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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