G.R.M. da Costa

Optimal reactive dispatch through primal-dual method

This paper presents an algorithm for the optimal reactive dispatch problem. The algorithm is based on Newtons method which it works with an augmented Lagrangian function associated with the original problem. The function aggregates all the equality and inequality constraints. The first order necessary conditions for optimality are reached by Newtons method, and by updating the dual variables and the penalty terms associated with the inequality constraints. The proposed approach does not have to identify the set of binding constraints and can be utilized for an infeasible starting point. The sparsity of the Hessian matrix of the augmented Lagrangian is completely exploited in the computational implementation. Tests results are presented to show the good performance of this algorithm.

Comparative studies of optimization methods for the optimal power flow problem

Abstract In this paper we have investigated three optimization approaches for solving the optimal power flow (OPF) problem: active set and penalty (ASP), primal–dual (PD), and primal–dual logarithmic-barrier (PDLB). All three approaches are Newton-based methods. This paper compares the main features of the above and reviews their methodologies. Results obtained in performance tests with traditional networks are summarized.

Real power losses reduction and loading margin improvement via continuation method

This letter presents an alternative approach for reducing the total real power losses by using a continuation method. Results for two simple test systems and for the IEEE 57-bus system show that this procedure results in larger voltage stability margin. Besides, the reduction of real power losses obtained with this procedure leads to significant money savings and, simultaneously, to voltage profile improvement. Comparison between the solution of an optimal power flow and the proposed method shows that the latter can provide near optimal results and so, it can be a reasonable alternative to power system voltage stability enhancement.

Primal-Dual Logarithmic Barrier and Augmented Lagrangian Function to the Loss Minimization in Power Systems

This article presents a new approach to minimize the losses in electrical power systems. This approach considers the application of the primal-dual logarithmic barrier method to voltage magnitude and tap-changing transformer variables, and the other inequality constraints are treated by augmented Lagrangian method. The Lagrangian function aggregates all the constraints. The first-order necessary conditions are reached by Newtons method, and by updating the dual variables and penalty factors. Test results are presented to show the good performance of this approach.

A new solution to the optimal power flow problem

A new approach to solving the optimal power flow problem is described, making use of some findings especially in the area of primal-dual methods for complex programming. In this approach, equality constraints are handled by Newtons method inequality constraints for voltage and transformer taps by the logarithmic barrier method and the other inequality constraints by the augmented Lagrangian method. Numerical test results are presented, showing the effective performance of this algorithm.

Improved Newton method for optimal power flow problem

This paper describes a new approach that improves the performance of the Newtons method for optimal power flow problem. The Lagrangian multipliers are calculated directly from the linearized system. The factorization is carried out on elements instead of structures in blocks. The main advantages are shorter processing times and reduced memory requirements. The paper compares this approach with the traditional Newtons method proposed by Sun et al. The effectiveness of the proposed approach has been examined by solving the 14-bus, 30-bus, 118-bus and Brazilian 810-bus systems.

Modified Newton method for reactive dispatching

Abstract This paper describes a new approach to the optimal reactive dispatch problem, based on an augmented Lagrangian function of the original problem. The Karush–Kuhn–Tucker (KKT) optimality conditions are solved by the modified Newton method. The second-order information in the original system of equations is approximated and the first-order information is kept intact The proposed method requires less computer memory than those algorithms currently available. The effectiveness of the proposed approach has been examined by solving the IEEE 30-bus and the BRAZILIAN 810-bus systems.

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

Abstract This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program.

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.

Distribution System Reconfiguration for Loss Reduction Based on Ant Colony Behavior

The problem of reconfiguration of distribution systems to minimize power loss was formulated as an optimization problem. This formulation takes into account the operational constraints on line flows and voltages and the radial topology. To solve this problem, the authors propose a method to optimize this reconfiguration of the distribution system, based on the behavior of colonies of ants. To illustrate the proposed method, a numerical example is presented