Question

For the single line diagram shown in below figure (all values are in p.u.), a series capacitance having reactance $X_c=-j0.05$ p.u. on system base is inserted in transmission line. Then for what value of $\delta$(in degrees), the real power flow through transmission line is 1 p.u.__________.

• A. 2.9

Answer 1

The correct option is A 2.9
Equivalent impedance of transmission line,
$Z_{eq}=0.1\angle {85}^o-j0.05$
$Z_{eq}=0.05\angle {80}^o$

Complex power flow through transmission line,

$S_{12}=V_1{I}_{12}^{\ast }$
$S_{12}=1\angle \delta {\left[\frac{1\angle \delta -1\angle 0^o}{0.05\angle {80}^o}\right]}^{\ast }$

=$20\angle \delta \left[1\angle \right({80}^o-\delta )-1\angle {80}^o]$
$S_{12}=20\angle {80}^o-20\angle ({80}^o+\delta )$

Real power flow through transmission line.

$P_{12}=20cos{80}^o-20cos({80}^o+\delta )$
$1=20cos{80}^o-20cos({80}^o+\delta )$

$\delta =co{s}^{-1}\left[\frac{20cos{80}^o-1}{20}\right]-{80}^o$

$\delta ={2.9}^o$