International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol.2, Issue 3 Sep 2012 64-74 © TJPRC Pvt. Ltd.,

AN EFFICIENT LOAD FLOW SOLUTION AND VSI ANALYSIS FOR RADIAL DISTRIBUTION SYSTEM LOKENDRA KUMAR1, DEEPESH SHARMA2 & SHUBRA GOEL3 1,3

Assistant Professor, Vidya College of Engineering , Meerut, Uttar Pradesh, India 2

Assistant Professor,BRCMCET ,Bahal, Haryana, India

ABSTRACT This paper presents a simple approach for load flow analysis of a radial distribution networks. The proposed method uses the simple recursive equation to compute the voltage magnitude and angle. The proposed approach has been tested on several Radial Distribution Systems of different size and configuration and found to be computationally efficient and analyze a voltage stability index in that network. It shows the value of voltage stability index at each node and predicts which node is more sensitive to voltage collapse. This paper also presents the effect on voltage stability index with variation in active power, reactive power, active and reactive power both.

KEYWORDS : Load Flow Analysis, Radial Distribution System, Voltage Stability Index, Voltage, Current, Active And Reactive Power.

65

An Efficient Load Flow Solution and VSI Analysis for Radial Distribution System

66

Lokendra Kumar & Deepesh Sharma & Shubra Goel

ASSUMPTION It is assumed that radial distribution networks are balanced and represented by their single-line diagrams.

PROPOSED METHOD Load Flow Method Consider a line connected between two nodes as shown in the fig 1

Fig 1. line connected between two nodes

Fig: 2 Basic phasor diagram of a line connected between two nodes Voltage equation calculated from above phasor diagram shown in fig:2 V2= (B[j]-A[j])1/2

...1

Where A[j] = P2R[j] +Q2X[j]-0.5V12 B[j] = [A[j]2- (P22+Q22) (R[j]2+X[j]2)]1/2 Where P2 and Q2 are total real and reactive power load feed through node 2 Ploss[j] =R[j]* (P22+ Q22)/ V22 Qloss[j] =X[j]* (P22+ Q22)/ V22 Angle Î¸2 =Angle of V1-(1/cos((1-(P2R2-Q2X2)/(V2V1))))

Voltage Stability Index The proposed voltage stability index will be formulated in this section. The sending end voltage can be written as

67

An Efficient Load Flow Solution and VSI Analysis for Radial Distribution System

V1 = V2 + I ( R + jX ) = V2 +

= V2 +

=

S i∗ ( R + jX ) V 2∗

(P

− jQ

j

V 2∗

V2

j

) (R +

jX )

+ PjR + Q j X + j( Pj X − Q jR )

2

V 2∗

…2

Now substitute the voltage by its magnitude, equation 1 can be written as

V1 =

(V

2 2

+ PjR + Q j X

) + (P 2

j

X − Q jR

)

2

V2

V1 V2 = V24 + ( Pj R + Q j X ) + 2 V2 2

2

(P R + Q X ) + (P X − Q R) j

j

j

2

j

…3

Rearranging equation2, it will become

V24 + ( Pj R + Q j X ) + ( Pj X − Q j R ) + 2 V2 2

2

2

(P R + Q X ) − V j

j

2

1

V2 = 0 2

2 2 V24 + ( Pj R + Q j X ) + ( Pj X − Q j R ) + V2  2 ( Pj R + Q j X ) − V1  = 0   2

2

The equation 4 is in form of

ax 2 + bx + c = 0

…4

. To guarantee that 3 is solvable, the following

b − 4ac ≥ 0 2

inequality constraint should be satisfied i.e.,

V1 4 − 4 V1

2

(P R + Q j

X ) − 4 ( Pj X − Q j R ) ≥ 0 2

j

With the increase of receiving end power demand, the left hand side of equation 4 approaches zero, and the two bus network reaches its maximum power transfer limit. So the voltage stability index is

VSI = V14 − 4 V1

2

( P R + Q X ) − 4( P X − Q R) j

j

j

2

j

…5

CASE STUDY In this paper we are testing the eq.4. by increasing the receiving end power demand. Case(1) When active & reactive power both increases with a multiplier K .Then eq.5. will be

VSI ( P & Q ) = V14 − 4 V1

2

( KP R + KQ X ) − 4 ( KP X − KQ R ) j

j

j

j

2

68

Lokendra Kumar & Deepesh Sharma & Shubra Goel

Case (2) When only active power increases with the multiplier K .Then eq. 5. Will be

VSI ( P) = V14 − 4 V1

2

( KP R + Q X ) − 4 ( KP X − Q R ) j

j

j

2

j

Case (3) When only reactive power increases with the multiplier K. Then eq. 5. Will be

VSI (Q ) = V14 − 4 V1

2

( P R + KQ X ) − 4 ( P X − KQ R ) j

j

j

2

j

RESULTS The result obtained from the load flow method (38 and 33 node system) has been considered for the study of voltage stability index analysis. The result for the 28- Node system and 33-Node system shown in table 1 and 2 along with the graph in figure 3 and 4 along with graph in figure 5 & 6

REFERENCES (1) W.H.Kersting and Mendive, ”An application of Ladder Network Theory to the solution of three phase Radial Load Flow Problem,” IEEE PES Winter Meeting, 1976. (2) W.H.Kersting ,”A Method To Design And Operation of Distribution system ,”IEEE Trans., vol.PAS103, pp 1945-1952, 1984. (3) R.A.Stevens, D.T.Rizy, and S.L.Puruker, ”Performance of Conventional Power Flow Routines for Real Time Distribution Automations Application ,” Proceeding of 18th south eastern Symposium on System Theory, (IEEE), pp. 196-200,1986. (4) Lokendra kr,R.ranjan,N.Yadav “ Novel Algorithm For Solving Of Radial Distribution Networks Using C++,” IFRSA’s International Journal Of Computing|Vol1|issue 4|October 2011 (5) M.E.Baran and F.F.Wu, “Optimal Sizing of Capacitor Placed on Radial Distribution System,” IEEE Trans., vol.PWRD-2,PP 735-743, 1989.S (6) Ulas Eminoglu and M.Hacaoglu, ” A New Power Flow Method for radial distribution system including Voltage Dependent Load Flow Modal,” Electric Power System Research, vol.76,pp 106114,2005. (7) Ranjan R. and D.Das, ”Novel computer Algorithm for solving radial distribution network,” Journal of electric power component and system, vol.31, no.1,pp 95-107,jan 2003. (8) P.Kessel and H.Gliavitsch, ”Estimating the voltage stability of a power system ,” IEEE Transaction on power delivery,vol.PWRD-1,NO.3 pp 346-354,jul 1986. (9) M.H.Haque, “A Fast Method for determining the voltage stability limit of a power system,” “Electric Power System Research, vol.32, pp 35-43,1995.

69

An Efficient Load Flow Solution and VSI Analysis for Radial Distribution System

(10) F. Gubina and B Strmcnic, ”A Simple approach to voltage stability assessment in radial networks,” IEEE Transaction of power system,vol.12,no.3,pp 1121-1128,AUG 1997.

S.No.

Node No.

Voltage Magnitude(P.U.)

Angle

1

1

1

0

2

2

0.95678

-1.7739

3

3

0.91151

-1.7672

4

4

0.88726

-1.8023

5

5

0.87129

-1.8197

6

6

0.81281

-1.7331

7

7

0.77494

-1.7685

8

8

0.75626

-1.8074

9

9

0.72416

-1.7759

10

10

0.685

-1.8488

11

11

0.66035

-1.7562

12

12

0.64956

-1.7772

13

13

0.62187

-1.8166

14

14

0.60039

-1.7643

15

15

0.58758

-1.7753

16

16

0.57835

-1.8056

17

17

0.57036

-1.8225

18

18

0.5675

-1.8195

19

19

0.9501

-1.841

20

20

0.94787

-1.8332

21

21

0.94509

-1.8474

22

22

0.94309

-1.8461

23

23

0.90572

-1.8463

24

24

0.90195

-1.8361

25

25

0.89877

-1.8434

26

26

0.80928

-1.8416

27

27

0.80807

-1.8395

28

28

0.80751

-1.8471

VSI

0.797673997 0.705037231 0.70777414 0.696541018 0.521350467 0.502450032 0.50641817 0.444384184 0.386954148 0.378121214 0.383615455 0.334355042 0.319556679 0.316145152 0.31083112 0.30461443 0.30707373 0.857739708 0.867278648 0.85896559 0.854552058 0.770414227 0.768258322 0.759956409 0.605573185 0.608196588 0.608197974

70

Lokendra Kumar & Deepesh Sharma & Shubra Goel

S.No.

Node No.

Voltage Magnitude(P.U.)

Angle

1

1

1

0

2

2

0.997024

-1.8464

3

3

0.982924

-1.8305

4

4

0.975433

-1.8407

5

5

0.96802

-1.8407

6

6

0.949553

-1.8382

7

7

0.946025

-1.8533

8

8

0.932363

-1.8307

9

9

0.926024

-1.8411

10

10

0.92016

-1.8419

11

11

0.918198

-1.8523

12

12

0.916681

-1.8474

13

13

0.910499

-1.8417

14

14

0.908206

-1.8489

15

15

0.906778

-1.8484

16

16

0.905395

-1.8483

17

17

0.903344

-1.8488

18

18

0.90273

-1.8499

19

19

0.996496

-1.8502

20

20

0.992919

-1.8464

21

21

0.992214

-1.8502

22

22

0.991789

-1.8497

23

23

0.979339

-1.8456

24

24

0.972667

-1.842

25

25

0.969342

-1.8463

26

26

0.947625

-1.849

27

27

0.945062

-1.8485

28

28

0.933624

-1.8506

29

29

0.925405

-1.8512

30

30

0.921847

-1.8486

31

31

0.917686

-1.8464

32

32

0.91677

-1.8501

VSI

0.97750862 0.88492637 0.88295501 0.85762879 0.75827594 0.79663604 0.71989823 0.72361773 0.70703595 0.71310664 0.70982353 0.67692071 0.68180369 0.68013802 0.67615419 0.66809386 0.67053897 0.98456008 0.95856285 0.96705921 0.96649308 0.9094501 0.8734755 0.87370057 0.80711546 0.79655438 0.73055688 0.71504245 0.71865483 0.70389943 0.71114872

71

An Efficient Load Flow Solution and VSI Analysis for Radial Distribution System

33

33

0.916487

-1.8508

0.71222868

For 28 node system

Fig-3

In this graph both voltage & VSI have same minimum Minimum voltage is at node n= 17, Maximum voltage is at node = 18

&

maximum

points

For 33 node system

Fig-4

The graph indicating that both voltage & VSI have same minimum & maximum point which is at node no 17 & 18 respectively.

72

Lokendra Kumar & Deepesh Sharma & Shubra Goel

Table 3 Result for the Effect of Change in Receiving End Power on VSI of 28 Node System

Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

P_Q 0

P 0

Q 0

0.0065 0.0044 0.0189 0.0176 0.0352 0.0021 0.0053 0.0004 0.0153 0.0016 0.0035 0.0116 0.0034 0.0016 0.0035 0.0027 0.0008 4E-05 0.0018 0.0011 0.0014 0.0008 0.0005 0.0003 0.0054 0.0015 0.0306 0.0078 0.0081 0.0119 0.0002 0.0008

0.003 5E-04 0.012 0.012 0.01 0.011 0.035 0.004 0.014 0.006 0.003 0.003 0.003 6E-04 4E-04 0.002 0.001 0.001 0.01 0.001 7E-04 0.01 0.018 0.008 0.001 0.004 0.019 0.011 0.003 0.002 0.001 5E-04

0.004727 0.007375 0.005049 0.000894 0.019394 0.003903 0.006119 0.007232 0.002335 0.003454 0.000798 0.003752 0.000881 0.001048 0.000396 0.001715 9.53E-05 0.000374 0.00138 0.000142 0.000511 0.000289 0.005474 0.003002 0.002101 0.003287 0.009552 0.013444 0.00688 0.0045 0.001086 5.95E-05

73

An Efficient Load Flow Solution and VSI Analysis for Radial Distribution System

Fig-5 Table 4- Result foe the effect of change in receiving end power on VSI of 33 Node system

This graph shows the value of(VSI Vs P_Q)i.e. the values of VSI when we are using multiplier both with P,Q to increase the value of receiving end power demand so that the left hand side eq. approaches to zero. Beyond these values at each node result becomes negative ,minimum value is at node = 11 VSIP = Varying the equation of VSI by using multiplier with P,minimum value is at node = 16 VSIQ = Varying the equation of VSI by using multiplier with Q,minimum value is at node = 25

Lokendra Kumar & Deepesh Sharma & Shubra Goel

74

Fig-6

This graph shows the value of(VSI Vs P_Q)i.e. the values of vsi when we are using multiplier both with p,q to increase the value of receiving end power demand so that the left hand side eq. approaches to zero. beyond these values at each node result becomes negative minimum value is at node = 18

.

VSIP = Varying the equation of VSI by using multiplier with P minimum value is at node = 15

.

VSIQ = Varying the equation of VSI by using multiplier with Q minimum value is at node = 32

6-EEE - IJEEER - An Efficient - Lokendra Kumar - Paid