### Zero sequence voltage in three-phase networks

With balanced network operation and inequality of the impedances in the consumer circuit, the phase voltages of the two circuits, and thus the neutral points are no longer congruent.

Between the neutral points, there is a voltage difference, which is referred to as the zero sequence voltage and the amount depends on the inequality of the impedances in the consumer circuit.

#### Three-phase three-wire network

The geometric sum of the complex effective values of the phase currents (see Figure 2) is zero and thus:

\frac{\underline{U}_{1N}+{\underline{U}_{NN''}}}{{\underline{Z}''_{1}}}+\frac{\underline{U}_{2N}+{\underline{U}_{NN''}}}{{\underline{Z}''_{2}}}+\frac{\underline{U}_{3N}+{\underline{U}_{NN''}}}{{\underline{Z}''_{3}}}=0

As a result:

\underline{U}_{NN''} = \frac{1}{3}[(\underline{U}_{1N''}+\underline{U}_{2N''}+\underline{U}_{3N''})-(\underline{U}_{1N}+\underline{U}_{2N}+\underline{U}_{3N})]

With symmetrical network operation __U___{1N} + __U___{2N} + __U___{3N} = 0 and thus the voltage __U___{NN“} equal to the zero component __U___{0}, which is therefore also called the zero sequence voltage.

\underline{U}_{NN''}=\frac{1}{3}(\underline{U}_{1N''}+\underline{U}_{2N''}+\underline{U}_{3N''})

Then also:

\underline{U}_{NN''}=-\frac{1}{3}[\underline{I}_{1}(\underline{Z}^{''}_{2}-\underline{Z}^{''}_{1})+\underline{I}_{3}(\underline{Z}^{''}_{2}-\underline{Z}^{''}_{3})]

#### The influence

The effect on the zero sequence voltage of unequal impedances in the consumer circuit (which in turn cause asymmetric currents) is directly recognizable from this equation.