# Phase voltage from unbalancd line voltages symmetrical components

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.

• Ean-Ebn = Eab. Ebn-Ecn = Ebc. Ecn - Ean = Eca. Three equations with three unknowns. Commented Jul 31, 2017 at 9:50
• how will i solve these equations Commented Jul 31, 2017 at 10:02
• I'm voting to close this question as off-topic because it is homework without work. And even with a hint didn't follow up. Commented Apr 1, 2020 at 4:38

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)

You cannot calculate phase to neutral voltages from phase to phase voltages if the zero sequence component is not 0. The problem is indeterminate because any value of zero sequence assumed would result in the same ph-ph quantities. This is because the zero sequence component in each phase to neutral voltage are all in phase and equal in magnitude with each other by definition. So, when you do the subtraction to calculate a ph-to-ph voltage the zero sequence quantities cancel out. VAB = VAn - VBn. Only the positive and negative sequence terms survive that calculation.

It can be done easily by using concept of operations on SHIFT OPERATOR (1@120°)

Basically, Draw a triangle and calculate the Center and then measure the phase voltages.

Line voltages consists positive and negative sequence component. Phase voltages include zero sequence component. Line voltages denote the sides of triangle. But the three phase voltage are the lines joining the edges of triangle with arbitrary centre inside the triangle. I have the concepts of generalized phase voltage.