Analysis of Simple Three-Phase Circuits

Four-Wire Systems

If the impedance voltage drops in the lines are negligible, then the voltage across each load is the source phase voltage.

Example 2.1

For the network of Figure 2.7(a), draw the phasor diagram showing voltages and currents and write down expressions for total line currents Ia, Ib, Ic, and the neutral current In.

Solution

Note that the power factor of the three-phase load is expressed with respect to the phase current and voltage.

(a) Four-wire system with single-phase unbalanced loads and three phase balanced motor load, (b) Phasor diagram

Figure 2.7 (a) Four-wire system with single-phase unbalanced loads and three phase balanced motor load, (b) Phasor diagram: only the phasors IZa and Ima have been added to show Ia. Ib, and Ic can be found in a similar way. Note: Van is the reference direction. Rotation is anticlockwise

The phasor diagram is shown in Figure 2.7(b). The line currents are as follows:

The neutral current (as the induction motor currents do not contribute to In)

Three-Wire Balanced Systems

The system may be treated as a single-phase system using phase voltages. It must be remembered, however, that the total three-phase active power and reactive power are three times the values delivered by a single phase.

 
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