Calculate the power factor of an AC circuit from real and apparent power, from real and reactive power, or from the phase angle.
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Power factor in AC circuits measures how effectively electrical power is being used, and it's calculated as the ratio of "real power" (in watts, the power that produces actual work) to "apparent power" (in volt-amperes, the product of RMS voltage and RMS current). It can also be calculated from "reactive power" (in VAR), which results from inductive or capacitive elements in the load, using the relationship PF = P ÷ √(P² + Q²), or directly from the phase angle between voltage and current (PF = cos θ). Power factor ranges between 0 and 1; the closer it is to 1, the more efficient the energy use, and many electric utility companies impose financial penalties on industrial facilities whose power factor falls below a certain threshold (usually 0.8 or 0.9), since a low power factor forces the utility's generation and distribution equipment to supply more current than the real, useful work being done would otherwise require.
A power factor below 1 means a facility is drawing more current from the electrical grid than the actual useful work it's performing would strictly require — the 'extra' current, associated with reactive power, doesn't do useful work itself but still has to be generated, transmitted, and delivered by utility infrastructure, which is exactly why utilities care enough about power factor to penalize facilities with poor values.
Reactive power arises specifically from inductive loads (motors, transformers) and capacitive loads that don't consume energy the way a resistive load does, but instead store and release energy cyclically as the AC voltage and current oscillate — the current associated with this back-and-forth energy exchange still flows through wires and equipment, generating real heating losses and consuming real generation and transmission capacity, even though it doesn't perform useful mechanical or thermal work at the end device.
Industrial facilities with large numbers of electric motors — factories, pumping stations, HVAC systems — are particularly prone to low power factor, since motors are significantly inductive loads. A facility running numerous motors without correction can easily see power factor drop to 0.7 or lower, meaning the current drawn is considerably larger than the current that would be needed if all that power were doing useful work at unity power factor.
Utilities penalize this because low power factor forces their generation, transformer, and distribution equipment to be sized larger than the facility's actual real power consumption would require, in order to handle the additional current associated with reactive power — infrastructure costs that the utility ultimately passes back to the offending customer through power factor penalty charges rather than spreading across the entire customer base.
The standard engineering solution is power factor correction, most commonly achieved by adding capacitor banks to a facility's electrical system. Since capacitive and inductive reactive power have opposite phase relationships, adding the right amount of capacitive reactive power can substantially cancel out the inductive reactive power from motors and similar equipment, pushing the facility's overall power factor back toward 1 and avoiding utility penalty charges, all without changing how the actual production equipment operates.
It means a larger portion of the current drawn from the supply isn't doing useful work, which increases losses in wiring and transformers and often triggers penalty charges from utility companies for commercial and industrial customers.
The most common method is adding power factor correction capacitors to offset inductive reactive power from motors and other inductive loads, bringing the power factor closer to 1.
In standard practical usage it's expressed as a value between 0 and 1 (sometimes labeled 'leading' or 'lagging' to indicate whether current leads or lags voltage), rather than as a negative number.