Active, reactive, and apparent power

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In a simple alternating current (AC) circuit consisting of a source and a linear load, both the current and voltage are sinusoidal. If the load is purely resistive, the two quantities reverse their polarity at the same time. At every instant the product of voltage and current is positive or zero, with the result that the direction of energy flow does not reverse. In this case, only active power is transferred.

If the loads are purely reactive, then the voltage and current are 90 degrees out of phase. For half of each cycle, the product of voltage and current is positive, but on the other half of the cycle, the product is negative, indicating that on average, exactly as much energy flows toward the load as flows back. There is no net energy flow over one cycle. In this case, only reactive power flows—there is no net transfer of energy to the load.

Practical loads have resistance, inductance, and capacitance, so both active and reactive power will flow to real loads. Power engineers measure apparent power as the magnitude of the vector sum of active and reactive power. Apparent power is the product of the root-mean-square of voltage and current.

Electrical engineers take apparent power into account when designing and operating power systems, because though the current associated with reactive power does no work at the load, it heats the conductors and wastes energy. Conductors, transformers and generators must be sized to carry the total current, not just the current that does useful work. Failure to provide for the supply of sufficient reactive power in electrical grids can lead to lowered voltage levels and under certain operating conditions to the complete collapse of the network or blackout.

Another consequence is that adding the apparent power for two loads will not accurately give the total apparent power unless they have the same displacement between current and voltage (the same power factor).

Conventionally, capacitors are considered to generate reactive power and inductors to consume it. If a capacitor and an inductor are placed in parallel, then the currents flowing through the inductor and the capacitor tend to cancel rather than add. This is the fundamental mechanism for controlling the power factor in electric power transmission; capacitors (or inductors) are inserted in a circuit to partially compensate reactive power 'consumed' by the load. Purely capacitive circuits supply reactive power with the current waveform leading the voltage waveform by 90 degrees, while purely inductive circuits absorb reactive power with the current waveform lagging the voltage waveform by 90 degrees. The result of this is that capacitive and inductive circuit elements tend to cancel each other out.^[1]

Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to differentiate between them):

• Active power,^[2] P, or real power:^[3] watt (W)
• Reactive power, Q: volt-ampere reactive (var)
• Complex power, S: volt-ampere (VA)
• Apparent power, |S|: the magnitude of complex power S: volt-ampere (VA)
• Phase of voltage relative to current, φ: the angle of difference (in degrees) between current and voltage; current lagging voltage (quadrant I vector), current leading voltage (quadrant IV vector)

In the diagram, P is the active power, Q is the reactive power (in this case positive), S is the complex power and the length of S is the apparent power. Reactive power does not do any work, so it is represented as the imaginary axis of the vector diagram. Active power does do work, so it is the real axis.

The unit for all forms of power is the watt (symbol: W), but this unit is generally reserved for active power. Apparent power is conventionally expressed in volt-amperes (VA) since it is the product of rms voltage and rms current. The unit for reactive power is expressed as var, which stands for volt-ampere reactive. Since reactive power transfers no net energy to the load, it is sometimes called "wattless" power. It does, however, serve an important function in electrical grids and its lack has been cited as a significant factor in the Northeast Blackout of 2003.^[4]

Understanding the relationship among these three quantities lies at the heart of understanding power engineering. The mathematical relationship among them can be represented by vectors or expressed using complex numbers, S = P + jQ (where j is the imaginary unit).

The complex power is the vector sum of active and reactive power.

The apparent power is the magnitude of the complex power.
  Active power, P
  Reactive power, Q
  Complex power, S
  Apparent power, |S|
  Phase of current, φ