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The replacement of delta or mesh by equivalent star connection is known as delta – star transformation. The two connections are equivalent or identical to each other if the impedance is measured between any pair of lines. That means, the value of impedance will be the same if it is measured between any pair of lines irrespective of whether the delta is connected between the lines or its equivalent star is connected between that lines.
We can now solve simple series, parallel or bridge type resistive networks using Kirchhoff´s Circuit Laws, Mesh Current Analysis or Nodal Voltage Analysis techniques. But in a balanced 3-phase circuit we can use star delta transformation techniques to simplify the analysis of the circuit and thereby reduce the amount of math’s involved which in itself is a good thing.

Standard 3-phase circuits or networks take on two major forms with names that represent the way in which the resistances are connected, a Star connected network which has the symbol of the letter, Υ (wye) and a Delta connected network which has the symbol of a triangle, Δ (delta).
If a 3-phase, 3-wire supply or even a 3-phase load is connected in one type of configuration, it can be easily transformed or changed it into an equivalent configuration of the other type by using either the Star Delta Transformation or Delta Star Transformation process.

Other links::
Lecture-03:    • Star - Delta  conversion. Lecture-03. Elec...  
Lecture-06:    • Star delta conversion, Lecture-06, Electri...  
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