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Optimal Placement of Distributed Generation Using Particle Swarm ...
Optimal Placement of Distributed Generation Using Particle Swarm Optimization Wichit Krueasuk Weerakorn Ongsakul Department of Electrical Engineering School of Environment, Resources and Faculty of Engineering Sripatum Development, Asian Institute of Technology University, Bangkok, Thailand Pathumthani, Thailand E-mail: wichit@spu.ac.th E-mail: ongsakul@ait.ac.th ABSTRACT Optimal placement of DG (OPDG) in distribution network is an optimization problem with continuous and This paper proposes a particle swarm optimization discrete variables. Many researchers have used (PSO) algorithm for optimal placement of distributed evolutionary methods for finding the optimal DG generation (DG) in a primary distribution system to placement [6]-[9]. minimize the total real power loss. The PSO provides a population-based search procedure in which individuals In fact, three types of DG are considered as follows: called particles change their positions with time. During Type 1: DG is capable of supplying only real power; flight, each particle adjusts its position according to its Type 2: DG is capable of supplying only reactive power; own experience, and the experience of neighboring Type 3: DG is capable of supplying real power but particles, making use of the best position encountered by consuming proportionately reactive power. itself and its neighbors. Initially, the algorithm randomly generates the particle positions representing the size and In [10], a Newton-Raphson algorithm based load flow location of DG. Each particle will move from its current program is used to solve the load flow problem. The position using the velocity and the distance from current methodology for optimal placement of only one DG type best local and global solution reached. The velocity 1 is proposed. Moreover, the heuristic search requires consists of inertia of the particle, memory, and exhaustive search for all possible locations which may cooperation between particles. The proposed PSO not be applicable to more than one DG. Therefore, in algorithm is used to determine optimal sizes and this paper, PSO method is proposed to determine the locations of multi-DGs. Three types of DG are optimal location and sizes of multi-DGs to minimize the considered and the distribution load flow is used to total real power loss of the distribution systems. calculate the exact loss. Test results indicate that PSO The organization of this paper is as follows. Section 2 method can obtain better results than the simple addresses the problem formulation. The DG type and heuristic search method on the 33-bus and 69-bus radial heuristic search method are explained in Section 3. The distribution systems. The PSO can obtain maximum loss PSO algorithm is represented in Section 4. A PSO reductions for each of three types of optimally placed computation procedure on for the OPDG problem is multi-DGs. Moreover, voltage profile improvement and given in Section 5. Simulation result on the test systems branch current reduction are obtained. are illustrated in Section 6. Then, the conclusion is given in Section 7. Keywords- Distributed Generation, DG types, Optimal DG size, Particle Swarm Optimization 2. PROBLEM FORMULATION 1. INTRODUCTION The real power loss reduction in a distribution system is required for efficient power system operation. The loss Distributed Generation (DG) is a small generator spotted in the system can be calculated by equation (1) [11], throughout a power system network, providing the given the system operating condition, electricity locally to load customers [1]. DG can be an alternative for industrial, commercial and residential n n applications. DG makes use of the latest modern PL = ∑∑ Aij ( Pi Pj + Qi Q j ) + Bij (Qi Pj − Pi Q j ) (1) technology which is efficient, reliable, and simple i =1 j =1 enough so that it can compete with traditional large generators in some areas [2] [3]. where, Rij cos (δ i −δ j ) Placement of DGs is an interesting research area due to Aij = VV j i economical reason. Distributed generation systems (such as fuel cells, combustion engines, microturbines, etc) can Rij sin (δ i −δ j ) Bij = reduce the system loss and defer investment on VV j i transmission and distribution expansion. Appropriate size and optimal locations are the keys to achieve it [4] where, Pi and Qi are net real and reactive power injection [5]. in bus ‘i’ respectively, Rij is the line resistance between bus ‘i’ and ‘j’, Vi and δi are the voltage and angle at bus wind turbines, induction generator is used to produce ‘i’ respectively real power and the reactive power will be consumed in the process [12]. The amount of reactive power they The objective of the placement technique is to minimize require is an ever increasing function of the active power the total real power loss. Mathematically, the objective output. The reactive power consumed by the DG (wind function can be written as: generation) in simple form can be given as in equation N SC (9) as in the case of [13] Minimize PL = ∑ Loss k (2) QDG = − ( 0.5 + PDG ) k =1 2 (9) Subject to power balance constraints N N The loss equation will be modified. After following the ∑ PDGi = ∑ PDi + PL i =1 i =1 (3) similar methodology of the first two types, optimal DG size can be found by solving equation (10). ≤ Vi ≤ Vi min max voltage constraints: Vi (4) 0.0032 Aii PDGi + PDGi [1.004 Aii + 0.08 Aii QDi − 0.08Yi ] + 3 (10) max ( X i − Aii PDi ) = 0 current limits: I ij ≤ I ij (5) Equation (10) gives the amount of real power that a DG where: Lossk is distribution loss at section k, NSC is should produce when located at but ‘i’, so as to obtain total number of sections, PL is the real power loss in the the minimum system loss whereas the amount of system, PDGi is the real power generation DG at bus i, reactive power that it consumes can be calculated from PDi is the power demand at bus i. equation (9). 3. DG TYPE AND HEURISTIC METHODLOGY 4. PARTICLE SWARM OPTIMIZATION Particle swarm optimization (PSO) is a population-based 3.1. DG TYPE 1 optimization method first proposed by Kennedy and Eberhart in 1995, inspired by social behavior of bird Certain type of DGs like photovoltaic will produce real flocking or fish schooling [16]. The PSO as an power only. To find the optimal DG size at but ‘i’, when optimization tool provides a population-based search it supplies only real power, the necessary condition for procedure in which individuals called particles change minimum loss is their position (state) with time. In a PSO system, n particles fly around in a multidimensional search space. ∑( A P − B Q ) 1 (6) Pi = PDGi − PDi = − ij j ij j During flight, each particle adjusts its position according Aii j =1 to its own experience (This value is called Pbest), and j ≠i according to the experience of a neighboring particle (This value is called Gbest),made use of the best position From equation (6), we obtain the following relationship: encountered by itself and its neighbor (Figure 1). n ∑( A P − B Q ) 1 (7) PDGi = PDi − ij j ij j Aii j =1 j ≠i Equation (7) gives the optimal DG size for each bus so as to minimize the total real power loss. 3.2. DG TYPE 2 For synchronous condenser DG, it provides only reactive Figure 1: Concept of a searching point by PSO power to improve voltage profile. To determine the optimal DG placement, we again differentiate the loss This modification can be represented by the concept of equation on either side with respect to Qi. The optimal velocity. Velocity of each agent can be modified by the DG size for every bus in the system is given by equation following equation: (8) vid+1 = ωvid + c1rand ×( pbestid − sid ) + c2rand × ( gbestd − sid ) (11) k k k k N ∑(A Q + Bij Pj ) 1 (8) QDGi = QDi − ij j Aii j =1 Using the above equation, a certain velocity, which j ≠i gradually gets close to pbest and gbest can be calculated. 3.3. DG TYPE 3 The current position (searching point in the solution space) can be modified by the following equation: Here, we consider that the DG will supply real power and in turn will absorb reactive power. In case of the s id+ 1 = s id + v id+ 1 , i = 1, 2 , ..., n , k k k (12) Start d = 1, 2 , ..., m Input system data (1) where s k is current searching point, s k +1 is modified Calculate the original loss using Bw-Fw Sweep (2) searching point, v k is current velocity, v k +1 is modified Initialize particle velocity of agent i, v pbest is velocity based on pbest, population (3) vgbest is velocity based on gbest, n is number of Calculate the total loss (4) particles in a group, m is number of members in a Record Pbest (5),Gbest(6) particle, pbesti is pbest of agent i, gbesti is gbest of the group, ωi is weight function for velocity of agent i, ci Update particle position and velocity (7) is weight coefficients for each term. No Check the stopping criterion (8) The following weight function is used: Particle Swarm Yes ωmax − ωmin Optimization ωi = ωmax − Print out location and .k (13) size of DG (9) kmax End where, ωmin and ωmax are the minimum and maximum weights respectively. k and kmax are the current and Figure 2: PSO-OPDG computational procedure maximum iteration. Appropriate value ranges for C1 and C2 are 1 to 2, but 2 is the most appropriate in many cases. Appropriate values for ωmin and ωmax are 0.4 and 6. SIMULATION RESULTS 0.9 [17] respectively. The distribution test systems are the 33 bus [18] and 69 bus [19] systems. The 33 bus system has 32 sections 5. PSO PROCEDURE with the total load 3.72 MW and 2.3 MVar shown in Figure 3. The original total real power loss and reactive The PSO-based approach for solving the OPDG problem power loss in the system are 221.4346 kW and 150.1784 to minimize the loss takes the following steps: kVar, respectively. The 69 bus system has 68 Sections with the total load of 3.80 MW and 2.69 MVar, shown in Step 1: Input line and bus data, and bus voltage limits. Figure 4. The original total real and reactive power Step 2: Calculate the loss using distribution load flow losses of the system are 230.0372 kW and 104.3791 based on backward-forward sweep. kvar, respectively. For PSO parameters, population Step 3: Randomly generates an initial population (array) size=200, Maximum generation (kmax) = 100. The of particles with random positions and velocities maximum number of DG is 3 for each type. on dimensions in the solution space. Set the iteration counter k = 0. Step 4: For each particle if the bus voltage is within the limits, calculate the total loss in equation (1). Otherwise, that particle is infeasible. Step 5: For each particle, compare its objective value with the individual best. If the objective value is lower than Pbest, set this value as the current Pbest, and record the corresponding particle position. Figure 3: The 33 bus radial distribution system. Step 6: Choose the particle associated with the minimum individual best Pbest of all particles, and set the value of this Pbest as the current overall best Gbest. Step 7: Update the velocity and position of particle using (11) and (12) respectively. Step 8: If the iteration number reaches the maximum limit, go to Step 9. Otherwise, set iteration index k = k + 1, and go back to Step 4. Step 9: Print out the optimal solution to the target problem. The best position includes the optimal locations and size of DG or multi-DGs, and the corresponding fitness value representing the minimum total real power loss. Figure 4: The 69 bus radial distribution system. Table 1: PSO result of the 69 bus test system Total real power loss Min Avg. Max (kW) 80.1933 95.4714 203.2326 Average Time (sec.) 5.6341 For DG type 1, the convergence characteristic of the best solution of PSO is shown in Figure 5. Figure 6 shows the total real power loss from 100 trials of PSO-OPDG. The average CPU time is 5.6341 second. Figure 6: The total loss distribution from 100 trials of a 69 bus test system The improvement in the voltage profile after optimally placing the DGs is shown in Figure 7. Without DG, the bus no. 64 has the lowest voltage of 0.8891 p.u. and the bus voltage has improved to 0.9453 p.u. after installing DG. Figure 5: Convergence characteristic of the 69 bus test system. For the 33 and 69 bus systems, in Tables 2-4, the PSO can obtain the same optimal size and location as the heuristic search [10] for one types 1-3 DG. For the 33 bus system, one type-1 DG can reduce the total real and reactive power loss by 47.49% & 43.12% compared to 28.29% & 27.55% and 26.01% & 23.05% for DG types 2 and 3, respectively. For three type-1 DGs, they can further reduce the real and reactive power loss by 65.60% & 64.73% compared to 34.56% & 34.24% and 24.66% & 22.03% for DG types 2 and 3, respectively. In the 69 bus system, three type-1 DGs can reduce the real Figure 7: Bus voltage before and after DG Installation and reactive power loss by 69.19% & 65.81% compared for DG type-1. to 35.53% & 33.78% and 29.71% & 29.13% for DG types 2 and 3, respectively. Table 2: Optimal DG placement for DG type 1 Table 3: Optimal DG placement for DG type 2 Table 4: Optimal DG placement for DG type 3 7. CONCLUSION generation: definitions, benefits and issues,” Energy Policy 33, pp787-798, 2005. In this paper, a particle swarm optimization for optimal [4] William Rosehart and Ed Nowicki, “Optimal placement of multi-DGs is efficiently minimizing the Placement of Distributed Generation,” 14th total real power loss satisfying transmission line limits PSCC, Sevilla, 24-28 June 2002. and constraints. 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