Piecewise Quadratic Cost Functions Research Articles

03/02630 Economic dispatch solutions with piecewise quadratic cost functions using improved genetic algorithm: Won, J-.R. and Park, Y.-M. International Journal of Electrical Power & Energy Systems, 2003, 25, (5), 355–361

03/02630 Economic dispatch solutions with piecewise quadratic cost functions using improved genetic algorithm: Won, J-.R. and Park, Y.-M. International Journal of Electrical Power & Energy Systems, 2003, 25, (5), 355–361

Economic dispatch solutions with piecewise quadratic cost functions using improved genetic algorithm

This paper presents economic dispatch (ED) solutions with piecewise quadratic cost functions using improved genetic algorithm (GA). GA is a searching or optimizing algorithm based on natural evolution principle. GA has demonstrated considerable success in providing good solutions to many nonlinear optimization problems. This paper proposes two methods in order to improve effectiveness of GA. The first is multi-stage algorithm. The second is the directional crossover. Projection method is introduced to satisfy a linear equality constraint from power balance. In case studies, these algorithms are tested for 6-generator system considering line losses, and 10-generator system with piecewise quadratic cost functions. Results are compared with the solutions of conventional methods.

An enhanced Lagrangian neural network for the ELD problems with piecewise quadratic cost functions and nonlinear constraints

This paper presents a new Lagrangian artificial neural network (ANN) and its application to the power system economic load dispatch (ELD) problems with piecewise quadratic cost functions (PQCFs) and nonlinear constraints. By restructuring the dynamics of the modified Lagrangian ANN [IEEE ICNN, 1 (1996) 537], stable convergence characteristics are obtained even with the nonlinear constraints. The convergence speeds are enhanced by employing the momentum technique and providing a criteria for choosing the learning rate parameters. Instead of having one convex cost function for each unit, which is normally the case in typical ELD problem formulations, more realistic multiple quadratic cost functions are used to reflect the effects of valve point loadings and possible fuel changes. In addition, the B matrix approach is employed for more accurate estimation of the transmission losses than treating them as a constant, which necessitate the inclusion of a nonlinear equality constraint. The effectiveness of the proposed ANN applied to the ELD problem is demonstrated through extensive simulation tests.

Evolutionary programming‐based economic dispatch for units with multiple fuel options

AbstractThis paper presents the application of evolutionary programming (EP) to economic dispatch of generators having piecewise quadratic cost functions. The proposed EP algorithm always determines the global or near global optimum without any restrictions on the shape of the cost functions. The method is applied to an example system with piecewise cost functions and the results are compared with those of the recent adaptive Hopfield neural network method. The test results prove that the EP method is simpler and more efficient for solving economic dispatch (ED) problems with multiple cost curves than many existing techniques.

Piecewise linear quadratic optimal control

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy.

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.

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. >

Hierarchical Economic Dispatch for Piecewise Quadratic Cost Functions

This paper presents a method to solve the economic power dispatch problem with piecewise quadratic cost functions. The solution approach is hierarchical, which allows for decentral i zed computations. An advantage of this approach is the capability to optimize over a greater variety of operating conditions. Traditionally, one cost function for each generator is assumed. In this formulation multiple intersecting cost functions are assumed. This method has appl ication to fossil generation units capable of burning gas and oil , as well as other problems which result in multiple intersecting cost curves for a particular unit. The results show that the solution method is practical and valid for real-time application. The motivation for this research stems from the actual operational and planning problems of a large Southwestern Utility.