Electrical Engineering ⇒ Topic : Solving Unbalanced 3-Wire Y Load by Y/delta Conversion
Solving Unbalanced 3-Wire Y Load by Y/Δ Conversion
Fig. (a) shows an unbalanced 3-wire Y-connected load while Fig. (b) shows the equivalent A-connected load. It was shown in chapter 3 that Y connection of resistances can be replaced by an equivalent Δ and vice-versa. With a.c., the same formulas hold good except that resistances are replaced by impedances (in complex form)
Thus the Y-load of Fig. (a) can be replaced by equivalent Δ-load having branch impedances
The equivalent A load can be solved to obtain the line currents. The line currents so calculated will be the line currents taken by the original unbalanced Y-load.
How to remember above relations ? The symmetry of above relations shows that one should not try to memorise them. It may be seen that numerator is the same in the three cases i.e., it is the sum of the cross products of star impedances viz. Z1Z2 + Z2Z3 + Z3Z1. However, denominator is that star impedance which is not included in the considered terminals. Thus, for Z12, the terminals are 1 and 2 and the star impedance not included in these terminals is Z3. Hence in this case Z3 is the denominator.
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