Simulate active, reactive and instant power.

In order to understand active power, reactive power and apparent power concept easiest way is to start from stationary AC signals. In every time instant product of voltage and current gives instant power P(t)=U(t)·I(t). For trigonometric waveform of voltage:


and current


Instant power is




is time invariant, i.e constant and it is an offset of given product. This offset is actually active power – P of stationary AC voltage and current signal. For given IMAX and UMAX, maximal theoretical (and practical) value for P is when φ=0 and it is


Cosine of phase angle – cos(φ) is called power factor. By analyzing fluctuating component


i.e. by analyzing surface and sign of the surface of that curve we can define reactive and apparent power. If we define absolute surface value as the sum of all surface pieces between the fluctuating component and x axis, then we are just defined apparent power. So, for finding apparent power we don’t need to know active power, since apparent power is always


Let’s have a look at figure bellow:


Apparent power is equal to overall grey surface, and active power is DC offset of this signal. What is reactive power then according to this geometry? Let’s define non-absolute surface value of fluctuation component as the sum of “positive surface value” i.e. sum of all surface pieces above x-axis and “negative surface value” as the sum of all surface pieces bellow x-axis. Calculated on this way, surface can be positive, negative or zero. This non-absolute surface represent amount of energy consumed by the load from the source. If this surface is zero, then energy amount consumed is zero, even though neither voltage or current is zero. Then active power is zero. Reactive power is kind of complement of active power and it is also defined as DC value with:


This value is not geometrically obvious as DC offset defined as active power P, but it is abstract and real amount of energy delivered by the source and not used by consumer.
Simulation for obtaining waveforms of active, reactive, apparent and instant power is given in link bellow.

Simulate active, reactive and instant power.


External links:

Active, reactive and apparent power on Hyperphysics
Active, reactive and apparent power on Allaboutcircuits

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