How to calculate power in an inductive load?

Answer 1

Inductive load power is reactive, it is given by the formula:

pL(t)=VL(t)IL(t),

in time domain (instant power);

PL(s)=VL,RMS(s)IL,RMS(s),

in Laplace transform domain (RMS denotes root mean square amplitude).

VL is the voltage across the inductor L and IL is its current (current enters in the "+" voltage reference pin, by applying user convention in which absorbed power is positive).

Power is reactive since voltage and current are always in quadrature:

VL(s) = s L IL(s),

in Laplace domain (derived from the time-domain formula vL(t)= L diL(t)/dt).

A real-life inductor will also show an active power term, which arises from parasitic resistance non-ideality; it can be modeled as a resistance DCR in series with the inductor itself:

pACT(t)=DCR IL(t)

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An inductive load such as an induction motor draws power from the supply with a power factor of less than 1.

Power = voltage x current x power factor.

This happens because the current reaches its peak in the ac cycle after the voltage, so that for a small part of the cycle power flows back into the supply from energy stored in the motor's internal magnetic field. The time-lag is measured in degrees and called the phase difference. 360 degrees denotes one complete cycle.

The power factor is the cosine of the phase difference, so that (for example) a resistive load has no phase difference so that the power factor is 1, while for a pure inductor the phase difference is 90 degrees and the power factor is zero.

If the rms voltage and current are expressed in complex-number form, also known as vectors or phasors, the real power is the real part of VI*, where the asterisk denotes the complex conjugate.

Another way to calculate the real power is to calculate the average value of the instantaneous power V x I. If the voltage is Vcos(wt) and the current is Icos(wt+phi) then those expressions can be multiplied together and trigonometry formulas used to show that the power factor is cos(phi) as stated.

Real power is measured from the average value of volts times amps with an instrument that contains a voltage coil and a current coil. The force produced is equal to the instantaneous power, and the instrument measures its average value muliplied by the time.