Question

5. Assuming that the voltage across the 40kW and 50kW loads has an angle of O degrees, please determine the following, using RMS values for each and assuming that the frequency is 60Hz. a) What is the real power, reactive power, and current phasor supplied by the source vs(t)1? b) Provide a phasor in RMS for the source vs(t) as well as a time-domain expression. c) Determine the total capacitance that must be placed in parallel with the two loads to force the combination to operate with unity power factor. What is the current phasor provided by the source in this case? Use your answers from part a and c to explain why would a utility provider desires its customers to correct power factor? d)

Answer 1

Voltage across the 40kW and 50kW loads has an angle of 0 degrees frequency frequency = 60 mu z Assuming that the voltage across the 40kW of 50kW loads has an angle 0 degree I_1 = I_L_1 - I_L_2 I_L_1 = (P/V cos 0)[cos^-1 (0.8) (40 times 10^3/220 times 0.8) I_L_1 = 227.2727 L-36.86 degree I_L_2 = 50 times 10^3/220 times 0.77 L-cos^-1 (0.77) = 295.16 L-39.64 degree I_2 = I_L_1 + I_L_2 = 522.282 L-38.43 degree E_2 = V_2 + I_2 (0.08 + j(2 pi times 60 times 500 times 10^-6) = 318.06 notequalto L9.25 degree I_L rightwardsdoublearrow -N_2 I_2/N_1 rightwardsdoublearrow -4I_2 = 2089.128 L141.57 degree \r\n V_s(t) = -E_2/4 + I_1 (0.01 + j(2 pi times 60 times 58 times 10^-6) V_s(t) = 123.197 L-165.59 degree times 0^- M_5 a) Real power = V_s I_s cos (V_s, I_s) = 155.465 kW I_S = I_1 = 2089.128 Amps V_s I_s sin (V_3 I_3) rightwardsdoublearrow 205.115 KV theta R b) c) Load Reactive power