Question

A 100-MVA 12.5-KV 0.85-PF lagging 50-Hz two-pole Y-connected synchronous generator has a synchronous reactance of 1.7 Q and a negligible armature resistance. I) What is the magnitude of the internal generated voltage at rated conditions? 2) What is its torque angle at these conditions? 3) What is its voltage regulation? 4) Ignoring the losses in this generator, what torque must be applied to its shaft by the prime mover at full load? 5) What is the maximum power the generator can produce at the rated conditions? 6) What would the voltage regulation of the generator be at 60Hz?

Answer 1

Given data. MVA - 100 MVA V = 12,5 KV PuF = cos Ⓡ = 0.85 (lagging) frequency; f = 50. Hz No. of Poles =P=2 connection type → star a l Synchronour Reactance - Xs = 172 Neglech Armature Resistance. 1. Magnitude of the internal generated voltage at rated conditions:- we know that Els = v oo + Taxe 100 MUA = V3 VL In I, 3 100x106 Vexve 100x106 V5 (12.5x1039 1 = 4618.802 A

In given problem connection type is star 4618.802 A . 1 a ELS' = vo + Ta Xs EL8° = 12.5X10°/6° + 4618.802 xj 1:7 TELS = 13169.59159 [30.45/v Iph. line to line generated magnitude voltage. Elin - B x 13.169 kv Eu - 22.309 RU Ô Torque angle = 8= 30.45° Voltage Regulation: ② we know that Voltage Regulation - E-vx100 = X100 22.809 - 12.5 1 12.5 = 82:47.7.

uTorque applied to shaft at full load by prime mover Given losser care Ignored. P = MUA X Cold p= 100x10° x 0.85 TT 85X100 W were know that Power = ß = TX Ws where -6, - 27TNT 60 1206 XL0160 P = T x 2TINS 60 60 IN ñ - GOP - 60x85X109 2TN, 2 T1 (5000) Ni = 3000 [ = 270563. 403 N.17 © Maximum power :- EL V we know that Pmax = Pmax = 22.809 X 12.5 x 10 1.7 imax 167.713 M Co

© The voltage regulation of the generator bo at 60 Hz At 50 Hz frequency Xs. = 1.7 2/pn At 60 Hz frequency Xs = ? 50 *Scotty = 6 x 1,7 1 Xsco R = 2,042/ Els at 60 HZ 36789 + 12.04 ELS = 12: 5x10 Loo LO+ 4618.862 1 EL = 14577-582 | 33. 32° for file o 14577.582 x Cu = 25242-126 = 25449.1126 - Now Reg - E x100 = 25249.1126 - 120500X 100 12.500 Veeg = 101.492.7. At 60 +3,
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