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PU Equivalent Circuits of 1-Phase Transformer & 3-Phase Balanced Transformer

For the power...

Question

For the power system shown below, specification of the components are as follows :

$G_{1} = 11 k V, 40 M V A, X = 5 %$
$T_{1} = \frac{11 k V}{33 k V}, 80 M V A, X = 10 % : T_{2} = \frac{33 k V}{11 k V}, 80 M V A, X = 10 %$

$M_{1} = 11 k V, 40 M V A X = 5 %$

$L i n e r e a c t a n c e X = 50 Ω$
$T h e r e a c t a n c e d i a g r a m o n b a s e M V A = 80 M V A i s$

A

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B

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C

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D

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Solution

The correct option is D
$W e k n o w t h a t, (Z_{p . u .})_{n e w} = (Z_{p . u .})_{o l d} \times \frac{(M V A)_{n e w}}{(M V A)_{o l d}} \times \frac{(k V)_{o l d}^{2}}{(k V)_{n e w}^{2}}$

$F o r G_{1} a n d M_{1} :$

$(X_{p . u .})_{n e w} = 0.05 \times \frac{80}{40} \times {(\frac{11}{11})}^{2} = j 0.1 p . u .$

For line :

$(X_{Ω})_{b a s e} = \frac{(k V)^{2}}{M V A} - = \frac{33^{2}}{80} = 13.6125 Ω$

$(X_{p . u .})_{l i n e} = \frac{A c t u a l v a l u e}{B a s e v a l u e} = \frac{50}{13.6125}$

$= j 3.673 p . u .$

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