- 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 a network are most often joined as a star or as a delta. Delta joins the branches end to end in a closed triangle. Star joins each branch to one common point so the arms form a Y. The two layouts can be swapped to simplify a mesh, so a delta-to-star or Star to Delta transformation is often required.
Delta To Star Conversion
Replacing a delta or mesh with an equivalent star is called delta – star transformation. The two networks match if the impedance between any pair of terminals is the same. Measure between the same pair of lines and you get the same value whether a delta or its equivalent star sits between those lines.
Label the three corners of a delta A, B and C. The electrical resistance between A-B, B-C and C-A is R1, R2 and R3.
The resistance between A and B is
Now join a star to A, B and C. The star arms RA, RB and RC go to A, B and C. The resistance measured between A and B is then
Because the networks are equivalent, the resistance between A and B must match in both.
The resistance between B and C also matches,
and the resistance between C and A matches,
Add (I), (II) and (III):
Subtract (I), (II) and (III) from (IV):
The delta-star rule is then:
the star resistance at a terminal equals the product of the two delta resistances that meet that terminal, divided by the sum of all three delta resistances.
If each delta side has the same resistance R, the star arm r is
Star To Delta Conversion
For star – delta transformation multiply (v), (VI) and (VI), (VII) and (VII), (V). That product sum is (v) × (VI) + (VI) × (VII) + (VII) × (V):
Divide (VIII) by (V), (VI) and (VII) in turn:
