Electrical Power Systems

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Resistance and Inductance of Transmission Lines 43 Example 2.10: A single circuit three phase transmission line is composed of three ACSR conductor per phase with horizontal configuration as shown in ig. 2.21. ind the inductive reactance per km at 50 Hz. The radius of each subconductor in the bundle is 1.725 cm. Solution: Using eqn. (2.79) HG ig. 2.21 Ds = (r¢d 2 ) 1/3 = 0. 7788 = 0.1395 m D eq = (D ab · D bc · D ca) 1/3 1725 . ´ ´ ( . ) 100 045 2 13 / I m KJ l ab ab¢ ab¢¢ a¢ b a¢ b¢ a¢ b¢¢ a¢¢ b a¢¢ b¢ a¢¢ b¢¢ q1/9 D ab = D D D D D D D D D D ab = 14 m, D a¢¢b¢¢ = 14 m, D a¢b¢ = 14 m, D ab¢¢ = 14.45 m, D a¢¢b = 13.55 m 2 2 S = (. 045) - (. 0225) = 0.389 m 2 2 Da¢b = ( 0. 389) ( 13. 775) + = 13.78 m 2 2 Dab¢ = ( 14. 225) ( 0. 389) D a¢b¢¢ = 14.23 m = D ab¢ + = 14.23 m; D ab¢ = D a¢b = 13.78 m D ab = {14 × 14.23 × 14.45 × 13.78 × 14 × 14.23 × 13.55 × 13.78 × 14} 1/9 m = 14 m = D bc; D ca » 28 m D eq = (14 × 14 × 28) 1/3 m = 17.6 m \ L = 0.4608 log D HG = 0.968 mH/km D eq s I KJ mH/km = 0.4605 log X L = Lw = 0.968 × 10 –3 × 2 × p × 50 = 0.304 W/km 17. 6 I mH/km HG 0. 1395KJ Example 2.11: A single circuit three phase transmission line is composed of four ACSR conductor per phase with horizontal configuration as shown in ig. 2.22. ind the inductance per km length of the transmission line. Radius of each conductor in the bundle is 1.725 cm.
44 Electrical Power Systems Solution: e j / ig. 2.22 HG D = 14 m d = 0.5 m r = 1.725 cm 1725 DS = r¢ 20 d = 7788 ´ ´ ´ 100 205 3 14 . 3 . (.) m = 0.2207 m D eq » (D ab D bc D ca ) 1/3 = (14 × 14 × 28) 1/3 = 17.638 m HG L = 0.4605 log D \ L = 0.876 mH/km. D eq s I KJ 17. 638 = 0.4605 log 02207 . I KJ 14 / I mH/km HG KJ Example 2.12: A 50 Hz, single phase transmission line and a telephone line are parallel to each other as shown in ig. 2.23. The transmission line carries an rms current of 200 amp. Assume zero current flows in the telephone wires. ind the magnitude of the voltage per km induced in the telephone line. Solution: ig. 2.23 2 2 Da1 = 4 + 3 = 5 m 2 2 Da2 = 6 + 3 = 6.708 m rom ig. 2.23, the flux linkages between conductor T 1 and T 2 due to current I a is HG l12 (Ia ) = 0.4605 Ialog Da2 D a1 I KJ mWb–T/km
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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 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 32 and 33: Resistance and Inductance of Transm
Page 34 and 35: 2.4.1 Internal Inductance igure 2.1
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 50 and 51: Solution: Using eqn. (2.14), Hx = I
Page 52 and 53: = 0.4605 log 6611 . 04 . Resistance
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 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 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 86 and 87: = 0.008993 m/km. Capacitance of Tra
Page 92 and 93: Synchronous Machine: Steady State a
Page 98 and 99: \ V = 138 Using eqn. (4.18), . 3 =
Page 100 and 101: 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
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( p) p The terms DPi and DQi Load l
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Load low Analysis 175 P2 = -35.77
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(1) P2( cal ) = -2.62 (1) P3( cal )
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Load low Analysis 179 Use deoupled
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0 Dd2 \ Dd3 0 ( ) ( ) NM \ 0 Dd2 L
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Assuming q ik - d i + d k » d ik,
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Table 7.4: Line impedances BUS code
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Symmetrical ault 187 is drawing 10
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\ X TH = ig. 8.4: Thevenin equivale
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ig. 8.5: Circuit diagram of Example
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= | Vo| | Vo| | Z| ´ × (MVA) Base
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\ 1 - V 1f = j0.14 × (-j4.165) \ V
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Base current I B = Per unit reactan
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Symmetrical ault 199 Example 8.9: T
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Solution: Let Base MVA = 12 Base Vo
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Solution: Let Base MVA = 100 Base V
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Therefore, current to be interrupte
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Circuit model under fault condition
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Symmetrical ault 209 Example 8.16:
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8.4 SHORT CIRCUIT ANALYSIS OR LARGE
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om equations. (8.9) and (8.10), we
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Using equation (8.14), Z BUS = L NM
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Symmetrical ault 217 Solution: Inje
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Hence, new Z = BUS 8.6.3 Type-3 Mod
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or L V 1 V M NM 2 V 0 n O QP = L ol
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Solution: (a) Using equation (8.11)
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Symmetrical ault 225 8.7 ig. 8.31 s
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has the following properties R S| T
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T stands for transpose. Using eqn.
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Using eqn.( 2.46) as given in Chapt
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Also I n = I a + I b + I c Using eq
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Symmetrical Components 235 ig. 9.4:
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Symmetrical Components 237 (b) - co
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Solution: I a + I b + I c = 0, I a
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Also note that I ab1 = I a1 3 30°
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Base voltage of transmission line 1
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Symmetrical Components 245 Example
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Symmetrical Components 247 Example
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9.5 Draw the zero-sequence network
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Unbalanced ault Analysis 251 Assumi
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The symmetrical components of the f
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Unbalanced ault Analysis 255 The bo
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ig. 10.9: Two conductors open. Unba
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Z 1 = j0.691 0.23 ´ 0. 691+ 0. 23
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Unbalanced ault Analysis 261 Exampl
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\ 3 ´ 1.0 ´ j0.4 j0.3 ´ j0.4 + j
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Denominator of eqns. (i) and (ii) Z
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Hence, rom eqn. (i), V b = V c Unba
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ig. 10.18 shows the sequence networ
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\ 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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