Cos Phi (Displacement Power Factor)

In a purely sinusoidal AC system, power factor equals the cosine of the phase angle φ between voltage and current waveforms — hence cos φ. A purely resistive load has cos φ = 1.0 (voltage and current in phase), while a purely inductive load has cos φ = 0 (current lagging voltage by 90°). Most industrial loads — induction motors, transformers, fluorescent lighting — draw lagging current with typical cos φ values of 0.7–0.85. This displacement power factor differs from the true or total power factor, which also includes the distortion component caused by harmonic currents from non-linear loads like variable frequency drives and LED drivers. Capacitor banks improve cos φ by supplying leading reactive current that partially cancels the lagging reactive current drawn by inductive loads. The required capacitor rating in kVAr is calculated as Q = P × (tan φ₁ − tan φ₂), where φ₁ and φ₂ are the angles before and after correction. Over-correction (leading power factor) can cause voltage rise and resonance problems, so automatic power factor correction controllers switch capacitor stages to maintain cos φ between 0.95 and 0.98. Utilities typically require cos φ above 0.9 or 0.95 and impose penalties for lower values.