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)

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

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

Interior point method for long-term generation scheduling of large-scale hydrothermal systems

This paper presents an interior point method for the long-term generation scheduling of large-scale hydrothermal systems. The problem is formulated as a nonlinear programming one due to the nonlinear representation of hydropower production and thermal fuel cost functions. Sparsity exploitation techniques and an heuristic procedure for computing the interior point method search directions have been developed. Numerical tests in case studies with systems of different dimensions and inflow scenarios have been carried out in order to evaluate the proposed method. Three systems were tested, with the largest being the Brazilian hydropower system with 74 hydro plants distributed in several cascades. Results show that the proposed method is an efficient and robust tool for solving the long-term generation scheduling 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.

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.

An adaptation of the dual-affine interior point method for the surface flatness problem

This paper presents an adaptation of the dual-affine interior point method for the surface flatness problem. In order to determine how flat a surface is, one should find two parallel planes so that the surface is between them and they are as close together as possible. This problem is equivalent to the problem of solving inconsistent linear systems in terms of Tchebyshev's norm. An algorithm is proposed and results are presented and compared with others published in the literature. (C) 2006 Elsevier B.V. All rights reserved.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um método eficiente para resolução do problema de Despacho Ótimo de Reativos com controle discreto do TAP dos transformadores

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

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)

Optimal reactive power flow via the modified barrier Lagrangian function approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

HOW TO EFFICIEN TLY INCORPORATE FACTS DEVICES IN OPTIMAL ACTIVE POWER FLOW MODEL

This paper presents for the first time how to easily incorporate facts devices in an optimal active power flow model such that an efficient interior-point method may be applied. The optimal active power flow model is based on a network flow approach instead of the traditional nodal formulation that allows the use of an efficiently predictor-corrector interior point method speed up by sparsity exploitation. The mathematical equivalence between the network flow and the nodal models is addressed, as well as the computational advantages of the former considering the solution by interior point methods. The adequacy of the network flow model for representing facts devices is presented and illustrated on a small 5-bus system. The model was implemented using Matlab and its performance was evaluated with the 3,397-bus and 4,075-branch Brazilian power system which show the robustness and efficiency of the formulation proposed. The numerical results also indicate an efficient tool for optimal active power flow that is suitable for incorporating facts devices.

Efficient heuristic algorithm used for optimal capacitor placement in distribution systems

An efficient heuristic algorithm is presented in this work in order to solve the optimal capacitor placement problem in radial distribution systems. The proposal uses the solution from the mathematical model after relaxing the integrality of the discrete variables as a strategy to identify the most attractive bus to add capacitors to each step of the heuristic algorithm. The relaxed mathematical model is a nonlinear programming problem and is solved using a specialized interior point method, The algorithm still incorporates an additional strategy of local search that enables the finding of a group of quality solutions after small alterations in the optimization strategy. Proposed solution methodology has been implemented and tested in known electric systems getting a satisfactory outcome compared with metaheuristic methods.The tests carried out in electric systems known in specialized literature reveal the satisfactory outcome of the proposed algorithm compared with metaheuristic methods. (C) 2009 Elsevier Ltd. All rights reserved.