Question

Zone 1 Zone 3 Zone 2 Xice j1002 BE SO MW 0.8 pf lagging Vload = 30 kV Ti 50 MVA 11/132 kV X= 10% Tz 50 MVA 132/33 kV X=12% Figure 1 2. A 500 MVA, 20 kV, 50 Hz synchronous generator with reactances Xd" = 0.15, Xá = 0.24, Xo = 1.1 p.u. and time constant To = 0.035, Tó' = 2.0, TA = 0.2 seconds is connected to a circuit breaker. The generator is operating at 5% above rated voltage and at no load when a bolted three-phase short circuit occurs on the load side of the breaker. The breaker interrupts the fault 4 cycles after fault inception. Determine: a. The generator's voltage in per unit (2 marks) b. The subtransient fault current in per unit (2 marks) C. The subtransient fault current in Ampere (3 marks) d. The maximum DC offset at 4 cycles in Ampere (3 marks) e. The rms AC fault current at 4 cycles in Ampere (3 marks) f. The rms asymmetrical fault current (2 marks)

Answer 1

7 perunit // Circan values in the question xa's xda oias / xd=11 Tal=2seo -0.15 Td": 00355 TA :012 de rated voltage Lo (4) The gewration is operating at sy aborc Therefore no-load coltage before the facult occor is given by 105 Eg: unit. = 1.05 per oms subtransient (6) is deformind wing the tristantaneous lac (o): Eg fault caroent Tau expression for ac fault canlist is giren by Srated ZIE 1.05 0115 (c) Base current of generador 500 barc E14.43 KA Vs Vrated уз & о This sms subtraistent dould current inka is the product of per-unit valco and basa curent. 7 X 14.43 = 101 ka za

op whoraryu (6) offat in any phase ideman (t)= V2 Illetita at/0.2. KA * V2 x 297 x 6 garrator as ta = 0.08s 4 -t/tall Given 60 Hz 4 cycles 460 I'dc max (0.08), 98.68 kA (e) kins de tuult current at ta ocks ze (t): E Eg [lated the telah dite jet let'e ta 7 Sin/wt x-f Zac (0.083):105 [Cotis strange Corps 21:05 [1-675+2.197 +017 t -0.08 e 0035 -0.08/2 + .e 1:1 unit =4.98 per 4 4.987 14.43. 71.86 kA

ff) Irms 6.68) 72 V [zac (0.00) + [VE 1" et 197² Iac (008)/172/2" 7.at TA e Iac(0.08) 71.86 Virolet **** 71.86 X 1.662 120 KA