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.
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 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} |

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