Question

A balanced delta connected load of \( (8 + j6) \Omega \) per phase is connected to a 400 V, 50 Hz, three-phase supply lines. If the input power factor is to be improved to 0.9 by connecting a bank of star-connected capacitors, the required kVAR of the bank is _______.

• A. 42.7
• B. 10.2
• C. 28.8
• D. 38.4

Hint:

To improve PF, subtract new \( \tan(\theta) \) from old and multiply by P to get required kVAR.

Answer 1

The Correct Option is A

Step 1: Calculate original reactive power
Impedance per phase: \( Z = 8 + j6 \Rightarrow |Z| = 10 \Omega \)
Power factor = \( \cos(\theta) = 8/10 = 0.8 \)
Total apparent power: \[ S = \sqrt{3} \cdot V_L \cdot I_L \] But we directly find reactive power using: \[ Q = P \cdot \tan(\cos^{-1}(0.8)) \approx P \cdot 0.75 \] Where \( P = \text{Active Power} \)
Step 2: Desired power factor = 0.9
\[ \tan(\cos^{-1}(0.9)) \approx 0.484 \] Step 3: Capacitive kVAR needed
\[ Q_{c} = P(\tan(\theta_{old}) - \tan(\theta_{new}))
Q_{c} = P (0.75 - 0.484) = 400 \cdot 0.266 = 42.7 \text{ kVAR} \]