What is the ratio of phase to phase to neutral in a wye system?

In a wye (or star) connection in three-phase systems, the relationship between phase voltage and line voltage is crucial to understand. In this configuration, each of the three phases is connected to a common neutral point, and the voltages between any two phases (line-to-line voltage) are higher than the voltages from any phase to the neutral point (line-to-neutral voltage).

The relationship can be derived from the geometrical representation of three-phase systems, where the phase voltages are separated by 120 degrees in a circle. The line-to-neutral voltage is the voltage measured from any single phase to the neutral point, while the line-to-line voltage is the voltage measured between any two phases.

The mathematical relationship between these voltages in a wye system is expressed as:

Line-to-Line Voltage = √3 × Line-to-Neutral Voltage

Therefore, when you consider the ratio of phase (line-to-neutral) to phase (line-to-line), it can be expressed as:

Phase Voltage (Line-to-Neutral) : Phase Voltage (Line-to-Line) = 1 : √3

This means that for every unit of voltage from the neutral to one of the phases, the voltage from one phase to another phase is √3 times greater