Electrical Power Systems

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Solution: (a) Using equation (8.11), I f = V Z + Z r º rr f Symmetrical ault 223 The Thevenin passive network for this system is shown in ig. 8.26 and Z BUS matrix for this system is already formulated in Example-8.19. or this case Z f = 0.0 and Z 33 = j0.350 \ If = V º 3 . (b) Using equation (8.14), 10 = = - j285 . pu Z j035 . Vif = V Z Z Z V º i - ir rr + f Bus 3 is faulted, i.e., r = 3, Zf = 0.0 33 b g Z13 . V3 Z33 HG \ V1f = V º º 1 \ V 1f = 0.2857 pu. r º - = 1 - j . j . Similarly, V 2f = 0.2857 pu, V 3f = 0.0 pu (c) Using equation (8.16), I f,ij = Y ij (V if – V jf ) 025 035 \ I f,12 = Y 12 (V 1f – V 2f) = Y 12 (0.2857 – 0.2857) \ If,12 = 0.0 If,13 = 1 b0. 2857 – 0g= – j14285 . pu j02 . I f,23 = –j1.4285 pu. (d) Using equation (8.17), we can write, ¢ Vg i - Vif If,gi = jx¢ g i + jxTi Note that transformer reactance is also included in above equation. V ¢ g1 = 1.0 pu (prefault no load voltage) V 1f = 0.2857 pu, x ¢ g1 = 0.4, xT1 = 0.10 c1-0. 2857h \ If,g1 = = –j1.4286 pu. 04 + 01 jc . . h Similarly, I f, g2 = –j1.4286 pu. I KJ
224 Electrical Power Systems EXERCISE 8.1 Three 20 MVA generators, each with 0.15 pu reactance, are connected through three reactors to a common bus-bar of voltage 11KV. Each feeder connected to the generator side of a reactor has 200 MVA circuit breaker. Determine the minimum value of reactor reactance. [Ans: 0.907W] 8.2 A transformer rated at 30 MVA and having a reactance of 0.05 pu is connected to the bus-bars of a transformer station which is supplied through two 33 KV feeder cables each having an impedance of (1 + j2). One of the feeder is connected to a generating station with plant rated at 60 MVA connected to its bus-bars having reactance of 0.10 pu and the other feeder to a station with 80 MVA of generating plant with a reactance of 0.15 pu. Calculate the MVA supplied to the fault in the event of a short circuit occurring between the secondary terminals the transformer. [Ans: 286 MVA] 8.3 A three phase short-circuit fault occurs at point in the system shown in ig. 8.28. Calculate the fault current. [Ans: 878.6 AMP] ig. 8.28 8.4 The three phase system shown in ig. 8.29. Calculate the subtransient fault current that results when a three phase short circuit occurs at , given that the transformer voltage on the high voltage side is 66 KV prior to the fault. ig. 8.29 8.5 Three 10 MVA generators each having a reactance of 0.2 pu are running in parallel. They feed a transmission line through a 30 MVA transformer having per unit reactance of 0.05 pu. ind the fault MVA for a fault at the sending end of the line. [Ans: 120 MVA] 8.6 An 11.2 KV bus-bar is fed from three synchronous generators as shown in ig. 8.30. Calculate the fault current and MVA if three phase symmetrical fault occurs on the bus-bar [Ans: 1071 MVA, 55.209 KA] ig. 8.30
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To My Wife Shanta Son Debojyoti and
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Preface During the last fifty years
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Contents Preface vii 1. Structure o
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Contents xi 9. Symmetrical Componen
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Structure of Power Systems and ew O
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1.2 REASONS OR INTERCONNECTION Stru
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Case-1: If P 1 = P 2 = P 3 = ... =
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Load factor, L = Maximum load = 3 M
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\ LD = 1 MW (c) rom eqn.(1.13), coi
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Case-2: Very short lasting peak. He
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1.9 DISADVANTAGES O LOW POWER ACTOR
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Resistance and Inductance of Transm
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2.4.1 Internal Inductance igure 2.1
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Therefore, we can write L 1 = L 11
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L a = 0.4605 n log R S| T| Resistan
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L = 0.4605 L Resistance and Inducta
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=(2Dd 1 · 2Dd 1) 1/4 = (2 Dd 1) 1/
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Solution. The distances from strand
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Solution: Using eqn. (2.14), Hx = I
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= 0.4605 log 6611 . 04 . Resistance
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Since from symmetry D b1= D b2, l 1
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\ D m = D D D D Resistance and Indu
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dg 1 2 \ Dsa = 0. 7788 ´ 0. 015 ´
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Capacitance of Transmission Lines 5
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V Ki = 1 pÎ N å q m 2 o m = 1 3.3
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Similarly for the 2nd transposition
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C an = log R S| T| 00242 . 1 1 1 1
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\ V12 = q ln pÎo \ C 12 = q \ C 12
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I chg = jw C anV LN \ |I chg| = w C
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Line length is 200 km. \ Can (total
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Now applying eqn. (3.7), we have C
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= 0.008993 m/km. Capacitance of Tra
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Synchronous Machine: Steady State a
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\ V = 138 Using eqn. (4.18), . 3 =
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om ig. 4.6, Synchronous Machine: St
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\ i asy max = from which Synchronou
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Postfault voltage Synchronous Machi
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or the reference phase a, E a = (Z
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5.3 THE PER-UNIT (pu) SYSTEM Power
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Power System Components and Per Uni
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Z L (pu) = Z L (ohm) (. 08+ j 03 .)
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\ VL (pu) = 0. 2033 - 76. 68° pu P
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Base impedance for the load is ( )
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Now we can write, \ |I| cos f = P |
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This is a simple series circuit. Th
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Eqns (6.15) and (6.17) can be writt
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Characteristics and Performance of
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om eqn. (6.6), Characteristics and
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as: \ |V S| = 145.13 kV. \ Sending
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Sending end power factor angle = 8.
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\ I R = V R = 208 Characteristics a
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6.6 VOLTAGE WAVES Characteristics a
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6.9 ERRANTI EECT Characteristics an
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Load low Analysis 7.1 INTRODUCTION
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Applying KCL to the independent nod
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y 10 = y 20 = y 30 = y13 ¢ y12 ¢
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\ V i = 1 Y ii L NM P - jQ i i * Vi
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n 2 i ii ii ik i k ik k i \ Pi - jQ
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Load low Analysis 157 ig. 7.6: P-re
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Load low Analysis 159 are permitted
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1 1 y13 = y31 = = = ( 10 - j30) Z (
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(1) \ V3 = 10011 . - 2. 06° After
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Load low Analysis 165 Using eqn. (7
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Load low Analysis 167 \ Q 2 = -|V 2
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|V 1| = 1.05,|V 2| = 1.0,|V 3| (1)
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\ 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 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
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Unbalanced ault Analysis 273 ig. 10
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Unbalanced ault Analysis 275 10.4 A
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where J = moment of inertia of roto
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Power System Stability 279 Pi - Pe
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Power System Stability 281 (a) ind
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On a per-phase basis, power at the
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x eq = 0.25 + 0.15 + 02 . ´ 02 . 0
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Power System Stability 287 system.
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Power System Stability 289 or P i (
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\ d1 Pi (dc - d0 ) = z Pmax dc sin
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dcr z 1 d0 cr zbPi-Bgdd d dm = C -
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We know, K1 = Pmax In ig. 11.14, P
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Solution: Prefault operation x A =
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\ cosd cr = 0.654 Power System Stab
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Similarly, the change in the power
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d (2) = d (1) + Dd (2) = 17.855 + 1
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ig. 11.19: Sample network of 11.4.
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Automatic Generation Control: Conve
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12.4 ISOCHRONOUS GOVERNOR Automatic
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Where D = PL = constant. f Theref
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\ T p = 32 3 sec. Automatic Generat
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om ig. 12.20, state-variable equati
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The area control error for area-1 a
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Automatic Generation Control in a R
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Corona 357 air around the conductor
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14.4 POTENTIAL GRADIENT OR THREE-PH
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Similarly, G b = G c = r r V bn ln
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Corona 363 In the above expressions
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P c = 2.1f HG log 10 Vn DI HG r K
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Solution: rom eqn. (14.38), air den
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\ V 0 = 110.15 KV(rms) V n = 220 3
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\ W = 55 ´ b69. 28 - 57g 2 635 . -
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Analysis of Sag and Tension 15.1 IN
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where Dl = l0. DT MA DT = T1 - T0 T
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when x = L l , s = 2 2 , \ l 2 = H
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or approximately, 2 d = wL 8H ig. 1
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Squaring eqn. (15.37), we get, s 2
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under the action of T, H and wx. or
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\ T max = 572.59 kg (d) rom eqn. (1
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ig. 15.6: Case of negative x 1. Ana
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where Analysis of Sag and Tension 3
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or 1-meter length of conductor, Ana
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(f ) Vertical sag = dcos q cos q =
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Analysis of Sag and Tension 395 = 0
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Analysis of Sag and Tension 397 Ass
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Analysis of Sag and Tension 399 Dis
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Total weight of the conductor = wl
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Analysis of Sag and Tension 403 Whe
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Optimal System Operation 16.1 INTRO
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Optimal System Operation 407 where
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Optimal System Operation 409 2. The
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Complete algorithm is given below:
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DP g1 = Î 2 DP g2 = Î 2 Using Tay
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Optimal System Operation 415 Equati
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\ 2 C2 = 0.18 Pg2 + 32 Pg2 + K2 Whe
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Optimal System Operation 419 Equati
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DP L = rom eqns (16.36) and (16.39)
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Optimal System Operation 423 Now we
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Optimal System Operation 425 The pr
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Example 16.6: Consider Ex-16.5, wit
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\ DP g (l) = 264.1657 MW rom eqn. (
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\ (4) 2 2 P = 0.00005 × (188.95) +
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Optimal System Operation 433 The te
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\ Also d P 3 d 2 P 3 3 =- G 32 si
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Let the current in line K be I K1.
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+ HG I K Optimal System Operation
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Now, \ V1 = 1.198 14. 5º, \d1 = 14
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Optimal System Operation 443 B 11 =
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Z 1 = (0.03 + j0.12)pu; I 1 = (1.3
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Objective Questions Objective Quest
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Objective Questions 449 26. or a de
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Objective Questions 451 56. Peak lo
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82. Inductance of a conductor due t
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Objective Questions 455 108. In ter
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Objective Questions 457 137. In a p
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Objective Questions 459 (c) are var
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203. A system is said to be effecti
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Answers of Objective Questions 1. (
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Bibliography Bibliography 465 1. O.
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Index accelerating (or decelerating
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methods for voltage control 115 mul
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