Question

A three phase induction Motor delivers an output of 15 h.p. at 83 % efficiency. The motor is d (delta) connected and is supplied by 440 V, three phase, 50 Hz supply. Line current drawn by motor is 22.36 Amp. What is motor power factor ? It is now decided to improve the power factor to 0.95 lag by connecting three similar capacitors in delta across the supply terminals. Determine the value of the capacitance of each capacitor. 

[Note : 1 h.p. = 745 watts]

Answer 1

Power factor = (15 x 745)/(0.83 x 1.732 x 440 x 22.36) = 0.79,  Lagging

φ = cos⁻¹ 0.79 = 37.8º I₁ = I_ph = 22.36/1.732 = 12.91 amp 

Active Current I_a = I₁ cos φ₁ = 12.91 × 0.79 = 10.2 amp

New Power-factor cos φ₂ = 0.95, φ₂ = 18.2º 

I₂ = 10.2/0.95 = 10.74 amp 

Capacitive current per phase = I₁ sin φ₁ − Ι₂sin φ₂ = 4.563 

Capacitive reactance per phase = 440/4.563 = 96.43 ohms 

Capacitance per phase = 33 μf 

These have to be delta-connected