Kwang Y. Lee

A particle swarm optimization for economic dispatch with nonsmooth cost functions

This work presents a new approach to economic dispatch (ED) problems with nonsmooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. A modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. A constraint treatment mechanism is devised in such a way that the dynamic process inherent in the conventional PSO is preserved. Moreover, a dynamic search-space reduction strategy is devised to accelerate the optimization process. To show its efficiency and effectiveness, the proposed MPSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost functions considering valve-point effects and multi-fuel problems. The results of the MPSO are compared with the results of conventional numerical methods, Tabu search method, evolutionary programming approaches, genetic algorithm, and modified Hopfield neural network approaches.

Diagonal recurrent neural networks for dynamic systems control

A new neural paradigm called diagonal recurrent neural network (DRNN) is presented. The architecture of DRNN is a modified model of the fully connected recurrent neural network with one hidden layer, and the hidden layer comprises self-recurrent neurons. Two DRNNs are utilized in a control system, one as an identifier called diagonal recurrent neuroidentifier (DRNI) and the other as a controller called diagonal recurrent neurocontroller (DRNC). A controlled plant is identified by the DRNI, which then provides the sensitivity information of the plant to the DRNC. A generalized dynamic backpropagation algorithm (DBP) is developed and used to train both DRNC and DRNI. Due to the recurrence, the DRNN can capture the dynamic behavior of a system. To guarantee convergence and for faster learning, an approach that uses adaptive learning rates is developed by introducing a Lyapunov function. Convergence theorems for the adaptive backpropagation algorithms are developed for both DRNI and DRNC. The proposed DRNN paradigm is applied to numerical problems and the simulation results are included.

Short-term load forecasting using an artificial neural network

This paper presents a new neural network training algorithm which reduces the required training time considerably and overcomes many of the shortcomings presented by the conventional back-propagation algorithm. The algorithm uses a modified form of the back-propagation algorithm to minimize the mean squared error between the desired and actual outputs with respect to the inputs to the nonlinearities. Artificial Neural Network (ANN) model using the new algorithm is applied to forecast the short-term electric load. Inputs to the ANN are past loads and the output of the ANN is the hourly load forecast for a given day.

A United Approach to Optimal Real and Reactive Power Dispatch

This paper presents a unified method for optimal real and reactive power dispatch for the economic operation of power systems. As in other methods, the problem is decomposed into a P-optimization module and a Q-optimization module, but in this method both modules use the same generation cost objective function. The control variables are generator real power outputs for the real power module; and generator reactive power outputs, shunt capacitors/reactors, and transformer tap settings for the reactive power module. The constraints are the operating limits of the control variables, power line flows, and bus voltages.

An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems

This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using an improved particle swarm optimization (IPSO). Although the particle swarm optimization (PSO) approaches have several advantages suitable to heavily constrained nonconvex optimization problems, they still can have the drawbacks such as local optimal trapping due to premature convergence (i.e., exploration problem), insufficient capability to find nearby extreme points (i.e., exploitation problem), and lack of efficient mechanism to treat the constraints (i.e., constraint handling problem). This paper proposes an improved PSO framework employing chaotic sequences combined with the conventional linearly decreasing inertia weights and adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. In addition, an effective constraint handling framework is employed for considering equality and inequality constraints. The proposed IPSO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones with ramp rate limits as well as transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. Also, the results are compared with those of the state-of-the-art methods.

Economic load dispatch for piecewise quadratic cost function using Hopfield neural network

The authors present a new method to solve the problem of economic power dispatch with piecewise quadratic cost function using the Hopfield neural network. Traditionally one convex cost function for each generator is assumed. However, it is more realistic to represent the cost function as a piecewise quadratic function rather than one convex function. In this study, multiple intersecting cost functions are used for each unit. Through case studies, the possibility of the application of the Hopfield neural network to the economic load dispatch problem with general nonconvex cost functions was shown. The proposed approach is much simpler and the results are very close to those of the numerical method. >

Adaptive Hopfield neural networks for economic load dispatch

A large number of iterations and oscillations are those of the major concern in solving the economic load dispatch problem using the Hopfield neural network. This paper develops two different methods, the slope adjustment and bias adjustment methods, in order to speed up the convergence of the Hopfield neural network system. Algorithms of economic load dispatch for piecewise quadratic cost functions using the Hopfield neural network have been developed for the two approaches. The results are compared with those of a numerical approach and the traditional Hopfield neural network approach. To guarantee and for faster convergence, adaptive learning rates are also developed by using energy functions and applied to the slope and bias adjustment methods. The results of the traditional, fixed learning rate and adaptive learning rate methods are compared in economic load dispatch problems.

Optimal reactive power planning using evolutionary algorithms: a comparative study for evolutionary programming, evolutionary strategy, genetic algorithm, and linear programming

This paper presents a comparative study for three evolutionary algorithms (EAs) to the optimal reactive power planning (ORPP) problem: evolutionary programming, evolutionary strategy, and genetic algorithm. The ORPP problem is decomposed into P- and Q-optimization modules, and each module is optimized by the EAs in an iterative manner to obtain the global solution. The EA methods for the ORPP problem are evaluated against the IEEE 30-bus system as a common testbed, and the results are compared against each other and with those of linear programming.

Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO

In this paper an improved coordinated aggregation-based particle swarm optimization (ICA-PSO) algorithm is introduced for solving the optimal economic load dispatch (ELD) problem in power systems. In the ICA-PSO algorithm each particle in the swarm retains a memory of its best position ever encountered, and is attracted only by other particles with better achievements than its own with the exception of the particle with the best achievement, which moves randomly. Moreover, the population size is increased adaptively, the number of search intervals for the particles is selected adaptively and the particles search the decision space with accuracy up to two digit points resulting in the improved convergence of the process. The ICA-PSO algorithm is tested on a number of power systems, including the systems with 6, 13, 15, and 40 generating units, the island power system of Crete in Greece and the Hellenic bulk power system, and is compared with other state-of-the-art heuristic optimization techniques (HOTs), demonstrating improved performance over them.

An efficient simulated annealing algorithm for network reconfiguration in large-scale distribution systems

This paper presents an efficient algorithm for loss minimization by using an automatic switching operation in large-scale distribution systems. Simulated annealing is particularly well suited for a large combinatorial optimization problem since it can avoid local minima by accepting improvements in cost. However, it often requires meaningful cooling schedule and a special strategy, which makes use of the property of distribution systems in finding the optimal solution. In this paper, we augment the cost function with the operation condition of distribution systems, improve the perturbation mechanism with system topology, and utilize the polynomial-time cooling schedule, which is based on the statistical calculation during the search. The validity and effectiveness of the proposed methodology is demonstrated in the Korea Electric Power Corporations distribution system.