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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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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