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.
Same will be applied for Delta connected Loads.