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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.

INTRODUCTION THE exact electrical performance of the system operating under steady state is required in efficient way known load−flow study that provides the real and reactive power losses of the system and voltages at different nodes of the system. With the growing market in the present time, effective planning can only be assured with the help of efficient load−flow study. The distribution network is radial in nature having high R/X ratio whereas the transmission system is loop in nature having high X/R ratio. Therefore, the variables for the load−flow analysis of distribution systems are different from that of transmission systems .The distribution networks are known as ill-conditioned. The conventional Gauss Seidel (GS) and Newton Raphson (NR) method does not converge for the distribution networks. A number of efficient load−flow methods for transmission systems are available in literature. A few methods had been reported in literature for load−flow analysis of distribution systems. The distribution system , which have separate feeders radiating from a single substation and feed the distribution at only one end are called radial distribution system (RDS). This paper presents two issue in RDS (a) load flow method (b) Voltage stability index. The radial distribution system have high R/X ratio. Due to this reason, conventional Newton-Raphson method and Fast Decoupled load flow method fails to converge in many cases. Kersting & Mendive [1] & Kersting[2] have developed load flow techniques based on ladder theory whereas Steven et al [3] modified it and proved faster than earlier methods. However, it fails to converge in 5 out of 12 case studies. L. Kumar and R.Ranjan[4] have


65

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

develop a load flow method based on simple recursive method. Baran & Wu [5] have developed a load flow method based on Newton Raphson method, but it requires a Jacobean matrix, a series of matrix multiplication, and at least one matrix inversion. Hence, it is considered numerically cumbersome and computationally inefficient. The choice of solution method for particular application is difficult. It requires a careful analysis of comparative merits and demerits of those methods available. A new power flow method for radial distribution networks with improved converge characteristics have been reported in [5] which is passed on polynomial equation on forward process and backward ladder equation for each branch of RDS. In first part of this paper load flow algorithm proposed, in this algorithm voltage at each node is calculated by using a simple recursive equation. And required minimum data preparation compared to other methods. The proposed method is tested on several systems and result is show for the two systems (33- node, 28-node). The second part of this paper presents a simple voltage stability index that will predict the node which is more sensitive to voltage collapse. The modern power distribution network is constantly being faced with an ever growing load demand. Distribution networks experiences distinct changes from a low to high load level every day. When a power system approaches the voltage stability limit, the voltage of some buses reduces rapidly for small increment in load and the controls or operators may not be able to prevent the voltage decay. In some cases, the response of controls or operators may aggravate the situation and the ultimate result is voltage collapse. The problem of voltage stability & voltage collapse have increased because of the increased loading, exploitation and improved optimization operation of power transmission system. The problem of voltage collapse is the inability of power system to supply the reactive power or by an excessive absorption of reactive power by the system itself. Thus the voltage collapse is a reactive problem and it is strongly affected by the load behaviour. Voltage collapse has become an increasing threat to power system security and reliability. One of the serious consequences of voltage stability problem is a system blackout. A fast method for finding the maximum load, especially the reactive power demand, at a particular bus through thevenin’s equivalent circuit before reaching the voltage stability limit is developed in (8) for general power system. Voltage instability in power network is a phenomenon of highly non-linear nature posing operational as well as prediction problem in power system control. The voltage instability is a local phenomenon in which variable and network parameters contain sufficient information to assess proximity to instability. Hence a direct analytical approach to voltage instability assessment for radial network is presented in (9). Voltage collapse is characterized by slow variations in system operating point due to increase in loads in such a way that the voltage magnitude gradually decreases until a sharp accelerated change occurs. The effectiveness of three simple voltage stability indices also compared in (10) provides information about the proximity of voltage instability of a power system. This paper presents the effect on VSI and voltage collapse point with increase of active power, reactive power and both active & reactive power. The results for 33-node system & 28 node system with magnitude of voltage, VSI, effect on VSI are shown along with their graphs.


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 θ2 =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.

APPENDICES Table1- Load Flow Solution of 28 Node Radial Distribution Systems

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

Table2- Load Flow Solution of 33 Node Radial Distribution Systems

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


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