Three-phase Electrical System

Three-phase voltage system consist of three dependent sources of alternating sinusoidal voltage. The three sources provides voltages which have equal amplitudes (Um1 = Um2 = Um3) and equal frequencies (f1 = f2 = f3), but they are phase shifted for 1/3 of the period or 120°. On Picture 1 is shown the principal schematic of the three-phase power source system and the waveforms of the provided voltages from the power source. The phases of the power source are marked as R (phase 1), S (phase 2) and T (phase 3). Somewhere, the phases are marked as L1, L2 and L3.

Picture 1: Three-phase power source and it's voltage waveforms


On Picture 2 are shown the equations for three-phase voltage source in time domain and in complex domain. The equation in complex domain actually represents a vector in a Re-Im plain, so, every vector for each phase can be represent in the proper vector diagram, as shown on the Picture 3. Every phase from the three-phase system is delayed for 120° from the previous phase, S phase is delayed from R phase for 120°, T phase is delayed from S phase for 120° and R phase is delayed from T phase for 120°.

Picture 2: Equations for three-phase power source in time & complex domain

Picture 3: Vector diagram of the three phases R, S and T


The wiring system for the three-phase power source can be:

1. 3-wired: without null-conductor (high-voltage networks for transfer of the electric energy)

2. 4-wired: with null-conductor (low-voltage networks)


In three-phase systems there are a two types of sizes, phase and line sizes. The phase sizes refer to one phase from the source or the electrical consumer and null point, while line sizes refer to ratio between the phase conductors. For example, the phase voltage of each phase is 220 V (this is voltage between phase and null, R-0; S-0 or T-0), and the line voltage between any two phases is 380 V (this is voltage between two phases, R-S, S-T or R-T).

In three-phase systems there are two basic connections of the electrical consumers (loads) to the three-phase sources: Star (Y) Connection and Delta (D) Connection.