A2-1 Electrical Power

Electrical power is often represented as a complex number. For DC circuits, only real power is relevant. For AC circuits, real and reactive power exist and need to be managed. Real power is the energy consumed or converted to do work. Reactive power does not do any work. It is often used to support magnetic or electric fields. Examples of this are an induction motor whereby a magnetic field is created for the motor to work. A portion of the apparent power is used as reactive power to establish this field so that electrical real power can be transformed into mechanical power via rotation.

Parameters

p = real power (watt). This is where energy is transferred typically to another form of energy like heat (eg a hot water heater), mechanical (eg a pump), radio(eg microwave oven) etc

s = apparent power (va). This is the total, complex power required to deliver the real power.

q = reactive power (var). This power is tied up with magnetic or electric fields needed to deliver the real power. This energy ideally oscillates each half cycle with a net real power consumption of 0. Examples are the magnetic field in a motor in order for the motor to work.

pf = power factor. Which is simply the ratio of real power (p) over apparent power (s)

v = volts. Either line or phase voltage depending if it is a polyphase system. $v_{\mathrm{line}}=\sqrt{3}·v_{\mathrm{phase}}$ .In Australia this is 415v (400v officially) and 240v (230v officially) respectively.

i = amps. Line current.

$$\mathrm{s\; =\; p+jq}$$ $\mathrm{pf\; =\; cos(\phi )}$ $$\mathrm{cos(\phi )}=\frac{p}{s}$$

This can be visualised by a right angle triangle

Ideally to minimise circuit losses, power factor should be 1. If power factor is less than 1 then more current is needed in the circuit to deliver the same real power thereby requiring larger cables, more voltage drop and more line resistive losses. Note the resistive losses are real power and this why network planners and engineers try to keep power factor as close to 1 as possible.