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Chapter 5—Electrical Network 5–24 The MOD-2 generator is rated at 3125 kVA, 0.8 pf, and 4160 V line to line. The typical per phase synchronous reactance for the four-pole, conventionally cooled generator is 1.38 pu. The generator is supplying power at rated voltage and frequency to an isolated load with a per phase impedance of 1.2 - j0.8 pu as shown in Fig. 14. Find the base, actual, and per unit values of terminal voltage V , generated voltage E, apparent power, real power, reactive power, current, generator inductance, and load capacitance. ✎☞✎☞✎☞ + E ♠ − j1.38 pu + V − > < > < > < 1.2 pu −j0.8 pu Figure 14: Per phase diagram for example problem. First we determine the base values, which do not depend on actual operating conditions but on nameplate ratings. V base = 4160 √ 3 = 2400 V E base = V base = 2400 V S base = 3125 3 = 1042 kVA P base = Q base = S base = 1042 kVA I base = S base 1, 042, 000 VA = = 434 A V base 2400 V Z base = V base I base = 2400 434 =5.53 Ω L base = X base ω o = Z base = 5.53 =14.7 mH ω o 377 C base = 1 X base ω o = 1 = 480 µF 5.53(377) Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 5—Electrical Network 5–25 The actual voltage is given in the problem as the rated or base voltage, so The per unit terminal voltage is then V = 2400 V V pu = V = 2400 V base 2400 =1 We now have to solve for the per unit current. I pu = V pu Z pu = 1/0o 1.2 − j0.8 = 1/0 o 1.44/ − 33.69 o =0.693/33.69o The actual current is = 0.577 + j0.384 I = I pu I base =(0.693/33.69 o )(434) = 300/33.69 o A The per unit apparent power is S pu = |V pu ||I pu | = (1)(0.693) = 0.693 The per unit real power is The per unit reactive power is P pu = |V pu ||I pu | cos θ = (1)(0.693) cos(−33.69 o )=0.577 The actual powers per phase are Q pu = |V pu ||I pu | sin θ = (1)(0.693) sin(−33.69 o )=−0.384 S = (0.693)(1042) = 722 kVA/phase P = (0.577)(1042) = 600 kW/phase Q = (−0.384)(1042) = −400 kvar/phase The total power delivered to the three-phase load would then be 2166 kVA, 1800 kW, and -1200 kvar. The generated voltage E in per unit is Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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