Game theoretical characterization of the multi-agent network expansion game

Dans les chaînes d’approvisionnement, les producteurs font souvent appel à des entreprises de transport pour livrer leurs marchandises. Cela peut entraîner une concurrence entre les transporteurs qui cherchent à maximiser leurs revenus individuels en desservant un produc- teur. Dans ce travail, nous considérons de telles situations où aucun transporteur ne peut garantir la livraison de la source à la destination en raison de son activité dans une région restreinte (par exemple, une province) ou de la flotte de transport disponible (par exemple, uniquement le transport aérien), pour ne citer que quelques exemples. La concurrence est donc liée à l’expansion de la capacité de transport des transporteurs. Le problème décrit ci-dessus motive l’étude du jeu d’expansion de réseau multi-agent joué sur un réseau appartenant à de multiples transporteurs qui choisissent la capacité de leurs arcs. Simultanément, un client cherche à maximiser le flux qui passe par le réseau en décidant de la politique de partage qui récompense chacun des transporteurs. Le but est de déterminer un équilibre de Nash pour le jeu, en d’autres termes, la strategie d’extension de capacité et de partage la plus rationnelle pour les transporteurs et le client, respectivement. Nous rappelons la formulation basée sur les arcs proposée dans la littérature, dont la solution est l’équilibre de Nash avec le plus grand flux, et nous identifions ses limites. Ensuite, nous formalisons le concept de chemin profitable croissant et nous montrons son utilisation pour établir les conditions nécessaires et suffisantes pour qu’un vecteur de stratégies soit un équilibre de Nash. Ceci nous conduit à la nouvelle formulation basée sur le chemin. Enfin, nous proposons un renforcement du modèle basé sur les arcs et une formulation hybride arc- chemin. Nos résultats expérimentaux soutiennent la valeur des nouvelles inégalités valides obtenues à partir de notre caractérisation des équilibres de Nash avec des chemins croissants rentables. Nous concluons ce travail avec les futures directions de recherche pavées par les contributions de cette thèse.In supply chains, manufacturers often use transportation companies to deliver their goods. This can lead to competition among carriers seeking to maximize their individual revenues by serving a manufacturer. In this work, we consider such situations where no single carrier can guarantee delivery from source to destination due to its operation in a restricted region (e.g., a province) or the available transportation fleet (e.g., only air transportation), to name a few examples. Therefore, competition is linked to the expansion of transportation capacity by carriers. The problem described above motivates the study of the multi-agent network expansion game played over a network owned by multiple transporters who choose their arcs’ capacity. Simultaneously, a customer seeks to maximize the flow that goes through the network by deciding the sharing policy rewarding each of the transporters. The goal is to determine a Nash equilibrium for the game, in simple words, the most rational capacity expansion and sharing policy for the transporters and the customer, respectively. We recap the arc-based formulation proposed in literature, whose solution is the Nash equilibirum with the largest flow, and we identify its limitations. Then, we formalize the concept of profitable increasing path and we show its use to establish necessary and sufficient conditions for a vector of strategies to be a Nash equilibrium. This lead us to the first path-based formulation. Finally, we propose a strengthening for the arc-based model and a hybrid arc-path formulation. Our experimental results support the value of the new valid inequalities obtained from our characterization of Nash equilibria with profitable increasing paths. We conclude this work with the future research directions paved by the contributions of this thesis

Nash Equilibria in the multi-agent project scheduling problem with milestones

Plánovanie projektov zvyčajne zahŕňa viacerých dodávateľov, ktorí majú na starosti rôzne práce v projektovom pláne. Každý dodávateľ má možnosť skrátiť trvanie svojej aktivity z maximálneho až na minimálny časový limit. Projektový manažér je zodpovedný za včasné dodanie projektu. V projektovom pláne stanovuje míľniky s príslušnými termínmi a pokutami za ich nesplnenie. Cieľom práce je nájsť stabilné riešenie s minimálnym časovým trvaním projektu. V stabilnom riešení nemá žiadny dodávateľ záujem zmeniť trvanie svojich aktivít, aby znížil svoje náklady. To pláti za predpokladu, že všetci ostatní dodávatelia nezmenia svoje stratégie. V práci navrhujeme využitie celočíselného lineárneho programovania s podmienkami generovanými v priebehu programu pre výpočet stabilného riešenia s minimálnym časovým trvaním projektu. Analýza výpočtov potvrdzuje efektívnosť nášho riešenia. Taktiež v práci skúmame ukazovatele v anglickej literatúre označované ako price of anarchy a price of stability, aby sme získali lepšiu predstavu o probléme z pohľadu projektového manažéra.Project scheduling often involves multiple contractors, who are in charge of activities in the project plan. They have the power to decrease the duration of their activities from normal duration to the incompressible limit. The project manager is responsible to deliver the project on time. He specifies the milestones with appropriate due dates and penalties in the project plan. The thesis aims to find a stable solution with minimal project duration. In a stable solution, no contractor has the interest to change the duration of his activities to reduce his expenses, since all other contractors do not change their strategies. We propose a mixed integer linear program formulation with lazy constraint generation for its calculation. Computation analysis confirms the effectiveness of our approach. We investigate the values of the price of anarchy and the price of stability to get useful insight for the project manager

Contingency Management in Power Systems and Demand Response Market for Ancillary Services in Smart Grids with High Renewable Energy Penetration.

Ph.D. Thesis. University of Hawaiʻi at Mānoa 2017

A Study of Problems Modelled as Network Equilibrium Flows

This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated. Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation

Computacional models for expansion planning of electric power distribution systems containing multiple microgrids and distributed energy resources under uncertainties

Orientador: Prof. Dr. Clodomiro Unsihuay VilaTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa : Curitiba, 05/12/2022Inclui referênciasResumo: Sistemas de distribuição incorporaram diversas tecnologias nos últimos anos, e a introdução de recursos energéticos distribuídos (DERs) proporcionam desafios para o planejamento da sua expansão e operação, como a inserção de geração distribuída (DG), sistemas de armazenamento de energia (ESSs), resposta da demanda (DR) e incertezas associadas com fontes de energia renováveis. Além disso, sistemas de distribuição modernos com múltiplas microrredes (MMG) e tecnologias para automação e monitoramento possibilitam a criação de um mercado local para comercialização de energia entre as microrredes. Devido às incertezas e ambientes competitivos gerados por microrredes que podem tomar suas próprias decisões e comercializar energia, a decisão para expansão do sistema é uma tarefa complexa feita pelo operador do sistema de distribuição (DSO). Dessa forma, essa tese propõe quatro modelos computacionais para o planejamento da expansão de sistemas elétricos de distribuição contendo MMGs e DERs sob incertezas. Cada modelo é projetado para um cenário específico: o primeiro soluciona o planejamento robusto para casos sem MMGs, não usa dados históricos e inclui confiabilidade; o segundo insere MMGs e contingências; o terceiro considera cenários com dados históricos disponíveis; e o quarto inclui o mercado de comercialização de energia para MMG em ambientes competitivos. Todos os modelos buscam minimizar os custos com investimento e operação na perspectiva do DSO, alocando novos componentes (DG, ESSs, capacitores e linhas) sob incertezas, considerando a coordenação das DERs, DR e confiabilidade/contingências. Eles são formulados como problemas multiníveis e solucionados através de decomposições multiestágio usando abordagens como adaptative robust optimization, distributionally robust optimization e column-andconstraint generation. Os métodos propostos são ilustrados usando uma versão modificada do sistema teste IEEE 123-bus. Os resultados mostram que os aspectos apresentados neste trabalho são importantes no planejamento da expansão de redes de distribuição pois reduzem o custo total ao mesmo tempo que melhor representam redes modernas. Incluir contingências melhora significativamente os índices de confiabilidade, reduzindo em 70% do índice EENS no caso de estudo. Cenários considerando mercado de energia tendem a aumentar o custo total do plano em ambientes de competição, 14% no caso de estudo. Ao mesmo tempo, esse caso tem a vantagem do compartilhamento de riscos entre o DSO e investidores. Ademais, os métodos propostos que usam dados históricos se comportam similarmente a métodos robustos ou estocásticos, dependendo do volume de dados disponível.Abstract: Power distribution systems have incorporated many new technologies in recent years, and the introduction of distributed energy resources (DERs) provides challenges for their operation and expansion planning, such as the inclusion of distributed generation (DG), energy storage systems (ESSs), demand response (DR), and uncertainties associated with renewable power sources. Moreover, modern distribution networks with multiple microgrids (MMG) and automation/monitoring technologies enable the creation of a market framework for local energy trading among the microgrids. Due to uncertainties and the competitive environment where microgrids can make their own decisions and trade energy, the expansion decision is a complex task performed by the distribution system operator (DSO). Thus, this dissertation proposes four computational models for the expansion planning of electric power distribution systems containing multiple microgrids and DERs under uncertainties. Each model is designed for specific scenarios: the first one solves a robust plan for cases without MMGs, has no historical data, and includes reliability; the second model inserts MMGs and contingencies; the third one considers cases having historical data; and the last model formulates the energy trading market for MMGs in competitive environments. All models aim to minimize the investment and operational costs from the DSO's perspective, placing new components (DG, ESSs, capacitors, and lines) under uncertainties, considering the DERs' optimal daily operation, DR, and reliability/contingency. They are formulated as multi-level problems and solved through multi-stage decompositions using robust adaptative optimization, distributionally robust optimization, and column-and-constraint approaches. The proposed methods are illustrated using a modified version of the IEEE 123-bus test system. The results show that the aspects presented in this work are important for the expansion planning of distribution networks since they reduce the total cost and better represent modern new tasks. Including contingencies significantly improves reliability indexes, reducing by 70% the EENS (Expected Energy Not Served) index in the study case. Scenarios considering energy trade markets tend to increase the total cost of the plan in competitive environments, 14% in the case study; at the same time, they have the benefit of sharing the investment risks among investors and the DSO. Furthermore, the proposed methods that use historical data behaved similarly to robust or stochastic approaches, depending on the amount of data available

Control and optimization approaches for energy-limited systems: applications to wireless sensor networks and battery-powered vehicles

This dissertation studies control and optimization approaches to obtain energy-efficient and reliable routing schemes for battery-powered systems in network settings. First, incorporating a non-ideal battery model, the lifetime maximization problem for static wireless sensor networks is investigated. Adopting an optimal control approach, it is shown that there exists a time-invariant optimal routing vector in a fixed topology network. Furthermore, under very mild conditions, this optimal policy is robust with respect to the battery model used. Then, the lifetime maximization problem is investigated for networks with a mobile source node. Redefining the network lifetime, two versions of the problem are studied: when there exist no prior knowledge about the source node’s motion dynamics vs. when source node’s trajectory is known in advance. For both cases, problems are formulated in the optimal control framework. For the former, the solution can be reduced to a sequence of nonlinear programming problems solved on line as the source node trajectory evolves. For the latter, an explicit off-line numerical solution is required. Second, the problem of routing for vehicles with limited energy through a network with inhomogeneous charging nodes is studied. The goal is to minimize the total elapsed time, including traveling and recharging time, for vehicles to reach their destinations. Adopting a game-theoretic approach, the problem is investigated from two different points of view: user-centric vs. system-centric. The former is first formulated as a mixed integer nonlinear programming problem. Then, by exploiting properties of an optimal solution, it is reduced to a lower dimensionality problem. For the latter, grouping vehicles into subflows and including the traffic congestion effects, a system-wide optimization problem is defined. Both problems are studied in a dynamic programming framework as well. Finally, the thesis quantifies the Price Of Anarchy (POA) in transportation net- works using actual traffic data. The goal is to compare the network performance under user-optimal vs. system-optimal policies. First, user equilibria flows and origin- destination demands are estimated for the Eastern Massachusetts transportation net- work using speed and capacity datasets. Then, obtaining socially-optimal flows by solving a system-centric problem, the POA is estimated

Model Predictive Control for Demand Response Management Systems in Smart Buildings

RÉSUMÉ Les bâtiments représentent une portion importante de la consommation énergétique globale. Par exemple, aux USA, le secteur des bâtiments est responsable de 40% de la consommation énergétique totale. Plus de 50% de la consommation d’électricité est liée directement aux systèmes de chauffage, de ventilation et de climatisation (CVC). Cette réalité a incité beaucoup de chercheurs à développer de nouvelles solutions pour la gestion de la consommation énergétique dans les bâtiments, qui impacte la demande de pointe et les coûts associés. La conception de systèmes de commande dans les bâtiments représente un défi important car beaucoup d’éléments, tels que les prévisions météorologiques, les niveaux d’occupation, les coûts énergétiques, etc., doivent être considérés lors du développement de nouveaux algorithmes. Un bâtiment est un système complexe constitué d’un ensemble de sous-systèmes ayant différents comportements dynamiques. Par conséquent, il peut ne pas être possible de traiter ce type de systèmes avec un seul modèle dynamique. Récemment, différentes méthodes ont été développées et mises en application pour la commande de systèmes de bâtiments dans le contexte des réseaux intelligents, parmi lesquelles la commande prédictive (Model Predictive Control - MPC) est l’une des techniques les plus fréquemment adoptées. La popularité du MPC est principalement due à sa capacité à gérer des contraintes multiples, des processus qui varient dans le temps, des retards et des incertitudes, ainsi que des perturbations. Ce projet de recherche doctorale vise à développer des solutions pour la gestion de consommation énergétique dans les bâtiments intelligents en utilisant le MPC. Les techniques développées pour la gestion énergétique des systèmes CVC permet de réduire la consommation énergétique tout en respectant le confort des occupants et les contraintes telles que la qualité de service et les contraintes opérationnelles. Dans le cadre des MPC, différentes contraintes de capacité énergétique peuvent être imposées pour répondre aux spécifications de conception pendant la durée de l’opération. Les systèmes CVC considérés reposent sur une architecture à structure en couches qui réduit la complexité du système, facilitant ainsi les modifications et l’adaptation. Cette structure en couches prend également en charge la coordination entre tous les composants. Étant donné que les appareils thermiques des bâtiments consomment la plus grande partie de la consommation électrique, soit plus du tiers sur la consommation totale d’énergie, la recherche met l’emphase sur la commande de ce type d’appareils. En outre, la propriété de dynamique lente, la flexibilité de fonctionnement et l’élasticité requise pour les performances des appareils thermiques en font de bons candidats pour la gestion réponse à la demande (Demand Response - DR) dans les bâtiments intelligents.----------ABSTRACT Buildings represent the biggest consumer of global energy consumption. For instance, in the US, the building sector is responsible for 40% of the total power usage. More than 50% of the consumption is directly related to heating, ventilation and air-conditioning (HVAC) systems. This reality has prompted many researchers to develop new solutions for the management of HVAC power consumption in buildings, which impacts peak load demand and the associated costs. Control design for buildings becomes increasingly challenging as many components, such as weather predictions, occupancy levels, energy costs, etc., have to be considered while develop-ing new algorithms. A building is a complex system that consists of a set of subsystems with di˙erent dynamic behaviors. Therefore, it may not be feasible to deal with such a system with a single dynamic model. In recent years, a rich set of conventional and modern control schemes have been developed and implemented for the control of building systems in the context of the Smart Grid, among which model redictive control (MPC) is one of the most-frequently adopted techniques. The popularity of MPC is mainly due to its ability to handle multiple constraints, time varying processes, delays, uncertainties, as well as disturbances. This PhD research project aims at developing solutions for demand response (DR) man-agement in smart buildings using the MPC. The proposed MPC control techniques are im-plemented for energy management of HVAC systems to reduce the power consumption and meet the occupant’s comfort while taking into account such restrictions as quality of service and operational constraints. In the framework of MPC, di˙erent power capacity constraints can be imposed to test the schemes’ robustness to meet the design specifications over the operation time. The considered HVAC systems are built on an architecture with a layered structure that reduces the system complexity, thereby facilitating modifications and adaptation. This layered structure also supports the coordination between all the components. As thermal appliances in buildings consume the largest portion of the power at more than one-third of the total energy usage, the emphasis of the research is put in the first stage on the control of this type of devices. In addition, the slow dynamic property, the flexibility in operation, and the elasticity in performance requirement of thermal appliances make them good candidates for DR management in smart buildings

Information requirements for strategic decision making: energy market

Over the last two decades, the electricity sector has been involved in a challenging restructuring process in which the vertical integrated structure (monopoly) is being replaced by a horizontal set of companies. The growing supply of electricity, flowing in response to free market pricing at the wellhead, led to increased competition. In the new framework of deregulation, what characterizes the electric industry is a commodity wholesale electricity marketplace. This new environment has drastically changed the objective of electricity producing companies. In the vertical integrated industry, utilities were forced to meet all the demand from customers living in a certain region at fixed rates. Then, the operation of the Generation Companies (GENCOs) was centralized and a single decision maker allocated the energy services by minimizing total production costs. Nowadays, GENCOs are involved not only in the electricity market but also in additional markets such as fuel markets or environmental markets. A gas or coal producer may have fuel contracts that define the production limit over a time horizon. Therefore, producers must observe this price levels in these other markets. This is a lesson we learned from the Electricity Crisis in California. The Californian market\u27s collapse was not the result of market decentralization but it was triggered by other decisions, such as high natural gas prices, with a direct impact in the supply-demand chain. This dissertation supports generation asset business decisions -from fuel supply concerns to wholesale trading in energy and ancillary services. The forces influencing the value chain are changing rapidly, and can become highly controversial. Through this report, the author brings an integrated and objective perspective, providing a forum to identify and address common planning and operational needs. The purpose of this dissertation is to present theories and ideas that can be applied directly in algorithms to make GENCOs decisions more efficient. This will decompose the problem into independent subproblems for each time interval. This is preferred because building a complete model in one time is practically impossible. The diverse scope of this report is unified by the importance of each topic to understanding or enhancing the profitability of generation assets. Studies of top strategic issues will assess directly the promise and limits to profitability of energy trading. Studies of ancillary services will permit companies to realistically gauge the profitability of different services, and develop bidding strategies tuned to competitive markets

Market-oriented micro virtual power prosumers operations in distribution system operator framework

As the European Union is on track to meet its 2020 energy targets on raising the share of renewable energy and increasing the efficiency in the energy consumption, considerable attention has been given to the integration of distributed energy resources (DERs) into the restructured distribution system. This thesis proposes market-oriented operations of micro virtual power prosumers (J.lVPPs) in the distribution system operator framework, in which the J.lVPPs evolve from home-oriented energy management systems to price-taking prosumers and to price-making prosumers. Considering the diversity of the DERs installed in the residential sector, a configurable J.l VPP is proposed first to deliver multiple energy services using a fuzzy logic-based generic algorithm. By responding to the retail price dynamics and applying load control, the J.lVPP achieves considerable electricity bill savings, active utilisation of energy storage system and fast return on investment. As the J.lVPPs enter the distribution system market, they are modelled as price-takers in a two-settlement market first and a chance-constrained formulation is proposed to derive the bidding strategies. The obtained strategy demonstrates its ability to bring the J.l VPP maximum profit based on different composition of DERs and to maintain adequate supply capacity to meet the demand considering the volatile renewable generation and load forecast. Given the non-cooperative nature of the actual market, the J.l VPPs are transformed into price-makers and their market behaviours are studied in the context of electricity market equilibrium models. The resulted equilibrium problems with equilibrium constraints (EPEC) are presented and solved using a novel application of coevolutionary approach. Compared with the roles of home-oriented energy management systems and price-taking prosumers, the J.lVPPs as price­ making prosumers have an improved utilisation rate of the installed DER capacity and a guaranteed profit from participating in the distribution system market

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