Question

Consider a system with the one-line diagram shown in below figure. The three phase transformer name plate ratings are listed. The transformer reactances are given in percentage, (10% = 0.1 p.u.). The transmission line and load impedances are in actual ohms. The generator terminal voltage (magnitude) is 13.2 kV (line-line) then the load voltage is _________ kV.

• A. 58.93

Answer 1

The correct option is A 58.93

Let, $S_{base}=10MVA$

$V_{base}=13.8kV$

Base impedance at section-3,

$Z_{3base}=\frac{(69\times {10}^3{)}^2}{10\times {10}^6}=476.1\Omega$

$Z_{load}=\frac{300}{476.1}=0.63p.u.$

Base impedance at section-2,

$Z_{2base}=\frac{(138\times {10}^3{)}^2}{10\times {10}^6}=1904.4\Omega$

$Z_{line}=\frac{j100}{1904.4}=j0.0525p.u.$

$X_{t1new}=0.1\times {\left(\frac{132}{138}\right)}^2\times \frac{10}{5}=0.183p.u.$

$X_{t2}=0.08p.u.$

$E_v=\frac{13.2}{13.8}=0.956p.u.$



$V_L=0.956\times \frac{0.63}{j(0.183+0.0525+0.08)+0.63}$

$V_L(p.u)=0.956\times \frac{0.63}{\sqrt{(0.3155{)}^2+(0.63{)}^2}}=0.854$

Voltage at load = $V_{L(p.u.)}\times V_{L\left(base\right)}$

= 0.854 $\times$ 69 kV

= 58.926 kV