# What is meant by average power in AC circuits?

I read that "The average power is the power averaged over a cycle or number of cycles."

I know that the average value of power for both active and reactive power is a constant number.

Buy I am confused that whether the cycle here means the complete cycles or cycles?

If power is averageed not "over a cycle or number of cycles" but supposes it is averaged over a quatter of cycle or two third of a cycle, will we get the same exact constant for the average power which we get for the average power over a complete cycle or cycles?

## 4 Answers

Actually we consider only complete cycles. If you consider half or quarter of cycle then the power that you obtain will be different. Consider a sinusoidal power wave its average for one complete cycle is either a constant or zero but will have different values depending upon the quarter cycle or portion of cycle you take.

Look at these various scenarios for the power waveform obtained when various phase angles are involved: -

The power waveform resulting from the multiplication of voltage and current sine waveforms is at twice the frequency of either voltage or current and is also sinusoidal.

Because it's at twice the frequency, if you averaged power over one half of the voltage or current period it still works out to be accurate. However, you should be able to see that if it is averaged over a different period such as a quarter or two-thirds (of voltage/current period) then you can get a significant error.

But, for instance, if you began averaging at the trough of the power waveform and finished at the peak (equivalent to a quarter voltage or current period) then you would get the right answer.

Average power is the average of all the instantaneous powers calculated by instantaneous V x I.

The average is taken over some interval of time. If the waveforms are periodic and you take the average over a time interval increasingly longer than the period, it approaches the average over one period because the error introduced by landing randomly somewhere in the last cycle is an increasingly smaller proportion of the summation.

If power is averageed not "over a cycle or number of cycles" but supposes it is averaged over a quatter of cycle or two third of a cycle, will we get the same exact constant for the average power which we get for the average power over a complete cycle or cycles?

You can't assume this due to phase shifts between the V and I. The average over a single quarter, half, and full cycle of a full rectified sine wave are the same, but this has nothing to do with power.

In electronic electricity meters the energy is typically averaged over one second.

For each second:

• the direction of the power is determined
• the active energy is added to +E or -E
• the reactive energy is added to the correct quadrant: F1, F4 or F2, F3

For each second, only one register of +E, -E and one of F1, F2, F3, F4 is active.

Only from one second to another the direction of active- and reactive- power (or energy) might change.