Star and Delta Connection.pdf

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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/DeltaconnectionisanarrangementofpassiveelementsR,LandC
suchthattheformedshaperesemblesastaroradeltasymbol.
Theseconnectionareneitherseriesandnorparallel.
Suchconnectionsaresimplifiedusingstar-to-deltaordelta-to-star
conversion.
SuchconnectionsarefoundincomplexDCcircuits,fullbridge
rectifiers.
SuchconnectionshaslargerapplicationinthreephaseACsystem.

14. STARCONNECTION
16
AstarnetworkisrearrangedformofTee(T)network.

15. STAR/WYE(Y)CONNECTION
17
Threeendsofresistorsareconnectedinwye(Y)orstarfashion.A
commonnodepointofstarconnectionisknownasneutral.
N

16. STARCONNECTION
18
Threewaysinwhichstarconnectionmayappearinacircuit.

17. DELTACONNECTION
19
WhenthreeresistorsareconnectedinafashiontoformaclosedmeshΔ,
connectionformedisknownasDeltaConnection.

18. DELTACONNECTION
20
Threewaysinwhichdeltaconnectionmayappearinacircuit.

19. DELTATOSTARTRANSFORMATION
21
Threeresistors connectedindeltaformanditsequivalent
starconnectionisshownbelow.
Delta andits equivalent Star,
AB BC CA
RR and R

20. DELTATOSTARTRANSFORMATION
22
•Twoarrangementsshownareelectricallyequivalent.
•ResistancebetweenAandBforstar=ResistancebetweenAand
Bfordelta.
•Therefore,()
A B AB BC CA
RRRRR 
(1)()
AB BC CA
AB
AB BC CA
RRR
RR
RRR



(2)
||

21. DELTATOSTARTRANSFORMATION
23
•SimilarlyforresistancebetweentwoterminalsB-CandC-A,
(3)()
CA AB BC
CA
AB BC CA
RRR
RR
RRR



(4)()
BC CA AB
BC
AB BC CA
RRR
RR
RRR




22. DELTATOSTARTRANSFORMATION
24
•Theobjectiveistofind intermsof .
•Subtracting(3)from(2)andaddingto(4)weobtain,
(5)
(6)ABCA
A
AB BC CA
RR
R
RRR

 ,
A B C
RR and R ,
AB BC CA
RR and R BCAB
B
AB BC CA
RR
R
RRR

 CABC
C
AB BC CA
RR
R
RRR


(7)

23. DELTATOSTARTRANSFORMATION
25
•Easywaytorememberdeltatostartransformationis,

Product of two adjacent arms of
Any arm of star connection =
Sum of arms of

24. STARTODELTATRANSFORMATION
26
Threeresistors connectedinstarformationandits
equivalentdeltaconnectionisshownbelow
Star and its Equivalent Delta,
A B C
RR and R

25. STARTODELTATRANSFORMATION
27
•Dividing(5)by(6)weobtain,
•Dividing(5)by(7)weobtain,CAA
B BC
RR
RR
 ABC
CA
B
RR
R
R

(8)
(9)A AB
C BC
RR
RR
 ABC
AB
C
RR
R
R

(10)
(11)

26. STARTODELTATRANSFORMATION
28
•Substituting(9)and(11)into(5),
•Similarly,BC
BC B C
A
RR
RRR
R

(12)
(13)
(14)AB
AB A B
C
RR
RRR
R
 CA
CA C A
B
RR
RRR
R


27. STARTODELTATRANSFORMATION
29
•Easywaytorememberstartodeltatransformationis,
Resistance between two terminals of Δ=
Sum of star resistances connected to those terminals +
product of same two resistances divided by the third

28. STAR\DELTATRANSFORMATION
30
•IfastarnetworkhasallresistancesequaltoR,itsequivalent
deltahasallresistancesequalto?
•IfadeltanetworkhasallresistancesequaltoR,itsequivalent
starhasallresistancesequalto?

29. STAR\DELTATRANSFORMATION
31
•IfastarnetworkhasallresistancesequaltoR,itsequivalent
deltahasallresistancesequalto3R.
•IfadeltanetworkhasallresistancesequaltoR,itsequivalent
starhasallresistancesequaltoR/3.

30. 32
SUMMARY

31. EQUIVALENTRESISTANCE
33
•Theequivalentresistanceofacircuitornetworkbetweenitsany
twopoints(orterminals)isthatsingleresistancewhichcanreplace
theentirecircuitbetweenthesepoints(orterminals).

32. DEFINITIONS
34
•STAR/DELTACIRCUITS:Thesecircuitsgenerallypossess
star/deltaconfigurationsandneedstobesimplifiedusingnecessary
transformationsandareconvertedintoseriesparallelcircuits.
NeitherSeries Nor ParallelCircuit

33. EQUIVALENTRESISTANCEOFSTAR/DELTACIRCUIT
35
•Thecircuitisacombinationofneitherseriesnorparallelcircuits.

34. EQUIVALENTRESISTANCEOFSTAR/DELTACIRCUIT
36
•RULE:Suchcircuitformstar/delta.Usestardeltatransformation
andconverttoequivalentseries-parallelcircuit.
•ChangingDeltaformedbypointsA,B,CintoequivalentStar,
•Thecircuitformedisnowcombinationofseries-parallelcircuit.
•Theseries-parallelcircuitisfurthersimplifiedtoseriescircuit./3
Y
RR
RR
RRR




35. EQUIVALENTRESISTANCEOFSTARDELTACIRCUIT
37
Thecircuitnowbecomesasimpleseries-parallelcircuitandcanbe
solvedeasily. A

36. EXERCISE/NUMERICAL ANALYSIS
38
Q.ConverttheYnetworktoanequivalentΔnetwork.

37. EXERCISE/NUMERICAL ANALYSIS
397.55
7.55 25
3
a
R ohms

  53
53 10
7.5
c
R ohms

 7.53
7.53 15
5
b
R ohms

 
Soln:

38. EXERCISE/NUMERICAL ANALYSIS
40
Q.ConverttheΔnetworktoanequivalentYnetwork.

39. EXERCISE/NUMERICAL ANALYSIS
41
Soln:1
1025
5
151025
bc
abc
RR
R ohms
RRR

  
  2
2515
7.5
50
ca
abc
RR
R ohms
RRR

  
 3
1510
3
50
ab
abc
RR
R ohms
RRR

  


40. EXERCISE/NUMERICAL ANALYSIS
42
Q.Usingdelta/startransformation,findequivalentresistanceacrossAC.

41. EXERCISE/NUMERICAL ANALYSIS
43
Soln:Deltacanbereplacedbyequivalentstar-connectedresistances,1
1020
2.86
104020
ABDA
AB DA BD
RR
R ohms
RRR

  
  2
1040
5.72
104020
ABBD
AB DA BD
RR
R ohms
RRR

  
  3
1040
11.4
104020
DABD
AB DA BD
RR
R ohms
RRR

  
 

42. EXERCISE/NUMERICAL ANALYSIS
44
Figurenowbecomes,  
(305.72)(1511.4)
2.86 18.04
305.721511.4
AC
R ohms
 
 
 

43. EXERCISE/NUMERICAL ANALYSIS
45
Q.CalculateequivalentresistanceacrossterminalsAandB.

44. EXERCISE/NUMERICAL ANALYSIS
46
Soln:ConvertinginnerSTAR(3ohms,3ohmsand1ohms)intoDelta.1
33
33 15
1
R ohms

 2
31
31 5
3
R ohms

 3
13
13 5
3
R ohms



45. EXERCISE/NUMERICAL ANALYSIS
47
Circuitnowbecomes,

46. EXERCISE/NUMERICAL ANALYSIS
48
Delta-connectedresistances1Ω,5Ωand8areconvertedinstar,'
1
184
1587
R ohms


 '
2
515
15814
R ohms


 '
3
8520
1587
R ohms




47. EXERCISE/NUMERICAL ANALYSIS
49
Circuitnowbecomes,45 2020
2.5 7.610
714 79
AB
R ohms
  
   
  
  
||

48. EXERCISE/NUMERICAL ANALYSIS
50
Q.CalculateequivalentresistanceacrossterminalsAandB.

49. EXERCISE/NUMERICAL ANALYSIS
51
Soln:ReplacinginnerSTARintoDELTA.

50. EXERCISE/NUMERICAL ANALYSIS
52
15.8ohmisinparallelwith5ohmand26.3ohmisinparallelwith
4ohm,circuitbecomes

51. EXERCISE/NUMERICAL ANALYSIS
53
Convertingupperdeltaintostar,

52. EXERCISE/NUMERICAL ANALYSIS
54
Nowequivalentresistancecanbecalculatedas,4.23
eq
R(3·8 + 2·98) || (1·99 + 3·5) + 1·2
ohms



53. EXERCISE/NUMERICAL ANALYSIS
55
Q.ObtaintheequivalentresistanceRabforthecircuitanduseitto
findcurrenti.

54. EXERCISE/NUMERICAL ANALYSIS
56
Soln:Inthiscircuit,therearetwoYnetworksandthreeΔnetworks.
Transformingjustoneofthesewillsimplifythecircuit.

55. EXERCISE/NUMERICAL ANALYSIS
57
WeconverttheY-networkcomprisingthe5-Ω,10-Ω,and20-Ωresistors
intodelta.1
510
510 17.5
20
R ohms

  2
520
520 35
10
R ohms

  3
1020
1020 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/NUMERICAL ANALYSIS
58
Combiningthethreepairsofresistorsinparallel,weobtain.(7.29210.5)21
17.79221
17.79221
ab
R
=9.632 ohms
  

 120
12.458
9.632
s
ab
v
iA
R
 
(12.5 || 17.5 Ω)
(15 || 35 Ω)
(30 || 70 Ω)
||

57. EXERCISE/NUMERICAL ANALYSIS
59
Q.DeterminetheloadcurrentinbranchEFinthecircuitshown.

58. EXERCISE/NUMERICAL ANALYSIS
60
Sol.ACGAformsdelta,Convertingittoequivalentstar.200500
111.11
900
AN
R ohms

 500200
111.11
900
GN
R ohms

 200200
44.44
900
CN
R ohms



59. EXERCISE/NUMERICAL ANALYSIS
61
Circuitcanberedrawnas111.11600711.11
NEF
R ohms  60044.44644.44
ND
R ohms 

60. EXERCISE/NUMERICAL ANALYSIS
62
BranchesNCDandNEFareinparallel,711.11||644.44=338ohms.
TotalcurrentIinthecircuit=100
0.222
111.11338
eq
V
IA
R
 


61. EXERCISE/NUMERICAL ANALYSIS
63
ToobtaincurrentinbranchEF,weapplycurrentdivisionformula.644.44
0.222
711.11644.44
0.1055
NCD
NEF
NCD NEF
R
II
RR
A






62. EXERCISE
64
Q.Asquareanditsdiagonalsaremadeofauniformcoveredwire.The
resistanceofeachsideis1Ωandthatofeachdiagonalis1·414Ω.
Determinetheresistancebetweentwooppositecornersofthesquare.

63. EXERCISE
65
Q.DeterminetheresistancebetweentheterminalsAandBofthenetwork.

64. EXERCISE
66
Q.Findthecurrentin10Ωresistorinthenetworkshownbystar-delta
transformation.

65. EXERCISE
67
Q.Usingstar/deltatransformation,determinethevalueofRforthe
networkshownsuchthat4Ωresistorconsumesthemaximumpower.

66. REFERENCES
68
[1]Charles.K.AlexanderandMatthewSadiku“FundamentalofElectricCircuits”,
McGraw-HillEducation,2PennPlaza,NewYork,NY10121,ch.2and3.
[2]EdwardHughes,JohnHiley,KeithBrownandIanMcKenzieSmithHughes
“Electrical&ElectronicTechnology”,PearsonEducationLimited,EdinburghGate,
England,ch.2and3.
[3]V.K.MehtaandRohitMehta“BasicElectricalEngineering”,S.Chand&Company
Pvt.Ltd.,RamNagar,NewDelhi,ch.2.