Electrical Engineering ⇒ Topic : Solving Unbalanced 3-Wire Y Load by Millmans Theorem
Solving Unbalanced 3-Wire Y Load by Millman's Theorem
We have seen that problems on unbalanced 3-wire, Y load can be solved by converting the given Y load into equivalent Δ-load. However, such a procedure involves lengthy calculations. J.E. Millman proposed a new technique to obtain the solution of unbalanced Y loads. Consider an unbalanced Y load connected to a balanced 3-phase supply as shown in Fig. 15.110. Here 0 is the star point of the supply (normally at zero potential) and O' is the load star point. Due to load unbalance, the potential of O' is different from that of O. If we know V0'0 (i.e., voltage of O' w.rt. 0), we caneasily determine the load phase voltages and the line currents of the unbalanced Y load. According to *Millman's theorem, the voltage V0'0 is given by
where VR0, VY0 and VB0 are the phase voltages of the supply and are equal in magnitude but 120° apart in phase. The quantities YR, YY. and YB are the admittances of the branches of the unbalanced Y load.
Fig. (b) shows the triangular phasor diagram. Here 0 is the star point of the supply and is located at the centre of the equilateral triangle RYB. The point 0' is the load star point. Due to load unbalance, 0' has some potential w.r.t. 0 and is shifted away from the centre of the triangle. Such a
diagram is very useful in analysing an unbalanced 3-wire star load because it gives at a glance the
picture of the happenings in the circuit. Thus
(i)distances OR, OY and OB are equal in magnitude but 120° apart from one another and represent the phase voltages of the supply.
(ii)distance 0'0 represents V0,0 i.e., potential of 0' w.r t. O.
(iii) distances 0' R, 0' Y and 0' B represent the load phase voltages. Note that load phase voltages are unequal in magnitude as well as differ in phase by unequal angle.
(iv) distances RY, YB and BR are equal in magnitude but *1200 apart in phase and represent the supply line voltages as well as load line voltages.
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