Very good information

1. INTRODUCTION
3
Star connections is generally used in long distance transmission lines as
insulation requirement is less in star connection.
Transmission Network

2. INTRODUCTION
4
Delta connections are generally used in distribution networks for short
distances.
Distribution Network

3. INTRODUCTION
5
Alternators and generators are usually star connected.
600 MW Turbo-Generator at power plant

4. INTRODUCTION
6
Transformer windings are connected in Star/Delta Connections.
A Three Phase Transformer with Name Plate

5. INTRODUCTION
7
Generating transformer near to power plant generator are connected in
star connection to provide grounding protection.
Generating Transformer

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

8. INTRODUCTION
10
Delta-Star Starters are installed in cement industries for high inertial load
applications.
Cement Industry

9. INTRODUCTION
11
Power capacitors in 3 phase capacitor bank connections are either delta
connected or star (wye) connected.
Delta connected capacitor bank

10. INTRODUCTION
12
The application of such connection is also used in high voltage direct
current (HVDC) systems.
Generating Transformer

11. INTRODUCTION
13
The application of such connection is also used in Wheatstone bridge
resistance measurement device.
Wheatstone Bridge

12. INTRODUCTION
14
STAR/Delta transformations and equivalent circuit calculations help in
simplification and understanding of complex electrical circuits.
Complex Electric Circuits

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.

14. STAR CONNECTION
16
A star network is rearranged form of Tee (T) network.

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

16. STAR CONNECTION
18
Three ways in which star connection may appear in a circuit.

17. DELTA CONNECTION
19
When three resistors are connected in a fashion to form a closed mesh Δ,
connection formed is known as Delta Connection.

18. DELTA CONNECTION
20
Three ways in which delta connection may appear in a circuit.

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.

30. 32
SUMMARY

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

36. EXERCISE/NUMERICALANALYSIS
38
Q. Convert the Y network to an equivalent Δ network.

37. EXERCISE/NUMERICALANALYSIS
39
7.5 5
7.5 5 25
3
a
R ohms

   
5 3
5 3 10
7.5
c
R ohms

   
7.5 3
7.5 3 15
5
b
R ohms

   
Soln:

38. EXERCISE/NUMERICALANALYSIS
40
Q. Convert the Δ network to an equivalent Y network.

39. EXERCISE/NUMERICALANALYSIS
41
Soln:
1
10 25
5
15 10 25
b c
a b c
R R
R ohms
R R R

  
   
2
25 15
7.5
50
c a
a b c
R R
R ohms
R R R

  
 
3
15 10
3
50
a b
a b c
R R
R ohms
R R R

  
 

40. EXERCISE/NUMERICALANALYSIS
42
Q. Using delta/star transformation, find equivalent resistance across AC.

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

  
   

42. EXERCISE/NUMERICALANALYSIS
44
Figure now becomes,
   
(30 5.72) (15 11.4)
2.86 18.04
30 5.72 15 11.4
AC
R ohms
  
  
  

43. EXERCISE/NUMERICALANALYSIS
45
Q. Calculate equivalent resistance across terminals A and B.

44. EXERCISE/NUMERICALANALYSIS
46
Soln: Converting inner STAR (3 ohms, 3 ohms and 1 ohms ) into Delta.
1
3 3
3 3 15
1
R ohms

   
2
3 1
3 1 5
3
R ohms

   
3
1 3
1 3 5
3
R ohms

   

45. EXERCISE/NUMERICALANALYSIS
47
Circuit now becomes,

46. EXERCISE/NUMERICALANALYSIS
48
Delta-connected resistances 1 Ω, 5 Ω and 8 are converted in star,
'
1
1 8 4
1 5 8 7
R ohms

 
 
'
2
5 1 5
1 5 8 14
R ohms

 
 
'
3
8 5 20
1 5 8 7
R ohms

 
 

47. EXERCISE/NUMERICALANALYSIS
49
Circuit now becomes,
4 5 20 20
2.5 7.6 10
7 14 7 9
AB
R ohms
 
   
     
   
 
   
 
||

48. EXERCISE/NUMERICALANALYSIS
50
Q. Calculate equivalent resistance across terminals A and B.

49. EXERCISE/NUMERICALANALYSIS
51
Soln: Replacing inner STAR into DELTA.

50. EXERCISE/NUMERICALANALYSIS
52
15.8 ohm is in parallel with 5 ohm and 26.3 ohm is in parallel with
4 ohm, circuit becomes

51. EXERCISE/NUMERICALANALYSIS
53
Converting upper delta into star,

52. EXERCISE/NUMERICALANALYSIS
54
Now equivalent resistance can be calculated as,
4.23
eq
R (3·8 + 2·98) || (1·99 + 3·5) + 1·2
ohms



53. EXERCISE/NUMERICALANALYSIS
55
Q. Obtain the equivalent resistance Rab for the circuit and use it to
find current i.

54. EXERCISE/NUMERICALANALYSIS
56
Soln: In this circuit, there are two Y networks and three Δ networks.
Transforming just one of these will simplify the circuit.

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)
||

57. EXERCISE/NUMERICALANALYSIS
59
Q. Determine the load current in branch EF in the circuit shown.

58. EXERCISE/NUMERICALANALYSIS
60
Sol. ACGA forms delta, Converting it to equivalent star.
200 500
111.11
900
AN
R ohms

 
500 200
111.11
900
GN
R ohms

 
200 200
44.44
900
CN
R ohms

 

59. EXERCISE/NUMERICALANALYSIS
61
Circuit can be redrawn as
111.11 600 711.11
NEF
R ohms
  
600 44.44 644.44
ND
R ohms
  

60. EXERCISE/NUMERICALANALYSIS
62
Branches NCD and NEF are in parallel, 711.11 || 644.44=338 ohms.
Total current I in the circuit =
100
0.222
111.11 338
eq
V
I A
R
  


61. EXERCISE/NUMERICALANALYSIS
63
To obtain current in branch EF, we apply current division formula.
644.44
0.222
711.11 644.44
0.1055
NCD
NEF
NCD NEF
R
I I
R R
A
 

 



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.

63. EXERCISE
65
Q. Determine the resistance between the terminals A and B of the network.

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.