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The paper offers a new vector-coordinate description for a complex-plane position of a neutral bias voltage phasor relevant to a three-phase circuit with an unbalanced load. It is assumed that no negative sequence voltage component is present, i.e. the supply three-phase system voltages are symmetric and sinusoidal. The so called “new coordinates” and being defined with the help of them barycentric coordinates on a balanced supply line-to-line voltages triangle have been introduced. The proposed approach made it possible to obtain simple enough analytical expressions. A RMS value of the positive sequence component and further a static phasor of the zero sequence voltage unbalance factor are described. They are based on three lineto-neutral load voltages voltmeter RMS readings only. Accordingly, these calculations need no phase measurements. The presented neutral bias voltage coordinates calculations might be useful in a three-phase load circuit monitoring, diagnostics (fault detection), protection and voltages unbalance compensation.

Applying barycentric coordinates on balanced supply voltages triangle to zero sequence voltage estimate without phase measurements