# 11.2. Three-Phase Three-Wire System

In case a star-connected load is unbalanced and if there is no neutral wire, then its star point is isolated from the star-point of the generator. The potential of the load star-point is different from that of the generator star-point. The potential of the former is subject to variations according to the unbalance of the load and under certain conditions of loading, the potentials of the two star-points may differ considerably. Such an isolated load star-point or neutral point is called a ‘floating’ neutral point because its potential is always changing and not fixed. All star-connected unbalanced load supplied from polyphase systems without a neutral wire, have floating neutral points. Any unbalancing of the load causes variations not only of the potential of star-point but also of voltages across the different branches of the load. Hence in that case, phase voltage is not  of the line voltage. In general, the phase voltages are not only unequal in magnitude but also subtend angles other than 120o with one another.

The following methods are used to tackle unbalanced star-connected loads ha oing isolated

neutral points.

1. By Kirchhoffs laws.
2. By star-delta conversion.
3. By applying Milliman’s Theorem.
4. By using Maxwell’s Mesh or Loop Current Method.

1. Kirchhoff’s Laws. By applying Kirchhoff’s laws, we get (Refer Fig. 47)

2.  Star-delta Conversion. In case of unbalanced star-connected load it is somewhat more convenient to convert it into equivalent delta-connected load and solve it.

If ZR, ZY and ZB be the impedances of the given star-connected load and ZRY, ZYB, ZBR be the impedances of the equivalent delta-connected load (Fig.48), then

Now the phase currents and line currents can be determined. (Refer worked examples).

3.      Milliman’s Theorem. Refer Fig. 49. A number of linear bilateral admittances YI, Y2, Y3, ……. , Yn are connected to a common point (or mode) O’. The voltages of the free ends of these admittances with respect to another common point O are V1O, V2O, V3O, ….., VnO. Then according to this theorem, the voltage of O’ with respect to A is given by