Question

Shunt capacitors are used to raise the power factor of the load of 100 kW from 0.8 lagging to unity. The supply is 3-$\varphi$, 50 Hz, 10 kV. If star capacitor bank is used, then the capacitance per phase required will be

• A. $0.81\mu F$
• B. $2.38\mu F$
• C. $7.15\mu F$
• D. $3.24\mu F$

Answer 1

The correct option is B $2.38\mu F$

Reactive power, Q = Active power $\times$ tan $\varphi$

$=100\times {10}^3\times tan\left(co{s}^{-1}0.8\right)$

$Q=75kVAR$

The capacitor bank should supply

$Q=75kVAR$

$Q_{ph}=\frac{75000}{3}=25kVAR$

$Q_{ph}=V_{ph}^2\omega C_{ph}$

$C_{ph}=\frac{Q_{ph}}{V_{ph}^2\times 2\pi f}$

$C_{ph}=\frac{25000}{{\left[\frac{10\times {10}^3}{\sqrt{3}}\right]}^2\times 2\pi \times 50}=2.38\times {10}^{-6}F$