Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Solving the multiobjective environmental/economic dispatch problem using weighted sum and ε-constraint strategies and a predictor-corrector primal-dual interior point method

This paper proposes a technique for solving the multiobjective environmental/economic dispatch problem using the weighted sum and ε-constraint strategies, which transform the problem into a set of single-objective problems. In the first strategy, the objective function is a weighted sum of the environmental and economic objective functions. The second strategy considers one of the objective functions: in this case, the environmental function, as a problem constraint, bounded above by a constant. A specific predictor-corrector primal-dual interior point method which uses the modified log barrier is proposed for solving the set of single-objective problems generated by such strategies. The purpose of the modified barrier approach is to solve the problem with relaxation of its original feasible region, enabling the method to be initialized with unfeasible points. The tests involving the proposed solution technique indicate i) the efficiency of the proposed method with respect to the initialization with unfeasible points, and ii) its ability to find a set of efficient solutions for the multiobjective environmental/economic dispatch problem.

Interior point algorithm for linear programming used in transmission network synthesis

This article presents a well-known interior point method (IPM) used to solve problems of linear programming that appear as sub-problems in the solution of the long-term transmission network expansion planning problem. The linear programming problem appears when the transportation model is used, and when there is the intention to solve the planning problem using a constructive heuristic algorithm (CHA), ora branch-and-bound algorithm. This paper shows the application of the IPM in a CHA. A good performance of the IPM was obtained, and then it can be used as tool inside algorithm, used to solve the planning problem. Illustrative tests are shown, using electrical systems known in the specialized literature. (C) 2005 Elsevier B.V. All rights reserved.

Um método previsor-corretor primal-dual de pontos interiores barreira logarítmica modificada, com estratégias de convergência global e de ajuste cúbico, para problemas de programação não-linear e não-convexa

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Procedimento híbrido envolvendo os métodos primal-dual de pontos interiores e branch and bound em problemas multiobjetivo de aproveitamento de resíduos de cana-de-açúcar

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Método previsor-corretor primal-dual de pontos interiores em problemas multiobjetivo de despacho econômico e ambiental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reactive power dispatch and planning using a non-linear branch-and-bound algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Interior-exterior point method with global convergence strategy for solving the reactive optimal power flow problem

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.

Combined Pool/Bilateral Short-Term Hydrothermal Scheduling Model for Day-Ahead Energy Markets

This paper proposes a combined pool/bilateral short term hydrothermal scheduling model (PDC) for the context of the day-ahead energy markets. Some innovative aspects are introduced in the model, such as: i) the hydraulic generation is optimized through the opportunity cost function proposed; ii) there is no decoupling between physical and commercial dispatches, as is the case today in Brazil; iii) interrelationships between pool and bilateral markets are represented through a single optimization problem; iv) risk exposures related to future deficits are intrinsically mitigated; v) the model calculates spot prices in an hourly basis and the results show a coherent correlation between hydrological conditions and calculated prices. The proposed PDC model is solved by a primal-dual interior point method and is evaluated by simulations involving a test system. The results are focused on sensitivity analyses involving the parameters of the model, in such a way to emphasize its main modeling aspects. The results show that the proposed PDC provides a conceptual means for short term price formation for hydrothermal systems.

Métodos híbridos de pontos interiores e de programação inteira 0-1 para problemas de custo de colheita da cana-de-açúcar e de custo de coleta e geração de energia relacionados à sua biomassa

Pós-graduação em Engenharia Elétrica - FEB

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

Security constrained optimal active power flow via network model and interior point method

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Método primal-dual previsor-corretor de pontos interiores e exteriores com estratégias de correção de inércia e suavização hiperbólica aplicado ao problema de despacho econômico com ponto de carregamento de válvula e representação da transmissão

Pós-graduação em Engenharia Elétrica - FEB

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)