The GATE Grind

GATE 2018 EE – Question 40

Power Systems · System stability concepts, Equal area criterion · 2 marks · Multiple choice

The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P=1.4\sin\delta+0.15\sin2\delta$, where $\delta$ is the load angle. Newton-Raphson method is used to calculate the value of $\delta$ for $P=0.8$ pu. If the initial guess is $30^\circ$, then its value (in degree) at the end of the first iteration is

  1. $15^\circ$
  2. $28.48^\circ$
  3. $28.74^\circ$
  4. $31.20^\circ$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $28.74^\circ$

Explanation

Let $f(\delta)=1.4\sin\delta+0.15\sin2\delta-0.8$. At $30^\circ$, $f=0.7+0.1299-0.8=0.0299$ and $f'=1.4\cos30^\circ+0.3\cos60^\circ=1.3624$. The update is $\delta_1=30^\circ-\frac{0.0299}{1.3624}\text{ rad}=30^\circ-1.26^\circ=28.74^\circ$.