The star to delta transformation can also be express as Y-Δ transformation, it is a mathematical method which used to solve different circuitries in the electric system. Its name wye-delta is due to the circuitry which it has when this technique applies to any circuitry. This transformation technique of the different circuitry was given by the Edwin Kennelly in 1899, who was an electrical engineer belongs to the United States of America. This conversion of circuitries is used for 3 phase circuits electrical system. Besides using in electrical circuitries star-delta transformation can also be used in maths to solve different planer graphs (these are such types of the graph which can make in a plane). In today’s post, we will have a look at its working, formula, equation, and uses. So, let’s get started with what is star-delta transformation.
What is Star Delta Transformation
- The (Y-∆) wye-delta transformation explains that the circuitries which has numerous resistances in three-phase arrangements can convert to another type of circuitry connection which is delta.
- To solve simplest ciruictries we use Kirchhoff’s current law, Kirchhoff’s voltage law, or ohm’s law but in cases of three-phase circuitries these laws difficult to apply due to complex circuitries.
- Three-phase circuits are connected in two ways to solve network, if they are connected in the Y like arrangements then called wye circuitry in this shape the all branches are connected with the common point.
- If the three-phase circuitry is connected like ∆ shape which is also a loop then it called the delta circuitry.
- Both of these circuits categories can be changed from one to other according to the network demand on which they are applying.
Equation of Star Delta Transformation
- Now we discuss how the transformation from star to delta occurs and find equation.
- In the given diagram, we discuss it for all resistances step by step.
- For resistance (A), the transformation values will be
(xy+ zy+ (zx/z))
- In the case of resistance (B), the value of transformation will be,
( yx+ zy+ (xz/y))
- For resistance (C), the transformation is
(yx + zy + (xz/x))
- By splitting each formula with the denominator value we will get three discrete alteration formulations which can be used to transform any ∆ resistor circuitry into a corresponding star circuitry.
- For resistsnce (A)
(xy+ zy+ (zx/z)) = (XY/Z + YZ/Z + ZX/Z) = ((XY/Z) +Y+X)
- In case of resistance (B)
( yx+ zy+ (xz/y))= (XY/Y + YZ/Y + ZX/Y) = ((ZX/Y) + X+Z)
- For resistance (C)
(yx + zy + (xz/x)) = (XY/X + YZ/X + ZX/X) = ((YZ/X) +Z+Y)
- The final equations for the star to ∆ adaptation are.
A= ((XY/Z) +Y+X)
B= ((ZX/Y) + X+Z)
C= ((YZ/X) +Z+Y)
- In this kind of adaptation, if the complete resistances values in the star assembly are equivalent then the resistances in the ∆ system will be 3-time of the star (*) system resistances (R).
- (Resistance (R) in ∆ System) = (3) x (Resistances in Star (*) System).
Example of Star Delta Transformation
- The star-∆ alteration complications are the finest samples to comprehend the idea of the circuitries.
- The resistance in a star system is represented with (X, Y, Z), which can be seen in above given diagram and the values of these resistances are (X= 80Ω), (Y= 120Ω), and (Z = 40Ω).
A= (XY/Z) +Y+X)
X= 80 Ω, Y= 120 Ω, and Z = 40 Ω
- By putting these parameters in the above formula we calculate the value of A.
A = (80 X 120/40) + 120 + 80 )= (240 + 120 + 80 )= (440 Ω)
- As we have find value of resistance (B) which is ((ZX/Y) + X+Z).
- Now we put values of in this equation to find the value of B.
B = ((40X80/120) + 80 + 40) = (27 + 120) = (147 Ω).
- Now we can calculate the value of resistance C by this equation
C= ((YZ/X) +Z+Y)
- Putting value in this equation we get C.
((120 x 40/80) + 40 + 120) = (60 + 160) = (220 Ω)
Delta To Star Transformation
- Now we see how we can converts delta circuitry back to the star connection.
- Let’s solve circuitry which is connected in the delta form and has 3 points a, b, c. The value of resistance among the joints a and b is (R1), resistance among the b and c is (R2), and c and d are (R3).
- The value of resistance among the points and b is given here.
(Rab) = (R1)ΙΙ(R1+R2)
- You can see there is another circuitry which is connected in the Y connection it has three branches a, a, c which has resistance (Ra, Rb, Rc).
- If we find the resistance among the points a and b then we have.
(Rab) = (Ra+Rb)
- As both of these circuitries are equivalent so the value of resistance measured among the points a and b.
- So the resistance values will also same in the among the point b and c.
(Rb + Rc)=[(R2). (R3+R1)]/(R1+R2+R3)—(y)
- And the value of resistance among the c and a will also same.
(Rc + Ra)=[(R3) x (R1+R2)]/(R1+R2+R3)—(z)
- If we add expressions (x),(y),(z) then we have.
- If we subtract the equation (x),(y), (z) from equation (d) then we have.
- The expression of the Y-Δ transformation can be defined as.
- From equations e,f,g we can conclude that the resistance in star configuration is equivalent to the multiple of the 2 resistors joined with the identical point divided by the sum of all resistors in the Δ circuitry.
- If in the delta circuitry the values of all resistors are identical then the correspondent resistance value (r) in the star circuit will be.
r = (R.R)/(R+R+R)
Advantage of Star Delta Conversion
- These are some advantages of this transformation which are described here.
- Star transformation is well suitable for transport voltages to long distances and it also has a neutral point which can be used to the unbalanced transient current of the circuitry to the ground.
- Delta transformation can transport balance three-phase voltage(V) without any neutral (n) wire which marks ∆ best for Transmission network.
It was a detailed article on Star Delta transformation if you have any question about it ask in comments. Take care until the next tutorial.