Real, Reactive and Apparent Power

With a phase shift, the product of voltage and current goes negative for part of every cycle — energy flowing back out of the load into the source. So average power is not the product of peaks, and the gap between them is the whole topic.

Real power P, watts

The average. Converted to heat, light or motion and never returned. P = VI·cos φ.

Reactive power Q, VAr

Sloshes into a field and back twice per cycle. Net transfer zero. Q = VI·sin φ.

Apparent power S, VA

What the current actually is. S = VI = √(P² + Q²). Every conductor and transformer is sized for this.

Power factor

P/S = cos φ. The fraction of the current doing useful work.

Copper cannot tell reactive current from real: it heats cables, loads transformers and drops voltage identically. Everything in the delivery system is sized for S, while the customer only benefits from P.

Energy meters measure real power, so reactive power delivers nothing the customer pays for — while costing the utility conductors, transformer capacity and I²R losses. Industrial tariffs therefore add a power-factor penalty or bill in kVA, which makes correction pay for itself in months. Domestic customers are not billed for it, because the aggregate is small and metering costs more than it recovers.

Inductive and capacitive reactive powers have opposite signs, so a capacitor bank supplies exactly what an inductive load demands. The reactive current then circulates locally between the two instead of travelling from the generator. Motors, transformers and fluorescent ballasts are all inductive, which is why the correction is always capacitive.

Do not over-correct. Past unity the power factor becomes leading and the line current rises again, and excess capacitance on a lightly loaded line pushes the voltage above nominal. That is why banks are switched in steps as load varies.

cos φ assumes sinusoidal current. A rectifier with a smoothing capacitor draws narrow spikes rich in harmonics, giving a poor power factor that no capacitor bank can correct.

Harmonics overheat neutral conductors — third harmonics from three phases add rather than cancel — and can resonate with the correction capacitors themselves. Active power-factor correction, which shapes the input current to follow the voltage, is now mandatory above modest power levels.