## Electrical engineering concepts

**Three phase system**

At the large-scale, alternating-current (ac) electricity is generated
and transmitted/distributed not as a single sinusoidal energy waveform,
but as three. In fact any number of phase-displaced waveforms are possible,
but in the technical/economic trade-off the **three phase** system is
optimal.

A three phase system can be observed as any system of three voltages
(or currents) in which the voltage (current) magnitudes and phase angles
have a fixed relationship with each other. A balanced three phase system
is one in which the magnitude of the three voltages is constant and the
phase displacement is constant and equal to 120°.

**Power factor**

The **power factor** is dependent upon the characteristics of the
electrical appliances connected and the relationship between the the amount
of **real** and **reactive** power which is absorbed.

In the **power
triangle** diagram, cos(theta) is the power factor and it indicates the
relative size of the reactive power component measured in Volt-Amperes-Reactive
(**VAR**).

When the **impedance** of the circuit is purely resistive, there
is no reactive component and the apparent power is equivalent to the real
power (i.e. cos(theta)=0). When reactive components are introduced (inductance
or capacitance) the impedance becomes a complex quantity with a resistive
and a reactive component:

The reactive power component normally results from inductance present
in the circuit. The inductor is a fundamental component of electrical networks
and, in practice, inductance is unavoidable in standard equipment such
as transformers, motors, and even cables. Inductance can be conceived as
a circuit component which acts to oppose any change in the current flowing
through it. The power triangle also reflects this phenomenon because the
power factor angle, theta, represents the amount by which the current **lags**
the voltage in an inductive circuit.

Therefore electrical circuits operate at a non-ideal (<1.0) power
factor and one which is termed **lagging** (due to inductance). There
is therefore a reactive power component which, whilst being the mathematically
termed "imaginary" component, causes increased current flow and
heating effects in wires and appliances (e.g. pump/fan motors).

The reduction of the reactive power component is desirable on technical
and energy-efficiency grounds. Furthermore the electricity supply utility
tariff structure penalises the reactive component of electrical load.