Electrical Power System Essentials

1.5 EQUIVALENT LINE-TO-NEUTRAL DIAGRAMS

When solving balanced three-phase systems, one can work with a single-phase equivalent of the three-phase system. In fact, the consecutive steps made to arrive at the balanced three-phase system consisting of three conductors in Figure 1.8 are reversed: the three-phase system is split up into three single-phase networks of which only one needs to be analyzed. When the voltages and currents are known in this single phase, one can simply obtain the expressions for the voltages and currents in the other two phases by rotating the corresponding phasors with 120 and 240 degrees.

When the three-phase network contains delta-connected elements, they have to be converted to their equivalent wye connections first, as shown in Figure 1.25. The delta-wye transformation formulas for both impedances and admittances are given in Table 1.2.

As we assume the system to be balanced (i.e.Z_ab = Z_ac = Z_bc and Y_ab = Y_ac = Y_bc), the two following delta-wye transformation formulas can be derived:

Figure 1.25 Conversion of a delta-connected load. to a wye-connected load.

Table 1.2 Delta wye transformation. Impedance Admittance

Example 1.8 Equivalent line-to-neutral ...