Question

Please answer question 4 with the graph and info given below the problem statement. Thank you : )

4. Assume that the generator field current is adjusted to supply 480 V under rated condi- tions. What is the static stability limit of this generator? (Note: You may ignore RA to make this calculation easier.) How close is the full-load condition of this generator to the static stability limit? Problems 2 to 4 refer to a four-pole, Y-connected synchronous generator rated at 300 kVA 480 V, 60 Hz, and 0.85 PF lagging. Its armature resistance RA is 0.04 Ω. The core losses of this generator at rated conditions are 10 kW, and the friction and windage losses are 13 kW. The open- circuit and short-circuit characteristics are shown in Figure P5-2. 1 1200 A 1200 1000 A 1000 800 A 800 600 A i 2 600 400 A S 400 200 A 200 7.08.0 9.0 10.0 0.0 1.0 2.0 3.04.0 5.06.0 Field current, A

Answer 1

From the given data, the parameters of a four-pole, Y-connected synchronous generator are, The power rating is, Spated = 300 kVA The terminal voltage is, V, = 480 V The power factor is, PF = 0.85 lagging The frequency is, fee = 60 Hz The resistance of armature is, RA = 0.04 12 The core losses at rated condition are, Pcare loss = 10 kW The friction and windage losses are, Prechloss = 13 kW If the field current is adjusted to supply 480 V under rated conditions, then the rated phase voltage is given by, The expression for the rating of synchronous generator is, Spated = 13V14 300 kVA 1.-13 (480) 1,= , _300x109 13 (480) 1 = 360.84 A

Since the power factor is 0.85 lagging, the value of phase angle is, cosA=0.85 0 = cos(0.85) 0=31.8° Now, the value of armature current is, LA = 360.842-31.8° A Draw the graph for OCC and the SCC for the generator. 1200 A 1000 A 800 A Open-circuit terminal voltage, V 600 A Isc. A H400 A + 360.84 A 200 A 0.0 1.0 2.0 3.0 2.6 A 4.0 5.0 6.0 Field current, A 7.0 8.0 9.0 10.0

From the above characteristics, The field current corresponding to the short circuit current of 360.84 A is, 2.6 A. The open circuit voltage at the field current of 2.6 A is, 435 V. Since the generator is Y-connected, the per phase open circuit voltage is, The saturated synchronous reactance of the generator is, 435 360.84 = 0.696 22 X

The internal generated voltage of the generator at rated conditions is, E =V, +1 (R+ jXs) 480 E = ++(360.842-31.8°)(0.04 + j0.696) Ex = 421.7373 + j205.8401 E = 469.29 226.02° kV The static stability limit of a synchronous generator is the maximum power that the generator can supply under any circumstances. The expression for the maximum power that the generator can supply is, Pmax = -> LA 1 480) P 3113 ) (469.29) Fmax = 0.696 P 561 kW max The full load power of this generator is less than the steady state stability limit.