Electrical Power Systems

More documents

Recommendations

Info

Index accelerating (or decelerating) power 278 accumulations of snow or ice 388 ACE participation factors 342 ACSR conductor 25 actual generated powers 349 admittance 148 Aeolian vibrations 402 air gap flux 80 algorithm for the iterative process 301 aliasing 336 amortisseur or damper windings 89 Ampere’s law 20 ancillary services 340 angle towers 393 angular momentum 276 approximate formula to relate the loss factor to the load factor 13 approximate loss formula 425 area control error (ACE) 328 armature current 92 armature voltage 81 attenuation constant 128 augmented cost function 409 Automatic Generation Control (AGC) 307 Average speed 301 balanced three phase currents 83 balanced three-phase network 96 base quantities 99 bias factor 329 booster transformers 120 boundary conditions at the fault point 251 bundle spacing 59 bundled conductors 32 capacitance 53 catenary curve 375 chain rule differentiation 432 characteristic impedance 142 characteristic odour 356 charging admittance 150 circuit breakers rated MVA 186 clearing time 291 Coincidence actor 6 Coincident Demand 4 Index 467 complex operator 226 complex power in a three-phase system 229 components of an electric power system 1 Composite requency Response Characteristic 320 Connected Load 4 connection of sequence nework 255 continuous-time domain 335 contract participation factor 341 contracted load 345 Contribution actor 6 control areas 322 Control of Power Output of Generating Units 311 Cooperative assistance between areas 322 Coordination Equation 410 corona characteristic 356 corona loss 364 cost function 409 cost of operation of generators 405 clearing time 291 critical angle 290 critical clearing angle 290 critical clearing time 292 current distribution factors 437 current limiting reactors 196 cylindrical or salient construction 79 damping coefficient 279 dc component current 92 DC off-set current 190 Demand 4 Demand actor 4 Demand Interval 4 deregulated utility structure 340 deregulation 339 direct axis reactance 86 Disadvantages of Low Power actor 15 DISCO participation matrix (DPM) 340 DISCOs 340 DISCOs have contract with the GENCOs 349 discrete domain 335 disruptive critical voltage 361 disruptive critical voltage gradient 361 disruptive strength of air 364 distributed phase winding 81 distribution system 1
468 Electrical Power Systems Diversity actor 5 double circuit line 30, 59 dynamic responses 318 economic design 373 elastic property of wire 374 electric breakdown 356 Electric charge 53 electric field 53 electric gradient 356 electro-static stresses 356 electromagnetic power 278 electromagnetic torque 278 Elongation 374 emergency loads 3 equal-area criterion 287 Equivalent inertia 280 equivalent p-model. 184 equivalent span length 388 equivalent star connection 98 Expression for total fuel cost 417 external flux 20 ACTS devices 304 fast primary and slow secondary control modes 318 ault current 213 ferranti effect 145 flux linkages 19 for determining the value of l 421 force of wind on conductor 389 frequency response characteristic 329 undamentals of Automatic Generation Control 318 galloping or dancing of conductors 403 Gauss’ theorem 53 Gauss-Seidel method 154 GENCOs 340 General expression of transmission loss 439 generated voltage 81 Generation Rate Constraint (GRC) 334 generator limits 412 generator-load system 314 gradient method 421 Ground clearance 393 heat energy 406 heat-rate curve 406 horizontal force due to wind pressure 391 ice coating is uniform over the surface 388 ill-conditioned problems 171 image charges 61 inadvertent interchange 322 incident wave 141 incremental cost 410 independent power producer 339 independent variables 417 inductance 18 inequality constraints 408 inertia constant 277 inertia constant in per unit 277 initial starting voltage 154 initial steady-state operating point 288 injected current I i 152 input energy rate 405 integral gains 329 inter-strand friction in the steel cable 402 interconnected operation 3 isochronous governor 309 Isolated Power System 315 Jacobain for the functions 171 Lagrange multiplier 410 Lagrange multipliers 409 law of conservation of power 417 leakage currents 18 leakage impedance of the transformer 236 Load buses 147 load characteristic of the generating unit 310 Load Diversity 6 Load actor 7 load flow 171 Load requency control (LC) 307 Load growth 13 load impedance per phase 100 load is sensitive to the speed (frequency) variation 314 Load Sharing by Parallel Generating Units 311 logical choice of frequency bias setting 330 long transmission line 127 loss coefficients or B-coefficients 439 Loss actor 7 luminous glow 357 magnetic flux density 21 magnetically coupled circuits 89 mathematical model of the steam turbine 312 Maximum Demand 4 maximum effective weight of the conductor 373 maximum overall efficiencies 406 maximum span 388 maximum value of the conductor tension 381 medium length lines 126
Page 3:
This page intentionally left blank
Page 6 and 7:
To My Wife Shanta Son Debojyoti and
Page 8 and 9:
Preface During the last fifty years
Page 10 and 11:
Contents Preface vii 1. Structure o
Page 12 and 13:
Contents xi 9. Symmetrical Componen
Page 14 and 15:
Structure of Power Systems and ew O
Page 16 and 17:
1.2 REASONS OR INTERCONNECTION Stru
Page 18 and 19:
Page 20 and 21:
Case-1: If P 1 = P 2 = P 3 = ... =
Page 22 and 23:
Load factor, L = Maximum load = 3 M
Page 24 and 25:
\ LD = 1 MW (c) rom eqn.(1.13), coi
Page 26 and 27:
Case-2: Very short lasting peak. He
Page 28 and 29:
1.9 DISADVANTAGES O LOW POWER ACTOR
Page 30 and 31:
Page 32 and 33:
Resistance and Inductance of Transm
Page 34 and 35:
2.4.1 Internal Inductance igure 2.1
Page 36 and 37:
Page 38 and 39:
Therefore, we can write L 1 = L 11
Page 40 and 41:
L a = 0.4605 n log R S| T| Resistan
Page 42 and 43:
L = 0.4605 L Resistance and Inducta
Page 44 and 45:
=(2Dd 1 · 2Dd 1) 1/4 = (2 Dd 1) 1/
Page 46 and 47:
Solution. The distances from strand
Page 48 and 49:
Page 50 and 51:
Solution: Using eqn. (2.14), Hx = I
Page 52 and 53:
= 0.4605 log 6611 . 04 . Resistance
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Since from symmetry D b1= D b2, l 1
Page 60 and 61:
\ D m = D D D D Resistance and Indu
Page 62 and 63:
dg 1 2 \ Dsa = 0. 7788 ´ 0. 015 ´
Page 64 and 65:
Page 66 and 67:
Capacitance of Transmission Lines 5
Page 68 and 69:
V Ki = 1 pÎ N å q m 2 o m = 1 3.3
Page 70 and 71:
Similarly for the 2nd transposition
Page 72 and 73:
Page 74 and 75:
C an = log R S| T| 00242 . 1 1 1 1
Page 76 and 77:
\ V12 = q ln pÎo \ C 12 = q \ C 12
Page 78 and 79:
I chg = jw C anV LN \ |I chg| = w C
Page 80 and 81:
Line length is 200 km. \ Can (total
Page 82 and 83:
Now applying eqn. (3.7), we have C
Page 84 and 85:
Page 86 and 87:
= 0.008993 m/km. Capacitance of Tra
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Synchronous Machine: Steady State a
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
\ V = 138 Using eqn. (4.18), . 3 =
Page 100 and 101:
om ig. 4.6, Synchronous Machine: St
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
\ i asy max = from which Synchronou
Page 108 and 109:
Postfault voltage Synchronous Machi
Page 110 and 111:
or the reference phase a, E a = (Z
Page 112 and 113:
5.3 THE PER-UNIT (pu) SYSTEM Power
Page 114 and 115:
Power System Components and Per Uni
Page 116 and 117:
Page 118 and 119:
Z L (pu) = Z L (ohm) (. 08+ j 03 .)
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
\ VL (pu) = 0. 2033 - 76. 68° pu P
Page 128 and 129:
Base impedance for the load is ( )
Page 130 and 131:
Now we can write, \ |I| cos f = P |
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
This is a simple series circuit. Th
Page 140 and 141:
Eqns (6.15) and (6.17) can be writt
Page 142 and 143:
Characteristics and Performance of
Page 144 and 145:
om eqn. (6.6), Characteristics and
Page 146 and 147:
as: \ |V S| = 145.13 kV. \ Sending
Page 148 and 149:
Page 150 and 151:
Sending end power factor angle = 8.
Page 152 and 153:
\ I R = V R = 208 Characteristics a
Page 154 and 155:
6.6 VOLTAGE WAVES Characteristics a
Page 156 and 157:
Page 158 and 159:
6.9 ERRANTI EECT Characteristics an
Page 160 and 161:
Load low Analysis 7.1 INTRODUCTION
Page 162 and 163:
Applying KCL to the independent nod
Page 164 and 165:
y 10 = y 20 = y 30 = y13 ¢ y12 ¢
Page 166 and 167:
\ V i = 1 Y ii L NM P - jQ i i * Vi
Page 168 and 169:
n 2 i ii ii ik i k ik k i \ Pi - jQ
Page 170 and 171:
Load low Analysis 157 ig. 7.6: P-re
Page 172 and 173:
Load low Analysis 159 are permitted
Page 174 and 175:
1 1 y13 = y31 = = = ( 10 - j30) Z (
Page 176 and 177:
(1) \ V3 = 10011 . - 2. 06° After
Page 178 and 179:
Load low Analysis 165 Using eqn. (7
Page 180 and 181:
Load low Analysis 167 \ Q 2 = -|V 2
Page 182 and 183:
|V 1| = 1.05,|V 2| = 1.0,|V 3| (1)
Page 184 and 185:
\ L NM e j ( 0) ( 0) ( 0) 1 1 1 2 n
Page 186 and 187:
( p) p The terms DPi and DQi Load l
Page 188 and 189:
Load low Analysis 175 P2 = -35.77
Page 190 and 191:
(1) P2( cal ) = -2.62 (1) P3( cal )
Page 192 and 193:
Load low Analysis 179 Use deoupled
Page 194 and 195:
0 Dd2 \ Dd3 0 ( ) ( ) NM \ 0 Dd2 L
Page 196 and 197:
Assuming q ik - d i + d k » d ik,
Page 198 and 199:
Table 7.4: Line impedances BUS code
Page 200 and 201:
Symmetrical ault 187 is drawing 10
Page 202 and 203:
\ X TH = ig. 8.4: Thevenin equivale
Page 204 and 205:
ig. 8.5: Circuit diagram of Example
Page 206 and 207:
= | Vo| | Vo| | Z| ´ × (MVA) Base
Page 208 and 209:
\ 1 - V 1f = j0.14 × (-j4.165) \ V
Page 210 and 211:
Base current I B = Per unit reactan
Page 212 and 213:
Symmetrical ault 199 Example 8.9: T
Page 214 and 215:
Solution: Let Base MVA = 12 Base Vo
Page 216 and 217:
Solution: Let Base MVA = 100 Base V
Page 218 and 219:
Therefore, current to be interrupte
Page 220 and 221:
Circuit model under fault condition
Page 222 and 223:
Symmetrical ault 209 Example 8.16:
Page 224 and 225:
8.4 SHORT CIRCUIT ANALYSIS OR LARGE
Page 226 and 227:
om equations. (8.9) and (8.10), we
Page 228 and 229:
Using equation (8.14), Z BUS = L NM
Page 230 and 231:
Symmetrical ault 217 Solution: Inje
Page 232 and 233:
Hence, new Z = BUS 8.6.3 Type-3 Mod
Page 234 and 235:
or L V 1 V M NM 2 V 0 n O QP = L ol
Page 236 and 237:
Solution: (a) Using equation (8.11)
Page 238 and 239:
Symmetrical ault 225 8.7 ig. 8.31 s
Page 240 and 241:
has the following properties R S| T
Page 242 and 243:
T stands for transpose. Using eqn.
Page 244 and 245:
Using eqn.( 2.46) as given in Chapt
Page 246 and 247:
Also I n = I a + I b + I c Using eq
Page 248 and 249:
Symmetrical Components 235 ig. 9.4:
Page 250 and 251:
Symmetrical Components 237 (b) - co
Page 252 and 253:
Solution: I a + I b + I c = 0, I a
Page 254 and 255:
Also note that I ab1 = I a1 3 30°
Page 256 and 257:
Base voltage of transmission line 1
Page 258 and 259:
Symmetrical Components 245 Example
Page 260 and 261:
Symmetrical Components 247 Example
Page 262 and 263:
9.5 Draw the zero-sequence network
Page 264 and 265:
Unbalanced ault Analysis 251 Assumi
Page 266 and 267:
The symmetrical components of the f
Page 268 and 269:
Unbalanced ault Analysis 255 The bo
Page 270 and 271:
ig. 10.9: Two conductors open. Unba
Page 272 and 273:
Z 1 = j0.691 0.23 ´ 0. 691+ 0. 23
Page 274 and 275:
Unbalanced ault Analysis 261 Exampl
Page 276 and 277:
\ 3 ´ 1.0 ´ j0.4 j0.3 ´ j0.4 + j
Page 278 and 279:
Denominator of eqns. (i) and (ii) Z
Page 280 and 281:
Hence, rom eqn. (i), V b = V c Unba
Page 282 and 283:
ig. 10.18 shows the sequence networ
Page 284 and 285:
\ V b = E a = 3752.8 0° 1763 . - 3
Page 286 and 287:
Unbalanced ault Analysis 273 ig. 10
Page 288 and 289:
Unbalanced ault Analysis 275 10.4 A
Page 290 and 291:
where J = moment of inertia of roto
Page 292 and 293:
Power System Stability 279 Pi - Pe
Page 294 and 295:
Power System Stability 281 (a) ind
Page 296 and 297:
On a per-phase basis, power at the
Page 298 and 299:
x eq = 0.25 + 0.15 + 02 . ´ 02 . 0
Page 300 and 301:
Power System Stability 287 system.
Page 302 and 303:
Power System Stability 289 or P i (
Page 304 and 305:
\ d1 Pi (dc - d0 ) = z Pmax dc sin
Page 306 and 307:
dcr z 1 d0 cr zbPi-Bgdd d dm = C -
Page 308 and 309:
We know, K1 = Pmax In ig. 11.14, P
Page 310 and 311:
Solution: Prefault operation x A =
Page 312 and 313:
\ cosd cr = 0.654 Power System Stab
Page 314 and 315:
Similarly, the change in the power
Page 316 and 317:
d (2) = d (1) + Dd (2) = 17.855 + 1
Page 318 and 319:
ig. 11.19: Sample network of 11.4.
Page 320 and 321:
Automatic Generation Control: Conve
Page 322 and 323:
12.4 ISOCHRONOUS GOVERNOR Automatic
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Where D = PL = constant. f Theref
Page 330 and 331:
Page 332 and 333:
\ T p = 32 3 sec. Automatic Generat
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
om ig. 12.20, state-variable equati
Page 342 and 343:
The area control error for area-1 a
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
Automatic Generation Control in a R
Page 354 and 355:
Page 356 and 357:
Page 358 and 359:
Page 360 and 361:
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Corona 357 air around the conductor
Page 372 and 373:
14.4 POTENTIAL GRADIENT OR THREE-PH
Page 374 and 375:
Similarly, G b = G c = r r V bn ln
Page 376 and 377:
Corona 363 In the above expressions
Page 378 and 379:
P c = 2.1f HG log 10 Vn DI HG r K
Page 380 and 381:
Solution: rom eqn. (14.38), air den
Page 382 and 383:
\ V 0 = 110.15 KV(rms) V n = 220 3
Page 384 and 385:
\ W = 55 ´ b69. 28 - 57g 2 635 . -
Page 386 and 387:
Analysis of Sag and Tension 15.1 IN
Page 388 and 389:
where Dl = l0. DT MA DT = T1 - T0 T
Page 390 and 391:
when x = L l , s = 2 2 , \ l 2 = H
Page 392 and 393:
or approximately, 2 d = wL 8H ig. 1
Page 394 and 395:
Squaring eqn. (15.37), we get, s 2
Page 396 and 397:
under the action of T, H and wx. or
Page 398 and 399:
\ T max = 572.59 kg (d) rom eqn. (1
Page 400 and 401:
ig. 15.6: Case of negative x 1. Ana
Page 402 and 403:
where Analysis of Sag and Tension 3
Page 404 and 405:
or 1-meter length of conductor, Ana
Page 406 and 407:
(f ) Vertical sag = dcos q cos q =
Page 408 and 409:
Analysis of Sag and Tension 395 = 0
Page 410 and 411:
Analysis of Sag and Tension 397 Ass
Page 412 and 413:
Analysis of Sag and Tension 399 Dis
Page 414 and 415:
Total weight of the conductor = wl
Page 416 and 417:
Analysis of Sag and Tension 403 Whe
Page 418 and 419:
Optimal System Operation 16.1 INTRO
Page 420 and 421:
Optimal System Operation 407 where
Page 422 and 423:
Optimal System Operation 409 2. The
Page 424 and 425:
Complete algorithm is given below:
Page 426 and 427:
DP g1 = Î 2 DP g2 = Î 2 Using Tay
Page 428 and 429:
Optimal System Operation 415 Equati
Page 430 and 431: \ 2 C2 = 0.18 Pg2 + 32 Pg2 + K2 Whe
Page 432 and 433: Optimal System Operation 419 Equati
Page 434 and 435: DP L = rom eqns (16.36) and (16.39)
Page 436 and 437: Optimal System Operation 423 Now we
Page 438 and 439: Optimal System Operation 425 The pr
Page 440 and 441: Example 16.6: Consider Ex-16.5, wit
Page 442 and 443: \ DP g (l) = 264.1657 MW rom eqn. (
Page 444 and 445: \ (4) 2 2 P = 0.00005 × (188.95) +
Page 446 and 447: Optimal System Operation 433 The te
Page 448 and 449: \ Also d P 3 d 2 P 3 3 =- G 32 si
Page 450 and 451: Let the current in line K be I K1.
Page 452 and 453: + HG I K Optimal System Operation
Page 454 and 455: Now, \ V1 = 1.198 14. 5º, \d1 = 14
Page 456 and 457: Optimal System Operation 443 B 11 =
Page 458 and 459: Z 1 = (0.03 + j0.12)pu; I 1 = (1.3
Page 460 and 461: Objective Questions Objective Quest
Page 462 and 463: Objective Questions 449 26. or a de
Page 464 and 465: Objective Questions 451 56. Peak lo
Page 466 and 467: 82. Inductance of a conductor due t
Page 468 and 469: Objective Questions 455 108. In ter
Page 470 and 471: Objective Questions 457 137. In a p
Page 472 and 473: Objective Questions 459 (c) are var
Page 474 and 475: 203. A system is said to be effecti
Page 476 and 477: Answers of Objective Questions 1. (
Page 478 and 479: Bibliography Bibliography 465 1. O.
Page 482 and 483: methods for voltage control 115 mul
show all

Electrical Power Systems

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?