Aurelio Ribeiro Leite de Oliveira

Optimal active power dispatch combining network flow and interior point approaches

In this paper, the optimal active power dispatch 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 is possible to reduce the linear system either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored offline. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved; its size, however, reduces to the number of generating units. These methods were applied to IEEE and Brazilian power systems and the numerical results were obtained using a C implementation. Both interior point methods proved to be robust and achieved fast convergence in all instances tested.

Using a hybrid preconditioner for solving large-scale linear systems arising from interior point methods

Abstract We devise a hybrid approach for solving linear systems arising from interior point methods applied to linear programming problems. These systems are solved by preconditioned conjugate gradient method that works in two phases. During phase I it uses a kind of incomplete Cholesky preconditioner such that fill-in can be controlled in terms of available memory. As the optimal solution of the problem is approached, the linear systems becomes highly ill-conditioned and the method changes to phase II. In this phase a preconditioner based on the LU factorization is found to work better near a solution of the LP problem. The numerical experiments reveal that the iterative hybrid approach works better than Cholesky factorization on some classes of large-scale problems.

A note on hybrid preconditioners for large-scale normal equations arising from interior-point methods

A previously developed approach for solving linear systems arising from interior-point methods applied to linear programming problems is considered and improved upon. The preconditioned conjugate gradient method is used to solve these systems in two different phases of the interior-point method: during the initial interior-point iterations, an incomplete Cholesky factorization preconditioner with controlled fill-in is used; in the second phase, near the optimal solution, a specialized preconditioner based upon the LU factorization is used to combat the high ill-conditioning of the linear systems in this phase. This approach works better than direct methods on some classes of large-scale problems. New heuristics are presented to identify the change of phases, thus achieving better computational results and solving additional problems. Moreover, new orderings of the constraint matrix columns are presented allowing savings in the preconditioned conjugate gradient method iteration number. Experiments are performed with a set of large-scale problems and both approaches are compared with respect to the number of iterations and running time.

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.

Métodos de pontos interiores para problema de fluxo de potência ótimo DC

The primal-dual and predictor-corrector versions of interior point methods are developed for an optimal DC power flow model where Kirchhoff laws are represented by a network flow model with surrogate constraints. The resulting matrix structure is explored reducing the linear system to be solved either to the number of buses or to the number of independent loops, leading to very fast iterations. 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 must be solved; its size, however, reduces to the number of generating units. Numerical results with C implementation are presented for IEEE test systems and large scale Brazilian systems. The interior point method shows to be robust, achieving fast convergence in all instances tested.

Improving an interior-point approach for large block-angular problems by hybrid preconditioners

The computational time required by interior-point methods is often dominated by the solution of linear systems of equations. An efficient specialized interior-point algorithm for primal block-angular problems has been used to solve these systems by combining Cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constraints. In some problems this power series preconditioner resulted to be inefficient on the last interior-point iterations, when the systems became ill-conditioned. In this work this approach is combined with a splitting preconditioner based on LU factorization, which works well for the last interior-point iterations. Computational results are provided for three classes of problems: multicommodity flows (oriented and nonoriented), minimum-distance controlled tabular adjustment for statistical data protection, and the minimum congestion problem. The results show that, in most cases, the hybrid preconditioner improves the performance and robustness of the interior-point solver. In particular, for some block-angular problems the solution time is reduced by a factor of 10.

Efficient implementation and benchmark of interior point methods for the polynomial L 1 fitting problem

Abstract Interior point methods specialized to the L 1 fitting problem are surveyed and the affine-scaling primal method is presented. Their main features are highlighted and improvements are proposed for polynomial fitting problems. For such problems, a careful handling of data avoids storing of matrices for the interior point approaches. Moreover, the computational complexity of iterations is reduced. An inexpensive way to compute a basic solution, using interpolation, is also provided. Extensive numerical experiments are carried out, including comparisons with a specialized simplex method. In general, the interior point methods performed better than the simplex approach. Among the interior point methods investigated, the dual affine scaling version was the most efficient.

Hopfield neural networks in large-scale linear optimization problems

Abstract Hopfield neural networks and affine scaling interior point methods are combined in a hybrid approach for solving linear optimization problems. The Hopfield networks perform the early stages of the optimization procedures, providing enhanced feasible starting points for both primal and dual affine scaling interior point methods, thus facilitating the steps towards optimality. The hybrid approach is applied to a set of real world linear programming problems. The results show the potential of the integrated approach, indicating that the combination of neural networks and affine scaling interior point methods can be a good alternative to obtain solutions for large-scale optimization problems.

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

ABSTRACT This paper presents a new formulation for the security con-strained optimal active power flow problem which enablesthe representation of three basic constraints: branch outage,generator outage and multiple equipment congestion. It con-sists of a network model with additional linear equality andinequalityconstraintsandquadraticseparableobjectivefunc-tion, which is efficiently solved by a predictor-correctorinte-rior point method. Sparsity techniques are used to exploit thematricial structure of the problem.Case studies with a 3,535-bus and a 4,238-branchBrazilian power system are presentedand discussed, to demonstrate that the proposed model canbe efficiently solved by an interior point method, providingsecurity constrained solutions in a reasonable time. Artigo submetido em 04/06/2008 (Id.: 00877)Revisado em 10/10/2008, 28/01/2009Aceito sob recomendacao do Editor Associado Prof. Eduardo N. Asada KEYWORDS :Security,activepowerdispatch,optimalpowerflow, network model, power flow controls, interior pointmethod

Primal-Dual Interior Point Method Applied to the Short Term Hydroelectric Scheduling Including a Perturbing Parameter

In this work, the primal-dual interior point method is studied and developed to solve the predispatch DC (direct current) problem that minimizes losses in the transmission and costs in the generation of a hydroelectric power system, formulated as a network flow model. The matrix obtained by the application of the interior point method is reduced of such form that the final linear system can be implemented of efficient form. Moreover, a modification of this method is made on the basis of a heuristic that determines a new perturbing parameter. This modified method(VPMPD) showed to be efficient in the practical and achieved convergence in fewer iterations when compared with an existing implementation of the network flow model, that does not take in consideration such perturbing parameter.