Principle / circuitAdvanced

Real, apparent & reactive power (kW · kVA · kVAr)

Three different 'powers' on an AC system — what each one is, and why they don't simply add up.

φReal power (kW)Reactive(kVAr)Apparent (kVA)power factor = kW / kVA = cos φ
Power triangle — real power (kW) and reactive power (kVAr) combine at right angles to give apparent power (kVA)

Three powers, one load

On AC, an inductive load deals with two things at once: real power (kW) that does the actual work — turning the shaft, making heat, giving light — and reactive power (kVAr) that only shuttles energy in and out of magnetic fields without doing work.

The supply has to deliver both together. Their combination is the apparent power (kVA) — the product of the voltage and the total current actually flowing. It's what sizes cables, transformers and switchgear, because they carry the whole current, working or not.

The power triangle

Because the reactive part is 90° out of phase with the real part, they don't add arithmetically — they add as a right-angled triangle. Real power is the base, reactive power the upright, and apparent power the hypotenuse. Power factor is the ratio of the base to the hypotenuse.

That geometry is why correcting power factor (shortening the reactive upright) brings the apparent power down close to the real power — the supply ends up delivering nearer to just the working load.

Reading a nameplate

A motor rated in kW tells you its mechanical output; the kVA it draws from the supply is larger, set by its efficiency and power factor. Sizing the supply, protection and cable from kW alone undersizes them — the current comes from the kVA.

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