Electrical – Phase voltage from unbalancd line voltages symmetrical components

symmetrical componentsvoltage-source

I'm trying to calculate the phase voltage of a given unbalanced sources star connected from the given line voltages. I'm trying to employ symmetrical component synthesis to find a solution.

I know the zero sequence component of line voltage is always zero.

To find the phase voltages with symmetrical components, I've to find all the three components, the positive and negative sequence component of the phase voltages are easy to find. But how can I find the zero sequence component of the phase voltage, from the given line data.

The given data are :

Eab = 2760 V

Ebc = 2300 angle(-138.6) V

Eca = 1840 angle(124.2) V

I'm trying to find Ean, Ebn, Ecn . I may be assumed that the neutral point is grounded.

Best Answer

Ean= Ea1(+ve seq)+ Ea2(-ve seq)+Ea0(zero seq)

Where Ea1= -j Eab1/√3 Ea2= -j Eab2/√3 Eao= -j Eabo/√3

Where Eab1 = 1/3 *( Eab + α Ebc+ α^2 Eca)