A 132 kV singlephase generator supplies power to two loads t

A 13.2 kV single-phase generator supplies power to two loads through a transmission hoe as shown. If the generator is directly connected to the loads via the transmission line as in Figure 1. what is the ratio of the magnitudes of load voltage to the generated voltage |V_load/V_GEN|? what is the current phasor (magnitude and phase) supplied from the generator? what are the current phasors (magnitude and phase) flowing through each load? what are the transmission losses of the system? what is the total active (real) power and reactive power are absorbed by the loads If a 1:10 step-up transformer (T_1) is placed at the output of the generator and a 10:1 transformer (T_2) is placed at the load end of the transmission line as in Figure 2, what is the new ratio of the load voltage to the generator voltage? what is the current phasor (magnitude and phase)in the transmission line? what is the current phasor (magnitude and phase) m the generator? what are the transmission losses of the system now? What do you notice about the load voltage when you compare your answer from a) part i) with b) part i)? Explain your answer What do you notice about the transmission line losses when you compare your answer from a) part iv) with b) part iv)? What is the percentage change m transmission Iine losses and explain why it has changed?

Solution

i) total impedance=60<53.1+[(600+j1000)*(500+j1200)]/[600+j1000+500+j1200]=(316+j597.07) ohms.

voltage drop across transmission line=[60<53.1*(13.2*1000)]/[316+j597.07]=1172.4<-9 volts.

load voltage=13.2*10^3-1172.4<-9=12043.4<0.872 volts.

vload/vgen=(12043.4<0.872)/(13.2*10^3)=0.912<0.872

ii) current phasor supplied from the generator=[13.2*1000]/[316+j597.07]=19.54<-62.1 amps.

iii) current through load1=[19.54<-62.1*(500+j1200)]/[600+j1000+500+j1200]=10.32<-58.15 amps.

current through load2=19.54<-62.1-10.32<-58.15=9.27<-66.49 amps.

iv) transmission losses=(19.54<-62.1)^2*(60<53.1)=22908.6<-71.1 watts.

v) active power=12043.4*19.54*cos(62.972)=106939.14 watts.

reactive power=12043.4*19.54*sin(62.972)=209626.58 vars.