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

AN EFFICIENT LOAD FLOW SOLUTION AND VSI ANALYSIS FOR

RADIAL DISTRIBUTION SYSTEM

LOKENDRA KUMAR 1, DEEPESH SHARMA2 & SHUBRA GOEL 3

1,3 Assistant Professor, Vidya College of Engineering , Meerut, Uttar Pradesh, India 2Assistant 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

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

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.

Lokendra Kumar & Deepesh Sharma & Shubra Goel 66

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]-0.5V 12

B[j] = [A[j] 2- (P22+Q2

2) (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+ Q2

2)/ V22

Qloss[j] =X[j]* (P22+ Q2

2)/ 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


1 2 ( )V V I R jX= + +

22

( )iSV R jX

V

∗

∗= + +

( )2

2

( )j jP jQ

V R jXV ∗

−= + +

2

2

2

( )j j j jV P R Q X j P X Q R

V ∗

+ + + −=

…2

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

( ) ( )2 22

2

12

j j j jV P R Q X P X Q RV

V

+ + + −=

( ) ( ) ( )2 2241 2 2 22j j j j j jV V V P R Q X V P R Q X P X Q R= + + + + + −

…3

Rearranging equation2, it will become

( ) ( ) ( )2 2 2 2 242 2 1 22 0j j j j j jV P R Q X P X Q R V P R Q X V V+ + + − + + − =

( ) ( ) ( )2 2 2 242 2 12 0j j j j j jV P R Q X P X Q R V P R Q X V + + + − + + − =

…4

The equation 4 is in form of

2 0ax bx c+ + = . To guarantee that 3 is solvable, the following

inequality constraint should be satisfied

2 4 0b ac− ≥

i.e.,

( ) ( )2241 14 4 0j j j jV V P R Q X P X Q R− + − − ≥

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

( ) ( )2241 14 4j j j jVSI V V P R Q X P X Q R= − + − −

…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

( ) ( )224

1 1( & ) 4 4j j j jVSI P Q V V KP R KQ X KP X KQ R= − + − −


Case (2)

When only active power increases with the multiplier K .Then eq. 5. Will be

( ) ( )224

1 1( ) 4 4j j j jVSI P V V KP R Q X KP X Q R= − + − −

Case (3)

When only reactive power increases with the multiplier K. Then eq. 5. Will be

( ) ( )224

1 1( ) 4 4j j j jVSI Q V V P R KQ X P X KQ R= − + − −

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.PAS-

103, 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 106-

114,2005.

(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.


(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 VSI

1 1 1 0 2 2 0.95678 -1.7739 0.797673997 3 3 0.91151 -1.7672 0.705037231 4 4 0.88726 -1.8023 0.70777414 5 5 0.87129 -1.8197 0.696541018 6 6 0.81281 -1.7331 0.521350467 7 7 0.77494 -1.7685 0.502450032 8 8 0.75626 -1.8074 0.50641817 9 9 0.72416 -1.7759 0.444384184 10 10 0.685 -1.8488 0.386954148 11 11 0.66035 -1.7562 0.378121214 12 12 0.64956 -1.7772 0.383615455 13 13 0.62187 -1.8166 0.334355042 14 14 0.60039 -1.7643 0.319556679 15 15 0.58758 -1.7753 0.316145152 16 16 0.57835 -1.8056 0.31083112 17 17 0.57036 -1.8225 0.30461443 18 18 0.5675 -1.8195 0.30707373 19 19 0.9501 -1.841 0.857739708 20 20 0.94787 -1.8332 0.867278648 21 21 0.94509 -1.8474 0.85896559 22 22 0.94309 -1.8461 0.854552058 23 23 0.90572 -1.8463 0.770414227 24 24 0.90195 -1.8361 0.768258322 25 25 0.89877 -1.8434 0.759956409 26 26 0.80928 -1.8416 0.605573185 27 27 0.80807 -1.8395 0.608196588 28 28 0.80751 -1.8471 0.608197974


Table2- Load Flow Solution of 33 Node Radial Distribution Systems

S.No. Node No.

Voltage Magnitude(P.U.)

Angle VSI

1 1 1 0

2 2 0.997024 -1.8464 0.97750862

3 3 0.982924 -1.8305 0.88492637

4 4 0.975433 -1.8407 0.88295501

5 5 0.96802 -1.8407 0.85762879

6 6 0.949553 -1.8382 0.75827594

7 7 0.946025 -1.8533 0.79663604

8 8 0.932363 -1.8307 0.71989823

9 9 0.926024 -1.8411 0.72361773

10 10 0.92016 -1.8419 0.70703595

11 11 0.918198 -1.8523 0.71310664

12 12 0.916681 -1.8474 0.70982353

13 13 0.910499 -1.8417 0.67692071

14 14 0.908206 -1.8489 0.68180369

15 15 0.906778 -1.8484 0.68013802

16 16 0.905395 -1.8483 0.67615419

17 17 0.903344 -1.8488 0.66809386

18 18 0.90273 -1.8499 0.67053897

19 19 0.996496 -1.8502 0.98456008

20 20 0.992919 -1.8464 0.95856285

21 21 0.992214 -1.8502 0.96705921

22 22 0.991789 -1.8497 0.96649308

23 23 0.979339 -1.8456 0.9094501

24 24 0.972667 -1.842 0.8734755

25 25 0.969342 -1.8463 0.87370057

26 26 0.947625 -1.849 0.80711546

27 27 0.945062 -1.8485 0.79655438

28 28 0.933624 -1.8506 0.73055688

29 29 0.925405 -1.8512 0.71504245

30 30 0.921847 -1.8486 0.71865483

31 31 0.917686 -1.8464 0.70389943

32 32 0.91677 -1.8501 0.71114872


33 33 0.916487 -1.8508 0.71222868

For 28 node system

Fig-3

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

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.


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

Nodes P_Q P Q

1 0 0 0

2 0.0065 0.003 0.004727 3 0.0044 5E-04 0.007375 4 0.0189 0.012 0.005049 5 0.0176 0.012 0.000894 6 0.0352 0.01 0.019394 7 0.0021 0.011 0.003903 8 0.0053 0.035 0.006119 9 0.0004 0.004 0.007232 10 0.0153 0.014 0.002335 11 0.0016 0.006 0.003454 12 0.0035 0.003 0.000798 13 0.0116 0.003 0.003752 14 0.0034 0.003 0.000881 15 0.0016 6E-04 0.001048 16 0.0035 4E-04 0.000396 17 0.0027 0.002 0.001715 18 0.0008 0.001 9.53E-05 19 4E-05 0.001 0.000374 20 0.0018 0.01 0.00138 21 0.0011 0.001 0.000142 22 0.0014 7E-04 0.000511 23 0.0008 0.01 0.000289 24 0.0005 0.018 0.005474 25 0.0003 0.008 0.003002 26 0.0054 0.001 0.002101 27 0.0015 0.004 0.003287 28 0.0306 0.019 0.009552 29 0.0078 0.011 0.013444 30 0.0081 0.003 0.00688 31 0.0119 0.002 0.0045 32 0.0002 0.001 0.001086 33 0.0008 5E-04 5.95E-05


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


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

Documents

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