Question

Shunt inductor at receiving end of a transmission line is operated at 96% of its rated voltage and 104% of its rated frequency. The reactive power consumed by it (as compared to rated capacity) is
1. 11.4% low
2. 12.07% high
3. 4.2% low
4. 4.2% high

Answer 1

Correct Answer - Option 1 : 11.4% low

Concept:

Reactive power in a shunt inductor is given by,

\(Q = \frac{{{V^2}}}{{{X_L}}} = \frac{{{V^2}}}{{2\pi fL}}\)

\(\frac{{{Q_2}}}{{{Q_1}}} = {\left( {\frac{{{V_2}}}{{{V_1}}}} \right)^2} \times \left( {\frac{{{f_1}}}{{{f_2}}}} \right)\)

Calculation:

\({Q_2} = Q_{1}{\left[ {\frac{{0.96{V_1}}}{{{V_1}}}} \right]^2}\left[ {\frac{{{f_1}}}{{1.04{f_1}}}} \right]\)

= 0.886Q₁ = 88.62 Q₁

Therefore, the reactive power consumed is 11.38% low.