Please solve Thank you For the given transformer model Use t

Please solve. Thank you!

For the given transformer model: Use the reduced model (ignore Rc and Xm) to determine the voltage and current at the primary. How accurate is the reduced model?

Solution

Ans)

   Turns ration N=100/1=100

Primary current Ip and secondary current be Is

Ip=Is/N² =(200-j100)/100²=(0.02-j0.01) A

Load Voltage VL= Is*ZL=(200-j100)*(400+j0)=80000-j40000 V

Transformer secondary Voltage Vs=VL+Is(0.04+j0.1)=80018-j39984 V by KVL on secondary side

Transformer Primary Voltage Vp=Vs*N=8001800-j3998400 V

Neglecting shunt branch

Primary source voltage Vs=Vp+Ip*(0.4+j0.2)=8001800.01-j3998400 V

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Now without neglecting the shunt branch

Ip\'=Ip+Ish where Ish is shunt branch current

Ish=(Vp/22000 )+(Vp/j16000)=113.82-j681.56 A

Ip\'=113.84-j681.57 A (Primary current without neglecting shunt branch)

Primary source voltage Vs=Vp+Ip\' *(0.4+j0.2)=8001981.85-j3998649.86 V

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Magnitude of Vs in both cases for comparison

Vs1=8945166.626 V

Vs2=8945440.975 V

(Vs2-Vs1)/Vs1 *100 = 0.003 almost zero (Voltage change as percentage)

so the circuit is 100% accurate or close to 99.997%