Optimal reconfiguration of electrical distribution network using the refined genetic algorithm

doi:10.1016/S0378-7796(02)00041-X

Electric Power Systems Research

Volume 62, Issue 1, 28 May 2002, Pages 37-42

https://doi.org/10.1016/S0378-7796(02)00041-X Get rights and content

Abstract

This paper proposes an improved method to study distribution network reconfiguration (DNRC) based on a refined genetic algorithm (GA). The DNRC model, in which the objective is to minimize the system power loss, is set up. In order to get the precise branch current and system power loss, a radiation distribution network load flow (RDNLF) method is presented in the study. The refined genetic algorithm is also set up, in which some improvements are made on chromosome coding, fitness function and mutation pattern. As a result, premature convergence is avoided. The proposed approach is tested on 16-bus and 33-bus distribution networks. Study results are given in the paper.

Introduction

It is known that distribution networks are built as interconnected meshed networks, while in the operation they are arranged into a radial tree structure. This means that distribution systems are divided into subsystems of radial feeders, which contain a number of normally-closed switches and a number of normally-open switches. From graph theory, a distribution network can be represented with a graph of G (N, B) that contains a set of nodes N and a set of branches B. Every node represents either a source node (supply transformer) or a sink node (customer load point), while a branch represents a feeder section that can either be loaded (switch closed) or unloaded (switch open). The network is radial, so that feeder sections form a set of trees where each sink node is supplied from exactly one source node. Therefore, the distribution network reconfiguration (DNRC) problem is to find a radial operating structure that minimizes the system power loss while satisfying operating constraints. In fact, this problem can be viewed as a problem of determining an optimal tree of the given graph. However, real distribution systems contain many nodes and branches (and switches), and the total number of trees is extremely large. Ordinary optimization methods have shown to be ineffective and impractical to this problem [1].

Merlin et al. proposed a heuristic approach to the DNRC problem [2]. It begins with all branches closed (a complete graph) and performs a procedure of opening branches which carry the least current. This method is a greedy algorithm that does not necessarily guarantee feasibility of the final solution.

Nahman et al. presented another heuristic approach in [3], [4]. The algorithm starts from a completely empty network, with all switches open and all loads disconnected. Load points are connected one by one by switching branches onto the current subtree. The search technique also does not necessarily guarantee global optima.

Recently, the branch exchange approach has been used in research on DNRC [5], [6], [7]. In fact, this is a gradient method in the space of a graph structure. In this method, one normally-open switch is closed, which forms a loop and violates the topological constraints. When a closed branch (or switch) in the loop opens, a new topology is produced. However, the existing branch exchange based algorithms are capable of finding only local optima, where the final solution heavily depends on the starting configuration.

At present, new methods based on artificial intelligence have been used in DNRC [8], [9]. Chiang et al. [8] presented a simulated annealing (SA) method to solve the DNRC problem, in which the SA was very time-consuming. It is needed to apply the improved SA with high speed to handle the DNRC problem. For the first time, genetic algorithm (GA) was applied to the global optimal solution of DNRC in [9], which has shown a better performance over the SA approach. In this paper, the GA method is further refined by modifying the string structure and fitness function:

1
In Ref. [9], the string used in GA describes all the switch positions and their ‘on/off’ states. The string can be very long and it grows in proportion with the number of switches. For large distribution systems, such long strings can not be effectively searched by GA. In this paper, the string will be shortened.
2
To reduce computational burden, approximate fitness functions was used in GA to represent the system power loss [9]. It may affect the accuracy and effectiveness of GA. GA is essentially unconstrained search procedures within the given represented space [10], [11], [12]. All information should be fully represented in the fitness function. Over-approximated fitness function would lead directly to unreliable solution.

In this paper, the DNRC model, in which the objective is to minimize the system power loss, is set up. Since the distribution network is a simple radial tree structure, in which the ratio of R/X is relatively big, even bigger than 1.0 for some transmission lines, neither P–Q decoupled method nor Newton–Raphson method is suited to compute the distribution network loadflow. Therefore, a radiation distribution network loadflow (RDNLF) method is presented in the study. In order to enhance performance of GA, some improvements are made on chromosome coding, fitness function and mutation pattern. Among these improved features, an adaptive process of mutation is developed not only to prevent premature convergence, but also to produce smooth convergence. The proposed approach is tested with satisfactory results on 16-bus and 33-bus distribution networks.

Section snippets

Brief description of GA

GAs are effective parameter search techniques. They are considered when conventional techniques have not achieved the desired speed, accuracy or efficiency [10]. GAs are different from conventional optimization and search procedures in the following ways [12].

1
GAs work with coding of parameters rather than the parameters themselves.
2
GAs search from a population of points rather than a single point.
3
GAs use only objective functions rather than additional information such as their derivatives.
4
GAs

Mathematical model of DNRC

The purpose of DNRC is to find a radial operating structure that minimizes the system power loss while satisfying operating constraints. Thus, the following model can represent the DNRC problem. $Min f= Σ_{b} | I_{b} |^{2} k_{b} R_{b} b ∈ NL$ such that $k_{b} | I_{b} |≤ I_{bmax} b ∈ NL$ $V_{imin} ≤ V_{i} ≤ V_{imax} i ∈ N$ $g_{i} (I, k)=0$ $g_{v} (V, k)=0$ $ϕ(k)=0$ where I_b is the current in branch b; R_b is the resistance of branch b. V_i is the node voltage at node i. k_b represents the topological status of the branches. k_b=1 if the branch b is closed, and k_b=0 if the branch b is

Refined GA approach to DNRC problem

Model M-1 may be solved by first generating all graph trees and subsequently by performing evaluation. However, real distribution systems contain many nodes and branches, and many trees. Conventional optimization methods have shown to be ineffective and impractical, because of dimensionality [1]. GAs has shown to be an effective and useful approach for the DNRC problem [9]. Some refinements of the approach are described in this paper.

Numerical examples

The proposed approach for distribution network reconfiguration is tested on 16-bus and 33-bus distribution systems as shown in Fig. 2, Fig. 3, respectively. System data and parameters are listed on Table 1, Table 2. The 16-bus test system contains 3 source transformers and 13 load nodes. The three initially-open switches are ‘4’, ‘11’ and ‘13’. The total system load is 23.7 MW, while the initial system power loss is 0.5114 MW. The 33-bus test system consists of one source transformer and 32

Conclusions

An improved method to study distribution network reconfiguration using GA is presented in the paper. The DNRC model, in which the objective is to minimize the distribution system loss, is formed. In the application of GA to the DNRC, some improvements of algorithms are made on chromosome coding, fitness function and mutation pattern. The genetic string used in the paper is shortened to minimize the required memories and to ensure search efficiency. The proposed process of adaptive mutation not

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Optimal reconfiguration of electrical distribution network using the refined genetic algorithm

Abstract

Introduction

Section snippets

Brief description of GA

Mathematical model of DNRC

Refined GA approach to DNRC problem

Numerical examples

Conclusions

Elect. Power Syst. Res.

An approach formula for counting trees in a graph

IEEE Trans. Circuit Syst.

Optimal loss reduction of distribution networks

IEEE Trans. Power Syst.

New methods for evaluating distribution automation and control system benefits

IEEE Trans. PAS