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A generator which apparent power is \$120MVA\$,and voltage is \$19.5kV,X_s=1.5p.u.\$. Now it is connected a transformer then connected to a transmission line. The rated value transformer is \$150MVA,230Y/18 \Delta kV\$, if now the base of transmission is \$100MVA,230kV\$, then what is the new per-unit value of transformer?

The solution of this is \$X^{new}_s=1.5\times \frac{100}{120} \times (\frac{19.5}{18})^2\$

My question:

Why isn't \$X^{new}_s=1.5\times \frac{100}{120} \times (\frac{19.5}{230})^2\$?

Here is my thinking:

The per-unit value=\$\frac{X_{real}}{X_{base}}\$,so the real \$X_{real}=1.5*\frac{(19.5k)^2}{120M}\$,now \$X_{base}=\frac{(230k)^2}{100M}\$. So the per-unit value should become \$\frac{1.5*\frac{(19.5k)^2}{120M}}{\frac{(230k)^2}{100M}}=1.5\times \frac{100}{120} \times (\frac{19.5}{230})^2\$

Can anyone tell me where I am wrong?

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