A heuristic method for feeder reconfiguration and service restoration in distribution networks

Electrical Power and Energy Systems 31 (2009) 309–314

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

A heuristic method for feeder reconfiguration and service restoration in distribution networks S.P. Singh a,*, G.S. Raju a, G.K. Rao b, M. Afsari a a b

Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221005, India Vignon’s Engineering College, Vadlamudi, AP 522213, India

a r t i c l e

i n f o

Article history: Received 5 March 2008 Received in revised form 12 March 2009 Accepted 16 March 2009

Keywords: Load flow Losses Network Optimization method Power distribution Power quality

a b s t r a c t A sequential switch opening method is proposed for minimum loss feeder reconfiguration in this paper. The algorithm is further extended for service restoration. The method is based on the branch power flow rather than the current flow as reported in earlier methods. The final algorithm arrives at opening of a branch in a loop carrying minimum resistive power flow to make the network radial causing minimum loss. The test results reveal that the proposed method yields optimal configuration with reduced computation burden and better restoration plan. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Alteration in the topology of a distribution network for efficient operation of the system results in reconfiguration. An effective feeder reconfiguration strategy takes advantage of the large degree of load diversity. Each distribution feeder has a different combination of commercial, industrial and residential loads. These loads tend to vary depending on the time of the day, weather and season. Feeder reconfiguration would allow for the transfer of load from heavily loaded portion of the power distribution system to locations that are relatively lightly loaded. This would not only improve the operating conditions but also enable the full utilization of system hardware capabilities. This could result in deferred capital expenditure and reduced operating expenses. The feeder reconfiguration is done during emergency for load restoration and in normal conditions for loss reduction and load balancing. Reconfiguration of the distribution network through sectionalizing and tie switches can reduce losses and improve voltage profile. Several methods are available in the literature to arrive at a switching strategy for loss minimization. A switch exchange type of heuristic method was suggested by Civanlar et al. [1] where a simple formula was developed for estimating change in losses due to a branch exchange. A filtering mechanism was also suggested to reduce the number of candidate switching options. Baran and Wu [2] developed an alternate branch exchange algorithm * Corresponding author. Tel.: +91 542 2575089; fax: +91 542 2368428. E-mail address: [email protected] (S.P. Singh). 0142-0615/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2009.03.013

along with a filtering mechanism. Aoki et al. [3] described a loss reduction strategy where a discrete optimization problem was solved. Merlin and Back [4] used a branch and bound method for an optimal solution of minimum losses. Based on this work and overcoming several approximations made there, Shirmohammadi and Wong [5] suggested a simple algorithm where the given radial network was first converted to a meshed form by closing all the tie switches. Then an optimal flow pattern was determined before reconverting the network to radial form by opening, in each loop, such a switch that disturbs the optimal flow pattern to a minimum extent. With a view to achieve larger loss reduction, Goswami and Basu [6] modified the method [5] by handling one loop at a time. This approach reduced the dimensionality of the problem. The authors also suggested three power flow methods, closely related to each other, for weakly meshed networks. However, these two methods [5] and [6] need computation of branch currents whereas the load flow solution is normally available in terms of power flow. Conversion of the branch power flows to current flows requires additional computational burden in the earlier methods. Huddleston et al. [7] minimized a quadratic loss function with linear constraints for minimum loss switching strategy. McDermott et al. [8] suggested a heuristic search method for feeder reconfiguration. The reconfiguration problem was visualized as simplex method by Fan et al. [9] and was solved using a single loop optimization. Lin and Chin [10] suggested an elegant heuristic method, based on indices, for loss minimization and service restoration. Recently evolutionary techniques have been proposed for distribution reconfiguration problem. Genetic Algorithm (GA) has been

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addressed for this problem by Lin et al. [11] due to its binary coding and global optimum feature. Jeon and Kim [12] proposed a hybrid method whose main search is based on Simulated Annealing and Tabu Search is integrated to improve the search efficiency of Simulated Annealing. Das [13] reported fuzzy multi objective approach that attempts to minimize the number of tie switch operations based on the heuristic rules and for each tie-switch operation, it maximizes the fuzzy satisfaction objective function for obtaining optimum configuration. However, each sectionalizing switch of loop formed by closure of selected tie-switch is tested for opening in order to obtain a radial configuration. The sectionalizing switch that yields optimum value of objective function is opened to obtain radial structure of the network. Thus, though number of tie switches to be closed is reduced but the number of sectionalizing switches which are tested is very high since each sectionalizing switch of the loop formed by closure of a tie switch is examined for optimality resulting in increased computation burden. Venkatesh and Ranjan [14] proposed fuzzy adoption of EP for reconfiguration. This also requires several iterations resulting in considerably high computational time. Further, involvement of enormous amount of load flow solutions restricts its application. Thus, most of the methods on feeder reconfiguration are based on either branch exchange or sequential switch opening in which attempts are made to reduce the switching options and repetitive load flow. The evolutionary and fuzzy techniques have also been reported in the recent past. In this work a power-based sequential switch opening method is proposed where there is no need to convert the nodal power to currents at different stages as done in most of the earlier methods. A branch carrying the minimum power in a meshed network is opened. This results in radial configuration with minimum loss and better voltage profile. Thus as many switching options are required as number of tie switches. The proposed methodology is tested on two widely referred systems and comparisons of these results with earlier methods indicate encouraging results.

through 6 are fed from feeder 1 and nodes 7 through 11 are on feeder 2. In the case of emergency, say fault in section s1 on feeder 1, the loads connected to nodes 1 through 6 are not served. Connecting the tie switch s7 or s13 and opening the sectionalizing switch s1 can restore the loads on the nodes 1 through 6. This operation transfers the loads supplied by feeder 1 on feeder 2. However, the choice of closing the tie switch/es and opening the sectionalizing switch/es depends on the criteria adopted to ensure that all the loads are served and the system operates in radial configuration. Similarly the transfer of load from one feeder to the other during normal operation for better performance of the network can be explained. This reconfiguration of the system leads to new state of the system. This state can be obtained by fresh load flow. Thus the feeder reconfiguration has two major computational steps, namely load flow and determination of new configuration based on appropriate criterion. The second step of reconfiguration is addressed in this paper. 3. Proposed method A widely used method of sequential switch opening was proposed by Shirmohammadi et al. [5] and was extensively studied by various workers in this field. The proposed methodology is an extension of this method resulting in a power-based formulation, instead of current flow, thus reducing the computational burden. Proceeding in a manner similar to that in Ref. [5], this method arrives at an interesting result through solution of a quadratic programming problem where the network real power loss is minimized subjecting to current balance at system nodes. 3.1. Notations n m Rk I

2. Statement of problem C The distribution networks consist of tie switches and sectionalizing switches. The tie switches are normally open and the sectionalizing switches are normally closed during operation. These are provided to meet the quality and quantity requirements of electrical energy during system emergencies and also during normal operations. Consider a two-feeder distribution system as shown in Fig. 1. The branches shown by dotted lines, 7 and 13, represent ties connecting feeders that are kept normally open. Other branches shown by continuous lines contain sectionalizing switches. It is assumed that every branch of the system has sectionalizing switch. Corresponding branch numbers identify all 13 sectionalizing switches. With the present status of the switches nodes 1

V A

ai1

number of nodes in the system number of branches in the system resistance of the branch k m-vector complex branch current with its components ak + jbk for branch k n-vector complex nodal current with its components ci + jdi for node i m-vector complex branch voltage with its components ek + jfk for branch k n  m network incidence matrix with its component ail for a branch connecting nodes i and l 1 if a branch is connected between nodes i and l and leaves node i 1 if a branch is connected between nodes i and l and enters node l 0 otherwise

3.2. Minimum loss strategy A line flow pattern resulting in a minimum resistive line loss in a meshed network will correspond to the optimal power flow pattern. This can mathematically be stated as

Minimize

m X

Rk jIk j2

ð1Þ

k¼1

Fig. 1. Sample 2-feeder system.

Subject to AI = C The constraint on line flows and voltages are ignored in this formulation. However, they can be incorporated by rejecting the solutions violating these constraints. Expressing Eq. (1) in terms of real and imaginary parts would yield

S.P. Singh et al. / Electrical Power and Energy Systems 31 (2009) 309–314

Minimize

m X

2

Rk ða2k þ bk Þ

ð2aÞ

k¼1

Subject to Aa ¼ c

ð2bÞ

and

Subject to Ab ¼ d

ð2cÞ

The above problem expressed by Eq. (2) needs an appropriate optimization method for its solution. Since it is a non-linear optimization problem subject to equality constraints, it can be converted to an unconstrained problem using Lagrangian multipliers as under

Minimize Z ¼

m X

2

Rk ða2k þ bk Þ  k1 ðAa  cÞ  k2 ðAb  dÞ

ð3Þ

k¼1

where k1 and k2 are Lagrangian multiplier vectors of order n. The solution of Eq. (3) can be obtained by equating the partial derivative of the functions with respect to relevant variables to zero as

@Z ¼0 @a

@Z ¼0 @k1

@Z ¼0 @b

@Z ¼0 @k2

Using Eq. (3), the partial derivatives with respect to ak and bk yield

2Rk ak þ k1i  k1l ¼ 0 2Rk bk þ k2i  k2l ¼ 0

ð4Þ ð5Þ

where i and l denote the two nodes of the branch k. Summing Eq. (4) over the entire loop yields m X

Rk ak ¼ 0

ð5Þ

Rk bk ¼ 0

ð6Þ

k¼1 m X k¼1

Multiplying Eq. (5b) by operator j and adding it to Eq. (5a) yield: m X

Rk ðak þ jbk Þ ¼ 0

ð6Þ

k¼1

or m X

Rk Ik ¼ 0

ð7Þ

311

branch in a mesh with minimum power flow yields radial configuration while retaining at the same time, the minimum loss power flow pattern. This is major departure from original work of Ref. [5] where minimum current is the criterion for opening a branch which requires additional computational burden of computing the currents whereas the information is available in terms of powers. 3.3. Interpretation Starting with an optimization problem expressed by Eq. (1), it is demonstrated that the minimum loss in a resistive network will occur if it is in the mesh form. This interpretation can be exploited for feeder reconfiguration in distribution network. In case all the tie switches are closed, which are open in radial structure, the network will be converted into a meshed network with the same number of meshes as tie switches. Opening the appropriate switches would result in radial structure. For example, closing the tie switches s13 and s7 (presently open) of sample 2-feeder system as shown in Fig. 1, the initial radial network will result in two meshes (mesh1: s1, s2, s5,13, s10, s11 and s12) and (mesh2: s3, s4, s6, s7,s8, s9, s10, s13 and s5). Thus the network is now in meshed form. If the impedances of all the branches are replaced by their respective resistances, the flow pattern of this meshed network will correspond to minimum loss. However, the network is to be operated radially. This can be achieved by opening a tie/sectionalizing switch from each mesh. This will cause change in flow pattern resulting in higher losses. However, the minimum loss flow pattern can be retained to a maximum extent by opening a tie/sectionalizing switch of the branch with lowest power flow. This can be achieved in this example in two steps. A branch having lowest power flow in mesh1 is identified, say s5, and opened at the first step. This will result in radial structure of mesh1 while retaining the same structure of mesh2. A fresh power flow would reveal lowest power flow branch in mesh2, say s4. Opening a tie/sectionalizing switch of this branch, the minimum power loss pattern will be disturbed to minimum extent and mesh2 will be converted to radial structure. In this way the entire network will be reconfigured to radial structure retaining the minimum loss power flow pattern. 3.4. Computational steps The interpretation of relations discussed in previous paragraph can be implemented on computer following the under-mentioned steps.

k¼1

Eqs. (2b) and (2c) are Kirchchoff’s Current Law (KCL) for the general meshed network and Eq. (7) is Kirchchoff’s Voltage Law (KVL) for the same network with branch impedances replaced by their resistances. So the above finding implies that Tellegen’s theorem given below by Eq. (8) is true for this network. m X

V k Ik ¼ 0

ð8Þ

k¼1

Now making the physically justifiable assumption that the node power factor at each of the nodes and the branch R/X ratio for each branch of the meshed network are the same, the Eq. (8) can be reduced partly to m X

Pk ¼ 0

ð9Þ

(1) Given the radial configuration, close all the tie switches in the system to convert it into meshed network. (2) Conduct the power flow with the branch impedances replaced by branch resistances and identify the real power flow in the branches. (3) Open a sectionalizing/tie switch of a branch having minimum real power flow in a mesh identified at step 2. This results in conversion of a meshed network corresponding to this branch into a radial network. (4) Check whether all the meshes have been converted to radial structure? If yes, go to step 6. Otherwise (5) Repeat steps 2–4 till the entire network becomes radial. This radial configuration results in minimum line losses. (6) Terminate the reconfiguration process and accept the results.

k¼1

Thus Eq. (9), derived through the optimal condition (7), ensures a power flow pattern with minimum line loss in each loop with impedances of loop branches replaced by their respective resistances. Once this flow is obtained, minimum disturbance to the network would cause minimum change in line loss. Hence opening a

3.5. Service restoration Faults do occur during operation of distribution network. Location of fault, isolation of faulted section and service to the healthy

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section are important functions of a distribution system. The service restoration deals with determination of a scheme to supply power to the affected areas following fault isolation. This can be accomplished by opening and/or closing certain switches in such a manner that the maximum possible loads are supplied. Obviously, there could be several combinations of switches to achieve this goal resulting in numerous solutions to this problem. However, the service restoration scheme that suggests best strategy of restoration while satisfying the following requirements [15,16] should be followed. (1) (2) (3) (4) (5) (6) (7)

Minimum restoration time. Restoration of maximum load. Minimum number of switching operations. Operation of switches close to tie switches. Radial structure of final network. No overloaded feeder and voltage limit violation. Minimum loss.

The load shedding mentioned at step (4) is to be judiciously decided by the operator depending upon the circumstances. 4. Simulation results The performance and advantages of the proposed reconfiguration algorithm are demonstrated on two widely referred systems namely. (1) 3-feeder system [1]. (2) 37-line system [2]. The comparison is based on the reduction in power loss, improvement in voltage profile and number of computational steps to arrive at final configuration. 4.1. 3-feeder system

3.5.1. Application of proposed methodology The proposed methodology of feeder reconfiguration can be extended for service restoration. The process starts with the isolation of faulty section and final restoration plan is achieved following the underwritten steps. (1) Close all the tie switches in the system to convert it into meshed network. (2) Conduct the power flow with the branch impedances replaced by branch resistances and identify the real power flow in the branches. (3) Open a sectionalizing/tie switch of a branch having minimum real power flow in a mesh identified at step 2. This results in the conversion of a meshed network corresponding to this branch into a radial network. (4) Check for the constraints violations on line flows and voltages? If yes, shed a bus load and go to step 2. Otherwise go to step 5. (5) Check whether all the meshes have been converted to radial structure? If yes, go to step 6. Otherwise (6) Repeat steps 2–5 till the entire network becomes radial. (7) Terminate the restoration process and accept the results.

This system consists of 16 nodes and 13 lines. There are three tie switches s15, s21 and s26 and 13 sectionalizing switches as shown in Fig. 2. The system is supplied by three feeding points with provision for load transfer from one feeder to other through aforementioned tie lines. The loss (system real power loss) for this initial configuration is 0.00511 pu. Proceeding in the manner suggested in the present work, optimal solution is obtained in three steps. This final configuration with open switches s26, s17 and s19 and with tie switches s15 and s21 closed, has a loss of 0.00466 pu, which is 8.806% less than that of initial configuration. The final configuration matches exactly with that reported by Lin et al. [10] and Civanlar [1] for this system but with less computational burden. This conclusion is drawn based on obvious reason of higher computational burden of Civanlar’s [1] method that requires more number (depending upon branch exchanges) of load flow solutions as compared to that of the number of tie (open) switches in the case of proposed method. Although the number of load flow solutions in Lin et al. [10] method is same as in the proposed method, evaluation of decision making indices requires additional computational time. The voltage profile of the final reconfigured system is given in Table 1. It is observed that voltage profile of the system has improved as compared to that of the initial configuration. The difference between the maximum and the minimum system voltage for the initial configuration is 0.03073 pu whereas for the final configuration it is 0.02842 pu. 4.2. 37-line system The 37-line system of [2] is shown in Fig. 3. The system contains 32 nodes with five tie switches (shown as dashed lines). The tie switches (s33, s34, s35, s36 and s37) are open in the initial configuration of the system. The final reconfigured system as obtained by the proposed method has a system loss of 0.013921 pu which is 31.10% lower than the original (initial) network configuration. The system voltage profile for the reconfigured system and the initial configuration is depicted in Table 2. The final reconfigured system has better system voltage profile than the initial one. The difference between the maximum and the minimum system voltage for the initial configuration is 0.08637 pu whereas for the final configuration it

Fig. 2. 3-Feeder system.

Table 1 Profile of 3-feeder system. System configuration

Open tie switches

System loss (pu)

Minimum voltage (pu)

Maximum voltage (pu)

Initial Final

s15, s21, s26 s26, s17, s19

0.00511 0.00466

0.96927 0.97158

1.00000 1.00000

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Fig. 4. 3-Feeder system (reconfigured system with fault at section s16).

Table 3 Comparison of restoration results for 3-feeder system. Method

Open switches

Closed switches

Minimum voltage Node Value (pu)

Loss (PU)

Load shed

Proposed Lin and Chin [3]

s18, s26 s17, s26

s17, s19 s19

12 8

0.0849 0.0656

No Node 12

0.95417 0.94848

Fig. 3. 32-Line system.

is 0.06204 pu. An identical final configuration was obtained in the literature by Lin and Chin [10], Goswami [6] and Baran [2]. The number of switching steps involved to arrive at the final configuration is five (number of tie switches) by the proposed method, whereas the heuristic method reported by Goswami and Basu [6] depends on the switching options selected. The method proposed by Goswami suggested three options of selecting the order of switching. The best method proposed by them took the same number of switching steps as in the present method. However, the computational involvement in the case of the former method is more as the calculation desires conversion of nodal power into nodal current. The proposed method arrives at the optimal solution in same number of computational steps, i.e. number of tie switches in the system, regardless of the switching option selected. The method of indices based on heuristics by Lin and Chin also arrive at the same solution points. The indices are lV and lL and depend on system voltage and line constants (R, X and position of the line), respectively. It can be observed that the index lL remains constant for a system irrespective of the loading condition. Hence, only lV depends on the loading condition of the system and effectively the decision for reconfiguration is based on voltage magnitude. Another departure of this method lies in closing of tie switches wherein all the tie switches are closed at a time and sectionalizing/tie switches are opened one by one. Once all the tie switches are closed, identification of loop corresponding to a particular tie switch becomes ambiguous which can lead to more number of loops than the switches.

take the final configuration after loss reduction as shown in Fig. 4. A fault is assumed in section s16. After isolation of fault, system will be divided into four groups as shown in the figure. Group 2 has load points without sources and is the affected group. On the other hand groups 3 and 4 have source points. The service to the load points of group 2 can be restored through either of these sources. This can be achieved by transferring the load of group 2 on any one or both the groups. Using the proposed method of restoration, switches s17 and s19 are to be closed and s18 is to be opened. This resulted in service to all the loads in the network without violating any voltage limits at loss of 0.0849 pu. The minimum voltage of 0.95417 pu was obtained at node 12. Lin and Chin [10] have also reported the results for this case. They found, through their method, that closure of switch s17 violates the voltage limit. The minimum voltage of 0.91446 was observed at node 12. Later switch s19 was selected to be closed. This also violated the voltage limits with minimum voltage of 0.92432 pu at node 8. Further, they suggested to shed the load at node 12, considering it to be a low priority load. This resulted in minimum voltage of 0.94848 pu at node 8. The results of the proposed method and method of Lin and Chin [10] are tabulated in Table 3. It can be seen from this table that the proposed method produces better restoration plan compared to method of Lin and Chin [10]. The minimum voltage observed is better without any load shedding. However, the losses are slightly more in the proposed method, which is due to higher load served in the absence of any load shedding. 5. Conclusions

4.3. Service restoration The example of 3-feeder system (Fig. 2) is sued to demonstrate the application of proposed method for service restoration. Let us

A new feeder reconfiguration methodology for minimum line losses based on nodal powers, rather than constant nodal currents, is presented that is faster than the existing methods but leads to

Table 2 Profile of 37-line system. System configuration

Open tie switches

System loss (pu)

Minimum voltage (pu)

Maximum voltage (pu)

Initial Final

s33, s34, s35, s36, s37 s7, s9, s14, s32, s37

0.020205 0.013921

0.91365 at bus 37 0.93796 at bus 32

1.00000 1.00000

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the same results. The proposed fast reconfiguration algorithm is tested on two systems. In each of the cases, the percent saving in real power losses is same as in the earlier methods. The test results reveal that better voltage profile is achieved after reconfiguration. The proposed method has been extended for service restoration. Test results obtained indicate that this method results in a better restoration plan as compared to the reported method of Lin and Chin [10]. References [1] Civanlar S, Grainger JJ, Yin H, Lee SSH. Distribution feeder reconfiguration for loss reduction. IEEE Trans Power Deliver 1988;3(4):1217–23. [2] Baran ME, Wu FF. Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans Power Deliver 1989;4(2):1401–7. [3] Aoki K, Kawabara H, Satoh T, Kanezashi M. An efficient algorithm for load balancing of transformers and feeders. IEEE Trans Power Deliver 1988;3(4):1865–72. [4] Merlin A, Back H. Search for a minimal-loss operating spanning tree configuration for an urban power distribution system. In: Proceedings of 5th PSCC, Cambridge, UK, September 1–5, 1975. p. 1–18. [5] Shirmohammadi D, Hong HW. Reconfiguration of electric distribution network for resistive line losses reduction. IEEE Trans Power Deliver 1989;4(2):1492–8. [6] Goswami SK, Basu SK. A new algorithm for the reconfiguration of distribution feeders for loss minimization. IEEE Trans Power Deliver 1992;7(3):1484–90.

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