The loss minimum reconfiguration problem in the open loop radial distribution system is basically one of complex combinatorial optimization, since the normal open sectionalizing switches must be determined appropriately. The genetic algorithm was successfully applied to the loss minimum reconfiguration problem. In the proposed algorithm, strings consist of sectionalizing switch status or radial configurations, and the fitness function consists of the total system losses and penalty value of voltage drop and current capacity violations. The loss minimum reconfiguration problem is formulated as a mixed integer programming problem. The essential components of the genetic algorithm are briefly described. A detailed solution methodology by the use of genetic algorithm is outlined. Numerical examples demonstrate the validity and effectiveness of the proposed methodology. >

Implementation of genetic algorithm for distribution systems loss minimum re-configuration

An improved TS algorithm for loss-minimum reconfiguration in large-scale distribution systems

This paper proposes a mixed-integer conic programming formulation for the minimum loss distribution network reconfiguration problem. This formulation has two features: first, it employs a convex representation of the network model which is based on the conic quadratic format of the power flow equations and second, it optimizes the exact value of the network losses. The use of a convex model in terms of the continuous variables is particularly important because it ensures that an optimal solution obtained by a branch-and-cut algorithm for mixed-integer conic programming is global. In addition, good quality solutions with a relaxed optimality gap can be very efficiently obtained. A polyhedral approximation which is amenable to solution via more widely available mixed-integer linear programming software is also presented. Numerical results on practical test networks including distributed generation show that mixed-integer convex optimization is an effective tool for network reconfiguration.

Minimum Loss Network Reconfiguration Using Mixed-Integer Convex Programming

Recently, integration of distributed generation (DG) in distribution systems has increased to high penetration levels. The impact of DG units on the voltage stability margins has become significant. Optimization techniques are tools which can be used to locate and size the DG units in the system, so as to utilize these units optimally within certain limits and constraints. Thus, the impacts of DG units issues, such as voltage stability and voltage profile, can be analyzed effectively. The ultimate goal of this paper is to propose a method of locating and sizing DG units so as to improve the voltage stability margin. The load and renewable DG generation probabilistic nature are considered in this study. The proposed method starts by selecting candidate buses into which to install the DG units on the system, prioritizing buses which are sensitive to voltage profile and thus improve the voltage stability margin. The DG units' placement and sizing is formulated using mixed-integer nonlinear programming, with an objective function of improving the stability margin; the constraints are the system voltage limits, feeders' capacity, and the DG penetration level.

Optimal Placement and Sizing Method to Improve the Voltage Stability Margin in a Distribution System Using Distributed Generation

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

A fuzzy multiobjective approach for network reconfiguration of distribution systems

Using a two-stage solution methodology and a modified simulated annealing technique, the authors develop a solution algorithm to the network reconfiguration problem, which is a constrained, multiobjective, nondifferentiable, optimization problem. This solution algorithm allows the designer to obtain a desirable, global noninferior point in a reasonable computation time. Also, given a desired number of switch-on/switch-off operations involved in the network configuration, the solution algorithm can identify the most effective operations. In order to reduce the computation time required, the idea of approximate calculations is explored and incorporated into the solution algorithm, where two efficient load-flow methods are employed; one for high temperature and the other for low temperature. The solution algorithm has been implemented in a software package and tested on a 69-bus system with very promising results. >

Optimal network reconfigurations in distribution systems. II. Solution algorithms and numerical results

A new formulation of the network reconfiguration problem for both loss reduction and load balancing that takes into consideration load constraints and operational constraints is presented. The number of switch-on/switch-off operations involved in network reconfiguration is put into a constraint. The new formulation is a constrained, multiobjective and nondifferential optimization problem with both equality and inequality constraints. A two-stage solution methodology based on a modified simulated annealing technique and the epsilon -constraint method for general multiobjective optimization problems is developed. A salient feature of the solution methodology is that it allows designers to find a desirable, global noninferior solution for the problem. An effective scheme to speed up the solution methodology is presented and analyzed. >

Optimal network reconfigurations in distribution systems. I. A new formulation and a solution methodology

Voltage collapse is generally caused by either of two types of power system disturbances: load variations; and contingencies. A number of performance indices intended to measure the severity of the voltage collapse problem have been proposed in the literature. However, few of these performance indices can answer questions such as: "can the system withstand another 100 MVar increase on bus 11?" This paper presents a new performance index that provides a direct relationship between its value and the amount of load demand that the system can withstand before collapse. One of the features that distinguishes the proposed performance is its development in the load-demand space and its ability to answer questions such as: "can the system withstand a simultaneous increase of 70 MW on bus 2 and 50 MVAr on bus 6?" This feature makes the performance index readily interpretable to operators. Moreover, the computation involved in the proposed performance index is relatively inexpensive in comparison with those required in existing solutions. Simulation results on the IEEE 39-bus system and a 234-bus power system are presented with promising results. >

Toward a practical performance index for predicting voltage collapse in electric power systems

This paper presents a more efficient formulation for computation of the maximum loading points of power systems. A distinguishing feature of the new formulation is that it is of dimension (n+1), instead of the existing formulation of dimension (2n+1), for n-dimensional load flow equations. This feature makes computation of the maximum loading points very inexpensive in comparison with those required in the existing formulation. A theoretical basis for the new formulation is provided. The new problem formulation is derived by using a simple reparameterization scheme and exploiting the special properties of the power flow model. Moreover, the proposed test function is shown to be monotonic in the vicinity of a maximum loading point. Therefore, it allows one to monitor the approach to maximum loading points during the solution search process. Simulation results on a 234-bus power system are presented. >

A more efficient formulation for computation of the maximum loading points in electric power systems

Given a nonlinear system of equations with or without varying parameters, the authors present a technique to solve the convergence problem at singular or near-singular roots of the system. A theoretical basis stemming from bifurcation theory for the proposed technique is given. Special attention is given to saddle-note bifurcation points (nose points) as found in power system applications. It is also shown that a previous method of solving ill-conditioning load flow solutions falls into the framework presented and is thereby theoretically justified. An efficient computational procedure is developed to solve ill-conditioning load flow solutions. It has the following features: it locally removes the singularity of the corresponding Jacobian; it only requires a simple modification of the standard load flow equations, with no added dimension; it adds just a few nonzero elements to the sparse Jacobian matrix of the load flow equations; and it enlarges the region of convergence around singular solutions. This method achieves its simplicity and efficiency by exploiting the special properties of linear parameter-dependence in load flow equations. Applications to compute nose points of power flow equations are demonstrated and were simulated on a practical power system. >

R. Jean-Jumeau

Papers

Optimal network reconfigurations in distribution systems. II. Solution algorithms and numerical results

Optimal network reconfigurations in distribution systems. I. A new formulation and a solution methodology

Toward a practical performance index for predicting voltage collapse in electric power systems

A more efficient formulation for computation of the maximum loading points in electric power systems

Parameterizations of the load-flow equations for eliminating ill-conditioning load flow solutions