A Method of Finding Capacitor Value for Power Factor Improvement

In electrical power systems, power factor (PF) is the ratio of real power (measured in kilowatts, kW) to apparent power (measured in kilovolt-amperes, kVA). An inefficient power factortypically caused by inductive loads like motors, transformers, and fluorescent lightingresults in higher currents, increased energy losses, and potential utility penalties. Improving the power factor involves introducing capacitance to counteract the inductive reactance.

The Principle of Correction

Inductive loads draw lagging reactive power (measured in kVAR). By installing capacitors, which draw leading reactive power, we can compensate for the lagging reactive power demand. The goal is to bring the power factor closer to unity (1.0), thereby reducing the total apparent power drawn from the source.

The Step-by-Step Calculation Method

To determine the required capacitor bank size, one must follow a systematic approach based on the current load and the target power factor.

1. Determine Current Load Parameters

Identify the real power (P) in kW and the existing power factor (PF1). You can derive the existing apparent power (S1) and reactive power (Q1) using the following:

2. Define the Desired Power Factor

Determine the target power factor (PF2). Most industrial facilities aim for a power factor between 0.90 and 0.98. Calculate the required reactive power (Q2) at the new target:

3. Calculate the Required Capacitor Rating (QC)

The difference between the existing reactive power and the target reactive power represents the size of the capacitor bank (in kVAR) needed:

Where 1 is the angle of the current power factor (arccos(PF1)) and 2 is the angle of the target power factor (arccos(PF2)).

Practical Example

Consider a facility with a load of 100 kW operating at a power factor of 0.70 lagging. The management wishes to improve the power factor to 0.95.

• Angle 1 = arccos(0.70) 45.57 | tan(45.57) 1.02
• Angle 2 = arccos(0.95) 18.19 | tan(18.19) 0.33
• QC = 100 (1.02 - 0.33) = 69 kVAR

In this scenario, installing a capacitor bank rated at approximately 69 kVAR would be necessary to achieve the desired correction.

Considerations and Best Practices

When selecting and installing capacitors, consider the following technical factors:

• Voltage Ratings: Ensure the capacitor is rated for the line voltage. Operating a capacitor above its rated voltage significantly shortens its lifespan.
• Harmonics: High levels of harmonic distortion in a system can lead to resonance. If the system contains variable frequency drives (VFDs) or other non-linear loads, detuned reactors should be installed in series with the capacitors.
• Placement: Capacitors can be installed at the service entrance (global correction), at the distribution panel (group correction), or directly at the motor terminals (individual correction). Individual correction is the most efficient for large, steady loads as it reduces line current throughout the entire circuit.
• Safety: Always include discharge resistors. Capacitors store energy even after the power is disconnected, posing a shock hazard to maintenance personnel.

By accurately calculating the necessary reactive power compensation, facility managers can optimize their electrical infrastructure, lower operational costs, and improve the overall stability of the power distribution system.