AC Power - Basic Calculations Using Real Numbers

Basic Calculations Using Real Numbers

A perfect resistor stores no energy, so current and voltage are in phase. Therefore there is no reactive power and . Therefore for a perfect resistor

For a perfect capacitor or inductor there is no net power transfer, so all power is reactive. Therefore for a perfect capacitor or inductor:

Where X is the reactance of the capacitor or inductor.

If X is defined as being positive for an inductor and negative for a capacitor then we can remove the modulus signs from Q and X and get

Instantaneous power is defined as:

where v(t) and i(t) are the time varying voltage and current waveforms.

This definition is useful because it applies to all waveforms, whether they are sinusoidal or not. This is particularly useful in power electronics, where nonsinusoidal waveforms are common.

In general, we are interested in the real power averaged over a period of time, whether it is a low frequency line cycle or a high frequency power converter switching period. The simplest way to get that result is to take the integral of the instantaneous calculation over the desired period.

This method of calculating the average power gives the real power regardless of harmonic content of the waveform. In practical applications, this would be done in the digital domain, where the calculation becomes trivial when compared to the use of rms and phase to determine real power.