Phasor and Complex Representation of Three Phase Supply

Three sinusoidal voltages with equal amplitude and frequency, but a phase difference of 120∘ (or 2π/3 radians) between them, constitute a three-phase supply. Common names for them include Phase R, Phase Y, and Phase B. For such a supply, the general form is as follows:

Graphical Representation

Phasor representation is a way of representing sinusoidal quantities. These include voltages and currents. They are represented as complex numbers in the complex plane. This method makes analysis easier. The phasor is represented as a rotating vector (phasor) with magnitude V_m​ and θ corresponding to the phase of the sinusoidal function.

Complex Form:

The two most typical connection configurations in a three-phase system are star and delta.

Star Connection:

In balanced three-phase star system,

• V_R = V_m∠0^∘
• V_Y= V_m∠−120^∘
• V_B= V_m∠+120^∘ == V_m∠-240^∘

The phasors connected in the star, where n is the neutral or star point. The phase voltages are denoted as V_nR, V_nY, and V_nB, which are also known as V_R, V_Y, and V_B.

Vector Representation of Phase Voltage

Delta Connection:

In balanced three-phase delta system,

• V_RY = V_m∠0^∘
• V_YB= V_m∠−120^∘
• V_BR= V_m∠+120^∘ == V_m∠-240^∘

Winding in Delta Form