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 Maria da Guia da Silva UFMA guia@dee.ufma.br 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 [,3,4] GA and Simulated Annealing (SA) were used to solve the switch allocation problem. In these papers, the objective function was associated with: 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. 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]:
Membership Grade Membership Grade 1) Protection Response The protection device (fuse or recloser) nearest to the fault operates to clear the fault. ) 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. 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 occurring 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 : 1 0.8 0.6 0.4 Small Medium Large 0. 0 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Input Variable Figure : Fuzzy Sets used to input variables. Figure 1: Operated Devices in a Contingency Simulation. 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: System Average Interruption Duration Index SAIFI System Average Interruption Frequency Index. ASAI Average Service Availability Index. ENS Average Energy Not Supplied. 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 0.8 0.6 0.4 0. 0 Very Small Small Medium Large 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BEN 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].
Thus, every section of the distribution network is evaluated and the benefit of the switch installation is stored in a vector. Rule #1 If (SIB is S) and (DSL is S) and (SL is S) then BEN is VS Rule # If (SIB is S) and (DSL is S) and (SL is M) then BEN is VS Rule #3 If (SIB is S) and (DSL is S) and (SL is L) then BEN is VS Rule #4 If (SIB is S) and (DSL is M) and (SL is S) then BEN is VS Rule #5 If (SIB is S) and (DSL is M) and (SL is M) then BEN is VS Rule #6 If (SIB is S) and (DSL is M) and (SL is L) then BEN is S Rule #7 If (SIB is S) and (DSL is L) and (SL is S) then BEN is VS Rule #8 If (SIB is S) and (DSL is L) and (SL is M) then BEN is VS Rule #9 If (SIB is S) and (DSL is L) and (SL is L) then BEN is M Rule #10 If (SIB is M) and (DSL is S) and (SL is S) then BEN is VS Rule #11 If (SIB is M) and (DSL is S) and (SL is M) then BEN is VS Rule #1 If (SIB is M) and (DSL is S) and (SL is L) then BEN is S Rule #13 If (SIB is M) and (DSL is M) and (SL is S) then BEN is S Rule #14 If (SIB is M) and (DSL is M) and (SL is M) then BEN is S Rule #15 If (SIB is M) and (DSL is M) and (SL is L) then BEN is M Rule #16 If (SIB is M) and (DSL is L) and (SL is S) then BEN is S Rule #17 If (SIB is M) and (DSL is L) and (SL is M) then BEN is S Rule #18 If (SIB is M) and (DSL is L) and (SL is L) then BEN is M Rule #19 If (SIB is L) and (DSL is S) and (SL is S) then BEN is VS Rule #10 If (SIB is L) and (DSL is S) and (SL is M) then BEN is VS Rule #1 If (SIB is L) and (DSL is S) and (SL is L) then BEN is S Rule # If (SIB is L) and (DSL is M) and (SL is S) then BEN is S Rule #3 If (SIB is L) and (DSL is M) and (SL is M) then BEN is S Rule #4 If (SIB is L) and (DSL is M) and (SL is L) then BEN is M Rule #5 If (SIB is L) and (DSL is L) and (SL is S) then BEN is M Rule #6 If (SIB is L) and (DSL is L) and (SL is M) then BEN is L Rule #7 If (SIB is L) and (DSL is L) and (SL is L) then BEN is L 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) 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 () 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. () 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 individuals with probability of 70%; Mutation Rate: 0.5%; stop criteria: 300 iterations. 5. 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 [1]. 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: where: 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 (3)
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; ) 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): (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 ()-(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. 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 ()). 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 ; for ; while: n k 1 x 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 : No. of Consumers 7,474 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 (hours/year) 8946 SAIFI (failures/year) 1.00897 Table : 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 : Reallocation of the switches installed in the network (75 switches).
9.75 9.75 x 106 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 9.7 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 the 9.715 stars indicate that the switch already installed should be kept in its position. The figure 8 shows the improvement in (in 9.71 percentage) compared with the of the original system. The results show a meaningful difference in the application of AG and PSO in the solution of the switch 9.705 allocation problem. It should be noted that the addition of the FES, in the PSO algorithm, resulted in a significant improvement in the index. 9.7 Figure 6: Switches placement using PSO algorithm - Case. 9.75 x 106 5.774 5.776 5.778 5.78 5.78 5.784 5.786 5.788 5.79 5.79 9.7 x 10 5 9.74 9.73 9.715 9.7 9.71 9.71 9.705 Figure 4: Geographic Information Sytem of the test system. Case Study: (h/year) - GA (h/year) - PSO Case 0 8946 8946 Case 1 1.98881 076 Case 1.7107 1.587 Case 3 1.5658 1.44415 Table 3: Case studies results. 9.75 x 106 9.7 Figure 7: Switches placement using PSO algorithm - Case 3. 9.7 5.774 5.776 5.778 5.78 5.78 5.784 5.786 5.788 5.79 5.79 30% 0% GA PSO 10% 0% -10% Case 1 Case Case 3 Figure 8: reduction regarding to the base-case. x 10 5 9.715 9.71 9.705 Figure 5: Switches placement using PSO algorithm - Case 1. 9.7 5.774 5.776 5.778 5.78 5.78 5.784 5.786 5.788 5.79 5.79 x 10 5 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 1 presents a comparison between two different versions of GA, for the case study 3:
Solution Density 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. 50 Switches.6.4 0 50 100 150 00 50 300 Figure 9: Convergence characteristics - Case 1. 75 Switches Figure 10: Convergence characteristics - Case. 1.4 Figure 11: Convergence characteristics - Case 3. AG PSO AG PSO 0 50 100 150 00 50 300 100 Switches GA PSO 50 100 150 00 50 300 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. 100 Switches GA Basic GA + FES 1.4 50 100 150 00 50 300 Figure 1: Convergence characteristics - Case 3. 100 Switches PSO + FES PSO Basic 1.4 50 100 150 00 50 300 Figure 13: Convergence characteristics - Case 3. From figures 1 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 0.04 0.0 PSO+FES PSO Basic 0 1.4 1.5 1.7 1.9.1 Figure 14: Solutions Probability Distribution.
Powered by TCPDF (www.tcpdf.org) 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 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 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. [1] M. A. Khanesar, M. Teshnehlab and M. A. Shoorehdeli, A Novel Binary Particle Swarm Optimization, Mediterranean Conference on Control and Automation, Athens Greece, July 7-9, 007. REFERENCES [1] R. E. Brown, Electric Power Distribution Reliability, Marcel Dekker, New York, 00, ISBN 0-847- 0798-. [] 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. 54-59, 17 (1) Jan. 00. [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.9-33,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, 005. [6] Y. Wenyu, L. Jian, Y. Jianmin, D. Hipeng, S. Meng. Optimal Allocation of Switches in Distribution Network. Intelligent Control and Automation, Hangzhou, China, 004. [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. 45-5, March 000. [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