1. INTRODUCTION
3
Star connections is generally used in long distance transmission lines as
insulation requirement is less in star connection.
Transmission Network
6. INTRODUCTION
8
AC motors winding are connected in star/delta connection depending on
requirement and application.
Three Phase Induction Motor Winding
7. INTRODUCTION
9
Star and Delta connections are used in starting of three phase induction
motors using STAR-DELTA Starter.
Star Delta Starter for Three phase Induction Motor
9. INTRODUCTION
11
Power capacitors in 3 phase capacitor bank connections are either delta
connected or star (wye) connected.
Delta connected capacitor bank
13. INTRODUCTION
15
Star/Delta connection is an arrangement of passive elements R, L and C
such that the formed shape resembles a star or a delta symbol.
These connection are neither series and nor parallel.
Such connections are simplified using star-to-delta or delta-to-star
conversion.
Such connections are found in complex DC circuits, full bridge
rectifiers.
Such connections has larger application in three phase AC system.
15. STAR/WYE (Y) CONNECTION
17
Three ends of resistors are connected in wye (Y) or star fashion. A
common node point of star connection is known as neutral.
N
19. DELTA TO STAR TRANSFORMATION
21
Three resistors connected in delta form and its equivalent
star connection is shown below.
Delta and its equivalent Star
,
AB BC CA
R R and R
20. DELTA TO STAR TRANSFORMATION
22
• Two arrangements shown are electrically equivalent.
• Resistance between A and B for star = Resistance between A and
B for delta.
• Therefore,
( )
A B AB BC CA
R R R R R
(1)
( )
AB BC CA
A B
AB BC CA
R R R
R R
R R R
(2)
||
21. DELTA TO STAR TRANSFORMATION
23
• Similarly for resistance between two terminals B-C and C-A,
(3)
( )
CA AB BC
C A
AB BC CA
R R R
R R
R R R
(4)
( )
BC CA AB
B C
AB BC CA
R R R
R R
R R R
22. DELTA TO STAR TRANSFORMATION
24
• The objective is to find in terms of .
• Subtracting (3) from (2) and adding to (4) we obtain,
(5)
(6)
AB CA
A
AB BC CA
R R
R
R R R
,
A B C
R R and R ,
AB BC CA
R R and R
BC AB
B
AB BC CA
R R
R
R R R
CA BC
C
AB BC CA
R R
R
R R R
(7)
23. DELTA TO STAR TRANSFORMATION
25
• Easy way to remember delta to star transformation is,
Product of two adjacent arms of
Any arm of star connection =
Sum of arms of
24. STAR TO DELTA TRANSFORMATION
26
Three resistors connected in star formation and its
equivalent delta connection is shown below
Star and its Equivalent Delta
,
A B C
R R and R
25. STAR TO DELTA TRANSFORMATION
27
• Dividing (5) by (6) we obtain,
• Dividing (5) by (7) we obtain,
CA
A
B BC
R
R
R R
A BC
CA
B
R R
R
R
(8)
(9)
A AB
C BC
R R
R R
A BC
AB
C
R R
R
R
(10)
(11)
26. STAR TO DELTA TRANSFORMATION
28
• Substituting (9) and (11) into (5),
• Similarly,
B C
BC B C
A
R R
R R R
R
(12)
(13)
(14)
A B
AB A B
C
R R
R R R
R
C A
CA C A
B
R R
R R R
R
27. STAR TO DELTA TRANSFORMATION
29
• Easy way to remember star to delta transformation is,
Resistance between two terminals of Δ =
Sum of star resistances connected to those terminals +
product of same two resistances divided by the third
28. STARDELTA TRANSFORMATION
30
• If a star network has all resistances equal to R, its equivalent
delta has all resistances equal to ?
• If a delta network has all resistances equal to R, its equivalent
star has all resistances equal to ?
29. STARDELTA TRANSFORMATION
31
• If a star network has all resistances equal to R, its equivalent
delta has all resistances equal to 3R.
• If a delta network has all resistances equal to R, its equivalent
star has all resistances equal to R/3.
31. EQUIVALENT RESISTANCE
33
• The equivalent resistance of a circuit or network between its any
two points (or terminals) is that single resistance which can replace
the entire circuit between these points (or terminals).
32. DEFINITIONS
34
• STAR/DELTA CIRCUITS: These circuits generally possess
star/delta configurations and needs to be simplified using necessary
transformations and are converted into series parallel circuits.
Neither Series Nor Parallel Circuit
33. EQUIVALENT RESISTANCE OF STAR/DELTA CIRCUIT
35
• The circuit is a combination of neither series nor parallel circuits.
34. EQUIVALENT RESISTANCE OF STAR/DELTA CIRCUIT
36
• RULE: Such circuit form star/delta. Use star delta transformation
and convert to equivalent series-parallel circuit.
• Changing Delta formed by points A,B,C into equivalent Star,
• The circuit formed is now combination of series-parallel circuit.
• The series-parallel circuit is further simplified to series circuit.
/ 3
Y
R R
R R
R R R
35. EQUIVALENT RESISTANCE OF STAR DELTA CIRCUIT
37
The circuit now becomes a simple series-parallel circuit and can be
solved easily. A
41. EXERCISE/NUMERICALANALYSIS
43
Soln: Delta can be replaced by equivalent star-connected resistances,
1
10 20
2.86
10 40 20
AB DA
AB DA BD
R R
R ohms
R R R
2
10 40
5.72
10 40 20
AB BD
AB DA BD
R R
R ohms
R R R
3
10 40
11.4
10 40 20
DA BD
AB DA BD
R R
R ohms
R R R
55. EXERCISE/NUMERICALANALYSIS
57
We convert the Y-network comprising the 5-Ω, 10-Ω, and 20-Ω resistors
into delta.
1
5 10
5 10 17.5
20
R ohms
2
5 20
5 20 35
10
R ohms
3
10 20
10 20 70
5
R ohms
(comes in parallel with 12.5 Ω)
(comes in parallel with 15 Ω)
(comes in parallel with 30 Ω)
56. EXERCISE/NUMERICALANALYSIS
58
Combining the three pairs of resistors in parallel, we obtain.
(7.292 10.5) 21
17.792 21
17.792 21
ab
R
=9.632 ohms
120
12.458
9.632
s
ab
v
i A
R
(12.5 || 17.5 Ω)
(15 || 35 Ω)
(30 || 70 Ω)
||
62. EXERCISE
64
Q. A square and its diagonals are made of a uniform covered wire. The
resistance of each side is 1 Ω and that of each diagonal is 1·414 Ω.
Determine the resistance between two opposite corners of the square.
64. EXERCISE
66
Q. Find the current in 10 Ω resistor in the network shown by star-delta
transformation.
65. EXERCISE
67
Q. Using star/delta transformation, determine the value of R for the
network shown such that 4Ω resistor consumes the maximum power.
66. REFERENCES
68
[1] Charles. K. Alexander and Matthew Sadiku “Fundamental of Electric Circuits”,
McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121, ch. 2 and 3.
[2] Edward Hughes, John Hiley, Keith Brown and Ian McKenzie Smith Hughes
“Electrical & Electronic Technology”, Pearson Education Limited, Edinburgh Gate,
England, ch. 2 and 3.
[3] V. K. Mehta and Rohit Mehta “Basic Electrical Engineering”, S. Chand & Company
Pvt. Ltd., Ram Nagar, New Delhi, ch. 2.