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GATE 2018 EE – Question 16

Power Systems · Basic concepts of electrical power generation, AC and DC transmission concepts, Models and performance of transmission lines and cables · 1 mark · Multiple choice

Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be

  1. greater than $\left|\frac{V_1V_2}{X}\right|$
  2. less than $\left|\frac{V_1V_2}{X}\right|$
  3. equal to $\left|\frac{V_1V_2}{X}\right|$
  4. equal to $\left|\frac{V_1V_2}{Z}\right|$

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Correct answer: (B) less than $\left|\frac{V_1V_2}{X}\right|$

Explanation

For a lossy line the maximum power transferred at the receiving end is $\frac{|V_1V_2|}{|Z|}-\frac{|V_2|^2R}{|Z|^2}$, which is less than $\frac{|V_1V_2|}{X}$ because $|Z|>X$ and the resistance dissipates power.