Optimal Allocation and Sizing of Distributed Generation in Distribution Network Using Modified Shuffled Leaping Algorithm

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1 Optimal Allocation and Sizing of Distributed Generation in Distribution Network Using Modified Shuffled Leaping Algorithm Negar Dehghani Mahmoudabadi* 1, Babak Farhang Moghadam 2, Hamed kazemipoor 3 1-MS of Engineering Technology, Parand Branch, Islamic Azad University, Parand, Iran 2-Institute for Management and Planning Studies, Tehran, Iran 3-Department of Engineering Technology, Parand Branch, Islamic Azad University, Parand, Iran Abstract: Distributed generation (DG) will be an important part in the future power networks because of their potential for solving some of the problems related to mitigating line losses and improving system voltage profile. This paper presents a modified shuffled frog leaping algorithm (MSFLA) for allocating DGs for reducing losses and improves voltage profile of power networks. The objective function contains Voltage Profile Improvement Index (VPII) and Line Loss Reduction Index (LLRI) used in this paper in order to compute the line losses and voltage profiles. This study comprises a comparison between the MSFLA and SFLA methods implemented by MATLAB software on IEEE-34 bus radial distribution system. The simulations results revealed that MSFLA method can present better performance than the SFLA method. Keywords: Distributed generation (DG), Line Loss Reduction Index (LLRI), Modified Shuffled Frog Leaping Algorithm (MSFLA), Voltage Profile Improvement Index (VPII). 1. Introduction Nowadays, Distributed Generations (DGs) have become one of the most interesting research areas in the power generation because they provide several services to utilities and consumers including standby generation, peaks smoothing capability, base load generation and better power reliability. DGs can extensively affect the flow of power and voltage at load buses. Impact of Distributed Generation on regulation can be positive or negative. Positive influences are generally called system support advantages that can be analyzed in terms of line losses and on-peak operating costs reduction, voltage profiles improvement, construction of new transmission lines elimination, system reliability, integrity and efficiency enhancement[3-4]. Locations and size of the DG's have been determined by the maximum potential advantages [1-5]. Compact DG technologies are fast becoming economically viable [6-7]. Conventional energy sources include oil, gas and coal. These conventional sources are usually fossil fuels. Their use leads to increased greenhouse gas emissions and other environmental damage. Our articles explore the environmental impact of obtaining and using conventional energy sources. Recently, different types of renewable energy sources (RES) such as wind electric conversion systems, geothermal systems, solar-thermal electric systems, photovoltaic systems and fuel cells are used as DG in power systems. Several published papers have calculated the line losses of system as objective function to be minimized for determining the location of DG [2-5]. A 2/3 rule is described in [7] to allocate the DGs on a radial distributed network with uniformly distributed loads. The presented method cannot be extended to a network with other kinds of loads. References [8-11] have used power flow algorithms to find the optimal location and capacity of DG at each load bus in network supposing that DG source can be placed at every load bus. Additionally, a large number of researchers have applied the evolutionary calculating ways for finding the optimal DG location [12-16]. A genetic tabu search algorithm has been presented for optimal DG allocation in distribution networks [15-17]. Methods presented in [9-10] give the placement of DG only, while, line losses depend on both of place and size. In the recent few years, with the advent of mimic animal abilities in problem solution, a branch of nature inspired metaheuristics, which are referred as swarm intelligence became inchmeal common[13-21]. Particle Swarm Optimization [18], Artificial Bee Colony [19], Ant Colony Optimization [20], etc. are some of the famous algorithms that they use of mimic animal attitude in problem modeling and solving [22-23].

2 This paper proposes a modified shuffled frog leaping algorithm (MSFLA) for distributed generation placement and sizing in order to reduction in line losses and to improve Voltage Profile. The SFLA is a metaheuristic optimization method spired from the mimetic evolution of a group of frogs when they are searching for food. In this paper, a novel frog leaping law is presented to enhance the local detection of the SFLA. The main idea behind this law is to extend the direction and the length of every frog s jump by imitating frog s realization and action uncertainties. The presented method can be done easily with basic mathematical and logic operation. 2. METHODS TO ASSESS THE ADVANTAGE OF DG In order to discuss and quantify the benefits of distributed generation proper mathematical models should be used along with distribution system models and power flow calculations to arrive at indices of advantages. Among a large number of various advantages two main ones are investigated: improving voltage profile and reducing line loss. 2.1.Index of Line Loss Mitigation One of the most important advantages given by connection of DG to grid is reduction in electrical line losses [14]. By installing DG line currents could be reduced, therefore it helps to decrease the electrical line losses. The presented index of line loss mitigation (ILLM) is given as: LLW ILLM DG LL (1) Wo DG In which LL w/dg is the whole of line losses in the system with the use of DG and LLWO/DG is the total line losses in the system without DG and it can be defined as: 2 3 M W i i DG i 1 LL I R D (2) I i is the per unit line current in distribution line I, with the use of DG D i (km) is the length of line R (pu/km) is the resistance of line M is the number of lines in the system. Also, LL Wo/DG is defined as: 2 3 M WO i i DG i 1 LL I R D (3) I i is the per-unit line current in distribution line i without the employment of DG. When ILLM is less than 1, the connection of DG reduces the line losses whereas ILLM=1 indicates that DG cannot influence on line losses. Also when ILLM becomes larger than 1, DG causes more line losses. This index can be calculated to determine the optimum location and capacity to install DG to maximize reduction of line loss. 2.2.Index of Voltage Profile Improvement The inclusion of DG results in improved voltage profile at various buses. The Index of Voltage Profile Improvement (IVPI) is defined as the voltage profile of the system with DG to the voltage profile of the system without DG [24]. VP IVPI VP W DG Wo DG (4) In which VP W and VP WO are the voltage profile system with and without DG respectively. The VP is DG DG defined as follows:

3 Vp N bus i 1 V V (5) i i, ref V i is the amplitude of voltage of bus i and V i,ref is the amplitude of voltage of slack bus. VP provides an opportunity to evaluate and aggregate the importance, values, and the voltage levels at which loads are being supplied at the different load busses in the power system. This equation must be used only after assuring that the voltages at all the load busses are within permissible minimum and maximum constraints. Under this condition all the load buses are given the same importance. In reality, DG can be connected to almost every bus in the system. Therefore, VPII can be used to choose the best placement for DG. 3. THE PRESENTED SHUFFLED FROG LEAPING ALGORITHM (SFLA) FOR OPTIMAL LOCATION AND SIZING OF DISTRIBUTED GENERATION (DG) IN A DISTRIBUTION NETWORK 3.1. The Objective Function The aim of the paper is to minimize the combined objective function defined to improve voltage profile and also decreasing line losses for different values of DG. The objective function is expressed as: n 2 Min F P λ V (6) total loss p p p 1 λ p is the penalty factor of bus voltages and generally assigned as assigned as 1,Ploss is the real power loss calculated from the load flow solution at the base case, VP is the voltage profile of the buses Limitations The limitations are listed as follows: Distribution line absolute power constraints P Line ij P Line ij. max (7) Line P and P ij. max are the absolute powers flowing over the distribution lines and the maximum transmission power Line ij maximum permissible amount flowing on between nodes i to j, respectively. Bus voltage magnitudes are constrained as V V V (8) min i max The second constraint involves a voltage magnitude at bus i. In which V min and V max are the minimum and maximum amounts of bus voltage magnitudes, respectively. Radial structure of the network M = N N (9) bus f N bus is the number of buses, M is the number of branches and N f is the number of power plants. DG Power limits min max Q Q Q (10) and DGi DGi DGi min max P P P (11) DGi DGi DGi P i and Q i are the transmitted active and reactive power of DG components at the i th bus.

4 Subject to power balance limits N sc N sc P P P (12) DGi Di L i1 i1 Where: N sc is the whole number of parts, P L is the real power loss in the system, P DGi is the active power generation DG at bus i, P Di is the demand of power at bus i Shuffled frog-leaping algorithm The Shuffled frog leaping algorithm is derived from a virtual population of frog in which individual frogs represent a set of possible solution. It is a meta-heuristic optimization method that emulators the mimetic evolution of a number of frogs when they are searching for the location that has the maximum amount of existing food. The algorithm includes parts of local search and global information exchange ([25-26]). The flowchart of the SFLA is depicted in Fig. 1. The local search block in the flowchart is illustrated later in Fig. 2. The SFLA is explained in details as follows. At the first step, Generate an initial population of N frogs, P={X 1, X 2... X N } that is created randomly. For S-dimensional problems (S variables), the position of a frog i th in the search space is shown as X i =[x 1,x 2,,x is ] T. A fitness function is defined to assess the frog s location. For minimizing the problems, the frog s fitness could be expressed as: 1 fitness (13) f (X) C In which f(x) is the cost function must be minimized, and C is a constant selected to be sure that the fitness value is positive. Then, the frogs are sorted in accordance with their fitness in a descending order. Then, the whole population is divided into m memeplexes, each including n frogs (i.e. N = n m), in such a way that the first frog is located in the first memeplex, the second frog is placed in the next memeplex, the m th frog is put in the m th memeplex, and the (m+1) th frog comes back to the first memeplex, etc. Let M k be the set of frogs in the k th memeplex, this process can be expressed by the following equation: M k X 1 P 1 l n, 1 k m k m l (14) The frogs with the worst and the best fitness are labeled as X b and X w within each memeplex, respectively. Additionally, the frog with the global best fitness is shown as X g. The worst frog X w leaps toward the best frog X b during memeplex evolution. In nature, due to imperfect perception, the worst frog cannot place exactly in the best frog s location. And due to inexact action, the worst frog cannot jump right to its target location. Because of these uncertainties and taking into account the fact that the worst frog could jump over the best one, a modified frog leaping law can be expressed as ([27]) (see Fig. 2):

5 Begin Initialize: - Population size(n) - Number of memeplexes(m) - Number of evolution step within each memeplex(jmax) Generate population (P) randomly Evaluate the fitness of (P) Sort (P) in descending order Partition (P) into m memeplexes Local Search Iterative updating the worse frog of each memeplex NO Shuffle the memeplexes Convergence criteria satisfied? Yes Determine the best solution End Figure 1. Flowchart of the SLFA D r X X (15) b w X X D D D (16), w max w new Figure 2. The original frog leaping rule 3.4. Modified Shuffled Frog Leaping Algorithm (MSFLA) According to the original frog leaping rule, in each memeplex, the worse frog correct its position towards the best frog's position or the global best position in the same memeplex. As a result, this frog leaping rule limits the local search space during each memeplex evolution step. This limitation might not only slow down the convergence speed, but also cause premature convergence. In nature, the worst frog cannot put totally the best frog s location, and due to wrong action, the worst frog cannot jump right to its aim position. Considering these uncertainties, we

6 discuss that the worst frog s new position is not necessary restricted in the line connecting its current position and the best frog s location. In addition, the worst frog can jump over the best one. This thought causes to a new frog leaping rule that extends the local search space as shown in Fig. 3. The new frog leaping rule is shown as: Figure 3. The new frog Leaping r D rc( X X ) W (17) b w T W rw 1 1,max,r2w 2,max,, rsw s,max (18) X w D if D Dmax X w ( new ) D X D if D D T D D w max max (19) In which, r is a random number between 0 and 1 and c is a random number in the range between 1 and 2; r i (1 i S) are uniformly distributed random numbers in the interval between 1 and 1. i, max(1 i S) is the most allowed understanding and the uncertainty in the i th dimension of the search space; and D max is the maximum permissible distance of one jump. The flow chart of the local memetic evolution using the modified frog leaping law is presented in Fig. 4. If the leaping generates a better solution, it substitutes the worst frog. Otherwise, the computations in [17-19] are repeated but according to the global best frog (i.e. X g replaces X b ). If it is impossible to improve the response in this case, the worst frog is eliminated and a new frog is randomly produced to replace it. The calculations continue for a definite number of memetic evolutionary stags in each memeplex, and then the entire population is mixed all together in the shuffling process. As long as the convergence criteria are not met, the local evolution and global shuffling repeat. In this paper, the SFLA will cease when either the relative change in the fitness of the best frog within a predefined number of consecutive shuffling iterations is less than a pre-specified error or the maximum definite number of shuffling iterations is reached. In comparison with the original frog leaping rule proposed in [26], the modified frog leaping rule presented in [27] develops the local search space in each memetic evolution stage; consequently it might make better the algorithm in term of convergence rate and solution performance provided that the vector W max =[w 1,max,,w S,max ] T is properly selected. However, if W max is too large, the directional characteristic of the frog leaping law will loss, and it causes the algorithm becomes more or less random search. Meanwhile, if W max is too small, the impact of perception and action uncertainties to the performance of the algorithm is not considerable. In this paper, to solve the mentioned defect, the SFLA will be improved by recommending that the uncertainty must reduce during the algorithm run. The idea is incentivized from the hypothesis that when the frogs get closer to the optimal location, their perception and action uncertainties become smaller. The maximum uncertainties are exponentially reduced according to the below expression: W W, ( 0 1) (20) ( iter ) iter ( 0) max max

7 Begin First memeplex: i = 1 First iteration: j = 1 Determine Xg, Xb and Xw Apply equations (17), (18) and (19) Yes Is Xw(new) better than Xw? Apply equations (17), (18) and (19) with replacing Xb by Xg Yes Is Xw(new) better than Xw? No Generate a new frog randomly Replace the worst frog Xw Next jump : j = j + 1 j Jmax? No Next memeplex: i = i + 1 i m? No End Yes Yes Figure 4. Flowchart of the local search using the new frog leap law Where iter is the iteration count and λ is the decay factor and. With these exponentially decaying uncertainties, the SFLA has a developed local search space to prevent premature convergence at the first iterations, and a focused local search space to hasten convergence rate at the next iterations. Table I: Line Data Table II: Load Data Line no From bus To bus Line no PL QL

8 Simulation Result 4.1.Test System The distribution test systems are the 34 bus systems. The original total active power loss and reactive power loss in the system are MW and MVar, respectively. The 34 bus system has 33 parts with the general load of MW and MVar, shown in Figure 5 [28].

9 Figure 5. Standard IEEE 34 bus system The number of maximum iteration for the MSFL algorithm is The number of memeplexes is 5. The number of frogs in memeplex is 20. The Local iteration number in each memeplexes is 5. The general number of iteration is 5. The number of DG (DG is capable of supplying only active power) for Optimal location and capacity is 10. The maximum active power of DG is 5 MW Results of power Loss Reduction and Improvement in Voltage Profile of the system The decrease in power loss is clear after installing ten DG as indicated in Table IV and Table V. It shows the reduction power losses with connection of DG for range of 50 kw. The power loss for the base case without DG connection is computed by load flow solutions and it is found to be kw. For DG rating of 50 kw the amounts of power loss significantly diminishes as shown in Table IV and Table V. The percentage of power loss reduction is by means of (LLRI) and a reduction of % is gained with SFLA and a decrease of 99.27% with MSFLA respectively. Table III. Optimal location and capacity of distributed generation MSLFA SLFA Bus Bus DG (KW) no no DG (KW)

10 Table IV: Power losses reduction results for a DG rating of 50 kw by MSFLA DG rating of 50 kw Method Power Loss (MW) ILLM Base Case MSFLA Reduction(%) Table V: power losses reduction results for a DG rating of 50 kw by SFLA DG rating of 50 kw Method Power Loss (MW) ILLM Reduction (%) Base Case SFLA Table VI and table VII show that for the SFLA and MSFLA methods, the amounts of the voltage profile of the network have enhanced significantly by installing a DG of 50 kw. The voltage profile of the base case was estimated to be p.u when a DG rating of 50 kw was connected for case study by SFLA and MSFLA. The voltage profile of the network has enhanced which obviously shows the need of a DG. The percentage of voltage profile improvement is by means of (VPII) and an improvement of 96.21% is gained with SFLA and a decrease of 96.29% with MSFLA respectively. Table VI: Voltage profile improvements for a DG rating of 50 kw by SFLA DG rating of 50 kw Method VP VPII Improvement(%) Base Case SFLA Table VII: Voltage profile improvements for a DG rating of 50 kw by MSFLA DG rating of 50 kw Method VP VPII Improvement (%) Base Case MSFLA Figure 6 indicates the variation of enhancement in voltage amplitude at bus 34 for a DG rating of 50 kw.

11 Figure 6. Voltage amplitude results by MSLFA 4. Conclusion The Distributed Generation (DG) in a distribution system presents many advantages like relieved transmission and distribution congestion, voltage profile enhancement, loss reduction, improvement in system. The presented paper has proposed a method to measure some of the advantages of DG such as, active power loss reduction and voltage profile enhancement of network. The results of the presented method as applied to IEEE-34 bus system obviously indicate that DG can enhance the voltage profile and decrease active power losses. Both sizes and locations of DG have to be investigated together very cautiously to obtain the maximum advantages of DG. This paper indicates that the modified shuffled frog leaping algorithm (MSFLA) has better capability to diminish the objective function by optimizing the DG in comparison with shuffled frog leaping algorithm (SFLA). References 1. D. Gautamand, N. Mithulananthan, Optimal DG placement in deregulated electricity market, EPSR. Vol.77, No.2, pp , M.H. Moradi, M. Abedini, A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems, Electrical Power and Energy System 34, pp , K. Abookazemi, M.Y. Hassan and M.S. Majid, A Review on Optimal Placement Methods of Distribution Generation Sources, IEEE International Conference on Power and Energy, Kuala Lumpur, Malaysia pp , Nov 29-Dec 1, E.K. Bawan, Distributed generation impact on power system case study: Losses and voltage profile, Universities Power Engineering Conference (AUPEC), nd Australasian, pp.1-6, M.H. Nehrir, C. Wang, and V. Gerez, Impact of wind power distributed generation on distribution systems, Proc. Of 17th International Conference on Electricity Distribution(CIRED), Barcelona, Spain, May P. Chiradeja, R. Ramakumar, A review of distributed generation and storage, 31th Annual Frontiers of Power Conf., Stillwater, UK, pp.1 11, S. Rahman, Fuel cell as a distributed generation technology, IEEE Power Engineering Society Summer Meeting, Vol. 1, pp , July S. Ghosh, S. P. Ghoshal and S. Ghosh, Optimal sizing and placement of distributed generation in a network system, Electric Power and Energy Systems, Elsevier, M. Vukobratovic, Z. Hederic and M. Hadziselimovic, Optimal Distributed Generation placement in distribution network, Energy Conference (ENERGYCON), 2014 IEEE International, pp , H.A. Hejazi, M.A. Hejazi, G.B. Gharehpetian and M. Abedi, Dispersed generation Site and Size Allocation Through a Techno Economical Multi-objective Differential Evolution Algorithm, IEEE International Conference

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