Active & reactive power
The key idea
Active power (P) does the work. Reactive power (Q) does no work — it moves back and forth to keep the voltage up. Apparent power (S) is what the network must actually carry, and it is bigger than the work alone.
The idea
On an AC network, power comes in two kinds.
Active power, P, in watts (W, kW, MW). This is the power that becomes something: motion, heat, light. It flows one way — from generation to load — and it is what the customer is billed for.
Reactive power, Q, in vars (var, kvar, Mvar). Motors, transformers and long cables build magnetic and electric fields to operate. The energy in those fields is not consumed — it sloshes back and forth between the source and the load, twice every cycle. That sloshing is reactive power. It does no net work, but the current that carries it is real current, in real conductors.
Apparent power, S, in volt-amperes (VA, kVA, MVA). The two kinds add at a right angle — S = √(P² + Q²) — and S is the total the equipment must be rated for.
The power factor is the ratio P/S: how much of what the network carries is doing work. A power factor of 1.0 means all of it. A power factor of 0.7 means the conductors carry 43% more current than the work alone would need.
Try it
The load below does the same 100 kW of work the whole time. Lower the power factor and watch what the network must carry.
To deliver 100 kW at this power factor, the network must carry 118 kVA. The extra 18 kVA does no work — but the cables and transformers must be sized for it.
Why it matters
- Equipment is sized by S, not by P. A transformer rating is in kVA. Poor power factor eats rating that could have served real load.
- Q is what holds the voltage up. Where reactive power runs short, voltage sags. That is why a generator "runs out" of voltage control when it hits its Q limit, and why capacitor banks — which supply Q locally — raise voltage.
- Losses follow current, not work. Line losses are I²R. The extra current that carries Q produces extra heat in every conductor on the way.
The math, if you want it
With RMS voltage V, RMS current I, and the angle φ between them: P = V·I·cos φ, Q = V·I·sin φ, S = V·I, and S² = P² + Q². The power factor is cos φ = P/S. In complex form, S = V · I* = P + jQ: reactive power is the imaginary part, which is precisely the "at a right angle" in the triangle. Inductive loads take Q (lagging, Q > 0); capacitive loads supply it (leading, Q < 0).
See it in Phasor
In Phasor you enter each load as P and Q (or P and power factor), and the power flow reports P, Q and loading for every branch — so you can see exactly where reactive power is coming from, and which feeders are carrying foam.