A Strategy to Solve the Multistage Transmission Expansion Planning Problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

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

Transmission-expansion planning using the DC model and nonlinear-programming technique

The paper presents a constructive heuristic algorithm (CHA) for solving directly the long-term transmission-network-expansion-planning (LTTNEP) problem using the DC model. The LTTNEP is a very complex mixed-integer nonlinear-programming problem and presents a combinatorial growth in the search space. The CHA is used to find a solution for the LTTNEP problem of good quality. A sensitivity index is used in each step of the CHA to add circuits to the system. This sensitivity index is obtained by solving the relaxed problem of LTTNEP, i.e. considering the number of circuits to be added as a continuous variable. The relaxed problem is a large and complex nonlinear-programming problem and was solved through the interior-point method (IPM). Tests were performed using Garver's system, the modified IEEE 24-Bus system and the Southern Brazilian reduced system. The results presented show the good performance of IPM inside the CHA.

Domain reduction using GRASP construction phase for transmission expansion planning problem

This paper proposes a new strategy to reduce the combinatorial search space of a mixed integer linear programming (MILP) problem. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) is employed to reduce the domain of the integer variables of the transportation model of the transmission expansion planning (TM-TEP) problem. This problem is a MILP and very difficult to solve specially for large scale systems. The branch and bound (BB) algorithm is used to solve the problem in both full and the reduced search space. The proposed method might be useful to reduce the search space of those kinds of MILP problems that a fast heuristic algorithm is available for finding local optimal solutions. The obtained results using some real test systems show the efficiency of the proposed method. © 2012 Springer-Verlag.

Strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem

This paper proposes strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem (TEP). The concept of the binary numeral system (BNS) is used to reduce the number of binary and continuous variables related to the candidate transmission lines and network constraints that are connected with them. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) and additional constraints, obtained from power flow equilibrium in an electric power system are employed for more reduction in search space. The multistage TEP problem is modeled like a mixed binary linear programming problem and solved using a commercial solver with a low computational time. The results of one test system and two real systems are presented in order to show the efficiency of the proposed solution technique. © 1969-2012 IEEE.

Avaliação de Localizção e preço de contrato de geração distribuida em um ambiente competitivo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A mixed-integer quadratically-constrained programming model for the distribution system expansion planning

This paper presents a mixed-integer quadratically-constrained programming (MIQCP) model to solve the distribution system expansion planning (DSEP) problem. The DSEP model considers the construction/reinforcement of substations, the construction/reconductoring of circuits, the allocation of fixed capacitors banks and the radial topology modification. As the DSEP problem is a very complex mixed-integer non-linear programming problem, it is convenient to reformulate it like a MIQCP problem; it is demonstrated that the proposed formulation represents the steady-state operation of a radial distribution system. The proposed MIQCP model is a convex formulation, which allows to find the optimal solution using optimization solvers. Test systems of 23 and 54 nodes and one real distribution system of 136 nodes were used to show the efficiency of the proposed model in comparison with other DSEP models available in the specialized literature. (C) 2014 Elsevier Ltd. All rights reserved.

A Modified Branch and Bound Algorithm to Solve the Transmission Expansion Planning Problem

In this paper a novel Branch and Bound (B&B) algorithm to solve the transmission expansion planning which is a non-convex mixed integer nonlinear programming problem (MINLP) is presented. Based on defining the options of the separating variables and makes a search in breadth, we call this algorithm a B&BML algorithm. The proposed algorithm is implemented in AMPL and an open source Ipopt solver is used to solve the nonlinear programming (NLP) problems of all candidates in the B&B tree. Strategies have been developed to address the problem of non-linearity and non-convexity of the search region. The proposed algorithm is applied to the problem of long-term transmission expansion planning modeled as an MINLP problem. The proposed algorithm has carried out on five commonly used test systems such as Garver 6-Bus, IEEE 24-Bus, 46-Bus South Brazilian test systems, Bolivian 57-Bus, and Colombian 93-Bus. Results show that the proposed methodology not only can find the best known solution but it also yields a large reduction between 24% to 77.6% in the number of NLP problems regarding to the size of the systems.

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

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Determining departure times in dynamic and stochastic maritime routing and scheduling problem

In maritime transportation, decisions are made in a dynamic setting where many aspects of the future are uncertain. However, most academic literature on maritime transportation considers static and deterministic routing and scheduling problems. This work addresses a gap in the literature on dynamic and stochastic maritime routing and scheduling problems, by focusing on the scheduling of departure times. Five simple strategies for setting departure times are considered, as well as a more advanced strategy which involves solving a mixed integer mathematical programming problem. The latter strategy is significantly better than the other methods, while adding only a small computational effort.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Hierarchical Forest Management Planning: A Bilevel Wood Supply Modelling Approach

Le processus de planification forestière hiérarchique présentement en place sur les terres publiques risque d’échouer à deux niveaux. Au niveau supérieur, le processus en place ne fournit pas une preuve suffisante de la durabilité du niveau de récolte actuel. À un niveau inférieur, le processus en place n’appuie pas la réalisation du plein potentiel de création de valeur de la ressource forestière, contraignant parfois inutilement la planification à court terme de la récolte. Ces échecs sont attribuables à certaines hypothèses implicites au modèle d’optimisation de la possibilité forestière, ce qui pourrait expliquer pourquoi ce problème n’est pas bien documenté dans la littérature. Nous utilisons la théorie de l’agence pour modéliser le processus de planification forestière hiérarchique sur les terres publiques. Nous développons un cadre de simulation itératif en deux étapes pour estimer l’effet à long terme de l’interaction entre l’État et le consommateur de fibre, nous permettant ainsi d’établir certaines conditions pouvant mener à des ruptures de stock. Nous proposons ensuite une formulation améliorée du modèle d’optimisation de la possibilité forestière. La formulation classique du modèle d’optimisation de la possibilité forestière (c.-à-d., maximisation du rendement soutenu en fibre) ne considère pas que le consommateur de fibre industriel souhaite maximiser son profit, mais suppose plutôt la consommation totale de l’offre de fibre à chaque période, peu importe le potentiel de création de valeur de celle-ci. Nous étendons la formulation classique du modèle d’optimisation de la possibilité forestière afin de permettre l’anticipation du comportement du consommateur de fibre, augmentant ainsi la probabilité que l’offre de fibre soit entièrement consommée, rétablissant ainsi la validité de l’hypothèse de consommation totale de l’offre de fibre implicite au modèle d’optimisation. Nous modélisons la relation principal-agent entre le gouvernement et l’industrie à l’aide d’une formulation biniveau du modèle optimisation, où le niveau supérieur représente le processus de détermination de la possibilité forestière (responsabilité du gouvernement), et le niveau inférieur représente le processus de consommation de la fibre (responsabilité de l’industrie). Nous montrons que la formulation biniveau peux atténuer le risque de ruptures de stock, améliorant ainsi la crédibilité du processus de planification forestière hiérarchique. Ensemble, le modèle biniveau d’optimisation de la possibilité forestière et la méthodologie que nous avons développée pour résoudre celui-ci à l’optimalité, représentent une alternative aux méthodes actuellement utilisées. Notre modèle biniveau et le cadre de simulation itérative représentent un pas vers l’avant en matière de technologie de planification forestière axée sur la création de valeur. L’intégration explicite d’objectifs et de contraintes industrielles au processus de planification forestière, dès la détermination de la possibilité forestière, devrait favoriser une collaboration accrue entre les instances gouvernementales et industrielles, permettant ainsi d’exploiter le plein potentiel de création de valeur de la ressource forestière.

Numerical enclosures of the optimal cost of the Kantorovitch’s mass transportation problem

International audience

Design and management of a supply chain: a joint location-inventory problem under uncertainty (Part A)

In this paper, a joint location-inventory model is proposed that simultaneously optimises strategic supply chain design decisions such as facility location and customer allocation to facilities, and tactical-operational inventory management and production scheduling decisions. All this is analysed in a context of demand uncertainty and supply uncertainty. While demand uncertainty stems from potential fluctuations in customer demands over time, supply-side uncertainty is associated with the risk of “disruption” to which facilities may be subject. The latter is caused by external factors such as natural disasters, strikes, changes of ownership and information technology security incidents. The proposed model is formulated as a non-linear mixed integer programming problem to minimise the expected total cost, which includes four basic cost items: the fixed cost of locating facilities at candidate sites, the cost of transport from facilities to customers, the cost of working inventory, and the cost of safety stock. Next, since the optimisation problem is very complex and the number of evaluable instances is very low, a "matheuristic" solution is presented. This approach has a twofold objective: on the one hand, it considers a larger number of facilities and customers within the network in order to reproduce a supply chain configuration that more closely reflects a real-world context; on the other hand, it serves to generate a starting solution and perform a series of iterations to try to improve it. Thanks to this algorithm, it was possible to obtain a solution characterised by a lower total system cost than that observed for the initial solution. The study concludes with some reflections and the description of possible future insights.