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.