What’s the Difference Between PF and cosφ?

In many industrial and commercial power systems, engineers often encounter a puzzling scenario: despite installing sufficient capacitor banks or Static Var compensators (SVCs) to offset reactive power (kVAR), the measured Power Factor (PF) still fails to meet utility requirements (e.g., below 0.9). This frustration frequently stems from a critical but overlooked distinction—the difference between Displacement Power Factor (cosφ) and True Power Factor (PF).

1. What Is Power Factor (PF)?
Power Factor (PF) is an important parameter that describes how efficiently electrical power is being used. It is defined as:

PF = P / S

Where:
- P: Active power (kW), the real power consumed by equipment to perform work
- S: Apparent power (kVA), the total power supplied, a product of voltage and current

A PF of 1 is ideal, meaning all current contributes to useful work.

2. What is cosφ?
cosφ refers to the cosine of the phase angle (φ) between the voltage and the fundamental component of the current:

cosφ = P₁ / S₁ = Fundamental active power / Fundamental apparent power

In ideal sinusoidal systems without harmonics, PF = cosφ.

 Why Are PF and cosφ Sometimes Different?

In the presence of harmonics, PF and cosφ differ due to:
- cosφ only considering the fundamental components
- PF accounting for all components, including harmonic currents

The real formula becomes:

PF = P / √(P² + Q² + D²)

Where D is the distortion power from harmonics. Thus, even if cosφ is high (e.g., >0.96), PF can still be low (e.g., 0.9) if harmonics are severe. Like below.

 How to Improve PF in the Presence of Harmonics?

In modern electrical systems with non-linear loads (VFDs, UPS, LED lighting, etc.), improving PF requires handling both reactive power and harmonics.

ASVG or AHF will be a good solution for loads with significant harmonic distortion (e.g., multiple VFDs, data centers, production lines).

For more information, please contact david@yt-electric.com