A Fuzzy Logic Voltage Collapse Alarm System for Dynamic Loads by Zhang Xi Master of Science in Electrical and Electronics Engineering 2012 Faculty of Science and Technology University of Macau
A Fuzzy Logic Voltage Collapse Alarm System for Dynamic Loads by Zhang Xi A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical and Electronics Engineering Faculty of Science and Technology University of Macau 2012 Approved by Supervisor Date
2 In presenting this thesis in partial fulfillment of the requirements for a Master's degree at the University of Macau, I agree that the Library and the Faculty of Science and Technology shall make its copies freely available for inspection. However, reproduction of this thesis for any purposes or by any means shall not be allowed without my written permission. Authorization is sought by contacting the author at Address: Faculty of Science and Technology, University of Macau Telephone: 62040924 Fax: N/A E-mail: xxbb212@gmail.com Signature Date
3 University of Macau Abstract A Fuzzy Logic Voltage Collapse Alarm System for Dynamic Loads by Zhang Xi Thesis Supervisor: Professor Wong Chi-Kong Electrical and Electronics Engineering The voltage collapse due to the failure of dynamic load restoration can suddenly occur before its static limitation, the estimation of this kind of voltage stability is still at the exploratory stage. In this thesis, fuzzy based voltage collapse alarm systems are proposed by considering both of static limitation and dynamic load restoration. The proposed alarm systems provide different degrees of alarm for the current operating state of power system and indicate that voltage collapse may occur, which is helpful for operators to take actions in advance. A lot of different voltage stability indices (VSIs) are studied, finally Line Stability Factor (LQP) is found to be an effective index to indicate the system transfer limitation when dynamic load is considered and it is selected as one of the inputs of the alarm systems. In order to represent the dynamic load characteristic, dq/dt and dp/dt are proposed to be the other inputs of the alarm systems. In the previous alarm system, all buses of the power system are monitored. However, voltage collapse often starts at weak area, then proliferates to the overall system and makes the whole system breakdown. As a result, in this thesis, not all the buses but only critical areas that contains the proposed reactive power valley (RPV bus), weak lines and VCA-connection lines between different voltage control areas (VCAs) are monitored. After the theoretical analysis is finished, verifications are done through Matlab simulation. The feasibility and efficiency of the alarm system is verified on IEEE 39-Bus New England System with induction motor as dynamic load.
4 Key words: Voltage Collapse, Alarm System, Power Transfer Limit, Voltage Stability Index, Load Dynamics, Power Restoration, Weak Area, Voltage Control Area (VCA), Reactive Power Valley (RPV), Weak Line
5 TABLE OF CONTENTS LIST OF FIGURES...7 LIST OF TABLES...10 LIST OF ABBREVIATIONS...11 ACKNOWLEDGMENTS...13 CHAPTER 1 Introduction...14 1.1 Project Study Background...14 1.2 Overview of Voltage Stability...15 1.2.1 Definition of voltage stability...16 1.2.2 Static analysis of voltage stability...18 1.2.3 Dynamic analysis of voltage stability...24 1.3 Literature Review of Voltage Collapse Assessment...36 1.3.1 Novel methods to assess voltage collapse...36 1.3.2 Voltage collapse assessment using AI technology...43 1.3.3 Voltage collapse assessment using fuzzy logic...54 1.4 Research Goals and Challenges...57 1.5 Thesis Organization...58 CHAPTER 2 Monitoring Targets...61 2.1 Voltage Control Areas (VCA)...61 2.2 Weak Buses...64 2.3 Weak Lines...68 2.4 Voltage Stability Weak Area...69 2.5 Case Study for Weak Area, Bus, Line...69 2.5.1 Case 1 (Motor stalls before limitation)...71 2.5.2 Case 2 (Motor stalls after limitation)...75 2.6 Chapter Summary...79 CHAPTER 3 Effective Indicators...81
6 3.1 Comparison of Line Voltage Stability Indices (VSI)...82 3.1.1 Indices formulation and their relations...82 3.1.2 Case studies for line VSIs...88 3.2 Comparison of Bus Voltage Stability Indices (VSI)...97 3.2.1 Indices formulation and their relations...97 3.2.2 Case study for bus VSIs...102 3.3 Indicators on Load Dynamics...103 3.3.1 Theoretical analysis...104 3.3.2 Case study for indicators on load dynamics...109 3.4 Chapter Summary...110 CHAPTER 4 Voltage Collapse Alarm System...113 4.1 Fuzzy Inference System (FIS)...114 4.1.1 Fuzzy sets and membership functions...114 4.1.2 Fuzzy rules...116 4.1.3 Generic fuzzy system...116 4.2 Voltage Collapse Alarm System (Structure 1)...118 4.3 Voltage Collapse Alarm System (Structure 2)...123 4.4 Case Study for Voltage Collapse Alarm System...127 4.4.1 Case 1 (Before power transfer limit)...128 4.4.2 Case 2 (After power transfer limit)...135 4.5 Chapter Summary...142 CHAPTER 5 Thesis Conclusion...144 BIBLIOGRAPHY...147 VITA...155
7 LIST OF FIGURES Number Page Fig. 1.1 Power system stability classifications...16 Fig. 1.2 Circuit representation...19 Fig. 1.3 P,V and I as a function of Rl, for a lossless system(r=0) and tanφ=0.2...20 Fig. 1.4 The V-P curves...21 Fig. 1.5 The V-Q curves...22 Fig. 1.6 Aggregate load response to a step-voltage change...26 Fig. 1.7 Slip-torque curves as V varies...31 Fig. 1.8 Motor fed through a line...31 Fig. 1.9 Network and motor QV curves...32 Fig. 1.10 Two-bus LTC system...32 Fig. 1.11 PV curve of two-bus system...33 Fig. 1.12 V-P Load restoration...34 Fig. 1.13 Radial system...37 Fig. 1.14 Thevenin equivalent of a power system seen from a load bus...37 Fig. 1.15 Simple line power system...38 Fig. 1.16 2-Bus Power System...39 Fig. 1.17 π equivalent branch Model for voltage stability research...40 Fig. 1.18 Load bus and rest of the system represented with a source and a line...48 Fig. 1.19 Major disadvantages of previous researches...57 Fig. 2.1 Reactive power valleys (RPV bus) ( + : power flow into the bus)...68 Fig. 2.2 Representation of weak lines...68 Fig. 2.3 Voltage control areas of IEEE 39-Bus System...71 Fig. 2.4 Weak buses in case 1...71 Fig. 2.5 critical VCAs with weak buses and weak lines (case 1)...73 Fig. 2.6 Weak buses in case 2...75 Fig. 2.7 critical VCAs with weak buses and weak lines (case 2)...77 Fig. 2.8 Flow chart of monitoring targets determination...80
8 Fig. 3.1. Two-bus power system model...82 Fig. 3.2. 39-Bus New England Test System...89 Fig. 3.3. Line stability indices (line 2423) and motor slip...92 Fig. 3.4. Powe flow and voltage characteristic (case1)...93 Fig. 3.5. LVSI when θ-δ approaches 90...94 Fig. 3.6. Line stability indices (line 2829) and motor slip...95 Fig. 3.7. Power flow and voltage characteristic (case2)...96 Fig. 3.8 Thevenin equivalent of a system...97 Fig. 3.9. A simple two-bus Thevenin equivalent system...99 Fig. 3.10. Bus indices and motor slip (bus 24)...103 Fig. 3.11 A typical induction motor model...105 Fig. 3.12 Active Power-Speed characteristic curve of induction motor...106 Fig. 3.13 Reactive Power-Speed characteristic curve of induction motor...107 Fig. 3.14 Admittance-voltage characteristics of induction motor...107 Fig. 3.15 power-voltage characteristics of induction motor...108 Fig. 3.16 Reactive power injected to a bus and dq/dt...109 Fig. 3.17 Active power injected to a bus and dp/dt...110 Fig. 3.18 Three effective indicators selected for the voltage collapse alarm system...112 Fig. 4.1 Basic structure of voltage collapse alarm system...114 Fig. 4.2 Representation of crisp and fuzzy subset of X...115 Fig. 4.3 Four modules of a fuzzy system...117 Fig. 4.4 Voltage collapse alarm system (structure 1)...118 Fig. 4.5 Membership function for input variable LQP...119 Fig. 4.6 Membership function for input variable dq/dt...119 Fig. 4.7 Membership function for input variable dp/dt...120 Fig. 4.8 Membership function for output variable DVSI...120 Fig. 4.9 Fuzzy inference system in structure 1...122 Fig. 4.10 Four degrees of alarm...123 Fig. 4.11 Voltage collapse alarm system (structure 2)...123 Fig. 4.12 Membership function for input variable dq/dt...124 Fig. 4.13 Membership function for input variable dp/dt...125 Fig. 4.14 Membership function for output variable DL...125
9 Fig. 4.15 Fuzzy inference system in structure 2...126 Fig. 4.16 dq/dt and dp/dt vs DL...127 Fig. 4.17 IEEE 39-Bus New England Test System...128 Fig. 4.18 Maximum of LQP for VCA3...129 Fig. 4.19 Maximum of dq/dt for VCA3...130 Fig. 4.20 Maximum of dp/dt for VCA3...130 Fig. 4.21 Three input indicators, VSL1 and voltage for critical VCAs (structure 1 in case 1)...132 Fig. 4.22 Three input indicators, VSL2 and voltage for critical VCAs (structure 2 in case 1)...134 Fig. 4.23 Comparison of VSL for two structures in case 1...135 Fig. 4.24 Maximum of LQP for VCA6...136 Fig. 4.25 Maximum of dq/dt for VCA6...137 Fig. 4.26 Maximum of dp/dt for VCA6...137 Fig. 4.27 Three input indicators, VSL1 and voltage for critical VCAs (structure 1 in case 2)...139 Fig. 4.28 Three input indicators, VSL2 and voltage for critical VCAs (structure 2 in case 2)...141 Fig. 4.29 Comparison of VSL for two structures in case 2...142
10 LIST OF TABLES Number Page Table. 1.1 Recent voltage collapse...14 Table. 1.2 Dynamic load state and demand variables...29 Table.1.3 Comparison of ES, FS, NN and GA...45 Table. 1.4 Previous researches of voltage collapse prediction using FL...56 Table. 1.5 Advantages of this research compared with others...58 Table. 2.1 Weak area for voltage collapse...69 Table. 2.2 Voltage control area of IEEE 39-Bus System...70 Table. 2.3 Weak buses in case 1...71 Table. 2.4 Weak area for voltage collapse (case 1)...72 Table. 2.5 RPV bus and weak lines for critical VCAs (case 1)...73 Table. 2.6 Weak buses stalled motors in critical VCAs with stalled time (case 1)...74 Table. 2.7 Weak buses in case 2...75 Table. 2.8 Weak area for voltage collapse (case 2)...76 Table. 2.9 RPV bus and weak lines for critical VCAs (case 2)...77 Table. 2.10 Weak buses stalled motors in critical VCAs with stalled time (case 2)...78 Table. 3.1 comparison of FVSI, L mn, LVSI and LQP...87 Table. 3.2 Line index ranking...90 Table. 3.3 Variation of line indices with motor(24) slip increases...92 Table. 3.4 Variation of line indices with motor(28) slip increases...95 Table. 4.1 Fuzzy logic rules...120 Table. 4.2 Four degrees of alarm...123 Table. 4.3 Fuzzy logic rules for dynamic load...125
11 LIST OF ABBREVIATIONS VS: Voltage Stability CPF: Continuation Power Flow VSM: Voltage Stability Margin LTC: Load Tap Changers SNB: saddle-node bifurcation VSI: Voltage Stability Index RPR: reactive power reserves AI: Artificial Intelligent Technology ES: Expert System FL: Fuzzy Logic ANN: Artificial Neural Networks GA: Genetic Algorithm DT: Decision Tree AIS: Artificial Immune System FORL: Function Optimization by Reinforcement Learning ACO: Ant Colony Optimization PSO: Particle Swarm Optimization CVM: Core Vector Machines VCA: Voltage Control Areas RPV: Reactive Power Valley WAMS: Wide Area Measurement System FVSI: Fast Voltage Stability Index LVSI: On Line Stability Index
12 LQP: Line Stability Factor L mn : Line Stability Index VCPI: Voltage Collapse Proximity Index PTSI: Power Transfer Stability Index VSL: Voltage Stability Level FIS: Fuzzy Inference System MF: Membership Function DVSI: Dynamic Voltage Stability Index DL: Dynamic Load
13 ACKNOWLEDGMENTS First and foremost, I would like to express my sincere thanks and gratitude to my supervisor Prof. Wong Chi-Kong, for his inspiring guidance and constant encouragement during the course of completing the project and preparing this thesis. I would like to thankfully acknowledge the financial support of the Research Committee of University of Macau in completion of the research related to the thesis. I would like to thank my friends Liu Zhu-Lin and Liu Miao who had rendered their help in the completion of the project. I would also take this opportunity to thank my roommates Zhai Shu, Luo Mei and Dong Shan-Shan for their help during my Master studies. I wish to appreciate my friends in Power Electronics Lab for their direct and indirect help for me. Last but certainly not the least, I also wish to express my gratitude to my family members for their motivation and support.