Phase-Neutral to Phase-Phase Calculation

If everything was as simple as multiplying by the square root of three then we could all be replaced a little easier.


This calculation can be used to find any phase to phase quantity from any two given phase to neutral quantities.

Whether the given quantities are voltage or current does not matter.


The principle involved is that the phase to phase quantity is equal to :

Phase 1 quantity minus Phase 2 quantity.


In terms of voltage :

VAB = VAN - VBN

VBC = VBN - VCN

VCA = VCN - VAN


In current terms :

IAB = IAN - IBN

IBC = IBN - ICN

ICA = ICN - IAN


In general terms :

Phase-Phase = Phase 1 - Phase 2


The process of subracting one polar-coordinate quantity from another is to :

1. Convert Phase 1 polar quantity to its rectangular coordinate equivalent.

2. Convert Phase 2 polar quantity to its rectangular coordinate equivalent.

3. Subract Phase 2 horizontal component from Phase 1 horizontal component.

4. Subract Phase 2 vertical component from Phase 1 vertical component.

5. Take the resulting horizontal and vertical components and convert them to their polar form equivalent.


Note that this is equivalent to multiplying a given phase by the square root of three
ONLY if the two given phase to neutral phasors are equal in magnitude and 120 degrees apart.