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

a r t i c l e i n f o a b s t r a c t

Article history: A sequential switch opening method is proposed for minimum loss feeder reconfiguration in this paper.
Received 5 March 2008 The algorithm is further extended for service restoration. The method is based on the branch power flow
Received in revised form 12 March 2009 rather than the current flow as reported in earlier methods. The final algorithm arrives at opening of a
Accepted 16 March 2009
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 compu-
tation burden and better restoration plan.
Keywords:
Ó 2009 Elsevier Ltd. All rights reserved.
Load flow
Losses
Network
Optimization method
Power distribution
Power quality

1. Introduction along with a filtering mechanism. Aoki et al. [3] described a loss
reduction strategy where a discrete optimization problem was
Alteration in the topology of a distribution network for efficient solved. Merlin and Back [4] used a branch and bound method for
operation of the system results in reconfiguration. An effective fee- an optimal solution of minimum losses. Based on this work and
der reconfiguration strategy takes advantage of the large degree of overcoming several approximations made there, Shirmohammadi
load diversity. Each distribution feeder has a different combination and Wong [5] suggested a simple algorithm where the given radial
of commercial, industrial and residential loads. These loads tend to network was first converted to a meshed form by closing all the tie
vary depending on the time of the day, weather and season. Feeder switches. Then an optimal flow pattern was determined before
reconfiguration would allow for the transfer of load from heavily reconverting the network to radial form by opening, in each loop,
loaded portion of the power distribution system to locations that such a switch that disturbs the optimal flow pattern to a minimum
are relatively lightly loaded. This would not only improve the oper- extent. With a view to achieve larger loss reduction, Goswami and
ating conditions but also enable the full utilization of system hard- Basu [6] modified the method [5] by handling one loop at a time.
ware capabilities. This could result in deferred capital expenditure This approach reduced the dimensionality of the problem. The
and reduced operating expenses. The feeder reconfiguration is authors also suggested three power flow methods, closely related
done during emergency for load restoration and in normal condi- to each other, for weakly meshed networks. However, these two
tions for loss reduction and load balancing. methods [5] and [6] need computation of branch currents whereas
Reconfiguration of the distribution network through sectional- the load flow solution is normally available in terms of power flow.
izing and tie switches can reduce losses and improve voltage pro- Conversion of the branch power flows to current flows requires
file. Several methods are available in the literature to arrive at a additional computational burden in the earlier methods. Huddle-
switching strategy for loss minimization. A switch exchange type ston et al. [7] minimized a quadratic loss function with linear con-
of heuristic method was suggested by Civanlar et al. [1] where a straints for minimum loss switching strategy. McDermott et al. [8]
simple formula was developed for estimating change in losses suggested a heuristic search method for feeder reconfiguration.
due to a branch exchange. A filtering mechanism was also sug- The reconfiguration problem was visualized as simplex method
gested to reduce the number of candidate switching options. Baran by Fan et al. [9] and was solved using a single loop optimization.
and Wu [2] developed an alternate branch exchange algorithm Lin and Chin [10] suggested an elegant heuristic method, based
on indices, for loss minimization and service restoration. Recently
* Corresponding author. Tel.: +91 542 2575089; fax: +91 542 2368428. evolutionary techniques have been proposed for distribution
E-mail address: sps_ee@bhu.ac.in (S.P. Singh). reconfiguration problem. Genetic Algorithm (GA) has been

0142-0615/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijepes.2009.03.013
310 S.P. Singh et al. / Electrical Power and Energy Systems 31 (2009) 309–314

addressed for this problem by Lin et al. [11] due to its binary cod- through 6 are fed from feeder 1 and nodes 7 through 11 are on
ing and global optimum feature. Jeon and Kim [12] proposed a hy- feeder 2.
brid method whose main search is based on Simulated Annealing In the case of emergency, say fault in section s1 on feeder 1, the
and Tabu Search is integrated to improve the search efficiency of loads connected to nodes 1 through 6 are not served. Connecting
Simulated Annealing. the tie switch s7 or s13 and opening the sectionalizing switch s1
Das [13] reported fuzzy multi objective approach that attempts can restore the loads on the nodes 1 through 6. This operation
to minimize the number of tie switch operations based on the heu- transfers the loads supplied by feeder 1 on feeder 2. However,
ristic rules and for each tie-switch operation, it maximizes the fuz- the choice of closing the tie switch/es and opening the sectionaliz-
zy satisfaction objective function for obtaining optimum ing switch/es depends on the criteria adopted to ensure that all the
configuration. However, each sectionalizing switch of loop formed loads are served and the system operates in radial configuration.
by closure of selected tie-switch is tested for opening in order to Similarly the transfer of load from one feeder to the other during
obtain a radial configuration. The sectionalizing switch that yields normal operation for better performance of the network can be ex-
optimum value of objective function is opened to obtain radial plained. This reconfiguration of the system leads to new state of
structure of the network. Thus, though number of tie switches to the system. This state can be obtained by fresh load flow. Thus
be closed is reduced but the number of sectionalizing switches the feeder reconfiguration has two major computational steps,
which are tested is very high since each sectionalizing switch of namely load flow and determination of new configuration based
the loop formed by closure of a tie switch is examined for optimal- on appropriate criterion. The second step of reconfiguration is ad-
ity resulting in increased computation burden. Venkatesh and Ran- dressed in this paper.
jan [14] proposed fuzzy adoption of EP for reconfiguration. This
also requires several iterations resulting in considerably high com- 3. Proposed method
putational time. Further, involvement of enormous amount of load
flow solutions restricts its application. A widely used method of sequential switch opening was pro-
Thus, most of the methods on feeder reconfiguration are based posed by Shirmohammadi et al. [5] and was extensively studied
on either branch exchange or sequential switch opening in which by various workers in this field. The proposed methodology is an
attempts are made to reduce the switching options and repetitive extension of this method resulting in a power-based formulation,
load flow. The evolutionary and fuzzy techniques have also been re- instead of current flow, thus reducing the computational burden.
ported in the recent past. In this work a power-based sequential Proceeding in a manner similar to that in Ref. [5], this method ar-
switch opening method is proposed where there is no need to con- rives at an interesting result through solution of a quadratic pro-
vert the nodal power to currents at different stages as done in most gramming problem where the network real power loss is
of the earlier methods. A branch carrying the minimum power in a minimized subjecting to current balance at system nodes.
meshed network is opened. This results in radial configuration with
minimum loss and better voltage profile. Thus as many switching 3.1. Notations
options are required as number of tie switches. The proposed
methodology is tested on two widely referred systems and compar- n number of nodes in the system
isons of these results with earlier methods indicate encouraging m number of branches in the system
results. Rk resistance of the branch k
I m-vector complex branch current with its components ak + jbk
2. Statement of problem for branch k
C n-vector complex nodal current with its components ci + jdi
The distribution networks consist of tie switches and sectional- for node i
izing switches. The tie switches are normally open and the section- V m-vector complex branch voltage with its components ek + jfk
alizing switches are normally closed during operation. These are for branch k
provided to meet the quality and quantity requirements of electri- A n  m network incidence matrix with its component ail for a
cal energy during system emergencies and also during normal branch connecting nodes i and l
operations. ai1 1 if a branch is connected between nodes i and l and leaves
Consider a two-feeder distribution system as shown in Fig. 1. node i
The branches shown by dotted lines, 7 and 13, represent ties con- 1 if a branch is connected between nodes i and l and enters
necting feeders that are kept normally open. Other branches node l
shown by continuous lines contain sectionalizing switches. It is as- 0 otherwise
sumed 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 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 pat-
tern. This can mathematically be stated as
X
m
Minimize Rk jIk j2 ð1Þ
k¼1

Subject to AI = C
The constraint on line flows and voltages are ignored in this for-
mulation. However, they can be incorporated by rejecting the solu-
tions violating these constraints.
Expressing Eq. (1) in terms of real and imaginary parts would
Fig. 1. Sample 2-feeder system. yield
 S.P. Singh et al. / Electrical Power and Energy Systems 31 (2009) 309–314 311

X
m
2 branch in a mesh with minimum power flow yields radial configura-
Minimize Rk ða2k þ bk Þ ð2aÞ
tion while retaining at the same time, the minimum loss power flow
k¼1
pattern. This is major departure from original work of Ref. [5] where
Subject to Aa ¼ c ð2bÞ minimum current is the criterion for opening a branch which re-
quires additional computational burden of computing the currents
and whereas the information is available in terms of powers.
Subject to Ab ¼ d ð2cÞ
3.3. Interpretation
The above problem expressed by Eq. (2) needs an appropriate
optimization method for its solution. Since it is a non-linear optimi- Starting with an optimization problem expressed by Eq. (1), it is
zation problem subject to equality constraints, it can be converted demonstrated that the minimum loss in a resistive network will
to an unconstrained problem using Lagrangian multipliers as under occur if it is in the mesh form. This interpretation can be exploited
X
m for feeder reconfiguration in distribution network. In case all the
2
Minimize Z ¼ Rk ða2k þ bk Þ  k1 ðAa  cÞ  k2 ðAb  dÞ ð3Þ tie switches are closed, which are open in radial structure, the net-
k¼1 work will be converted into a meshed network with the same
where k1 and k2 are Lagrangian multiplier vectors of order n. number of meshes as tie switches. Opening the appropriate
The solution of Eq. (3) can be obtained by equating the partial switches would result in radial structure. For example, closing
derivative of the functions with respect to relevant variables to the tie switches s13 and s7 (presently open) of sample 2-feeder
zero as 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:
@Z @Z @Z @Z s3, s4, s6, s7,s8, s9, s10, s13 and s5). Thus the network is now in
¼0 ¼0 ¼0 ¼0
@a @k1 @b @k2 meshed form. If the impedances of all the branches are replaced
Using Eq. (3), the partial derivatives with respect to ak and bk by their respective resistances, the flow pattern of this meshed net-
yield work will correspond to minimum loss. However, the network is to
be operated radially. This can be achieved by opening a tie/section-
2Rk ak þ k1i  k1l ¼ 0 ð4Þ alizing switch from each mesh. This will cause change in flow pat-
2Rk bk þ k2i  k2l ¼ 0 ð5Þ tern resulting in higher losses. However, the minimum loss flow
pattern can be retained to a maximum extent by opening a tie/sec-
where i and l denote the two nodes of the branch k. Summing Eq. (4)
tionalizing switch of the branch with lowest power flow. This can
over the entire loop yields
be achieved in this example in two steps. A branch having lowest
X
m
power flow in mesh1 is identified, say s5, and opened at the first
Rk ak ¼ 0 ð5Þ step. This will result in radial structure of mesh1 while retaining
k¼1
the same structure of mesh2. A fresh power flow would reveal low-
X
m est power flow branch in mesh2, say s4. Opening a tie/sectionaliz-
Rk bk ¼ 0 ð6Þ ing switch of this branch, the minimum power loss pattern will be
k¼1 disturbed to minimum extent and mesh2 will be converted to ra-
Multiplying Eq. (5b) by operator j and adding it to Eq. (5a) yield: dial structure. In this way the entire network will be reconfigured
to radial structure retaining the minimum loss power flow pattern.
X
m
Rk ðak þ jbk Þ ¼ 0 ð6Þ
k¼1
3.4. Computational steps

or The interpretation of relations discussed in previous paragraph

X
m can be implemented on computer following the under-mentioned
Rk Ik ¼ 0 ð7Þ steps.
k¼1

Eqs. (2b) and (2c) are Kirchchoff’s Current Law (KCL) for the (1) Given the radial configuration, close all the tie switches in
general meshed network and Eq. (7) is Kirchchoff’s Voltage Law the system to convert it into meshed network.
(KVL) for the same network with branch impedances replaced by (2) Conduct the power flow with the branch impedances
their resistances. So the above finding implies that Tellegen’s the- replaced by branch resistances and identify the real power
orem given below by Eq. (8) is true for this network. flow in the branches.
(3) Open a sectionalizing/tie switch of a branch having mini-
X
m
V k Ik ¼ 0 ð8Þ mum real power flow in a mesh identified at step 2. This
k¼1 results in conversion of a meshed network corresponding
to this branch into a radial network.
Now making the physically justifiable assumption that the node
(4) Check whether all the meshes have been converted to radial
power factor at each of the nodes and the branch R/X ratio for each
structure? If yes, go to step 6. Otherwise
branch of the meshed network are the same, the Eq. (8) can be re-
(5) Repeat steps 2–4 till the entire network becomes radial. This
duced partly to
radial configuration results in minimum line losses.
X
m (6) Terminate the reconfiguration process and accept the
Pk ¼ 0 ð9Þ results.
k¼1

Thus Eq. (9), derived through the optimal condition (7), ensures a
power flow pattern with minimum line loss in each loop with 3.5. Service restoration
impedances of loop branches replaced by their respective resis-
tances. Once this flow is obtained, minimum disturbance to the net- Faults do occur during operation of distribution network. Loca-
work would cause minimum change in line loss. Hence opening a tion of fault, isolation of faulted section and service to the healthy
312 S.P. Singh et al. / Electrical Power and Energy Systems 31 (2009) 309–314

section are important functions of a distribution system. The ser- The load shedding mentioned at step (4) is to be judiciously
vice restoration deals with determination of a scheme to supply decided by the operator depending upon the circumstances.
power to the affected areas following fault isolation. This can be
accomplished by opening and/or closing certain switches in such 4. Simulation results
a manner that the maximum possible loads are supplied. Obvi-
ously, there could be several combinations of switches to achieve The performance and advantages of the proposed reconfigura-
this goal resulting in numerous solutions to this problem. How- tion algorithm are demonstrated on two widely referred systems
ever, the service restoration scheme that suggests best strategy namely.
of restoration while satisfying the following requirements [15,16]
should be followed. (1) 3-feeder system [1].
(2) 37-line system [2].
(1) Minimum restoration time.
(2) Restoration of maximum load. The comparison is based on the reduction in power loss,
(3) Minimum number of switching operations. improvement in voltage profile and number of computational
(4) Operation of switches close to tie switches. steps to arrive at final configuration.
(5) Radial structure of final network.
(6) No overloaded feeder and voltage limit violation. 4.1. 3-feeder system
(7) Minimum loss.
This system consists of 16 nodes and 13 lines. There are three
tie switches s15, s21 and s26 and 13 sectionalizing switches as
3.5.1. Application of proposed methodology shown in Fig. 2. The system is supplied by three feeding points
The proposed methodology of feeder reconfiguration can be ex- with provision for load transfer from one feeder to other through
tended for service restoration. The process starts with the isolation aforementioned tie lines. The loss (system real power loss) for this
of faulty section and final restoration plan is achieved following the initial configuration is 0.00511 pu. Proceeding in the manner sug-
underwritten steps. gested in the present work, optimal solution is obtained in three
steps. This final configuration with open switches s26, s17 and
(1) Close all the tie switches in the system to convert it into s19 and with tie switches s15 and s21 closed, has a loss of
meshed network. 0.00466 pu, which is 8.806% less than that of initial configuration.
(2) Conduct the power flow with the branch impedances The final configuration matches exactly with that reported by Lin
replaced by branch resistances and identify the real power et al. [10] and Civanlar [1] for this system but with less computa-
flow in the branches. tional burden. This conclusion is drawn based on obvious reason of
(3) Open a sectionalizing/tie switch of a branch having mini- higher computational burden of Civanlar’s [1] method that re-
mum real power flow in a mesh identified at step 2. This quires more number (depending upon branch exchanges) of load
results in the conversion of a meshed network correspond- flow solutions as compared to that of the number of tie (open)
ing to this branch into a radial network. switches in the case of proposed method. Although the number
(4) Check for the constraints violations on line flows and volt- of load flow solutions in Lin et al. [10] method is same as in the
ages? If yes, shed a bus load and go to step 2. Otherwise proposed method, evaluation of decision making indices requires
go to step 5. additional computational time.
(5) Check whether all the meshes have been converted to radial The voltage profile of the final reconfigured system is given in
structure? If yes, go to step 6. Otherwise Table 1. It is observed that voltage profile of the system has
(6) Repeat steps 2–5 till the entire network becomes radial. improved as compared to that of the initial configuration. The
(7) Terminate the restoration process and accept the results. difference between the maximum and the minimum system volt-
age 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 configu-
ration 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 ini-
Fig. 2. 3-Feeder system. tial configuration is 0.08637 pu whereas for the final configuration it

Table 1
Profile of 3-feeder system.

System configuration Open tie switches System loss (pu) Minimum voltage (pu) Maximum voltage (pu)
Initial s15, s21, s26 0.00511 0.96927 1.00000
Final s26, s17, s19 0.00466 0.97158 1.00000
 S.P. Singh et al. / Electrical Power and Energy Systems 31 (2009) 309–314 313

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

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

Method Open Closed Minimum voltage Loss Load

switches switches Node Value (pu) (PU) shed
Proposed s18, s26 s17, s19 12 0.95417 0.0849 No
Lin and Chin [3] s17, s26 s19 8 0.94848 0.0656 Node 12

Fig. 3. 32-Line system.

take the final configuration after loss reduction as shown in
is 0.06204 pu. An identical final configuration was obtained in the Fig. 4. A fault is assumed in section s16. After isolation of fault, sys-
literature by Lin and Chin [10], Goswami [6] and Baran [2]. tem will be divided into four groups as shown in the figure. Group
The number of switching steps involved to arrive at the final 2 has load points without sources and is the affected group. On the
configuration is five (number of tie switches) by the proposed other hand groups 3 and 4 have source points. The service to the
method, whereas the heuristic method reported by Goswami and load points of group 2 can be restored through either of these
Basu [6] depends on the switching options selected. The method sources. This can be achieved by transferring the load of group 2
proposed by Goswami suggested three options of selecting the or- on any one or both the groups.
der of switching. The best method proposed by them took the same Using the proposed method of restoration, switches s17 and s19
number of switching steps as in the present method. However, the are to be closed and s18 is to be opened. This resulted in service to
computational involvement in the case of the former method is all the loads in the network without violating any voltage limits at
more as the calculation desires conversion of nodal power into no- loss of 0.0849 pu. The minimum voltage of 0.95417 pu was ob-
dal current. The proposed method arrives at the optimal solution in tained at node 12. Lin and Chin [10] have also reported the results
same number of computational steps, i.e. number of tie switches in for this case. They found, through their method, that closure of
the system, regardless of the switching option selected. switch s17 violates the voltage limit. The minimum voltage of
The method of indices based on heuristics by Lin and Chin also 0.91446 was observed at node 12. Later switch s19 was selected
arrive at the same solution points. The indices are lV and lL and to be closed. This also violated the voltage limits with minimum
depend on system voltage and line constants (R, X and position voltage of 0.92432 pu at node 8. Further, they suggested to shed
of the line), respectively. It can be observed that the index lL re- the load at node 12, considering it to be a low priority load. This
mains constant for a system irrespective of the loading condition. resulted in minimum voltage of 0.94848 pu at node 8. The results
Hence, only lV depends on the loading condition of the system of the proposed method and method of Lin and Chin [10] are tab-
and effectively the decision for reconfiguration is based on voltage ulated in Table 3. It can be seen from this table that the proposed
magnitude. Another departure of this method lies in closing of tie method produces better restoration plan compared to method of
switches wherein all the tie switches are closed at a time and sec- Lin and Chin [10]. The minimum voltage observed is better without
tionalizing/tie switches are opened one by one. Once all the tie any load shedding. However, the losses are slightly more in the
switches are closed, identification of loop corresponding to a par- proposed method, which is due to higher load served in the
ticular tie switch becomes ambiguous which can lead to more absence of any load shedding.
number of loops than the switches.
5. Conclusions
4.3. Service restoration
A new feeder reconfiguration methodology for minimum line
The example of 3-feeder system (Fig. 2) is sued to demonstrate losses based on nodal powers, rather than constant nodal currents,
the application of proposed method for service restoration. Let us 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 s33, s34, s35, s36, s37 0.020205 0.91365 at bus 37 1.00000
Final s7, s9, s14, s32, s37 0.013921 0.93796 at bus 32 1.00000
314 S.P. Singh et al. / Electrical Power and Energy Systems 31 (2009) 309–314

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