Question

The relation between the voltage-phase angle & and the impedance angle , for the steady-state stability limit of a loss-less transmission line is,

(a) delta = theta_{z}/2

(b) 8=0,

(c) delta = 2theta_{x}

(d) delta = theta_{z}/4​

Answer 1

Answer: (d) delta = theta_{z}/4​

Answer 2

Given,

The relation between the voltage-phase angle & and the impedance angle , for the steady-state stability limit of a loss-less transmission line is,

(a) delta = theta_{z}/2

(b) 8=0,

(c) delta = 2theta_{x}

(d) delta = theta_{z}/4​

Solution,

The power transferred by the line,

$\[ = \frac{{{V_s}{V_R}}}{{{X_l}}}\sin \delta \]$

where,

$\[{{V_s=}}\]$Sending end voltage

$\[{{V_R}}\]$=Receiving end voltage

$\[{{X_l}}\]$=Line reactance

$\[\delta \]$=Power angle

The angle of the line

$\[\begin{array}{l} = R + jX\\ = \left| Z \right|\angle \theta \end{array}\]$

Therefore, in order for the maximum steady state stabilty limit of loss-less transimission line is

$\[ \Rightarrow \theta = \frac{\delta }{2}\]$

Hence, the correct option is $\[\theta = \frac{\delta }{2}.\]$