Question

A power system shown below has following specifications of components:
$G_1:$ 22 kV, 20 MVA, X = 5%
$G_2:$ 22 kV, 20 MVA, X= 5%
$T_1:$ 22 kV/100 kV, 18 MVA, X = 10%
$T_2=$ 100 kV/22kV, 18 MVA, X = 10%
$T_{x-line}:=$ 110 kV, X = 90 $\Omega$



If the base voltage of 22 kV of $G_1$ as is taken as base voltage and 40 MVA as base MVA, the corresponding impedance diagram will be(in pu).

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

We know, $Z_{pu}=Z_{act}\times \frac{MV{A}_{base}}{k{V}_{base}^2}$

For generators $G_1$ and $G_{2^{\prime }}$ base voltage remains same but MVA doubled to 40 MVA and $Z_{pu}=0.5$ pu.

$\therefore Z_{punuw}=Z_{puold}\times \frac{MV{A}_{new}}{MV{A}_{old}}\times {\left(\frac{k{V}_{old}}{k{V}_{new}}\right)}^2$

$=0.05\times \frac{40}{20}(1{)}^2=0.10or10\%$

For transformers base voltage is same and per unit value is given as 10% or 0.10 pu.

$\therefore$ $X_{pubase}=0.10pu\times \frac{40}{18}=0.22$ pu

For transmission line, hv side voltage will be base value,

$Z_{pu}=Z_{act}\times \frac{MV{A}_{base}}{(k{V}_{base}{)}^2}=90\times \frac{40}{(100{)}^2}=0.36pu$