What is Power Factor: Improvement, Formula And Definition

What is Power Factor?

Power factor (PF) is the ratio of active power P, measured in watts or kilowatts, to apparent power S, measured in volt-amperes or kilovolt-amperes. It shows how much source and conductor capacity is required for the transferred active power. Its magnitude is from 0 to 1. Some meters use a signed value from -1 to 1 to identify power-flow direction or leading and lagging operation, so the sign convention must be stated.

Unity power factor means active power equals apparent power. With sinusoidal voltage and current, this also means zero phase displacement and zero net reactive power. For a distorted waveform, unity requires both zero displacement and no distortion current. Unity PF uses source current capacity fully for active power, but it does not by itself state the load’s energy-conversion efficiency.

Many installations operate below unity because motors, transformers and electronic loads draw reactive or harmonic current. Suitable power factor correction can reduce selected current components. The target is normally a specified value near unity rather than exact unity, because load variation and overcompensation can create leading PF or voltage problems.

The definitions of active, reactive and apparent power explain this ratio.

Power Defined: Instantaneous electrical power is voltage multiplied by current. Active power is its average over time and represents net electrical energy transferred per unit time.

Power Factor Clarified: True PF uses active power divided by the product of RMS voltage drop and RMS current for a single-phase load. Three-phase measurement requires the applicable total-power and apparent-power definition.

In ideal steady-state DC circuits supplied by constant voltage sources, ideal inductors have zero voltage and ideal capacitors have zero current. Real components still have winding resistance, dielectric leakage and other losses.

For a resistive DC load, electrical power becomes heat or another form of transferred energy. The voltage and current have constant polarity, and power is:

In AC circuits, inductors and capacitors contribute frequency-dependent reactance to impedance:

An ideal inductor stores and returns magnetic-field energy, while an ideal capacitor stores and returns electric-field energy. Practical components also dissipate power through resistance, dielectric loss and core loss. Their reactive behaviour can displace current relative to voltage.

For sinusoidal linear circuits containing a resistor, inductors and capacitors, source current can lead or lag source voltage. Nonlinear loads can also distort current, so a single phase angle does not describe their total PF.

The cosine of the fundamental voltage-current phase angle is displacement electrical power factor. It equals true PF only when the relevant waveforms are sinusoidal and the system definition is appropriate. True PF remains P/S and includes harmonic current.

Reactive elements exchange energy with the source during each cycle. The inductor uses a magnetic field, while a capacitor uses an electric field. Reactive power is therefore a signed rate of cyclic energy exchange, not a permanently stored fraction of apparent power.

The total power in this case is:

This quantity is apparent power, denoted by S and measured in volt-amperes. Active power P is the average net power transferred to the load, measured in watts.

For sinusoidal single-phase operation, P = VI cosφ in watts. For general waveforms, active power is the average of instantaneous voltage multiplied by instantaneous current.

Reactive power Q represents cyclic energy exchange associated with electric and magnetic fields. Motors and transformers need magnetising current, and power systems use reactive power to manage voltage. This current still loads conductors and equipment even though its average energy transfer over a cycle is zero.

For sinusoidal single-phase operation, Q = VI sinφ in var. Positive and negative signs distinguish inductive and capacitive operation under the chosen convention. A power triangle illustrates the relationship for sinusoidal conditions.

For sinusoidal operation, S² = P² + Q^2, and the electrical power factor is P/S. With harmonics or unbalance, additional non-active components mean this simple triangle is incomplete.

Power Factor Improvement

Power factor correction reduces reactive current, distortion current or both, depending on the equipment. Capacitors and synchronous condensers mainly correct displacement PF. Active filters and active-front-end converters can also reduce selected harmonics. Any design must use true PF and displacement PF correctly.

Reasons for power factor improvement include:

• For a sinusoidal single-phase load, P = VI cosφ. At fixed active power and voltage, improving lagging displacement PF reduces current. This can release capacity in correctly sized cables, transformers and switchgear. New conductor sizing must still satisfy ampacity, voltage-drop, fault and protection requirements.
• Higher current increases I²R loss and voltage drop in generators, transformers, cables and lines. Reducing upstream reactive current can reduce these losses and improve voltage regulation. Harmonic current requires separate mitigation because ordinary capacitors may not reduce it.
• For a specified kW load, higher PF reduces required kVA and can release existing equipment capacity. It does not change an installed machine’s nameplate kVA rating.

At the design stage, lower required kVA can reduce equipment size or defer an upgrade. Retrofitting correction equipment does not physically reduce existing machines.

The economic target depends on the utility tariff, load profile, losses, equipment capacity and correction-system cost. Exact unity can be unnecessary, and leading PF can be undesirable.

Methods of Power Factor Improvement

Three traditional methods for correcting lagging displacement power factor are:

• Capacitor Banks
• Synchronous Condensers
• Phase Advancers

Capacitor Banks

Many motors, transformers and magnetic loads draw lagging reactive current. Supplying part of that current locally reduces the fundamental phase displacement seen by the upstream source.

A shunt capacitor or switched bank supplies leading reactive power near the load, so less lagging reactive current flows through upstream conductors. Automatic banks add or remove steps as the load changes.

Capacitor banks improve displacement between fundamental voltage and current. Harmonic studies, discharge provisions, switching transients, resonance and overvoltage must be checked before installation.

Synchronous Condensers

A synchronous condenser is an unloaded three-phase synchronous machine operated to control reactive power and support system voltage.

Changing excitation lets the synchronous motor absorb or supply reactive power within its capability curve. An overexcited condenser supplies capacitive vars to a system with lagging loads.

From the network viewpoint, an overexcited synchronous condenser draws leading current and supplies reactive power. Unlike a static capacitor bank, it can provide continuously adjustable vars and rotating inertia, but it has mechanical, excitation and loss considerations.

Phase Advancers

A phase advancer is a legacy AC exciter used with a wound-rotor induction motor. It does not apply to a squirrel-cage rotor.

Mounted on the motor shaft and connected to slip rings, it supplies rotor excitation at slip frequency. This reduces the stator magnetising current needed for the air-gap flux.

With sufficient excitation it can make the stator current leading. Modern installations more often use capacitors, synchronous condensers or power-electronic compensation.

Power Factor Calculation

For a single-phase power factor calculation, measure true-RMS voltage with a voltmeter, true-RMS current with an ammeter and active power with a wattmeter. One power analyser is preferable because it samples voltage and current together and can report true PF, displacement PF and harmonics.

For sinusoidal single-phase operation, P = VI cosφ watts.

For any single-phase waveform, true PF = P/(V_rms I_rms). Use the meter’s total three-phase P and S for unbalanced or distorted three-phase systems.

For sinusoidal single-phase operation, Q = VI sinφ var. Do not infer Q from this phase-angle equation when harmonics make the waveforms nonsinusoidal.

For a lagging sinusoidal load, a local shunt capacitor can supply part of the required vars. Required correction is Qc = P(tanφ1 – tanφ2). Convert kvar to capacitance with the correct frequency, RMS voltage and single-phase, star or delta connection formula:

For the same load operating point, power factor improvement supplies some reactive power locally and reduces upstream reactive current. It does not remove the load’s magnetising requirement or automatically correct harmonic distortion. Verify target PF, load variation, harmonic resonance, switching duty, discharge time and protection before selecting equipment.