Most of the world's electrical power is generated, transmitted, and distributed as alternating current. Three-phase power systems use three AC voltages offset from one another by 120 degrees, providing more efficient transmission and a more constant power output than single-phase systems. Compared with single-phase, three-phase delivery requires less conductor material for the same power capacity and produces a non-pulsating power flow, which is especially valuable for driving motors and heavy industrial loads.
A transformer is a device that transfers AC electrical energy between circuits via electromagnetic induction, allowing voltage levels to be stepped up for efficient long-distance transmission or stepped down for safe consumer use. The voltage ratio is set by the turns ratio of the transformer's windings: \(V_1/V_2 = N_1/N_2\), where \(N\) represents the number of turns in each coil. More turns on the secondary winding yield a higher output voltage; fewer turns yield a lower output voltage.
In AC power systems, the relationship between voltage and current is characterized by the power factor, \(PF = \cos(\theta)\), where \(\theta\) is the phase angle between them. Real (active) power, \(P = VI \cos(\theta)\), is the actual power consumed by the load and is measured in watts. Reactive power, \(Q = VI \sin(\theta)\), is the power alternately stored and released by inductors and capacitors, measured in volt-amperes reactive (VAR). Apparent power, \(S = VI\), is the product of RMS voltage and current, measured in volt-amperes (VA), and is related to the other quantities by \(S^2 = P^2 + Q^2\). Power factor correction, often implemented by adding capacitors to offset inductive loads, reduces transmission losses and improves efficiency in industrial and commercial power systems.