Three Phase Systems

Phasor representation

Suppose is a phasor.

Definitions

Attenuation & Phase Shift

Suppose a linear, passive network has the input and output as:

Here is the attenuation or magnification factor and is the phase shift.

Power

Power on a 1-phase circuit can be easily found using 1-phase power formula:

Here is the complex conjugate of the current phasor.

Symmetrical Components

A technique used to handle unbalanced voltages or current sources. Any unbalanced system of three-phase circuits can be decomposed into three symmetrical components:

• Positive sequence ()
  Has same phase sequence as the original 3-phase system
• Negative sequence ()
  Has reverse phase sequence as the original 3-phase system
• Zero sequence ()
  Has equal magnitude and phase angle in all 3-phases

The above equation can be simplified as below. Here .

Symmetrical component matrix

Power

Impedances