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AC circuits are usually three-phase for electrical distribution and electrical transmission purposes. Single phase circuits are commonly used in our domestic supply system.

The total power of a three-phase AC circuit is equal to three times the single phase power.

So if the power in a single phase of a three-phase system is ‘P’, then the total power of the three-phase system would by 3P (provided the three-phase system is perfectly balanced).

But if the three-phase system is not exactly balanced, then the total power of the system would be the sum of the power of individual phases.

Suppose, in a three phase system, the power at R phase is PR , at Y phase is PY and at B phase is PB, then total power of the system would be

This is simple scalar sum, since power is a scalar quantity. This is the season, if we consider only single phase during calculating and analyzing of three phase power, it is enough.

Let us consider, network A is electrically connected with network B as shown in the figure below:

Let us consider the expression of the voltage waveform of a single phase system is:

Where V is the amplitude of the waveform, ω is the angular velocity of propagation of the wave.

Now, consider the current of the system is i(t) and this current has a phase difference from the voltage by an angle φ. That means current wave propagates with φ radiant lag in respect of the voltage. The voltage and current waveform can be represented graphically as shown below:

The current waveform in this case can be represented as:

Now, the expression of the instantaneous power,

[where Vrms and Irms is the root mean square value of voltage and current waveform]

Now, let us plot the term P versus time,

It is seen from the graph that, the term P does not have any negative value. So, it will have a nonzero average value. It is sinusoidal with a frequency twice of system frequency. Let us now plot second term of the power equation, i.e. Q.

This is purely sinusoidal and has a zero average value. So from of these two graphs, it is clear that P is the component of power in an AC circuit, which actually transported from network A to network B. This power is consumed in network B as electric power.

Q on the other hand does not really flow from network A to network B. Rather it oscillate between network A and B. This is also component of power, actually flowing into and out of the inductor, capacitor like energy storage elements of the network.

Here, P is known as the real or active part of the power and Q is known as imaginary or reactive part of the power.

Hence, P is called real power or active power, and Q is called imaginary or active power. The unit of active power is Watt, whereas the unit of reactive power is Voltage Ampere Reactive or VAR.