jeas_0808_117

8/10/2019 jeas_0808_117

1/5

VOL. 3, NO. 4, AUGUST 2008 ISSN 1819-6608

ARPN Journal of Engineering and Applied Sciences

2006-2008 Asian Research Publishing Network (ARPN). All rights reserved.

www.arpnjournals.com

A LOOP BASED LOAD FLOW METHOD FOR WEAKLY MESHED

DISTRIBUTION NETWORK

S. Sivanagaraju1, J. Viswanatha Rao2and M. Giridhar31Department of EEE, J.N.T.U. College of Engineering, Anantapur, A.P., India

2Department of EEE, Madanapalle Institute of Technology and Sciences, Madanapalle, India3Department of EEE, SITAMS College of Engineering, Chittur, India

E-mail: [email protected]

ABSTRACTA distinctive load flow solution technique is proposed for the analysis of weakly meshed distribution systems. The

special topological characteristics of distribution networks have been fully exploited to make the solution possible. Abranch-injection to branch-current matrix is formed (BIBC). This matrix is obtained by applying Kirchhoffs current lawfor the distribution network. Using the same matrix a solution for weakly meshed distribution network is proposed. Busvoltages are found by forward-sweep of the network. Test results of 33-bus and 69-bus systems are given to illustrate the

performance of the proposed method.

Keywords:load flow, weakly meshed distribution network, radial.

1. INTRODUCTIONThe analysis of distribution system is an

important area of activity as distribution systems providethe final link between the bulk power system andconsumers. A distribution circuit normally uses primary ormain feeders and lateral distributors. A main feederoriginates from the substation and passes through themajor load centers. Lateral distributors connect theindividual load points to the main feeder and are defined

as radial distribution systems. Radial systems are popularbecause of their simple design and low cost.Even though the Fast decoupled Newton method

[1] works well for transmission system, its convergenceperformance is poor for most radial distribution systemsdue to their high R/X ratios which deteriorate the diagonaldominance of the jacobian matrix. For these reasons,several non-Newton types of methods [2-5], that consist offorward/backward sweeps on a ladder system have beenproposed. Recent research proposed some new ideas onhow to deal with the special topological characteristics ofdistribution systems, but these ideas require new dataformat or some data manipulations. In [3], the author

proposed a compensation-based technique to solvedistribution load flow problems. They have developed abranch numbering scheme to enhance the numericalperformance of the solution of the solution method andbroke the interconnected grid into number of break pointsin order to convert it into a radial network by directapplication of Kirchhoffs voltage and current laws. Theyhave computed the break point currents by using muti-portcompensation technique. Branch power flows rather thanbranch currents were later used in the improved versionand presented in [4]. However, the main disadvantage oftheir method is that the branch and node-numberingscheme and data preparation are highly involved. Another

difficulty of their method is that if new branch is inserted,numbering of branch of that part of network is necessary.Baran and Wu [6] have obtained the load flow solution fordistribution system by iterative solution of three

fundamental equations representing real power, reactivepower and voltage magnitude. They computed systemjacobian matrix by using chain rule. In their method, themismatches and jacobian matrix calculation involve onlythe evaluation of simple algebraic expressions and notrigonometric functions. Chaing [7] has proposeddecoupled and fast-decoupled distribution load flowalgorithm. Very fast-decoupled load flow algorithmproposed by Chaing is very attractive. It does not require

any jacobian matrix construction and factorization butmore computation be involved because it solves threefundamental equations representing the real power,reactive power and voltage magnitude. Goswami and basu[8] have presented an approximate direct solution methodfor solving radial and meshed distribution networks. Theyhave also broken the loop branches (break points) in orderto convert it into a radial network similar to that ofshirmohamadi, et al.[3]. However, the main limitation oftheir method is that no node in the network is a junction ofmore than three branches, i.e., one in coming and twooutgoing branches.

Literature survey on distribution load flow as

mentioned above shows that most of the authors haveconcentrated on solving radial distribution networks. Onlyshirmohammadi, et al. and Goswami and basu have madean attempt to solve meshed distribution networks. Theirmethods have some limitations as discussed above and arenot computationally faster.

The main objective of this study was to present anew method of load flow solution for meshed distributionnetworks. Here, multi-port compensation technique is usedfor computation of break point current injections. Theeffectiveness of the proposed method is tested with twotest systems.

55

8/10/2019 jeas_0808_117

2/5





2. LOAD FLOW SOLUTION OF RADIALDISTRIBUTION NETWORK

The proposed method is developed based on a

derived matrix bus-injection to branch current matrix andequivalent current injections. In this section, the developedprocedure will be described in detail. For distributionnetworks, the equivalent current injection based model ismore practical [3]. For bus-i, the complex load SI isexpressed asSi= Pi+jQi i =1,2n ------(1)and the corresponding equivalent current injection at thekthiteration of solution isIi

k= ((Pi+jQi)/Vik)* -------(2)

Where Vik and Ii

k are the bus voltage and equivalentcurrent injection of bus-i at the kthiteration, respectively.

2.1. BIBC Matrix development

4 5

B3 B41 2 3

I I4B1 B2

5

6 I6 B6I2 I3 B5

Figure-1.Simple distribution system.

A simple distribution network shown in Figure-1is used as an example. The current injections are obtainedfrom eq. (2), the relationship between the bus currentinjections and branch currents can be obtained by applyingKirchhoffs current law (KCL) to the distribution network.Using the algorithm of finding nodes beyond all branchesproposed by Ghosh et al.The branch currents can then beformulated as functions of equivalent current injections.For example, the branch currents B1, B3 and B5, Can beexpressed as

B1= I2+ I3+ I4+ I5+ I6B3= I4+ I5 ----------(3)B6= I6Therefore, the relationship between the bus currentinjections and branch currents ssed

q. (4) can be expressed in general form as

njecti ent matrix, theBIBC matrix is a upper triangular matrix and containsvalues of 0 and +1 only.

he branch numberch jj are given by

-------(7)

_LOSS = |I (jj)| X (jj) ---------(8)

. LOAD FLOW SOLUTION OF MESHED

Some distribution feeders serving high-densitynormally

dial is extended forweakly m

f equation (4) we have

Eq. (9) can be rewritten as

urrent of tie branch 6 can be calculated asB6 = V5-V6/ Z66

D FOR

The computational steps involved in solving the

thes under:

can be expre

E

[B] = [BIBC][I] -------(5)Where BIBC is bus i on to branch curr

The receiving end bus voltages are found by a forwardsweep through the ladder network using the generalizedequation as

V (m2) = V (m1) I (jj) Z (jj) ---- (6)Where m1, m2 are the sending and receiving endsjj is t

The real and reactive power loss of branP_LOSS = |I (jj)|2R (jj) --

2Q3

DISTRIBUTION NETWORK

load areas contain loops created by closing

switches. The proposed method for raeshed distribution feeders. Existence of loops inthe system does not affect the bus current injections, butnew branches need to be added to the system. Fig.3 showsa simple case with a one loop. Taking the new branchcurrent into account, the current injections of bus 5 andbus 6 will beI15= I5+ B6I16= I6- B6Modification o

)9(

66

654

2

10000

0100001100

1111

543

+

=

BI

BI

I

I

B

BB

LILC Matrix

C------- (10)

4. ALGORITHM OF PROPOSED METHO

MESHED NETWORK

load flow problem of a single source network byproposed method are given a

31111021

IB

B

1

+

=

6

6

10

01

01

11

11

6

5

4

3

2

10000

01000

01100

11110

11111

5

4

3

2

1

B

B

I

I

I

I

I

B

B

B

B

B

)4(

6

5

4

3

2

10000

01000

01100

11110

11111

5

4

3

2

1

=

I

I

I

I

I

B

B

B

B

B

56

8/10/2019 jeas_0808_117

3/5





(i) Rea

(iii)each branch-using BIBC matrix

ber of branches)X(twice the number of

(v)

(vi) atrix currents are injected in to the tie-

(vii) the voltage magnitude at the receiving end

(viii) C matrix, branch

n.

5. Rof the proposed method is

lustrated with two different cases as follows:

Case-I.

ata are given in [10]. Thead flow results of radial and meshed systems as case a

d the system data. Construct the tree and numberthe branches. Assume the initial voltage at all buses assource bus voltage.

(ii)

Compute current injections at each bus using eq. (2).From the computed current injections; compute thebranch currents infrom eq. (4).

(iv) For meshed network, LILC matrix is formed fromBIBC matrix as given by eq.(9).The order of LILCmatrix is (numtie switches)Compute the current injections at tie line nodes usingeq. (10)Using LILC mswitch nodes in opposite directions.Compute

bus of each branch using eq.(6).Once currents are injected using LILcurrents are updated and again radial load flow is runwhich completes one mesh iteratio

(ix) Repeat steps (ii) to (viii) till the max. magnitude ofvoltage difference between consecutive iterations isless than 0.0001 p.u

ESULTS AND ANALYSISThe effectiveness

il

Illustrates the 33-bus radial distribution system

and mesh distribution sytem.

Case-II. Illustrates the 69-bus radial distribution systemand mesh distribution system.

Case-I. Figure-2 shows a 33-bus distribution system.The line, load and tie switch dloand case b are given in Table-1.

Figure-2.Single line diagram of a 33-bus network with5-tie lines.

Table-1. Load flow results of 33 bus system.

Bus Case (a) Case (b)

No. |V| (p.u) |V| (p.u)

1 1.00000 1.000002 0.99703 0.997563 0.98295 0.988044 0.97548 0.983615 0.96809 0.979316 0.94972 0.968697 0.94626 0.966868 0.94626 0.964349 0.94142 0.9611010 0.93515 0.9581011 0.92934 0.9576612 0.92848 0.95688

13 0.92698 0.9537414 0.92088 0.9525715 0.91862 0.9518416 0.91720 0.9511417 0.91584 0.9501018 0.91381 0.9497919 0.91321 0.9963620 0.99650 0.9868021 0.99293 0.9847122 0.99222 0.9828123 0.99158 0.9848624 0.97937 0.9789525 0.97270 0.9760126 0.96938 0.9675027 0.94780 0.9659228 0.94524 0.9588729 0.93381 0.9538130 0.92560 0.9516131 0.92205 0.9490532 0.91789 0.9484933 0.91697 0.94832

Case-II.T as es with 6 em. The line,load and t it given in e Load flow

sults of 69 bus radial distribution system are given in

his c e Illustrat 9 bus systie sw ch data are ref[6]. Th

re

Table-2. The Load flow results of 69 bus mesheddistribution system are given in Table-3.The voltagemagnitude at the root bus was considered to be 1.0 p.u. Itwas found that the voltage magnitudes in the case of meshdistribution system are higher than that of radialdistribution system because of the inclusion of tie lines.

57

8/10/2019 jeas_0808_117

4/5





Table-2. Load flow results of 69 bus radial distributionsystem.

Bus |V| (p.u) 35 0.99916

1 1.0000 0.999810 362 0.99996 37 0.999643 0.99993 38 0.999484 0.99983 39 0.999445 0.99900 40 0.999446 0.99005 41 0.998747 0.98074 42 0.998458 0.97852 43 0.998419 0.97818 44 0.9984010 0.97319 45 0.9983011 0.97209 46 0.9983012 0.96894 47 0.99978

13 0.96602 48 0.9985414 0.96313 49 0.9947015 0.96026 50 0.9941516 0.95973 51 0.9770017 0.95885 52 0.9721418 0.95884 53 0.9693419 0.95838 54 0.9660920 0.95808 55 0.9616021 0.95760 56 0.9572122 0.95759 57 0.9347123 0.95752 58 0.9236124 0.95737 59 0.9193125 0.95720 60 0.9142626 0.95713 61 0.9068227 0.95711 62 0.9065328 0.99992 63 0.9061429 0.99985 64 0.9042330 0.99976 65 0.9036531 0.99974 66 0.9720432 0.99965 67 0.9720433 0.99945 68 0.9686134 0.99922 69 0.96861

TT 7 k r

Table-3. Load flow results of 69 bus mesh distributionsystem.

P = 238.5Q =106.9

412

kWVA

No of iterations: 3

Bus |V| (p.u) 35 0.99917

1 1.0000 0.999820 362 0.99997 37 0.999183 0.99994 38 0.998524 0.99986 39 0.998325 0.99940 40 0.998316 0.99442 41 0.994227 0.98925 42 0.992538 0.98801 43 0.992309 0.98786 44 0.9922510 0.98566 45 0.9916811 0.98518 46 0.9916812 0.98379 47 0.99981

13 0.98252 48 0.9985714 0.98125 49 0.9947315 0.98000 50 0.9941916 0.97976 51 0.9871017 0.97938 52 0.9842018 0.97937 53 0.98253

19 0.97917 54 0.9805920 0.97904 55 0.9779121 0.97883 56 0.9752922 0.97883 57 0.9618623 0.97880 58 0.9552424 0.97873 59 0.9526725 0.97865 60 0.9496626 0.97862 61 0.9452327 0.97862 62 0.9450528 0.99994 63 0.9448229 0.99987 64 0.9436830 0.99977 65 0.9433431 0.99975 66 0.9851532 0.99967 67 0.9851533 0.99947 68 0.9836534 0.99924 69 0.98365

5 1

TP = 238.TQ =106.9

472

kWkVAr

No of iterations: 3

58

8/10/2019 jeas_0808_117

5/5





6. CONCLUSIONSAn efficient load flow method for solving weakly

systems has been developed. The

applicati

c O. 1974. Fast decoupled load flow.IEEE Trans. PAS-93, pp. 859-869.

[2] An application ofladder network theory to the solution of three phase

[3] ng HW, Semlyen A, Luo GX.1988. Compensation based power flow method for

[4] . Efficient load flow forlargely weakly meshed networks. IEEE Trans. onPower Syst. 5(4): 1309-1316.

r Syst. 10(2): 671-679.

[6]

Trans. On Power Delivary. 4(1): 725-734.

[7]ion system

analysis. IEEE Trans on Power Syst. Vol. 10, pp.

[8]. IEEE Proceedings Part C,

38(6): 78-88.

[9]n in distribution systems for loss

reduction and load balancing. IEEE Transon PERD,

[10]orks. IEE Part C,

146(4): 641.

[5] Cheng CS, Shirmohammadi D. 1995. A three phasepower flow method for real-time distribution systemanalysis. IEEE Trans. on Powemeshed distribution

on of the proposed method is simple andstraightforward. However, for a meshed network, a loopmatrix LILC is used in finding currents flowing in eachloop formed by each tie-switch. This method can also beeasily extended for different load models.

REFERENCES

Baran M.E and Wu F F. 1989. Optimal Capacitorplacement on Radial distribution systems. IEEE

Zimmerman RD, Chiang HD. 1995. Fast decoupledpower flow for unbalanced radial distribut

[1] Stott B, Alsa 2045-2052. November.

S. K. Goswami and S. K. Basu. 1991. Direct solutionof distribution systems

Kersting WH, Mendive DL. 1976.

radial load flow problems. IEEE PES winter meeting,paper No. A 76 044-8.

Shirmohammadi D, Ho

Baran M.E and Wu F F. 1989. NetworkReconfiguratio

1989, PWRD-4 (2), pp. 1401-1407.

S. Ghosh and D. Das. 1994. Method for load flowsolution of Radial distribution netw

weakly meshed distribution networks. IEEE Trans. onPower Syst. 3(2): 753-762.

Luo GX, Semlyen A. 1990

59

jeas_0808_117

Documents

Transcript of jeas_0808_117