Harmonic Resonance in Power Transmission Systems due to the Addition of Shunt Capacitors by Hardik U. Patil A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science Approved July 2015 by the Graduate Supervisory Committee: Gerald Heydt, Chair George Karady Raja Ayyanar ARIZONA STATE UNIVERSITY August 2015 ABSTRACT Shunt capacitors are often added in transmission networks at suitable locations to improve the voltage profile. In this thesis, the transmission system in Arizona is considered as a test bed. Many shunt capacitors already exist in the Arizona transmission system and more are planned to be added. Addition of these shunt capacitors may create resonance conditions in response to harmonic voltages and currents. Such resonance, if it occurs, may create problematic issues in the system. It is main objective of this thesis to identify po- tential problematic effects that could occur after placing new shunt capacitors at selected buses in the Arizona network. Part of the objective is to create a systematic plan for avoid- ance of resonance issues. For this study, a method of capacitance scan is proposed. The bus admittance matrix is used as a model of the networked transmission system. The calculations on the admit- tance matrix were done using Matlab. The test bed is the actual transmission system in Arizona; however, for proprietary reasons, bus names are masked in the thesis copy in- tended for the public domain. The admittance matrix was obtained from data using the PowerWorld Simulator after equivalencing the 2016 summer peak load (planning case). The full Western Electricity Coordinating Council (WECC) system data were used. The equivalencing procedure retains only the Arizona portion of the WECC. The capacitor scan results for single capacitor placement and multiple capacitor placement cases are presented. Problematic cases are identified in the form of ‘forbidden response. The harmonic voltage impact of known sources of harmonics, mainly large scale HVDC sources, is also presented. i Specific key results for the study indicated include: • The forbidden zones obtained as per the IEEE 519 standard indicates the bus 10 to be the most problematic bus. • The forbidden zones also indicate that switching values for the switched shunt ca- pacitor (if used) at bus 3 should be should be considered carefully to avoid reso- nance condition from existing. • The highest sensitivity of 0.0033 per unit for HVDC sources of harmonics was ob- served at bus 7 when all the HVDC sources were active at the same time. ii ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my advisor Dr. Gerald T. Heydt, for his constant support and encouragement throughout this thesis. Without his patience, mo- tivation, enthusiasm, positive attitude, incredible wisdom, and guidance the completion of this thesis would have been difficult. I could not have any better advisor and mentor for my thesis and I am forever grateful to him. I would also like to thank Dr. George Karady and Dr. Raja Ayyanar for their time and effort to be a part of my graduate supervisory committee. I would also like to thank an industrial sponsor for the financial support they pro- vided for this thesis. I would also like to thank Messrs. Jeff Loehr and Thomas LaRose for the engineering advice they provided. I am also thankful to Messrs. Brain Keel and Michael Chandler for the advice they provided. I am also grateful to Messrs. Ahmed Salloum and Parag Mitra for guiding me in the software that were used for this thesis. Finally, and most importantly, I would like to sincerely and gratefully thank my parents, Mr. Ulhas Patil and Mrs. Milan Patil for their faith, unwavering love, continuous motivation and support. I would also like to extend my thanks to my friends and colleagues for their unending love and encouragement. iii TABLE OF CONTENTS Page LIST OF FIGURES ......................................................................................................... viii LIST OF TABLES ............................................................................................................ xii NOMENCLATURE ........................................................................................................ xiii CHAPTER 1 RESONANCE IN POWER TRANSMISSION SYSTEMS ............................................1 1.1 Objectives and Goals of This Study.......................................................................... 1 1.2 The Phenomenon of Resonance in Electric Power Transmission Systems .............. 2 1.3 The Literature of Resonance in Power Systems ....................................................... 3 1.4 Power System Models at Frequencies Greater than 60 Hz ..................................... 10 1.5 Case studies ............................................................................................................. 14 1.6 Sources of Harmonics ............................................................................................. 18 1.7 Organization of the Thesis ...................................................................................... 19 2 THE CALCULATION AND ANALYSIS OF RESONANCE USING COMMERCIAL SOFTWARE TOOLS ...................................................................21 2.1 Pertinent Commercial Software Tools .................................................................... 21 2.2 System Data Used ................................................................................................... 21 2.3 The System Impedance and Admittance Matrix from the System Data ................. 22 iv CHAPTER Page 2.4 Calculation of Driving Point Impedance ................................................................ 24 2.5 Frequency Scan ....................................................................................................... 26 2.6 Capacitance Scan .................................................................................................... 26 2.7 Summary ................................................................................................................. 29 3 ANALYSIS USING PLANNING CASE DATA ..........................................................31 3.1 Explanation and Presentation of Results................................................................. 31 3.2 Results for Single Capacitor Placement .................................................................. 31 3.3 Capacitance Scans for the Case of Multiple Shunt Capacitor Placement ............... 59 3.4 Discussion of Results .............................................................................................. 59 4 FORBIDDEN ZONES ...................................................................................................64 4.1 Definition of the Term ‘Forbidden Zone’ as Applied to the Placement of Shunt Capacitors ............................................................................................................... 64 4.2 Results for the Test Bed System ............................................................................. 65 4.3 Principal Observations on the Forbidden Zones ..................................................... 65 5 IMPACT OF HVDC SOURCES ON THE TEST BED SYSTEM ...............................68 5.1 HVDC Sources in Transmission Systems............................................................... 68 5.2 Results of HVDC Source Impacts for the Test Bed System ................................... 68 5.3 Observations ........................................................................................................... 73 v CHAPTER Page 6 CONCLUSIONS AND RECOMMENDATIONS ........................................................74 6.1 Conclusions ............................................................................................................. 74 6.2 Recommendations and Future Work ...................................................................... 75 REFERENCES ..................................................................................................................77 APPENDIX A FORWARD BACKWARD SUBSTITUTION METHOD FOR THE CALCULATION OF X IN AX=B ............................................................................82 A.1 Forward/Backward Substitution ............................................................................ 83 A.2 Application in Matlab ............................................................................................ 84 B MATLAB CODE USED FOR THE CREATION OF THE CAPACITANCE SCANS ......................................................................................................................85 B.1 Matlab Code Used for the Harmonic Assessment of Single Shunt Capacitor Placement ............................................................................................................... 86 B.2 Matlab Code for Multiple Shunt Capacitor Bank Placement Cases ...................... 88 C SELECTED PHASE ANGLE PLOTS FOR CAPACITANCE SCAN RESULTS ...91 C.1 Selected Phase Angle Plots for Capacitance Scan Results Obtained from Matlab ........................................................................................................................... 92 vi APPENDIX Page D MATLAB CODE FOR EVALUATION OF IMPACT OF HVDC SOURCES .......98 D.1 Matlab Code Used for Evaluation of Impact of HVDC Sources ........................... 99 vii LIST OF FIGURES Figure Page 1.1 Three Simple Load Models used for Harmonic Analysis ........................................... 15 2.1 The Original Network and its Equivalenced Network ................................................ 23 2.2 The Flow for Obtaining the System Bus Admittance Matrix ..................................... 27 2.3 A Typical Frequency Scan for Parallel Resonance..................................................... 28 2.4 A Typical Capacitance Scan ....................................................................................... 28 3.1 Capacitance Scan at Bus 1 for Fundamental Frequency ............................................. 34 3.2 Capacitance Scan at Bus 1 for Harmonic Order 5 ...................................................... 34 3.3 Capacitance Scan at Bus 1 for Harmonic Order 7 ...................................................... 35 3.4 Capacitance Scan at Bus 1 for Harmonic Order 11 .................................................... 35 3.5 Capacitance Scan at Bus 1 for Harmonic Order 13 .................................................... 36 3.6 Capacitance Scan at Bus 2 for Fundamental Frequency ............................................. 36 3.7 Capacitance Scan at Bus 2 for Harmonic Order 5 ...................................................... 37 3.8 Capacitance Scan at Bus 2 for Harmonic Order 7 ...................................................... 37 3.9 Capacitance Scan at Bus 2 for Harmonic Order 11 .................................................... 38 3.10 Capacitance Scan at Bus 2 for Harmonic Order 13 .................................................. 38 3.11 Capacitance Scan at Bus 3 for Fundamental Frequency ........................................... 39 3.12 Capacitance Scan at Bus 3 for Harmonic Order 5 .................................................... 39 3.13 Capacitance Scan at Bus 3 for Harmonic Order 7 .................................................... 40 3.14 Capacitance Scan at Bus 3 for Harmonic Order 11 .................................................. 40 3.15 Capacitance Scan at Bus 3 for Harmonic Order 13 .................................................. 41 3.16 Capacitance Scan at Bus 4 for Fundamental Frequency ........................................... 41 viii Figure Page 3.17 Capacitance Scan at Bus 4 for Harmonic Order 5 .................................................... 42 3.18 Capacitance Scan at Bus 4 for Harmonic Order 7 .................................................... 42 3.19 Capacitance Scan at Bus 4 for Harmonic Order 11 .................................................. 43 3.20 Capacitance Scan at Bus 4 for Harmonic Order 13 .................................................. 43 3.21 Capacitance Scan at Bus 5 for Fundamental Frequency ........................................... 44 3.22 Capacitance Scan at Bus 5 for Harmonic Order 5 .................................................... 44 3.23 Capacitance Scan at Bus 5 for Harmonic Order 7 .................................................... 45 3.24 Capacitance Scan at Bus 5 for Harmonic Order 11 .................................................. 45 3.25 Capacitance Scan at Bus 5 for Harmonic Order 13 .................................................. 46 3.26 Capacitance Scan at Bus 6 for Fundamental Frequency ........................................... 46 3.27 Capacitance Scan at Bus 6 for Harmonic Order 5 .................................................... 47 3.28 Capacitance Scan at Bus 6 for Harmonic Order 7 .................................................... 47 3.29 Capacitance Scan at Bus 6 for Harmonic Order 11 .................................................. 48 3.30 Capacitance Scan at Bus 6 for Harmonic Order 13 .................................................. 48 3.31 Capacitance Scan at Bus 7 for Fundamental Frequency ........................................... 49 3.32 Capacitance Scan at Bus 7 for Harmonic Order 5 .................................................... 49 3.33 Capacitance Scan at Bus 7 for Harmonic Order 7 .................................................... 50 3.34 Capacitance Scan at Bus 7 for Harmonic Order 11 .................................................. 50 3.35 Capacitance Scan at Bus 7 for Harmonic Order 13 .................................................. 51 3.36 Capacitance Scan at Bus 8 for Fundamental Frequency ........................................... 51 3.37 Capacitance Scan at Bus 8 for Harmonic Order 5 .................................................... 52 3.38 Capacitance Scan at Bus 8 for Harmonic Order 7 .................................................... 52 ix