DECENTRALIZE CONTROL PARADIGMS FOR ENHANCEMENT OF POWER SYSTEM STABILITY
ABDUL SALEEM MIR
DEPARTMENT OF ELECTRICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI
JULY 2020
© Indian Institute of Technology Delhi (IITD), New Delhi, 2020
DECENTRALIZE CONTROL PARADIGMS FOR ENHANCEMENT OF POWER SYSTEM STABILITY
by
ABDUL SALEEM MIR
Department of Electrical Engineering
Submitted
in fulfilment of the requirements of the degree of Doctor of Philosophy to the
INDIAN INSTITUTE OF TECHNOLOGY DELHI
JULY 2020
CERTIFICATE
This is to certify that the thesis entitled “Decentralized Control Paradigms for Enhancement of Power System Stability” submitted by Mr. Abdul Saleem Mir, to Indian Institute of Technology Delhi for the award of the degree of Doctor of Philosophy is a bonafide record of research work carried out by him under my supervision. The contents of this thesis have not been submitted to any other institute or university for the award of any degree or diploma.
Prof. Nilanjan Senroy
Professor
Department of Electrical Engineering Indian Institute of Technology Delhi New Delhi-110016, India.
Date:
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Acknowledgements
I would like to express my sincere gratitude to my research supervisor Prof. Nilanjan Senroy whose encouragement, motivation, supervision, guidance, enthusiasm and personal support from the preliminary to the concluding level enabled me to develop an understanding of the subject. It is an honor for me to have been working under his supervision and being part of his working group.
I acknowledge my deep sense of gratitude to the members of the doctoral research committee Prof.
Sukumar Mishra, Prof. B. K. Panigrahi and Dr. Ashu Verma for their valuable suggestions and scrutiny of this work. I am also grateful to Prof. A. R. Abhyankar, Dr. Shubhendu Bhasin and Dr.
Abhinav Kumar Singh for their co-operation and help in my research.
I am indebted to all my seniors, especially Dr. Ganesh P. Prajapat, Dr. Deepak Reddy, Dr. Manas Jena, Dr. Mudassir Maniar and Dr. Pratyasa Bhui, for healthy discussions and personal support. I am also grateful of my batchmates, juniors and friends, especially, Mrs. Sayari Das, Mr. Zamir Ahmad Wani, Mrs. Ayesha Firdaus, Mr. Rajiv Jha, Mr. Shivraman, Mr. Diptak Pal, Ms. Nisha, Mrs. Tabia, Mr. Debargha Brahma, Mr. Debasish Mishra, Ms. Megha, Ms. Shazia, Mr. Bharat, Mr. Pankaj and Mr. Arpan who have assisted me throughout and made my life in IIT Delhi very delightful. I would also like to acknowledge the support of my B. Tech friends especially, Mr.
Saqib Yousuf, Mr. Aamir Rafiq, Mrs. Tabish Nazir Mir, Mr. Anjum Rauf, Mr. Kaisar Ahmad, Mr.
Faisal and Mr. Saqib Nisar. Finally, I would like to make a special acknowledgement to my friend/brother Dr. Janibul Bashir for encouragement and support throughout.
Last but not the least, I owe my deepest gratitude to my parents, siblings and relatives for their love, affection, care and constant encouragement throughout the research work. Finally, I wish to mention very special acknowledgement to my parents, Mr. Abdul Rashid Mir and Mrs. Rafiqa Jubali Bhat, for their continuous support, love and encouragement.
Dated: Abdul Saleem Mir
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Abstract
This dissertation primarily focuses on the mitigation of instabilities in the power system via novel auxiliary stabilizers and intelligently controlled energy storage systems. Improving the stability margins in a power system allows the higher flow of power through interties which translates into a measurable economic benefit. Dynamic state estimator using local measurements acts as a precursor for the auxiliary stabilizers as they utilize unmeasurable interior states of the machine in the control law. Further, bulk integration of renewable energy requires fast-acting energy sources/sinks at the time of the disturbance. In this context, intelligently controlled fast-acting energy storage systems have been suggested to mitigate intermittency, enhance transient and frequency stability margins. Several aspects investigated in this thesis are as follows-
1) A nonlinear dynamic state estimator has been recommended to estimate the unmeasurable states of the machine using analogue measurements from the generator (terminal) bus instrument transformers. This methodology is well suited for enhancing system control, assessing dynamic security and monitoring oscillatory modes to name a few.
2) A decentralized nonlinear excitation controller utilizing terminal bus voltage and frequency measurements as exogenous inputs and machine states (estimated locally) in the robust optimal control law for significant enhancement in the dynamic and transient stability margins has been proposed.
3) Grid integrated low inertia DFIG wind energy conversion system (WECS) exhibits prolonged oscillations following a network disturbance. A computationally adaptive optimal damping controller using DFIG-WECS interior states (estimated locally) has been suggested for the mitigation. Compared to its predecessors, proposed stabilizer being robust and cost effective improves the stability significantly.
4) Performance of auxiliary stabilizers is affected by the system nonlinearities like saturation limits, dead-bands, rate constraints etc. In this context, effective use of properly controlled fast acting storage facilities like flywheel energy storage system and ultrabattery storage is suggested. Modelling and control architecture of the new storage technology namely ultrabattery and flywheel storage has been introduced and discussed for subsequent use in power system stability enhancement.
5) The application of an intelligently controlled flywheel energy storage system (FESS), to
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mitigate the intermittency in wind power injection, as well as enhance the transient stability of the connected multimachine power system has been investigated.The main contributions are –a) enhanced use of DFIM based FESS for transient stability improvement following a network disturbance, b) demonstrating the intelligent controller development and its application for the flexible operation of the FESS facility, and c) intermittency mitigation via FESS considering actual wind speed profile.
6) The use of intelligent virtual synchronous generator and constrained LQR based ultrabattery storage has been suggested for improved frequency control.
Keywords:
Adaptive control, cubature-Kalman-filter (CKF), decentralized, dynamic state estimator, damping control, DFIG, linear quadratic regulator (LQR), neural networks (NNs), optimal control, phasor measurement unit (PMU), power systems, stability.vii
सार
यह शोध प्रबंध मुख्य रूप से उपन्यास के माध्यम से बबजली व्यवस्था में अस्स्थरताओं के शमन पर केंबित है सहायक स्टेबलाइजसस और समझदारी से बनयंबित ऊजास भंडारण प्रणाली। स्स्थरता
में सुधार एक पावर बसस्टम में माबजसन अंतर के माध्यम से शस्ि के उच्च प्रवाह की अनुमबत देता है जो अनुवाद करता है एक औसत दजे का आबथसक लाभ। स्थानीय माप का उपयोग कर गबतशील राज्य आकलनकतास एक के रूप में कायस करता है सहायक स्टेबलाइजसस के बलए अग्रदूत के रूप में वे मशीन के अनम्य आंतररक राज्यों का उपयोग करते हैं बनयंिण कानून। इसके
अलावा, अक्षय ऊजास के थोक एकीकरण के बलए तेजी से काम करने वाली ऊजास की आवश्यकता
होती है गड़बड़ी के समय स्रोत / डूब इस संदभस में, बुस्िमानी से तेजी से अबभनय को बनयंबित बकया ऊजास भंडारण प्रणाबलयों को आंतराबयकता को कम करने, क्षबणक को बढाने और आवृबि
स्स्थरता माबजसन। इस थीबसस में जांच बकए गए कई पहलू इस प्रकार हैं-
1) एक गैर-गबतशीलगबतशीलराज्यआकलनकतास कोअचूकका अनुमानलगानेकी बसफाररशकी गई है
जनरेटर (टबमसनल) बस से एनालॉगमापकाउपयोग करते हुएमशीनकीस्स्थबत उपकरणट्ांसफामसर।यह पिबतप्रणालीबनयंिणकोबढानेकेबलएअच्छीतरहसेअनुकूलहै, गबतशीलसुरक्षाकाआकलनऔरकुछ नामकरनेकेबलएदोलनमोडकीबनगरानीकरना।
2) टबमसनल बस वोल्टेज और आवृबि का उपयोग एक बवकेन्द्रीकृत अरेखीय उिेजना बनयंिक बबहजासत आदानोंऔर मशीनराज्योंके रूप में माप (स्थानीय रूप से अनुमाबनत) मजबूतमें गबतशील और क्षबणक स्स्थरतामेंमहत्वपूणसवृस्िकेबलएइष्टतमबनयंिणकानूनमाबजसनप्रस्ताबवतबकयागयाहै।
3) बग्रडएकीकृतकमजड़ताडीएफआईजीपवनऊजासरूपांतरणप्रणाली (डब्ल्यूईसीएस) प्रदबशसतकरताहै
एक नेटवकसगड़बड़ी के बाद लंबे समय तक दोलनों। एककम्प्यूटेशनल रूप से अनुकूली डीएफआईजी- डब्ल्यूईसीएसआंतररकराज्यों (स्थानीयरूपसे अनुमाबनत) काउपयोगकरकेइष्टतमबभगोनाबनयंिकरहा
है शमनकेबलएसुझावबदया।अपनेपूवसवबतसयोंकीतुलना में, प्रस्ताबवत स्टेबलाइजरमजबूतहो रहाहै और प्रभावीलागतस्स्थरतामेंकाफीसुधारकरतीहै।
4) सहायकस्टेबलाइजससकाप्रदशसनसंतृस्िजैसीप्रणालीकीगैर-प्रभाबवतताओंसे प्रभाबवतहोताहैसीमाएं, डेड-बैंड, दरकीकमीआबद।इससंदभसमें, ठीकसे बनयंबितका प्रभावीउपयोगफ्लाईव्हीलऊजासभंडारण प्रणाली औरपराबैंगनीभंडारणकीतरहतेजीसे अबभनयभंडारणकीसुबवधाहै सुझाव बदया।नई भंडारण
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प्रौद्योबगकीकीमॉडबलंगऔरबनयंिणवास्तुकलापराबैंगनीऔरचक्काभंडारणशुरूबकयागयाहैऔरबाद केउपयोगकेबलएचचासकीगईहैबबजलीप्रणालीकीस्स्थरतामेंवृस्ि।
5) एकबुस्िमानीसेबनयंबितचक्काऊजासभंडारणप्रणाली (एफईएसएस)काअनुप्रयोगपवनऊजासइंजेक्शन में आंतराबयकताको कमकरें, साथ ही क्षबणक स्स्थरता को बढाएंकनेक्टेड मल्टीमाबचन पावरबसस्टमकी
जांच कीगई है।मुख्य योगदानकर रहेहैं - क) क्षबणकस्स्थरता मेंसुधार केबलएडीएफआईएमआधाररत एफईएसएसकाएकबढाया उपयोगबनम्नबलस्खतएकनेटवकसगड़बड़ी, ख) बुस्िमानबनयंिकबवकासऔर उसके प्रदशसन एफईएसएस सुबवधा के लचीले संचालन के बलए आवेदन, और सी) आंतराबयक शमन वास्तबवकपवनगबतप्रोफाइलपरबवचारकरतेहुएएफईएसएसकेमाध्यमसे।
6) बुस्िमानआभासीतुल्यकाबलकजनरेटरऔरबववशएलक्यूआरआधाररतपराबैंगनीकाउपयोगभंडारण मेंसुधारआवृबिबनयंिणकेबलएसुझावबदयागयाहै।
कीवर्ड:
अनुकूलीबनयंिण, क्यूरेचर-कलमन-बफल्टर (सीकेएफ), बवकेन्द्रीकृत, गबतशीलराज्यअनुमानक, बभगोना बनयंिण, डीएफआईजी, रैस्खक बिघात बनयामक (एलक्यूआर), तंबिका नेटवकस (एनएन), इष्टतम बनयंिण, चरणमापकइकाई (पीएमयू), पावरबसस्टम, स्स्थरता।ix
Contents
CHAPTER 1: Introduction ... 1
1.1 General ... 1
1.2 State-of-the-Art & Research Motivation ... 3
1.2.1 Decentralized Dynamic State Estimation in Power Systems ... 3
1.2.2 Decentralized Nonlinear Excitation Control ... 4
1.2.3 Stability Enhancement of DFIG-WECS via Optimal Damping Controller ... 6
1.2.4 Control of Energy Storage Systems (ESS) for Power System Applications ... 7
1.2.5 Intermittency Mitigation and Transient Stability Enhancement via Controlled ESS ... 9
1.2.6 Intelligently Controlled ESS for Frequency Control in Power Systems ... 10
1.3 Thesis Objectives ... 12
1.4 Brief Overview of the Work Done ... 13
1.5 Prime Contributions from this Thesis ... 17
1.6 Thesis Organization ... 18
CHAPTER 2: Decentralized Dynamic State Estimation ... 20
2.1 General ... 20
2.2 Studied System and Problem Description ... 21
Certificate i
Acknowledgements iii
Abstract v
Contents ix
List of Figures xiii
List of Tables xvi
List of Abbreviations and Symbols xvii
x
2.3 Adaptive Detection Methodology ... 36
2.4 Dynamic State Estimation Algorithm ... 40
2.5 Choice of Sigma Points and Filter Stability ... 42
2.6 Observability Condition ... 44
2.7 Case Studies ... 45
2.8 Conclusion ... 51
CHAPTER 3: Decentralized Nonlinear Excitation Control ... 52
3.1 General ... 52
3.2.1 Controller Design for Decentralized Power System (3.9) ... 56
3.2.2 Stability of the Decentralized Power System ... 58
3.3.1 Function Approximation(FA) ... 60
3.3.2 Tuning of Critic NN Weights ... 61
3.3.3 Tuning of Actor NN Weights and SPIA ... 61
3.5.1 Nonlinear time-domain simulations ... 63
3.5.2 Modal Analysis ... 66
3.5.3 Transient Stability Evaluation ... 69
3.5.4 Real-Time (RT) Implementation ... 70
CHAPTER 4: Stability Enhancement of Grid Connected DFIG ... 72
4.1 General ... 72
4.2 Modeling of the Studied System ... 72
4.3 Robust Estimation of DFIG-WECS States ... 78
4.4 Robust Estimation/Control of DFIG-WECS States ... 80
4.4.1 Performance of RSCKF-DSE for DFIG-WECS against its precursors ... 80
4.4.2 Performance of ADP based Optimal Controller ... 81
4.4.3 ADP controlled DFIG in multimachine environment ... 87
4.5 Implementation: Scaled Laboratory Prototype ... 90
4.6 Conclusion ... 91
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CHAPTER 5: Energy Storage Systems: Modelling and Control ... 92
5.1 General ... 92
5.2 Voltage Source Converter based Ultrabattery Energy Storage System ... 94
5.2.1 Ultrabattery and its Power Conditioning System ... 94
5.3 Flywheel Energy Storage System ... 99
5.4 Conclusion ... 101
CHAPTER 6: Wind Power Smoothing and Stability Enhancement via Intelligently Controlled FESS ... 102
6.1 General ... 102
6.2 Model of the Studied System ... 102
6.2.1 Flywheel Modelling and Its Control ... 104
6.2.2 Supervisory Control Based on AWFNN ... 104
6.2.3 Controller Performance Comparison ... 110
6.3 Wind Speed Modelling ... 111
6.4 Case Study: Wind Power Smoothing, FESS Sizing and Transient Stability Enhancement ... 113
6.4.1 Wind Power Smoothing ... 113
6.4.2 FESS Sizing Strategy ... 114
6.4.3 Transient stability enhancement ... 115
6.4.4 Real-Time Implementation ... 120
6.5 Conclusion ... 120
CHAPTER 7: Intelligently Controlled Energy Storage System for Frequency Control in Power Systems ... 122
7.1 General ... 122
7.2 Frequency Control in an Autonomous Power Systems ... 123
7.2.1 Self-tuning UBESS-VSM ... 125
7.2.2 Back-Propagation Algorithm (BPA) ... 128
7.2.3 Learning Rates: Convergence and Stability of ANPC ... 129
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7.2.4 Performance Evaluation ... 132
7.2.5 Conclusion ... 137
7.3 Frequency Control in the Connected Power Systems ... 137
7.3.1 ANPC and CLQR Based UBESS ... 139
7.3.2 Simulation Studies ... 139
7.3.3 Conclusions ... 140
CHAPTER 8: Conclusions ... 142
8.1 Summary of the Work ... 142
8.2 Scope of the Future Work ... 144
References ... 146
Appendix 𝓐 ... 162
Appendix 𝓑 ... 163
Appendix 𝓒 ... 165
Publications from the Thesis ... 168
Bio-Data ... 169
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LIST OF FIGURES
Figure 2.1. Schematic of the proposed methodology ... 22
Figure 2.2. NYPS-NETS 16 machine 68 bus Power System [6] ... 22
Figure 2.3. Phasor estimation dynamics of the voltage phasor of 9th unit. ... 39
Figure 2.4. Tuning of gains for signal parameter estimation. ... 39
Figure 2.5 Schematic of the DDSE algorithm using robust SRCKF. ... 40
Figure 2.6 Voltage phasor of 13th machine (a) Estimated amplitude, (b) Estimated frequency (c) parameter estimation errors. ... 45
Figure 2.7 DDSE algorithms Comparison: Estimation of 9th unit states for the base case. ... 47
Figure 2.8 Bar plots and pdfs of the state estimation errors for 9th unit for the base case. ... 47
Figure 2.9 . Estimation of ω13 with DC bias in the measurement (V13) ... 48
Figure 2.10 . (a) Estimation of ω9 for colored noise for the base case (b) Bar plot and pdf of the estimation error in ω9 ... 48
Figure 2.11. Observability test: Estimation of 𝛼9 ... 49
Figure 3.1. Schematic of the system and control methodology. ... 53
Figure 3.2. Adaptive Actor-Critic Structure of the Decentralized System. ... 53
Figure 3.3. Single-Line diagram of IEEE 16 machine 68 bus test system. ... 54
Figure 3. 4. Continuous-time PIA for tuning actor/critic weights. ... 62
Figure 3. 5. (a) Critic parameters (b) Convergence of AC NN weights. ... 62
Figure 3. 6. Dynamic performance of proposed NAOC scheme against its precursors. ... 64
Figure 3. 7. Dynamic performance of NAOC for changed operating conditions. ... 65
Figure 3. 8. Eigen value plot (controller performance comparison). ... 67
Figure 3. 9. Eigen Values (Comparison with PSS (Larsen & Swann)). ... 68
Figure 3. 10. Transient stability performance comparison. ... 69
Figure 3. 11. Schematic diagram for real-time implementation. ... 71
Figure 3. 12. Real-time results (a) NAOC performance in real-time (RT) (b) Controller performance comparison ... 71
Figure 4.1 Schematic of grid connected DFIG-WECS ... 74
Figure 4.2 DFIG-WECS: RSC Control Architecture ... 75
Fig. 4.3. (a) Flowchart of proposed RSCKF based ADP algorithm (b) Consolidated control architecture of RSCKF based ADP algorithm. ... 77
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Fig. 4.4. DSE of unobservable states from noisy measurements: (a) turbine speed 𝜔𝑡, (b) 𝑒𝑞′ .. 79
Fig. 4.5. (a) Convergence of P𝑘. (b) Convergence of ℱ𝑘. ... 82
Fig. 4.6. Performance comparison (wind speed change) (a) DFIG rotor speed (b) DFIG stator voltage (c) DFIG Power (d) Changed operating condition (𝑣𝑤 = 9.5𝑚/𝑠, 𝑉𝑏 = 0.9 𝑝𝑢). ... 83
Fig. 4.7. Polar plot of low frequency modes. ... 84
Fig. 4.8. Eigenvalue loci of low frequency modes: (a) 0.01 ≤ 𝑥T ≤ 0.15, (b) 1.5 ≤ 𝑙𝑚 ≤ 5.... 85
Fig. 4.9. Performance Comparison: Test-system subjected to a voltage-sag (a) DFIG Stator Voltage (b) Rotor Speed (c) Rotor Current (d) Rotor Speed: Changed operating condition. ... 87
Fig. 4.10. Test system 2: Modified WSCC 9-Bus System with WECS [28]. ... 88
Fig. 4.11. Multimachine environment: 3-phase fault (F1) near bus ⑨... 88
Fig. 4.12. Multimachine environment: wind change from 12m/s to 11m/s for 1s. (a) Active power supplied by DFIG-WECS (b) G3 speed in 𝑝. 𝑢. ... 89
Fig. 4.13. Experimental results (a-c) Wind speed change. (d-f) test-system subjected to a voltage- sag. ... 89
Fig. 4.14. Experimental Scaled Laboratory setup at IIT Delhi. ... 90
Fig. 5.1. Ultrabattery Energy Storage System Connected to the Grid. ... 93
Fig. 5.2. Ultrabattery Energy Storage System Connected to the Grid. ... 93
Fig. 5.3. (a) UBESS inner loop (b) Tracking performance of inner loop (c) CLQR ... 96
Fig. 5.4. Control loops of the UBESS-VSC (dq-frame) ... 98
Fig. 5.5. (a) DFIM based FESS (b) RSC Control loops of the FESS ... 98
Fig. 5.6. (a) DFIM based FESS block diagram for PI-Tuning (b-c) Tuning Performance ... 99
Fig. 5.7. (a) P-Control (b) Q-Tracking (c) Speed (𝜔𝑓𝑙) of FESS ... 99
Fig. 6.1. (a) Test System (b) Flywheel Energy Storage System ... 103
Fig. 6.2. (a) Active power control loop of RSC of FESS. (b) Reactive power control loop of RSC of FESS (c) AWFNN based model identifier. ... 103
Fig. 6.3. (a) Block diagram of the proposed control scheme. (b) AWFNN performance against other intelligent schemes... 106
Fig. 6.4. (a) Nonlinear system identification (AWFNN performance) (b) Identification error (c, d, e) Controller Performance comparison. ... 107
Fig. 6.5. (a) Van’ der Hoven Wind Spectrum (b) Von Karman Wind Spectrum (c) Wind speed (d) Power output of the windfarm ... 112
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Fig. 6.6. Case study 1: (a-b) Wind power smoothing performance. ... 112 Fig. 6.7. (a) FESS tracking performance (b) Flywheel speed 𝜔𝑓𝑙(𝑝. 𝑢. ). ... 113 Fig. 6.8 (a) WECS DFIG Speed (b) Windfarm Terminal Voltage (c) 𝑃𝑓𝑙𝑦 (d) 𝑄𝑓𝑙𝑦 (e) 𝜔𝑓𝑙. .... 116 Fig. 6.9. G2: a 3-phase fault between bus ⑦ and bus ⑧ with clearing time of 185ms. (a) 𝛿2𝐶𝑂𝐼 (𝑟𝑎𝑑. ). (b) 𝜔2𝐶𝑂𝐼(rad./s). (c) 𝑉2(p.u.). ... 117 Fig. 6.10. Normalized control efforts for the two case studies. ... 119 Fig. 6.11. RT-Results: a 3-phase fault between bus ⑦ and bus ⑧ (clearing time = 185ms). (a) WECS DFIG Speed (p.u.) (b) 𝛿2𝐶𝑂𝐼 (𝑟𝑎𝑑. ).. ... 120 Fig. 7. 1. (a) Block diagram of the VSM control strategy (b) UBESS based VSM ... 123 Fig. 7. 2. Autonomous wind-diesel power system with self-tuning UBESS-VSM ... 123 Fig. 7. 3. Effect of 𝑘𝑣 and 𝑘𝑑 on system frequency (𝑓) following a step (80kW) increase in load.
(a) Effect of 𝑘𝑣 on system frequency (𝑓), (𝑘𝑑 = 0). (b) Effect of 𝑘𝑑 on system frequency (𝑓), (𝑘𝑣 = 0). (c) Effect of 𝑘𝑣 and 𝑘𝑑 modulation on frequency (𝑓) (d) Effect of 𝑘𝑣 and 𝑘𝑑 modulation on ROCOF (slope) (e) Effect of 𝑘𝑣 and 𝑘𝑑 modulation on settling time. ... 126 Fig. 7. 4. Adaptive neuro predictive model (System Identification) ... 127 Fig. 7. 5 (a) Tracking control of nonlinear system [29] via ANPC under external disturbances. (b) Tracking error (c) Adaptive learning-rate (𝜂𝐼) (d) Adaptive learning-rate (𝜂𝑐). ... 130 Fig. 7. 6 (a) Consolidated VSM control block diagram (b) Step Response (c) Control effort. .. 132 Fig. 7. 7. Case study 1: Step change in load and constant wind power ... 134 Fig. 7. 8. (a) Van der Hoven Spectrum (b) Wind Speed (𝑚𝑠 − 1) ... 135 Fig. 7. 9 Case study 2: Response under dynamic wind conditions: MAE1 = 1𝑁𝑖 = 1𝑁𝑓𝐶𝑃 − 𝑓𝑆𝑇 ... 136 Fig. 7. 10. Modified WSCC 9-Bus System (with UBESS and Windfarms) ... 137 Fig. 7. 11. (a) Intelligent CLQR Schematic (b) Parameter updates (𝛼1, 𝛼2, 𝛼3, 𝛽1, 𝛽2, 𝛽3) .... 138 Fig. 7. 12 Case study: Step change in load (a) Bus ① frequency (Hz) (b) Bus ① ROCOF (Hz/s) (c) Bus ④ UBESS Power (MW) (d) Bus ④ UBESS Voltage (V). ... 138
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LIST OF TABLES
Table 2.1 𝜇: 𝐵𝑖𝑎𝑠 ; 𝜎: 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐸𝑟𝑟𝑜𝑟 (𝑆𝐸) ... 49
Table 3.1 (IPF=Interarea Power flow, FL=Faulted Line) ... 66
Table 3.2 Improvement in Inter-area Mode Damping ... 67
Table 3.3 Transient Stability Improvement (TSI)... 68
Table4.1𝜇 = 𝑚𝑒𝑎𝑛;𝜎 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 ... 81
Table4.2Controller Performance Comparison ... 84
Table4.3(𝑓𝑛= 𝑚𝑜𝑑𝑒𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦,𝜉𝑑′ = 𝑚𝑜𝑑𝑒𝑑𝑎𝑚𝑝𝑖𝑛𝑔𝑟𝑎𝑡𝑖𝑜) ... 84
Table 4.4. Weak grid conditions: 𝑥𝑇 = 0.12 𝑝. 𝑢. ... 85
Table 4.5. (𝐹𝑎𝑢𝑙𝑡 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠: 𝐹𝑖𝑔. 15): Transient Stability Improvement ... 88
Table 6.1. Controller Performance Improvement ... 109
Table 6.2: Smoothing Performance a Comparison ... 113
Table 6.3: Transient Stability Index (TSI) ... 118
Table 6.4: Transient Stability Margin (TSM) ... 118
Table 7.1: Scenario 1 (Step Change in Load) ... 135
Table 7.2: Scenario 2 (Dynamic Wind Conditions)... 135
Table 7.3: Computation Time Comparison ... 135
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LIST OF ABBREVIATIONS AND SYMBOLS DDSE Decentralized Dynamic State Estimation
ADM Adaptive Detection Methodology CT Current Transformer or Continuous time PT/VT Potential/Voltage Transformer
AC Actor-Critic
NETS-NYPS New England Test System (NETS)- New-York Power System (NYPS) WECC Western Electricity Coordinating Council
NN Neural Networks
ARE Algebraic-Riccati-equation HJB Hamilton–Jacobi–Bellman FA Function Approximation PIA Policy Iteration Algorithm
NAOC Nonlinear Adaptive Optimal Controller
DFIG Doubly Fed Induction Generator based Wind Turbine system
WECS Wind Energy Conversion System
DAE Differential-Algebraic-Equations
ODE Ordinary-Differential-Equations
PMSG Permanent Magnet Synchronous Generator
FRC Full Rated Converter
RSC Rotor Side Converter
GSC Grid Side Converter
MPPT Maximum Power Point Tracking
LQR Linear Quadratic Regulator
PSS Power System Stabilizer
UKF Unscented Kalman Filter
CKF Cubature Kalman Filter
PCS Power Conditioning System
FAST Fatigue, Aerodynamic, Structural and Turbulence simulator
NREL National Renewable Energy Laboratory, Department of Energy, U.S.
PMU Phasor Measurement Unit
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WSCC Western System Coordinating Council
𝜔𝐵, 𝜔 Base elec. speed (rad/s), machine speed in p.u.
H, 𝑓V Machine inertia (s), stator voltage (V) freq. in p.u.
Pe, Ie Electrical power and stator current resp.
𝛿, 𝜃 Rotor angle and stator voltage phase angle in rad.
V𝑟∗, E𝑓𝑑 AVR reference voltage, field excitation voltage V𝑟, V𝑠 AVR filter voltage and PSS output resp.
V𝑎 AVR regulator voltage
𝑒𝑑′, 𝑒𝑞′ Transient d and q axis emfs in p.u.
𝜓𝑑, 𝜓𝑞 Subtransient damper coil d and q axis emfs in p.u. 𝑝𝑖=1…3 PSS states, 𝑓I =frequency of the stator current.
𝑣𝑞, 𝑣𝑑 q and d axis stator voltages (V𝑡 = 𝑣𝑑 + 𝑗𝑣𝑞) in p.u.
𝑖𝑞, 𝑖𝑑 q and d axis stator currents (I𝑒 = 𝑖𝑑 + 𝑗𝑖𝑞) in p.u.
𝒙, 𝒖 State and pseudo-input (or input) vectors respectively 𝒚, 𝑛𝑥 Measurement vector, State vector dimension.
𝑎(𝑡) Instantaneous CT/PT measurement
𝓼, 𝓺 Column vectors ofprocess and pseudo-input noises resp.
𝓻 Column vector of noise in 𝒚
𝒫𝑥, 𝒫𝑦 State and measurement covariance matrices resp.
𝒫𝑥𝑦 Cross-correlation covariance matrix 𝒫𝑥𝓆 Cross-covariance matrix of 𝒙 and 𝓺 𝒫𝜉 = [𝒫𝑥𝒫𝑥𝓆T ; 𝒫𝑥𝓆𝒫𝓆]
Q𝜉 Constant additive process noise covariance matrix R𝑦 Constant measurement noise covariance matrix Ts Sampling time in seconds
𝐻𝑡 Turbine inertia constant 𝐻𝑔 DFIG inertia constant 𝜔𝑡 Turbine angular speed 𝜔𝑟 DFIG angular speed 𝜃𝑡𝑤 Shaft twist angle
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𝜔𝐵 Base electrical speed
𝑃𝑡𝑝𝑢 Turbine power
𝑇𝑠 Shaft torque
𝑇𝑒 Generator electrical torque
𝑇𝑡 Turbine torque
𝑐𝑑 Shaft damping coefficient
𝑘𝑠 Stiffness of the shaft
𝑉𝑤 Wind speed
VDC DC link voltage
𝐕𝒔 DFIG Stator terminal voltage
𝐕𝒃 Infinite bus voltage
𝑥T Transmission line reactance
𝑥C Grid side converter transformer reactance
P𝑒 Generator active power
Q𝑒 Generator reactive power
𝜃𝑡𝑤 Angular position of the turbine shaft
𝑣𝑞𝑠, 𝑣𝑑𝑠, 𝑣𝑞𝑟 𝑎𝑛𝑑 𝑣𝑑𝑟 DFIG q-axis and d-axis stator and rotor voltages, respectively 𝑖𝑞𝑠, 𝑖𝑑𝑠, 𝑖𝑞𝑟 𝑎𝑛𝑑 𝑖𝑑𝑟 DFIG q-axis and d-axis stator and rotor currents, respectively
“^” Estimated value of the respective variable Superscript/Subscript 𝑝𝑢 = Per unit value of the respective variable Superscript/Subscript ref/REF = Reference value of the respective variable Superscript/Subscript 𝑘 = 𝑘𝑡ℎ instant of time.
Subscript 𝑝 = 𝑝𝑡ℎ machine.
(. )𝑝 Subscript: continuous variable of 𝑝𝑡ℎ machine.
(. )𝑝0 Subscript: steady state value of continuous variable ( .̃ ) = (. ) − (. )0; Variable transformation
𝜔𝐵, 𝜔 Base elec. speed (rad/s), machine speed in p.u.
H, 𝑓 Machine inertia (s), stator voltage (V) freq. in p.u.
𝜏E, 𝜏M Electrical and mechanical torques in p.u. resp.
𝜏E0, 𝜏M0 Steady state electrical and mechanical torques
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𝛿, 𝜃 Rotor angle and stator voltage phase angle in rad.
𝛼,𝜏̃𝑚,𝜏̃𝑒 𝛼 = 𝛿 − 𝜃 and 𝜏̃𝑚 = 𝜏M− 𝜏M0; 𝜏̃𝑒 = 𝜏E− 𝜏E0 V𝑟∗, E𝑓𝑑 AVR reference voltage, field excitation voltage 𝑒𝑑′, 𝑒𝑞′ Transient d and q axis emfs in p.u.
𝜓𝑑, 𝜓𝑞 Subtransient damper coil d and q axis emfs in p.u.
V𝑟, V𝑠𝑠 AVR filter voltage, controller output reference 𝑣𝑞, 𝑣𝑑 q and d axis stator voltages (V𝑡= 𝑣𝑑 + 𝑗𝑣𝑞) in p.u.
𝑖𝑞, 𝑖𝑑 q and d axis stator currents (I= 𝑖𝑑 + 𝑗𝑖𝑞) in p.u.
𝜏𝑞0′ , 𝜏𝑑0′ q and d axis transient time-constants (s) 𝜏𝑞0′′ , 𝜏𝑑0′′ q and d axis subtransient time-constants (s)
𝓀D, 𝜏𝑟 Damping coefficient and AVR filter time constant 𝒙, 𝒖 State vector and control input respectively
𝒚, 𝒗 Output and exogenous input vectors respectively 𝑛𝑥, 𝑛𝑢 State and control vector dimensions respectively W1∗, 𝜑 Ideal critic NN weight and NN activation function Ŵ2, Ŵ1 Estimated weight vectors of actor and critic NNs.
𝛿𝑣, N𝑛 Function approximation error and no. of neurons 𝑥𝑞′′, 𝑥𝑑′′ Subtransient q and d axis reactances
𝑥𝑞′, 𝑥𝑑′ Transient q and d axis reactances 𝑥𝑞, 𝑥𝑑 Synchronous q and d axis reactances
𝑥𝑙, 𝑟𝑎 Armature leakage reactance and resistance resp.
𝓀1′ = (𝑥𝑞′′− 𝑥𝑙)(𝑥𝑞− 𝑥𝑞′)/(𝑥𝑞′ − 𝑥𝑙) 𝓀2′ = (𝑥𝑞′ − 𝑥𝑞′′)(𝑥𝑞− 𝑥𝑞′)/(𝑥𝑞′ − 𝑥𝑙)2 𝓀3′ = (𝑥𝑑′′− 𝑥𝑙)(𝑥𝑑− 𝑥𝑑′)/(𝑥𝑑′ − 𝑥𝑙) 𝓀4′ = (𝑥𝑑′ − 𝑥𝑑′′)(𝑥𝑑 − 𝑥𝑑′)/(𝑥𝑑′ − 𝑥𝑙)2
𝓀1 = 𝓀1′/(𝑥𝑞− 𝑥𝑞′), 𝓀2 = (𝑥𝑞′ − 𝑥𝑞′′)/(𝑥𝑞′ − 𝑥𝑙) 𝓀3 = 𝓀3′/(𝑥𝑑− 𝑥𝑑′), 𝓀4 = (𝑥𝑑′ − 𝑥𝑑′′)/(𝑥𝑑′ − 𝑥𝑙) 𝒵𝑎2 = (𝑥𝑙2+ 𝑟𝑎2)
𝐓𝐫𝐢𝐚 (. ) General traingularization algorithm
