Star to Delta Conversion
To get the delta connection resistors RAB,RBC,RCA from the star connection, Consider the star connection as shown below:
Divide equation (5) by equation (6),
[Tex]\frac{R_A}{R_B}=\frac{\frac{R_{AB}R_{CA}}{R_{AB} +R_{BC} + R_{CA}}}{\frac{R_{AB}R_{BC}}{R_{AB} +R_{BC} + R_{CA}}}[/Tex]
[Tex]\frac{R_{A}}{R_{B}}=\frac{R_{CA}}{R_{BC}}[/Tex]
RCA=(RARBC)/RB[Tex]R_{CA}=\frac{R_{A}R_{BC}}{R_B}[/Tex]
Similarly divide equation (5) by equation (7),
[Tex]\frac{ R_A}{R_C}=\frac{R_{AB}}{R_{BC}}[/Tex]
[Tex]R_{AB} =\frac{R_AR_{BC}}{R_C}[/Tex]
Substitute RAB, RCA in equation (5),
[Tex]R_A=\frac{\frac{(R_AR_{BC})^{2}}{R_BR_C}}{\frac{R_AR_{BC}}{R_C}+\frac{R_AR_{BC}}{R_B}+R_{BC}}[/Tex]
[Tex]R_A=\frac{(R_AR_BC)^{2}}{R_AR_BR_{BC}+R_AR_CR_{BC}+R_BR_CR_{BC}}[/Tex]
[Tex]1 = \frac{(R_AR_{BC})^{2}}{R_{BC}(R_AR_B+R_AR_C+R_BR_C)}[/Tex]
[Tex]1 =\frac{R_AR_{BC}}{R_AR_B+R_AR_C+R_BR_C}[/Tex]
[Tex]R_AR_B+R_AR_C+R_BR_C=R_AR_{BC}[/Tex]
[Tex]R_{BC}=R_B+R_C+\frac{R_BR_C}{R_A}[/Tex]
Similarly,
[Tex]R_{AB}=R_{A}+R_{B}+\frac{R_AR_B}{R_C}[/Tex]
[Tex]R_{CA}=R_C+R_A+\frac{R_CR_A}{R_B}[/Tex]
Star and Delta Connection
Star and delta connections are the types of three-phase circuits. Electric circuits are divided into Single-phase AC circuits and Three-phase AC circuits. A Single-phase system consists of two conductors, one is called phase (through which current flows) and the other is called neutral ( acts as a return way to complete the circuit). A Three-phase system consists of three conductors, which is the more economical way to transmit power than a single-phase system. In electrical circuit analysis there are certain type of complex circuits that have resistances connected in either series or parallel. These complex arrangements are usually connected in the T, Y, Delta or pi connections. Among these star and delta are some common types of connection.
Table of Content
- Star Connection
- Delta Connection
- Delta to Star Conversion
- Star to Delta Conversion
- Solved Example
- Star Vs Delta Connection
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