英文版电力系统分析(上册)第五章.pdf

Chapter 5 3 phase Short circuit Transient of Power Systems Chapter 5 3 phase Short circuit Transient of Power Systems 5 1 The Overall Concept of Short circuit The Cause of Short circuit The Type of Short circuit The Consequences of Short circuit The Purpose of Short circuit Calculation Chapter 5 3 phase Short circuit Transient of Power Systems 3 f 3 f 1 1 f 5 1 The Overall Concept of Short circuit Types of Short circuit Schematic diagramSymbolType 3 phase short circuit Double line ground Line line Single line ground 2 f 1 f Chapter 5 3 phase Short circuit Transient of Power Systems 2 22 sin sin RR LL arctg LLRR E I tIi tEe m m m m 5 2 Short circuit of Constant Voltage Source Circuit 0 i mE t mI Chapter 5 3 phase Short circuit Transient of Power Systems R L arctg LR E I tIi tEe m m pm m 222 sin sin 5 2 Short circuit of Constant Voltage Source Circuit mE t pmI 0p i mE t mI 0 i Chapter 5 3 phase Short circuit Transient of Power Systems R L arctg LR E I tIi tEe m m pm m 222 sin sin 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i mE t mI 0 i Chapter 5 3 phase Short circuit Transient of Power Systems R L arctg LR E I tIi tEe m m pm m 222 sin sin 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap i a T t appm eitIi 0 sin Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap ipmmII R L arctg LR E I tIi tEe m m pm m 222 sin sin a T t appm eitIi 0 sin Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap ipmmII a T t appm eitIi 0 sin t 0 0 ap i Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap ipmmII a T t appm eitIi 0 sin imumsubiapmax 0 t Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap ipmmII a T t appm eitIi 0 sin t imumiapmax 0 Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap ipmmII a T t appm eitIi 0 sin t a a T t pm oo pm T t appm eItI eitIi 900sin sin 0 Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit pmim T pmpmim IkeIIi a 01 0 1 819991 0 86455 F t 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 5 2 a a T t pm oo pm T t appm eItI eitIi 900sin sin 0 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 pimim Iki2 Chapter 5 3 phase Short circuit Transient of Power Systems a T t appm eitIi 0 sin 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap ipmmII 0 10t 00 020 040 060 08 0 5 1 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 819991 0 86455 F t 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 5 2 1 81873 0 997717 F t 0 50t 00 10 20 30 4 1 0 5 0 0 5 1 1 5 2 Chapter 5 3 phase Short circuit Transient of Power Systems a T t appm eitIi 0 sin 5 2 Short circuit of Constant Voltage Source Circuit mE t mI pmI 0p i 0 i 0ap ipmmII 0 10t 00 020 040 060 08 0 5 1 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 819991 0 86455 F t 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 5 2 1 81873 0 997717 F t 0 50t 00 10 20 30 4 1 0 5 0 0 5 1 1 5 2 Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit a T t ap o pm eitIi 0 90sin 1 819991 0 86455 F t 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 5 2 2 2 2 1 T t T t tt dti T I Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit 2 2 2 2 2 2 11 T t T t aptpt T t T t tt dtii T dti T I 1 819991 0 86455 F t 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 5 2 a T t ap o pm eitIi 0 90sin Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit a T t ap o pm eitIi 0 90sin 22 2 2 22 2 2 2 2 2 2 2 1 11 aptpt T t T t aptaptptpt T t T t aptpt T t T t tt II dtiiii T dtii T dti T I 2 2 01 0 222 1 21 2 imp p T paptptim kI IeIIII a Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit 2 1 21 impim kII pmimim Iki Summary 1 819991 0 86455 F t 0 10t 00 020 040 060 08 1 0 5 0 0 5 1 1 5 2 Fault location Kim At generator buses 1 9 Step up transformer buses 1 85 others 1 8 Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit Short circuit MVA tavt IVS3 pavd IVS3 3 3 p B p BB pav d I I I IV IV S Chapter 5 3 phase Short circuit Transient of Power Systems 5 2 Short circuit of Constant Voltage Source Circuit pavd IVS3 pimim Iki2 2 1 21 impim kII 222222 LR E Ior LR E I p m pm Summary Fault location Kim At generator buses 1 9 Step up transformer buses 1 85 others 1 8 Chapter 2 The Elements of Power System and Its Equivalent Circuit 2 4 Per Unit System 2 4 5 The equivalent circuit of power system 3 approximate equivalent circuit in p u 868 0 1 334 0 2 24 0 3 7 0 4 46 1 5 504 0 626 0 5 10 30 G N N X KVV MVAS 121 5 10 5 10 5 31 1 T s N k V MVAS 6 6 110 5 10 15 1 T s N k V MVAS kml kmx 80 4 0 kml kmx 5 2 08 0 5 3 0 6 R N N X KAI KVV Chapter 5 3 phase Short circuit Transient of Power Systems 5 3 The Physical Analysis of Synchronous Machine 3 phase Short circuit Transient Chapter 5 3 phase Short circuit Transient of Power Systems 5 3 The Physical Analysis of Synchronous Machine 3 phase Short circuit Transient G Chapter 5 3 phase Short circuit Transient of Power Systems 5 3 The Physical Analysis of Synchronous Machine 3 phase Short circuit Transient 0 Ri dt d Let R 0 0 dt d If R 0 00 Chapter 5 3 phase Short circuit Transient of Power Systems 5 3 The Physical Analysis of Synchronous Machine 3 phase Short circuit Transient Chapter 5 3 phase Short circuit Transient of Power Systems 5 3 The Physical Analysis of Synchronous Machine 3 phase Short circuit Transient Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding 3 4 Steady state Analysis of Synchronous Machine Chapter 3 Basic Equations of Synchronous Machines Let fadq ixE qqd ddqq ixv ixEv dq qd v v qqq fadddd ix ixix q i d v q E d i q v The steady state equivalent circuit of synchronous machine a d axis b q axis a b d x q x 3 4 Steady state Analysis of Synchronous Machine Chapter 3 Basic Equations of Synchronous Machines Let fadq ixE qqd ddqq ixv ixEv q q d d d qq IjxV IjxEV q i d v q E d i q v The steady state equivalent circuit of synchronous machine a d axis b q axis a b d x q x 3 4 Steady state Analysis of Synchronous Machine Chapter 3 Basic Equations of Synchronous Machines Let fadq ixE qqd ddqq ixv ixEv qE d jx dI qV q jx qI dV The steady state equivalent circuit of synchronous machine a d axis b q axis qE d jx dI qV q jx qI dV The steady state equivalent circuit of synchronous machine a d axis b q axis q q d d d qq IjxV IjxEV Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 ffdadf qqq fadddd ixix ix ixix ffff dqq qdd irv v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding ffdadf qqq fadddd ixix ix ixix ffff dqq qdd irv v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding ffdadf qqq fadddd ixix ix ixix ffff dqq qdd irv v v If only symmetric component is considered then 0 0 q d Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding ffdadf qqq fadddd ixix ix ixix ffff dqq qdd irv v v If only symmetric component is considered then 0 0 q d qqq ffdadf fadddd ix ixix ixix dq qd v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ffdadf fadddd ix ixix ixix dq qd v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ffdadf fadddd ix ixix ixix dq qd v v qqq d f ad df f ad d ix i x x x x x 2 dq qd v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ffdadf fadddd ix ixix ixix dq qd v v qqq d f ad df f ad d ix i x x x x x 2 dq qd v v qqq ddqd ix ixE dq qd v v Let f ad ddf f ad q x x xx x x E 2 Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ddqd ix ixE dq qd v v qqd ddqq ixv ixEv q i d v q E d i q v The transient equivalent circuit of synchronous machine a d axis b q axis a b d x q x Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ddqd ix ixE dq qd v v qqd ddqq ixv ixEv q i d v q E d i q v The transient equivalent circuit of synchronous machine a d axis b q axis a b d x q x q q d d dq q IjxV IjxEV Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ddqd ix ixE dq qd v v qqd ddqq ixv ixEv The steady state equivalent circuit of synchronous machine a d axis b q axis q E d jx dI qV q jx qI dV The transient equivalent circuit of synchronous machine a d axis b q axis q q d d dq q IjxV IjxEV Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ddqd ix ixE dq qd v v qqd ddqq ixv ixEv The steady state equivalent circuit of synchronous machine a d axis b q axis q E d jx dI qV q jx qI dV The transient equivalent circuit of synchronous machine a d axis b q axis q q d d dq q IjxV IjxEV QE q E E qq Ij Ij d Ij q dd Ij dq Ij q V V d V I d I q I q d Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding qqq ddqd ix ixE E d jx I V q q d d dq q IjxV IjxEV Let QE q E E qq Ij Ij d Ij q dd Ij dq Ij q V V d V I d I q I q d q dqq d IxxjEE IjxEV Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding The steady state equivalent circuit of synchronous machine a d axis b q axis q E d jx dI qV q jx qI dV The transient equivalent circuit of synchronous machine qE d jx dI qV q jx qI dV Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding The steady state equivalent circuit of synchronous machine a d axis b q axis q E d jx dI qV q jx qI dV The transient equivalent circuit of synchronous machine qE d jx dI qV q jx qI dV 0 qt d T t dddt I IeIII d Where d q d d q d x E I x E I IeIII d T t t d q d q x E I x E I Chapter 5 3 phase Short circuit Transient of Power Systems 5 4 3 phase Short circuit Current Calculation of Generators without Damper Winding 0 d d d d T x x T 0 d d d d T x x T Transient current Steady state current Time constant 5 1 A synchronous machine is operating in steady state conditions with parameters Xd 1 0 Xq 0 6 Xd 0 30 Td0 5s and operating variables V 1 I 1 cos 0 85 a Find the voltages Eq Eq And sketch its phasor diagram b If 3 phase short circuit happens at generator terminals find the transient short circuit current steady state short circuit current c If 3 phase short circuit happens at generator terminals find the expression of symmetrical component of short circuit current d If 3 phase short circuit happens at Xe 0 5 from the generator terminals find the expression of symmetrical component of short circuit current Chapter 5 3 phase Short circuit Transient of Power Systems 5 3 The Physical Analysis of Synchronous Machine 3 phase Short circuit Transient Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv riv 0 0 000 QQqaqQ DDfaddadD Dadffdadf Qaqqqq Dadfadddd ixix ixixix ixixix ix ixix ixixix 000 Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv 0 0 QQqaqQ Qaqqqq DDfaddadD Dadffdadf Dadfadddd ixix ixix ixixix ixixix ixixix If only symmetric component is considered then 0 0 q d Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv 0 0 QQqaqQ Qaqqqq DDfaddadD Dadffdadf Dadfadddd ixix ixix ixixix ixixix ixixix If only symmetric component is considered then 0 0 q d Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQQ DDD ffff qdqq dqdd ir ir irv riv riv 0 0 QQqaqQ Qaqqqq DDfaddadD Dadffdadf Dadfadddd ixix ixix ixixix ixixix ixixix If only symmetric component is considered then 0 0 q d dq qd v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQqaqQ Qaqqqq DDfaddadD Dadffdadf Dadfadddd ixix ixix ixixix ixixix ixixix If only symmetric component is considered then 0 0 q d dq qd v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding dq qd v v QQqaqQ Qaqqqq DDfaddadD Dadffdadf Dadfadddd ixix ixix ixixix ixixix ixixix ddqd ixE 2 2 2 2 adfD adfDad dd DadffadD adfD ad q xxx xxxx xx xxxx xxx x E where qqdq ixE Q aq qq Q Q aq d x x xx x x E 2 where Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQqaqQ Qaqqqq DDfaddadD Dadffdadf Dadfadddd ixix ixix ixixix ixixix ixixix ddqd ixE qqdq ixE dq qd v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding QQqaqQ Qaqqqq DDfaddadD Dadffdadf Dadfadddd ixix ixix ixixix ixixix ixixix ddqd ixE qqdq ixE dq qd v v Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding ddqd ixE qqdq ixE dq qd v v qqdd ddqq ixEv ixEv q qd d d dq q IjxEV IjxEV Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding qqdd ddqq ixEv ixEv q qd d d dq q IjxEV IjxEV The sub transient equivalent circuit of synchronous machine a d axis b q axis q E d jx dI qV q jx qI dV d E Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding qqdd ddqq ixEv ixEv q qd d d dq q IjxEV IjxEV q E d jx dI qV q jx qI dV The sub transient equivalent circuit of synchronous machine a d axis b q axis d E QE q E d E E q q Ij Ij d d d Ij qV dV V dI qI I q d Ij q Chapter 5 3 phase Short circuit Transient of Power Systems 5 5 3 phase Short circuit Current Calculation of Generators with Damper Winding q qd d d dq q IjxEV IjxEV q E d jx dI qV q jx qI dV The sub transient equivalent circuit of synchronous machine a d axis b q a