SWITCHES ALLOCATION IN DISTRIBUTION NETWORK USING
PARTICLE SWARM OPTIMIZATION BASED ON FUZZY EXPERT
SYSTEM
Tiago Alencar
UFMA
tiagoalen@gmail.com
Anselmo Rodrigues
UFMA
schaum.nyquist@gmail.com
Abstract – The electric utilities must satisfy two competitive goals during the planning process: to reduce investments costs and ensure that the reliability targets are
achieved. An alternative to carry out these objectives is the
optimal allocation of sectionalizing switches in the power
electric distribution network. These switches are efficient
in decreasing the restoration time of the electrical energy
supply for the customers. This paper proposes a comparison between two heuristics algorithms used for solution of
switch allocation problem: Genetic Algorithm (GA) and
Particle Swarm Optimization (PSO). Both algorithms are
based on Fuzzy Expert System (FES). The FES was used to
include engineering judgment in the solution of the switch
allocation problem. The models and techniques proposed
were validated and applied in a large scale substation of
the Electricity Utility of Maranhão, in the northeast region
of Brazil. The results showed that the PSO outperform GA
in convergence rate and solution quality.
Keywords: Distribution Network, Reliability, Switch
Allocation, Particle Swarm Optimization, Genetic
Algorithm, Expert Fuzzy Systems.
1 INTRODUCTION
The distribution network is the portion of the power
system that concentrates a larger rate of reliability problems. The improvement of the distribution network
reliability is highly associated with better consumer’s
service and quality [1]. Thus, it is important to consider
reliability aspects in distribution network planning.
One way to make effective improvements in the distribution network reliability is the allocation or reallocation of sectionalizing switches. The allocation decreases
the costumers restoration time during an outage. The
switches are also used for load transfers to adjacent
feeders during the restoration process. Due to this, the
allocation of sectionalizing switches is an important
approach to get an expressive gain in reliability of the
distribution network.
The switch allocation is a discrete optimization problem with a vast solution space. Problems like this are
hard to solve using analytical approach, because there is
not an analytical expression that associates the reliability indices with the switches’ positions. Thus, the better
way to solve this kind of problem is using a heuristic
approach.
In [2,3,4] GA and Simulated Annealing (SA) were
used to solve the switch allocation problem. In these
papers, the objective function was associated with:
17th Power Systems Computation Conference
Maria da Guia da Silva
UFMA
guia@dee.ufma.br
maintenance, installation and interruption costs. The GA
performs parallel search, while the SA is based on local
search techniques. Due to this, the GA obtains a better
global solution than the SA.
Recently, new meta-heuristic algorithms have been
used in the switch placement problem, for example: Ant
Colony [5], Differential Evolution [6]. These new algorithms were used to minimize interruption, installation
and maintenance costs.
It is important to emphasize that none of the cited
references consider infeasibility associated with the
solutions, that is, the maximum number of switches that
must be installed. In other words, the proposed methods
do not take into account budget constraints in terms of
investments for the utility. In addition, these papers do
not consider the application of the proposed methodologies in large distribution networks.
In [7], a Fuzzy Expert System (FES) is used in the initialization of the GA. This GA is used to minimize the
system total cost (interruption and installation costs).
The application of the FES in the GA has resulted in
meaningful improvements in the performance of the GA
regarding to random initialization.
The main propose of this paper is to compare two algorithms: PSO and GA, combined with a FES, to solve
the optimum allocation switch problem. The main contribution of this paper regarding to [6] are: i) The feeders sections length has been included as an input variable in the FES; ii) The FES was used to repair the infeasible solutions found by the algorithms in the optimization process; iii) The PSO algorithm is based on FES.
The proposed method was tested in a real large scale
substation belonging to the electric utility of Maranhão
state in Brazil. The results showed that the PSO outperform GA in convergence rate and solution quality.
2
RELIABILITY ASSESSMENT IN
DISTRIBUTION SYSTEM
In this paper, the reliability indices are estimated using Analytical Simulation (AS). The AS evaluates each
contingency impact (lines, transformers and protection
system) considering the contingency’s duration and
frequency to assess the reliability indices [1].The evaluation of a contingency impact on distribution systems
can be summarized in the following steps [1]:
Stockholm Sweden - August 22-26, 2011
ring at the beginning of the section being
considered.
 Downstream Load (DSL): This is a normalized measure of how much load is connected downstream of the section being considered.
 Section Length (SL): This is a normalized
measure of the length of the section being
considered.
In the representation of the input variables were used
three triangular fuzzy sets: small, medium and large. As
shown in figure 2:
Medium
Small
1
Membership Grade
1) Protection Response – The protection device (fuse
or recloser) nearest to the fault operates to clear the
fault.
2) Upstream Restoration – Sectionalizing devices
upstream the fault, such as Normally Closed (NC)
switches, isolators and fuses, are operated to isolate the
fault. This operation allows the reinitialization of the
device used to clear the fault and the restoration of the
energy supply for all customers upstream the fault.
3) Downstream Restoration – Sectionalizing devices
downstream the fault are identified to isolate components from the fault location. This operation allows the
closing of the Normally Open (NO) switches to restore
the energy supply to customers.
4) Repairing Process – The faulted device is fixed and
the system returns to its pre-fault state.
The devices associated with steps 1,…,4 are shown
in figure 1.
Large
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Input Variable
Figure 2: Fuzzy Sets used to input variables.
The AS method can be used to generate reliability indices associated with individual load points or with the
system as whole. The main indices used to assess the
reliability of distribution networks are [1]:
A. Load Point Indices:

– Average Failure Rate;

– Annual Unavailability;

– Average Restoration Time.
B. System Indices:
 SAIDI – System Average Interruption Duration Index
 SAIFI – System Average Interruption Frequency Index.
 ASAI – Average Service Availability Index.
 ENS – Average Energy Not Supplied.
3
FUZZY EXPERT SYSTEM TO THE SWITCH
ALLOCATION PROBLEM
The Fuzzy Expert System (FES) was developed to
solve specialist human tasks, inside a specific knowledge domain [8]. The heuristic knowledge about a
system can be used to help to build a good project. In
this paper, a FES is used to evaluate the benefit of
switch installation in the beginning of a feeder section.
The FES applied to solve this problem has the follows input variables [7]:
 Number of Siblings (SIB): This is a normalized measure of the branching that is occur-
17th Power Systems Computation Conference
0.9
1
The output variable, that represents the benefit of
switch instalation for a particular section (BEN), is
formed by four triangular fuzzy sets: very small, small,
medium and large. The figure 3 shows the fuzzy sets to
the output variable:
1
Membership Grade
Figure 1: Operated Devices in a Contingency Simulation.
0.8
Medium
Small
Very Small
Large
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
BEN
0.6
0.7
0.8
0.9
1
Figure 3: Fuzzy Sets used to output variables.
After defining the fuzzy sets to the input and output
variables, the fuzzy rules must be generated for the FES.
The fuzzy rules for this problem is shown in table 1.
Fuzzy inference is used to determine the output value
( ), which is a number in the interval between 0 and 1.
This value is evaluated for every section of the network and represents the worth of installing a switch in
this section.
In the inference process, every input variable (that is
originally non-fuzzy) is converted into a fuzzy number
based on the fuzzy sets that represents the input variables.
Then, the fuzzy rules are evaluated using the minmax method [9]. The result obtained is a fuzzy function.
In this paper, the value that represents the output is
computed using the center of gravity method [10].
Stockholm Sweden - August 22-26, 2011
Thus, every section of the distribution network is
evaluated and the benefit of the switch installation is
stored in a vector.
Rule #1
Rule #2
Rule #3
Rule #4
Rule #5
Rule #6
Rule #7
Rule #8
Rule #9
Rule #10
Rule #11
Rule #12
Rule #13
Rule #14
Rule #15
Rule #16
Rule #17
Rule #18
Rule #19
Rule #10
Rule #21
Rule #22
Rule #23
Rule #24
Rule #25
Rule #26
Rule #27
If (SIB is S) and (DSL is S) and (SL is S)
If (SIB is S) and (DSL is S) and (SL is M)
If (SIB is S) and (DSL is S) and (SL is L)
If (SIB is S) and (DSL is M) and (SL is S)
If (SIB is S) and (DSL is M) and (SL is M)
If (SIB is S) and (DSL is M) and (SL is L)
If (SIB is S) and (DSL is L) and (SL is S)
If (SIB is S) and (DSL is L) and (SL is M)
If (SIB is S) and (DSL is L) and (SL is L)
If (SIB is M) and (DSL is S) and (SL is S)
If (SIB is M) and (DSL is S) and (SL is M)
If (SIB is M) and (DSL is S) and (SL is L)
If (SIB is M) and (DSL is M) and (SL is S)
If (SIB is M) and (DSL is M) and (SL is M)
If (SIB is M) and (DSL is M) and (SL is L)
If (SIB is M) and (DSL is L) and (SL is S)
If (SIB is M) and (DSL is L) and (SL is M)
If (SIB is M) and (DSL is L) and (SL is L)
If (SIB is L) and (DSL is S) and (SL is S)
If (SIB is L) and (DSL is S) and (SL is M)
If (SIB is L) and (DSL is S) and (SL is L)
If (SIB is L) and (DSL is M) and (SL is S)
If (SIB is L) and (DSL is M) and (SL is M)
If (SIB is L) and (DSL is M) and (SL is L)
If (SIB is L) and (DSL is L) and (SL is S)
If (SIB is L) and (DSL is L) and (SL is M)
If (SIB is L) and (DSL is L) and (SL is L)
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
then
BEN is VS
BEN is VS
BEN is VS
BEN is VS
BEN is VS
BEN is S
BEN is VS
BEN is VS
BEN is M
BEN is VS
BEN is VS
BEN is S
BEN is S
BEN is S
BEN is M
BEN is S
BEN is S
BEN is M
BEN is VS
BEN is VS
BEN is S
BEN is S
BEN is S
BEN is M
BEN is M
BEN is L
BEN is L
5
ALGORITHMS BASED ON FES TO SOLVE
THE SWITCH ALLOCATION PROBLEM
This paper proposes a comparison between two metaheurist algorithms based on FES to solve the switch
allocation problem: GA and PSO.
5.1 Genetic Algorithm
The GA is used to solve the switch allocation problem because it presents the following advantages: i)
capacity to do parallel search; ii) flexibility to include
constraints; iii) easy to use the FES in feasibility restoration and population initialization.
The first step in the application of GA is the definition of the solution codification. In the problem of
switch allocation, there is no need for special codification, because the vector of decision variable can be
represented directly by a binary string with length .
The optimization process follows the basic steps in
the GA [11]: i) population initialization; ii) objective
function and constraints evaluation; iii) crossover and
mutation; iv) stop criteria.
The GA used in the switch allocation has the following features: population size: 150 individuals; selection
method: tournament between 2 individuals with probability of 70%; Mutation Rate: 0.5%; stop criteria: 300
iterations.
Table 1: Fuzzy Rules to the FES, where: VS = very small,
S = small, M = medium, L = Large, BEN = benefit.
4 PROBLEM FORMULATION
The switch allocation problem is solved by determining the number and positions of the switches on the
distribution network to obtain a project with low cost
and high reliability. The beginning of each sections of
the main feeder is a candidate point to receive the
switch.
The mathematical formulation to the problem of
switch allocation is:
(1)
5.2 Particle Swarm Optimization
Originally, the PSO was intended to simulate graphically the bird flocks. Each individual (particle) within
the swarm is represented by a vector in the multidimensional search space. The movement of the individuals is
determined by an assigned vector called velocity vector
[12].
Each individual updates his velocity based on the actual velocity and the best position that it has explored
and the best global position explored by the swarm.
Consequently, the velocity updating of the individual is
carried out as follows:
(3)
where:
(2)
Where
is the maximum number of switches
that should be installed in the system and is a vector
with the same dimension as the number of candidates
points to receive the switches ( ). Thus, if
= 1 one
switch should be installed in the position , otherwise,
=0.
The equation (2) represents indirectly the budget
constraint associated with the installation of switches on
the network. The objective of the algorithm is finding a
configuration of switches that satisfies costs constraint
and maximizes the reliability.
17th Power Systems Computation Conference
is the new velocity of the individual ;
is the old velocity of the individual ;
is the inertia weight;
and
are two parameters
called acceleration coefficients;
and
are random variables with uniform distribution between 0 e 1.
is the best position found by the swarm;
is the best position found by the individual .
and
are updated every iteration.
The main feature that drives PSO is the iteration between individuals. The swarm individuals share information to define the next movement. Depending on how
the information is shared, several topologies of communication are defined. In this paper, the star topology was
used. In this topology, every individual shares information with all individuals, forming a fully connected
Stockholm Sweden - August 22-26, 2011
network. So, each individual imitates the best individual.
The PSO algorithm can be summarized in the following steps [10]:
1) Initialize the swarm , normally, the positions
are randomly initialized,
is an array that indicates the switch outline;
2) Evaluate the performance of each individual,
using the current position
;
3) Compare the performance of each individual to
its best performance already obtained: if
then:
This comparison is made through the objective
function of the algorithm.
4)
Compare the performance of each
individual with the best global performance: if
then:
5) Update the velocity of the particle using the equation (3);
6) Move the particle to a new position, using the
follow strategy: In the binary PSO version, the
velocity indicates the probability that a bit
changes its position from 0 to 1, in the switch allocation problem, it indicates the probability of
the point
to receive the switch in the
individual . So, there should be made normalization in velocity to put it in the range [0, 1].
This normalization is carried out using the sigmoid function according to equation (4):
The initialization of the population, using the FES, is
based on:
i) Generate a uniform random number
in the
range [0,1];
ii) Compare
with the benefit value associated
with the installation of a switch :
iii) Repeat the steps (i) and (ii) for i=1,…,n. Where n
is the number of sections in the network.
iv) Repeat the steps (i)-(iii) to all the individuals of
the GA or PSO populations.
During the optimization process, some individuals
can violate the constraint associated with the maximum
number of switches (equation (2)). In this paper, the
infeasible individuals are repaired using a deterministic
rectification algorithm. This algorithm is summarized as
follows:
i) Sort in ascending order the benefit list ( );
ii) Set the entries of the benefit list (B) as follows:
and set
n
; for
; while:
x
k 1
k
 n max
iii) Repeat the step (ii) for all the individuals that violate the constraint associated with the maximum
number of switches installed.
7 TESTS AND RESULTS
The proposed algorithms were tested in a large scale
substation of the Electricity Utility of Maranhão, in the
northeast region of Brazil. The main characteristics of
this substation are shown on table 2:
(4)
Finally, the position is updated using the
equation (5):
(5)
Where:
the subscribed
represents the particle from
the individual .
is an uniform random number in the range
[0,1];
7) Repeat the steps (2)-(6) until the convergence
criteria be reached;
The PSO used in the switch allocation problem has
the follows features: number of individuals: 150;
=
1.0;
and
= 0.8; number of iterations: 300;
6
APPLICATION OF THE FES ON THE
OPTIMIZATION ALGORITHMS
The FES explained in the section 3, is used in the optimization process of the GA and PSO in two ways:
population initialization and repair of the infeasible
solutions.
17th Power Systems Computation Conference
No. of Consumers
27,474
Total Power
146,849.5 kW
No. of NO switches
33
No. of NC switches
75
No. of load points
809
No. of devices
4,950
network total length
103.5 km
SAIDI (hours/year)
1.88946
SAIFI (failures/year)
1.00897
Table 2: Test system characteristics.
The Geographic Information System (GIS) of the test
system is showed in figure 4.
The algorithms were applied in the test system considering four case studies:
Case 0: Original system, with 75 switches (basecase).
Case 1: Allocation of 50 switches in the distribution
network, without considering the switches in the original system.
Case 2: Reallocation of the switches installed in the
network (75 switches).
Stockholm Sweden - August 22-26, 2011
6
9.7225
Case 3: Allocation of 100 switches in the network,
without considering the switches in the original system.
The results obtained from each case study are shown
9.722
in table 3. The one-line diagram to one feeder of the
system, in GIS coordinates, are shown in figures 5, 6 e
7, respectively. In these figures, the squares indicate the
points where new switches should be installed and the9.7215
stars indicate that the switch already installed should be
kept in its position.
The figure 8 shows the improvement in SAIDI (in 9.721
percentage) compared with the SAIDI of the original
system.
The results show a meaningful difference in the application of AG and PSO in the solution of the switch9.7205
allocation problem. It should be noted that the addition
6
Figure
6: Switches placement using PSO algorithm - Case 2.
x 10
of the FES, in the PSO algorithm, resulted in a signifi9.7225
cant improvement in the SAIDI index.
9.72
6
9.726
x 10
x 10
5.774
5.776
5.778
5.78
5.782
5.784
5.786
5.788
5.79
5.792
5
x 10
9.725
9.722
9.724
9.7215
9.723
9.722
9.721
9.721
9.7205
Figure
4: 5.77
Geographic
Sytem
of the5.81test system.
5.76
5.78 Information
5.79
5.8
5.82
9.72
5.75
5.83
5
x 10
Case Study:
SAIDI (h/year) - GA
SAIDI (h/year) - PSO
Case 0
1.88946
1.88946
Case 1
1.98881
1.80726
Case 2
1.71207
1.5827
Case 3
1.56528
1.44415
Figure 7: Switches placement using PSO algorithm - Case 3.
9.72
5.774
5.776
30%
20%
5.778
5.78
5.782
5.784
5.786
5.788
5.79
5.792
5
x 10
GA
PSO
10%
6
9.7225
x 10 Table 3: Case studies results.
0%
-10%
9.722
Case 1
Case 2
Case 3
Figure 8: SAIDI reduction regarding to the base-case.
The convergence characteristics of the algorithms
were compared using the best solution obtained in each
iteration. These characteristics are shown in figures 9,
10 and 11.
From figures 9, 10 and 11, it can be observed that the
PSO algorithm has better convergence characteristic
than the GA, since it has lower premature convergence
problem. Consequently, the PSO explorates the solution
space better than the GA.
Additionally, the figure 12 presents a comparison between two different versions of GA, for the case study
3:
9.7215
9.721
9.7205
Figure 5: Switches placement using PSO algorithm - Case 1.
9.72
5.774
5.776
5.778
5.78
5.782
5.784
5.786
5.788
5.79
5.792
5
x 10
17th Power Systems Computation Conference
Stockholm Sweden - August 22-26, 2011
50 Switches
2.6
AG
PSO
SAIDI
2.4
100 Switches
2.2
50
100
150
200
250
150
200
250
300
100 Switches
2.2
PSO + FES
PSO Basic
2
SAIDI
75 Switches
AG
PSO
2.2
2
1.8
1.6
1.4
1.8
50
100
150
200
250
300
Iterations
1.6
Figure 13: Convergence characteristics - Case 3.
50
100
150
200
250
300
Iterations
Figure 10: Convergence characteristics - Case 2.
100 Switches
2.2
GA
PSO
2
1.8
1.6
50
100
150
200
250
300
Iterations
Figure 11: Convergence characteristics - Case 3.
Simirlally, the figure 13 presents a comparison
between the two different versions of PSO, for the case
study 3:
i) PSO Basic: PSO with the same parameters of the
proposed method, but with random initialization and
without the rectification algorithm.
ii) PSO + FES: Proposed method that uses the FES in
the population initialization and rectification algorithm.
17th Power Systems Computation Conference
From figures 12 and 13, it can be observed that the
algorithm convergence characteristic is similar but the
quality of the solution is better when FES is used. It was
also observed that, when the number of switches to be
installed is increased, there is no such difference in the
solution reached by the two PSO algorithms (figure 13).
It demonstrates that when the number of switch to be
installed is large, there is no need to consider many
criteria in the allocation. But even though in this scenario the PSO based on FES algorithm has more chance to
reach the better solution. Figure 14 shows the probability distribution for two PSO algorithms. The use of the
FES in the PSO has as characteristic that good solutions
is more likely to be found.
0.06
Solution Density
SAIDI
100
300
Figure 9: Convergence characteristics - Case 1.
SAIDI
50
Figure 12: Convergence characteristics - Case 3.
Iterations
1.4
1.6
Iterations
2
0
1.8
1.4
2.2
1.8
0
GA Basic
GA + FES
2
SAIDI
i) GA Basic: GA with the same parameters of the proposed method, but with random initialization and without the rectification algorithm;
ii) GA + FES: Proposed method that uses the FES in the
population initialization and rectification algorithm.
PSO+FES
PSO Basic
0.04
0.02
0
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
SAIDI
Figure 14: Solutions Probability Distribution.
Stockholm Sweden - August 22-26, 2011
8
CONCLUSION
This paper presents a comparison between methodologies for the switch placement problem in distribution
network: Genetic Algorithm (GA) and Particle Swarm
Optimization (PSO). These methodologies were used to
minimize the SAIDI index subject to the budget constraints. Furthermore, the GA and PSO are combined
with a Fuzzy Expert System (FES) to generate the initial
population and to repair infeasible solutions.
These results have shown that the introduction of the
expert engineering knowledge in the optimization algorithm has great potential to improve the quality of the
solutions obtained, since it has the capability to perform
an oriented smart search in the solution space. Moreover, the convergence characteristic of the PSO is better
than the GA in the solution of the switches allocation
problem. The application of the proposed method in real
large scale system showed that is possible to obtain
significant reductions in the SAIDI index with the installation of switches in the feeders.
1995.M. Michalewicz, “Genetic Algorithms + Data
Structures = Evolution Programs”. Springer. 1996.
ISBN 3-540-60676-9.
[11] M. Michalewicz, “Genetic Algorithms + Data
Structures = Evolution Programs”. Springer. 1996.
ISBN 3-540-60676-9.
[12] M. A. Khanesar, M. Teshnehlab and M. A. Shoorehdeli, “A Novel Binary Particle Swarm Optimization”, Mediterranean Conference on Control and Automation, Athens – Greece, July 27-29, 2007.
REFERENCES
[1] R. E. Brown, Electric Power Distribution Reliability,
Marcel Dekker, New York, 2002, ISBN 0-82470798-2.
[2] R. Billinton, S. Jonnavithul, “Optimal Switching
Device Placement in Radial Distribution Systems”,
IEEE on Trans. Power Delivery, 11 (3) Jul., pp.
1646 – 1651, July 1996.
[3] J. Teng, C. Lu. “ Feeder-Switch Relocation for Customer Interruption Cost Minimization. IEEE Trans.
On Power Delivery, pp. 254-259, 17 (1) Jan. 2002.
[4] R. E. Brown, S. Gupta, R. D. Christie, S. S. Venkata,
“A Genetic Algorithm for Reliable Distribution System Design”. Intelligent Systems Applications to
Power Systems-ISAP’96, pp.29-33,Orlando, Eua,
1996.
[5] T. Tsao, Y. Chang, W. Tseng. “Reliability and Costs
Optimization for Distribution System Placement
Problem”. Transmission and Distribution Conference and Exhibition, Dalian, China, 2005.
[6] Y. Wenyu, L. Jian, Y. Jianmin, D. Hipeng, S. Meng.
“Optimal Allocation of Switches in Distribution
Network”. Intelligent Control and Automation,
Hangzhou, China, 2004.
[7] R. E. Brown, “The impact of heuristic initialization
on distribution system reliability optimization”. International Journal of Engineering Intelligent Systems for Electrical Engineering and Communications, pp. 45-52, March 2000.
[8] J. Kennedy, R. C. Eberhart, “A Discret Binary Version of the Particle Swarm Algorithm”,IEEE, 1997.
[9] El-Hawary, “Electric Power Applications on Fuzzy
Systems”. IEEE Press. 1998.
[10] J. Mendel, “Fuzzy Logic Systems for Engineering”.
Proc. Of the IEEE, pp. 345-377, 83 (3), March
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