Line and Phase Voltage in Three-Phase Systems

The line voltage and the phase voltage are two different ways of measuring voltage within a three-phase system.

In a three-phase distribution system with a neutral, we find five conductors:

• Three Phases (L1, L2, L3).
• One Neutral (N).
• One Ground (PE).

The voltage depends on the two points between which we define it.

Phase Voltage ()

In a star-connected source, the phase voltage, , also called the simple voltage, is the voltage between a phase and the neutral. When referring to a load, the phase voltage is the voltage applied to each branch and depends on whether it is connected in star or delta.

Line Voltage ()

The line voltage is the voltage between two different phases. It is also called the compound voltage.

The √3 Factor

Where does the 400 come from? If one phase has 230V and the other also has 230V… Shouldn’t the difference be 0V or 460V? No, because they are 120 degrees out of phase. They do not reach their peak simultaneously.

The geometric relationship between these two vectors forms a triangle that is resolved using the square root of 3.

If we do the calculation with the current European standard:

That is why we nominally state 400V.

Why does 400 V appear?

Many people think: “If L1 has 230V and L2 has 230V… the difference should be zero.” That would be true if they were identical voltages and in phase. But they are 120 degrees out of phase.

When subtracted as phasors, we obtain another sine wave whose RMS value is times greater: 400 V. Its peak value is approximately 566 V.

Safety in Measurement

Both 230 V and 400 V can cause serious or fatal injuries. Do not open or measure a live panel unless you have the proper training, authorization, procedure, and equipment.