Minimal Loss Configuration for Large-Scale Radial Distribution Systems using Adaptive Genetic Algorithms

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1 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Minimal Loss Configuration for Large-Scale Radial Distribution Systems using Adaptive Genetic Algorithms Anil Swarnkar, Member, IEEE, Nikhil Gupta, Member, IEEE, K. R. Niazi, Senior Member, IEEE Department of Electrical Engineering Malaviya National Institute of Technology Jaipur, India Abstract This paper presents a new method for reconfiguration of radial distribution systems for minimisation of real power loss using Adaptive Genetic Algorithm without involving any additional cost for the installation of tap changing transformers, capacitors and concerned switching equipments. The initial population for Genetic Algorithm is created using a heuristic approach and the genetic operators are adapted with the help of graph theory to generate feasible radial topologies throughout the evolutionary process. This avoids tedious mesh checks and thus reduces the computational burden. The effectiveness of the proposed method is demonstrated on three different test distribution systems. The application results show that the proposed method is efficient and promising for minimisation of real power loss of radial distribution systems. Keywords- Distribution Systems, Genetic Algorithm, Real Power Loss, Reconfiguration I. INTRODUCTION Reconfiguration of radial distribution systems is a very effective and efficient means to reduce distribution network losses, to improve voltage profile, to manage load congestion and to enhance system reliability. Distribution networks are generally structured in mesh but operated in radial configuration for effective co-ordination of their protective schemes and to reduce the fault level. The aim of reconfiguration of radial distribution system (RDS) is to obtain a radial operating configuration that minimises real power loss while satisfying all the operational constraints without islanding of any node(s). The reconfiguration of a distribution system is a process that alters feeder topological structure by managing the open/close status of sectionalising and tieswitches in the system under contingencies or under normal operating conditions. Extensive research work has been carried out in the area of reconfiguration of RDS. These research efforts can be broadly classified into conventional approaches and AI based approaches. The conventional approaches include heuristic optimisation techniques and classical optimisation techniques. Merlin et al. [1] were first to report a method for distribution system reconfiguration to minimise line loss. They formulated the problem as integer mixed non-linear optimisation problem and solved it through a discrete branch-and-bound technique. Civanlar et al. [2] suggested a branch exchange type heuristic method, in which a computationally efficient formula was developed to determine change in loss in radial distribution system due to switch exchange between two adjacent branches. Shirmohammadi et al. [3] proposed a method based on [1]. Goswami et al. [4] extended the method of [2] by limiting the switch exchange within a single loop each time. The method is computationally less demanding. Baran et al. [5] developed a heuristic algorithm based on the idea of branch exchange for loss minimisation and load balancing. Martín et al. [6] presents a new heuristic approach of branch exchange to reduce the power loss of distribution systems based upon the direction of the branch power flows. Gohokar et al. [7] describes the formulation of the reconfiguration problem using network topology approach considering single loop optimisation based upon highest voltage drop across the open switches. An algorithm has been developed to check radiality of the network. In the area of AI based approaches, Nara et al. [8] introduced genetic algorithm (GA) for reconfiguration of RDS with minimum loss. Lin et al. [9] and Zhu [10] proposed refined GAs for feeder reconfiguration. Delbem et al. [11] proposed a GA, which incorporates a new tree encoding based on graph chain, for optimal feeder reconfiguration. A fuzzy mutated GA was proposed by Prasad et al. [12]. Mendoza et al. [13] proposed a new methodology for minimal loss reconfiguration using GA with the help of fundamental loops. Enacheanu et al. [14] presented a method based on GA for the loss minimisation in distribution networks, using matroid theory and graph theory. Su et al. [15] introduced an ant colony search algorithm to solve the optimal network reconfiguration problem for power loss reduction. The network reconfiguration problem is solved using the proposed ant colony search algorithm method and compared the results with the genetic algorithm and the simulated annealing algorithm. Li et al. [16] proposed a combination of the binary PSO algorithm and the discrete PSO algorithm for minimising the power loss of a distribution network. Irving et al. [17] employed GA for multi-objective constraint optimisation problem to reconfigure distribution

2 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, network under contingencies. Hong et al. [18] suggested a method based on GA to determine the network configuration, formulated as a fuzzy multi-objective problem. Prufer number is used in GA to ensure the radial structure. Huang et al. [19] presented an enhanced GA-based fuzzy multi-objective approach to solve the reconfiguration of RDS problem in a radial distribution system. Lin et al. [20] presented application of immune algorithm for reconfiguration of RDS for loss minimisation and load balancing in feeders and transformers. Hsiao et al. [21] presented the application of evolutionary programming for multi-objective feeder reconfiguration. Das [22] suggested a fuzzy multi-objective approach for feeder reconfiguration which incorporates a heuristic rule base. Falaghi et al. [23] proposed a methodology for reconfiguration of RDS in the presence of distributed generation sources. The multi-objective considerations are handled using a fuzzy approach. Ramírez-Rosado et al. [24] presented a new multiobjective tabu search meta-heuristic algorithm to solve a multiobjective fuzzy model for optimal planning of distribution systems. Ahuja et al. [25] proposed a hybrid algorithm based on artificial immune systems and ant colony optimisation for reconfiguration of RDS, which is formulated as a multiobjective optimisation problem. Augugliaro et al. [26] dealt with the problem of voltage regulation and power loss minimisation for automated distribution systems, using multiobjective, fuzzy set based heuristic optimisation method. Zhang et al. [27] presented a joint optimisation algorithm of combining reconfiguration of RDS and capacitor control for loss reduction in distribution systems by employing improved adaptive genetic algorithm. Zhang et al. [28] presented the multi-objective distribution network optimisation model with the optimal network loss, load balancing, and power supply voltage. It applied hybrid genetic particle swarm optimisation algorithm to search the optimisation. In deregulated business environment, the purpose of distribution network reconfiguration is to achieve efficiency and to hold down the cost by reducing energy losses while maintaining desired degree of reliability and power quality. The reconfiguration of distribution system for loss minimisation is a complex, combinatorial optimisation problem. The Genetic Algorithm is considered to be an efficient method for solving the large-scale combinatorial optimisation problem, due to its ability to search global or near global optimal solutions. This paper presents a new method for minimising real power loss of a distribution network through reconfiguration which exploits the benefits of heuristic, graph theory and Genetic Algorithm and therefore an Adaptive Genetic Algorithm (AGA) is developed. The proposed algorithm modifies the genetic operators to create feasible individuals using a new approach without mesh checks using graph theory. The proposed new approach generates only feasible individuals while maintaining the radiality of the system. This drastically reduces computational burden of GA. Moreover, the initial population of better fitness is created using heuristic rules, which also reduces the computational time. The genetic codification is carried out using real numbers instead of the binary numbers. The organisation of the paper is as follows. Formulation of problem for loss minimisation is discussed in Section II. The solution methodology using proposed AGA is explained in Section III, in Section IV the method is illustrated with the help of an example, in Section V application results of the proposed method on test distribution systems are discussed and finally conclusions are presented in Section VI. II. PROBLEM FORMULATION One of the principal objectives of distribution network reconfiguration is to find radial operating structure that minimises the system real power loss while satisfying operating constraints. In this paper it has been assumed that the three-phase distribution system is balanced and all the loads of the nature of constant power. The reconfiguration problem of RDS is formulated as below: Minimise P Q E 2 2 n n Rn (1) 2 n 1 Vn Subject to V min V V max (2) (i) = 0 (3) where, V n, P n and Q n are voltage, real power and reactive power at the sending end of the n th branch respectively, R n is the resistance of the n th branch and E is the total number of branches in the distribution system. Equation (1) corresponds to the objective function to be optimised and represents total real power loss of the distribution system. Equation (2) considers voltage constraints for each node of the system. Equation (3), deals with the radial topology constraint. It ensures radial structure of the i th candidate topology. III. PROPOSED ADAPTED GENETIC ALGORITHM The development of GA is largely credited to the work of Holland [29] and Goldberg [30]. Since then GAs have evolved and become a promising tool to solve complex optimisation problem. The Genetic Algorithms are derivative free stochastic optimisation methods inspired by the concept of natural selection and evolutionary process. While GA is used to solve the reconfiguration problem of a distribution network, the genetic operations may transform the feasible individuals into infeasible ones owing to radiality constraint. Therefore, the conventional GA is not suitable to solve the reconfiguration problem of distribution networks and needs modification using some engineering knowledge base. In the proposed AGA, the genetic operators are modified using graph theory to generate feasible individuals at each stage of the genetic evolution. A. Reconfiguration using Graph Theory The proposed methodology creates feasible individuals at each stage of the genetic evolution using the fundamentals of

3 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, graph theory. The fundamental loops are determined for the distribution network by closing all tie-switches. The number of fundamental loops of the meshed distribution network is equal to the number of tie-switches of the system [31] and is given by the relation L = E N + 1 (4) where, E = total number of elements (sectionalizing and tieswitches) of the network and N = total number of nodes of the network According to graph theory, radial topologies may be obtained when exactly L numbers of switches of a meshed network are being opened. Therefore, the length of genetic chromosomes can be taken as L, where each gene of the genetic chromosome is denoted by a non-repeated real number which represents the open switch of the distribution network. However, only some particular sets of L number of genes ensures radial topologies without islanding of one or more system nodes and these are called as feasible individuals. In this paper, the genetic operators, i.e., accentuated crossover and directed mutation proposed by Mendoza et al. [13] are modified to generate feasible individuals during initialization, crossover and mutation. Mendoza et al. [13] have used loop vectors to ensure the generation of feasible individuals. However, this approach only searches for the isolation of exterior nodes and does not take into account the isolation of interior nodes. Therefore, this strategy may produce infeasible individuals. In the proposed AGA, in addition to loop vectors, common branch vectors and the prohibited group vectors are introduced to avoid the generation of infeasible individuals during each stage of the genetic evolution as discussed below: 1) Obtain all the fundamental loops of the meshed network. Create loop vectors L k, containing the set of elements of the k th fundamental loops. k =1, 2,, L 2) Determine common branch vectors, C ij, containing the set of elements common between two loop vectors L i and L j. 3) Determine prohibited group vector R k, the set of common branch vectors incident at the k th principal node(s) of the distribution network. 4) Let, G m denotes the m th gene of a chromosome, then for this chromosome to be feasible the following rules must be satisfied: Rule-1: G m must belong to the m th loop vector. Rule-2: Only one element can be selected from a common branch vector. Rule-3: All the common branch vectors of any prohibited group vector cannot participate simultaneously to form a chromosome. The Rule-1 prevents any islanding of the nodes situated at the perimeter of the network, whereas Rule-2 and Rule-3 prevent the islanding of the nodes situated at the interior of the network. Therefore, while encoding the individuals, these three rules ensure the radial topology of the distribution network without islanding of any node(s) and thus it avoids the probability to generate infeasible individuals. In general, the genetic chromosome encoding may be defined as shown in Fig. 1. G 1 Є L 1 G 2 Є L 2 G m Є L m G L Є L L Fig. 1. Chromosome encoding for the proposed AGA The generation of only feasible individuals during crossover and mutation drastically reduces the computational burden of GA while solving reconfiguration problems for large-scale distribution systems. The reduction in computational time during initialization using proposed AGA is discussed in the next sub-section. B. Initialization using Heuristic and Population Growth In the conventional GA, the initial population is created randomly to surf almost whole search area. While the reconfiguration problems of RDS, the initial population so created may contain a large number of infeasible and/or low fitness individuals. This will result in prohibitively large computational burden. Therefore, conventional GA as such cannot be applied for reconfiguration problems of RDS. In the proposed method, initial population is created using heuristic technique, which provides individuals with a fair degree of fitness. However, in certain cases heuristic may not provide adequate number of feasible individuals. In such cases, the feasible individuals may be grown to acquire the requisite number using mutation. The initial population so created will reduces the computational time. The heuristics [2]-[6] are referred to create initial population. Following are the steps to generate initial population for the proposed AGA: 1) Read system data and perform load flow on the base case radial configuration to evaluate the real power loss. 2) Select any one fundamental loop and exchange the opened switch with the adjacent switch of its either side. 3) Check the radial topology using loop vectors, common branch vectors and prohibited group vectors, if radiality constraint violates then select next switch in sequence. 4) Evaluate the real power loss of the radial structure obtained in step 3. 5) Repeat step 3 and 4, until the loss reduction is achieved. 6) If real power loss increases, exchange the opened switch with the switch on the other side of the tie-switch of the selected loop and repeat steps ) Repeat steps 2-6 for the remaining fundamental loops of the system. All the valid radial topologies generated during the above heuristic process constitute the initial population for AGA. Once the initial population of size p is created, their fitness is evaluated using (1). C. Crossover The crossover operator allows the exchange of genetic information among different candidate solutions. The idea is that the new individuals that emerge in the population contribute to increasing the diversity, thus allowing the exploration of new points in the search space. In the proposed

4 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, AGA, a multi-point crossover [17] is used to produce offsprings. In each crossover, one parent is selected using roulette wheel selection and another parent is selected randomly from the current population. The generated offspring, if infeasible, may be corrected by loop vectors, common branch vectors and the prohibited group vectors. In this way, the accentuated crossover of [13] is modified. Thus in each crossover two offsprings are created. The fitness of each offspring is also evaluated. Out of p+2 individuals, the best p individuals are selected according to their fitness. The crossover rate is normally kept around 90%. D. Mutation Mutation is used to allow GA to avoid local optima and to explore new search areas. In the proposed AGA, one element (gene) in the chromosome to be muted is selected randomly for mutation and its replacement is guided by loop vectors, common branch vectors and the prohibited group vectors to ensure radial topology of the distribution network. In this way, the directed mutation of [13] is modified. The fitness of the muted individuals is also evaluated. In the literature, the mutation rate is normally selected between 2-10%. In the proposed AGA, the mutation rate is not kept constant but it decreases linearly and governed by the predefined initial mutation rate, mutation step size and final mutation rate. E. Termination Condition If all the individuals of the current population reach to the solution with same fitness or the number of generations reach the value of predefined maximum generations then AGA is terminated and final result is printed. At the end of each generation, elitism is used to preserve the best individual. Therefore, there are five loop vectors. The network topology suggests seven common branch vectors C 12 = {33}, C 25 = {8], C 23 = { }, C 15 = {6 7}, C 14 = {3 4 5}, C 45 = { } and C 35 = {34}. The loop vectors and the common branch vectors are shown in Table I. TABLE I LOOP VECTORS AND THE COMMON BRANCH VECTORS Loop Vectors Common Branch Vectors L 1 = [ ] C 12 = [33] L 2 = [ ] C 23 = [ ] L 3 = [ ] C 14 = [3 4 5] L 4 = [ ] C 35 = [34] L 5 = [ C 25 = [8] ] C 15 = [6 7] C 45 = [ ] The loop vectors and the common branch vectors for the system can be pictorially represented by the Venn-diagram shown in Fig. 3. The prohibited group vectors and the corresponding islanded principal node(s) for the system may be obtained from the Venn-diagram are shown in Table II. IV. ILLUSTRATIVE EXAMPLE Fig. 3. Venn-diagram of the IEEE 33-bus system TABLE II PROHIBITED GROUP VECTORS AND ISLANDED PRINCIPAL NODE (S) The Prohibited Group Vectors Principal node(s) Islanded R 5 = {C 14 C 15 C 45} 5 R 7 = {C 12 C 15 C 25} 7 R 8 = {C 23 C 25 C 35} 8 R 57 = {C 12 C 14 C 25 C 45} 5,7 R 78 = {C 12 C 15 C 23 C 35} 7,8 R 578 = {C 12 C 14 C 23 C 35 C 45} 5,7,8 Fig. 2. IEEE 33-bus system To understand the application of graph theory, let us consider the example of IEEE 33-bus system, shown in the Fig. 2. For this system E =37, N=33 and L = = 5. For this test system, total five switches have to be open to form an individual to maintain the radial topology, one from each loop vector as per Rule-1. Let the individual { } is created at any stage of the AGA. Which is not a feasible individual in accordance to the Rule-2, since both 6, 7 Є C 15. If this individual is selected, then node 6 will be islanded. Considering another individual { }, which is also not a feasible individual in accordance to the Rule-3, since 7 Є

5 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, C 15, 3 Є C 14, 25 Є C 45 and the prohibited group vector R 5 is {C 14 C 15 C 45 }. If this individual is selected, then the principal node 5 will be islanded. There are many more such infeasible individuals exists until or unless they are guided by Rule-2 and Rule-3, in addition to Rule-1. The genetic operators, i.e., crossover and the mutation have been adapted using fundamentals of graph theory to ensure feasible radial topologies of the genetic individuals and thereby the proposed AGA has been adapted using graph theory. The incorporation of the engineering knowledge base of the graph theory in the proposed AGA certainly enhances its efficiency as depicted by the test results in the following section. V. TEST RESULTS AND DISCUSSION The proposed algorithm is tested on three different test distribution systems. The upper and lower bus-bar voltage limit is kept at 1.0 p.u. and 0.9 p.u. respectively. The crossover rate is kept constant at 0.9. The mutation rate is not kept constant but decreases linearly from 0.15 with a step size of 0.01 till it become 0.02 and then it held constant at The population size and the maximum generations for these test distribution systems are given in Table III. The algorithm was developed in MATLAB, and the simulation is done on a computer with Pentium Duo, 2.20 GHz, 1 GB RAM. TABLE III POPULATION SIZE AND MAXIMUM GENERATIONS Test System Population size Maximum generations 33-bus System bus System bus System A. 33-bus system [5] This is a kv system having 33 buses, 37 branches and 5 tie-lines. The normally open switches are (33, 34, 35, 36, 37). For this case, the initial losses are kw. The total system loads arc MW and 2.30 MVAr. The proposed AGA opens branches (7, 9, 14, 32, 37). With this configuration the losses are kW. This solution is identical to those obtained by a number of approaches available in the technical literature as shown in Table IV. The average CPU time using the proposed method is 2.14 s. TABLE IV COMPARISON OF TEST RESULTS FOR 33-BUS SYSTEM B. 84-bus System [15] Method Open Switches Power Loss (kw) [3] 7, 10, 14, 32, [10] 7, 9, 14, 32, [6] 7, 9, 14, 32, Proposed 7, 9, 14, 32, This system is an 11.4 kv practical distribution network of the Taiwan Power Company (TPC). It consists of 11 feeders, 83 normally closed switches, and 13 normally open switches (84 buses, 96 branches and 13 tie-lines). The total system loads are MW and MVAr. The original configuration has branches 84 to 96 opened. For this case, the initial losses are kW. The configuration obtained by the proposed AGA has branches (55, 7, 86, 72, 13, 89, 90, 83, 92, 39, 34, 42, 62) opened. This solution is identical to those obtained by a number of approaches available in the technical literature as shown in Table V. The average CPU time for the proposed method is s. TABLE V COMPARISON OF TEST RESULTS FOR 84-BUS SYSTEM Method Open switches Power loss (kw) SA [15] 55, 7, 86, 72, 13, 89, 90, 83, 92, 39, 34, GA [15] 55, 7, 86, 72, 13, 89, 90, 83, 92, 39, 34, ACSA 55, 7, 86, 72, 13, 89, 90, 83, 92, 39, 34, [15] Proposed 55, 7, 86, 72, 13, 89, 90, 83, 92, 39, 34, C. 136-bus system [32] This is a 13.8 kv real distribution system in a medium size city of Brazil and the data for this system can be found in [32]. It consists of 8 feeders, 135 normally closed switches, and 21 normally open switches (136 buses, 156 branches and 13 tielines). The original configuration has branches 136 to 156 opened. The nominal active and reactive loadings are MW and 7.93 MVAr respectively. TABLE VI COMPARISON OF TEST RESULTS FOR 136-BUS SYSTEM Method Open Switches Real Power Loss (kw) [32] 136:141, 53, 143:152, 106, 154: [33] 7, 51, 53, 84, 90, 96, 106, 118, 126, 128, 137, , 139, 141, 144, 145, 147, 148, 150, 151, 156 [34] :156 [35] Proposed For this case, the initial losses are kw. The configuration obtained by the proposed method has branches (7, 35, 51, 90, 95, 106, 118, 126, 135, 137, 138, 141, 142, 144, 145, 146, 147, 148, 150, 151, 155) opened. This solution is better to those obtained by a number of approaches available in the technical literature as shown in Table VI. The average CPU time for the proposed method is s. VI. CONCLUSIONS In this paper, a new method for reconfiguration of RDS for real power loss minimization is presented. The proposed method utilizes the advantages of heuristics to create initial population with better fitness. In the proposed AGA, in addition to topological concept of loop vectors, the concepts of common branch vectors and prohibited group vectors using graph theory have been introduced to avoid generation of infeasible

6 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, individuals at each stage of the of the genetic evolution. This strategy drastically reduces the computational burden and hence results in less computational time. The proposed AGA has been applied on three different test distribution systems. The application results show that the proposed method provides a promising tool for reconfiguration of RDS for real power loss minimization. The proposed method can be extended to deal with the problem of multi-objective distribution system reconfiguration. REFERENCES [1] A. Merlin, and H. Back, Search for a minimum-loss operating spanning tree configuration in an urban power distribution Proc. 5 th Power System Computation Conf., Cambridge, U.K, pp. 1 18, [2] S. Civanlar, J. J. Grainger, H. Yin, and S. S. H. Lee, Distribution feeder reconfiguration for loss reduction, IEEE Trans. Power Delivery, vol. 3 (3), pp , [3] D. Shirmohammadi, and W. H. 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