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:
Vt=33003=1905.25δ=ϕ−θ=14.904Ef=Vtcosδ+IdXd=1905.25cos(14.9)+215.925∗4.0=2707.0472VV_t= \frac{3300}{\sqrt3}=1905.25 \\ \delta = \phi -\theta = 14.904\\ E_f= V_t \cos \delta +I_dX_d= 1905.25 \cos(14.9) +215.925*4.0=2707.0472 V\\Vt=33300=1905.25δ=ϕ−θ=14.904Ef=Vtcosδ+IdXd=1905.25cos(14.9)+215.925∗4.0=2707.0472V
Developed power=EfVtXdsinδ+Vt22(1X2−1Xd)sin2δ=4.688∗3.34.01sin14.9+3.322(12.88−14.01)sin2∗14.9=1.256MWDeveloped \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\\ = \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\\ =1.256 MWDeveloped power=XdEfVtsinδ+2Vt2(X21−Xd1)sin2δ=4.014.688∗3.3sin14.9+23.32(2.881−4.011)sin2∗14.9=1.256MW
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