718 IEEE Transactions on Power Systems, Vol. 12, No. 2, May 1997

UTIQN SYSTEM PLANNING USING BRANCH EXC UE

S.K.Goswami ELectrical Engineering Department

Power System Section Jadavpur University

Calcutta 700032. INDIA

Abstract : This paper reports the development of a new algorithm for the planning of radial distribution systems. The algorithm is based on branch exchange technique. Branch exchange has been applied in two stages - between the elements of the network under each substation, called intrazone branch exchange and between the elements of the networks under adjacent substations, called interzone branch exchange. Intrazone exchange determines the optimum network configuration of each substation and interzone exchange determines the optimum service area of each substation. A complete power flow IS required after each successful branch exchange. A new algorithm has also been proposed for the load flow of radial distribution networks. The algorithm is not based on node and branch numbering schemes and can handle multiple number of zones and therefore is particularly suitable for planning environment.

Keywords: Planning, distribution system, branch exchange, power llow.

have also been proposed (12). Aoki et.al have proposed an approximate method based on branch exchange technique (1,2). The author in this paper proposes a new algorithm based on the branch exchange technique. Branch exchanges have been implemented in two stages (i)to optimize the network configuration of each distribution zone, and (ii)to find the optimal service area of each distribution zone. Power flow is an integral part of the planning algorithm. A new power flow algorithm has also been proposed. Most of the distribution power flows are based on some special numbering schemes. In planning environment, when the network configuration changes at every step of the solution algorithm such numbering scheme becomes too costly in respect of solution times. The power flow algorithm proposed by the author is not based on such numbering scheme and works very efficiently. Moreover it can handle more than one distribution zone which is very useful in planning studies.

INTRODUCTION THE DISTRIBUTION PLANNING P ~ O B L E ~

Distribution system planning is a combinatorial optimization problem where the objective is to determine the optimum way of supplying a given set of loads. The process involves the selection of the number, location and size of the substations and the primary feeder configuration such that the cost of installation along with the cost of energy loss is a minimum while maintaining the radiality of the network and at the same time not violating the capacity and voltage drop constraints in any part of the network. The cost function to be optimized to solve the above problem is concave in nature and involves many integer variables. Mathematical programming techniques have been extensively used in the past (3 -10) to solve the distribution planning problem and a number of methods have been developed using linear, mixed integer and quadratic programming techniques. Recently methods based on simulated annealing and Genetic algorithm

Given the number of probable substations NS and the number of feasible feeder connections NF to connect NL number of load points, the problem in distribution planning is to select the required number of substations , m, and to form m number of radial network Sj(nj,fj), where n. and fj are the load nodes and the feeders connecting these nodes to substation j , such that the cost of installation plus the cost of operation is a minimum, while the node voltages and feeder and transformer capacities are kept within the specified limits. The problem may be expressed mathematically as:

NS NS F.

Minimize c=xc(sj) + Subject to the conditions : vj >vmin i(fj),( imaxj ; and Tmin. ( tc. ( Tmaxj.

i i ( fk j2 . Rk .Pe j = I j = I k=I

3 \ J \ Where S. = network j

cis;) = cost of network j i(flk) = current through feeder k Rk = resistance of feeder k pe = energty cost tc. - flow through transformer j F! 1 Feeders of network j Id = Probable number of substations imaxi= Capacity limit of i'th feeder Tmaxj , Tmin. - Maximum and minimum capacity

96 SM 486-1 PWRS A paper recommended and approved by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the 1996 IEEWPES Summer Meeting, July 28 -August 1, 1996, in Denver, Colorado. Manuscript submitted December 22, 1995; made available for printing April 23, 1996.

limits of j'th transformer. J -

0885-8950/97/$10.00 0 1996 IEEE

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PROPOSED METHOD OF SOLUTION

An iterative algorithm has been proposed by the author to solve the problem formulated above. To start with , we assume that the required number of substations is equal to the number of probable substation locations. The optimum numbler and locations of substations along with the feeder configurations to connect the load points to the substations are then determined as shown in the algorithm of Fig. 1

(i)Assume the required number of substations, m = NS (ii)Fonm initial radial networks S.(n. f-); j=l, ..... m

identify intrazone ties Sf(n.,f!),Jj'=Jl,m, where f. are the tie lines of the J J J distribution zone j, n. are the nodes associated with f.

identif:y interzone ties s..(nk,fk); where fk are the tie Ihes connecting zones i and j and nk are the associated nodes of zones i and j. (iii)For each j ,

(iv)Por all possible i & j,

$)Check for the optiinality of the solution. (vi)If the optimum is not reached, identify the most costly substation and close it. Make m=m-1 and go to step (ii) Fix. I The outline of the plunning algorithm

J 11

perform branch exchanges between s.and sf 1 J '

perform branch exchanges between si and s. through the tie lines in

r 1

Steps mentioned above are discussed in more details in the following.

FORIMATION OF THE INITIAL RADIAL NETWORKS

The branch exchange algorithm starts from a set of initial radial networks. These initial networks are formed by constructing the spanning trees of the distribution network, the rolot of each tree being a substation node . The algorithm of forming the spanning trees s ' , j= l , ... m is shown in Fig. 2 J

(i)For each substation, j ,j=l,..m, initialize a network S . , with each substation node. (ii)For each j , detect the expandable nodes of s. Measure the distances of all the probable incoming nodes from the substation. Probable incoming nodes are the nodes that may be connected to the expandable nodes. An expandable node is the node from which network expansion is still possible. (iii)incllude the node nearest to a substation amongst the candidate nodes. Augment the network s., by the node and the connecting line. (iv)l<epeat the process for all the load nodes. When all the load nodes are entered the required trees are formed. S:. S;; are then found out from the unconnected lines.

1

J '

J

Fig..? Formution oj"the initiul networks

BRANCH EXCHANGE

The branch exchange technique, applied for the reconfiguration of distribution network, basically converts a radial network into a meshed network by connecting the tie lines. The radial structure is restored again by opening some other lines of the network so as to minimize an objective function . The exact form of the objective function being dependent upon the purpose of reconfiguration. In the

proposed algorithm branch exchange technique is implemented by forming one loop only at a time (1 1). Two types of branch exchanges are performed (i) Branch exchange within each distribution zone - called intrazone branch exchange. (ii)Branch exchange between the adjacent distribution zones- called interzone exchange.

INTRAZONE EXCHANGE

In this case the configuration of a distribution network is changed by exchanging the elements between s j and sj.,Thus the intrazone branch exchange determines the optimum configuration of the network under each distribution substation. The algorithm for intrazone branch exchange is given in Fig. 3.

(;)Take a tie line t. from s. J (ii)Starting from the end nodes of t- trace the paths in both directions upto the source to form a loop. (iii)Determine the modified solution for the loop (iv)Determine the branch to be opened to satisfy one of the following criteria in order of priority. (a) to reduce the capacity limit violations of the feeders of the loop if such

violation exists. (b) to reduce the voltage limit violations of the nodes of the loop if such

violation exists. (c) to reduce the cost of installation and cost of energy loss for network s. J if limit violation does not exist.

(v) Perform full load flow in case of successful branch exchange. (vi) Repeat (i) to (v) till an improvement is obtained from the branch

exchange.

J

Fig. 3 Steps in intruzone brunch exchunge

A successful branch exchange here refers to that case where the branch to be opened for opening the loop is not the tie line inserted to form the loop. The reason for assigning priorities in selecting the branch for opening a loop is that an optimal solution must also be a feasible one. Thus the feasibility of the solution has to be checked first.Thus , the first objective is to reduce the limit violations, if any violation exist. Limit violations may be in the form of line overload or poor node voltages.Out of these line overload is more severe and must be removed. Voltage limit violation may be avoided by placing capacitors, if is unavoidable in planning stage. But the capacity limit violation can not be managed without reconductoring . Thus, the line overloading has given the highest priority. If overeload does not exist, existance for voltage limit violation is checked. If lthe voltage and current limits are not violated, the objective is to reduce the system cost, and the line in the loop opening of which will cause maximum reduction in cost is removed from the loop. Branch exchange within a substation continues till a branch exchange rsults in a cost reduction or an improvement is achieved in case of limit violations.

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Source

--

Fig. 5 A loop of intrustation brunch exchange

INTERZONE EXCHANGE

S totion-I Station -2

0

- - Tie

Fig. 6 A loop of interstation branchexchange

In this case nodes are exchanged between two adjacent distribution zones, Si and S., through the interzone ties J Sij.Interzone branch exchanges thus determine the optimum service area of each distribution substation. Fig. 4 shows the algorithm for interzone branch exchange.

(i)Take a tie t- from s. . 1J 1J (ii)From the two end nodes o f t . . move towards the sources in si & s. to form

the required loop. (iii)Determme the modified solution for the loop (iv)Determine the branch of the loop to be opened so as to reduce the system cost. (v)Perform load flow for zones i & j in case of successful branch exchange. (vi)Repeat (i) to (v) so long as the cost reduction is obtained due to branch exchange. Fig. 4. Steps in the interzone brunch exchange

1J 1

The objective function in case of interzone exchange is to reduce the system cost. In case of interzone exchanges limit violations of the feeders are not checked. It is assumed that such violations, if any, can be removed by branch exchange within each substation and the objective of the branch exchange is therefore, to reduce the system cost.

CRITERIA FOR OPENING LOOP

Three techniques have been attempted for opening the loops while implementing the branch exchanges: (i)To reduce line overload (ii)?'o improve voltage profile (iii)To reduce the system cost

Line overload: overload is reduced by implementing the 'load balancing' in the branches of the loop and the line to be opened to restore the radial configuration is selected in

~ i g . 7 Pertuinlng to optimal ,flow pattern

such a way that the maximum percentage loading at both ends of the included tie is nearly same.

Improving the voltage profile: In case of voltage limit violation the line to be opened is selected so as to establish the optimal flow pattern in the branches of the loop. The optimal flow pattern reduces the power loss and at the same time improves the voltage profile.

Cost reduction: System cost has two components, (i)the cost of the components and (ii) the cost of energy loss. Thus cost reduction is attempted in two ways by reducing the installation cost and by reducing the energy loss in the system.Cost reduction in both the methods are calculated and the method giving better economy is selected. In case (i) the cost of the lines in the loop are compared and the line with the maximum cost is opened to restore the radial configuration. Loss reduction in the branches of the loop is achieved by forcing the optimal flow pattern in the branches of the loop.

Load balancing: As already mentioned, branch exchange is performed with the objective of balancing the load in the branches of the loop in case of line overload. The percentage loadings in both parts of the loops are calculated. Loads are then transfered by transfering one node at a time from the overloaded part to the other part of the loop and the new percentage loadings are calculated.The process is continued until the maximum percentage loadings in both sides of the included tie are found to be nearly same.This is indicated by the higher value of the maximum percentage loading of the previously less loaded part than the overloaded part of the loop. Referring to fig. 6, and assuming that part of the loop represented by the lines d-e-f is overloaded, attempt is made to open line f, thus transferring the load of node n3 to the other part of the loop represented by lines a-b-c. This action connects the tie line to this part. The percentage loading in both the parts are calculated and if the difference is found to

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I Sendin Receivin Line Membershi

be large enough the next attempt is to open line e, which takes node n2 also to the other part a-b-e-tie-f. If the maximum percentage loading of this part exceeds that of the other part the load exchange operation is stopped and the line exchanged in the previous step is selected for opening.

Optimal flow pattern : Optimal flow pattern is that flow pattlxn in the network which will cause minimum power loss and it corrcsponds to the flow pattern obtained by solving the KVI, and KCL equations of the network with the branch impedances replaced by the branch resistances only( 1 1). Since we form one loop only at a time, determination of optimal flow pattern can be done very easily by considering loads as constant currents. Considering the loop in fig. 7 the optimal flow in branch b is,

5

k= 1

6

k= 1

c i k . rk

ib = ___._._.__._._.___________

'k

The flows in other branches can be easily calculated by appllying KCL at each node of the loop. Optimum flow pattlern can be established by opening the branch having minimum flow.

COMPLETE ALGORITHM

Intrazone exchange and interzone exchanges are performed repeatedly. A set of interzone and intrazone branch exchanges constitute an iteration of the algorithm. The branch exchanges continues till the system cost or limit violation can be minimized. When the optimum solution is obtained for the selected substations, we check the optimality of the substation capacity. If the optimum is not reached a new solution is obtained by reducing the number of substation by one. The substation to be closed for the next solution is determined on the basis of the cost per KVA of the substations. Cost per KV.4 is calculated as : (cost of the substation + cost of feeders + cost of energy loss) / Total KVA load of the sub:rtation. The substation having the maximum cost per KV.4 is closed and a new optimum network configuration is obtained with the selected substations. This process is repeated till a cost reduction is achieved by reducing the number of substation. A complete load flow is performed after each successful branch exchange. Since the number of successful branch exchanges are generally much less than the number of exchanges attempted, number of full load flows are not many. It may be noted here that the solution obtained frorn radial load flow has to be changed every time when a branch exchange is attempted. This however, does not need full load flow and can be obtained very easily by minor modifications of the available load flow results.

POWER FLOW

Most of the power flow methods available for distribution networks are based on some node and branch ordering techniques. Using node and branch ordering techniques will not be of much help in the planning environment because nodes and branches are transfered from one zone to another at every solution step. Ordering techniques can improve the efficiency of the power flow algorithm for networks of constant configurations. In the planning problems network

Roo!

P

Fig.8 A two-zone example system

g Node 10 S 5 7 5

20 20 20 30 30 21 32 1 1

32

g Node S 10 3 1 I 20 30 29 20 12 6 16 14 I 8 S

40 21 42 17 32 2

I 1s 12 6 SO 18 4 9

P 1 1 1 I 1

I 1 1 1 2 2 2 2 2

1

configurations are always changing until the final solution is reached. Moreover, planning problems require load flow algorithms that can solve multiple zone distribution systems. A simple power flow method has been developed by the author to solve the problem. The author likes to call the algorithm as 'structured power flow' because the algorithm uses the speciality in the network structure. In this method network connection is represented by a very simple and effective way in tabular form. No special ordering technique

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is needed. Lines are represented assocaited with their end nodes as connected between 'sending' and 'receiving' nodes. The sending end node of a line is entered at the left column of the table whereas the receiving end node enters at the right column. Each node, excepting the substation , must appear as a receiving node before appearing as a sending node in the network table. This ensures that the exact structure of the network is copied in the network table.The advantage of this representation is that as we traverse from top to the bottom of the table, we move from root to the leaves of the network in the direction of power flow. Moreover, the node and line numbers need not be continuous. This is very important in case of planning problem where feeders are connected to different substations. A membership value for nodes and lines are to be maintained to indicate in which substation a node or a line is connected. Table 1 shows the representation of the network of fig. 8.The load flow algorithm simply consists of forward and backward traverses of each network table as described below:

I.Set Lone-number, i = I enter into the network table of zone i 2.Assumc node voltages = voltage at the substation node 3.calculate node currents &Backward traverse: Calculate line currents from the bottom to the top of the S.Forward traverse: Calculate node voltages from the top to the bottom o f the network table 6 Converged?

network table

No: go to step 3 Yes: increment zone number, i=i+l

$20 to SteD 1 Fig 9 The loud f low ulgorithm

Because o l the network representation in the tabular form as explained above, implementation of the backward and forward traverse becomes straight forward as shown in Fig 10

Backward traverse: Determination of line currents: set n = bottom row of the network table for i = n to 1, step = -1

source- i =net(i,I) receiving-i = net(i,2) CUR(1ine-i) = Inode(receiving-i)

(line-i = net(i,3)

Inode( source-i)=Inode(source-i)+Inode(receiving-i) } Forward traverse: Node voltage calculation: for i = 1 to n, step = I

source-I = net(i,l) { line-i = net(i,3)

receiving-i = net(i,2) V(receiving_i) = V(source-i) - CUR(line_i)*Z(line-i) }

CUR t line current Inode t current leaving a node net t network table Fig. 10 Implementation of' the loud,flow ulgorithm

Modification of the radial load flow solution to obtain the solution for the loops: The radial load flow solution has to be modified whenever a loop is formed in order to attempt a

branch exchange. A simple method reported in (1 1) has been applied to obtain an approximate modified solution. It has been shown (11) that an approximate solution is quite acceptable for solving reconfiguration problem.

NUMERICAL EXAMPLE

Test results for two example networks are reported here in order to demonstrate the effectiveness of the developed planning algorithm.

Table 2: Substation data,for test system 1 Substation Node Capacity MVA Cost Million Rs

I 50 3.1

4 6 3 10 5

Table 4 : line data for test system 1 Line From To Cost Loss cost coefficient

Rs) Node Node (M1llion Million Rs/MVA

1 1 3 0.58 0.0205 2 1 5 0.62 0.0222 3 1 7 0.50 0.0171 4 1 10 0.10 0 5 2 10 0.5 0.0171 6 2 3 0.5 0.0171 I 2 5 0.42 0.0137 8 2 6 0.774 0.0274 9 2 4 0.74 0.0274 10 2 7 0.56 0.0240 11 7 8 0.58 0.0205 12 9 10 0.64 0.0274 13 3 4 0.70 0.0257 14 5 6 0.66 0.0240 15 I 9 0.74 0.0274

Test System -1: This network is the example considered by Ponnavaiko & Rao (5) and is a problem of selecting the optimal locations for 132/33 kV substations and the 33 kv feeder routings to feed the demands at the 33/11kv substations in the area. Maximum permissible capacity of each substation is 50 MVA and installation cost is Rs 3.1 million. Capacity of each feeder is 12MVA. Load and branch data for the test system are given in Table 3 & 4 respectively. The planning problem is first attempted assuming both the substations as 'open'. Initial spanning trees are shown in Fig. 1 l(a) as firm lines, whereas dotted lines are the ties. After the branch exchange the final solution is as shown in Fig. 11(b) . The cost per kVA of the stations are now calculated. Since the capacity of each substation is 50 MVA, either of the substations is capable enough to supply the total demand.

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Table 5 : Results or Test S stem 2 Initial Cost Final Cost Number of Number of

exchange exchange attempted executed

Solution2 972 585 C t

b

c

Fig. 1 I (u) Initiul cocfigurution (b ) Configururion ufter brunch exchunges (c) F i n d configurution ,,for test system I

Substation is therefore closed as the cost per kva of station 2 appears to be higher from the first solution. A new solution is then obtained with station 1 as the source node. The final solution is as shown in Fig . 1 l(c)

2

Test System 2: The second example is an expansion planning problem of a 6.6 kV, 58 node, 65 branch test system(l,2) having four substation nodes (nodes 1, 2, 56, & 57). The original system has 32 nodes, including three substation nodes. The final network configuration is dependent upon the initial configuration. Starting with two different initial configurations the final solutions were obtained after three and four iterations respectively. Initial and final costs , Number of branch exchange attempted and number of successful branch exchanges for the two solutions attempted are given in Table 5. The total number of complete load flows for the two cases were 6 and 9 respectively.

CONCLUSION

A new iterative planning algorithm has been proposed in this paper. Branch exchange technique has been successfully

applied in the past in solving the network reconfiguration problem. This paper used the branch exchange technique in solving the network planning problem. A new load flow algorithm has also been presented. The proposed load flow method is particularly suitable for network planning and is not based on any special node or branch ordering scheme, The number of load flows to solve the planning problem is equal to the number of successful branch exchanges. Modified load flows are required whenever a branch exchange is attempted by creating a loop. Such solution requires very minor modification of the radial load flow solution and can be obtained at the cost of very little computational efforts. The developed algorithm has been applied in two planning examples and the results obtained have been reported.

REFERENCES

(1) K.Aoki, K.Nara, T.Satoh, M.Kitagawa, K.Yamanaka, 'New Approximate Optimization Method for Distribution System Planning', IEEE Trans. PWRS, February '90, pp 126 - 132. (2) K.Nara, T.Satoh, H.Kuwabara, K.Aoki, M.Kitagawa, T.Ishihara, 'Distribution System Expansion Planning by Multistage Branch Exchange', IEEE Trans. PWRS, February '92, pp 208 - 214. (3) T.H.Fawzi, S.M.EI - Sobki, 'A New Planning Model For Distribution Systems', IEEE Trans. PAS, September '83, pp 3010 - 3014. (4) M.A.El-Kady, 'Computere Aided Planning of Distribution Substation and Primary Feeders', IEEE Trans. PAS, June '84, pp 1 I83 - 1 189. (5) M.Ponnaviakko, K.S.Prakasa Rao, S.S.Venkata, 'Distribution System Planning through a Quadratic Mixed Integer Programming Approach, IEEE Trans. PWRD, October '87, pp 1157 - 1163. (6) H.K.Youssef, R.Hackam, M.A.Abu -El-Magd, 'Novel Optimization Model for Long Range Distribution Planning', IEEE Trans. PAS, November '85, pp 3195 - 3202. (7) T.Gonen, 1.J.Ramrez Rosado, 'Optimal Multistage Planning of Power Distribution Systems', IEEE Trans. PWRD, April 1987, pp 512 - 518. (8) G.L.Thompson, D.L.Wall, 'A Branch and Bound Model for Choosing Optimal Substation Locations', IEEE Trans. PAS, May '81, pp 2683 - 2688. (9) D.L.Wall, G.L.Thompson, J.E.D.Northcote-Gree n, 'An Optimization Model for Planning Radial Distribution Networks', IEEE Trans. PAS, January/February, '80, pp 1061 - 1068. (1 0) R.N.Adams, M.A.Laughton, 'Optimal Planning of Power Networks Using Mixed Integer Programming', Proc. IEE, February, '74, pp 139 - 147 ( I I ) S.K.Goswami, S.K.Basu, 'A New Algorithm for the Reconfiguration of Distribution Feeders for Loss Minimization', LEEE Trans. PWRD, July '92, pp I484 - 1491. ( 1 2) V.Miranda, J.V.Ranito, L.M.Proenca, 'Genetic Algorithms In Optimal Multistage Distribution Network Planning', IEEE Trans. PWRS, November, 1994, pp 1927 - 1933.

BIOGRAPHY

S.K.Goswami Obtained B.E, M.E.E and Ph.D degrees in 1980, 1982 and 1991 respectively. At present he is working as a reader In the Electrical Engineering department of Jadavpur University, Calcutta.