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Three Phase Balanced Supply to Unbalanced Load

Let us consider the Star connected Unbalanced Loads, Za, Zb, Zc supplied by Balanced Phase Voltage V.
Current Magnitudes in Each phase Ia, Ib, Ic.
Ia=V/Za; Ib=V/Zb; Ic=V/Zc
Assume zero sequence current.
Equivalent Balanced Circuit will be drawn with Equivalent Impedance Ze, Equivalent Current Ie.
Power is equal.
VIa+VIb+VIc=3VIe
Ie= (Ia+Ib+Ic)/3: Arithmetic Mean.
Ze= V/Ie= 3V/((V/Za)+(V/Zb)+(V/Zc))
Ze= Harmonic Mean of Impedance.
Ze = 3ZaZbZc/(ZaZb+ZbZc+ZcZa)
Same will be applied for Delta connected Loads.

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