ABSTRACT Interior point methods have been widely used to determine the solution of large-scale linear programming problems. The predictor-corrector method stands out among all variations of interior point methods due to its efficiency and fast convergence. In each iteration it is necessary to solve two linear systems to determine the predictor-corrector direction. Solving such systems corresponds to the step which requires more processing time, and therefore, it should be done efficiently. The most common approach to solve them is the Cholesky factorization. However, Cholesky factorization demands a high computational effort in each iteration. Thus, searching for effort reduction, the continued iteration is proposed. This technique consists in determining a new direction through projection of the search direction and it was inserted into PCx code. The computational results regarding medium and large-scale problems, have indicated a good performance of the proposed approach in comparison with the predictor-corrector method.

Este trabalho apresenta uma nova formulação do problema de fluxo de potência ótimo corrente contínua com restrições de segurança de três tipos: perda de ramo, perda de gerador e múltiplas perdas. A formulação emprega um modelo de fluxo em redes com restrições adicionais de igualdade e desigualdade e função objetivo quadrática separável que é eficientemente resolvido por um método de pontos interiores preditor-corretor. Técnicas de esparsidade são utilizadas para explorar a estrutura matricial do problema. Estudos de caso para o Sistema Interligado Nacional com 3535 barras e 4238 ramos são apresentados e discutidos, a fim de demonstrar que o modelo proposto pode ser resolvido através de um método de pontos interiores de maneira eficiente, fornecendo soluções que respeitam as restrições de segurança em um tempo computacional razoável.

This paper presents a new formulation for the security constrained optimal active power flow problem which enables the representation of three basic constraints: branch outage, generator outage and multiple equipment congestion. It consists of a network model with additional linear equality and inequality constraints and quadratic separable objective function, which is efficiently solved by a predictor-corrector interior point method. Sparsity techniques are used to exploit the matricial structure of the problem.Case studies with a 3,535-bus and a 4,238-branch Brazilian power system are presented and discussed, to demonstrate that the proposed model can be efficiently solved by an interior point method, providing security constrained solutions in a reasonable time.