In this article we will discuss about:- 1. Introduction to Delta-Star Transformation 2. Delta-Star Transformation 3. Star-Delta Transformation.
Introduction to Delta-Star Transformation:
Three resistances connected nose-to-tail as shown in Fig. 2.42 (a), are said to be delta- (or A) or mesh- connected (they form a mesh). Three resistances connected together at a common point O, as shown in Fig. 2.42 (b), are said to be star – (or Y) connected. If the nodes (A, B, and C) to which the two sets of resistances are connected are part of a larger network, it is possible to assign values to the two sets of resistances so that they have exactly the same effect on the network.
If, therefore, delta-connected resistances are part of a network it is possible to substitute them by the star-connected ones and vice versa. The obvious advantages are that a delta-star transformation eliminates a mesh which reduces by one the variables and equations necessary to solve a network by mesh analysis whereas star-delta transformation eliminates a node (node O) which reduces by one the variables and equations necessary to solve a network by node analysis.
Delta-Star Transformation:
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The replacement of delta or mesh by equivalent star system is known as delta-star transformation.
The two systems will be equivalent or identical if the resistance measured between any pair of lines is same in both of the systems, when the third line is open.
Hence resistances between terminals B and C:
These relationships may be expressed as follows:
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The equivalent star resistance connected to a given terminal is equal to the product of the two delta resistances connected to the same terminal divided by the sum of the delta connected resistances.
If the three delta-connected resistances have the same value RD, the three resistances in the equivalent star for identical systems will be:
Star-Delta Transformation:
Multiplying equations. (2.25) and (2.26), (2.26) and (2.27) and (2.27) and (2.25) and then adding them we get:
The above relationship may be expressed as below:
The equivalent delta resistance between two terminals is the sum of the two star resistances connected to those terminals plus the product of the same divided by the third star resistance.
If the three star-connected resistances have the same value, say RS, the three resistances of the equivalent delta for identical systems will be:
The advantage of delta-star transformation may be shown by reference to network of Fig. 2.43. Fig. 2.43 (a) illustrates the network before conversion, where the dotted lines are drawn around the delta connection to be transformed into a star. Fig. 2.43 (b) illustrates the same network after transformation. The currents in the transformed form [Fig. 2.43 (b)] are much simpler to determine.
The advantage of star-delta transformation can be illustrated by reference to network of Fig. 2.44. Figure 2.44 (a) illustrates the network prior to transformation, with the dotted lines around the star to be transformed. Fig. 2.44 (b) illustrates the same network after transformation. The original network is now reduced to a simple series parallel connection of resistances.