Question

The a-phase voltage of an ideal balanced three-phase Y-connected source is Van-13.2kV<0° and the frequency is 60Hertz. The source is connected to a A-connected 3-phase balanced load of 100+j750 per phase. The lines are considered perfect. The phase sequence of the source is abc Use the a-phase sequence as a reference. a) Draw the 3-phase circuit b) Give Van, Voor and V, Derive VAB and derive Vec,and VcA c) Calculate lAB and derive Isc and IcA d) Calculate the total average power, reactive power, and complex power at the load

Answer 1

" V_p = 13.2 kV V_an = 13.2 kV angle 0 V_bn = V_an angle -120 = 13.2 k angle -120 V V_an = V_an angle + 120 = 13.2 angle + 120 kV V_AB = squareroot V_p angle 30 = squareroot 3 times 13.2 times 10^3 angle 30 = 22.86 angle 30 kV V_BC = squareroot 3 V_p angle -90 = squareroot 3 times 13.2 times 10^3 angle -90 = 22.86 angle -90 kV V_CA = squareroot 3 V_p angle + 150 = squareroot 3 times 13.2 times 10^3 angle + 150 = 22.86 angle + 150 kV I_AB = V_AB/z_A = 22.86 angle 30 times 10^3/(100 + 75j) = 182.88 angle -36.869 A I_BC = V_BC/z_A = 22.86 times 10^3 angle -90/(100 + 75j) = 182.88 angle -126.869 A I_CA = V_CA/z_A = 22.86 times 10^3 angle + 150/(100 + 75j) = 182.88 angle 113.131 A I_a = I_AB squareroot 3 angle -30 = 182.88 times squareroot 3 angle -30 - 36.869 = 316.757 angle -66.869 A S_L = 3 middot