Calculating the Value of a Parallel Capacitor to Adjust Power Factor

How can we adjust the power factor of a system from 0.75 to 0.9 lagging?

Given that a plant consumes 60 kW at a power factor of 0.75 lagging from a 240-V rms 60-Hz line, what is the value of the capacitor needed to change the power factor to 0.9 lagging when placed in parallel with the load?

Answer:

The question is about calculating the value of a parallel capacitor to adjust a system's power factor from 0.75 to 0.9. The value of the capacitor needed is approximately 1.23 μF.

To adjust the power factor of a system from 0.75 to 0.9 lagging, we need to calculate the value of the capacitor that when placed in parallel with the load will introduce the required capacitive reactance. The initial power consumed by the load is given, and by determining the change in current after adding the capacitor, we can calculate the value of the capacitor needed to achieve the desired power factor adjustment.

The initial current consumed by the load with a power factor of 0.75 lagging is calculated using the formula P = VIcos(θ). By adding the capacitive reactance of the capacitor in parallel, the new current can be determined. The difference in currents will give us the reactive power supplied by the capacitor, which is needed to adjust the power factor.

Using the given system parameters, the capacitive reactance and the value of the capacitor in Farads can be calculated to achieve a power factor of 0.9 lagging. The final result is approximately 1.23 μF, indicating the required capacitance to adjust the power factor.