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.

Let's talk: public evaluation of large projects: variational inequialities, bilevel programming and complementarity. a survey

Large projects evaluation rises well known difficulties because -by definition- they modify the current price system; their public evaluation presents additional difficulties because they modify too existing shadow prices without the project. This paper analyzes -first- the basic methodologies applied until late 80s., based on the integration of projects in optimization models or, alternatively, based on iterative procedures with information exchange between two organizational levels. New methodologies applied afterwards are based on variational inequalities, bilevel programming and linear or nonlinear complementarity. Their foundations and different applications related with project evaluation are explored. As a matter of fact, these new tools are closely related among them and can treat more complex cases involving -for example- the reaction of agents to policies or the existence of multiple agents in an environment characterized by common functions representing demands or constraints on polluting emissions.

Optimal Contract Pricing of Distributed Generation in Distribution Networks

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimal contract pricing of distributed generation under a competitive framework

A bilevel programming approach for the optimal contract pricing of distributed generation (DG) in distribution networks is presented. The outer optimization problem corresponds to the owner of the DG who must decide the contract price that would maximize his profits. The inner optimization problem corresponds to the distribution company (DisCo), which procures the minimization of the payments incurred in attending the expected demand while satisfying network constraints. The meet the expected demand the DisCo can purchase energy either form the transmission network through the substations or form the DG units within its network. The inner optimization problem is substituted by its Karush- Kuhn-Tucker optimality conditions, turning the bilevel programming problem into an equivalent single-level nonlinear programming problem which is solved using commercially available software. © 2010 IEEE.

Localização e preço de contrato ótimo da geração distribuída em sistemas de distribuição radiais de energia elétrica

Pós-graduação em Engenharia Elétrica - FEIS

A Bilevel Approach to Transmission Expansion Planning Within a Market Environment

We present a bilevel model for transmission expansion planning within a market environment, where producers and consumers trade freely electric energy through a pool. The target of the transmission planner, modeled through the upper-level problem, is to minimize network investment cost while facilitating energy trading. This upper-level problem is constrained by a collection of lower-level market clearing problems representing pool trading, and whose individual objective functions correspond to social welfare. Using the duality theory the proposed bilevel model is recast as a mixed-integer linear programming problem, which is solvable using branch-and-cut solvers. Detailed results from an illustrative example and a case study are presented and discussed. Finally, some relevant conclusions are drawn.

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.

Integer Linear Programming for Sequence Problems: A general approach to reduce the problem size

Sequence problems belong to the most challenging interdisciplinary topics of the actuality. They are ubiquitous in science and daily life and occur, for example, in form of DNA sequences encoding all information of an organism, as a text (natural or formal) or in form of a computer program. Therefore, sequence problems occur in many variations in computational biology (drug development), coding theory, data compression, quantitative and computational linguistics (e.g. machine translation). In recent years appeared some proposals to formulate sequence problems like the closest string problem (CSP) and the farthest string problem (FSP) as an Integer Linear Programming Problem (ILPP). In the present talk we present a general novel approach to reduce the size of the ILPP by grouping isomorphous columns of the string matrix together. The approach is of practical use, since the solution of sequence problems is very time consuming, in particular when the sequences are long.

Maximum likelihood Linear Programming Data Fusion for Speaker Recognition

Biometric system performance can be improved by means of data fusion. Several kinds of information can be fused in order to obtain a more accurate classification (identification or verification) of an input sample. In this paper we present a method for computing the weights in a weighted sum fusion for score combinations, by means of a likelihood model. The maximum likelihood estimation is set as a linear programming problem. The scores are derived from a GMM classifier working on a different feature extractor. Our experimental results assesed the robustness of the system in front a changes on time (different sessions) and robustness in front a change of microphone. The improvements obtained were significantly better (error bars of two standard deviations) than a uniform weighted sum or a uniform weighted product or the best single classifier. The proposed method scales computationaly with the number of scores to be fussioned as the simplex method for linear programming.

Tarification logit dans un réseau

Le problème de tarification qui nous intéresse ici consiste à maximiser le revenu généré par les usagers d'un réseau de transport. Pour se rendre à leurs destinations, les usagers font un choix de route et utilisent des arcs sur lesquels nous imposons des tarifs. Chaque route est caractérisée (aux yeux de l'usager) par sa "désutilité", une mesure de longueur généralisée tenant compte à la fois des tarifs et des autres coûts associés à son utilisation. Ce problème a surtout été abordé sous une modélisation déterministe de la demande selon laquelle seules des routes de désutilité minimale se voient attribuer une mesure positive de flot. Le modèle déterministe se prête bien à une résolution globale, mais pèche par manque de réalisme. Nous considérons ici une extension probabiliste de ce modèle, selon laquelle les usagers d'un réseau sont alloués aux routes d'après un modèle de choix discret logit. Bien que le problème de tarification qui en résulte est non linéaire et non convexe, il conserve néanmoins une forte composante combinatoire que nous exploitons à des fins algorithmiques. Notre contribution se répartit en trois articles. Dans le premier, nous abordons le problème d'un point de vue théorique pour le cas avec une paire origine-destination. Nous développons une analyse de premier ordre qui exploite les propriétés analytiques de l'affectation logit et démontrons la validité de règles de simplification de la topologie du réseau qui permettent de réduire la dimension du problème sans en modifier la solution. Nous établissons ensuite l'unimodalité du problème pour une vaste gamme de topologies et nous généralisons certains de nos résultats au problème de la tarification d'une ligne de produits. Dans le deuxième article, nous abordons le problème d'un point de vue numérique pour le cas avec plusieurs paires origine-destination. Nous développons des algorithmes qui exploitent l'information locale et la parenté des formulations probabilistes et déterministes. Un des résultats de notre analyse est l'obtention de bornes sur l'erreur commise par les modèles combinatoires dans l'approximation du revenu logit. Nos essais numériques montrent qu'une approximation combinatoire rudimentaire permet souvent d'identifier des solutions quasi-optimales. Dans le troisième article, nous considérons l'extension du problème à une demande hétérogène. L'affectation de la demande y est donnée par un modèle de choix discret logit mixte où la sensibilité au prix d'un usager est aléatoire. Sous cette modélisation, l'expression du revenu n'est pas analytique et ne peut être évaluée de façon exacte. Cependant, nous démontrons que l'utilisation d'approximations non linéaires et combinatoires permet d'identifier des solutions quasi-optimales. Finalement, nous en profitons pour illustrer la richesse du modèle, par le biais d'une interprétation économique, et examinons plus particulièrement la contribution au revenu des différents groupes d'usagers.

A coupling cutting stock-lot sizing problem in the paper industry

An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

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

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.