Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

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Fig. 8.3-1 

IllustratingequivalencebetweenaY-connectedsourceanda
D
-connectedsource
Hence,foreverysetoflinevoltagesandlinecurrentsobservedinathree-phasecircuit,
thereexistadelta-connectedsourceandastar-connectedsourcewhichwilljustifythe
observedlinequantitiesandwhichareindistinguishablefromoutside.
Therefore, if a balanced three-phase source is really 
D
-connected, it may be replaced by an 
equivalent Y-connected source for purposes of analysis. The details of phase-source currents in 
the real delta-connected source can be obtained after the circuit problem is solved using the star 
equivalent source.

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8.12


SinusoidalSteady-StateinThree-PhaseCircuits
8.3.2 
equivalence Between a y-connected load and a 
D
-connected load
But there is nothing new in this equivalence – we already know that any Y-connected set of impedances 
can be transformed into a 
D
-connected impedance and vice versa. Therefore, any given three-phase 
balanced 
D
-connected impedance can be converted into a three-phase balanced Y-connected impedance 
such that the terminal voltage and current behaviour remain unaffected. 
The individual branch currents in the branches of delta in the real delta-connected load can be 
obtained after line quantities have been obtained by using its equivalent Y-connected model. Three-
phase symmetry and 1/
√
3 factor connecting line currents and phase currents in a delta-connected 
system can be used for this purpose. The impedance to be used in Y-connected load is 1/3 times the 
impedance present in 
D
-connected load. See Fig. 8.3-2.
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