# Balanced Star to Delta & Delta to Star Conversion

As we know any balanced Star connected system can be completely replaced by an equivalent Delta connected system. This means that a three phase Star connected balanced system having line voltage V_{L} and line current I_{L} can be replaced by an equivalent Delta connected system having phase voltage V_{L} and phase current I_{L} / 1.732. But for replacing a balanced Star connected system with Delta connected system we need to know how to find the equivalent Delta connected system or Star connected system. In this post we will discuss this aspect.

Let the line voltage for Star connection be V_{L} and line current be I_{L}.

So, impedance Z_{Y}= Phase Voltage / Phase Current

But for Star connection, Phase Voltage = Line Voltage / 1.732 = V_{L} / 1.732

and Phase Current = Line Current = I_{L}

Therefore,

Impedance Z_{Y} = V_{L}/ (1.732I_{L}) …………………(1)

Now we will calculate impedance for Delta connection assuming same voltage and current as in Star connection.

Impedance Z _{Δ} = Phase Voltage / Phase Current

But for Delta connection, Phase Voltage = Line Voltage = V_{L }

and Phase Current = Line Current / 1.732 = I_{L} / 1.732

Therefore,

Impedance Z Δ = Phase Voltage / Phase Current

= V_{L} / (I_{L}/ 1.732)

= 1.732V_{L} / I_{L}

But from equation (1),

VL = 1.732Z_{Y}I_{L}

So, Impedance Z _{Δ} = 1.732x(1.732Z_{Y}I_{L}) / I_{L}

= 3Z_{Y}

Thus we see that for balanced load,

Z _{Δ }= 3Z_{Y} |

This blog would be so useful to me… Please keep on have touch your articles …. Espcially HV AC SIDE… THX

Thank you very much Vinoth Kumar! Please share the articles.