An integral control formulation of Mean-field game based large scale coordination of loads in smart grids

Pressure on ancillary reserves, i.e.frequency preserving, in power systems has significantly mounted due to the recent generalized increase of the fraction of (highly fluctuating) wind and solar energy sources in grid generation mixes. The energy storage associated with millions of individual customer electric thermal (heating-cooling) loads is considered as a tool for smoothing power demand/generation imbalances. The piecewise constant level tracking problem of their collective energy content is formulated as a linear quadratic mean field game problem with integral control in the cost coefficients. The introduction of integral control brings with it a robustness potential to mismodeling, but also the potential of cost coefficient unboundedness. A suitable Banach space is introduced to establish the existence of Nash equilibria for the corresponding infinite population game, and algorithms are proposed for reliably computing a class of desirable near Nash equilibria. Numerical simulations illustrate the flexibility and robustness of the approach

Mathematical optimization techniques for demand management in smart grids

The electricity supply industry has been facing significant challenges in terms of meeting the projected demand for energy, environmental issues, security, reliability and integration of renewable energy. Currently, most of the power grids are based on many decades old vertical hierarchical infrastructures where the electric power flows in one direction from the power generators to the consumer side and the grid monitoring information is handled only at the operation side. It is generally believed that a fundamental evolution in electric power generation and supply system is required to make the grids more reliable, secure and efficient. This is generally recognised as the development of smart grids. Demand management is the key to the operational efficiency and reliability of smart grids. Facilitated by the two-way information flow and various optimization mechanisms, operators benefit from real time dynamic load monitoring and control while consumers benefit from optimised use of energy. In this thesis, various mathematical optimization techniques and game theoretic frameworks have been proposed for demand management in order to achieve efficient home energy consumption scheduling and optimal electric vehicle (EV) charging. A consumption scheduling technique is proposed to minimise the peak consumption load. The proposed technique is able to schedule the optimal operation time for appliances according to the power consumption patterns of the individual appliances. A game theoretic consumption optimization framework is proposed to manage the scheduling of appliances of multiple residential consumers in a decentralised manner, with the aim of achieving minimum cost of energy for consumers. The optimization incorporates integration of locally generated and stored renewable energy in order to minimise dependency on conventional energy. In addition to the appliance scheduling, a mean field game theoretic optimization framework is proposed for electric vehicles to manage their charging. In particular, the optimization considers a charging station where a large number of EVs are charged simultaneously during a flexible period of time. The proposed technique provides the EVs an optimal charging strategy in order to minimise the cost of charging. The performances of all these new proposed techniques have been demonstrated using Matlab based simulation studies

Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games

We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are beyond reach with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex-concave saddle point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN). We show the potential of our method on up to 100-dimensional MFG problems

Urban load optimization based on agent-based model representation

Tese de mestrado integrado em Engenharia da Energia e do Ambiente, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, em 2018O sistema energético atravessará uma profunda transformação nos próximos anos à medida que a produção renovável distribuída, a flexibilidade no lado do consumo e as funcionalidades de SmartGrid são implementadas. Este processo, conduzido em grande parte pelas imposições causadas pelos efeitos das alterações climáticas, implica profundas transformações na produção e consumo de energia e torna a transição energética extremamente urgente. Simultaneamente, novos players, entidades e modelos de negócio têm emergido em quase todos os níveis da cadeia energética desde a produção, a transmissão, distribuição e comercialização até à gestão da rede elétrica, num movimento conduzido pelo processo de particionamento (unbundling) do sistema elétrico e pela exigência de um sistema mais descentralizado e horizontal. O efeito combinado desta nova paisagem energética torna possíveis novas funcionalidades e arquitecturas de sistema na mesma medida em que coloca enormes problemas de natureza física e matemática mas também enormes questões económicas, sociais e políticas que terão, necessariamente, de ser abordadas e resolvidas. A Gestão do Consumo é um termo abrangente que representa tanto os mecanismos de Resposta na Procura (Demand Response) ou a Gestão no Lado da Procura (Demand-Side Management) e que se impõe como um dos problemas actuais mais importantes em sistemas energéticos inteligentes caracterizados por altas penetrações renováveis e mecanismos de mercado. Para resolver estes problemas, um conjunto de métodos matemáticos e computacionais têm sido propostos nos últimos anos. Otimização distribuída e sistemas inteligentes, sistemas baseados em agentes de software e teoria de jogos encontram-se entre algumas das ferramentas usadas para otimizar o consumo de energia e determinar o agendamento e a alocação ótima de equipamentos e máquinas para consumidores residenciais, comerciais e industriais. Na sequência de trabalhos prévios disponíveis na literatura da especialidade, o presente trabalho propõe um modelo geral para abordar o problema da otimização de cargas através de arquitecturas e métodos baseados no paradigma dos Agentes. O trabalho começa por definir agentes em pontos críticos da rede elétrica e os seus processos internos de raciocínio representados por modelos de otimização matemática. Seguidamente as interações entre agentes são modeladas como um jogo de dois níveis (bi-level game) entre uma entidade gestora da rede e consumidores de energia tipificados de forma a coordenar o carregamento de diversos equipamentos, incluindo veículos elétricos, e determinar uma solução admissível para o sistema global. A funcionalidade geral do modelo proposto é demonstrada através da sua implementação em software proprietário e recorrendo a um conjunto de dados específicos. Está, então, pronto para ser complementado e refinado no futuro de forma a ser aplicado em problemas do mundo real, de grandes dimensões, mas também novas implementações em software open source de forma a ficar acessível a novos utilizadores.The energy system is expected to go through a phase change in coming years as distributed generation, demand flexibility and SmartGrid features gets implemented. The main driver for this process, climate change, imposes constraints on energy production and consumption making energy transition extremely urgent. Simultaneously, new players, entities and business models have emerged at almost all levels of the energy chain from production, transmission, distribution and commercialization down to power grid management driven by the unbundling process and the call for a more decentralized and horizontal energy system. The combined effect of this new energy landscape makes new system’s architectures and functionalities desirable and possible, but poses huge physical, mathematical, engineering, economic and political questions and problems that need to be tackled. Load Management is one broad term depicting Demand-Side Management and Demand Response mechanisms and is one of the pressing problems on smart energy systems. To solve them, a plethora of computational and mathematical methods have been proposed in recent years. Distributed optimization and intelligence, software agents, agent-based systems and game theory are among the tools used to optimize load consumption and determine optimal device scheduling for residential, commercial and industrial power consumers Following previous work found in literature, the present work proposes a general framework to treat the load optimization problem using agent-based architectures and models. We start by defining agents at critical points within the power grid as well as their internal reasoning process depicted by mathematical optimization models. We then proceed to model the cooperative interactions between agents as a Bi-level game between a grid entity and typified power consumers in order to coordinate the charging of several appliances and electrical vehicles and determine a feasible solution for the global system. We show the general functionality of the framework by implementing it in software and applying it to specific datasets. The framework is suitable for further refinement and development when applied to real world problems