Investigation of Simulated Annealing, Ant-Colony and Genetic Algorithms for Distribution Network Expansion Planning with Distributed Generation

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1 Investigation of Simulated Annealing, Ant-Colony and Genetic Algorithms for Distribution Network Expansion Planning with Distributed Generation Majid Gandomkar, Hajar Bagheri Tolabi Department of Electrical Engineering Islamic Azad University, Saveh Branch, Saveh, IRAN ABSTRACT This paper investigates the use of ant-colony optimization, simulated annealing, and genetic algorithms for distribution network expansion planning (DNEP) including distributed generation (DG). It may be introduced as a combinatorial optimization method that determines the location and capacity of feeders and substations while minimizing the network loss and installation cost. In this paper, DGs are considered in the network expansion planning due to their importance in regulated distribution network.. The implementation of each algorithm for DNE is described and the performance of algorithms is compared with each other. The proposed methods are successfully applied to planning a real distribution network KEY-WORDS Ant-colony, Genetic Algorithm, Simulated Annealing, Distribution Planning 1. Introduction Distribution network planners continually endeavor to develop new planning strategies for their network in order to serve the load growth and provide their customers with a reliable electricity supply. Traditional planning studies for serving the forecasted load demand in distribution systems were carried out by considering addition of new substations, or expanding the existing substation capacity and associated new feeder requirements. Competitive electricity market forces the distribution network planners to investigate the economical and technical feasibility of new expansion alternatives such as distributed generations [1]. Distributed Generations scheme includes a set of small generators, scattered throughout a power system, to satisfy the electric energy consumption of electrical customers. DGs scheme often offers a set of valuable alternatives in addition to the traditional sources of electric power generation for industrial, commercial and residental consumers. It employs the latest modern generation technologies in an extensive form and it can be efficient, reliable, and simple to own and operate comparing with other electrical power systems. In some cases DGs provide significantly lower cost and higher reliability versus those which can be obtained from the electrical grid. In others, it can augment the grid so that the combination of grid and DGs provide higher performance than either could alone. However it offers an alternative that utility planners should explore it for the best solution problems [2-3]. Distribution network planning involves identification of the best equipment, along with its location, and schedule of deployment. The solutions of the problem are the set of all feasible combinations of sites and sizes realizing the schedule of deployment of equipments (substations, feeders, DGs) in distribution network. However, the high dimension of the possible solution is the real difficulty in solving the problem. Therefore, artificial intelligence techniques have come to be the most widely used tool for DNEP problem. In this study, the applications of antcolony, simulated annealing and Genetic Algorithm have been investigated. Since cost is an important attribute in distribution network planning, almost invariably one of the planner s chief goals is to minimize overall cost [4]. In this paper, the important task of planning the optimal number and position of DGs has been faced. This optimization permits selection of the best location of generators to minimize total cost including investments for electric grid upgrade and cost of power losses, along the planning duration. 2. Problem Formulation The problem is to determine sites, sizes and schedule of deployment of distributed generators, substations and feeders to minimize the sum of distribution network investment and cost of power losses. The following assumptions are adopted to formulate the problem: 1. Maximum number of installable DGs is given. 2. Total installation capacity of DGs is given. 3. Candidates of DG installation position for each load point are given. 4. The upper and lower limits of node voltage are given. 5. The current capacities of conductors are given. For total cost minimization, the objective function is given by ISSN: ISBN:

2 S S S S ( F SP t Y SP t + θ SP t ( X SP t )) + SP S F F F F f = ( F L t Y L t + θ L t ( X L t )) + (1) Yeart L F P P P P ( F LP t Y LP t + θ LP t ( X LP t )) LP P Constraints: (Maximum number of DGs) YLP P t D (2) t LP P (Total capacity of DGs) P P F LP t Y LP t C (3) t LP P (Only one DG can be installed in one load point) YLP P t 1 (4) t (Upper and lower voltage limit) Vi Vn ± V for i Network Nodes (5) (Current capacity limit) Ii Ii max for i Network Sections (6) Where, SP : Candidate Substation Place node, S : Existing Substation Node L : Candidate Line F : Existing Feeder LP : Candidate Load Point, P : Power Plant Node, F t : Investment cost for installing project which installed at location at year t, Y t : 0-1 variable for determining whether project (substation, feeder or DG) is installed at location at year t (1: installed, 0: not installed), X t : Power consumption (substation or feeder) or generation (DG) of project which installed at location at year t, θ t ( ) : Function of operation cost (DG) or losses cost (substation or feeder) of project at location at year t with power X t, D : Maximum number of the distributed generations in the distribution network, C : Total injected power of distributed generations in the distribution network, Vi : Voltage magnitude of node i, Vn : Nominal voltage magnitude in the network, V : Maximum permissible voltage deviation, Ii: Current of section i in the distribution network, max Ii : Maximum current capacity of section i in the distribution network. For a better comparison, and considering discount rate, for each cost at each year a uniform annual value is used. 3. Description of Algorithms Each of the search algorithms, except for the random search, seeks to obtain an antenna configuration that optimizes a fitness (or objective) function, the value of which depends on the chromosome describing the configuration. 4.1 Simulated Annealing Simulated annealing, one of the first nature-based algorithms to be devised [5], [6], attempts to search large solution spaces by modeling the behavior of a material in the cooling process. The objective function of the DNEP is used to represent the energy of a fictitious material. Optimal schedule yield an objective function of zero, while all suboptimal configurations produce objective functions in the positive range. Each iteration of the SA algorithm starts with a DNEP configuration, changes the state of a randomly chosen project, and monitors the change in energy of the DNEP by evaluating the objective function. The new configuration either replaces the old configuration or is discarded, depending on a probability P given by the Boltzman distribution: E / kt P( E) = e (7) Here E is the change in energy between configurations, T is the current temperature of the system, and k is Boltzman s constant. If the energy is lower in a new configuration then the new configuration is always accepted. If the energy is higher, implying the new configuration is worse; the new configuration is accepted with probability P. Accepting some poorer schedules helps ensure that local minima do not dominate the search. A chosen number of iterations is performed, and then the temperature is decreased and the same number of iterations is again performed. The process is repeated until the temperature cools to a prechosen value, or a given total number of iterations has been completed. A critical part of the SA algorithm is the annealing schedule, which determines the manner in which the temperature is decreased. The geometric annealing schedule is used here [6]: n Tn = T 0 Γ (8) where T 0 is the initial temperature and Γ is the cooling rate. ISSN: ISBN:

3 4.2 Genetic Algorithm The genetic algorithm [7-8], which mimics survival of the fittest among competing organisms and used in this study, is standard in most respects. An initial population of chromosomes is constructed randomly, with each bit in a chromosome corresponding to a project state and the next two bits represent its size. The DNEP is then scheduled according to each chromosome in succession, and the fitness of each answer is evaluated. A selection process follows, during which a new population of size is created. During selection, individuals are chosen from the old population with a probability equal to the ratio of the individual fitness to the total fitness of the old population. Regardless of the result, the individuals with the highest fitness values are selected to guarantee their genetic information will be passed along to the next generation. After selection, individuals are paired off as parents and crossed over times. Each time crossover occurs, the chromosomes are split at a random bit location and their partial bit strings (all bits before the random bit) are swapped between the parents. Following crossover, a mutation is performed by negating each bit on each chromosome. The fitness of the resulting population is evaluated, and the process is repeated for generations. 4.3 Ant-Colony Optimization Ant-colony optimization (ACO) is a relatively new algorithm that mimics the food foraging behavior of ants [9-11]. Individual ants are simple creatures that exhibit activities that appear to be random, disorganized, and unmotivated. The collective behavior of a colony of ants, however, is highly organized and efficient. This is evident in the foraging behavior of colonies, wherein ants find food and quickly bring it back to their nest. A simple diagram of ant foraging behavior is shown in Fig. 1. Two ants leave their nest in different directions at the same time to search for food. As they move about, they deposit a pheromone trail that evaporates slowly and is detectable by other ants. If no pheromone exists initially outside the nest, the paths of the two ants are generally random. Now, assume that ant 1 finds food source 1 while ant 2 is still wandering randomly. Ant 1 picks up some of the food and returns to the nest by following its own pheromone trail, laying additional pheromone on the return trip. Ant 1 arrives at the nest near the same time that ant 2 discovers food source 2. When the next set of ants leaves the nest to search for food, they detect twice as much pheromone on the path to food source 1 than on the path to food source 2, neglecting any evaporation of pheromone. The probability is thus higher that the ants will take the path to food source 1, and as they travel they lay additional pheromone. By this means, the ants bring food source 1 back to the nest in an efficient manner. When food source 1 is exhausted, many ants return to the nest without food, but some continue randomly beyond food source 1, and by this means discover new food sources, including the remains at food source 2. Fig. 1: Diagram of ants foraging for food The evaporation of pheromone is also an important part of the foraging process, helping to deemphasize older trails leading to exhausted food sources. ACO algorithms attempt to exploit the efficiency of ant foraging behavior by creating an abstract environment of possible paths, and simulating ants traveling along these paths. 5. Objective Function Evaluation According to Eq. (1), losses are one of the important parts of the objective function. For calculation of feeders and substations losses and also for considering the voltage and current limits in each network (chromosome) the required load flow software [12] is employed and it is run for each network. This power flow software is capable of modeling the distributed generations and unbalanced loads. 6. Numerical Example In order to test the proposed algorithm, a real distribution network has been considered. Fig. 2 shows the sample network diagram before planning (year =0). Table 1 shows more details of this network's specifications. Different experiments with different random number seeds were carried out to investigate the performance of the proposed algorithms. A number of tests on the performance of the proposed algorithms have been carried out on the example to determine the most suitable GA, SA and ACO parameters setting. Tables 2-4 show the parameters setting for the proposed algorithms. These ISSN: ISBN:

4 parameters were found through trial and error to provide reasonable results for each algorithm. Cooling rate 0.97 Temperature steps 50 iterations It was seen that the setting parameters are independent of DG technology and are dependent to the network. Table 5 shows comparison of results of the proposed algorithms. The results show that power losses will decrease with optimal DG allocation in the network. With optimal DG allocation, the power losses have decreased up to 38% and total costs for planning period are decreased about 28.7% for the example network. Furthermore, with optimal DG planning, it is necessary to install substation 3 at 8 th instead of 5 th year. 4 Fig. 2: The existing sample network, before its expansion (year=0) Table 1 Specifications of example Number of distribution load nodes 69 Number of substation place 3 (70,71,72 Demand of network (year=1) kva Demand of network (year=10) kva Capacities of DGs 500,1000,1500, 2000 kva Maximum total capacity of DGs (C) 4000 kva Maximum number of DGs (D) 8 Permissible voltage drop 5% Investment cost of DG 1030 $/kw Operation cost of DG $/kwh Power cost 690 $/kw Energy cost 0.07 $/kwh Table 2 GA Resultant Control Parameters Population Size Crossover Probability Mutation Probability Generation Distance (G) 0.8 Table 3 ACO resultant control parameters Pheromone constant Evaporation factor 0.75 Allowable edge probability 0.05 Total ants 40 iterations 1000 Table 4 SA resultant control parameter Initial temperature 1.0 K Table 5 Comparison of results of the proposed algorithms ACO GA SA Total Capacity of Installed DGs (kva) Total Investment Costs (1000 $) Total Power Losses (kw) Total Costs of Planning (1000 $) Conclusion Distributed Generations are predicted to play a more important role in the structure of electric power system in near future. With so many new distributed generations being installed, it is critical to assess the power system impacts accurately. These DG units can be employed in a manner to avoid the degradation of power quality, reliability, and control of the utility system. On the other hand, DGs have a great potential to improve distribution system performance and it should be encouraged. For this reason, it is important that distribution network planners can have useful and efficient tools to take into account the opportunities of DGs, and avoid the costly and timeconsuming impact studies. On the basis of these considerations, in this study a new implementation of Ant- Colony optimization, Genetic Algorithm and Simulated Annealing for optimal planning of distribution network with Distributed Generation is illustrated. In this paper, the total costs including investment costs of all equipments, costs of losses, and operation costs of DGs were considered for optimum planning of distribution networks. The effects of the proposed ACO,GA and SA methods to solve the problem are demonstrated by an example. The proposed methods were successfully applied to a real distribution network considering a 10 year planning period. The results showed that all of three developed methods could be employed for optimization of a network more than one hundred node. The purpose of this study is not to decide which algorithm works best, but to ISSN: ISBN:

5 investigate whether these particular three algorithms are candidates for use with an DNEP. It is left to future research to refine each algorithm as necessary for a particular application of the DNEP with DGs. References 1. R.C. Dugan, TE. Mc Dermott & G.J. Ball, Planning for distributed generation, IEEE Industrial Applied Magazine, Vol.7, 2001, H.L. Willis, W.G. Scott, distributed power generation, New York: Marcel Dekker; CIGRE WG 37-23, Impact of increasing contribution of dispersed generation on the power system, Final Report, Electra, G. Celli, F. Pillo, OPTIMAL DISTRIBUTED GENERATION ALLOCATION IN MV DISTRIBUTION NETWORKS, Proc. IEEE Conf. on Power Industry Computer Applications, Sydney, Australia, 2001, W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, NumericalRecipes in C, The Art of Scientific Computing. New York: Cambridge Univ. Press, H. Cohn and M. Fielding, Simulated annealing: Searching for an optimal temperature schedule, Soc. Industr. Appl. Mathemat. J. Optimization, vol. 9, no. 3, pp , J. H. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor, 1975: Univ. Michigan Press. 8. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley, M. Dorigo and A. Colorni, The ant system: Optimization by a colony of cooperating agents, IEEE Trans. Syst., Man, Cybern. Part B, vol. 26, pp. 1 13, Jan M. Dorigo and L. M. Gambardella, Ant colony system: A cooperative learning approach to the traveling salesman problem, IEEE Trans. Evol. Comput., vol. 1, pp , Jan M. Dorigo and G. DiCaro, Ant algorithms for discrete optimization, Artificial Life, vol. 5, no. 3, pp , CS. Cheng, D. Shirmohammadi, A THREE- PHASE POWER FLOW METHOD FOR REAL- TIME DISTRIBUTION SYSTEM ANALYSIS, IEEE Transactions on Power Delivery, Vol. 10, 1995, ISSN: ISBN: