Active, Reactive and Apparent Power: Calculation and Differences

To understand your electricity bill and reactive penalties, you must distinguish three power concepts: active power, reactive power and apparent power. This article defines all three, shows how they relate and gives a practical calculation method.

The Three Powers: Active, Reactive, Apparent - **Active power (P, kW):** The power that does real work — producing heat, motion, light. This is the "useful" power billed on your meter. - **Reactive power (Q, kVAr):** Does no work; it is drawn so inductive loads like motors and transformers can build a magnetic field. It needlessly burdens the grid and, past a limit, causes a reactive penalty. - **Apparent power (S, kVA):** The vector sum of active and reactive power; the total load the grid and transformer must carry.

The Power Triangle and Formulas These three form a right triangle (the power triangle): - **S = √(P² + Q²)** — apparent power - **Q = √(S² − P²)** — reactive power - **P = S × cosφ** — active power (cosφ = power factor) - **Q = P × tanφ** — reactive power from active power

Here cosφ (power factor) is the ratio of active to apparent power (P/S) and shows how efficiently energy is used.

Practical Calculation Example Say a facility has active power P = 200 kW and power factor cosφ = 0.80: - Apparent power: S = P / cosφ = 200 / 0.80 = **250 kVA** - φ = arccos(0.80) = 36.87° → tanφ = 0.75 - Reactive power: Q = P × tanφ = 200 × 0.75 = **150 kVAr**

So while doing 200 kW of useful work, the facility also draws 150 kVAr of reactive power — potentially enough to trigger a penalty.

Reactive Energy and the Penalty Under Turkish regulation, inductive reactive energy may not exceed 20% of active energy and capacitive 15%. A low-power-factor facility like the one above raises cosφ to 0.98 with compensation, sharply cutting reactive power and avoiding the penalty. Use the compensation tool to size the required capacitor kVAr.

Monitor the Powers in Real Time with SolarTools SolarTools reads active, reactive and apparent power plus power factor from energy analyzers in real time; it shows how much reactive power each line draws and warns as you approach the penalty limit. So instead of calculating once and forgetting, you keep the power balance continuously under control.