AC power
In an electric circuit, instantaneous power is the time rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductors and capacitors may result in periodic reversals of the direction of energy flow. Its SI unit is the watt.
This article is about power in AC systems. For information on utility-supplied AC power, see Mains electricity.The portion of instantaneous power that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as instantaneous active power, and its time average is known as active power or real power.[1]: 3 The portion of instantaneous power that results in no net transfer of energy but instead oscillates between the source and load in each cycle due to stored energy is known as instantaneous reactive power, and its amplitude is the absolute value of reactive power.[2][1]: 4
Phase of voltage relative to current, φ: the angle of difference (in degrees) between current and voltage; . Current lagging voltage ( I vector), current leading voltage (quadrant IV vector).
quadrant
In a simple alternating current (AC) circuit consisting of a source and a linear time-invariant load, both the current and voltage are sinusoidal at the same frequency.[3] If the load is purely resistive, the two quantities reverse their polarity at the same time. Hence, the instantaneous power, given by the product of voltage and current, is always positive, such that the direction of energy flow does not reverse and always is toward the resistor. In this case, only active power is transferred.
If the load is purely reactive, then the voltage and current are 90 degrees out of phase. For two quarters of each cycle, the product of voltage and current is positive, but for the other two quarters, the product is negative, indicating that on average, exactly as much energy flows into the load as flows back out. There is no net energy flow over each half cycle. In this case, only reactive power flows: There is no net transfer of energy to the load; however, electrical power does flow along the wires and returns by flowing in reverse along the same wires. The current required for this reactive power flow dissipates energy in the line resistance, even if the ideal load device consumes no energy itself. Practical loads have resistance as well as inductance, or capacitance, so both active and reactive powers will flow to normal loads.
Apparent power is the product of the RMS values of voltage and current. Apparent power is taken into account when designing and operating power systems, because although the current associated with reactive power does no work at the load, it still must be supplied by the power source. Conductors, transformers and generators must be sized to carry the total current, not just the current that does useful work. Insufficient reactive power can depress voltage levels on an electrical grid and, under certain operating conditions, collapse the network (a blackout). Another consequence is that adding the apparent power for two loads will not accurately give the total power unless they have the same phase difference between current and voltage (the same power factor).
Conventionally, capacitors are treated as if they generate reactive power, and inductors are treated as if they consume it. If a capacitor and an inductor are placed in parallel, then the currents flowing through the capacitor and the inductor 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 for reactive power 'consumed' ('generated') 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.[4]
Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to differentiate between them):
These are all denoted in the adjacent diagram (called a power triangle).
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 power is the watt (symbol: W). Apparent power is often expressed in volt-amperes (VA) since it is the product of RMS voltage and RMS current. The unit for reactive power is 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.[7] 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 + j Q (where j is the imaginary unit).