Power factor and why keep it high

Power factor (cos φ) is the cosine of the angle between voltage and current. It equals the ratio of true power to apparent power, P/S = kW/kVA. It shows what fraction of the supplied kVA does useful work.

Why it should be as high as possible

For a given load power P at voltage V, the current is I = P/(V cos φ). At a low power factor the supply must also carry an extra "wattless" (reactive) current that only flows back and forth and does no useful work.

• Large current for the same power. I = P/(V cos φ) for single phase, or P/(√3 V_L cos φ) for three phase. A low cos φ means a larger current.
• Higher copper loss. Loss = I²R rises as 1/cos²φ in the cables, transformers and generator windings.
• Poor voltage regulation. The large current causes a bigger voltage drop (IR and IX) in lines and transformers, so the load voltage falls.
• Larger equipment size and cost. Generators, transformers, switchgear and cables must be rated in kVA, not kW, so they are bigger and costlier for the same useful power.
• Reduced capacity. The same kVA rating delivers less kW (kW = kVA × cos φ), so a plant cannot supply as many loads.
• Lower efficiency and heavier tariff. Utilities usually charge a penalty on low power factor (below about 0.8 to 0.9).

Example

A 10 kW single-phase load at 400 V needs:

• at cos φ = 1: I = 10000/400 = 25 A
• at cos φ = 0.5: I = 10000/(400 × 0.5) = 50 A, so twice the current and four times the line loss.

Hence power companies require industrial consumers to keep the power factor high (typically above about 0.85 to 0.9), usually by fitting capacitor banks near the load.