . . . . 4.3 Frequency Stability of Isolated Operation . . . . . . . . . . . . 4.3.1 Theoretical Derivation with the Hurwitz Criterion 4.3.2 Numerical Simulation . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Stable Operation Regarding Rotor Angle Stability . . . . . . . . . . . 5.1 Hydraulic—Mechanical—Electrical Coupling Mechanism: Eigen-Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Influence of Water Column Elasticity (Te) . . . . . . . . . . 5.1.2 Influence of Mechanical Components of Governor (Ty) 5.1.3 Influence of Water Inertia (Tw) . . . . . . . . . . . . . . . . . . 5.1.4 Influence on Tuning of PSS . . . . . . . . . . . . . . . . . . . . 5.2 Quantification of Hydraulic Damping: Numerical Simulation . 5.2.1 Method and Model . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Quantification of the Damping Coefficient . . . . . . . . . . 5.2.3 Influence and Significance of the Damping Coefficient . 5.3 Discussion on Quick Response of Hydraulic—Mechanical Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Efficient Operation and Balancing Renewable Power 6.1 Wear and Tear Due to Frequency Control . . . . . . 6.1.1 Description and Definition . . . . . . . . . . . . 6.1.2 Cause . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Analysis on Influencing Factors . . . . . . . .

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6.2 Controller Filters for Wear Reduction Considering Frequency Quality of Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Method and Model . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 On-Site Measurements . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Time Domain Simulation . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Frequency Domain Analysis: Stability of the System . . 6.2.5 Concluding Comparison Between Different Filters . . . . 6.3 Framework for Evaluating the Regulation of Hydropower Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 The Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Burden Quantification . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Regulation Performance . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 Regulation Payment . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Stable Operation Regarding Frequency Stability . . . 7.1.2 Stable Operation Regarding Rotor Angle Stability . . 7.1.3 Efficient Operation and Balancing Renewable Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 General Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Author Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Abbreviations and Symbols

0-D 1-D 2-D 3-D AVR GV GVO HPP OF PF PFC PI PID PJM PSAT PSS RB RBA SISO SPS SvK TSO VRE

Zero dimensional One dimensional Two dimensional Three dimensional Automatic voltage regulator Guide vane Guide vane opening Hydropower plant Opening feedback Power feedback Primary frequency control Proportional–integral Proportional–integral–derivative PJM interconnection LLC Power system analysis toolbox Power system stabilizer Runner blade Runner blade angle Single input and single output Simpowersystems Svenska kraftnät Transmission system operator Variable renewable energy

Latin Symbols a aw A

Runner blade angle (pu) Velocity of pressure wave (m/s) Cross-sectional area of pipeline (m2) xxi

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AP AS atk BLa BLgv BM, BP CM, CP bp bp2 bp3 c D D1 Dp Dt Ed00 Efd eg Eq0 Eq00 eqy, eqx, eqh ey , ex , eh f fD f0 fc fg fi fp ft G g G1 G2 GF Gg GP

Abbreviations and Symbols

Cross-sectional area of turbine inlet (m2) Cross-sectional area of turbine outlet (m2) Runner blade angle at time step tk (pu) Runner backlash (pu) Guide vane backlash (pu) Intermediate variables of method of characteristic (m2/s) Intermediate variables of method of characteristic (m3/s) Governor droop (pu) Governor droop of the rest of the units in the grid (pu) Governor droop in Model 3 (pu) Pressure propagation speed in penstock (m/s) Common damping coefficient (pu) Diameter of runner (m) Inner diameter of the pipe (m) Equivalent hydraulic turbine damping coefficient (“the damping coefficient”) (pu) d-axis component of the sub-transient internal EMF (pu) Excitation emf (pu) Coefficient of load damping (pu) q-axis component of the transient internal emf (pu) q-axis component of the sub-transient internal emf (pu) Partial derivative of turbine discharge with respect to guide vane opening, speed and head (pu) Partial derivative of turbine power output with respect to guide vane opening, speed and head (pu) Frequency or turbine rotational speed (pu) Darcy–Weisbach coefficient of friction resistance (pu) Rated frequency of power system (50 Hz in this thesis) (Hz) Given frequency (Hz) Generator frequency (Hz) Frequency of oscillation corresponding to an eigenvalue (Hz) Frictional coefficient of penstock (pu) Frictional coefficient of tunnel (pu) Comprehensive gate opening (pu) Gravitational acceleration (m/s2) Gain from frequency deviation to power deviation for the Kaplan unit (pu) Gain from frequency deviation to power deviation for the lumped hydropower plant (pu) Fitting function of the comprehensive gate opening (pu) Transfer function describing the grid (pu) Transfer function describing the head variation due to the discharge deviation in the penstock (pu)

Abbreviations and Symbols

GPI GS Gt h H h0 H0 h1 Hp Hs hy0 I d, I q J K1 K2 K3 Ka Kd Ki Kp Ks Kx, KPe L M M11 Mg mg MR MR-base Mt mt n n11 nc nr PA,i, PB,i Paymile Paystrength pc Pe, Pm pg

xxiii

Gain from GVO deviation to frequency deviation for the PI controller (pu) Transfer function describing the head variation due to the discharge deviation in the surge tank (pu) Transfer function describing the Francis turbine and waterway system (pu) Water head (pu) Water head in the pipeline (m) Initial water head (pu) Net head of turbine (m) Derivative of water head with respect to time (s−1) Water head at turbine inlet (m) Water head at turbine outlet (m) Head loss of draw water tunnel (pu) d- and q-axis component of the armature current (pu) Moment of inertia (kgm2) Scaling factor in Model 1 (pu) Scaling factor of the lumped hpp in Model 2-K-2 (pu) Scaling factor of the lumped hpp in Model 2-K-3 (pu) Gain of exitation system (automatic voltage regulator) (pu) Governor parameter for the proportional term (s) Governor parameter for the integral term (s−1) Governor parameter for the derivative term (pu) Gain of power system stabilizer (pu) Gain of power system stabilizer for selecting different inputs (pu) Length of penstock (m) System inertia (s) Unit mechanical torque (N/m2.5) Resistance torque of generator (Nm) Relative resistance torque of generator (pu) Regulation mileage (MW) Base value of regulation mileage (MW) Mechanical torque (Nm) Relative mechanical torque (pu) Rotational speed (rpm) Unit rotational speed (m0.5/s) Given rotational speed (rpm) Rated rotational speed (rpm) Absolute value of a local maximum or local minimum of speed deviation (pu) Amount of mileage payment (pu) Amount of strength payment (pu) Given power (MW) Electromagnetic active power and mechanical power (pu) Generator power (pu)

xxiv

pl pm pm, k pm0 pm2 Pm-rated pr PRMSE Pstep q q0 Q11 Qe, Qg Qp Qs qt qy s SR SR1, SR1-pu SR2, SR2-pu SR-base SRT t T0, T1, T2 0 00 Td0 ,Td0 Tdel-a Tdel-gv Te Tf TF Tj tk tp 00 Tq0 Tr Ts Tw Twp Twt Twy Ty Tya

Abbreviations and Symbols

Load (pu) Active power (pu) Active power at time step k (pu) Initial active power (pu) Active power of the lumped HPP (pu) Rated power of generating unit (MW) Rated power of generating unit (MW) A root mean square error used for quantifying Dt (pu) Increase in output power caused by a frequency step change from 50 to 49.9 Hz (MW) Discharge (pu) Initial discharge (pu) Unit discharge (m0.5/s) Reactive power of generator (pu) Discharge of turbine inlet (m3/s) Discharge of turbine outlet (m3/s) Discharge of turbine (pu) Discharge of draw water tunnel (pu) Complex variable in Laplace transform (s−1) Regulation strength (MW/Hz) Regulation strength of the Kaplan unit (pu) Regulation strength of the lumped hydropower plant (pu) Base value of regulation strength (MW/Hz) Regulation strength of all the units in the grid (pu) Time (s) Parameters of power system stabilizer (s) Open-circuit d-axis transient and sub-transient time constants (s) Delay time in runner control (s) Delay time in guide vane control (s) Time constant of water column elasticity, Te = L/c (s) Period of frequency oscillation (s) Surge tank time constant (s) Mechanical time constant (s) Number of time step (–) Time constant in grid inverse model (s) Open-circuit d-axis sub-transient time constants (s) Time constant in exitation system (automatic voltage regulator) (s) Time constant of surge (s) Water starting time constant (s) Water starting time constant of penstock (s) Water starting time constant of tunnel (s) Water starting time constant of draw water tunnel (s) Time constant of guide vane servo (s) Time constant of runner blade servo (s)

Abbreviations and Symbols

V V1 Vg Vgd, Vgq VPSS Vs Vsd, Vsq x Xd , Xd0 , Xd00 00 00 XdR , XqR xf Xq , Xq00 Xs

y yc YGV, dist yPI yPID YRB, dist yservo z

xxv

Average flow velocity of pipeline section (m/s) Signal between washout and phase compensation block in power system stabilizer (pu) Voltage at the generator terminal (pu) d- and q-axis component of the voltage at the generator terminal (pu) Output signal of power system stabilizer (pu) Infinite bus voltage (pu) d- and q-axis component of the infinite bus voltage (pu) Position (m) d-axis synchronous, transient and sub-transient reactance of generator (pu) 00 00 XdR ¼ Xd00 þ Xs ; XqR ¼ Xq00 þ Xs (pu) Relative value of speed (frequency) deviation, xf = (fg – fc)/fc (pu) q-axis synchronous and sub-transient reactance of generator (pu) Total reactance of transmission line (between generator and infinite bus) (pu) Guide vane opening (pu) Given value of guide vane opening (pu) Movement distance of guide vane (pu) Guide vane opening signal between PI terms and servo (pu) Guide vane opening signal after PID terms (pu) Movement distance of runner blade (pu) Guide vane opening signal after the servo (pu) Relative change value of water level in surge tank (pu)

Greek Symbols a, ap aHP aHS d D Df Dh DH

Elasticity coefficient of penstock (pu) Correlation coefficient of kinetic energy at turbine inlet (m−2) Correlation coefficient of kinetic energy at turbine outlet (m−2) Power (or rotor) angle (rad) Stands for a deviation from a steady-state value (–) Frequency deviation from set-point value (pu) Water head deviation   from initial value (pu)

Dhp

Water head deviation from initial value due to hydraulic dynamics in penstock (pu) Water head deviation from initial value due to hydraulic dynamics in surge tank (pu) Speed deviation (pu) Discharge deviation from initial value (pu) Time step in simulation (s)

Dhs Dn Dq Dt

DH ¼

aHP 2gA2P

aHS 2  2gA 2 QP (m) S

xxvi

Dy DZ Dη η ηI ηSj ηst h n u x x0

Abbreviations and Symbols

Guide vane opening deviation from set-point value (pu) Absolute change value of water level in surge tank (m) Efficiency change (pu) Turbine efficiency (pu) Interpolation function of the turbine efficiency (pu) Average value of the instantaneous efficiency during the operation period under a specific strategy (Sj) (pu) On-cam steady-state efficiency (pu) Angle between the axis of pipeline and horizontal plane [rad) Damping ratio of an oscillation (–) Power factor angle at the generator terminal (rad) Angular velocity of the generator (pu) Synchronous angular velocity in electrical radians (equals to 2pf0) (rad/s)

Note that the symbols in subsection 2.1.3 of mathematical variables for theory introduction are explained within the text, and they are not listed here

Chapter 1

Introduction

Hydropower has played an important role in the safe, stable and efficient operation of electric power systems for a long time. Hydropower not only generates electricity as the largest global renewable source, but also shoulders a large portion of the regulation and balancing duty in many power systems all over the world. Hydropower technology is relatively mature, but new challenges are still emerging. First, with current trends toward de-carbonization in the electricity sector [1], the amount of electricity generated by variable renewable energy (VRE) sources has been constantly growing [2, 3]. Dealing with generation intermittency of VRE in an effective and efficient manner is a growing research field [3–6]. High VRE integration [7] and fewer heavy synchronously connected generators, which imply less inertia [8], lead to crucial consequences for power system stability. Second, a hydropower generation system is a complex nonlinear power system including hydraulic, mechanical and electrical subsystems (details in Sect. 1.2). The generator size and the complexity of waterway systems in hydropower plants (HPPs) have been increasing. Especially in China [9, 10] dozens of HPPs with at least 1000 MW capacity are being planned, designed, constructed or operated. Third, many large HPPs are located far away from load centres, forming many hydro-dominant power systems, such as the cases in Sweden [11] and China [12]. In recent years, there has been a tendency that the new turbines experience fatigue to a greater extent than what seem to be the case for new runners decades ago [13], and the maintenance needs at HPPs are affected [14], due to more regulation movements caused by increasingly more integration of VRE. In some countries, as in Sweden, primary frequency control (PFC) is a service that the transmission system operator (TSO) buys from the power producers. In other countries, as in Norway and China, there is also an obligation for the producers to deliver this service, free of charge. However, there are costs related to this, e.g. due to design constraints and auxiliary equipment when purchasing a new unit or system, due to wear and tear that affects the expected life time and maintenance intervals, and due to efficiency loss when a unit operates in a condition that deviates from the best efficiency point, etc.

© Springer Nature Switzerland AG 2019 W. Yang, Hydropower Plants and Power Systems, Springer Theses, https://doi.org/10.1007/978-3-030-17242-8_1

1

2

1 Introduction

Based on the aforementioned aspects, the demand on the quality of regulation emanating from hydropower units has been increasing. Stable and efficient operation of HPPs and their interaction with power systems is of great importance.

1.1 Power System Stability Power system stability is generally defined as a property of a power system, and it enables the system to remain in a stable operating state under normal operating conditions and to restore an equilibrium after a disturbance [15]. Three forms of power system stability are defined as follows [16]. (1) Frequency stability refers to the ability of a power system to maintain steady frequency after a severe system disturbance leading to a significant imbalance between generation and load. It depends on the ability to maintain and restore equilibrium between system generation and load, with minimum unintentional loss of load [16]. (2) Rotor angle stability refers to the ability of synchronous machines in a power system to remain synchronized after a disturbance. It depends on the ability to maintain and regain stability between electromagnetic torque and mechanical torque of each synchronous machine in the system [16]. (3) Voltage stability means the capability of a power system to maintain steady voltages at all buses in the system after a disturbance from a given initial operating condition. It is determined by the ability to maintain and restore equilibrium between load demand and load supply from the power system [16]. In this thesis, the main focus is on the frequency stability and the rotor angle stability of power systems. In order to maintain frequency stability, generating units change their power output automatically according to the change of grid frequency, to make the active power balanced again. This is the PFC. PFC of electrical power grids is commonly performed by units in HPPs, because of the great rapidity and amplitude of the power regulation. PFC supplied by hydropower units is a core content of this thesis. It is worth noting that the term “stability” is also used with respect to control theory, which is introduced in Sect. 2.1.3.

1.2 Features of Hydropower Generating Systems In this section, important features of hydropower generating systems are highlighted, as main analysis objects of the works throughout the thesis.

1.2 Features of Hydropower Generating Systems

3

Fig. 1.1 Simple illustration of a HPP: a hydraulic—mechanical—electrical coupling system [https://water.usgs.gov/edu/wuhy.html (accessed on March 14th, 2017)]

1.2.1 Hydraulic—Mechanical—Electrical Coupling System A HPP is a complex nonlinear system integrating hydraulic—mechanical—electrical subsystems, as shown in Fig. 1.1. A core scientific challenge is to reveal the coupling mechanisms and oscillation characteristics of diverse physical variables within multiple subsystems. For describing transient processes in HPPs, there are several common time constants, such as:    , Td0 , Tq0 ), mechanical transient and sub-transient time constants of generator (Td0 time constant (T j ) regarding the electrical subsystem; water starting time constant (T w ), time constants of water column elasticity (T e ), servo (T y ), and surge (T s ) in surge tank or gate shaft, etc. regarding the hydraulic and mechanical subsystems. The common ranges of these time constants are presented in Fig. 1.2, indicating the interactions among the multiple variables.

1.2.2 Problems of Oscillations There are different oscillation issues with various periods existing in hydropower generating systems, as illustrated by the measured data in Fig. 1.3 (350 s oscillation), Fig. 1.4 (60 s oscillation) and Fig. 1.5 (1 s oscillation). In terms of different categories of stability studied in this thesis, oscillation periods regarding frequency stability (>20 s) is normally larger than the ones regarding

4

1 Introduction

Fig. 1.2 Common ranges of some standard time constants in the hydropower system, indicating the interactions among the multiple variables. The definitions of the symbols are in the section Abbreviations and symbols. Time constants regarding the electrical subsystem (generator) are in red, and time constants regarding hydraulic and mechanical subsystems are in blue Fig. 1.3 Oscillations with a period around 350 s: measurements of guide vane opening (GVO) and power output under a load step disturbance in a Chinese HPP with a surge tank

Fig. 1.4 Oscillation with a period around 60 s: measured frequency of the Nordic power system

rotor angle stability ( E dz ). π A A A (3.41) The describing function of a floating dead zone of size E fdz (backlash) [13] is ⎤ ⎡      2 E f dz E f dz E f dz ⎦ 2E f dz 1 π + 1− − N f dz (A) = ⎣ + ar csin 1 − π 2 A A A A 

   E f dz 2  1 2E f dz −j (3.42) A > E f dz − π A A Here, the parameter A means the amplitude of the periodical input signal.

3.3.2.2

Transfer Functions for Nyquist Stability Criterion

In order to investigate the system stability, the open-loop systems with different filters are examined by the Nyquist stability criterion, as introduced in Sect. 2.1.3.3. For analysing the system with the dead zone and floating dead zone, the transfer function of the open-loop system is Φ1 (s) = C(s)P(s)G(s) =

b01 s 3 + b11 s 2 + b21 s + b31 . a01 s 4 + a11 s 3 + a21 s 2 + a31 s + a41

(3.43)

For the open-loop system with the linear filter, the transfer function is Φ2 (s) = F f 1 (s)C(s)P(s)G(s) =

b02 s 3 + b12 s 2 + b22 s + b32 . a02 s 4 + a12 s 3 + a22 s 2 + a32 s + a42

All the transfer function coefficients here are shown in Appendix A.

(3.44)

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3 Various Hydropower Plant Models

3.3.3 Model 6 Model 6 is built for eigen-analysis on the rotor angle stability in Sect. 5.1. The corresponding model for time domain simulation is Model 5.

3.3.3.1

Details of the Model

The overall structure of Model 6 is the same with Model 5, as shown in Fig. 3.9. It is a SMIB system with an extended model of a HPP described by a state matrix, ignoring all the nonlinear factors. The generator and the power grid are modelled with the same approach as Model 4, as shown in Eq. (3.21) through (3.24). The AVR and the PSS (with the speed input and the power input) are the same as the ones in Model 5 and 5-S, with the output saturation removed, as described in Eqs. (3.25) and (3.32). The turbine and waterway system is described by a linear model, the same as the one in Model 5. The corresponding equation of the turbine is 

q = eqy y + eqω ω + eqh h . Pm = e y y + eω ω + eh h

(3.45)

The corresponding equation of the elastic water column is −Tw s h = . q 1 + αTe2 s 2

(3.46)

From Eqs. (3.45) and (3.46), two differential equations are deduced:  dh dt dh 1 dt

= h 1  =

1 αTr2

  dω dh −h − Tw eqy dy + e + e qω qh dt dt dt

(3.47)

The governor system is a linearized version of the one in Model 5, as illustrated in Fig. 3.11, excluding the nonlinear components with dashed-outline. The equation of frequency control with the OF is  dy P I  dω + b p K i y P I = −K p − K i ω. 1 + bp K p dt dt

(3.48)

The equation of the PF is dy P I dPe dω = −b p K p − b p K i Pe − K p − K i ω. dt dt dt

(3.49)

3.3 Models for Theoretical Derivation

45

Note that the PF signal here is the electromagnetic power, not the mechanical power. The servo is described by Ty

3.3.3.2

dy = y P I − y. dt

(3.50)

State Matrix for Eigen-Analysis

As introduced in Sect. 2.1.3.5, the small signal stability of the system can be analysed by investigating the eigenvalues of the state matrix. For the whole system of Model 6, there are twelve differential equations, i.e. five equations for the generator, one equation for the AVR, two equations for the PSS, two equations for the turbine with the waterway system, one equation for the servo and one equation for the PI controller. Hence, a 12 × 12 state matrix with twelve corresponding state variables is derived, as shown in

(3.51) All the non-zero elements, ai, j , of the state matrix are given in Appendix A. Analyses are conducted based on damping ratios corresponding to different eigenvalues in the system for each case. The smallest damping ratio is selected as the main indicator of the system stability.

3.4 Numerical Models in MATLAB for HPPs with Kaplan Turbines (Model 2-K) Model 2-K (“K” is short for “Kaplan turbine”) is a numerical HPP model with a Kaplan turbine implemented in applying Simulink, calibrated with measurements

46

3 Various Hydropower Plant Models

Fig. 3.15 Model 6: Overall model structure of a hydropower system with a Kaplan turbine. Some detailed set points and feedback signals are omitted here, but included in the more detailed block scheme shown in the following content

from two Swedish HPPs (HPP 6 and HPP 7). It is established for quantifying relative values of regulation burden and performance of PFC in Sect. 6.3. Model 2-K is divided into several sub-models, i.e. Model 2-K-1, Model 2-K2 and Model 2-K-3 for different purposes that are introduced in Sect. 6.3. In this section, Model 2-K-1 and Model 2-K-2 are presented, and Model 2-K-3 is introduced additionally in Sect. 6.3. The per-unit (pu) system is adopted for describing all the models. The overall structure of the model is shown in Fig. 3.15. The open loop “hydropower plant” model with the red dashed outline is Model 2-K-1, for simulating the transient processes within a HPP. In this thesis, it is mainly applied for computing the efficiency (η), power output (pm ), GVO and RBA. The closed loop model with the blue dashed outline is Model 2-K-2, for simulating the frequency quality of the whole power system.

3.4.1 System Components 3.4.1.1

Kaplan Turbine and Waterway System

The Kaplan turbine and waterway system model is illustrated in Fig. 3.16. The active power from the turbine is described by the classical simplified non-linear model [6, 14]:  √ q = q0 + q = G h = G h 0 + h,

(3.52)

pm = ηqh = ηGh 3/2 .

(3.53)

3.4 Numerical Models in MATLAB for HPPs with Kaplan Turbines (Model 2-K)

47

Fig. 3.16 Block diagram of a model of Kaplan turbine and waterway system in Model 2-K. The signal of RBA is presented in blue, for distinguishing it from the GVO signal

The above two equations are for single-regulated turbines, e.g. Francis turbines. While for the double-regulated turbine, G is a comprehensive gate opening that is identified from the values of GVO (y) and RBA (a), as shown in a fitting function G = G F (y, a).

(3.54)

The efficiency value is from an interpolation function η = η I (y, a).

(3.55)

These two functions are achieved from on-site measurement data that is presented separately in Sect. 3.4.2. The head is affected by hydraulic dynamics from the elastic penstock, draw water tunnel and surge tank [14], as shown in 

h = h 0 + h . h = h p + h s

(3.56)

In terms of frequency domain, the transfer function describing the head variations due to discharge deviations in the penstock is Twp α p Te f p s 2 + Te s + f p h p = G p (s) = − · . q Te 1 + α p Te2 s 2

(3.57)

For the head variations due to discharge deviations in the surge tank, the transfer function is h s Twt s + f t = G s (s) = − . q Twt Ts s 2 + Ts f t s + 1

(3.58)

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3 Various Hydropower Plant Models

Fig. 3.17 Block diagram of governor system of the Kaplan turbine in Model 2-K

When the turbine damping (D) [14] is included, the equation of the active power becomes pm = ηGh 3/2 − DG f.

3.4.1.2

(3.59)

Governor System with Filters

The model of a governor system for a Kaplan turbine is demonstrated in Fig. 3.17. A standard PID (proportional–integral–derivative) controller with droop, common mechanical components and a 2-D (two-dimensional) lookup table, and the artificial filter for the signal of RBA are included. The filter for RBA is a floating dead zone (or floating dead band) that is the same as the one presented in Sect. 3.2.1, which is equivalent to the backlash in the Simulink model.

3.4.1.3

Power Grid

For investigating the frequency quality under different operation strategies, a simplified model [8, 15] representing the Nordic power grid is applied, as shown in Fig. 3.15. The transfer function is the same as the one in Model 2-L, as described in Eq. (3.31).

3.4.1.4

Lumped HPP

The lumped HPP represents the rest of regulating units in the power grid, by assuming that all the regulation in the grid is provided by hydropower. The principle of modelling the lumped HPP is the same as it is for Model 2-L, expect for the disposition of the corresponding scaling factor.

3.4 Numerical Models in MATLAB for HPPs with Kaplan Turbines (Model 2-K)

49

Fig. 3.18 Block diagram of a model of lumped HPP in Model 2-K. The model contains a governor and a simplified representation of Francis turbine

As shown in Fig. 3.18, the model contains a governor and a simplified representation of a Francis turbine and waterway system, as described in G t (s) =

−Tw s + 1 . 0.5Tw s + 1

(3.60)

3.4.2 Turbine Characteristic from Measurements Model development regarding the turbine characteristics is a key point here. As shown in Table 3.1, a specific model for describing turbine characteristic is developed for Model 2-K, comparing to the common approach by applying turbine characteristics curves. More exactly, the comprehensive gate opening and efficiency, as shown in Eqs. (3.54) and (3.55), are modelled from specific on-site index tests [16, 17] data from HPP 6 and HPP 7. Here, the principle of the approach is introduced and more details can be found in the published work [18]. The measured scatter data of comprehensive gate opening and efficiency can be calculated for a limited operating region and applied for the fitting or the interpolation. By applying the surface fittings, the turbine characteristics for a larger operation range can be obtained. A relatively higher efficiency accuracy is demanded by the economic analysis, and it can be achieved by interpolation of the efficiency data. However the measurement data are only available in a certain range, hence extra data for larger operating points are added from the fitting data for the extrapolation.

3.4.2.1

Fittings

The comprehensive gate opening and efficiency for each HPP are fitted to a quadratic polynomial surface using G = G F (y, a) = pG00 + pG10 a + pG01 y + pG20 a 2 + pG11 ay + pG02 y 2 , (3.61)

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3 Various Hydropower Plant Models

Fig. 3.19 Fitting of data of HPP 7: a comprehensive gate opening GF and b turbine efficiency data. The efficiency value is normalized with respect to the maximum efficiency value

η = η F (y, a) = pη00 + pη10 a + pη01 y + pη20 a 2 + pη11 ay + pη02 y 2 .

(3.62)

where, pGij and pηij are the coefficients of the fitting. The fittings are demonstrated in Fig. 3.19, taking HPP 7 as an example. The fitting of an operating point far from the on-cam range might not be accurate, however, this will not affect the results of this study because the fitting is only applied for small disturbance simulations.

3.4 Numerical Models in MATLAB for HPPs with Kaplan Turbines (Model 2-K)

51

Fig. 3.20 Interpolation of turbine efficiency data of HPP 7. The red scatters are extracted from the fitting for extrapolation

3.4.2.2

Interpolations and Extrapolation of Efficiency

Piecewise cubic interpolation is applied to obtain the final efficiency data, as shown in Fig. 3.20. By adopting the added points (in red) from the fitting data, the small operation range covered by the index tests is extended, then the efficiency data can support all the small disturbance simulations (in Sect. 6.3).

References 1. Bao H, Yang J, Fu L (2009) Study on nonlinear dynamical model and control strategy of transient process in hydropower station with francis turbine. In: Power and Energy Engineering Conference. APPEEC 2009. Asia-Pacific, 1–6, IEEE 2. Bao H (2010) Research on setting condition of surge chamber and operation control of the hydropower station (In Chinese). Wuhan University, Wuhan 3. Streeter VL, Wylie EB (1978) Fluid transients. McGraw-Hill, New York 4. Yang W et al (2015) A mathematical model and its application for hydro power units under different operating conditions. Energies 8:10260–10275 5. Machowski J, Bialek J, Bumby J (2011) Power system dynamics: stability and control. Wiley, Hoboken 6. Kundur P, Balu NJ, Lauby MG (1994) Power system stability and control. McGraw-hill, New York 7. Saarinen L, Norrlund P, Lundin U (2016) Tuning primary frequency controllers using robust control theory in a power system dominated by hydropower. In: CIGRE Session 2016 8. Saarinen L (2017) The frequency of the frequency: on hydropower and grid frequency control. Uppsala University 9. Ljung L, Glad T (2000) Control theory-multivariable and nonlinear methods. Taylor and Francis 10. IEEE Guide for the Application of Turbine Governing Systems for Hydroelectric Generating Units. In: IEEE Std 1207-2011 (Revision to IEEE Std 1207-2004), 1-131 (2011) 11. Ghrist WD III (1986) Floating deadband for speed feedback in turbine load control. (ed. USPTO) 12. Hägglund T (2013) A unified discussion on signal filtering in PID control. Control Eng Pract 21:994–1006

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13. Vander Velde WE (1968) Multiple-input describing functions and nonlinear system design. McGraw-Hill, New York 14. Demello F et al (1992) Hydraulic-turbine and turbine control-models for system dynamic studies. IEEE Trans Power Syst 7:167–179 15. Saarinen L, Norrlund P, Lundin U (2016) Tuning primary frequency controllers using robust control theory in a power system dominated by hydropower. In: CIGRE Session 2016, Paris, France 16. Kercan V, Djelic V, Rus T, Vujanic V (1996) Experience with Kaplan turbine efficiency measurements–current meters and/or index test flow measurement. In: Proceedings of the IGHEM, Montreal, Canada 17. Adamkowski A, Lewandowski M, Lewandowski S (2014) Selected experiences with optimization tests of the Kaplan-type hydraulic turbines. J Energy Power Eng 8 18. Yang W et al (2018) Burden on hydropower units for short-term balancing of renewable power systems. Nat Commun 9:2633

Chapter 4

Stable Operation Regarding Frequency Stability

The stable operation of HPPs regarding frequency stability of power systems is analysed in this chapter. In Sect. 4.1, case studies on different operating conditions of HPPs are conducted, and the simulation performance of Model 1 based on TOPSYS is presented. In Sect. 4.2, response time of PFC in HPPs is investigated under gridconnected operation. In Sect. 4.3, frequency stability of HPPs in isolated operation is studied. All the content in these three sections mainly focus on active power control, of which the ultimate goal is achieving a better frequency stability of power systems.

4.1 Case Studies on Different Operating Conditions The application of Model 1 based on TOPSYS is presented in this section by comparing simulations with on-site measurements, based on four engineering cases: a Swedish HPP (HPP 1 shown in Fig. 3.2) and three Chinese HPPs (HPP 2—HPP 4 shown in Fig. 4.1). The aim of Model 1 is to achieve accurate simulation and analysis of different operation cases, e.g. small disturbance, large disturbance, start-up and no-load operation, etc. A good simulation in Model 1 is a crucial basis of the thesis, such as for the studies in Sect. 4.2 (grid-connected operation), Sect. 4.3 (isolated operation) and Sect. 6.1 (grid-connected operation).

4.1.1 Comparison of Simulations and Measurements For normal operation (small disturbances in grid-connected operation and isolated operation), the comparison between simulations with Model 1 and measurements are shown in Fig. 4.2 through Fig. 4.4. © Springer Nature Switzerland AG 2019 W. Yang, Hydropower Plants and Power Systems, Springer Theses, https://doi.org/10.1007/978-3-030-17242-8_4

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4 Stable Operation Regarding Frequency Stability

Overall, the simulation has a good agreement with the measurements. As shown in Fig. 4.2, the effect of backlash is reflected: the GVO keeps stable for a short period during the direction change process (e.g. around t = 28 s). In Fig. 4.3, after the frequency step change, the phenomenon of power reverse regulation caused by water inertia is simulated accurately, as well as the gradual power increase or decrease due to the surge (after 20 s). However, the simulation of the power decrease has a lower value than the measurement. This deviation could be ascribed to the characteristic curve, to some extent, the on-site measurements inevitably deviate from the simulation that is based on the data from the model tests. The oscillation after a load step change is examined by simulation and compared with the measurements, as shown in Fig. 4.4. The simulation reflects the real operating condition well: under the power control mode in HPP 3, the power oscillates with the surge oscillation under certain governor parameter settings due to a relatively small cross section of the surge tank.

Fig. 4.1 TOPSYS models of three Chinese HPPs: HPP 2—HPP 4 in Table 2.1

Fig. 4.2 Grid-connected operation: power output and opening from simulation and measurement under sinusoidal frequency input (HPP 1). In the figures of this thesis, the “M” refers to measurements and the “S” means simulation

4.1 Case Studies on Different Operating Conditions

55

Fig. 4.3 Grid-connected operation: power from simulation (“S-”) and measurement (“M-”) under step frequency input (HPP 2)

Fig. 4.4 Isolated operation: simulation (“S-”) and measurement (“M-”) of the power oscillation under power control mode (HPP 3)

For the start-up process, a case study of HPP 2 is simulated and compared with measurements, as shown in Fig. 4.5. In the simulation with the original characteristic curve of the turbine (S), the simulated frequency increase process is approximately 30% shorter than the measured one, hence the opening from simulation decrease to the no-load opening slightly earlier than the measured opening. Therefore, the curve was modified by decreasing the efficiency. With this revised characteristic curve, the new simulation (S2) fits the measurement well. It demonstrates that the inaccurate

56

4 Stable Operation Regarding Frequency Stability

Fig. 4.5 Frequency and opening from simulation and measurement during a start-up process (HPP 2). The “S” means the simulation with the original characteristic curve of turbine, and the “S2” means the simulation with the modified characteristic curve

Fig. 4.6 Simulation and measurement of the a GVO and pressure in the volute; and b pressure in the draft tube, during a load rejection process (HPP 4)

simulation mainly hinges on errors in the characteristic curve, which is especially error-prone in the small-opening operation range. Due to that for the small-opening operation range, the original input data achieved from the characteristic curve is not accurate enough and very sparse, it is hard to obtain a good predictive simulation. For the load rejection process, the pressures at the inlet of the volute and in the draft tube are simulated and compared with measurements in HPP 4, as demonstrated in Fig. 4.6. For the simulated pressure, there is a small static deviation from the measurement after load rejection. It might be due to the water head error caused by the characteristic curve and imprecise parameters of the waterway system. Moreover, the pulsating pressure at volute and draft tube in the measurement cannot be reproduced by the simulations because of the limitation of the one-dimensional

4.1 Case Studies on Different Operating Conditions

57

characteristic method. The pressure measurement in the draft tube might also be difficult to compare to modelled values, due the swirl not being modelled in the 1-D modelling approach, making the actual water velocity past the pressure transducer deviate from the mean velocity in an unknown way.

4.1.2 Discussion The results above show that Model 1 can yield trustworthy simulation results for different physical quantities of the unit under various operating conditions. The main error sources of the simulation are the characteristic curves of the turbine, provided by manufacturers, which directly causes small deviations of power output and affects the rotation speed and pressure values. The reason might be that the characteristic curves do not really describe the on-site dynamic process accurately, and the error is especially obvious in the small-opening operation range. Furthermore, waterway system parameters might also have errors that impact the simulation.

4.2 Response Time for Primary Frequency Control For evaluating the regulation quality of hydro units in PFC, a key is the power response time. How do the regulation and water way system affect the response time? How should governor parameters be set to control the power response time? These problems are the focuses of this section. The aim of this section is to investigate general rules for controlling the power response time of PFC. Firstly, specifications of the response of PFC in different regions are introduced. Then, from the analytical aspect, a time domain solution for GVO response and a response time formula are deduced. Case studies of HPP 2 are conducted by simulations based on Model 1, to investigate various influencing factors. The response time (deployment time) T response and the delay time T delay of power response process are the key indicators in this section, as shown in Fig. 4.7. The difference between the power response and the GVO response is the focus.

4.2.1 Specifications of Response of PFC Strictly speaking, the parameters need to be tuned and tested for PFC in every HPP, for meeting the requirement of specifications that varies in different regions. (1) China Electricity Council

58

4 Stable Operation Regarding Frequency Stability

Fig. 4.7 Illustration of different times under frequency step disturbance. The opening means GVO

Based on specifications of China Electricity Council [1], if the units are operating on 80% of the rated load, the power response for a frequency step should meet a series of requirements. The most crucial requirements are: the power adjustment quantity should reach 90% of the static characteristic value within 15 s. If the rated head of the unit is larger than 50 m, the power delay time should be less than 4 s. (2) ENTSO-E According to the specifications of ENTSO-E [2], the time for starting the action of primary control is a few seconds starting from the incident, the deployment time of 50% of the total primary control reserve is at most 15 s, and the maximum deployment time rises linearly to 30 s for the reserve from 50 to 100%. (3) The Nordic power grid Currently, the Norwegian TSO Statnett has no specific requirements on the response time, but prescribes limits on certain quantities, such as on the delay between frequency deviation and incipient GV motion, on the resolution in frequency measurement, on the permanent droop, and on how to measure these parameters [3]. In Sweden, the TSO Svenska Kraftnät (SvK) has demands on response time, but no requirements on details [4]. The requirements depend on the magnitude of the frequency deviation, and if it exceeds 0.1 Hz, 50% should be delivered within 5 s, and 100% within 30 s.

4.2 Response Time for Primary Frequency Control

59

4.2.2 Formula and Simulation of Response Time Based on the theory in Sect. 2.1.3.1, a formula for the GVO response time of PFC under opening control is deduced, for a PI controller with droop and servo. The main variables of the formula are governor parameters, as described in T1 = −

 1 + bp K p  ln (1 + b p K p − b p K i Ty )(1 − ) . b p Ki

(4.1)

Here,  is the target value, for example, it is set to 90% according to specifications of China Electricity Council [1]. Simulations based on HPP 2 under different conditions are conducted to analyse the sensitivity of response time with respect to the main parameters. The default settings of the simulation are given in Appendix B. In order to investigate the influence of surge in upstream surge tank, a HPP model without surge tank is built, still by applying Model 1. More exactly, in the simplified model, the surge tank and the upstream pipeline before the tank are replaced by a reservoir. The simulation results are shown in Table 4.1. The power response time, T 4 , can be expressed as T4 = T1 + T = T1 + T1 + T2 + T3 .

(4.2)

The time difference T (as shown in Fig. 4.7), between the power response time (T 4 ) and the analytical response time of GVO (T 1 ), is mainly affected by the rate limiting and numerical algorithm (ΔT 1 ), the water inertia (ΔT 2 ) and the surge (ΔT 3 ). More detailed results can be found in the published work[5].

4.3 Frequency Stability of Isolated Operation For HPPs with surge tank, the Thoma criterion [6, 7] is often violated to diminish the cross section of surge tank with the scale getting larger nowadays. Therefore, the surge fluctuation is aggravated and frequency stability becomes more deteriorative [8]. Recently, some huge Chinese HPPs encountered this instability problem during the commissioning, measurements under a load step disturbance are shown in Fig. 1.3. Hence, the focus of this section is on stabilizing the very low frequency oscillation (see Sect. 1.2.2) of an isolated HPP caused by surge fluctuation. In this section, by means of theoretical derivation based on Model 3-F, stability conditions under two control modes are contrasted through adopting the Hurwitz criterion. Then, the frequency oscillations are simulated and investigated with different governor parameters and operation cases, by applying Model 1. The engineering case here is HPP 2.

0.2

10.0

2.0

2.0

2.0

2.0

2.0

2.0

6

7

8

9

10

11

2.0

3

5

2.0

4

2.0

2

Kp

4.0

4.0

4.0

4.0

4.0

4.0

4.0

4.0

2.0

6.0

4.0

Ki

Parameters

1

No.

0.04

0.04

0.04

0.04

0.06

0.02

0.04

0.04

0.04

0.04

0.04

bp

 (%)

0.020 70

0.020 80

0.500 90

0.005 90

0.020 90

0.020 90

0.020 90

0.020 90

0.020 90

0.020 90

0.020 90

Ty

7.6

10.4

15.5

15.0

10.2

29.4

17.2

14.5

30.1

10.0

15.0

Formula T1

7.6

10.2

15.0

14.8

9.8

29.0

14.6

15.0

29.2

9.8

14.6

Simulation T2

Response time of opening (s)

9.2

11.6

16.4

16.2

12.0

29.2

16.0

16.4

30.0

11.4

16.0

Without surge tank, T3

9.6

12.4

21.6

21.2

13.2

229.4

21.0

21.6

232.2

12.4

21.2

With surge tank, T4

Response time of power (s)

1.4

−0.2

1.6

1.4

−0.5 0.0

2.2 1.4

−0.2

0.2

−0.4 −0.4

1.4

0.8

−0.9

1.4

1.6

−0.2 0.5

1.4

−0.4

−2.6

T2 = T3 − T2

T1 = T2 − T1

Time difference T (s)

0.4

0.8

5.2

5.0

1.2

200.2

5.0

5.2

202.2

1.0

5.2

T3 = T4 − T3

Table 4.1 The response time of frequency step under different conditions. T1 and T2 are calculated by Eq. (4.1) and simulation respectively, and T3 is simulated with the simplified model; Response time of opening or power means the time when the opening or power reaches the target value . All the simulations are conducted with rate limiting which is 12.5%/s. The green bar in each cell indicates the relative magnitude of the values in the corresponding cells, except for the cells highlighted by yellow (the values in the yellow cells are much larger)

60 4 Stable Operation Regarding Frequency Stability

4.3 Frequency Stability of Isolated Operation

61

Fig. 4.8 Stability region in Ki -n coordinates of two control modes

4.3.1 Theoretical Derivation with the Hurwitz Criterion Based on Model 3-F in Sect. 3.3.1 and the theory in Sect. 2.1.3.2, a stability condition of frequency oscillation under frequency control and power control is obtained. The stability region is the region which satisfies the stability condition in K i − n coordinates by substituting the system parameters of different states into the stability condition. Here, n (n = F/F th ) stands for the coefficient of cross section area of the surge tank, where F and F th are the real area and Thoma critical area, respectively. A set of curves of stability region boundaries is achieved under two control modes based on the stability condition, as shown in Fig. 4.8. The stability region of power control is much larger than which of frequency control. There is no proportional gain (K p can be regarded as 0) in power control, and it is conducive to the stability. However under frequency control, when K p is set to near 0, the stability region is still smaller than for power control.

4.3.2 Numerical Simulation Based on Model 1 in TOPSYS, numerical simulations are conducted to validate the result of the theoretical derivation, as shown in Figs. 4.9 and 4.10. Through the simulation, the conclusion drawn in the theoretical derivation is verified: the power control produces a better effect on stability than the frequency control. More exactly, under the frequency control, it is hard to stabilize the frequency by adopting any of the three sets of parameters. Even when K p is set to nearly 0, to compare with the power controller that is without proportional component (K p = 0), the frequency

62

4 Stable Operation Regarding Frequency Stability

Fig. 4.9 Frequency oscillation under frequency control with different governor parameters

Fig. 4.10 Frequency oscillation under power control with different governor parameters

instability still occurs. While under the power control, frequency stability is well ensured, and the contradiction between rapidity and stability is also indicated. Besides, it is necessary to have an additional discussion on the power control. The applying of the power control in the isolated operation condition is an ideal case, which cannot be implemented in the practical HPP operation. It is because that the load is unknown in reality, therefore the given power cannot be set properly. However, the conclusion based on the idealized case can supply the understanding and guidance for the stability in an islanded operation, which means the operation of a generating unit that is interconnected with a relatively small number of other generating units [9]. In the islanded system, some units operate in the frequency control mode to balance the changing peak load, and other units adopt the power control to maintain the stability. This issue is also a suggested topic for future work. More results and discussions are in the published work [10].

References 1. China Electricity Council (2007) DL/T 1040-2007 -The grid operation code (in Chinese) 2. European Network of Transmission System Operators for Electricity (2009) ENTSO-E operation handbook, policy 1 (2009): load-frequency control and performance

References

63

3. Statnett (2012) Funksjonskrav i kraftsystemet 2012 (in Norwegian) 4. Kraftnät S (2012) Regler för upphandling och rapportering av primärreglering FCR-N och FCR-D (från 16 November 2012, in Swedish) 5. Yang W, Yang J, Guo W, Norrlund P (2016) Response time for primary frequency control of hydroelectric generating unit. Int J Electr Power Energy Syst 74:16–24 6. Jaeger C (1977) Fluid transients in hydro-electric engineering practice, Blackie, Glasgow 7. Krivchenko GI (1988) Admissibility of deviating from the Thoma criterion when designating the cross-sectional area of surge tanks. Hydrotech Constr 22:403–409 8. Fu L, Yang J, Bao H, Li J (2009) Effect of turbine characteristic on the response of hydroturbine governing system with surge tank. In: Power and energy engineering conference, 2009. APPEEC 2009. Asia-Pacific 1–6 9. IEEE Guide for the application of turbine governing systems for hydroelectric generating units. In: IEEE Std 1207-2011 (Revision to IEEE Std 1207-2004) pp 1–131 (2011) 10. Yang W, Yang J, Guo W, Norrlund P (2015) Frequency stability of isolated hydropower plant with surge tank under different turbine control modes. Electr Power Compon Syst 43:1707–1716

Chapter 5

Stable Operation Regarding Rotor Angle Stability

The stable operation of HPPs regarding rotor angle stability of power systems is studied in this chapter. In Sect. 5.1, a fundamental study on hydraulic-mechanicalelectrical coupling mechanism for small signal stability of HPPs is conducted by eigen-analysis. Considerable influence from hydraulic-mechanical factors is shown, and it is further quantified in Sect. 5.2: An equivalent hydraulic turbine damping coefficient and the corresponding methodology are proposed to quantify the contribution on damping of rotor angle oscillations from hydraulic turbines based on refined simulations. In Sect. 5.3, the quick hydraulic—mechanical response is discussed to support the results in this chapter. The engineering case of all sections is HPP 5.

5.1 Hydraulic—Mechanical—Electrical Coupling Mechanism: Eigen-Analysis This section aims to conduct a fundamental study on hydraulic-mechanical-electrical coupling mechanism for small signal stability of HPPs, focusing on the influence from hydraulic-mechanical factors. For the local mode oscillation [1] in a SMIB system, the theoretical eigen-analysis (Sect. 2.1.3.5) is the core approach based on Model 6 (Sect. 3.3.3) that is a twelfthorder state matrix. Numerical simulation by applying Model 5 (Sect. 3.2.2) is also conducted for validation. As shown in Fig. 1.2, three principal time constants for water column elasticity (T e ), water inertia (T w ), and servo (T y ) in the hydraulicmechanical subsystem are the main study objects. They are analysed under two modes of frequency control (OF and PF) without the PSS. Then, the influence from the hydraulic-mechanical subsystem on tuning of the PSS is investigated. Detailed parameter values and operating settings are given in Appendix B.

© Springer Nature Switzerland AG 2019 W. Yang, Hydropower Plants and Power Systems, Springer Theses, https://doi.org/10.1007/978-3-030-17242-8_5

65

66

5 Stable Operation Regarding Rotor Angle Stability

5.1.1 Influence of Water Column Elasticity (Te ) Through Model 6, for each case (one combination of the value of K p and T e ), the smallest damping ratio (ξ ) of all oscillation modes is plotted. As shown in Fig. 5.1a, when the value of T e is small (short penstock), the increased response rapidity of the frequency control (indicated by an increase of the K p value) with OF leads to a smaller damping ratio of the system. On the contrary, when the value of T e is larger than a certain value, the system becomes more stable with stronger frequency control. Moreover, the trend is inverted when the governor applies PF, as shown in Fig. 5.1b; the increased strength of the frequency control stabilizes the system with the small value of T e . Also, PF generally leads to higher damping ratios than OF. The observations above are validated by time domain simulations. As presented in Fig. 5.2, the black line, the blue line and the red line correspond to cases with a high, medium and low damping ratio respectively. The simulation results of these three sets of parameters fit the damping ratio well. In short, the impact of water column elasticity is important and it differs from the feedback mode of the frequency control.

Fig. 5.1 The smallest damping ratio (ξ) of all oscillation modes under different values of governor parameters (Kp ) and time constant of water column elasticity (Te ). a The feedback mode is OF; b The feedback mode is PF

5.1 Hydraulic—Mechanical—Electrical Coupling Mechanism: Eigen-Analysis

67

Fig. 5.2 Time domain simulation of the process after the three phase fault: Rotational speed. The result validates the cases in Fig. 5.1

5.1.2 Influence of Mechanical Components of Governor (Ty ) The rapidity of the GVO response is highly affected by the mechanical components in the governor system, e.g. servo, backlash, rate limiter, etc. In the state matrix, these components are simplified and represented by the servo time constant (T y ). As shown in Fig. 5.3, a small value of T y leads to a quicker response of GVO, and brings clearer influence on system stability. The influence of T y is more obvious when K p is larger. A time domain simulation in Fig. 5.4a illustrates the influence and it corresponds to the result in Fig. 5.3b. Moreover, the linear theoretical model can result in negative damping ratios (Figs. 5.1 and 5.3). However the simulated oscillations are not divergent, because of the added damping by the nonlinear components (mainly from the rate limiter) in the numerical model, as shown in Fig. 5.4b.

5.1.3 Influence of Water Inertia (Tw ) The water inertia, represented by the water starting time constant (T w ), is normally regarded as adverse to system stability, especially in islanded operating conditions, as presented in Sect. 4.3. By contrast, for the SMIB system, the influence of water inertia is not monotonic, as demonstrated in Figs. 5.5 and 5.6. It is shown that the effect of water inertia differs from that of water column elasticity. Figures 5.5a and 5.6 present that a larger value of T w leads to smaller damping ratio when the value of water column elasticity (T e ) is around 0.4. However, the increase of T w results in slightly more stable cases when the value of T e is large

68

5 Stable Operation Regarding Rotor Angle Stability

Fig. 5.3 The smallest damping ratio (ξ) of all the oscillation modes under different values of servo time constant (Ty ) and governor parameters (Kp ). a The feedback mode is OF, Te = 1.0 s; b The feedback mode is OF, Te = 0.01 s; c The feedback mode is PF, Te = 1.0 s; d The feedback mode is PF, Te = 0.01 s

or small, as demonstrated in Figs. 5.6 and 5.5b. When the governor adopts the PF, the system is more stable under larger water inertia in this case, and this is validated by time domain simulations (Fig. 5.7).

5.1.4 Influence on Tuning of PSS Here, the influence of hydraulic-mechanical factors on tuning of the PSS is investigated. The damping effects under implementation of the PSS with different settings of gain K s under various conditions are shown in Fig. 5.8. Two main insights are obtained here. (1) The optimal parameters values vary with different types of feedback. More exactly, for achieving the largest damping ratio, the K s value differs in four cases, shown in Fig. 5.8a–d. The optimal value of K s changes with different types of PSS, meanwhile, the tuning is also affected by the water column elasticity. (2) The stability margin changes considerably under various conditions. The frequency control with the PF generally results in a higher damping ratio, and this is validated by the time domain simulations in Fig. 5.9. In short, it can be observed that there is still room for optimizing the parameters and performance of the PSS by considering the effect of the hydraulic-mechanical factors.

5.2 Quantification of hydraulic damping: numerical simulation

69

Fig. 5.4 Simulation of rotational speed after the three phase fault. The governor adopts the OF; a cases under different values of Ty : the result validates the cases in Fig. 5.3b; b cases with and without rate limiter

5.2 Quantification of Hydraulic Damping: Numerical Simulation Damping coefficient is a common term (D) used in power system stability analysis, and its general form is described in a linearization of the swing equation T j ω˙ = Pm − Pe − Dω

(5.1)

However, the variation range of D in the hydropower field is still unclear; it is normally assumed to be positive and often set to zero to obtain a conservative result. Therefore the swing equation is rewritten as

70

5 Stable Operation Regarding Rotor Angle Stability

Fig. 5.5 The smallest damping ratio (ξ) of all oscillation modes under different values of water starting time constant (Tw ) and governor parameters (Kp ). a The governor adopts the OF, Te = 0.4 s; b The governor adopts the OF, Te = 0.01 s; c The governor adopts the PF, Te = 0.4 s; d The governor adopts the PF, Te = 0.01 s Fig. 5.6 The smallest damping ratio (ξ) of all the oscillation modes under different values of Tw and Te . The governor adopts OF

Fig. 5.7 Simulation of rotational speed after the three phase fault under different values of Tw . The governor adopts PF. The result validates the cases in Fig. 5.5d

5.2 Quantification of hydraulic damping: numerical simulation

71

Fig. 5.8 The smallest damping ratio (ξ) of all the oscillation modes under different gains of PSS (Ks ): a OF in governor and speed input in PSS; b OF in governor and power input in PSS; c PF in governor and speed input in PSS; d PF in governor and power input in PSS

Fig. 5.9 Simulation of rotational speed after the three phase fault under different modes (OF and PF) of governor. The PSS adopts speed input and the gain (Ks ) is set to 4.0. The result validates the cases in Fig. 5.8a, c

T j ω˙ = Pm − Pe .

(5.2)

The aim of this section is to quantify the contribution from a hydraulic turbine to the damping of local mode electromechanical oscillations [1]. An equivalent hydraulic turbine damping coefficient (Dt , simplified as “the damping coefficient” in the following context) is introduced here, as described in   T j ω˙ = Pm − Pe = Pm,const − Dt ω − Pe .

(5.3)

72

5 Stable Operation Regarding Rotor Angle Stability

Table 5.1 Different numerical models in this section Model

Description

Purpose

4

TOPSYS model with refined hydraulic-mechanical subsystem introduced in Sect. 3.1.2

Refined simulation

4-S

Simplified version of Model 4, with the swing equation in (5.3)

Quantifying the damping coefficient by the comparison with Model 4

5-S

A MATLAB/SPS model mentioned in Sect. 3.2.2

Verifying the TOPSYS model (Model 4 and 4-S)

In this study, the focus is on the mechanical power (Pm ), instead of the electromagnetic power (Pe ) that is the main analysis object in previous studies. The purpose of introducing the damping coefficient is as follows. (1) Quantifying the value of Dt can clarify an long-standing issue: how large is the damping contribution from the hydraulic system? (2) For analysis of large power systems, the mechanical power simulation in HPPs is inevitably simplified and less accurate, misleading the analysis of power system oscillations. The quantified damping coefficient can be easily implemented in models of complex multiple-machine systems, hence the mechanical power in the system can be set to constant without losing the influence from the hydraulic system on the system stability (shown in Sect. 5.2.3). (3) Considering the damping coefficient can affect the system parameter tuning, including the PSS tuning (shown in Sect. 5.2.3). In this section, firstly, the corresponding methodology is introduced. Then, the quantitative results of the damping coefficient are presented in different cases with and without the application of PSS. Lastly, the influence and significance of the damping coefficient are demonstrated in case studies.

5.2.1 Method and Model 5.2.1.1

Method of Quantifying the Damping Coefficient

The method of quantifying the damping coefficient is based on simulations by Model 4 and Model 4-S (“S” is short for “simplified”), as shown in Table 5.1. The only difference between these two models is that the swing equation in Model 4 and Model 4-S is (5.2) and (5.3) respectively; it means that the mechanical power is simplified as constant and the whole model of the hydraulic subsystem is ignored in Model 4-S. The detailed steps are as follows: (1) Step 1: Apply Model 4 to simulate transient processes of a HPP after a three phase fault;

5.2 Quantification of hydraulic damping: numerical simulation

73

Fig. 5.10 TOPSYS model of HPP 5, of which a single unit is connected to an infinite bus

(2) Step 2: Adopt Model 4-S to simulate transient processes with different values of the damping coefficient Dt . Other conditions remain the same as the case in Step 1. (3) Step 3: Compare the damping performance (reflected by the rotational speed) from the two simulation models; among results from Model 4-S with different values of Dt , one of the curves has the best agreement with the simulation from Model 4; thus the corresponding value of Dt is the quantified damping coefficient for this case. The detailed method for determining the agreement between results from two models in Step 3 is by applying the root mean square error (RMSE), as described in   N 1   2 PR M S E =  P4,i − P4−S,i (5.4) N i=1 Here, Pi means a value of a local maximum or local minimum (peaks of a curve) of speed deviation (ω); the subscript 4 and 4-S stand for Model 4 and Model 4-S respectively; N is the total number of local maxima and minima during a certain time period (10 s in this work). The minimum value of the PRMSE indicates the best agreement of two curves of rotational speed simulated by Model 4 and Model 4-S. The engineering case of this section is HPP 5, as shown in Fig. 5.10. Detailed parameter values and operating settings are given in Appendix B.

5.2.1.2

Model Verification

Here, the verification of the TOPSYS Model is presented. The hydraulic-mechanical subsystem of the model has been verified by measurements in different cases, as shown in Sect. 4.1. Therefore, the main focus here is verifying the electrical subsystem, by comparing the electrical transients simulated from Model 4-S (TOPSYS) and Model 5-S (SPS) in Table 5.1.

74

5 Stable Operation Regarding Rotor Angle Stability

Fig. 5.11 Model 5-S in SPS. The block with dashed outline shows the implementation of the simplified mechanical power by applying the damping coefficient (Dt )

Model 5-S is a standard SPS model, as shown in Fig. 5.11, and the swing equation of it is described by (5.3). Comparisons between simulations by Model 4-S and Model 5-S are shown in Fig. 5.12. In both models, the mechanical power is constant. Generally, the simulations by Model 4-S have a good agreement with the results from Model 5-S. The main difference occurs in the damping performance, which is expected. The reason is the stator transients, which contribute to the damping [1], are included in the SPS model but ignored in the equivalent circuit model in TOPSYS. Therefore, the TOPSYS model leads to slightly more conservative results; however it does not affect much the quantification of the damping coefficient, since both Step 1 and 2 are conducted by the TOPSYS model.

5.2.2 Quantification of the Damping Coefficient Here, the quantification results of the damping coefficient are presented for different cases with and without the application of the PSS. The simulation cases are listed in Table 5.2. Without the application of the PSS, two examples of quantifying the damping coefficients are shown in Fig. 5.13. The values of the damping coefficient are quantified as 2.0 and −1.1 respectively. The main reason for the difference in the damping performance is the phase shift in the mechanical power response with respect to the rotational speed deviation, and the delay time is the most influential fact affecting the phase shift. A crucial point here is that the damping coefficient can vary over a considerable range and can even be negative, while previously the contribution is unclear and normally assumed to be positive.

5.2 Quantification of hydraulic damping: numerical simulation

75

Fig. 5.12 Comparison between Model 4 (TOPSYS) and Model 4-S (SPS), without the application of PSS. In both models, the mechanical power Pm is constant. a Rotational speed; b Excitation voltage; c Generator terminal voltage; d Electromagnetic active power Table 5.2 Different simulation cases under the three phase fault. Other settings of all the cases are the same, apart from the descriptions. The “delay” means the delay time in the turbine governor Case

Description

Purpose

1

Delay = 0.30 s; No PSS

Demonstrating a positive and a negative damping coefficient under cases without the PSS

2

Delay = 0.50 s; No PSS

3

Delay = 0.25 s; with PSS

4

Delay = 0.50 s; with PSS

Demonstrating a positive and a negative damping coefficient under cases with the PSS

76

5 Stable Operation Regarding Rotor Angle Stability

Fig. 5.13 Quantification of the damping coefficients for cases without the PSS

The change processes of the GVO and mechanical power under case 1 and case 2 are shown in Fig. 5.14. The phase shift between the mechanical power and GVO is approximately 180°, clearly demonstrating the non-minimum-phase response of the mechanical power. Also, it is shown clearly that the phase shift between the power and the speed is changed due to different delay times. For the cases with application of the PSS, the influence from the hydraulic turbine is still obvious. As shown in Fig. 5.15, the damping coefficient is quantified as 1.5 and −2.1 respectively for case 3 and case 4. The quantifying method is basically the same as above, the only difference is that the PSS is activated in both Model 4 and Model 4-S. Considering the influence from mechanical power can contribute to a better tuning of PSS, as further discussed below. The quantified damping coefficient is convenient to add in cases of PSS tuning for complex multiple-machine systems in which the detailed hydraulic modelling needs to be ignored.

5.2.3 Influence and Significance of the Damping Coefficient In this part, firstly, the influence of the damping coefficient on the PSS tuning is presented for a SMIB system. Secondly, the effect of the damping coefficient on

5.2 Quantification of hydraulic damping: numerical simulation

77

Fig. 5.14 Simulation of GVO, mechanical power and speed. a Case 1; b Case 2. The GVO and mechanical power are deviations from initial values. The curves of speed are exactly the same as the ones in Fig. 5.13

multi-machine system stability is shown, based on the WSCC 3-machine 9-bus system [2] without the implementation of PSS.

5.2.3.1

Influence on the PSS Tuning

Three cases after the three phase fault are simulated by Model 4-S, as shown in Fig. 5.16. In order to neutralize the effect of a negative damping (−2.0), the gain of PSS (K s ) needs to be increased from 2.0 to 9.0.

5.2.3.2

Influence on Multi-machine System Stability

For showing the influence of the damping coefficient on multi-machine system stability, a simple case study is conducted based on the WSCC 3-machine 9-bus system [2], by applying the PSAT.1 1 Power

System Analysis Toolbox (PSAT): http://faraday1.ucd.ie/psat.html (accessed on March 14th, 2017)

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5 Stable Operation Regarding Rotor Angle Stability

Fig. 5.15 Quantification of the damping coefficients under the application of the PSS

Fig. 5.16 Simulations of three cases with the implementation of PSS

The system model is shown in Fig. 5.17, a fault occurs on bus 7 at 1.0 s and the clearing time is 1.083 s. The PSS is not applied and the AVR type is the same as the one above. The setting of the AVR is: K a = 400 pu, T r = 0.01 s. Two cases are compared: the first is the original system in which the damping coefficients of all the machines are 0. For the second, a positive damping coefficient (Dt = 2.0 pu) is applied in machine 2. The results are shown in Fig. 5.18. The rotor angle difference (δ 21 ) between machine 1 and machine 2 is taken as an indicator of the system stability [2]. The original system (Dt = 0) is unstable (red dashed line); while under the second condi-

5.2 Quantification of hydraulic damping: numerical simulation

79

Fig. 5.17 Model of the WSCC 3-machine 9-bus system in PSAT

Fig. 5.18 Rotor angle difference (δ21 ) between machine 1 and machine 2 under two conditions

tion, the contribution from the damping (Dt = 2.0 pu) in machine 2 leads to a stable system.

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Fig. 5.19 Measurements in a Swedish HPP after a step change of the GVO set-point: active power and deviation of GVO control signal and feedback signal

5.3 Discussion on Quick Response of Hydraulic—Mechanical Subsystem A key point of this chapter is whether the responses of GVO and mechanical power of turbines are quick enough to trigger an obvious coupling effect between the hydraulicmechanical subsystem and the electrical subsystem. Previously the effect of turbine governor has often been ignored in the small signal stability analysis [1]; however in recent years, the rapidity of PFC has been demanded in order to ensure quick response, as shown in Sect. 4.2. Figure 5.19 shows the on-site measurements in a Swedish HPP, supporting the simulations in this chapter in the following aspects. (1) The fast GVO response is demonstrated clearly, and the largest rate can reach the rate limit (0.1pu/s). (2) A delay in the governor system, around 0.25 s between two GVO signals, is shown. (3) In terms of the measured active power, a non-minimum phase response is clearly presented. Furthermore, the rapid GVO response after a three phase fault is also shown in simulations in previous studies [3–5]. Also, in this thesis, practical nonlinear components (servo, backlash, rate limit) are included and all these factors tend to slow the governor response. In short, the concern on the response rapidity of hydraulic—mechanical subsystem is fully considered in this study, and the cases are realistic.

References

81

References 1. Kundur P, Balu NJ, Lauby MG (1994) Power system stability and control. McGraw-Hill, New York 2. Anderson PM, Fouad AA (2003) Power system control and stability. Wiley, New York 3. Akhrif O, Okou FA, Dessaint LA, Champagne R (1999) Application of a multivariable feedback linearization scheme for rotor angle stability and voltage regulation of power systems. IEEE Trans Power Syst 14:620–628 4. Dobrijevic DM, Jankovic MV (1999) An approach to the damping of local modes of oscillations resulting from large hydraulic transients. IEEE Trans Energy Convers 14:754–759 5. Mei S, Gui X, Shen C, Lu Q (2007) Dynamic extending nonlinear H∞ control and its application to hydraulic turbine governor. Sci China Ser E Technol Sci 50:618–635

Chapter 6

Efficient Operation and Balancing Renewable Power Systems

In this chapter, the efficient operation of HPPs during balancing actions for renewable power systems is studied, focusing on PFC that acts on a time scale from seconds to minutes. In Sect. 6.1, the problem description, cause and initial analysis of wear and tear of turbines are presented. Based on the analysis results, a controller filter is proposed in Sect. 6.2 as a solution for reducing the wear of turbines and maintaining the regulation performance, reflected by the frequency quality of power systems. Then in Sect. 6.3, the study is further extended by proposing a framework that combines technical plant operation with economic indicators, to obtain relative values of regulation burden and performance of PFC.

6.1 Wear and Tear Due to Frequency Control 6.1.1 Description and Definition In terms of wear and tear of hydropower turbines, there are different views and corresponding indicators to evaluate. From a point of view of control, this study focuses on the movements of the GVs in Francis turbines. The GV movements are expressed by the variations of GVO. Two core indicators are discussed, as shown in Fig. 6.1: (1) The first is the movement distance which is the accumulated distance of GV movements; (2) The second is the movement amount which means the total number of movement direction changes. One movement corresponds to one direction change. Some distance and amount of GV movement for a regulating unit are always expected. Hence, blindly decreasing the movement is obviously not advisable. However, excessive values of these two indicators bring three types of wear and tear as follows.

© Springer Nature Switzerland AG 2019 W. Yang, Hydropower Plants and Power Systems, Springer Theses, https://doi.org/10.1007/978-3-030-17242-8_6

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Fig. 6.1 Illustration of two very important indices of wear and tear: distance and amount of GV movement

Fig. 6.2 Histogram of simulated GVO movements for real frequency record of a week in March, 2012. 19,942 is the number of movements with the distance from 0 to 0.2%

(1) In the perspective of tribology, there is a linear positive correlation between movement distance and material deterioration on the bearing [1]. (2) From the standpoint of hydraulics, direction changes of the actuator leads to dynamic loads on the turbine runner [2, 3]. (3) A huge amount of actuator movement implies a multitude of load cycles, which might increase the structure fatigue. In [4], the measurements show that when Kaplan turbines operate in frequency control mode instead of in discharge control mode, the movement distance of blade angle range will be increased up to ten times, and the amount of load cycles increases from 3–136 to 172–700 for the same period of time. It is worth noting that there is a great amount of GV movements with small amplitudes. Reference [5] found that during 4 months of observations in HPPs, between 75 and 90% of all GVO movements are less than 0.2% of full stroke. In this thesis, a simulation is conducted and it demonstrates a similar result: 93.9% of all GVO movements are less than 0.2% of full stroke, as shown in Fig. 6.2. More importantly, from the engineering experience, the wear and tear on the materials from small movements is believed to be more serious than from large movements. On the other hand, the regulation value from the small movements is not very obvious. Therefore, decreasing the number of small movements should be a priority.

6.1 Wear and Tear Due to Frequency Control

85

Fig. 6.3 Time-domain illustration of small frequency fluctuations. Ts is the sampling time. The frequency change process from point A to B is a “frequency fluctuation”, as used in this thesis

Fig. 6.4 For the frequency data with 1 s sampling time in the month (March 2012). a Histogram of values of frequency fluctuations; the total amount of frequency fluctuations is 899,308. The total amount of small frequency fluctuations is 666,241. b Histogram of time lengths of the 666,241 small frequency fluctuations

6.1.2 Cause Here, a crucial reason for small GV movements is revealed: fluctuations of power system frequency. In order to exemplify the characteristics, measured frequency data of the Nordic power grid frequency is discussed, as shown in Figs. 6.3 and 6.4. From intuitive observations of Fig. 6.3, the frequency oscillation can be roughly divided into two “components”: (1) very low frequency “fundamental” (with long period, larger than 10–20 s); (2) high frequency “harmonic” (with short period, less than 1–2 s depending on the sampling time). The “fundamental” is generally a random signal, while in recent years, the grid frequency oscillations with some specific long periods appear in different power

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systems, e.g. Nordic power grid (with the period around 60 s) [6, 7], Colombian power grid (with the period around 20 s) [8]. Besides, long period oscillation of grid frequency in Great Britain and Turkey are presented in [9] and [10] respectively. For the short-period “harmonic”, this work defines a “frequency fluctuation” as a monotonic frequency changing process between a local maximum (or minimum) and a neighbouring local minimum (or maximum), as shown in Fig. 6.3. From Fig. 6.3, one could have an intuition that, for the frequency changing process, direction variations happen every one or two sampling periods. The intuition is further verified by Fig. 6.4. The green columns are only for the frequency fluctuations with small values which are within ± 2.5 MHz. Figure 6.4 demonstrates two important features: (1) the values of frequency fluctuations are mostly very small, within ± 2.5 MHz which equals to 5 × 10−5 pu; (2) the time lengths of small fluctuations are also extremely small. In short, the results indicate that the power system frequency experiences both long period “fundamental” oscillations and “harmonic” fluctuations with small amplitude and high frequency. The frequency input would lead to the unfavourable amount of small GV movements. More data and discussions can be found in the published works [11, 12].

6.1.3 Analysis on Influencing Factors In this part, the GV movement is analysed by theoretical analysis based on ideal sinusoidal frequency input and simulations with real frequency records. The influences on wear and tear of different factors, e.g. governor parameters, PF mode and nonlinear governor factors, are explored.

6.1.3.1

Method and Model

Numerical simulations of PFC are conducted under both OF and PF, by applying Model 1. The engineering case here is HPP 1. Detailed settings are given in Appendix B. In terms of theoretical analysis, basic analytical formulas based on idealized frequency deviation signals are deduced. For idealized frequency deviation signals as described in     f = A f sin 2π t T f = A f sin(ωt),

(6.1)

the following formula is proposed to estimate the accumulated movement distance (Dy ): Dy = 4 ·

Ttotal G P I · Gm · A f . Tf

(6.2)

6.1 Wear and Tear Due to Frequency Control

87

Here, Af is the amplitude of the sinusoidal input frequency signal, T total and T f represent the total time and a period respectively. GPI is the gain of the PI controller and Gm is the product of the gains of mechanical components (backlash and lag), as shown below:

GPI

     1 + 2π 2 · K p 2 

 Tf Ki 1 = 2 , pu/pu ,  2  bp  1+b K 1 + 2π · b p Kp i p Tf  B L gv

, pu/pu , Ain 1 =   2 1 + Ty2 2π T f

G backlash = 1 − G lag

(6.3)

(6.4) (6.5)

Here, Ain is the input amplitude, while BL gv represents the value of backlash. T y stands for the lag in the main servomotor. Here, a simpler representation of the backlash is applied, comparing to Eq. (3.42) that is based on the describing function method. Additionally, the response time (Sect. 4.2), i.e. the time it takes for the opening to reach 63.2% (≈ 1 − e−1 ) of its final value after a step disturbance is Tr =

 1 + bp K p

1 − ln(1 + b p K p ) , [s]. b p Ki

(6.6)

The response time indicates the rapidity of PFC.

6.1.3.2

Results: Influencing Factors on Wear and Tear

Here, the influence of different factors is discussed, based on Eq. (6.2) and simulations under sinusoidal input signal, Δf with amplitude 0.025 Hz (0.0005 pu), and with a real record of frequency deviation in the Nordic power system. As shown in Table 6.1, the governor parameters have essential influence on the GVO movements. The theoretical formulae for ideal input reflects the trend for real movements well, as can be seen from the comparison between the formula calculation and simulation results of movement distance. In Table 6.1, under different parameter settings, the change tendencies of movement distance under ideal and real frequency are in good agreement, for both OF and PF modes. Therefore the formulae are effective to achieve a good tendency estimation. Note that in the formula, the gain and movement distance are directly determined by the period. However, the “period” of real frequency is changing all the time and hard to get an approximate value. This brings a difficulty of applying the formula to estimate the real condition, but it will not influence the tendency prediction.

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Table 6.1 Influence of governor parameters under OF and PF. For the movement distance, the total calculation and simulation time is two hours. Movement distance under OF and the response time are calculated by formulas; other values are from simulation. PF 75% and 100% mean that the GVO set point is at 75 and 100% of rated value, respectively. 4. Groups 1 to 4 are Vattenfall standard sets of parameters

b P K P K I Response No. [pu] [pu] [s -1] time (s)

1 2 3 4 5 6 7

0.10 0.04 0.02 0.01 0 0 0

1.00 1.00 1.00 2.00 1 10 2

0.167 0.417 0.833 1.667 10 0.83 2

59.71 59.95 59.99 59.99 5.00 58.90 24.98

Movement distance (D y ) under Sinusoidal frequency (with backlash) OF Tf = Tf = 60s 120s 0.17 0.23 0.70 0.76 1.62 1.67 3.49 3.46 10.35 5.68 2.29 1.70 3.92 3.44

PF-100% Tf = Tf = 60s 120s 0.19 0.26 0.77 0.82 1.70 1.75 3.65 3.62 11.83 6.24 2.88 2.09 4.32 3.76

Movement distance under real frequency

OF 0.23 0.71 1.54 3.25 7.69 1.99 3.09

PF 75% 0.27 0.75 1.57 3.24 7.22 2.61 3.20

PF 100% 0.28 0.78 1.64 3.41 8.90 2.67 3.43

In terms of the application of PF, as shown in Table 6.1, the influence is normally not too large; however the difference could be relatively substantial under large gain conditions. Besides, PF may lead to either increase or decrease of movement, comparing with OF. More discussions on nonlinear factors and two main influence factors under PF, operation set point and surge (water level fluctuation in surge tank), can be found in the published work [11].

6.2 Controller Filters for Wear Reduction Considering Frequency Quality of Power Systems Aiming at the aforementioned problem in Sect. 6.1 and the initial results, in this section, applying a suitable filter in the turbine controller is proposed as a solution for wear reduction. However, the controller filters impact the active power output and then affects the power system frequency. Therefore, the purpose of this section is the trade-off between two objectives: (1) reducing the wear and tear of the turbines; (2) maintaining the regulation performance, reflected by frequency quality of power systems. The widely-used dead zone is compared with a floating dead zone and a linear filter, by time domain simulation and frequency domain analysis. The filters are introduced in Sect. 3.2.1.

6.2 Controller Filters for Wear Reduction Considering Frequency Quality …

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Fig. 6.5 Simulink model of a “grid inverse” for computing the load disturbance, as highlighted by red

6.2.1 Method and Model The governor system (Fig. 3.8) in Model 2-L (Sect. 3.2.1) is applied to simulate the GV movements, based on a measured one-day grid frequency data. Then, the frequency under the influence of the different filters can be simulated and compared by using Model 2-L, based on a certain load disturbance. The mean value and standard deviation (SD) are chosen as the indicators to evaluate the frequency quality [13, 14]. However, load disturbances in power systems are unknown. Therefore a “grid inverse” [7] model is built, as shown in Fig. 6.5, to compute a load disturbance from the existing measured frequency. The transfer function of the grid inverse model is shown in G r (s) =

Ms + D . tps + 1

(6.7)

To avoid high amplification of high frequency noise in the grid frequency signal, a pole with time constant t p (set to 0.1) is added [15]. In terms of the theoretical analysis, the describing functions (Sect. 2.1.3.4) and Nyquist criterion (Sect. 2.1.3.3) are adopted to examine the frequency response and stability of the system with different filters. Model 3-L is applied, as described in Sect. 3.3.2.

6.2.2 On-Site Measurements Here, on-site measurements and its comparison with simulations are presented. The measurement was conducted in HPP 8. The measurement length is 6800 s, and Fig. 6.6 shows a 3000 s period of comparison between the simulation and the mea-

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Fig. 6.6 Comparison of the simulated GVO and the GVO measured in HPP 8. The measurement noise is demonstrated in the small plot inside the right figure Table 6.2 Statistics of the one-day GVO movements under different conditions of the servo (Ty) and backlash

Backlash 0 0.01% 0.02% 0.03% 0.04% 0.05% 0.10%

Movement distance (full strokes) Number of movements Ty = 0 Ty = 0.1 Ty = 0.2 Ty = 0 Ty = 0.1 Ty = 0.2 128.13 48.83 45.50 2519586 577804 330166 56.67 43.64 43.47 510284 8122 3472 45.20 43.27 43.16 90310 3078 2946 43.56 42.98 42.87 15306 2850 2806 43.12 42.70 42.59 4260 2744 2704 42.82 42.43 42.33 2992 2656 2628 41.53 41.18 41.09 2462 2366 2342

surement. The detailed information is shown in Appendix B. As shown in Fig. 6.6, the simulation matches the measurement well in time domain.

6.2.3 Time Domain Simulation Further results of time domain simulation are presented here. In the following simulations, the governor parameter setting adopts Ep3 (see Table B.2 in Appendix B), which leads to relatively large gain and GV movements. Other settings are also given in Appendix B. Firstly, the cases without any filters are presented in Table 6.2, showing that without any filters, the governor system (especially the actuator) inherently filters the majority of the frequency fluctuations. This can also be observed from the measurements above: The time length of a GV movement is relatively long, the average value is 35.1 s (6800 s divided by 194 movements). The period value is 60–70 s, corresponding to the period of “fundamental” frequency fluctuation in Nordic power grid. This further shows that the GV movement is mainly determined by the “fun-

6.2 Controller Filters for Wear Reduction Considering Frequency Quality …

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Table 6.3 Statistics of the one-day GVO movements and the frequency quality with different filter types. The GVO movement is simulated by the governor model in Model 2-L, under two frequency input data with different sampling times. The frequency quality is computed by Model 2-L. Ts is the sampling time of the data. In the column 50-Mean , the values refer to the mean frequency deviations; for example, the value 0.00104 Hz means the mean value of the frequency without any filter is 49.99896 Hz. SD stands for the standard deviation

Filter type

Value setting (pu)

Guide vane opening Ts = 1 s Ts = 0.02 s distance

42.25 strokes No filter (pu) \ 100.0% ±0.01% 89.9% Frequency ±0.02% 80.4% filter - Dead ±0.05% 54.6% zone (Edz) ±0.1% 22.4% Frequency 2×0.01% 96.5% filter 2×0.02% 88.5% Floating 2×0.05% 56.1% dead zone 2×0.1% 17.2% Frequency 1.0 99.1% filter 2.0 97.5% 3.0 95.4% Linear (Tf1) ±0.1% 98.7% GVO filter ±1.0% 87.6% Dead zone ±2.0% 77.2% (Edz) ±5.0% 46.7% GVO filter - 0.1% 94.4% Floating 0.5% 77.6% dead zone 1.0% 62.5% 2.0% 43.0% (Efdz) 1.0 99.1% GVO filter 2.0 97.5% Linear (Tf2) 3.0 95.4%

No filter(abs)

\

amount 2614 100.0% 99.5% 96.8% 83.9% 43.8% 87.7% 71.7% 34.5% 4.7% 96.4% 93.5% 89.8% 99.7% 92.8% 85.7% 55.0% 83.6% 56.8% 40.9% 23.5% 96.4% 93.5% 89.8%

distance 42.32 strokes 100.0% 89.9% 80.4% 54.5% 22.3% 99.4% 93.6% 62.5% 19.7% 99.0% 97.4% 95.3% 98.7% 87.6% 77.1% 46.7% 94.4% 77.6% 62.5% 43.0% 99.0% 97.4% 95.3%

Frequency quality

amount 50 - Mean 2628 100.0% 99.1% 96.6% 84.6% 43.1% 97.0% 81.1% 40.9% 6.5% 97.0% 92.2% 88.9% 99.7% 93.3% 85.7% 55.1% 83.5% 56.5% 40.8% 23.4% 97.0% 92.2% 88.9%

0.00104 Hz 100.0% 121.0% 142.7% 221.1% 354.1% 105.4% 103.5% 114.9% 104.2% 100.0% 100.1% 100.1% 102.6% 124.8% 149.8% 232.4% 100.0% 99.6% 101.2% 97.6% 100.0% 100.1% 100.1%

SD 0.0414 Hz 100.0% 108.9% 118.1% 146.2% 193.8% 103.7% 112.9% 149.1% 229.7% 102.0% 106.3% 125.1% 101.0% 110.7% 121.5% 153.9% 101.0% 107.1% 117.3% 143.7% 102.0% 106.3% 125.1%

damental” component of the input frequency, and the influence of the “harmonic” component is not significant. The performances of different filters are presented in Table 6.3. It is shown that the traditional filter, dead zone, indeed reduces the movement distance, but not the movement amount. In contrast, the floating dead zone has a good performance for the distance and especially for the movement amount. The linear filter could also decrease both two indicators, however the effect is not obvious. The frequency quality, the crucial trade-off factor, is analysed under different filters here. As demonstrated in Table 6.3, the dead zone leads to a poor frequency

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Fig. 6.7 Histogram of the one-day frequency simulated by the Nordic power system model with three types of filters

quality. By contrast, the linear filter only slightly increases the standard deviation. The floating dead zone results in a medium performance of the frequency quality. The effects of these three types of filters are obvious from the histogram in Fig. 6.7. The floating dead zone and the linear filter increase the standard deviation, but the distribution is still single-peaked even with a large parameter setting. However, the dead zone leads to a very unfavourable double-peaked distribution.

6.2.4 Frequency Domain Analysis: Stability of the System Here, the Nyquist stability criterion is applied to test the stability of the system with different filters. Firstly, the nonlinear filters are tested, as shown in Fig. 6.8. The system is stable with the dead zone under these parameter settings. In contrast, the floating dead zone leads to a limit cycle oscillation in the system with the Ep3 parameter setting; while when the system adopts the Ep0 setting, the oscillation is avoided. However, the describing function framework only gives indication of the system stability, therefore the result is verified by a time-domain simulation of a load step change (+ 1 × 10−2 pu), as shown in Fig. 6.8b. Nevertheless, in Sect. 6.2.3, even with the limit cycle oscillation under the Ep3 setting, the frequency quality under the floating dead zone is still acceptable. Then, the influence of the linear filter is discussed, as described in Fig. 6.9a. For the system with the Ep3 parameter setting, the critical value of the filter constant, T f 1 or T f 2 , is approximately 4.0 s. It is validated clearly by time-domain simulation, as shown in Fig. 6.9b.

6.2 Controller Filters for Wear Reduction Considering Frequency Quality …

93

Fig. 6.8 a Frequency-domain result: the Nyquist curve of the open-loop system under different governor parameters and the negative reciprocal of the describing functions. b Time-domain result: the system frequency after a load step change (+ 1 × 10−2 pu), simulated by Model 2-L

Fig. 6.9 a Frequency-domain result: gain margin and phase margin of the system with the linear filter. b Time-domain result: the system frequency after a load step change (+ 1 × 10−2 pu), simulated by Model 2-L

6.2.5 Concluding Comparison Between Different Filters The main conclusion of this section is shown in Table 6.4. It suggests that the floating dead zone, especially the GVO filter after the controller, outperforms the widely-used dead zone on the trade-off between the wear reduction and frequency quality.

6.3 Framework for Evaluating the Regulation of Hydropower Units In this section, a framework is proposed as shown in Fig. 6.10, combining technical operation strategies with economic indicators, to obtain relative values of regulation burden and performance of PFC.

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Table 6.4 Comparison between different filters Filter

Advantages

Disadvantages

Dead zone

1. Deceasing the GV movement distance effectively 2. No obvious influence on system stability

Two fatal points: 1. Worst frequency quality: the double-peaked distribution 2. Not very effective in reducing the GV movement amount, which is the main goal

Floating dead zone

1. Well reducing the GV movement amount 2. Deceasing the GV movement distance effectively 3. Good frequency quality, especially with the GVO filter

Might cause limit cycle oscillation (however it can be avoided, i.e. by tuning the governor parameters; even with the limit cycle oscillation, the frequency quality is still acceptable)

Linear filter

1. Best frequency quality 2. Can decrease both the movement distance and amount to some extent

1. Cannot obviously decrease both the movement distance and amount 2. Might cause system instability (however it can be avoided, i.e. by tuning the governor parameters)

Fig. 6.10 Framework for quantifying and evaluating the regulation of hydropower units. Efficiency loss as well as wear and fatigue are adopted to represent the burden; regulation mileage and frequency quality are applied to evaluate the regulation performance

For the quantification, Model 2-K is applied and calibrated with measurements from HPP 6 and HPP 7. Kaplan turbines are studied here, since they are more complicated in terms of control. Hence, the methodology and results can easily be simplified and extended to other turbine types. Burden relief strategies and their consequences are discussed, under two idealized remuneration schemes for PFC, inspired by the ones used in Sweden and in parts of the USA. They differ in the underlying pricing philosophy mainly in that the Swedish one does not take actual delivery into account, but rather compensates for the reserved capacity.

6.3 Framework for Evaluating the Regulation of Hydropower Units

95

Fig. 6.11 Illustration of the combinator table for the turbine in the HPP 6 (a) and HPP 7 (b). In each figure, seven on-cam operating points are highlighted by blue scatters, they are within the maximum efficiency range

6.3.1 The Framework In the framework, burden is represented by efficiency loss and wear/fatigue, and regulation performance is evaluated using regulation mileage and frequency quality. The technique to quantify burden and regulation performance and the corresponding indicators that serve as the main outputs of the numerical simulations are introduced in Sect. 6.3.2. Optimizing the regulation conditions of hydro units is the key to easing their incurred burden. Various regulation conditions are comprehensively compared by varying the turbine governor parameters (Ep1–Ep3 in Table B.2 in Appendix B), operating set-points (seven points in Fig. 6.11) and regulation strategies (Sect. 6.3.2). Under different conditions, the following two idealized pricing schemes of regulation payments are concisely analysed: strength payment and mileage payment that are inspired respectively by the ones used by the TSO SvK in Sweden and by PJM Interconnection LLC (PJM), a regional transmission organization in the USA [16]. The schemes are detailed in Sect. 6.3.2. Various simulations are conducted to test the above-mentioned indicators based on HPP 6 and HPP 7, as illustrated in Fig. 6.12.

6.3.2 Methods Here, the detailed methods are introduced. It is worth noting that the burden (efficiency loss, wear and fatigue) is discussed from a physical perspective. Further economic modelling to obtain the gain or loss of profit from regulation is not included, while it is necessary in the future to fully characterize the effects of PFC on system economics.

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Fig. 6.12 Illustration of the simulation structure. The models 2-K-1 through 2-K-3 are introduced in Sect. 6.3.2. The blocks with dashed outline represent the selections in simulation setting based on different conditions: i varies from 1 to 3, for three sets of governor parameters Ep1–Ep3; j varies from 1 to 4, for three regulation strategies (S1–S3) and an ideal on-cam case (S0); k varies from 1 to 2 for two HPPs; n varies from 1 to 7 for seven operating set-points. The set in the parenthesis with simulation presents different cases conducted in the model. In total, there are 168 (3 × 4×2 × 7) and 24 (3 × 4×2 × 1) simulation cases conducted in Model 1 and Model 2 respectively. The terms in the parenthesis with the output variables show the actual needed set of results for analysing the corresponding indicator in this work

6.3.2.1

Numerical Models

As shown in Fig. 6.12, three models are applied. Model 2-K-1 and Model 2-K-2 are presented in Sect. 3.4, and Model 2-K-3 is introduced here. In Sect. 6.2.1, a method of simulating and evaluating the frequency quality for units with Francis turbines is introduced. Here, the method is improved and extended for Kaplan turbines. Model 2-K-3 is for computing the unknown sequence of one-day load disturbance from the original measured frequency, as shown in Fig. 6.13. The “grid inverse” model is shown in Eq. (6.7) in Sect. 6.2.1, and the detailed parameters are given in Table B.5 in Appendix B. The value of time constant t p is set to 0.1 s in this study. In Model 2-K-3, all the regulating HPPs in the Nordic power grid are lumped into one scaled HPP with the scaling factor (K 3 ). The model of the lumped HPP is introduced in Sect. 3.4.1. HPP 6 and HPP 7 are applied as engineering cases. One unit of each HPP is taken as the study case. The detailed parameter values of the two HPPs are shown in Table B.6 in Appendix B. For HPP 6, the dynamic processes under normal PFC is simulated by Model 2-K-1 and compared to the measurements under the governor parameters Ep1 (Table B.2), as shown in Fig. 6.14. The simulation of the GVO, the

6.3 Framework for Evaluating the Regulation of Hydropower Units

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Fig. 6.13 Block diagram of Model 2-K-3 with the “grid inverse” model for computing the load disturbance; the lumped HPP block is described in the part with dashed outline in Fig. 3.18

Fig. 6.14 Comparison of measurement and simulation during a period of normal PFC. a GVO (y) and RBA (α), the deviation value is shown. b Active power

RBA and the power output has a good agreement with the measurements, showing that the model can yield trustworthy simulation results.

6.3.2.2

Regulation Strategies

The following operation strategies S1–S3 and an ideal case S0 are analysed. (1) S1: normal PFC in which GV and RB regulate without any artificial filter (widely implemented); (2) S2: PFC with a floating dead zone filter for reducing the movement

98

6 Efficient Operation and Balancing Renewable Power Systems

Fig. 6.15 Compositions of efficiency losses analysed in this work

of runner blades; (3) S3: PFC with the runner blades being totally fixed (no RB movements); (4) S0: Normal PFC in an ideal on-cam condition, and it is unrealistic and only implemented to identify the off-cam loss in normal PFC.

6.3.2.3

Method of Quantification

Here, the method of quantification of the burden and quality of regulation is introduced. (1) Efficiency loss The losses are classified into the following compositions, as illustrated in Fig. 6.15. The loss in steady state operation, − ηst , is

 −ηst = 1 − ηst , pu .

(6.8)

A negative value of the efficiency change η indicates an efficiency loss. ηst is the on-cam steady state efficiency that is a constant value taken from the interpolation, and it varies for different operating points. In this section, the main object is the extra efficiency loss due to regulation, which is given as

 −η S j = ηst − η S j , pu .

(6.9)

Here, ηSj is the average value of the instantaneous efficiency during the operation period (one day) under a specific strategy (S j ). More specifically, the efficiency loss in transient due to deviation from the set-point (on-cam) can be obtained as

 −η S0 = ηst − η S0 , pu .

(6.10)

The loss due to off-cam in normal PFC is achieved by the difference between ηS0 and ηS1 . For example, the extra loss due to off-cam condition under strategy S2 and S3 is ηS0 − ηS2 and ηS0 − ηS3 , respectively. (2) Wear and fatigue

6.3 Framework for Evaluating the Regulation of Hydropower Units

99

For quantifying the wear and fatigue of turbines, we use the two indicators introduced in Sect. 6.1.1 for both GV and RB: the movement distance and the movement amount. The movement distance can be described in ⎧ N  ⎪ ⎪ ⎪ YGV,dist = |yis − yis−1 | ⎪ ⎪ ⎨ is=1 . (6.11) N ⎪  ⎪ ⎪ ⎪ |ais − ais−1 | ⎪ ⎩ Y R B,dist = is=1

Here, N is the total amount of samples and is means the sample number. y and a represent GVO and RBA respectively. (3) Regulation mileage The regulation mileage is introduced to quantify the amount of work hydropower units expend to follow a regulation signal, as described in M R = Pm−rated

N     pm,is − pm,is−1 , [MW].

(6.12)

is=1

Here, pm is the active power in per unit; Pm-rated is rated power of the Kaplan turbine, and its unit is MW. (4) Frequency quality The frequency quality is evaluated to comprehensively reflect the regulation performance of the hydropower unit. As presented in Sect. 6.2.1 and in the lower part of Fig. 6.12, the core idea is comparing the new frequency sequence of the power system under different regulation conditions, to examine whether the frequency quality is deteriorated. The frequency quality is mainly evaluated through the root mean square error (RMSE with respect to the rated frequency 50 Hz) of the frequency sequence. In Sect. 6.2, the frequency quality reflects the influence of a lumped unit that represents all the generating units in the grid. By contrast, the method here examines the influence of the regulation from a single Kaplan unit on the frequency of the whole grid.

6.3.2.4

Regulation Payment

In this section, only relative values of payment are considered. Clearing prices are not considered in the quantification. The strength payment Paystrength , inspired by SvK, is computed as  Pstep , [MW/Hz] S R = 0.1 . (6.13) SR , [pu] Paystr ength = SR−base

100

6 Efficient Operation and Balancing Renewable Power Systems

Table 6.5 Overall results of different operation conditions from one-day simulation. The bar in each cell indicates the relative magnitude of the values with the same color. The results of efficiency loss are condensed from Table 6.6. The results of GV movement are based on HPP 6, because there is little difference on the indicators between two HPPs. The operating point does not influence much on movement of GV and RB, hence only the results from point 5 are shown. For frequency quality, the values of the change of root mean square error are shown; negative and positive values are shown with green and grey bars respectively, and positive values indicate better frequency quality. The regulation mileages are shown with purple bar, and the detailed results are in Fig. 6.16 Parameter

Ep1 (b p = 0.04)

Strategy

S1

Avg-HPP 6

Burden

Efficiency change [pu] GV movement [/]

Regulation performance

Ep2 (b p = 0.02) S3

S1

S2

Ep3 (b p = 0.01) S3

S1

S2

S3

-0.023% -0.034% -0.069% -0.085% -0.105% -0.281% -0.340% -0.375% -1.167%

Min-HPP 6

-0.196% -0.207% -0.217% -0.370% -0.394% -0.476% -0.680% -0.712% -1.441%

Avg-HPP 7

-0.016% -0.046% -0.091% -0.083% -0.108% -0.409% -0.365% -0.397% -1.652%

Min-HPP 7

-0.403% -0.422% -0.461% -0.585% -0.609% -1.004% -1.100% -1.127% -2.242%

Distance

7.177

7.177

7.177

14.782

14.782

14.782

30.094

30.094

30.094

Amount

2039

2039

2039

2257

2257

2257

2550

2550

2550

Dist.-HPP 6

4.027

0.245

0

10.731

1.515

0

24.663

5.831

0

5.843

0.509

0

13.649

2.131

0

28.186

6.866

0

1237

19

0

1567

48

0

1877

174

0

28

0

RB Dist.-HPP 7 movement Amount-HPP 6 [pu] Amount-HPP 7

Payment

S2

1329

1621

58

0

1887

184

0

0.52%

0.45%

-0.07%

1.56%

1.48%

0.38%

0.43%

0.38%

-0.04%

1.31%

1.25%

0.38%

1094.8

573.2

482.0

2412.3

1324.2

996.5

506.1

442.3

2026.6

1156.8

958.9

Frequency quality [pu]

HPP 6

Mileage [MW] Strength [pu]

HPP 6

100.0% 79.7%

33.5% 204.6% 191.1% 54.6% 421.9% 422.3% 43.6%

HPP 7

81.3%

25.6% 162.9% 150.2% 32.1% 317.3% 308.4%

Mileage [pu]

HPP 6

100.0% 51.0%

46.3% 243.6% 127.5% 107.2% 536.7% 294.6% 221.7%

HPP 7

89.9%

41.6% 212.4% 112.6% 98.4% 450.9% 257.4% 213.3%

0

-0.09% -0.28%

HPP 7

0

-0.06% -0.24%

HPP 6

449.5

229.3

207.9

HPP 7

404.1

207.5

187.0

954.7

67.5% 46.2%

s d s q q s d s < Vg ¼ þ X 00 X 00 Iq ¼

qR

> : DV ¼ @Vg Dd þ g @d

dR

@Vg @Eq00

DEq00

þ

@Vg @Ed00

DEd00



¼ K8 Dd þ K9 DEq00 þ K10 DEd00  00 00 Eq00 Vs cos d  Vs2 cos 2d þ Ed00 Vs sin d XqR  XdR

Ed00 Vs sin d Eq00 Vs cos d þ þ 00 00 00 X 00 XdR XqR XdR qR    00 00 00 XqR  XdR Vs sin d  Ed E 00 Vs sin d  Ed00 K2 ¼ 00d þ þ ; 00 00 X 00 XdR XqR XdR qR   00 00 Vs cos d  Eq00 XqR  XdR Eq00  Vs cos d Eq00 Vs sin d  00 þ ; K4 ¼ ; K3 ¼ 00 00 X 00 00 XdR XdR XqR XdR qR K1 ¼

K5 ¼ K8 ¼

;

1 Vs cos d 1 ; K7 ¼  00 ; 00 ; K6 ¼ 00 XdR XqR XqR Vgd Vs cos dXq00 00 Vg XqR



Vgq Vs sin dXd00 Vgq xs Vgd xs ; K9 ¼ 00 00 ; K10 ¼ V X 00 : Vg XdR Vg XdR g qR

The values of the state variables in the coefficients K1 − K10 are initial steady-state values.

Appendix B

(1) Simulation settings in Sect. 4.2 (Table B.1) Table B.1 The default settings of the simulation of PFC Upstream level (m)

Downstream level (m)

Initial power (MW)

Frequency step (Hz)

bp

Kp, Ki, Kd

Ey, Ef

1639.3

1332.3

476

−0.2

0.04

9, 8, 0

0, 0.05

(2) Parameters and settings in Sect. 4.3 • Governor parameters: Kd = 0, Ty = 0.02 s, bp = 0.04 pu, ep = 0.04 pu, Ef = Ey =Ep= 0; • Characteristic coefficient of power grid load: eg = 0.0; • Transmission coefficient of ideal turbine: eh = 1.5 pu, ex = −1 pu, ey = 1 pu, eqh = 0.5 pu, eqx = 0, eqy = 1 pu; • Cross section area of surge tank (F): 415.64 m2; • Thoma critical section area for stability (Fth): 416.08 m2.

(3) Parameter values of HPP 5 in Chap. 5 The values of the generator parameters are estimated from field simulations of standard tests in [1, 2]. • Generator: the nominal apparent power is 206 MVA, and the line-to-line voltage is 21 kV; Xd = 0.768 pu, Xd0 ¼ 0:249 pu, Xd00 ¼ 0:187 pu, Xq = 0.512 pu, Xq00 ¼ 0:189 pu, 0 00 00 Td0 ¼ 7:880 s, Td0 ¼ 0:049 s, Tq0 ¼ 0:0283 s, Tj = 7.0 s; • Transformer and transmission line: Xs = 0.30 pu; © Springer Nature Switzerland AG 2019 W. Yang, Hydropower Plants and Power Systems, Springer Theses, https://doi.org/10.1007/978-3-030-17242-8

117

118

Appendix B

• Turbine characteristic (for a normal operating point): eqy = 0.66 pu, eqx = 0.1 pu, eqh = 0.47 pu, ey = 0.5 pu, ex = −0.96 pu, eh = 1.45 pu; • Penstock: Tw = 1.34 s (calculated under the rated condition: discharge is 275.0 m3/s and water head is 73.0 m), a = 0.33 pu, Te = 0.115 s (length of the penstock is 115 m).

(4) Operating settings of HPP 5 in Sect. 5.1 • Initial steady-state condition: Pe = 0.90 pu, cosu = 0.90 (Qg = 0.436), Vs = 1.00 pu; • Turbine governor (for both two feedback modes): bp = 0.04 pu, Kp = 9.0 pu, Ki = 5.0 s−1, Ty = 0.2 s, Backlash = 0.001 pu, Limiting rate = 0.1 pu/s; • AVR: Tr = 0.05, Ka = 100, the regulator output limit is ±2.0 pu; • PSS (speed input): Kx = 1 pu, KPe = 0, Ks = 9.5 pu, T0 = 1.4 s, T1 = 0.154 s, T2 = 0.033 s; • PSS (power input): Kx = 0, KPe = 1 pu, Ks = 2.5 pu, T0 = 1.4 s, T1 = 0.154 s, T2 = 3.0 s.

(5) Operating settings of HPP 5 in Sect. 5.2 • Initial steady-state condition: Pe = 0.90 pu, cosu = 0.90 (Qe = 0.436), Vs = 1.00 pu; • Governor: bp = 0.04 pu, Kp = 8.0 pu, Ki = 1.0 s−1, Ty = 0.2 s, the backlash value is 0.001 pu, the limiting rate is 0.1 pu/s; • AVR: Tr = 0.05, Ka = 100 pu, the output limit is ±4.0 pu; • PSS: Kx = 1, KPe = 0, Ks = 9.5 pu, T0 = 1.4 s, T1 = 0.354 s, T2 = 0.033 s; the output limit is ±0.05 pu.

(6) Default simulation settings in Sect. 6.1 • • • •

Upstream level and downstream level: 213.1 and 78.3 m; Initial power: 122.0 MW; Amplitude and period of sinusoidal frequency: 0.1 Hz and 60 s; Turbine governor: Kp = 1.0 pu, Ki = 0.833 s−1, Kd = 0, bp = 0.02 pu, Edz = 0, Backlash-By = 0.001 pu, Ty (lag) = 0.02 s.

(7) Detailed information of measurements in Sect. 6.2 The original sampling frequency is 200 Hz, and the sampling time of the signals is averaged to 0.2 s. The governor parameter in the simulation is the same as the values in the HPP during the measurement, which are the standard parameter settings EP1 in Vattenfall HPPs, see Table B.2. The values of the lag, the backlash and the delay are set to 0.25 s, 0.00029 pu and 0.097 s respectively. The default parameter settings of the actuator in Sect. 6.2 is shown in Table B.3.

Appendix B

119

Table B.2 Standard controller parameters in Vattenfall HPPs Parameter

Ep0

Ep1

Ep2

Ep3

bp (or Ep) Kp Ki

0.1 1 1/6

0.04 1 5/12

0.02 1 5/6

0.01 2 5/3

Table B.3 The default parameter settings of the actuator in Sect. 6.2 Parameter

Servo (Ty)

Saturation

Rate limiting

Backlash

Value

0.2

(0,1 pu)

±0.1 pu/s

0.05  10−2 pu

Table B.4 Parameters of the plant and the grid in Sect. 6.2 Symbol

Parameter

Value

K Tw M D

Scaling factor Water time constant System inertia Load damping constant

10  bp (pu) 1.5 (s) 13 (s) 0.5 (pu)

(8) Detailed information for Sect. 6.3 (Tables B.5 and B.6)

Table B.5 Parameters of the plant and the grid in Sect. 6.3. The value of M and D are updated, comparing from the values in Table B.4 Symbol

Parameter

Value

Tw M D

Water time constant System inertia Load damping constant

1.5 (s) 14.6 (s) 0.66 (pu)

Table B.6 Parameter values of the HPP 6 and HPP 7 for simulation settings. There is no surge tank in HPP 7, hence the values of Twt, Ts and ft are shown as N/A HPP 6 Para. Ty Tya Tdel-gv Tdel-a BLgv BLa Twp

Value

Para.

Value

HPP 7 Para.

0.25 s 0.90 s 0.097 s 0.410 s 0.00029 pu 0.00132 pu 1.7 s

Twt Tr Ts a ft

13.2 s 0.1 s 350.0 s 0.33 0.0065  q0

Ty Tya Tdel-gv Tdel-a BLgv

fp

0.0120  q0

BLa

Dt

0

Twp

Value

Para.

Value

0.25 s 0.90 s 0.097 s 0.410 s 0.00029 pu 0.00132 pu 1.01 s

Twt Tr Ts a ft

N/A 0.07 s N/A 0.33 N/A

fp

0.010  q0

Dt

0

Author Biography

Dr. Weijia Yang is presently working as a faculty member at the School of Water Resources and Hydropower Engineering (the State Key Laboratory of Water Resources and Hydropower Engineering Science) in Wuhan University, Wuhan, China. He received his B.S. and M.S. degrees from School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China in 2011 and 2013, respectively. He obtained his Ph.D. degree in 2017 at Division of Electricity, Department of Engineering Sciences, Uppsala University, Uppsala, Sweden. During the Ph.D. study, he mainly cooperated with the Vattenfall R&D in Sweden, and had short-term study visit to the Energy-Water Resource Systems team at the Oak Ridge National Laboratory, USA and the SMart grid And Renewable energy Technology (SMART) Lab at the University of Saskatchewan in Canada. He mainly works in the interdisciplinary field regarding hydraulics, mechanics, electrical and control engineering, by applying theoretical analysis, numerical simulations, physical model tests and on-site measurements. His current research interests include dynamic characteristics of hydropower systems (pumped storage systems), interaction between hydropower plants and power systems, etc. He has published over 30 journal articles and peer-reviewed conference papers, contributed to an IET book (two chapters), and given several oral

© Springer Nature Switzerland AG 2019 W. Yang, Hydropower Plants and Power Systems, Springer Theses, https://doi.org/10.1007/978-3-030-17242-8

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122

Author Biography

presentations at international conferences/seminars held by the IAHR, the IEEE and the journal Applied Energy, etc. Currently, he is leading and participating in several research projects supported by the National Natural Science Foundation of China (NSFC), the State Grid Corporation of China and the China Southern Power Grid, etc. He is engaged in the IEC/TC4/WG 36 as an IEC expert, and is a member of the IAHR and the IEEE. He also serves as a reviewer for multiple international journals. Dr. Weijia Yang’s full list of publications is available at: www.researchgate.net/profile/Weijia_Yang2

References

1. 2.

Lidenholm J, Lundin U (2010) Estimation of hydropower generator parameters through field simulations of standard tests. IEEE Trans Energy Convers 25:931–939 Bladh J (2012) Hydropower generator and power system interaction, Uppsala University

© Springer Nature Switzerland AG 2019 W. Yang, Hydropower Plants and Power Systems, Springer Theses, https://doi.org/10.1007/978-3-030-17242-8

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