VAr planning using genetic algorithm and linear programming

A combined methodology consisting of successive linear programming (SLP) and a simple genetic algorithm (SGA) solves the reactive planning problem. The problem is divided into operating and planning subproblems; the operating subproblem, which is a nonlinear, ill-conditioned and nonconvex problem, consists of determining the voltage control and the adjustment of reactive sources. The planning subproblem consists of obtaining the optimal reactive source expansion considering operational, economical and physical characteristics of the system. SLP solves the optimal reactive dispatch problem related to real variables, while SGA is used to determine the necessary adjustments of both the binary and discrete variables existing in the modelling problem. Once the set of candidate busbars has been defined, the program implemented gives the location and size of the reactive sources needed, if any, to maintain the operating and security constraints.

Interior point algorithm for linear programming used in transmission network synthesis

This article presents a well-known interior point method (IPM) used to solve problems of linear programming that appear as sub-problems in the solution of the long-term transmission network expansion planning problem. The linear programming problem appears when the transportation model is used, and when there is the intention to solve the planning problem using a constructive heuristic algorithm (CHA), ora branch-and-bound algorithm. This paper shows the application of the IPM in a CHA. A good performance of the IPM was obtained, and then it can be used as tool inside algorithm, used to solve the planning problem. Illustrative tests are shown, using electrical systems known in the specialized literature. (C) 2005 Elsevier B.V. All rights reserved.

Determination of the optimal quantity of crop residues for energy in sugarcane crop management using linear programming in variety selection and planting strategy

The aim of this work was to present organizational models for optimizing the reduction of crop residue generated by the sugarcane culture. The first model consisted of the selection of varieties of sugarcane to be planted meeting the mill requirements and, at the same time, to minimize the quantity of residue produced. The second model discussed the use of residue to produce energy. This is related to the selection of variety and quantity to be planted, in order to meet the requirements of the mill, to reduce the quantity of residue, and to maximize as much as possible the energy production. The use of linear programming was proposed. The two models presented similar results in this study, and both may be used to define the varieties and areas to be cultivated. (C) 2001 Published by Elsevier B.V. Ltd.

Heterogeneity correction in the construction of optimized planning in radiotherapy using linear programming

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Design and management optimization of trickle irrigation systems using non-linear programming

A non-linear model is presented which optimizes the lay-out, as well as the design and management of trickle irrigation systems, to achieve maximum net benefit. The model consists of an objective function that maximizes profit at the farm level, subject to appropriate geometric and hydraulic constraints. It can be applied to rectangular shaped fields, with uniform or zero slope. The software used is the Gams-Minos package. The basic inputs are the crop-water-production function, the cost function and cost of system components, and design variables. The main outputs are the annual net benefit and pipe diameters and lengths. To illustrate the capability of the model, a sensitivity analysis of the annual net benefit for a citrus field is evaluated with respect to irrigated area, ground slope, micro-sprinkler discharge and shape of the field. The sensitivity analysis suggests that the greatest benefit is obtained with the smallest microsprinkler discharge, the greatest area, a square field and zero ground slope. The costs of the investment and energy are the components of the objective function that had the greatest effect in the 120 situations evaluated. (C) 1996 Academic Press Limited

Efficient linear programming algorithm for the transmission network expansion planning problem

The transmission network planning problem is a non-linear integer mixed programming problem (NLIMP). Most of the algorithms used to solve this problem use a linear programming subroutine (LP) to solve LP problems resulting from planning algorithms. Sometimes the resolution of these LPs represents a major computational effort. The particularity of these LPs in the optimal solution is that only some inequality constraints are binding. This task transforms the LP into an equivalent problem with only one equality constraint (the power flow equation) and many inequality constraints, and uses a dual simplex algorithm and a relaxation strategy to solve the LPs. The optimisation process is started with only one equality constraint and, in each step, the most unfeasible constraint is added. The logic used is similar to a proposal for electric systems operation planning. The results show a higher performance of the algorithm when compared to primal simplex methods.

Towards an intelligent graphical interface for linear programming modelling

The increase of computing power of the microcomputers has stimulated the building of direct manipulation interfaces that allow graphical representation of Linear Programming (LP) models. This work discusses the components of such a graphical interface as the basis for a system to assist users in the process of formulating LP problems. In essence, this work proposes a methodology which considers the modelling task as divided into three stages which are specification of the Data Model, the Conceptual Model and the LP Model. The necessity for using Artificial Intelligence techniques in the problem conceptualisation and to help the model formulation task is illustrated.

Design of microirrigation systems in sloping lands using linear programming

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions; (b) different types of DGs are represented by their capability curves; (c) the short-circuit current capacity of the circuits is modeled through linear expressions; and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.© 2012 Elsevier B.V. All rights reserved.

Bilevel approach for optimal location and contract pricing of distributed generation in radial distribution systems using mixed-integer linear programming

In this study, a novel approach for the optimal location and contract pricing of distributed generation (DG) is presented. Such an approach is designed for a market environment in which the distribution company (DisCo) can buy energy either from the wholesale energy market or from the DG units within its network. The location and contract pricing of DG is determined by the interaction between the DisCo and the owner of the distributed generators. The DisCo intends to minimise the payments incurred in meeting the expected demand, whereas the owner of the DG intends to maximise the profits obtained from the energy sold to the DisCo. This two-agent relationship is modelled in a bilevel scheme. The upper-level optimisation is for determining the allocation and contract prices of the DG units, whereas the lower-level optimisation is for modelling the reaction of the DisCo. The bilevel programming problem is turned into an equivalent single-level mixed-integer linear optimisation problem using duality properties, which is then solved using commercially available software. Results show the robustness and efficiency of the proposed model compared with other existing models. As regards to contract pricing, the proposed approach allowed to find better solutions than those reported in previous works. © The Institution of Engineering and Technology 2013.

DESIGN OF MICROIRRIGATION SYSTEMS IN SLOPING LANDS USING LINEAR PROGRAMMING

Quando a área a ser irrigada apresenta um elevado gradiente de declive na direção das linhas de derivação, uma opção de dimensionamento é o uso de tubulações com vários diâmetros para economizar no custo e também para manter a variação de pressão dentro dos limites desejados. O objetivo deste trabalho foi desenvolver um modelo de programação linear para dimensionar sistemas de irrigação por microaspersão com linhas de derivação com mais de um diâmetro e operando em declive, visando a minimização do custo anualizado da rede hidráulica e do custo anual com energia elétrica, além de assegurar que a máxima variação de carga hidráulica na linha será respeitada. Os dados de entrada são: configuração da rede hidráulica do sistema de irrigação, custo de todos os componentes da rede hidráulica e custo da energia. Os dados de saída são: custo anual total, diâmetro da tubulação em cada linha do sistema, carga hidráulica em cada ponto de derivação e altura manométrica total. Para ilustrar a potencialidade do modelo desenvolvido, ele foi aplicado em um pomar de citros no Estado de São Paulo, Brasil. O modelo demonstrou ser eficiente no dimensionamento do sistema de irrigação quanto à obtenção da uniformidade de emissão desejada. O custo anual com bombeamento deve ser considerado no dimensionamento de sistemas de irrigação por microaspersão porque ele gera menores valores de custo anual total quando comparado com a mesma alternativa que não considera aquele custo.

Short-term expansion planning of radial electrical distribution systems using mixed-integer linear programming

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Planejamento de Fontes Reativas em Sistemas de Energia Elétrica utilizando a técnica de Decomposição de Benders e o algoritmo de Branch-and-Bound

This paper presents the Benders decomposition technique and Branch and Bound algorithm used in the reactive power planning in electric energy systems. The Benders decomposition separates the planning problem into two subproblems: an investment subproblem (master) and the operation subproblem (slave), which are solved alternately. The operation subproblem is solved using a successive linear programming (SLP) algorithm while the investment subproblem, which is an integer linear programming (ILP) problem with discrete variables, is resolved using a Branch and Bound algorithm especially developed to resolve this type of problem.

Multi-area decentralized optimal VAr planning using the Dantzig-Wolfe decomposition principle

This paper presents a new methodology for solving the optimal VAr planning problem in multi-area electric power systems, using the Dantzig-Wolfe decomposition. The original multi-area problem is decomposed into subproblems (one for each area) and a master problem (coordinator). The solution of the VAr planning problem in each area is based on the application of successive linear programming, and the coordination scheme is based on the reactive power marginal costs in the border bus. The aim of the model is to provide coordinated mechanisms to carry out the VAr planning studies maximizing autonomy and confidentiality for each area, assuring global economy to the whole system. Using the mathematical model and computational implementation of the proposed methodology, numerical results are presented for two interconnected systems, each of them composed of three equal subsystems formed by IEEE30 and IEEE118 test systems. © 2011 IEEE.

Decomposição de Dantzig-Wolfe aplicada ao problema de planejamento de reativos em sistemas de potência multi-áreas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)