Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev

Networking Theory

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Electrical Engineering (EE) : Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev

The document Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev is a part of the Electrical Engineering (EE) Course Networking Theory.
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Delta Network
Consider the following delta network as shown in the following figure.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
The following equations represent the equivalent resistance between two terminals of delta network, when the third terminal is kept open.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev

Star Network
The following figure shows the equivalent star network corresponding to the above delta network.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
The following equations represent the equivalent resistance between two terminals of star network, when the third terminal is kept open.
RAB = RA + RB
RBC = RB + RC
RCA = RC + RA

Star Network Resistances in terms of Delta Network Resistances
We will get the following equations by equating the right-hand side terms of the above equations for which the left-hand side terms are same.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev    Equation 1
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev   Equation 2
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev    Equation 3
By adding the above three equations, we will get
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev   Equation 4
Subtract Equation 2 from Equation 4.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
By subtracting Equation 3 from Equation 4, we will get
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
By subtracting Equation 1 from Equation 4, we will get
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
By using the above relations, we can find the resistances of star network from the resistances of delta network. In this way, we can convert a delta network into a star network.
Example
Let us calculate the resistances of star network, which are equivalent to that of delta network as shown in the following figure.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Given the resistances of delta network as R1 = 10 Ω, R2 = 60 Ω and R3 = 30 Ω.
We know the following relations of the resistances of star network in terms of resistances of delta network.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Substitute the values of R1, R2 and R3 in the above equations.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
So, we got the resistances of star network as RA = 6 Ω, RB = 18 Ω and RC = 3 Ω, which are equivalent to the resistances of the given delta network.

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