such a combinatorial problem. This paper presents an efficient meta-heuristic method for reconfiguration of distribution systems. A Tabu Search (TS) algorithm is ...
A New Intelligent Optimization Technique for Distribution Systems Reconfiguration S. F. Mekhamer
A. Y. Abdelaziz
F. M. Mohammed
M. A. L. Badr
Electrical Power and Machines Department Faculty of Engineering Ain Shams University Cairo, Egypt change resulting from the transfer of a group of loads from one feeder to another feeder. Since the method is based on heuristics, it is not easy to take a systematic way to evaluate an optimal solution. Baran, et al. proposed two different methods with varying degree of accuracy to approximate power flow in systems. The search method has an acceptable convergence characteristic however it can get stuck in local minimum [2]. The method is very time consuming due to the complicated combinations in large-scale systems. In recent years, meta-heuristic methods have been studied for solving combinatorial optimization problems to obtain an optimal solution of global minimum. Typical meta-heuristic methods include Simulated Annealing (SA), Genetic Algorithm (GA) and Tabu Search (TS). SA is analogous to the annealing process of the heat bath of metal and optimizes the solution by cooling parameter called temperature [3]. Chiang, et al. proposed a two-stage solution methodology based on a modified Simulated Annealing technique for solving the reconfiguration problem of distribution systems [4, 5]. This solution algorithm gives a near optimal solution. GA is based on the natural selection of biology. GA optimizes the solution by using genetic operations such as reproduction, crossover, and mutation [6]. Nara, et al. proposed GA based method for feeder reconfiguration [7]. However, the previous methods do not work so well in large sized optimization problem because they are based on stochastic algorithms. Also, they are very time consuming. Kim, et al. presented an artificial neural network based method for feeder reconfiguration [8]. However it can get stuck in local minimum in case of large scale distribution systems. That is why this paper focuses on TS [9, 10]. TS introduces an adaptive memory called tabu list into the local search of the hill-climbing method. The tabu list plays an important role to escape from a local minimum. TS efficiently find nearly globally optimal solutions due to the deterministic optimization. Also, TS is easier to tune up than SA and GA. Mori, et al. proposed a parallel TS (PTS) based method for feeder reconfiguration [11]. PTS introduces two parallel schemes. One is the decomposition of the neighborhood with parallel processors to reduce computational efforts.
Abstract The loss minimization problem is one of the most important problems to save the operational cost in distribution systems. Therefore, more efficient approaches are required to handle such a combinatorial problem. This paper presents an efficient meta-heuristic method for reconfiguration of distribution systems. A Tabu Search (TS) algorithm is used to reconfigure distribution systems so that active power losses are globally minimized with turning on / off sectionalizing switches. TS algorithm is introduced with some modifications such as using a tabu list with variable size according to the system size; this should lead to robust algorithm, and prevent cycling. Also, a random multiplicative move is used in the search process to diversify the search toward unexplored regions. A new method to check the radial topology of the system is presented. The proposed method is applied to 32-node and 69-node distribution systems. The obtained results using the proposed TS approach are compared with results obtained using Simulated Annealing (SA) approach and Parallel Tabu Search (PTS) approach in the previous work to examine the performance.
1.
INTRODUCTION
Network reconfiguration is the process of altering the topological structures of distribution feeders by changing the open/ closed status of the sectionalizing and tie switches [1]. During normal operating conditions, networks are reconfigured for two purposes: (1) to reduce the system power losses and (2) to relieve overloads in the network. In recent years distribution system automation is widely proceeded to smooth operation and control in distribution systems. Optimizing reconfigurations of distribution system is important to reduce system loss. As a result, the studies on feeder reconfiguration are made by turning on or off sectionalizing switches. The problem of the reconfiguration results in a combinatorial optimization. However, it is hard to determine an optimal configuration in large–scale radial distribution systems due to many possible combinations. Civanlar, et al. developed a branch-exchange method that considered the on-off conditions of the sectionalizing switches in discrete numbers [1]. They proposed an approximate formula to estimate the loss
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The other is the multiplicity of the tabu length to improve the solution accuracy. PTS algorithm gives results better than results obtained by SA, Parallel Simulated Annealing (PSA), GA, and Parallel Genetic Algorithm (PGA). This paper proposes a modified TS algorithm to enhance the solution accuracy for reconfiguration of distribution systems. The proposed method is applied to the 32-node system shown in Fig. 2 and the 69- node system shown in Fig. 3. A comparison is made between SA, PTS and the proposed TS algorithm to examine the performance. 2.
applied similar ideas to various classical problems [9-10]. TS presents some solutions to prevent cycling and to avoid entrapment in local minima, and explores the search space in order to minimize the objective function f(x). The method starts with defining a neighborhood N(x) of the current solution x as a finite set of feasible solutions. In classical descent method, if a solution x* in N(x) with f(x*) < f(x) is found, the move from x to x* is performed and the procedure is iteratively repeated. The method is trapped in local minimum with no solution x* is found in N(x) that lowers the objective function value. But among all the visited solutions in N(x) the best one is selected in tabu– search, which is stored by using tabu list. This strategy prohibits tabu move which can prevent cycling to previously visited solutions and escape entrapment in local minimum. 3.1 Design of Move 1. Add / Subtract move 2. Multiplicative move 3. Constrained multiplicative move 3.2 Tabu List The tabu list is another important concept in Tabu Search. When the move is accepted, the move and its reverse are recorded in the tabu list. The basic role of the tabu list is to identify cycling and escape from local minimum. The dimension of the tabu list is updated every iteration according to the problem size. 3.3 Aspiration Criterion If the evaluation objective function value of a trail solution is smaller than that of the current best solution, this move can be accepted, even thought the move is listed in the tabu list. 3.4 Tabu Search Algorithm Step 1: Set iteration count k = 0 and generate initial solution. Step 2: Update iteration count k = k+1 and randomly generate a series of solutions from the solution space. Evaluate the objective function value of each solution. Choose the best solution to be initial solution. Step 3: Generate a family of trail solutions; this will lead to a group of feasible trail solutions x1, x2, ……..., xm. Calculate f(x1), f(x2),…………..., f(xm) respectively. Step 4: Search neighborhood. Select the best solution from above-mentioned group of trail solutions as x*. If x* is not listed in the tabu list or it is listed in tabu list but aspiration criterion is satisfied, update x with x*, i.e. let x = x*. Step 5: Check convergence: If convergence criterion is satisfied, go to step 7. Otherwise go to step 6. Step 6: Update tabu list and return to step 2. Step 7: Evaluate the best solution. Step 8: End. Fig. (1) shows a flow chart for the TS algorithm.
PROBLEM FORMULATION
This section describes the formulation of distribution system reconfiguration problem. The objective of the reconfiguration is to minimize the distribution losses with turning on / off sectionalizing switches. The reconfiguration problem has the following constrains: 1. Power flow equations. 2. Upper and lower bounds of nodal voltages. 3. Upper and lower bounds of line currents. 4. Feasible conditions in terms of network topology. Mathematically, the problem can be formulated as follows: Cost function: Min Z =
( PI2 + QI2 ) VI2
L
∑ rI I =1
(1)
Subject to: g(x) = 0 min
Vi
min Ii
(2) max
< Vi < Vi
(3)
max Ii
(4)
det(A) = 1 or -1 radial system
(5)
det(A) = 0 not radial where: Z: Cost function L: No. of transmission lines P: Active power loss at bus i Q: Reactive power at bus i V i : Voltage at bus i
(6)
