I read and derived formulas for balanced delta source to Wye source; it is given by Vy = Vd / sqrt(3)<30 but in some places I see people only dividing by sqrt(3) for conversions are keeping angle 0, is it the correct way for conversion ?


If one doesn't care about the angle but only the magnitude then
\$ V_Y = \frac {1}{\sqrt 3} V_{\Delta} \$ is all you need.

For example, if I have a delta-star transformer feeding an induction motor nobody cares if the phases are 30° out because it is completely isolated from the delta side. Only the voltage magnitude will matter.


simulate this circuit – Schematic created using CircuitLab

Figure 1. Phasor representation of star (wye) and delta voltages in a three-phase system.

It is a fairly trivial exercise to prove the √3 relationship between the phase to phase and phase to neutral phasors.


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