Edméa Cássia Baptista

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.

Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

This paper proposes a predictor-corrector primal-dual interior point method which introduces line search procedures (IPLS) in both the predictor and corrector steps. The Fibonacci search technique is used in the predictor step, while an Armijo line search is used in the corrector step. The method is developed for application to the economic dispatch (ED) problem studied in the field of power systems analysis. The theory of the method is examined for quadratic programming problems and involves the analysis of iterative schemes, computational implementation, and issues concerning the adaptation of the proposed algorithm to solve ED problems. Numerical results are presented, which demonstrate improvements and the efficiency of the IPLS method when compared to several other methods described in the literature. Finally, postoptimization analyses are performed for the solution of ED problems.

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.

Mixed-integer nonlinear model for multiproduct inventory systems with interior point and branch-and-bound method

Inventory management can be considered as one of the main components of planning and production control. In the literature numerous mathematical models are presented for inventory management, which approach different aspects related to this management. The development of efficient inventory models and the adoption of appropriate optimization methods for solving these models are needed to support in making decisions to inventory management. In this paper, we propose an inventory model that works with multiple products and multiple resource constraints, deciding between the continuous review and periodic review systems. This model is formulated as a nonlinear mixed integer optimization problem. It explores for the resolution of this model, an approach based on Branch-and-Bound method and interior point method. In order to propose this model and choose the method for its resolution, initially an investigation in the literature review on the topic is done. Then, the concept of continuous review and periodic review systems is explored. Finally, two computational tests are proposed, one to compare the results of proposed nonlinear model with the linear model and the other to verify its efficiency and applicability. The results show the potential of the model and solution method used to work with inventory system.

Coevolutionary Genetic Algorithm Based on the Augmented Lagrangian Function for Solving the Economic Dispatch Problem

This paper proposes a coevolutionary augmented Lagrangian method (AGCE) for solving the classic economic dispatch problem. This problem becomes non-convex and non-differentiable if valve-point loadings effects are considered in the cost curves of thermal units. In such cases, the evolutionary approaches have proven to be efficient for solving the primal economic dispatch problem; however, the great majority of these methods are not capable of solving the associated dual problem. Furthermore, the solutions obtained by these methods cannot be evaluated concerning their optimality. The AGCE works in the primal-dual subspaces and is able to calculate both primal and dual optimal values. For such a purpose, AGCE processes, in parallel, the evolution of two distinct groups of individuals, associated with primal and dual variables, respectively. The “clouds” of primal and dual points become iteratively denser, and converge to the saddle points associated with the problem, even in the presence of non-differentiability points. Therefore, AGCE makes possible the evaluation of optimality of its solution points. In the results, the AGCE is compared with a traditional interior point method and with a genetic algorithm that works only in the primal subspace.

Network-Constrained Multiperiod Auction for Pool-Based Electricity Markets of Hydrothermal Systems

Network-constrained market clearing procedures in pool-based electricity markets of hydropower systems have traditionally neglected the constraints associated with physical and operating aspects of hydroelectric generation (hydraulic constraints). Such constraints are generally taken into account by means of expost procedures, which may lead to suboptimal results regarding social welfare function. This paper proposes a network-constrained auction model for hydrothermal systems that represents the hydraulic constraints in detail. The objectives of the paper are twofold: the analysis of the impact of hydraulic constraints on market clearing prices and on generation/consumption scheduling and the analysis of the influence of strategic offering of hydro plants in the operation of a hydraulic cascade. As some of the hydraulic constraints are nonlinear and intertemporal, linearization techniques are applied, resulting in a mixed-integer linear programming problem.

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

Abstract 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.

O problema multiobjetivo de despacho econômico/ambiental e uma comparação entres os métodos de restrições canalizadas progressivas e de reescalamento não-linear com o NSGA-II

Este trabalho propoe um metodo deterministico de otimizacao que envolve um metodo de reescalamento nao-linear, tecnicas de correcao de inercia, metodos de suavizacao de funcoes e de restricoes canalizadas progressivas para resolucao do Problema Multiobjetivo de Despacho Economico e Ambiental com Pontos de carregamento de Valvula (PMDEA-PV). O PMDEA-PV e formulado como um problema multiobjetivo, nao-linear, nao-convexo e nao-diferenciavel e devido a essas dificuldades, normalmente, e resolvido utilizando de abordagens heuristicas. A tecnica de suavizacao e utilizada neste trabalho para lidar coma nao-diferenciabilidade, enquanto a estrategia de correcao de inercia para gerar apenas direcoes de descida para o metodo de reescalamento nao-linear; o metodo de restricoes canalizadas progressivas trata a natureza multiobjetivo do problema e por fim, o metodo de reescalamento nao-linear e usado para resolver os subproblemas gerados a partir da estrategia anterior. O metodo proposto e aplicado em dois sistemas teste, de 3 e 10 geradores e os resultados sao comparados com os obtidos pelo metodo heuristico de otimizacao: Non-Dominated Sorting Genetic Algorithm (NSGA-II), mostrando sua eficiencia.

A Modified Barrier and Barrier Method and the Optimal Power Flow Problem

This work proposes an approach that uses a union of methods based on logarithmic barrier function and modified logarithmic barrier function for the resolution of the reactive optimal power flow problem. In this proposed approach the inequality constraints are transformed into equalities by adding the slack variables, which are handled by logarithmic barrier function or modified logarithmic barrier function, and the equality constraints are handled by means of Lagrange multipliers. These methods are used in two steps. Initially, the method based on the logarithmic barrier function is applied until the transition condition is satisfied. After the method based on modified logarithmic barrier function is used until the stop condition is satisfied. Numerical tests carried out with the IEEE 14, 30, 57 and 118 bus electrical systems indicate that the proposed approach is efficient in the resolution of the reactive optimal power flow problem and the results obtained by the proposed approach were compared with the logarithmic barrier method and the logarithmic barrier method modified, separately.

A Proposed Methodology Involving Progressive Bounded Constraints And Interior-Exterior Methods in Smoothed Economic/Environmental Dispatch Problems

This paper proposes a methodology involving the primal-dual predictor-corrector interior/exterior point, the progressive bounded constraints and the arctangent smoothing methods, to be applied in economic/environmental dispatch multi-objective problem with valve-point load effects. The interior/exterior point method explores the logarithmic barrier modified function, which belongs to the nonlinear rescaling methods, allowing it a relaxation of the feasible set that includes its boundary, to iterate with exterior and unfeasible points. To treat non-convex functions, the inertia correction strategy is considered to ensure that it produces descent directions, avoiding the convergence to stationary points which are not local minima. Besides, the arctangent smoothing technique is used to treat nonsmooth functions and their modular parts, which are the main characteristic of the economic dispatch function. The progressive bounded constraints method are used to transform the multi-objective problem into a set of mono-objective subproblems and to allow that the economic/environmental dispatch multi-objective problem was solved by the proposed methodology, which was applied to solve test problem with nineteen and forty generating units. The results are compared with others published in the literature and with the solver Knitro.