modern-power-systems-analysis-d-p-kothari-i-j-nagrath-

@ !no.* 50 Full load ri,iectiontechniquefor ; ,, of single phasetwo wire line delta connected 374 Lossesas function of improving systemstability 500 of three-phaselines 59 generation 260 Fusion 23 Inequality constraints Gausselimination 623 on control variables 274 constants) Inertia constant 436 representation 122 assumptionsin calculating 266,269 Generator(seeSynchronousgenerator) Infinite bus Ll2 equation for 267 Generatorload model 296 Infinite line 145 symmerrical(balanced) lO7 Generatoroperatingcost 243 Inner product 607 Maintenance 32 Geometricmean distance(GMD) Input-outputcurve of a unit 243 unbalanced 394 Interrupting capacityof breakers 345 Magnetohydrodynamic (MHD) mutual 55 Interconnectedpower systems 10 Loading capability 557 self 55 Interference with communication Geometricmeanradius (GMR) 55 Load factor 3 generation 23 Governors,characteristics 298 circuits 6l-63 deadband 32I Irrverseof matrix 6L3 Load flow problem 196 Magnetomotiveforce aroundclosed free operation 301 Iterative algorithm for NR method for load path 47 model with GRC 32I Load flow methods Gradient method 272 flow studies 218 Graph comparisonof 229 MATLAB connected 189 linear 189 continuation 599 examples 651 oriented 189 . theory 189 decoupled 222 introduction to 640 Greenhouseeffect 16 programs 652 Growth of installedcapacityin India 30 FDLF 223 Growth of power systemsin India 29 Gauss 205 programming 640 HVDC 572 Matrices Hydraulic'amplifier 292 Jacobianmatrix 2I4,272 Gauss-Seidel204 Hydroelectricpowergeneration l7 elementsof 2I4,629 Hyperbolic'functions 142, 143 Newton-Raphson 213 additionof 610 Ideal transformer 99 decoupled 223 associativelaw 6l l Illconditioning 229, 545 commutativelaw 611 Impedance Kalman filtering approach 583 rectangularversion Z2I equalityof 610 application to short term load Load forecasting 9 driving point 187 forecasting 583 transfer 187 Load forecastingtechniques multiplicationof 611 Impedancediagram 98 Kimbark, E.W. 508 Incidencematrix (seeBus incidence Kinetic energy 435 estimationof averageand associativelaw 6lI matrix) Kirchhoff's current law (KCL) 186. distributivelaw 611 Incident waves I44 Kirchmayer, Leon K. 325 trend terms 577 singularand nonsingular lncrementalfuel cost 244 Incrementaltransmissionloss 260 Kron, G. 265 estimationof periodic Inductionmotors 122,344 Kuhn Tucker theorem(theorY) 632 lnductance components 581 (seealso matrix) 610 definition 45 due to internalflux 46 incorporationof weathervariables 5g3 Matrix '607 mutual 46 of compositeconductorlines 54 time seriesapproach 592 definition of doublecircuit threc-phaseline 66 autoregressivemodels Sgz diagonal 608 Lagrangian function 279, 632 autoregressivemoving-average element of 607 identity 609 Lagrange multiplier 219, 632 models582 Laplace transformation 294 Load frequencyconrrol (LFC) and null 608 Leakage reactance331 economicdispatchcontrol 305 symmetric 609 decentralizedcontrol 323 Leakance 129 transposeof 609 Lcast squaresestimation 532 digital 322 unit 508 the basic solution 532 single areacase 29I zero (seea/so Bus admittancematrix: Bus impedancematrix; Linear graph (see GraPh) two area 307 Line charging current(seecapacitance) with cRC 320 rmr Eoltrr i ^ ^^\\ J r f zAo rvg Ul.,O Load management 33 Link 190 Medium transmissionline 137 Line-to-line (LLXault 402 Load prediction Method of images g3 Line compensation on-line techniques586 Methodsof voltagecontrol 173 L-. -^-:^^ u^ a^ -l P^ ^4lr+/ r^t-u-r J 1r ?t O7 , 1/ '/lvO Q AAl \\ lDl Yf ll.tl 1 A ^^)^r^ Eoz Mini hydelplants 18 uy ugrrrrJ rrluugllt Joo Micro hydelplants lg Model by shuntcapacitors 179,498 non-dynamicmodel 596 5g6 Load ' time varying model long term 587 angle(seealso powerangle; generatorload 42 torque angle) 110 usingeconometricmodels 5g7 of speedgoverningsystem 2g3 Long transmissionline equations l4Z turbine Z9S bus 198 cvaluntionof ABCD con$tsnts l42 oontro I I hypcrbolicformof l4Z Modil'icdEuler'smethodfor stability analysis 495 compcnsation 557

Modification of Z for network Optimal (two area)loadfrequency of transformer 390 Reactance control 310 of transmissionlines 389 directaxis 118.121 BUS Positive sequencenetworks leakage,of transformers 101 Optimal ordering I89, 627 in fault studies 398 of bundledconductors changbs360 Cptimal operation of generatorson a bus Mutual (transfer) admittance I87 Mutual coupling 46 Optimal operating strategy 242 Optimal reactivepower flow NationalThermalPower Corporation of Zsu5elements 417 inductive 67 (NTPC) 4r problem 272 Power Optimal scheduling of hydrothermal , quadratureaxis Ll7 Negativesequencecomponents 370 accelerating 46? Negativesequenceimpedance 383 system 276 angle 437 subtransient 332 Optimal unit commitment 250 _apparent 106 of passiveelements 383 Optimal security constrainedunit by symmetriccomponents 374 synchronous111,332 of synchronoums achines 386 complex 105 commitment 256 factor 105, 112, Il5 transient 332 table 334 Optimum generationscheduling 259 flow througha transmissionline 158 of transformers 390 Optimum real power dispatch(sZe in three-phasecircuits Il2 Reactancediagram 98 of transmissionlines 390 maximum transmitted I59 Negativesequencenetworks optimum generationscheduling) real and reactive (seealso Reactor Reactiveload forecast 587 in fault analysis 399 examples 409 Parameterestimation 552 power;Realpower) 106 Reclosure 474 of powersystems 386 Parametersof overheadlines 45 Poweranglecurve 1I5,444 of unloadedgenerators 388 Patton,A.D. 254,256 Power system Referencebus 198 of Zr* elements 417 Penaltyfactor 260,275 Network Penaltyfunction 270,275 compensation 556 Reflectedwaves 144 branch 190 Percentvalue 99 engineer 39 modelformulation for SLFE 185 Perunit system state estimation 538 Regulating transformers(see Transformer, node 90 structure 10 observability 545, 549 changeof base 101 studies 39 regulating) primitive 191 definitioir of 99 Primitive impedance(admittance) Nodes 190 selectionof base 100 matrix I92 Regulatingconstant(R) 294 Node eliminationtechniquefor stability Performancechart of synchronous Primitive network (seeNetwork) I9l study 444 machines 119 Propagationconstant l4l Regulationof voltage 130 Nominal- t circuitof medium Performanceindex GI) 316 Proportionalplus integral control 303 transmissionline 138 Phaseconstants 143 Proximity effect 7L Reheatturbine model 295 Nominal-T representationof medium Phaseshift in star-delta Pumpedstoragescheme 18 transmissionlinc 137 transformers 377 Reliability considerationsfor economic Non-linearprogrammingproblem 632 Planningcommission 4L Non-linearprogrammingtechnique 279 z'-equivalent dispatch 253 Nuclearreactors 2I for long line 152 for mediumlengthline 138 Reluctancepower . 118 zrmodel for transformer with off-nominal turns ratio 234 Repair rate 255 \\ Plantcapacitytactor 4 Reserve 254 Plnntusefactor 4 Photovoltaicgeneration 2l Resistanceof lines 7O Pilctvulve 292 Point-by-pointsolutionof swing RotatingVAR generator 176 equation 481 Positive sequencecomponents 370 Rigid limits 275 P o s i t i v e s e q u e n c ei m p e d a n c e of pa-ssiveelements i8l Qurdrrturcaxis synchronous Salient pole synchrono-ugsenerator ll7 of syfrrwus nrchirc,s 3E3 reactance I17 Saturatedreactor 563 SCADA 634 table 334 Rcuctivcpowcr 106 Scalarproduct 607 control of flow: by machine Sctrlnrandv0ctorfunctions 614 derivativesof 614 Objectivefunction 270, 27I, 275 excitation ll3, I14 Securityanalysis 256 Off-nominalturn (tap) ratio or off-nominal injectionof 175 S c n s i t i v i t yl u c t o r s tap setting 234 <lls' ynchronoums achincs generationshift factors 520 with ovcr cxcitutiou l 14 line outagedistribution factors 520 One lincdiugrtnr 98 Seqtienceimpedances On-line with underexcitation 114 lirr synchronoums achines 3ti5 ol passiveelements 383 -+^+^ ^.+1.-^+i^- <AA t - c t a u u n s n t pw i l , u v u r r u B cr c v s l LI J- - - l - - r ! - - - , r ^ : - ^ ^ , , : r l ^ . . . . 1 r - - . ^ - l - - , . . l144 of transformers 386 of transmissiolnincs 3E5 Jlctlly\\,DLlllldllutl J1a tablelbr typicalvaluesof 334 techniquesfor non-stationary signof l06 Sequenceimpedanceasnd sequencenetworks load prediction 586 Real power 106 ul ptr$ E'rs\\stL'nl iss ARMA models 5E6 f'ormulas for 159, 160 of syrrchrowus mar.+tiffi 3t5 of transformers 390 rime r-ar1-ingmcxlel -s36 in sr nchrtrn(lus nt&('hin('s I l-5. I l9 i Apaaror a 370 Real dme computer control of Wn l cstrrdla 310 Ww'q $-r-Silems 6Y ft'dmrl hrsd fltrrr' srrludon :?0

lndex lndex S e q u e n c en e t v i o r k c o n n e c t i o n sf o r some factois affecting 496 Symmetrical comPonets transformer (TCPST) 572 unsymmetricalfaults 4OO,403,4A5 voltage 591 definition of 369 Stability limit Thyristor controlled reactor (TCR) 563 Sequen,:enetworks steadysrate 456 of unsymmetricalPhasors 372 powerin terms of 374 Thyristor controlledvoltageregulator constructionof sequencenetworks t . Tr .rLl!.fv rD\\,,\\ J{?tt - \\ Short circuit current limiters 499 Start up cost 250 algorithm for large sYstemsustng TSC) 564 Short circuit megavoltamperes 345 Short circuit ratio (SCR) 498 Statcbm 562 zBUs350 Tie line power 307 Short term load forecasting Stateelectricity boards 303 selectionof circuit breakers 344 Tolerance 206 estimatingof stochastic State estimation shortcircuit current computation Torque angle(seealsoPower angle) 438 component 583 innovation model approach 588 externalsystemequivalencing 545 throughthe Thevenin's Tracking stateestimationof power using Kalman filtering of powersystems 538 theorem 341 systems 544 approach 583 using the periodicload model 581 the injections oniy algorithm 540 shortcircuit of a synchronousmachine Transformers Short transmission line equations 12,9 the line only algorithm 543 Short transmissionline equivalent nonlinearmeasurements 535 on load 339 control (seeregulatingbelow) 231 circuit 129 problemsof illconditioning 545 stochasticcomponent 583 on no load 330 off-norninal tapes 234 Shunt capacitors Statevariablemodel 3lz transienton a transmissionline 320 per unit representatioonf lOl effect upon voltageregulation 132 for power factor correction 133 Symmetricalshort circuit phaseshift in Y-A 377 for voltagecontrol 175 Simulink 640 current 329, 331 phaseshifting 232 basics 648 Statevariables 199,312, 494 Synchronisingpower polarity markings 377 example 648 Staticload flow equarions(SLFE) 198 coefficient I 18, 308, 455 regulating 232 Single line-ro-ground(LG) fault 399 Static reservecapacity 254 Synchronousreactance33I equivalentcircuit of 234 Skin effect 71 Synchronousmachine for magnitudecontrol 232 StaticVAR generator 175,565 for phaseanglecontrol 233 Slack bus 198 StaticVAR sysrem 562,565 armaturereaction 108 State-vector 198 Soft limit 275 construction 108 sequenceimpedancesof 385 Solid LG fault 407 Sparsematrix 188 Steadystaresrabiliry 454- dynamicsof 435 T C U L 1 7 7 . 2 3\\2 Sparsity 188,I 89,623 Step-by-stepfofmulationof bus e q u i v a l e nct i r c u i t l l l Triangularisationand back Speedchanger 293 Speedgoverningsystem 293 impedancematrix excitation 113 substitution 623 S p e e d r e g u l a t i o nc o n s t a n t( s e er e g u l a t i o n additionof a branch 357 inertiaconstantsof 435 Transientreactance 332 constant) additionof a link 359 Stiffnessof sy,nchroneums achine 455 leakagereactance 331 Transientstability Spinning reserve 245, 254 Steepesdt escentmethod(seeGradient Stabiliry method) ioadangleof I 10 definitionof 433 analysisfor multimachinesystem 497 -' operating(performance)chart ll9 digital computersolutionmethod 610 definition 433 n(qr. of valuesof sequenceimpedances equalareacriterion 461 dynamic 434 study 461 Suboptimalconrrol 318 of 385 Euler modifiedmethod 495 Substation steady state 454 per unit reactance,table 334 m u l t i g e n e r a t o r c a s e4 8 7 transient,defined 434 bulkpowcr 13 phasordiagrams 112 numcricasl olutionof swing cquation clearing angle 466 clearing time 466 distribution l3 for singlegeneratorcase 480 critical clearingangle 467 critical clearing time 467 S u p e r c o n d u c t i n g m a c h i n el 4 T circuitof medium lengthline 137 Transmissioncapability12 equal areacriterion 461 Surge impbdance(see also characteristic point-by-pointmerhod 4gl Taylor seriesexpansion 213 Transmissionlevel l3 impedance) 145 TCUL (tapchangingunderload)(see SVC (Static var compensator) 562.565 Transmissionloss (seeLossesas function Swing bus (seeSlack bus) transformers) of plant generation)' Thevenin'stheorem Transmissionloss formula 261 Swingcurve 459,495 in calculationof three-phasefault derivationof 264 determinationusing modified Euler's currents 341, 35O Transpositionof transmissionlines 60 tml lavrLht nl v-u| a, {7nJ< in caleulationof unsymmetricaflault tl vn lvrsallsar nr vnva nqnqnif qnne fl, I step-by-stepdeterminationof 481 currents 416 to balanceinductance 6l Swing equation 438, 480, 494 T h r e e p h a s ec i r c u i t s Tree 190 statevariableform 495 power in lO7 Tunedpowerlines 15t Switching voltageand currentin 107 Turbinefastvalving 499 singlepole 500 Threephasefaults (seeFaults) Turbine model 295 threepole 500 Thyristorcontrolled brakingresistor 577. Turbine speedgoverningsystem 292 Symmetricmarrix 609 Thyristor controlled phaseshifting Two-area load frequencycontrol 307

Index Two reaction theory Il7 equations: for long line 142 for medium transmissionlines Unit comrnitment 250 1 3 7- t 3 9 branch and bound technique 250, for short transmissionlines l/g 252 dynamic programmingmethod Z5l stability 524, 592 reliability (security) methodsfor improVing 5Zg considerations 253 Voltage controlledbus 198 securityconstrained 256 Voltage regulation 130 stait-up consideration Z5g Unit matrix 609 Voltage stability 591 Unsyrirmetricalfaults (seealso Faults) analysis 592,5gl analysisu,singZsu5 rhbthod 416 criteria of 596 with IdVDC links 599 symmetriCal component analysis of 398 Watts (seeqlso Real power) 106 Wavelength 145 Use of computersand microprocessors Waves,incident and reflected 144, I45 in power systems', 39 Weighted least squaresestimation 533 Weighting marrix 534 VAR (see also Reactive power) Variance 582 Y\"r, (seeBus admittancematrix) Vector Y-A transfonners 96 column 607 phaseshift in 377 single-phase quivalentof 96 control (seecontrol vector) zero sequencenetwor[s of 397 disturbance 27l equation 271 Z^.,^ (seeBus impedancematrix) null 605 BUS of fixed parameters Ig9 ./' orthogonal 607 Zero sequencecomponents 371 row 607 Zero sequenceimpedance state(see Statevector) sum 606 of circuit elements 384 of synchronousmachines 384 unit 606 Velocity of propagation 146 table' 334 Voltage of transformers 387 collapse 528, 592 of transmissionlines 3g5 preventionof 526,593, 600 Zero sequencenetworks in fault studies 399 control by transformers i'77 of delta connectedloads 389 control by VAR injecrion I75 of transformers 387 eff'ectof capacitorson l3Z, 175 of unloadedgenerators 384 of Y-connecredloads 397