Power Factor Correction Equations
Power factor is the ratio of real power (kW) to apparent power (kVA). Correcting it requires installing capacitors that supply reactive power (kVAR), effectively reducing the total apparent power drawn from the grid.
Where:
- P = Real power in kW
- PF_i = Initial power factor
- PF_t = Target power factor
Frequently Asked Questions
The required capacitor bank size (kVAR) is calculated by taking the real power (kW) and multiplying it by the difference between the tangents of the initial and target power factor angles.
Power factor (PF) = Real Power (kW) / Apparent Power (kVA) = cos φ. It ranges from 0 to 1.0. A PF of 0.8 means only 80% of electrical energy drawn from the grid is doing useful work; 20% is reactive power cycling back and forth. Low PF forces electrical infrastructure (cables, transformers, switchgear) to be oversized to handle the extra current — costing money even though no useful work is done.
Low (lagging) power factor is caused by inductive loads that draw lagging reactive current: induction motors (especially when lightly loaded — PF can drop to 0.3–0.5 at no-load); transformers; fluorescent and HID lighting with magnetic ballasts; arc furnaces; and welding equipment. Most industrial facilities run at PF of 0.7–0.9 without correction.
Required capacitor bank size: Qc (kVAR) = P × (tan φ1 − tan φ2). Where P is load in kW, φ1 is the current power factor angle (arccos of existing PF), φ2 is the target power factor angle (arccos of target PF). Example: 100 kW load at 0.75 PF, target 0.95 PF: Qc = 100 × (tan 41.4° − tan 18.2°) = 100 × (0.882 − 0.329) = 55.3 kVAR.
Most utilities impose penalty tariffs when PF drops below 0.85 or 0.90. Penalties typically add 1–3% to the bill per 0.01 below the threshold. For example, operating at 0.75 PF instead of 0.90 could add 15–45% to electricity costs. Beyond billing, low PF causes: overloaded cables and transformers, increased I²R losses, voltage sag, and reduced available capacity in distribution equipment.
Displacement PF (DPF) = cos of the phase angle between fundamental voltage and current — the classic power factor measured by older instrumentation. True (total) PF also accounts for harmonic distortion: PF_true = DPF / √(1 + THD_I²). Variable speed drives (VFDs), UPS systems, and switch-mode power supplies generate significant current harmonics, making true PF lower than displacement PF. Modern power quality meters measure both.