Electric Power Explained: Single-Phase, Three-Phase, Active, Reactive and Apparent Power

Understanding electric power means understanding more than watts. In AC circuits, voltage and current may be out of phase, so engineers distinguish between active power, reactive power and apparent power. These concepts help explain how electrical equipment uses energy, why power factor matters, and how utilities manage voltage.

Key terms

• Electric power is the rate at which electrical energy is transferred or converted.
• Active power (P) is the average power that performs useful work, such as producing heat, light or mechanical motion. It is measured in watts (W).
• Reactive power (Q) is power that moves back and forth between the source and the electric or magnetic fields of AC equipment. It is measured in volt-amperes reactive (var).
• Apparent power (S) combines active and reactive power and describes the overall voltage and current demand on equipment. It is measured in volt-amperes (VA).
• Power factor describes how effectively apparent power is converted into active power. For a sinusoidal system, it is the cosine of the phase angle between voltage and current.

Complex power and the power triangle

Single-phase AC power

Single-phase power is common in homes and small commercial installations. A single alternating voltage supplies the load.

Resistance, inductance and capacitance

• Resistance (R) opposes current and converts electrical energy into heat. In an ideal resistor, voltage and current are in phase.
• Inductance (L) stores and releases energy in a magnetic field. An ideal inductor causes current to lag voltage.
• Capacitance (C) stores and releases energy in an electric field. An ideal capacitor causes current to lead voltage.

For ideal components, a resistor consumes active power, while an inductor or capacitor exchanges reactive power with the source. Real-world components also have losses.

Instantaneous power

If voltage and current are sinusoidal,

Three-phase power

Three-phase systems use three AC voltages of the same frequency, separated by 120 electrical degrees. They are widely used in power generation, transmission and industrial equipment because they can deliver power smoothly and efficiently to balanced loads.

These formulas apply to balanced sinusoidal systems. For unbalanced systems or distorted waveforms, use phase-by-phase calculations or appropriate power measurement methods.

Why reactive power matters

Reactive power does not represent net energy converted into useful work over a complete AC cycle, but it is essential to the operation of many electrical systems. Motors and transformers need magnetic fields to operate, and those fields require reactive power.

Reactive power also affects voltage. If reactive demand is high and local support is insufficient, voltage can fall. If capacitive support is excessive for the load, voltage can rise. Grid operators manage this balance to help keep voltage within operating limits. The U.S. Department of Energy describes voltage support as injecting or absorbing reactive power to maintain transmission-system voltages within required ranges. U.S. Department of Energy: Voltage Control

Power factor correction and reactive power compensation

A low power factor means more current is needed to supply a given amount of active power. Higher current can increase losses and use more of the capacity of cables, transformers and other equipment.

Common voltage-support and compensation equipment includes:

• Capacitor banks, which supply reactive power to inductive loads.
• Shunt reactors, which absorb excess reactive power, often under light-load conditions.
• Synchronous condensers, which can generate or absorb reactive power as operating conditions change.
• Static VAR compensators and other power-electronic devices, which provide adjustable reactive support.
• Transformer tap changers, which adjust voltage by changing the transformer ratio.

where \(Q_c\) is the capacitive reactive power supplied, in var, when the correction improves the power factor. Compensation should be sized for the actual installation and operating conditions; overcompensation can create voltage and power-quality problems.

Summary

Active power performs useful work; reactive power supports the electric and magnetic fields needed by AC equipment; and apparent power represents the combined demand on the electrical system. Knowing how these quantities relate helps engineers select equipment, assess power factor, and maintain reliable voltage in single-phase circuits, three-phase installations and power networks.