# 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 VL and line current IL can be replaced by an equivalent Delta connected system having phase voltage VL and phase current IL / 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.

Thus if we are given a balanced load having an impedance of Z in each phase connected in Star then for our convenience we can replace the Star connection by equivalent Delta connected system with an impedance of three times that of in Star connection.

Let the line voltage for Star connection be VL and line current be IL.

So, impedance ZY= Phase Voltage / Phase Current

But for Star connection, Phase Voltage = Line Voltage / 1.732 = VL / 1.732

and Phase Current = Line Current  = IL

Therefore,

Impedance ZY = VL/ (1.732IL)  …………………(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 = VL

and Phase Current = Line Current / 1.732  = IL / 1.732

Therefore,

Impedance Z Δ = Phase Voltage / Phase Current

= VL / (IL/ 1.732)

= 1.732VL / IL

But from equation (1),

VL = 1.732ZYIL

So, Impedance Z Δ = 1.732x(1.732ZYIL) / IL

= 3ZY

Thus we see that for balanced load,

 Z Δ = 3ZY

### 2 thoughts on “Balanced Star to Delta & Delta to Star Conversion”

1. vinoth kumar says:

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

1. admin says:

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

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