Star to Delta and Delta to Star conversions

We have seen Star and delta connection is Transformers. Now Star into delta conversions allows us to convert impedances connected together from one type of connections to another. This conversion can be done by using Kirchoff’s circuit laws.

Star to Delta Conversion
In three phase power supply Star to delta conversion can be done easily by using these transformations.
Circuit for the conversion is as shown below:-
Star to Delta Conversion

There are following formula used for conversion for Star to delta.

Resistance RA= R1R2 + R2R3 + R3R1        ……………… (i)
                                      R3
Resistance RB= R1R2 + R2R3 + R3R1   ……………… (ii)
                                      R2
Resistance RC= R1R2 + R2R3 + R3R1   ……………… (iii)
                                      R1

Delta to Star Conversion
Now you see from above formula when there is need to calculate equivalent resistance in delta connection while conversion from Star connections is sum of product of every two branch resistances in star connections divided by resistance if opposite branch. From equation (i) you see that while calculating resistance in delta across branch RA then this will be equal to sum of product of two branches divided by resistance of opposite node. Similarly resistance value of other branches can be calculated.

Diagram for conversion from Delta to Star is as below:-
Delta to Star conversion


Now let’s see when there is conversion from Delta to Star then following formula can be used:-
Resistance R1=     RA RB  ……………………………..(a)
`                         RA+RB+RC
Resistance R2=    RA RC    ……………………………..(b)
                           RA+RB+RC
Resistance R3=    RB RC    ……………………………..(c)
                           RA+RB+RC

Now from above we can see that while conversion from delta to star connections resistance of branch  which is under calculation is equal to product of two branches which are connected to Node divided by Sum of resistances of all branches .
From equation 1 we have seen that while calculating resistance across branch RA , resistance will be product of resistances connected to node1 while in delta divided by sum of resistances in all branches.

From above you can see that it will be easy to convert star into delta and delta into star by using these formula’s. This conversion is used to analyze the circuits. These transformations are applicable for both resistance and impedances.
These Transformations are used to solve complex circuits.





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