V.A. de Sousa

Modified barrier method for optimal power flow problem

In this paper is presented a new approach for optimal power flow problem. This approach is based on the modified barrier function and the primal-dual logarithmic barrier method. A Lagrangian function is associated with the modified problem. The first-order necessary conditions for optimality are fulfilled by Newtons method, and by updating the barrier terms. The effectiveness of the proposed approach has been examined by solving the Brazilian 53-bus, IEEE 118-bus and IEEE 162-bus systems.

Optimal power flow: a tool for managing the transmission congestion

This paper presents a study of the Lagrange multipliers in congested transmission systems. The Lagrange multiplier indicates the sensitivity of constraints related with the objective function. The Lagrange multipliers are obtained via optimal power flow with transmission constraints. Optimal power flow problem is solved by primal-dual logarithmic barrier method. The results obtained in networks (53 and 118 bus) show that the proposed technique is able to improve system planning.

A new approach type-Newton for optimal reactive dispatch problem

This paper presents a new approach that improves the performance of the Newtons method for optimal reactive dispatch problem. In this approach the inequality constraints are divided into two groups: constraints treated by penalty function, which are added to the objective function through penalty factors, and constraints treated by barrier function that are grouped with the set of active constraints (power flow equations). The first order necessary conditions for optimality are reached by Newtons method, and by updating the penalty and barrier terms. The factorization is carried out on elements instead of structures in blocks. The main advantage is not to identify the biding constraints set. The effectiveness of the proposed approach has been examined by solving the 53-bus and 118-bus systems.

Transmission loss allocation by sensitivity approach

This paper presents an approach to the allocation of transmission losses to the agents of a power system operating under pool conditions, which consider all the operational constraints of the system. The approach belongs to the family of incremental methods of allocation. The technique is based on the perturbation of optimum theorem, which works with a Lagrangian function associated with the perturbed problem. Starting from an optimal operating point obtained by solution of an optimal power flow problem, the new optimal operating point that satisfies constraints after making a small increment in the loads is calculated directly. This solution is used to obtain the allocation coefficients of the losses for the generators and loads of the system. Numerical results are obtained for the well-known transmission networks, IEEE 14-bus and IEEE 30-bus, to illustrate the approach.

An enhanced model applied to the optimal power flow problem

This paper presents a study about optimal active and reactive dispatch with line flow constraints. The primal-dual logarithmic barrier method was used to solve the problem. The results obtained in networks of 8 and 118 busses show that the proposed technique is able to improve system operation.

Analysis of Numeric Conditioning of Hessian Matrix of Lagrangian Via Singular Values

This paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first- order necessary conditions of the Lagrangian function are solved by Newtons method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis.

Optimal Power Flow via Interior-Exterior Method

This paper presents a new approach to the resolution of the optimal power flow problem. In this approach the inequality constraints are treated by the modified barrier and primal-dual logarithmic barrier methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables, which are perturbed by the barrier parameter. A Lagrangian function is associated with the modified problem. The first-order necessary conditions are applied to the Lagrangian, generating a nonlinear system which is solved by Newtons method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. Numerical tests on the Brazilian CESP and South-Southeast systems and a comparative test indicated that the new approach efficiently resolves of the Optimal Power Flow problem.

Newton's method associated to the interior point method for optimal reactive dispatch problem

In this study is presented an algorithm for optimal reactive dispatch problem. The algorithm is based on Newtons method and Primal-dual logarithmic barrier method. A Lagrangian function is associated with the modified problem. The first order necessary conditions for optimality are reached by Newtons method, and by updating the penalty and barrier terms. The proposed approach does not have to identify the biding constraints set and can be utilized to infeasible starting point. The effectiveness of the proposed approach has been examined by solving the Brazilian 53-bus and IEEE 162-bus systems.