1.1 The main transmission network of Eskom The classical two generator model 11

Transcription

1 LIST OF FIGURS Figure Page 1.1 The main transmissin netwrk f skm The classical tw generatr mdel Obtaining the lcatin f the electrical centre. The line cnnecting A with B represents the netwrk vltage Defining the slip cycle Vltage vectr diagram f the classical tw generatr mdel Cnstructing the impedance lcus frm the vltage vectr diagram Netwrk used t shw the effect shunts culd have n the seen impedance Thevenin equivalent btained at Pint C (applicable t any netwrk) Prtectin equivalent fr a pi equivalent prtected element The unfaulted netwrk fr which Clarke cnstructs the swing lcus Distance relay with three znes f prtectin Operating characteristics f a distance relay 34 xiii

2 2.12 Impedance seen at Pint C during nrmal lad cnditins, swings and ut-f-step cnditins Different duble blinder ut-f-step characteristics The quadrilateral inner characteristic (zne Z ) and the 44 quadrilateral uter characteristic (zne Z 6 ) 2.1 The Blean lgic f the ut-f-step circuit f the Sel 321- relay The reach settings fr znes Z and Z The Out-f-step distance element lgic f the SL 321- relay Typical implementatin f Z 6 and Z fr the case where the 0 relay is situated at Pint C f the netwrk shwn in figure The ideal implementatin f Z 6 and Z cnstructed fr the case 1 where the relay is situated at Pint C f the netwrk shwn in figure Layut f the 400 kv Hydra busbar. SC is an abbreviatin fr Series Cmpensated; BC is an abbreviatin fr Bus Cupler and BS is an abbreviatin fr Bus Sectin Tplgy f the imprved tw generatr mdel 6 xiv

3 3.3 Steady state lad flw f the Mpumalanga-t-Western-Cape netwrk. The phrase detailed netwrk mdel refers t this netwrk Main transmissin netwrk f skm 8 3. Vltage, frequency and pwer angle measured at Atlas and Hydra Vltage and frequency measured at Grtvlei, Atlas and Tutuka Pwer angle that develps between the synchrnus rtating reference and the Grtvlei, Atlas and Tutuka busbar vltage The simplified Mpumalanga-t-Western-Cape netwrk. The phrase simplified netwrk mdel refers t this netwrk User interface t the xcel rutine used t slve Z 72 TI 3.10 The duble Π mdel (charging nly) used t mdel the line charging f the MPU t PRS/BT sectin Lad flw f the tie line when the line charging is mdelled accrding t equatin An illustratin f hw the MVAR rating f the shunts used t mdel the line charging is changed Lad flw f the tie line fr the case where the tuning f the line charging shunts make the VAR generatrs t generate apprximately zer VARS 80 xv

4 3.14 Lad flw f the tie line when the VAR generatrs are switched ff Defining the feeders A1, B1, A2 and B lectrical parameters f feeder A2 and feeder B Average VAR cntributin the tie line SVCs make during the first slip cycle The time it takes Study 2 t cmplete the first slip cycle Parameters and vectrs used t describe the Western Cape generatin pl lectric circuit f the equivalent Mpumalanga generatr. The high vltage busbar f Mpumalanga is made up f the 400 kv Grtvlei, Atlas and Tutuka busbars Pwer Tutuka imprts frm Kendal in the simplified netwrk mdel shwn in figure Parameters and vectrs used t describe the tw generatr mdel f the Mpumalanga generatin pl Vltage and frequency measured at Matla and Arnt during the first slip cycle Time it takes the imprved tw generatr mdel t cmplete ne slip cycle 104 xvi

5 3.2 Steady state lad flw f the imprved tw generatr mdel used t mdel the Mpumalanga-t-Western-Cape netwrk Sample variatin f the magnitude f L d ( s) Defining the saturatin functin S The vltage at the Keberg, Muldersvlei and Hydra busbars during the first slip cycle Cmpsite lad mdel PSS/ uses Cntrlled reactr and fixed capacitr t prvide cntrlled VAR supply Frm f Static VAR System representatin PSS/ uses Respnse time f the TCR Digital Fault Recrder data f the Hydra-Drërivier pwer angle The time it takes different pwer equipment t react t a change in the vltage Netwrk phenmena and their time frames The vltage behind transient reactance and the angle it has when the detailed netwrk mdel is in steady state The vltage behind transient reactance and the angle it has when the imprved tw generatr mdel is in steady state 133 xvii

6 4.13 Cmparing the impedance lcus that the imprved tw generatr mdel traces with the impedance lcus the detailed netwrk mdel traces (ut-f-step relay is lcated at Hydra lking twards Mpumalanga) Cmparing the impedance lcus that the imprved tw generatr mdel traces with the impedance lcus the detailed netwrk mdel traces (ut-f-step relay is lcated at Hydra lking twards Keberg) Impedance lcus the detailed netwrk mdel traces (ut-f-step relay is lcated at Hydra lking twards Mpumalanga). The impedance lcus the imprved tw generatr mdel traces is als shwn - lad is cnstant impedance Impedance lcus the detailed netwrk mdel traces (ut-f-step relay is lcated at Hydra lking twards Keberg). The impedance lcus the imprved tw generatr mdel traces is als shwn lad is cnstant impedance Impedance magnitude and slip traced fr the aggregated large and small inductin mtrs at Hydra. The impedance f the equivalent shunt at Hydra is als traced Steady state lad flw f the imprved tw generatr mdel used t mdel the Mpumalanga-t-Western-Cape netwrk Impedance lcus the imprved tw generatr mdel traces when the netwrk shunts are mdelled. The ut-f-step relay is situated at the lcatin marked C1 in figure xviii

7 .3 Z has a classical cmplex plane psitin (refer t Chapter 2, 14 figure 2.19) when the shunts are nt mdelled. The ut-f-step relay is situated at the lcatin marked C1 in figure.1.4 Impedance lcus the imprved tw generatr mdel traces when all the shunts are remved. The ut-f-step relay is situated at the lcatin marked C1 in figure General impedance chart Psitin f AB = ZY in the cmplex plane. ZX lcates 147 terminal A and Z Z lcates terminal B.7 Value f ZC at C1 when = A A = 0. Observer lks 149 tward Mpumalanga.8 Value f ZC at C1 when = B B = 0. Observer lks 149 tward Mpumalanga.9 Cmplex plane psitin f AB at C1. ZX lcates terminal A 10 and Z Z lcates terminal B.10 Impedance lcus the classical tw generatr mdel traces A and B n the Mpumalanga side f Hydra. The netwrk shunts are mdelled A and B n the Keberg side f Hydra. The netwrk 13 shunts are mdelled xix

8 .13 Impedance lcus the imprved tw generatr mdel traces when the netwrk shunts are mdelled. The ut-f-step relay is situated at the lcatin marked C2 in figure Cmplex plane psitin f the netwrk impedance AB = ZY at 1 the lcatin marked C2 in figure.1.1 Value f Z C at C2 when = A A = 0. Observer lks tward 16 Keberg.16 Value f Z C at C2 when = B B = 0. Observer lks tward 16 Keberg.17 Pwer angle, δ, that develps between Hydra and Muldersvlei 16 increases beynd 180 during the first slip cycle.18 Impedance lcus the classical tw generatr mdel traces δ when the current at C1 peaks Marking the lcatin f Z 1 and Z 2 n the general impedance 19 chart. φ = δ + θ k An illustratin hw t psitin Z t ensure detectin f the utf-step cnditin at the lcatin marked C1 in figure.1 xx

9 .22 An illustratin hw t psitin Z f the SL 321- relay t 161 ensure detectin f the ut-f-step cnditin at the lcatin marked C1 in figure.1.23 δ when the current at C2 peaks An illustratin hw t psitin Z f the SL 321- relay t 162 ensure detectin f the ut-f-step cnditin at the lcatin marked C2 in figure..2 Netwrk SL Applicatin Guide uses t illustrate the calculatin f ut-f-step settings Typical arrangement f the ut f step characteristics An illustratin hw t psitin Z f the SL 321- relay fr the 167 case where the ut-f-step relay is situated at the lcatin marked C1 in figure.1.28 An illustratin hw t psitin Z f the SL 321- relay fr the 168 case where the ut-f-step relay is situated at the lcatin marked C2 in figure.1 A.1 Defining the angles δ, δ MPU and δ 174 A.2 Defining δ, δ Q AXIS, i δ, the d-axis, d ( ), and q-axis, 174, cmpnents f the vltage behind transient reactance f q ( ) the Keberg generatr xxi

10 A.3 Values the d-axis and q-axis cmpnents f the vltage behind transient reactance btain at Keberg during the first slip cycle 17 A.4 The values f the d- and q-axis cmpnents f the vltage,, behind transient reactance at Keberg; the rtr angle at Keberg and the angle that develps between the rtating reference and at the end f the first slip cycle 179 A. The angles that develp between the synchrnus rtating reference and, MAT, ARN, TUT and KN 180 B.1 Steady state lad flw when the lads, line charging, line resistance and vltage regulating shunts are mitted frm the detailed netwrk mdel shwn in figure 3.3. All the series capacitrs installed in the Hydra-t-Muldersvlei sectin are remved 18 B.2 Steady state lad flw when the lads, line charging, line resistance and vltage regulating shunts are mitted frm the detailed netwrk mdel shwn in figure B.3 Simplified netwrk f the imprved tw generatr mdel 188 B.4 Reducing the imprved tw generatr mdel int a T netwrk 190 C.1 Pwer angles and vltages used when cmputing a, b and c 19 C.2 Steady state lad flw when the lads, line charging, line resistance and vltage regulating shunts are mitted frm the detailed netwrk mdel shwn in figure xxii

11 C.3 Netwrk used t btain the electrical distance a Parameters f the electric circuit used t mdel the Primary Pl Parameters f the Secndary Pl generatr Lad flw f the three generatr mdel f the Mpumalanga-t- Western-Cape netwrk 219 F.1 Vectr diagram f a salient ple generatr in the transient state 220 F.2 Vectr diagram f a salient ple generatr in steady state 221 G.1 Sample lad class mix fr a busbar 226 G.2 Sample residential energy usage fr typical winter days 227 H.1 Decay in d and q measured at Keberg 241 H.2 The d- and q- axis equivalent circuits f a generatr in the transient state [1, p184]. When in the transient state i 0 1 d = i2 q = 243 I.1 The per unit impedance seen at Hydra when δ MPU δ = I.2 The per unit impedance seen at Hydra when δ MPU δ = I.3 Impedance lcus traced by the detailed netwrk mdel btained fr the case where the ut-f-step relay is lcated at Hydra and the frward directin f the relay is twards Mpumalanga 20 xxiii

12 I.4 Prcdure used t mark the netwrk cnditin δ MPU δ = and δ MPU δ = 240 n the impedance lcus shwn in figure I.3 I. Impedance lcus traced by the detailed netwrk mdel btained fr the case where the ut-f-step relay is lcated at Hydra and the frward directin f the relay is twards Keberg 21 I.6 Prcdure used t mark the netwrk cnditin δ MPU δ = and δ MPU δ = 240 n the impedance lcus shwn in figure I. J.1 Value f ZC at C1 when = A A = 0. Observer lks 24 tward Mpumalanga J.2 Value f ZC at C1 when = B B = 0. Observer lks 24 tward Mpumalanga J.3 A and B n the Mpumalanga side f Hydra. The 2 netwrk shunts are mdelled J.4 Value f ZC at C1 when the current at C1 peaks. Observer 2 lks tward Mpumalanga xxiv