Glossary term

Reactive Power

The component of power in an AC circuit associated with energy alternately stored and returned by inductive and capacitive elements, performing no net work.

Branch: Electrical Engineering
Glossary type: quantity
Content: Glossary term
Updated: May 22, 2026
Revision: v0.2.0 · reviewed

Definition

quantity

Reactive power is the component of apparent power in an AC circuit that oscillates between the source and reactive elements — inductors and capacitors — without being converted into useful work or heat, representing energy temporarily stored in magnetic or electric fields.

In AC circuits, inductors and capacitors store energy during one half-cycle and return it during the next. This exchange of energy between source and reactive element produces a current component that is 90° out of phase with the voltage. Although reactive power does no net work — it performs no heating, drives no motors, produces no light — it still flows through conductors and transformers, increasing their current loading and therefore their resistive losses. Managing reactive power is essential for voltage regulation and efficient power system operation.

In an AC circuit with sinusoidal voltage $v(t) = V_\text{peak} \cos(\omega t)$ and current $i(t) = I_\text{peak} \cos(\omega t - \phi)$ , where $\phi$ is the phase angle between them, the instantaneous power is:

p(t) = v(t) \cdot i(t) = V_\text{rms} I_\text{rms} \cos\phi + V_\text{rms} I_\text{rms} \cos(2\omega t - \phi)

The first term is constant (the active power $P = V_\text{rms} I_\text{rms} \cos\phi$ ); the second term oscillates at twice the supply frequency. Expanding the oscillating term gives:

p(t)=P+P\cos(2\omega t)+Q\sin(2\omega t)

Reactive power is the quadrature component of complex power, not the total amplitude of the twice-frequency power oscillation:

Q = V_\text{rms} \cdot I_\text{rms} \cdot \sin\phi

The unit of reactive power is the volt-ampere reactive (VAR), distinguished from the watt to emphasise that reactive power does no net work. $Q$ is positive for inductive loads ( $\phi > 0$ , current lagging voltage) and negative for capacitive loads ( $\phi < 0$ , current leading voltage).

Physical origin

In an ideal inductor, voltage leads current by 90°. The inductor stores energy in its magnetic field during the first quarter cycle and returns it to the source during the second. In each full cycle, the net energy transferred is zero — but a current flows throughout. In an ideal capacitor, current leads voltage by 90°, and the same exchange occurs with electric field energy. The reactive power $Q$ quantifies the rate of this energy exchange — not the rate of dissipation, but the rate of temporary storage and retrieval.

In a purely resistive circuit, $\phi = 0$ and $Q = 0$ : all power is active. In a purely inductive or capacitive circuit, $\phi = \pm 90°$ and $P = 0$ : all power is reactive and no useful work is done.

Consequences in power systems

Although reactive power does no useful work, it is not without cost. Reactive current flows through all conductors, transformers, and switchgear in the network, contributing to the total current magnitude:

|I_\text{total}| = \sqrt{I_\text{active}^2 + I_\text{reactive}^2}

This increased current causes additional resistive ( $I^2 R$ ) losses and requires larger conductor and equipment ratings for a given active power delivery. Voltage regulation is also affected: reactive power flow along inductive transmission lines causes voltage drops, and reactive power injection (from capacitors or generators) is the primary tool for voltage support.

In power systems, generators can produce or absorb reactive power by adjusting their excitation. Capacitor banks and static VAR compensators (SVCs) inject reactive power locally. Flexible AC transmission systems (FACTS) devices provide dynamic reactive power control. The coordinated management of reactive power across a power grid is called reactive power dispatch, and it is solved simultaneously with active power dispatch to minimise losses and maintain voltages within specified limits.

Relationship to apparent power

Reactive power $Q$ , active power $P$ , and apparent power $S$ are related by the power triangle:

S^2 = P^2 + Q^2

This relation reflects the vector nature of complex power $\tilde{S} = P + jQ$ , where $j$ is the imaginary unit. The apparent power $S = |\tilde{S}|$ is the magnitude of complex power and represents the total current-voltage product without regard to phase. The power factor $\cos\phi = P/S$ measures the fraction of apparent power that is active.

Common mistakes

A common mistake is to say reactive power is “wasted power”. It does not perform net work, but it is often necessary to establish magnetic and electric fields in AC equipment. Another mistake is treating reactive compensation as a universal fix: capacitor banks, inverter VAR control, transformer taps, and network operating limits must be coordinated to avoid overvoltage, resonance, harmonic amplification, or poor dynamic response. A good review states sign convention, voltage level, load profile, harmonic distortion, equipment ratings, and whether the value is measured at the load, feeder, transformer, or grid interconnection.

REF

Disciplines

Reactive Power

Definition

See also