# Why phase to neutral voltage is 230V where Phase to phase is 400V in a 3 phase line?

A three-phase system is a common type of polyphase system, widely used in power generation, transmission, and distribution. It consists of three alternating currents (or voltages) that reach their peak values at different times. The three phases are typically denoted as A, B, and C.

In a three-phase power system, we often encounter two types of voltages: phase-to-neutral voltage (also known as line-to-neutral voltage) and phase-to-phase voltage (also known as line-to-line voltage). In many parts of the world, the standard phase-to-neutral voltage is 230V, while the phase-to-phase voltage is 400V. Have you wondered why phase to phase becomes 400V?

## Phase-to-Neutral Voltage

The phase-to-neutral voltage, often denoted as V_{LN}, is the potential difference between one of the phases and the neutral point. In a balanced three-phase system, the neutral point is at zero potential, and the magnitude of V_{LN} is the same for all three phases, the standard value for V_{LN} is 230V.

## Phase-to-Phase Voltage

The phase-to-phase voltage, often denoted as V_{LL}, is the potential difference between any two phases. In a balanced three-phase system, the magnitude of V_{LL} is the same for all three pairs of phases, the standard value for V_{LL} is 400V.

### Relationship Between V_{LN} and V_{LL}

The relationship between V_{LN} and V_{LL} in a three-phase system can be derived from the geometry of the phasor diagram. In a balanced three-phase system, the three-phase voltages can be represented as vectors (phasors) of equal magnitude but different phase angles, separated by 120 degrees.

If we consider a Y-connected system (where the neutral point is the common connection point), the phase-to-phase voltage is the vector sum of two phase-to-neutral voltages. The magnitude of the phase-to-phase voltage is √3 times the magnitude of the phase-to-neutral voltage; Refer: Line to Line voltage calculation in a Three-Phase supply.

Therefore, we have:

V_{LL} = √3 * V_{LN}

Substituting the standard values:

400V = √3 * 230V