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Electric Power Systems Research 78 (2008) 372–381
Optimised placement of control and protective devices in electric
distribution systems through reactive tabu search algorithm
Luis G. Wesz da Silva a , Rodrigo A. Fernandes Pereira a ,
Juan Rivier Abbad b,c , José R. Sanches Mantovani a,∗
a
São Paulo State University-UNESP, Department of Electrical Engineering,
Avenida Brasil, 56, Zip Code 15385-000 Ilha Solteira, SP, Brazil
b Universidad Pontificia Comillas, ICAI, Madrid, Spain
c UNSW, Sydney, Australia
Received 27 November 2006; received in revised form 6 March 2007; accepted 10 March 2007
Available online 30 April 2007
Abstract
Optimised placement of control and protective devices in distribution networks allows for a better operation and improvement of the reliability
indices of the system. Control devices (used to reconfigure the feeders) are placed in distribution networks to obtain an optimal operation strategy
to facilitate power supply restoration in the case of a contingency. Protective devices (used to isolate faults) are placed in distribution systems to
improve the reliability and continuity of the power supply, significantly reducing the impacts that a fault can have in terms of customer outages,
and the time needed for fault location and system restoration. This paper presents a novel technique to optimally place both control and protective
devices in the same optimisation process on radial distribution feeders. The problem is modelled through mixed integer non-linear programming
(MINLP) with real and binary variables. The reactive tabu search algorithm (RTS) is proposed to solve this problem. Results and optimised
strategies for placing control and protective devices considering a practical feeder are presented.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Network protection systems; Restoration; Reliability; Reactive tabu search
1. Introduction
Efficient and safe planning of distribution systems includes,
among other investments, the placement of control and protective devices in strategic places of the network to improve
power supply quality and reliability indices. Control devices
include any device that an operator can use to open or close a
circuit (either manually or remotely controlled), in order to control power supply interruptions when a permanent fault occurs
as well as for the execution of expansion works and preventive maintenance interventions in network components. In this
paper, reclosers and isolators (manual and automatic sectionalizing switches) are considered to be control devices. Protective
devices include any device that operates automatically to isolate
∗
Corresponding author. Tel.: +55 18 3743 1150; fax: +55 18 3743 1163.
E-mail addresses: [email protected] (L.G.W. da Silva),
[email protected] (R.A. Fernandes Pereira), [email protected]
(J.R. Abbad), [email protected] (J.R. Sanches Mantovani).
0378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2007.03.005
any permanent and/or temporary fault in a feeder. In this paper,
fuses and reclosers are considered to be protective devices. In all
of these cases, during the planning stage it ought to be foreseen
that the network should have a set of switches for the reconfiguration to reduce the area to be disconnected as much as possible
[1,2] and, consequently, the loads that will be disconnected when
permanent faults occur. In general, the impact caused to customers, due to control and protective device placement in the
system, is related to the interruption frequency and duration.
Various papers, which deal separately with the optimised placement of control devices (switches) for network restoration [3–7]
and protective devices [8–10], are found in literature.
Ref. [3] proposes a mathematical model for the optimal
placement of control devices in radial distribution systems. In
this model, outage, maintenance and investment costs are considered, and the objective is to optimise the relation between
sectionalizing switch placement costs and the corresponding
benefits related to the improvement of the reliability indices.
The optimisation problem is solved using the simulated annealing technique. In the model proposed in [2] for the placement
L.G.W. da Silva et al. / Electric Power Systems Research 78 (2008) 372–381
of automatic sectionalizing switches in radial or weakly meshed
distribution networks, reliability of supply is the main concern.
In [4], a model for the optimal placement of control devices considering the cost of non-supplied energy and the investment cost
of sectionalizing switch placement is presented. Repairing times
and failure rates of the network and the sectionalizing switches
are taken into account. The problem is solved using genetic algorithms. In [6] the switch placement problem is formulated as a
combinatorial optimisation problem with a non-linear and nondifferentiable objective function. So as to solve the problem, an
optimisation algorithm based on the philosophy of ant colonies
is used.
In [8], the problem of protection device placement is formulated as a binary (0/1) integer non-linear programming problem
that is solved using genetic algorithms. In [9,10], a binary linear
programming model is developed for the placement of protection devices, fault locators and sensors in the network, in order
to improve the reliability indices of the system. Both technical
and economic constraints related to the coordination and selectivity among protection devices and the number of devices to
be placed is considered. For its solution, classic multiobjective
programming techniques along with fuzzy logic, among others, are proposed. Ref. [12] presents a mixed integer non-linear
programming (MINLP) model, with real and binary variables,
for the control and protective device placement problem. The
model proposed in [12] is solved in two steps: (1) protective
devices are placed considering specific constraints for each
feeder; (2) maintaining protective devices, placed during the
first step, in their position, control devices are optimally placed.
Reclosers are considered to be both protective and control
devices.
This paper presents a novel technique to carry out optimised placement of control and protective devices in the same
optimisation process, simultaneously. The problem is modelled
through MINLP with real and binary variables. The reactive
tabu search algorithm (RTS) is proposed to solve this problem.
In order to illustrate the application of this technique, a practical, 13.8 kV, 134 nodes, overhead, three-wire feeder with a
delta-grounded wye connection substation transformer, is used.
373
The mathematical model for control and protective devices
placement and replacement for system restoration proposed in
this work, has been designed using the concept of interruption
costs and the historical database of permanent and temporary
fault indices in the system [3,4,6,8–10,12]. It is formulated as a
combinatorial optimisation problem with a non-linear objective
function, non-differentiable, including real and integer variables
and a set of linear and non-linear constraints that is detailed
following.
2.1. Objective function
The proposed objective function is the sum of the fixed cost
due to the placement and replacement of switches and protective
devices, and the cost of interruptions. In the mathematical model,
the type of customer (residential, commercial and industrial), the
connected load (L), the permanent (λ) and temporary (γ) fault
rates, the costs associated with individual customer interruptions
(long- and short-time interruptions), and the feeder’s length is
considered. The average cost of interruptions (both temporary
and permanent) is used to compute the total cost of interruptions [6,9,10,12]. These costs can be assessed from surveys or
simply be based on any pre-established standards imposed by
the regulatory agencies with its associated penalization. These
standards usually measure the number and duration of the interruptions in the system through, for example, the system average
interruption frequency index (SAIFI) and the system average
interruption duration index (SAIDI) of distribution systems.
The objective function for each feeder i of the distribution
system is composed by the following terms:
f = FCi +
n
seci
(CIPj + CITj )
(1)
j=1
2. Mathematical model
Fixed costs (FCi ) are related to the investment for the purchase
and installation of control and/or protective devices. In the case
of replacement, involved fixed costs are basically due to the repositioning of control and/or protective devices. These costs are
written as:
FCi =
FCPjk Xjk +
FCCj Yj
(2)
Optimising control and protective devices placement and/or
replacement for distribution network restoration means the
searching for the best points to place different types of devices
to minimize the sum of the cost of investment in the network and
reduce the interruptions costs. The mathematical model should
consider the search for optimal solutions that is both technically
and economically viable. For example, fuses will clear faults
very cheaply in the short term, but since the number of faults
may be large and most of them temporary, protecting the system
against temporary faults using reclosers may be cheaper in the
long term [11]. The number and types of protective devices to
be installed in a particular feeder will depend on the importance
of the system, magnitude and type of load, circuit configuration
and exposure to risks of different nature, which can lead the
system towards permanent or temporary fault conditions.
The interruption costs for each feeder i of a given distribution
network is given by annual cost of interruption due to the occurrence of a permanent fault (CIPj ) and interruption costs due to
the occurrence of temporary faults (CITj ) in the section j of
feeder i. The cost of each interruption is calculated taking into
account the location of all control and protective devices on the
radial distribution feeder.
Fig. 1 illustrates a generic distribution system presenting
seven feeders as well as the protective and control devices placed
on the feeders. The feeder is divided into sections according
to the location of the installed devices. That is, every installed
device establishes two sections: the upstream section will see
the device at its receiving node (at the end of the section) and
the downstream section will see the device at its sending node
(at the beginning of the section). A fault in any section will
j∈Q
j ∈ CH
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Fig. 1. Scheme for section establishments by means of protective and control devices for a generic distribution system.
affect the rest of the sections differently, depending on the type
of the installed devices. Therefore, the costs of an interruption
will depend on the type of the devices installed. This is because
the load restoration plan for permanent fault occurrence at each
section depends on these devices. Sections of the distribution
network are classified according to the device installed at its
beginning:
• Sections with a recloser (or circuit breaker) at the beginning (dsj = 1): Reclosers are used for switching and protection
against permanent and temporary faults. When a permanent
fault occurs at this kind of section, the fault is only isolated in this section, whereas customers from downstream
sections can be restored (supplied by neighbouring feeders)
and customers from upstream sections do not suffer power
interruption. Costs of interruptions include the costs of repair
and switching (load re-managing for the neighbouring feeders). When a temporary fault occurs at this kind of section,
all customers located in-series and downstream to the recloser
will experience a temporary outage. The costs of interruptions
in these sections are those associated to short interruptions.
Customers from upstream sections will not suffer power interruption. In Fig. 1, sections i, iii and viii illustrate this type of
section.
• Sections with a fuse at the beginning (dsj = 2): Model developed in this work considers fuse cutouts to be placed only for
protection purposes. Fuse cutouts have only a protection function and do not present switching capability. In order to isolate
a fault that occurs in this kind of section, two sectionalizing
switches, one placed upstream and another placed downstream to the fuse cutout, must be opened. Customers from
adjacent sections to this switching device can be restored,
i.e., other neighbouring feeders can supply them. Costs of
interruptions are the costs of repair and switching (load remanaging). When a temporary fault occurs at this kind of
section, the closest upstream in-series protective device with
automatic reclosing capability will be tripped. All customers
located in-series and downstream to this device will experience a temporary outage. Cost of interruptions in these
sections are those associated to short interruptions. Customers
L.G.W. da Silva et al. / Electric Power Systems Research 78 (2008) 372–381
from sections upstream to the automatic reclosing device will
not suffer power interruption. In Fig. 1, sections iv, v and vii
illustrate this type of section.
• Sections with an isolator at the beginning (dsj = 3): Isolators do not have protective function. When a permanent or
temporary fault occurs at this kind of section, an upstream
in-series recloser will be tripped, if the fault is within its protection zone, otherwise the closest upstream in-series fuse
will blow. If the tripped protective device is a fuse, sections
defined by the isolator and defined by the fuse, are isolated.
In the case of the protective device being a recloser, if the
only section defined by the isolator is isolated, customers
from downstream sections can be restored (switched for other
neighbouring feeder). Costs of interruptions are the costs of
repair and switching (load re-managing). When a temporary
fault occurs at this kind of section, the closest upstream inseries protective device with automatic reclosing capability
will be tripped. All customers located in-series and downstream of this device and within will experience temporary
outage. Cost of interruptions of these sections are those costs
associated to short interruptions. Customers in upstream sections will not suffer power interruption. In Fig. 1, sections ii, vi
and ix illustrate this type of section. Mathematically the permanent and temporary interruptions costs can be established
through the equations:
CIPj =
n
seci
375
of sections upstream to the permanent-faulted section and the
cost of interruptions to customers of downstream sections. In
this way, the CIP for any section j of a generic feeder can be
interpreted as following:
• For permanent faults at section j, loads from this section
should be isolated from the system to repair the faulted
element. This presents a cost associated to long time interruptions.
• For permanent faults at section j, in order to analysis the
effects of the fault on the loads that not belongs of this section,
the type of device that defines section j has to be verified to
assign the cost of interruption:
(a) For sections defined by reclosers (dsj = 1) or fuses
(dsj = 2), loads located upstream to the faulted section do
not suffer power supply interruptions since both reclosers
and fuses are actuated by permanent faults. To assign the
cost of interruption time for loads located downstream to
the faulted section the type of device that defines section
j has to be verified according the following criteria: if
the type of device that defines section j is fuses (dsj = 2),
the interruption time for loads located downstream to the
faulted section is greater in order to the repairs to be
performed. In this model, the possibility of having a fuse
λk lk (LRk CRR + LCk CRC + LIk CRI)
k=1
⎧
0,
if dsk =
3
⎪
⎪
⎨
M
λk lk +
⎪
(LRm CCR + LCm CCC + LIm CCI), if dsk = 3
⎪
k=1
⎩
n
seci
m=1
⎧ L
⎪
⎪
⎪
(LRm CRR + LCm CRC + LIm CRI), if dsk = 2
⎪
⎪
⎪
⎪
m=k+1
⎪
⎪
⎧
⎪
⎪
⎪
RS ≥ LTm
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
L
⎨ RS ∈ Ωi
⎪
n
seci
⎨ (LRm CCR + LCm CCC + LIm CCI), if dsk = 2
+
λk lk
⎪
⎪
⎪
m=k+1
⎪
⎪
Vi > Vlower
⎪
k=1
⎪
⎪
⎪
⎪
⎪
⎩
⎪
⎪
Vi ∈ Ωi
⎪
⎪
⎧
⎪
⎪
⎪
⎪
⎪
L
⎨ RS < LTm
⎪
⎪
⎪
⎪
RS ∈ Ωi
(LRm CRR + LCm CRC + LIm CRI), if
⎪
⎪
⎪
⎩ m=k+1
⎩
dsk = 2
CITj = γj lj (LRj CTR + LCj CTC + LIj CTI) + γj lj
L
(3)
(LRm CTR + LCm CTC + LIm CTI) + γj lj
m=j+1
⎧
0,
if dsj = 1
⎪
⎪
⎨
MT
× ⎪
(LRm CTR + LCm CTC + LIm CTI), if dsj = 1
⎪
⎩
m=1
CIPj is the sum of the cost of interruptions to customers of the
permanent-faulted section, the cost of interruptions to customers
(4)
with switching operation capacity is not being considered. The cost is, therefore, associated to the interruption
repair time; and, if the type of device that defines section
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j is reclosers (dsj = 1) or isolators (dsj = 3). Loads located
downstream to the faulted section can be re-managed to
a neighbouring feeder, if there is enough reserve capacity
and the minimal operating voltage magnitude constraint
is not violated. In this case, a short-term interruption
occurs due to the load re-managing (switching) of the
faulted section to neighbouring feeders. The cost is, therefore, associated to an interruption switching time. If load
re-managing is not possible, a greater interruption time
will be necessary to repair and restore the service at section j. The cost is, therefore, associated to the interruption
repair time.
(b) Sections defined by isolators (dsj = 3): Some devices (a
recloser or a fuse) placed upstream to the faulted section
will actuate. However, some time (shorter than the repair
time) will be needed to manually open the isolator and
to restore the power to upstream sections. The cost is,
therefore, associated to the interruption switching time.
CITj is the interruption costs due to the occurrence of temporary faults in the feeder and reflects the effects of short power
interruption due to the actuation of protective devices with automatic reclosing. This cost is incorporated in the model aimed at
minimizing the drawbacks of temporary faults by the adequate
placement of these devices. The different terms of CIT for any
generic section j of a given distribution system can be interpreted
as follows:
• For a temporary fault at section j, the closest in-series downstream recloser or substation circuit breaker with reclosing
relay is tripped. Therefore, in-series and downstream loads
of this protective device are disconnected temporarily due to
occurrence of that fault. The cost is, therefore, associated with
a short-time interruption. This way for temporary faults at section j, firstly the dsj of the section is verified: if the section is
defined by a recloser (dsj = 1) loads from the upstream section j do not suffer alterations in their operation due to the fact
that the recloser actuates for temporary faults. In other words,
only loads from downstream sections experience an interruption; and, if the section is defined by a isolator (dsj = 3)
or fuse (dsj = 2), a protective device with automatic reclosing upstream from this section and in-series with the faulted
point should actuate. The cost is, therefore, associated with a
short-time interruption.
are considered through a fast and efficient distribution network
power flow algorithm [13].
Constraints of economical nature are related to the installation and operation cost of devices, as well as the type and
importance of loads.
3. Technical solution
This section presents the technique employed to solve the
optimisation model proposed.
3.1. Selection of candidate points for the placement of
control and protective devices
The candidate points for the placement of control and protective devices are selected based on rules established from
technicians’ and engineers’ knowledge on network operation
and planning. Recloser and fuse placement candidate points are
the following:
• Recloser or fuse placement at the beginning of long lateral
branches in addition to the main line reclosers or circuit
breakers.
• Recloser or fuse placement at the ending node of sections
containing important loads that can not suffer reclosing effects
and require high service continuity.
• Recloser placement at the beginning of laterals that feed loads
that can suffer reclosing effects and classified as special or of
great importance.
• Recloser placement at the beginning of laterals that supply
important loads located in areas subjected to a high number
of temporary faults and that can suffer reclosing effects.
For placing isolators, candidate points are defined considering:
• total amount of loads or customers that are part of a given
section;
• nature and importance of load;
• socio-economic characteristics of each type of
customer—residential, commercial, industrial, public
services, schools and hospitals;
• permanent and temporary fault rates for the set of customers
from each section of the distribution network.
2.2. Constraints
3.2. Reactive tabu search
Constraints that should be incorporated into the optimised
placement problem of switch and protective device present
technical and economic nature. Constraints of technical nature
considered in the proposed model include coordination and
selectivity of the protection along with system topology (number of in-series devices), power supply capacity of substations
and feeders, feeder capacity limitations, fulfilment of real and
reactive power demands, as well as quality of the power supply service, such as voltage profile. In this work, technical
constraints related to the operation of the distribution system
The mathematical model for protective devices and switches
placement and replacement is a MINLP problem and, for its
solution, a specialized RTS algorithm [14] is proposed.
3.2.1. Codification
A codification in decimal integer base is used for mapping
possible solutions for the problem of optimised placement of
protective and control devices, as illustrated in Fig. 2. Each section (or branch) of the feeder that is a candidate is assigned
L.G.W. da Silva et al. / Electric Power Systems Research 78 (2008) 372–381
377
Fig. 2. Implemented codification scheme—RTS.
a value depending on which device has been placed: 0 for no
device, 1 for a recloser, 2 for a fuse and 3 for an isolator.
The feeder is divided in a main section and lateral branches.
It is possible to install any type of device, considered in this
paper, in the main section. The lateral branches are subdivided
into two categories: first lateral category, where several types
of protective devices can be installed, and second lateral category, where only fuses can be installed. Each section has been
previously defined as belonging to a certain type that depends
on which devices are allowed to be placed in it. Seven types
of sections are defined, and the devices allowed in each case
are the following: Type 1: reclosers, fuses, and isolators; Type
2: reclosers and isolators; Type 3: reclosers and fuses; Type 4:
fuses and isolators; Type 5: fuses; Type 6: reclosers; Type 7:
isolators.
3.2.2. Initial configuration
The RTS starts from an initial configuration where a certain number of devices of each type is placed in the feeder. A
good-quality initial configuration is used as a starting solution
to obtain a good algorithm performance. In order to generate
this configuration, an exploration of the search space of the
feeder under analysis is carried out, so a suitable quantity of
control and protective devices can be determined. Maximum
quantity of control and protective devices for placement and
replacement is fixed and established by technical and economic
criteria. Devices are placed randomly considering a placement
order according to their importance for the system’s reliability.
That is, first reclosers, then isolators and finally fuses are placed
at different buses j, satisfying the definition of each type of section (type = 1, 2, . . ., 7), for each one of the i feeders of the
system.
3.2.3. Fitness function
The RTS algorithm uses a fitness function, that includes the
value of the objective function for each set of placed control and
protective devices, for which additional terms are added in order
to represent penalties assigned to the violation of the power flow
constraints in the feeder.
3.2.4. Neighbourhood structure
For the RTS algorithm to search for new feasible solutions, a neighbourhood structure has to be defined. The RTS
algorithm will look for a better solution than the current
one in a set of neighbouring solutions. In this work, two
sets of neighbours have been defined. The first set of neighbours N(x) contains all the possible solutions where a single
device has been moved from its current location to any other
allowed location within the feeder that does not already have
another device installed. The second set of neighbours is
defined by increasing in one unit, each type of device independently.
The search mechanism within this definition of neighbourhood is structured as follows:
(i) Random placement of one more recloser in the system. If
the number of placed reclosers is greater than the allowed
maximum, go to step (ii). Otherwise perform a search in
the first set of neighbours N(x). If a better solution is found,
go to step (i).
(ii) Random placement of one more isolator in the system. If
the number of placed isolators is greater than the allowed
maximum, go to step (iii). Otherwise perform a search in
the first set of neighbours N(x). If a better solution is found,
go to step (i).
(iii) Random placement of one more fuse in the system. If the
number of placed fuses is greater than the allowed maximum, stop the search. Otherwise perform a search in the
first set of neighbours N(x). If a better solution is found, go
to step (i), if not stop the search.
3.2.5. Tabu list
During implementation of the RTS algorithm, two lists are
used to store the attributes (number and location of the different devices) of solutions already evaluated: a tabu list (TL) of
variable size and a list with long-term memory that stores the
attributes of those solutions that are selected more than once
throughout the search process.
The TL keeps the evaluated solutions of a pre-established
number of iterations, considering also a maximum number of
devices that can change their positions simultaneously. Solutions evaluated during the search along with the number of
times they have been evaluated are stored in the long-term memory. In this way, after the last movement is performed, it can
be verified if there are repeated solutions and if so, the number of iterations between the two visits can be calculated. The
reactive mechanism increases rapidly the size of the TL when
configurations are being repeated. On the other hand, this list
can be slowly reduced if, after a specified number of iterations, there are no repeated solutions. In addition to these two
mechanisms to make the list grow or shrink, there is another
situation where the size of the list might be altered. If the
list grows too much, making all movements prohibited (and
no aspiration criterion is satisfied), the escape mechanism is
used.
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Fig. 3. A practical, 13.8 kV, 134-node overhead three-wire distribution feeder.
3.2.6. Escape mechanism
The escape mechanism is implemented as a random generation of a new initial solution. When several repeated solutions
appear, a new random placement of the devices is carried out
in order to obtain a current configuration far away from the
local optimum solutions that cause the cycling phenomenon.
When the escape mechanism is applied the tabu search process
is re-initialized.
3.2.7. Stop criterion
The stop criterion adopted is a maximum number of allowed
iterations.
4. Tests and results
The actual development and tests are focused on the placement of control and protective devices in overhead and radial
distribution feeders, which present a three-phase main line with
lateral branches, some of which may be single or two-phase
circuits.
The proposed technique has been tested on a 13.8 kV, real-life
134-bus feeder [15]. This feeder has eight interconnection lines
with seven neighbouring feeders (two interconnections belong
to the neighbour feeder 3), as shown in Fig. 3 and Table 1. Taking
into account the criteria presented in Subsection 3.1, thirty-six
(36) possible locations were selected for the placement of isolators, thirty-eight (38) for the placement of fuses and eleven (11)
for placement of reclosers. Permanent and temporary fault rates
used in this test are λ = 0.072 and γ = 0.98 faults/(km year−1 ).
Table 1
Capacity of neighbouring feeders (including reserve capacity)
Feeder
Capacity, kW
2
3 (two connections)
4
5
6
7
8
11,910.00
12,170.00
12,750.00
13,190.00
21,603.00
17,302.00
21,800.00
Table 2 shows the repair and switching costs used in this
work, adapted from [16]. The effect of the protective devices
due to reclosing sequences are considered by the model through
the term called CIT. Considered values for CTR, CTC and CTI
are equal to US$ 1.00.
Table 3 shows the control and protective devices fixed costs.
These costs are composed by costs of devices purchase, material for installation and labour costs practiced in the Brazilian
market. A fixed cost of US$ 5,000.00 year−1 for reclosers is
considered as able to simulate a life cycle of 5 years. Fixed costs
Table 2
Repair cost (RC) and switching cost (SC), by category of customer
Category
RC, US$/kW (4 h)
SC, US$/kW (1.5 h)
Residential
Commercial
Industrial
6
120
18.544
0.4
60
9.62
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Table 3
Control and protection equipment fixed costs
Device
Cost, US$
Recloser
Fuse
Sectionalizing switch
25,000.00
1,000.00
2,730.00
corresponding to fuses and isolators in Table 3 are not modified
to consider the life cycle of 5 years.
The considered constraints for the 134-bus feeder are the
following:
• the maximum number of reclosers is four (4);
• there is no limitation for the number of fuses to be placed;
• fuses cannot be installed in the main section of the feeder nor
in connections with future load currents above 50 A;
• there is one circuit breaker between buses 1 and 2;
Table 4
Best solutions found
379
• the maximum number of in-series fuses is equal to three (3);
• fuses cannot be placed upstream to a recloser;
• flow capacity of the feeders and reserve capacity of substations should not be violated.
In order to validate the efficiency of the model and the proposed technique, four tests were carried out on the practical
feeder. The different tests considered different maximum numbers of reclosers: 0, 1, 3 and 4. The best solution found for
the placement of reclosers, isolators and fuses for each test are
shown in Table 4. The corresponding temporary interruption
costs (CIT), permanent interruption costs (CIP), fixed costs (FC)
and total cost of interruption (CI) are also shown in Table 4.
4.1. Comments about performed tests
Test 1 shows the important role that the recloser plays in the
system’s reliability. In this configuration, the circuit breaker with
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L.G.W. da Silva et al. / Electric Power Systems Research 78 (2008) 372–381
reclosing relay, placed between buses 1 and 2, is the only device
with the capacity to eliminate temporary faults. The sensitivity
of this device is limited to its protection zone. Temporary faults
outside its protection zone are treated through the actuation of
fuses, unnecessarily disconnecting the set of customers within
where the fault took place, requiring therefore a network restoration process. In the proposed model, this aspect is considered in
the CIT, which presents a high value, compared to the other
configurations shown in Table 4.
5. Conclusions
In this paper, a novel approach for an integrated placement
and replacement of control and protective devices in distribution network feeders was presented. The problem was modelled
as a MINLP. This model considers the main actual physical
aspects of the problem that directly affect the investment costs
and improvement of reliability indices.
The reactive tabu search algorithm proposed for solving the
MINLP was developed through a codification system and neighbourhood structure that considers the actual physical structure
of problem under analysis. The obtained results showed the
excellent performance of the algorithm. Of course, as RTS is a
metaheuristic algorithm, global optimum cannot be guaranteed.
The proposed technique found good-quality solutions, which
fulfilled imposed physical and operational constraints, for tests
carried out with a practical feeder. For each test, a proposed
set of good-quality solutions, including the best solution found
and shown in Table 4, was obtained. Taking into account the
utility’s operating and maintenance procedures, engineers and
technicians can analyse this set of solutions, and they can adopt
the most suitable configuration according to their belief.
Acknowledgements
Authors gratefully acknowledge the financial support from
CNPq and Fapesp (Grant no. 02/04811-9), as well as Prof.
Dionı́zio Paschoareli Jr. for his support in the revision of this
paper.
Appendix A. List of symbols
CITj
CRC
CRI
CRR
CTC
CTI
CTR
dsj
FCi
FCCj
FCPjk
lj
L
LC(·)
LI(·)
LR(·)
LTm
M
MT
n seci
Q
CCC
CCI
CCR
CH
CIPj
cost of interruptions to commercial customers within
a determined interval time for performing load remanaging into other section;
cost of interruptions to industrial customers within
a determined interval time for performing load remanaging into other sections;
cost of interruptions to residential customers within
a determined interval time for performing load remanaging into other section;
set of points where the placement of sectionalizing
switches is allowed;
interruption annual costs due to permanent faults at
section j;
RS
Vi
Vlower
Xjk
Yj
Ωi
interruption annual costs due to temporary faults at
section j;
cost of interruptions to commercial customers within
a determined interval time for performing repairs in
section (·);
cost of interruptions to industrial customers within a
determined interval time for performing repairs in section (·);
cost of interruptions to residential customers within
a determined interval time for performing repairs in
section (·);
cost of interruptions to commercial customers due to
occurrence of a temporary fault at section j;
cost of interruptions to industrial customers due to
occurrence of a temporary fault at section j;
cost of interruptions to residential customers due to
occurrence of a temporary fault at section j;
variable that determines time and cause of the power
supplying interruption of section j, taking into account
the kind of control and protective device that is placed
at the sending node of section j, and ds = 1 for recloser,
ds = 2 for fuse and ds = 3 for isolator;
fixed costs are related to the investment for the acquisition and installation of control and/or protective
devices;
installation fixed cost of sectionalizing switch at point
j;
installation fixed cost of protective device type k at
point j;
length of section j (km).
set of downstream sections of the section j;
commercial loads connected at section (·);
industrial loads connected at section (·);
residential loads connected at section (·);
total load that should be transferred to neighbouring
feeders in order to isolate a fault in section m;
set of upstream sections of the j section for the next
section with ds = 1 or 2;
set of sections upstream of the section j, up to some
section with ds = 1;
total number of sections of feeder i. Defined as a function of the quantity of placed devices;
set of point where the placement of protective devices
is allowed;
reserve capacity of feeders in the neighbourhood of
feeder i (Ωi );
buses voltage magnitude of the neighbouring feeders
of i (Ω);
limits of minimum operation allowed for the voltage
magnitude on the system buses;
decision binary variable for placement of protective
devices type k at point j;
decision binary variables for placement of sectionalizing switches at point j;
neighbouring feeders of feeder i that present interconnection switches placed for operation planning and
allow load re-managing of feeder i;
L.G.W. da Silva et al. / Electric Power Systems Research 78 (2008) 372–381
λj
γi
permanent fault rate of section j (fault/(km year−1 ));
temporary fault rate of section j (fault/(km year−1 ));
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