Unbalanced Supply to Balanced Loads

Let us consider the Star connected Balanced Loads, Z supplied by Unbalanced Phase Voltage Va,Vb,Vc.
Current Magnitudes in Each phase Ia, Ib, Ic.
Ia=Va/Z; Ib=Vb/Z; Ic=Vc/Z
Equivalent Balanced Circuit will be drawn with Equivalent Voltage Ve, Equivalent Current Ie.
Power is equal.
VaIa+VbIb+VcIc=3VeIe
Ie= sqrt[(Ia^2+Ib^2+Ic^2)/3]:
Ve= sqrt[(Va^2+Vb^2+Vc^2)/3]
Quadratic Mean.
Same will be applied for Delta connected Loads.

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