Reconfiguration of distribution system using fuzzy multi-objective approach

doi:10.1016/j.ijepes.2005.08.018

International Journal of Electrical Power & Energy Systems

Volume 28, Issue 5, June 2006, Pages 331-338

https://doi.org/10.1016/j.ijepes.2005.08.018 Get rights and content

Abstract

The paper presents an algorithm for network reconfiguration based on fuzzy multi-objective approach. Multiple objectives are considered for load balancing among the feeders, minimum deviation of the nodes voltage, minimize the power loss and branch current constraint violation, while subject to a radial network structure in which all loads must be energized. These objectives are modeled with fuzzy sets to evaluate their imprecise nature and one can provide his or her anticipated value of each objective. These four objectives are first fuzzified and then a fuzzy satisfaction objective function is formed and maximized for each tie-switch operation. Heuristic rules are also incorporated in the algorithm for minimizing the number of tie-switch operation. The effectiveness of the proposed method is demonstrated through an example.

Introduction

Distribution networks are configured radially. Their configurations may be varied with manual or automatic switching operations so that the loads are supplied at the cost of possible minimum resistive line losses, increase system security and enhance power quality. Reconfiguration also relieves the overloading of the network components. The change in network configuration is performed by opening/closing of sectionalizing and tie-switches of the network. These switchings are performed in such a way that the radiality of the network is maintained and all the loads are energized. Obviously, the greater the number of switches, the greater are the possibilities for reconfiguration and better are the effects.

Considerable research has been conducted for loss minimization in the area of network reconfiguration of distribution systems [1]. Distribution system reconfiguration for loss reduction was first proposed by Merlin and Back [2]. They have used a branch and bound type optimization technique to determine the minimum loss configuration. In this method, all network switches are first closed to form a meshed network. The switches are then opened successively to restore radial configuration. Based on the method of Merlin and Back [2], a heuristic algorithm has been suggested by Shirmohammadi and Hong [3]. Here also, the solution procedure starts by closing all the network switches which are then opened one after another so as to establish the optimum flow pattern in the network. Many approximations of the method of Merlin and Back have been overcome in this algorithm. Borozan et al. [4] have presented a network reconfiguration technique similar to that of Shirmohammadi and Hong [3]. However, their methodology contains three main parts: real time load estimation, effective determination of power loss configuration and cost/benefit evaluation. Civanlar et al. [5] made use solely of heuristics to determine a distribution system configuration, which would reduce line losses. Civanlar et al. made use of what is known as a ‘branch exchange’ operation for switching operations: the opening of any switch was required to correspond to the closure of another switch, ensuring that the radial nature of the distribution system would be preserved. Baran and Wu [6] have made an attempt to improve the method of Civanlar et al. [5] by introducing two approximation formulas for power flow in the transfer of system loads. The power flow equations used by Baran and Wu [6] were defined by recursive approximation of P, Q and V at each node. Kashem et al. [7] have proposed a branch exchange method for network reconfiguration. This is basically an extensive search method and need to consider all the tie-switches. Chen and Cho [8] have performed an analysis of an hourly reconfiguration schedule. They have studied the hourly load patterns over an interval of a year in order to define the hourly load conditions for each season. They have used branch and bound technique for obtaining minimum loss configuration. Nara et al. [9] have proposed a method of distribution system reconfiguration for reduction of real power loss using genetic algorithm. Lin et al. [10] have applied refined genetic algorithm to network reconfiguration problem for reduction of resistive line losses. In this method, the authors have refined the conventional crossover and mutation scheme by a competition mechanism to avoid premature convergence. Huang [11] has proposed one genetic algorithm based fuzzy approach for network reconfiguration of distribution system. Although the researchers [9], [10], [11] have demonstrated the effectiveness of genetic algorithm for network reconfiguration but solution time is highly prohibitive. Lin and Chin [12], [13] have presented an algorithm for distribution feeder reconfiguration. They have used voltage index, ohmic index and decision index to determining the switching operation. Huang and Chin [14] have proposed an algorithm based on fuzzy operation to deal with the feeder reconfiguration problem. Their approach tries to minimize power loss and acquire the load balance at the same time. Liu et al. [15], Jung et al. [16] and Auguliaro et al. [17] have proposed artificial intelligence based applications in a minimum loss configuration. Hsiao [18] has proposed fuzzy multi-objective based evolution programming method for network reconfiguration. In this method, objective function has been formulated using fuzzy min–max principle.

In the light of the above developments, this work formulates the network reconfiguration problem as a multiple objectives problem subject to operational and electric constraints. The problem formulation proposed herein consider four different objectives related to:

1.
minimization of the system's power loss
2.
minimization of the deviation of nodes voltage
3.
minimization of the current constraint violation
4.
load balancing among various feeders.

At the same time, a radial network structure must remain after network reconfiguration in which all loads must be energized. These four objectives are modeled with fuzzy sets to evaluate their imprecise nature. Heuristic rules are also incorporated in the proposed algorithm for minimizing the number of tie-switch operations.

Section snippets

Optimization in fuzzy environment

In fuzzy domain, each objective is associated with a membership function. The membership function indicates the degree of satisfaction of the objective. In the crisp domain, either the objective is satisfied or it is violated, implying membership values of unity and zero, respectively. On the contrary, fuzzy sets entertain varying degrees of membership function values from zero to unity. Thus, fuzzy set theory is an extension of standard set theory [19].

When there are multiple objectives to be

Membership function for real power loss reduction (μL_i)

Let us define $x_{i} = \frac{PLOSS (i)}{{PLOSS}^{0}}, for i = 1, 2, \dots, N_{k}$ Eq. (1) indicates that if x_i is high, power loss reduction is low and if x_i is low, power loss reduction is high.

Membership function for real power loss reduction is given in Fig. 1. From Fig. 1, μL_i can be written as: $μ L_{i} = {\begin{array}{l} \frac{(x_{\max} - x_{i})}{(x_{\max} - x_{\min})} & for x_{\min} < x_{i} < x_{\max} \\ 1 & for x_{i} \leq x_{\min} \\ 0 & for x_{i} \geq x_{\max} \end{array}$

In the present work, it has been assumed that x_min=0.5 and x_max=1.0.

Membership function for maximum node voltage deviation (μV_i)

Basic purpose of this membership function is that the deviation of nodes voltage should be less.

Let us define $y_{i} = \max | V_{S} - V_{i, j} |, for i = 1, 2, \dots, N_{k}; j = 1, 2, \dots,NB$

If maximum value of nodes voltage deviation is less, then a higher membership value is assigned and if deviation is more, then a lower membership value is assigned.

Fig. 2 shows the membership function for maximum node voltage deviation. From Fig. 2, we can write $μ V_{i} = {\begin{array}{l} \frac{(y_{\max} - y_{i})}{(y_{\max} - y_{\min})} & for y_{\min} < y_{i} < y_{\max} \\ 1 & for y_{i} \leq y_{\min} \\ 0.0 & for y_{i} \geq y_{\max} \end{array}$

In the present work, y_min

Membership function for maximum branch current loading index (μA_i)

Basic purpose for this membership function is that to minimize the branch current constraint violation. Let us define $Branch current loading index = \frac{| I (i, m) |}{I_{c} (m)}, for i = 1, 2, \dots, N_{k}; m = 1, 2, \dots,LN$ when maximum value of branch current loading index exceeds unity, membership value will be lower and as long as it is less than or equal to unity, membership value will be maximum, i.e. unity. Let us define $z_{i} = \max (\frac{| I (i, m) |}{I_{c} (m)}), for i = 1, 2, \dots, N_{k}; m = 1, 2, \dots,LN$

Membership function for maximum branch current loading index is

Membership function for feeder load balancing (μB_i)

Load balancing is one of the major objectives of network reconfiguration. An effective strategy to increase the loading margin of heavily loaded feeders is to transfer part of their loads to lightly loaded feeders. Feeder load balancing index may be given as $F_{i, j} = \frac{({IF}_{i, j} - {IF}_{i}^{avg})}{{IF}_{i}^{avg}} for i = 1, 2, \dots, N_{k}; j = 1, 2, \dots,NF$ where ${IF}_{i}^{avg} = \frac{1}{NF} \sum_{j = 1}^{NF} {IF}_{i, j}$

Let us define $u_{i} = \max | F_{i, j} |, for i = 1, 2, \dots, N_{k}; j = 1, 2, \dots,NF$ Eq. (10) indicates that a better load balancing can be achieved if the value of u_i is low. Therefore, for lower u_i,

Fuzzy multi-objective formulation

The four objectives described in the previous sections are first fuzzified, and then, dealt with by integrating them into a fuzzy satisfaction objective function J through appropriate weighting factors as given below: $Max J_{i} = W_{1} μ µ L_{i} + W_{2} μ µ V_{i} + W_{3} μ µ A_{i} + W_{4} μ µ B_{i}, for i = 1, 2, \dots, N_{k}$

The proper weighting factors used are W₁=W₂=W₃=W₄=0.25 in which these four objectives are assumed to be equally important. The weighting factors can be varied according to the preferences of different operators.

Heuristic rules for minimizing the number of tie-switch operations

The optimal switching strategies for network reconfiguration proposed by most of the researchers need to consider every candidate switch to evaluate the effectiveness of loss reduction and extensive numerical computation is often required. In the present paper, heuristic rules are considered which minimize the number of tie-switch operations. These heuristic rules are explained below.

In the first iteration, compute the voltage difference across all the open tie-switches and detect the open

Explanation of the proposed method

For the purpose of explanation, consider the sample radial distribution system as shown in Fig. 5. It is assumed that every branch has a sectionalizing switch. This system has four tie-branches and four tie-switches (Fig. 5). Initially, run the load flow program for radial distribution networks. Now compute the voltage difference across all the open tie-switches and detect the open tie-switch across which the voltage difference is maximum. Say, out of these four open tie-switches, voltage

Example

The tested system is a 11 kV radial distribution system having two substations, four feeders, 70 nodes and 78 branches (including tie-branches) as shown in Fig. 11. Tie-switches of this system are open in normal condition. Data for this system are given in Appendix A. The proposed method has been implemented on Pentium IV computer.

Before network reconfiguration, total real power loss of this system is 337.45 kW and minimum voltage is V_min=V₆₇=0.88389 p.u.

Fig. 12 shows the final radial

Conclusions

In the present work, an algorithm based on heuristic rules and fuzzy multi-objective approach has been proposed to solve the network reconfiguration problem in a radial distribution system. The objectives considered attempt to maximize the fuzzy satisfaction of the load balancing among the feeders, minimization of power loss, deviation of nodes voltage and branch current constraint violation subject to radial network structure in which all loads must be energized. Another advantage of the

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Reconfiguration of distribution system using fuzzy multi-objective approach

Abstract

Introduction

Section snippets

Optimization in fuzzy environment

Membership function for real power loss reduction (μLi)

Membership function for maximum node voltage deviation (μVi)

Membership function for maximum branch current loading index (μAi)

Membership function for feeder load balancing (μBi)

Fuzzy multi-objective formulation

Heuristic rules for minimizing the number of tie-switch operations

Explanation of the proposed method

Example

Conclusions

Electr Power Syst Res

Int J Electr Power Energy Syst

Inf Control

Reconfiguration for electric distribution networks for resistive line loss reduction

IEEE Trans Power Deliv

Improved method for loss minimization in distribution networks

IEEE Trans Power Syst

Distribution feeder reconfiguration for loss reduction

IEEE Trans Power Deliv

Network reconfiguration in distribution systems for loss reduction and load balancing

IEEE Trans Power Deliv

Network reconfiguration for enhancement of voltage stability in distribution networks

IEE Proc Gener Transm Distrib

Energy loss reduction by critical switches

IEEE Trans Power Deliv

Membership function for real power loss reduction (μL_i)

Membership function for maximum node voltage deviation (μV_i)

Membership function for maximum branch current loading index (μA_i)

Membership function for feeder load balancing (μB_i)