Mercado da energia eléctrica: uma modelação MPCC-NLP

O problema apresentado está relacionado com o mercado de energia eléctrica, modelado como um jogo de Stackelberg, onde a empresa líder de mercado tem o poder de manipular os preços e a capacidade de produção, de forma a maximizar o seu lucro. Devido às suas características particulares, o problema foi formulado como um Problema de Optimização com Restrições de Complementaridade (MPCC) e, posteriormente reestruturado num Problema de Programação Não Linear (NLP), com o intuito de tirar partido das suas propriedades, utilizando software específico

Dynamic Congestion and Tolls with Mobile Source Emission

This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical program with equilibrium constraints (MPEC) problem and then reformulated as a mathematical program with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty-based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the Proceedings of the 20th International Symposium on Transportation and Traffic Theory, 2013, the Netherland

A Comparative Analysis of Contact Models in Trajectory Optimization for Manipulation

In this paper, we analyze the effects of contact models on contact-implicit trajectory optimization for manipulation. We consider three different approaches: (1) a contact model that is based on complementarity constraints, (2) a smooth contact model, and our proposed method (3) a variable smooth contact model. We compare these models in simulation in terms of physical accuracy, quality of motions, and computation time. In each case, the optimization process is initialized by setting all torque variables to zero, namely, without a meaningful initial guess. For simulations, we consider a pushing task with varying complexity for a 7 degrees-of-freedom robot arm. Our results demonstrate that the optimization based on the proposed variable smooth contact model provides a good trade-off between the physical fidelity and quality of motions at the cost of increased computation time.Comment: 6 pages, 7 figures, 4 tables, IROS 2018 camera-ready versio

A Holistic Approach to Human-Supervised Humanoid Robot Operations in Extreme Environments

Nuclear energy will play a critical role in meeting clean energy targets worldwide. However, nuclear environments are dangerous for humans to operate in due to the presence of highly radioactive materials. Robots can help address this issue by allowing remote access to nuclear and other highly hazardous facilities under human supervision to perform inspection and maintenance tasks during normal operations, help with clean-up missions, and aid in decommissioning. This paper presents our research to help realize humanoid robots in supervisory roles in nuclear environments. Our research focuses on National Aeronautics and Space Administration (NASA’s) humanoid robot, Valkyrie, in the areas of constrained manipulation and motion planning, increasing stability using support contact, dynamic non-prehensile manipulation, locomotion on deformable terrains, and human-in-the-loop control interfaces

Solving mathematical programs with complementarity constraints as nonlinear programs

programs with complementarity constraints as nonlinear programs

INTEGRATED DYNAMIC DEMAND MANAGEMENT AND MARKET DESIGN IN SMART GRID

Smart Grid is a system that accommodates different energy sources, including solar, wind, tidal, electric vehicles, and also facilitates communication between users and suppliers. This study tries to picture the interaction among all new sources of energy and market, besides managing supplies and demands in the system while meeting network's limitations. First, an appropriate energy system mechanism is proposed to motivate use of green and renewable energies while addressing current system's deficiencies. Then concepts and techniques from game theory, network optimization, and market design are borrowed to model the system as a Stackelberg game. Existence of an equilibrium solution to the problem is proved mathematically, and an algorithm is developed to solve the proposed nonlinear bi-level optimization model in real time. Then the model is converted to a mathematical program with equilibrium constraints using lower level's optimality conditions. Results from different solution techniques including MIP, SOS, and nonlinear MPEC solvers are compared with the proposed algorithm. Examples illustrate the appropriateness and usefulness of the both proposed system mechanism and heuristic algorithm in modeling the market and solving the corresponding large scale bi-level model. To the best knowledge of the writer there is no efficient algorithm in solving large scale bi-level models and any solution approach in the literature is problem specific. This research could be implemented in the future Smart Grid meters to help users communicate with the system and enables the system to accommodate different sources of energy. It prevents waste of energy by optimizing users' schedule of trades in the grid. Also recommendations to energy policy makers are made based on results in this research. This research contributes to science by combining knowledge of market structure and demand management to design an optimal trade schedule for all agents in the energy network including users and suppliers. Current studies in this area mostly focus either in market design or in demand management side. However, by combining these two areas of knowledge in this study, not only will the whole system be more efficient, but it also will be more likely to make the system operational in real world

Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context: Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context

This dissertation focuses on selected issues in regard to the mathematical modeling of electricity markets. In a first step the interrelations of electric power market modeling are highlighted a crossroad between operations research, applied economics, and engineering. In a second step the development of a large-scale continental European economic engineering model named ELMOD is described and the model is applied to the issue of wind integration. It is concluded that enabling the integration of low-carbon technologies appears feasible for wind energy. In a third step algorithmic work is carried out regarding a game theoretic model. Two approaches in order to solve a discretely-constrained mathematical program with equilibrium constraints using disjunctive constraints are presented. The first one reformulates the problem as a mixed-integer linear program and the second one applies the Benders decomposition technique. Selected numerical results are reported