Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the curse of dimensionality, heuristics-based swarm intelligence can be an efficient alternative. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. This paper presents a detailed overview of the basic concepts of PSO and its variants. Also, it provides a comprehensive survey on the power system applications that have benefited from the powerful nature of PSO as an optimization technique. For each application, technical details that are required for applying PSO, such as its type, particle formulation (solution representation), and the most efficient fitness functions are also discussed.

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Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems

A capacitor sizing problem for capacitors placed on a radial distribution system is formulated as a nonlinear programming problem, and a solution algorithm is developed. The object is to find the optimal size of the capacitors so that the power losses will be minimized for a given load profile while considering the cost of the capacitors. The formulation also incorporates the AC power flow model for the system and the voltage constraints. The solution algorithm developed for the capacitor sizing problem is based on a Phase I-Phase II feasible directions approach. Novel power flow equations and a solution method, called DistFlow, for radial distribution systems are introduced. The method is computationally efficient and numerically robust, especially for distribution systems with large r/x ratio branches. DistFlow is used repeatedly as a subroutine in the optimization algorithm for the capacitor sizing problem. The test results for the algorithm indicate that the method is computationally efficient and has good convergence characteristics. >

Optimal sizing of capacitors placed on a radial distribution system

Optimal power flow using particle swarm optimization

The authors describe a heuristic method for the reconfiguration of distribution networks in order to reduce their resistive line losses under normal operating conditions. The proposed approach is characterized by convergence to the optimum or a near-optimum solution and the independence of the final solution from the initial status of the network switches. The methodology has been implemented in a production-grade computer program, DISTOP (Distribution Network Optimization). The compensation-based power flow technique developed at Pacific Gas and Electric Company for the efficient solution of weakly meshed distribution networks is an essential part of this loss reduction methodology. Important implementation aspects of the methodology and the results of its application to several realistic distribution networks are presented. Numerous test results have indicated that the proposed technique is computationally robust and efficient and, hence, suitable for both planning and operations studies. >

Reconfiguration of electric distribution networks for resistive line losses reduction

A direct approach for unbalanced three-phase distribution load flow solutions is proposed in this paper. The special topological characteristics of distribution networks have been fully utilized to make the direct solution possible. Two developed matrices-the bus-injection to branch-current matrix and the branch-current to bus-voltage matrix-and a simple matrix multiplication are used to obtain load flow solutions. Due to the distinctive solution techniques of the proposed method, the time-consuming LU decomposition and forward/backward substitution of the Jacobian matrix or Y admittance matrix required in the traditional load flow methods are no longer necessary. Therefore, the proposed method is robust and time-efficient. Test results demonstrate the validity of the proposed method. The proposed method shows great potential to be used in distribution automation applications.

A direct approach for distribution system load flow solutions

A power flow method is described for solving weakly meshed distribution and transmission networks, using a multiport compensation technique and basic formations of Kirchoff's laws. This method has excellent convergence characteristics and is robust. A computer program implementing this scheme was developed and successfully applied to several practical distribution and transmission networks with radial and weakly meshed structures. The method can be applied to the solution of both the three-phase (unbalanced) and single-phase (balanced) representation of the network, however, only the single-phase representation is treated in detail. >

A compensation-based power flow method for weakly meshed distribution and transmission networks

An efficient method for calculating the load flow solution of weakly meshed transmission and distribution systems is presented. Its essential advantages over a previous approach are the following: (1) It uses active and reactive powers as flow variables rather than complex currents, thus simplifying the treatment of P, V buses and reducing the related computational effort to half; (2) It uses an efficient tree-labeling technique which also contributes to the computational efficiency of the procedure; (3) It uses an improved solution strategy, thereby reducing the burden of mismatch calculations which is an important component of the solution process. Results of tests with 30, 243, 1380, and 4130 bus systems are given to illustrate the performance of the proposed method. >

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Efficient load flow for large weakly meshed networks

The author's consider a new formulation of optimal power flow (OPF) that makes it eminently suitable for accurate incremental modeling. G. Zoutendijk's method of feasible directions (1960) for solving the nonlinear programming problems is adapted for the solution of the OPF. Hydraulic modeling of systems with a considerable share of hydraulic generation is considered. The method is very efficient as it is designed to exploit the special structure of the problem. >

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Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology

An efficient method is described for the solution of the short-term hydro-thermal dispatch problem including optimal power flow (OPF) as the mathematical model of the thermal subsystem. This approach has the capability of taking into account the following effects: coupling of cascaded multichannel reservoirs, water time delays, reservoir head variations, load flow, and other constraints due to security and environmental considerations. The problem is decomposed into hydro and thermal subproblems which are then solved iteratively. An effective adjustment has been proposed to take into account the nonlinear relation between the two subproblems to speed up the convergence of the iterative process. In this adjustment, as well as in solving the thermal subproblem, equations of coordination and OPF are combined for better computational efficiency. On the basis of the proposed approach, four different methods, which differ in the degree of details in modeling the thermal system, have been tested and investigated. Numerical examples are included to demonstrate the advantages of the approach. >

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G. X. Luo

Papers

A compensation-based power flow method for weakly meshed distribution and transmission networks

Efficient load flow for large weakly meshed networks

Hydrothermal optimal power flow based on a combined linear and nonlinear programming methodology

Short-term hydro-thermal dispatch detailed model and solutions