Chapter 1: Modelling Power System Components

Section V: Balanced Operation Of a Three-Phase Citcuit

In the language of Power Systems, a three-phase circuit is said to be balanced if the following conditions are true.

  • If all the sources and loads are y-connected.
  • There is no mutual inductance between the phases.
  • All neutrals are at the same potential.
  • As a consequence of the points (2) and (3) above, all phases are decoupled.
  • All network variables are balanced sets in the same sequence as the sources.

Consider the three-phase circuit shown in Fig. 1.20 that contains three balanced sources Ea , Eband Ec along with three balanced source impedances, each of value Zs. The sources supply two balanced loads - one wye-connected with impedance of Zy and the other Δ-connected with impedance of ZΔ . Since this is a balanced network, the sum of the currents at the neutrals N (or n ) is zero. Therefore the neutral are at the same potential. Transforming the Δ-connected load to an equivalent y, we get the per phase equivalent circuit as shown in Fig. 1.21. In this fashion an entire power system can be converted into its per phase equivalent. The line diagram showing a per phase equivalent circuit is called a single-line diagram.