Question #230229

A 1.5 MVA ,3.3 kV, 40 pole, three-phase star connected asynchronous alternator has reactance of Xd = 4.01Ω/phase and Xq = 2.88Ω/phase.For a lagging power factor of 0.8 when delivering full load. Calculate a developed power:

Expert's answer

"V_t= \\frac{3300}{\\sqrt3}=1905.25 \\\\\n\\delta = \\phi -\\theta = 14.904\\\\\nE_f= V_t \\cos \\delta +I_dX_d= 1905.25 \\cos(14.9) +215.925*4.0=2707.0472 V\\\\"

"Developed \\space power = \\frac{E_f V_t}{X_d} \\sin \\delta + \\frac{V_t^2}{2}(\\frac{1}{X_2}-\\frac{1}{X_d})\\sin2 \\delta\\\\\n= \\frac{4.688*3.3}{4.01} \\sin 14.9 + \\frac{3.3^2}{2}(\\frac{1}{2.88}-\\frac{1}{4.01})\\sin2*14.9\\\\\n=1.256 MW"

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