Synchronized Rotor Angle Measurement of Synchronous Machines David Christopher Mazur Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Electrical Engineering Jaime De La Ree Virgilio Centeno William T. Baumann April 13, 2012 Blacksburg, Virginia Keywords: Torque Angle, Synchronous Machine, Precision Time Protocol, Programmable Automation Controller, Synchronized Actuation, Time Synchronization Copyright 2012 Synchronized Rotor Angle Measurement of Synchronous Machines David Christopher Mazur ABSTRACT A key input parameter to governor feedback control and stability protection of generators is the angle of the induced voltage internal to the generator. Current practice is to estimate this value using measurements from the terminals of the generator and mathematical models. This project aims to develop a system that would directly measure the internal angle of the generator using a rotary encoder on the shaft of the machine. This document describes the theory and experimental setup of this proposed system and outlines the test procedure of experimentation. DEDICATION This work is dedicated to my family. Thank you for always being there and believing in me. You have taught me over the years that I am capable of anything that I put my mind to. This document is proof that anything is possible and that the North American engineering spirit is truly alive and well. Thank you! I hope that this document may serve as a concrete reference for machinery and machinery control. Ce travail est dédié à ma famille. Je vous remercie d'être toujours là et de croire en moi. Vous m'avez appris au fil des ans que je suis capable de tout ce que je mets mon esprit à. Ce document est la preuve que tout est possible et que l'Amérique du Nord d'ingénierie esprit est bien vivant et bien. Je vous remercie! iii ACKNOWLEDGEMENT It should be noted that this project would not have been possible without the support of Rockwell Automation Incorporated. I would like to take the time to give a special thank you to Mr. Frank Kulaszewicz and Mr. Blake Moret for financing this project. Additionally, I would like to thank Mr. Fred Discenzo and Mr. David Mayewski for helping the throughout this process. Most importantly, I would like to thank my advisor Dr. Jaime De La Ree for standing by my side and for his intricate guidance on this project. iv T C ABLE OF ONTENTS Contents ABSTRACT ........................................................................................................................ ii Dedication ......................................................................................................................... iii Acknowledgement ............................................................................................................ iv Table of Contents .............................................................................................................. v Table of Equations ............................................................................................................ x Table of Figures............................................................................................................... xii 1. Chapter 1 Introduction ........................................................................................... 1 A. Introduction .............................................................................................................. 2 2. Chapter 2 Previous Attempts at Measuring Rotor Angle .................................... 3 A. Introduction .............................................................................................................. 4 B. V.A. Kinitsky ............................................................................................................ 4 1) Solution Overview .................................................................................................. 5 2) Pros of Solution ...................................................................................................... 9 3) Cons of Solution ..................................................................................................... 9 C. D.G. Lewis and W. E. Austin ................................................................................ 10 1) Solution Overview ................................................................................................ 10 2) Pros of Solution .................................................................................................... 11 3) Cons of Solution ................................................................................................... 12 D. Virginia Tech Approach ........................................................................................ 12 3. Chapter 3 Machine Models ................................................................................... 14 A. Introduction ............................................................................................................ 15 B. Steady State Model Cylindrical Rotor ................................................................. 15 1) Rotor Self-Inductance ........................................................................................ 18 2) Stator-to-Rotor Mutual Inductances ................................................................ 19 3) Stator Inductances .............................................................................................. 20 C. Steady State Model Salient Pole Rotor ................................................................ 24 1) D-Q-0 Reference Frame ..................................................................................... 25 2) Direct and Quadrature Axis Quantities ........................................................... 27 3) Equivalent Circuit .............................................................................................. 28 D. Seven Variable Dynamic State Space Model ....................................................... 29 1) Definitions............................................................................................................ 29 v 2) Resistance Matrices ............................................................................................ 30 3) Flux Linkage Equations ..................................................................................... 31 4) Overall Flux Linkage Matrix............................................................................. 31 5) Voltage Equations in Matrix Form ................................................................... 33 6) Torque.................................................................................................................. 35 7) Acceleration Equation ........................................................................................ 35 8) Solving State Space Equations .......................................................................... 35 E. Conclusions ............................................................................................................. 36 4. Chapter 4 Plant Componenets That Utilize Torque Angle ................................ 38 A. Introduction ............................................................................................................ 39 B. Active Power and Frequency Control .................................................................. 39 1) Speed Governor Fundamentals ......................................................................... 40 2) Isosynchronous Governor .................................................................................. 41 C. Exciter Systems ...................................................................................................... 42 1) V/Hz Limiter ....................................................................................................... 43 D. Power System Stabilizer ........................................................................................ 44 E. Applications ............................................................................................................ 44 1) Local Area Applications ..................................................................................... 44 2) Wide Area Applications ..................................................................................... 46 F. Conclusions ............................................................................................................. 46 5. Chapter 5 Time Synchronization ......................................................................... 47 A. Introduction ............................................................................................................ 48 B. Network Time Protocol .......................................................................................... 49 C. Global Positioning System (GPS) ......................................................................... 50 1) Definition .............................................................................................................. 50 2) Pulse-Per-Second (PPS) ....................................................................................... 50 3) IRIG-B .................................................................................................................. 50 D. Precision Time Protocol......................................................................................... 51 1) Definition .............................................................................................................. 51 2) Master-Slave Relationship .................................................................................... 52 3) The Use of Tunable Clocks .................................................................................. 54 4) Clock Type ........................................................................................................... 56 E. Common Industrial Protocol................................................................................. 58 F. Quality of Service (QoS) ........................................................................................ 59 vi G. Conclusion .............................................................................................................. 61 6. Chapter 6 Experimental Setup and Componenet Justification ......................... 62 A. Introduction ............................................................................................................ 63 B. Mechanical Components........................................................................................ 63 1) Minimum Encoder Specifications ........................................................................ 63 2) Mechanical Couplings .......................................................................................... 65 C. Embedded Solution vs. Automation Controller .................................................. 66 D. Programmable Logic Controller vs. Programmable Automation Controller for Power Applications ..................................................................................................... 66 1) Local Control Logix Rack .................................................................................... 68 2) Remote I/O Rack .................................................................................................. 69 3) Network Hardware ............................................................................................... 72 E. Network Topologies and Architectures ................................................................ 76 1) Linear Topology ................................................................................................... 76 2) Device Level Ring ................................................................................................ 77 3) Star Topology ....................................................................................................... 77 F. Chosen Network Topology..................................................................................... 78 G. Software Algorithm ............................................................................................... 81 H. Conclusions ............................................................................................................. 84 7. Chapter 7 Experimental Trials and Analysis ...................................................... 86 A. Introduction ............................................................................................................ 87 B. Infinite Bus Connection ......................................................................................... 87 1) Synchroscope ........................................................................................................ 88 2) Infinite Bus No Time Synchronization ................................................................. 90 3) Infinite Bus Time Synchronized via PTP ............................................................. 91 C. Constant Frequency Source .................................................................................. 96 D. Dynamometer Loading .......................................................................................... 98 E. Conclusions ........................................................................................................... 102 8. Chapter 8 Conclusions and Future Work ......................................................... 103 A. Overall Conclusions ............................................................................................. 104 B. Future Work ......................................................................................................... 108 9. Works Cited ........................................................................................................... 110 10. Appendix A Three Phase Machinery Primer .................................................. 112 A. Windings ............................................................................................................... 113 B. Saliency .................................................................................................................. 113 vii C. Electromagnetic Field Interactions .................................................................... 113 D. Definition of Synchronism ................................................................................... 115 E. Functionality-- Single Phase Machines .............................................................. 115 F. Three Phase Machines ......................................................................................... 117 G. Torque ................................................................................................................... 118 11. Appendix B Seven State Matrix Reduction ..................................................... 121 1) Ls Matrix ........................................................................................................... 122 2) Lsr Matrix ......................................................................................................... 122 3) Lr Matrix ........................................................................................................... 122 4) Magnetization Inductances .............................................................................. 123 5) Mutual to Magnetizing Inductance Relationship .......................................... 123 6) Reduction of the Lsr Matrix ............................................................................ 124 7) Reduction of the Lr Matrix.............................................................................. 124 8) Flux Linkage Matrix Equation ........................................................................ 124 9) Revised Voltage Matrix Equations ................................................................. 124 10) Transformation of the Ls Matrix .................................................................. 125 11) Transformation of the Lr Matrix .................................................................. 125 12) Transformation of the Lsr Matrix ................................................................ 125 13) (Lsr)T transformed......................................................................................... 126 14) Ls Transformed .............................................................................................. 126 15) Lr Transformed .............................................................................................. 126 16) Speed Voltages ................................................................................................ 126 12. Appendix C Precision Time Protocol ............................................................... 128 A. Best Master Clock Algorithm ................................................................................ 129 B. CIP Sync Object ..................................................................................................... 131 13. Appendix D Component Selection .................................................................... 133 A. Local Rack Component Descriptions ................................................................. 134 B. Remote Rack Components .................................................................................. 138 14. Appendix E Infinite Bus Test Data .................................................................. 140 A. No Time Synchronization Data ........................................................................... 141 B. Varying Frequency with Time Synchronization Data ...................................... 148 C. Fluke Metering Test Data.................................................................................... 173 15. Appendix F Dynamometer Testing Results ..................................................... 198 A. 7.5 HP Machine .................................................................................................... 199 viii 1) Raw Data ............................................................................................................ 199 2) Plots .................................................................................................................... 203 B. 10 HP Machine ..................................................................................................... 205 1) Raw Data ............................................................................................................ 205 2) Plots .................................................................................................................... 211 16. Appendix G MATLAB Code ............................................................................ 213 ix T E ABLE OF QUATIONS Equation 2.1 ........................................................................................................................ 5 Equation 2.2 ........................................................................................................................ 6 Equation 2.3 ........................................................................................................................ 7 Equation 2.4 ........................................................................................................................ 7 Equation 2.5 ...................................................................................................................... 11 Equation 3.1 ...................................................................................................................... 15 Equation 3.2 ...................................................................................................................... 18 Equation 3.3 ...................................................................................................................... 18 Equation 3.4 ...................................................................................................................... 19 Equation 3.5 ...................................................................................................................... 19 Equation 3.6 ...................................................................................................................... 20 Equation 3.7 ...................................................................................................................... 20 Equation 3.8 ...................................................................................................................... 20 Equation 3.9 ...................................................................................................................... 20 Equation 3.10 .................................................................................................................... 21 Equation 3.11 .................................................................................................................... 21 Equation 3.12 .................................................................................................................... 21 Equation 3.13 .................................................................................................................... 21 Equation 3.14 .................................................................................................................... 22 Equation 3.15 .................................................................................................................... 22 Equation 3.16 .................................................................................................................... 22 Equation 3.17 .................................................................................................................... 22 Equation 3.18 .................................................................................................................... 22 Equation 3.19 .................................................................................................................... 23 Equation 3.20 .................................................................................................................... 23 Equation 3.21 .................................................................................................................... 23 Equation 3.22 .................................................................................................................... 23 Equation 3.23 .................................................................................................................... 24 Equation 3.24 .................................................................................................................... 27 Equation 3.25 .................................................................................................................... 27 Equation 3.26 .................................................................................................................... 30 Equation 3.27 .................................................................................................................... 30 Equation 3.28 .................................................................................................................... 30 Equation 3.29 .................................................................................................................... 31 Equation 3.30 .................................................................................................................... 31 Equation 3.31 .................................................................................................................... 32 Equation 3.32 .................................................................................................................... 32 Equation 3.33 .................................................................................................................... 32 Equation 3.34 .................................................................................................................... 33 Equation 3.35 .................................................................................................................... 33 Equation 3.36 .................................................................................................................... 35 Equation 3.37 .................................................................................................................... 35 Equation 3.38 .................................................................................................................... 35 Equation 3.39 .................................................................................................................... 36 x