- Star and Delta Connections Definition: Star and Delta connections are two ways to connect three branches in an electrical network, forming either a Y shape or a triangle.
- Delta to Star Conversion Formula: To convert Delta to Star, use the formula where the Star resistance at a terminal equals the product of the Delta resistances at that terminal, divided by the sum of all Delta resistances.
- Impedance Equality: The impedance between any two points in a Star or Delta configuration remains the same after conversion, ensuring the circuits are equivalent.
- Star to Delta Conversion: For converting from Star to Delta, specific formulas are used, which are derived from the properties of the original and converted resistances.
- Practical Application: Star to Delta conversion simplifies complex electrical network analysis, making it easier to understand and solve circuit problems.
Three branches in an electrical network can be connected in various forms, with Star and Delta being the most common. In a Delta connection, the branches form a closed triangular loop, connected end-to-end. In a Star connection, each branch connects to a common central point, creating a Y shape. These connections can be transformed from one form to another to simplify complex networks, making Delta to Star or Star to Delta transformation often necessary.
Delta To Star Conversion
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.
Imagine a Delta system with three corner points labeled A, B, and C. The electrical resistance between points A and B, B and C, and C and A are R1, R2 and R3 respectively.
The resistance between the points A and B will be,
Now, connect a Star system to points A, B, and C. The three arms of the Star system, labeled RA, RB and RC, connect to points A, B, and C respectively. If we measure the resistance between points A and B, it will be,
Since the two systems are identical, resistance measured between terminals A and B in both systems must be equal.
Similarly, the resistance between points B and C is equal in both systems,
And resistance between points C and A being equal in the two systems,
Adding equations (I), (II) and (III) we get,
Subtracting equations (I), (II) and (III) from equation (IV) we get,
The relation of delta – star transformation can be expressed as follows.
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 delta connected system has same resistance R at its three sides then equivalent star resistance r will be,
Star To Delta Conversion
For star – delta transformation we just multiply equations (v), (VI) and (VI), (VII) and (VII), (V) that is by doing (v) × (VI) + (VI) × (VII) + (VII) × (V) we get,
Now dividing equation (VIII) by equations (V), (VI) and equations (VII) separately we get,
