Real, reactive & apparent power
About this app
Power triangle with apparent power S = U·I, real power P = U·I·cosφ and reactive power Q = U·I·sinφ; phase angle via slider, curves u(t), i(t), p(t) and reactive-power compensation via a switchable capacitor.
Three kinds of power
In AC circuits voltage and current are often shifted by an angle φ. Apparent power S = U·I (in VA) is the product of the RMS values. Only real power P = U·I·cos φ (in W) is converted into work or heat. Reactive power Q = U·I·sin φ (in var) oscillates between the source and the fields of inductors or capacitors. On average it does no work, but it still loads the cables. The three form a right triangle: S² = P² + Q². The power factor is cos φ.
What the app shows
Three boards sit side by side: the instantaneous values u(t), i(t) and p(t) = u·i, the power triangle with S, P and Q, and a phasor diagram of U and I. Where p(t) turns negative, energy flows back to the source. A values panel shows cos φ, S, P, Q, the effective angle and whether the load is inductive, capacitive or purely resistive.
Things to try
Set a phase angle between −85° and +85° and watch the triangle steepen while p(t) dips below zero more often. Choose an inductive load with positive φ, as with a motor. Then switch on the compensation capacitor and raise the compensation level: reactive power falls, φ approaches zero, cos φ rises and the triangle flattens, while P stays the same.
Frequently asked questions
- What is the difference between real and reactive power?
- Real power P is actually converted into work, heat or light and is measured in watts. Reactive power Q oscillates between the grid and the magnetic or electric fields of the load and is measured in var. It does no work on average but causes currents and therefore losses in the lines.
- What does the power factor cos φ mean?
- The power factor cos φ is the ratio of real power to apparent power, P/S. It is 1 for a purely resistive load and lower for motors and other inductive loads. A low power factor means a lot of current for little useful power.
- How does power factor correction work?
- Inductive loads such as motors draw inductive reactive power. A capacitor connected in parallel supplies capacitive reactive power that offsets it fully or partly. This lowers the phase angle and the current drawn from the grid, while the real power stays the same.
- What can I adjust in the power triangle app?
- You set phase angle, voltage and current and can add a compensation capacitor with an adjustable compensation level. The app shows the curves u(t), i(t) and p(t), the power triangle, the phasor diagram and the values S, P, Q and cos φ.
Subject: Electrical engineering fundamentals
More from Electrical engineering fundamentals
- Diode & rectifier
- Three-phase power
- Electric field & Coulomb
- Electromagnetic induction
- Kirchhoff's laws
- Capacitor & RC circuit
- Magnetic field & Lorentz force
- Ohm's law
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