Question

How to calculate capacitor bank value to maintain unity power factor with some suitable example?

Answer 1

To calculate the capacitor bank value required to maintain a unity power factor (i.e., a power factor of 1) for a load, we need to correct the lagging power factor of the system by adding capacitive reactive power (which leads the current) to counteract the inductive reactive power (which lags the current).

Here’s the step-by-step process to calculate the required capacitor bank value:

Step 1: Find the Total Reactive Power of the Load (Q)

First, determine the total reactive power (Q) of the system. This can be calculated using the formula:

\[
Q = P \times (\tan(\cos^{-1}(pf)))
\]

Where:

1. P = Active power (in watts)
   

1. pf = Power factor of the load (less than 1 for a lagging power factor)
   

1. \(\tan(\cos^{-1}(pf))\) gives the reactive power in terms of active power.
   

Step 2: Find the Capacitive Reactive Power (Qc) Needed

Once you have the total reactive power \(Q\) from Step 1, the required capacitive reactive power \(Qc\) to maintain a unity power factor will be equal to the reactive power that the load consumes (but with a negative sign since capacitors provide reactive power in the opposite direction to inductive loads).

So, to compensate for the inductive reactive power, the value of the capacitor bank \(Qc\) will be:

\[
Qc = Q
\]

Example:

Let’s consider an example where:

1. The active power (P) of the load is 50 kW.
   

1. The current power factor (pf) of the system is 0.8 lagging.
   

Step 1: Calculate Reactive Power (Q) of the Load

Using the formula:

\[
Q = P \times \tan(\cos^{-1}(pf))
\]

Substitute the values:

\[
Q = 50 \, \text{kW} \times \tan(\cos^{-1}(0.8))
\]

\[
Q = 50 \times \tan(36.87^\circ)
\]

\[
Q = 50 \times 0.75
\]

\[
Q = 37.5 \, \text{kVAR}
\]

So, the reactive power of the load is 37.5 kVAR.

Step 2: Calculate the Capacitor Bank Value

To correct the power factor to unity, we need to add a capacitive reactive power \(Qc\) of 37.5 kVAR.

Thus, the required capacitor bank size is 37.5 kVAR.

This will correct the power factor from 0.8 lagging to 1 (unity).

Conclusion:

To maintain a unity power factor (1) with a 50 kW load having a 0.8 lagging power factor, you need to install a capacitor bank of 37.5 kVAR. This will offset the reactive power consumed by the load, bringing the system’s power factor to unity.