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 \sin 2 \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

GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 55 of 65

Marks: +1, -0

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 δ+0.15 \sin 2 δ

, where

δ

is the load angle. Newton-Raphson method is used to calculate the value of

δ

for

P=0.8

pu. If the initial guess is

30^{∘}

, then its value (in degree) at the end of the first iteration is

Solution:

P(δ) \;\; =1.4 \sin δ+0.15 \sin 2 δ=0.8

=1.4 \sin δ+0.15 \sin 2 δ-0.8=0

P^{'}(δ)=\;{d}/{d δ}(p(δ))

=1.4 \cos δ+0.30 \cos 2 δ

Given,

δ_{0}=30^{∘}

By using Newton Raphson method

∆ δ=δ_{1}-δ_{0}=\;{f(δ_{0})}/{f^{'}(δ_{0})}=-\;{P(δ_{0})}/{P^{'}(δ_{0})}

δ_{1}-30^{∘} \;\; =\;{1.4 \sin 30^{∘}+0.15 \sin 60^{∘}-0.8}/{1.4 \cos 30^{∘}+0.3 \cos 60^{∘}}

δ_{1}-30^{∘} \;\; =-0.0219 {rad}=-1.26^{∘}

δ_{1} \;\; =28.74^{∘}

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