Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be molded by different MISOCPs. To motivate our method practically, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service networks. Four different MISOCPs are developed and compared on sets of benchmark test problems. The new formulations efficiently solve large-size test problems, which cannot be solved by the best existing method. Then, the general applicability of our method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality

Economic efficiencies of the energy flows from the primary resource suppliers to the electric load centers

The economic efficiency of the electric energy system depends not only on the performance of the electric generation and transmission subsystems, but also on the ability to produce and transport the various forms of primary energy, particularly coal and natural gas. However, electric power systems have traditionally been developed and operated without a conscious awareness of the energy system-wide implications, namely the consideration of the integrated dynamics with the fuel markets and infrastructures. This has been partly due to the difficulty of formulating models capable of analyzing the large-scale, complex, time-dependent, and highly interconnected behavior of the integrated energy system. In this dissertation, a novel approach for studying the movements of coal, natural gas, and electricity in an integrated fashion is presented. Conceptually, the model developed is a simplified representation of the national infrastructures, structured as a generalized, multiperiod network composed of nodes and arcs. Under this formulation, fuel supply and electricity demand nodes are connected via a transportation network and the model is solved for the most efficient allocation of quantities and corresponding prices for the mutual benefits of all. The synergistic action of economic, physical, and environmental constraints produces the optimal pattern of energy flows. Key data elements are derived from various publicly available sources, including publications from the Energy Information Administration, survey forms administered by the Federal Energy Regulatory Commission, and databases maintained by the Environmental Protection Agency. The results of different test cases are analyzed to demonstrate that the decentralized level of decision-making combined with imperfect competition may be preventing the realization of potential cost savings. An overall optimization at the national level shows that there are opportunities to better utilize low cost generators, curtailing usage of higher cost units and increasing electric power trade, which would ultimately allow customers to benefit from lower electricity prices. In summary, the model developed is a simulation tool that helps build a better understanding of the complex dynamics and interdependencies of the coal, natural gas, and electricity networks. It enables public and private decision makers to carry out comprehensive analyses of a wide range of issues related to the energy sector, such as strategic planning, economic impact assessment, and the effects of different regulatory regimes

Pricing transport networks with fixed residential location

We consider a congestible static traffic network which is used by different households and analyse the conditions for optimal congestion taxes on network links, when not all links in the network can be taxed (partial network pricing). This is done under two assumptions about the toll revenues. First, lump sum transfers are assumed to be available. It is shown that social welfare maximisation leads to unequal treatment of equal households, because of differences in transport costs, and that constraints on network pricing imply complex deviations from marginal social cost pricing, because of network interactions. The second assumption is that the congestion tax revenue is redistributed to households according to predetermined shares. In that case, the optimal link taxes consist of a Pigouvian component, a Ramsey-Mirrlees component and a network interaction component. The taxes will deviate from marginal external congestion costs, even in the absence of network pricing constraints. This result is qualitatively different from the partial equilibrium analysis. Stylised examples of two networks are used to illustrate (a) the impact of unequal treatment of equals and of tax redistribution rules on optimal link taxes and on their effectiveness in terms of social welfare, and (b) the effect of network pricing constraints. The results suggest that (1) the effectiveness of congestion taxes is strongly reduced when not all links in the network can be taxed, (2) assignment inefficiencies are of less importance than excess demand levels when no taxes are present, and (3) that optimal parking charges may outperform partial pricing schemes when the assignment inefficiencies are small.congestion; road transport; pricing; networks

Dispatching and Rescheduling Tasks and Their Interactions with Travel Demand and the Energy Domain: Models and Algorithms

Abstract The paper aims to provide an overview of the key factors to consider when performing reliable modelling of rail services. Given our underlying belief that to build a robust simulation environment a rail service cannot be considered an isolated system, also the connected systems, which influence and, in turn, are influenced by such services, must be properly modelled. For this purpose, an extensive overview of the rail simulation and optimisation models proposed in the literature is first provided. Rail simulation models are classified according to the level of detail implemented (microscopic, mesoscopic and macroscopic), the variables involved (deterministic and stochastic) and the processing techniques adopted (synchronous and asynchronous). By contrast, within rail optimisation models, both planning (timetabling) and management (rescheduling) phases are discussed. The main issues concerning the interaction of rail services with travel demand flows and the energy domain are also described. Finally, in an attempt to provide a comprehensive framework an overview of the main metaheuristic resolution techniques used in the planning and management phases is shown

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

Mathematical programming-based models for the distribution networks' decarbonization

(English) Climate change is pushing to decarbonize worldwide economies and forcing fossil fuel-based power systems to evolve into power systems based mainly on renewable energies sources (RES). Thus, increasing the energy generated from renewables in the energy supply mix involves transversal challenges at operational, market, political and social levels due to the stochasticity associated with these technologies and their capacity to generate energy at a small scale close to the consumption point. In this regard, the power generation uncertainty can be handled through battery storage systems (BSS) that have become competitive over the last few years due to a significant price reduction and are a potential alternative to mitigate the technical network problems associated with the intermittency of the renewables, providing flexibility to store/supply energy when is required. On the other hand, the capacity of low-cost generation from small-scale power systems (distributed or decentralized generation (DG)) represents an opportunity for both customers and the power system operators. i.e., customers can generate their energy, reduce their network dependency, and participate actively in eventual local energy markets (LEM), while the power system operator can reduce the system losses and increase the power system quality against unexpected external failures. Nevertheless, incorporating these structures and operational frameworks into distribution networks (DN) requires developing sophisticated tools to support decision-making related to the optimal integration of the distributed energy resources (DER) and assessing the performance of new DNs with high DERs penetration under different operational scenarios. This thesis addresses the distribution networks' decarbonization challenge by developing novel algorithms and applying different optimization techniques through three subtopics. The first axis addresses the optimal sizing and allocation of DG and BSS into a DN from deterministic and stochastic approaches, considering the technical network limitation, the electric vehicle (EV) presence, the users capacity to modify their load consumption, and the DG capability to generate reactive power for voltage stability. Besides, a novel algorithm is developed to solve the deterministic and stochastic models for multiple scenarios providing an accurate DERs capacity that should be installed to decrease the external network dependency. The second subtopic assesses the DN capacity to face unlikely scenarios like primary grid failure or natural disasters preventing the energy supply through a deterministic model that modifies the unbalance DN topology into multiple virtual microgrids (VM) balanced, considering the power supplied by DG and the flexibility provided by the storage devices (SD) and demand response (DR). The third axis addresses the emerging transactive energy (TE) schemes in DNs with high DERs penetration at a residential level through two stochastic approaches to model a Peer-to-peer (P2P) energy trading. To this end, the capability of a P2P energy trading scheme to operate on different markets as day-ahead, intraday, flexibility, and ancillary services (AS) market is assessed, while an algorithm is developed to manage the users' information under a decentralized design.(Català) El cambio climático está obligando a descarbonizar las economías de todo el mundo forzando a los sistemas de energía basados en combustibles fósiles a evolucionar hacia sistemas de energía basados principalmente en fuentes de energía renovables (FER). Así, incrementar la energía generada a partir de renovables en el mix energético está implicando retos transversales a nivel operativo, de mercado, político y social debido a la estocasticidad asociada a estas tecnologías y su capacidad de generar electricidad a pequeña escala cerca al punto de consumo. En este sentido, la incertidumbre en la generación de energía eléctrica puede ser manejada a través de sistemas de almacenamiento en baterías (BSS) que se han vuelto competitivos en los últimos años debido a una importante reducción de precios y son una potencial alternativa para mitigar los problemas técnicos de red asociados a la intermitencia de las renovables, proporcionando flexibilidad para almacenar/suministrar energía cuando sea necesario. Por otro lado, la capacidad de generación a bajo costo a partir de sistemas eléctricos de pequeña escala (generación distribuida o descentralizada (GD)) representa una oportunidad tanto para los clientes como para los operadores del sistema eléctrico. Es decir, los clientes pueden generar su energía, reducir su dependencia de la red y participar activamente en eventuales mercados locales de energía (MLE), mientras que el operador del sistema eléctrico puede reducir las pérdidas del sistema y aumentar la calidad del sistema eléctrico frente a fallas externas inesperadas. Sin embargo, incorporar estas estructuras y marcos operativos en las redes de distribución (RD) requiere desarrollar herramientas sofisticadas para apoyar la toma de decisiones relacionadas con la integración óptima de los recursos energéticos distribuidos (RED) y evaluar el desempeño de las nuevas RD con alta penetración de RED bajo diferentes escenarios de operación. Esta tesis aborda el desafío de la descarbonización de las redes de distribución mediante el desarrollo de algoritmos novedosos y la aplicación de diferentes técnicas de optimización a través de tres dimensiones. El primer eje aborda el dimensionamiento y localización óptimos de GD y BSS en una RD desde enfoques determinísticos y estocásticos, considerando la limitación técnica de la red, la presencia de vehículos eléctricos (VE), la capacidad de los usuarios para modificar su consumo de carga y la capacidad de GD para generar potencia reactiva para la estabilidad del voltaje. Además, se desarrolla un algoritmo novedoso para resolver los modelos determinísticos y estocásticos para múltiples escenarios proporcionando una capacidad precisa de RED que debe instalarse para disminuir la dependencia de la red externa. El segundo subtema evalúa la capacidad de la RD para enfrentar escenarios improbables como fallas en la red primaria o desastres naturales que impidan el suministro de energía, a través de un modelo determinista que modifica la topología de la RD desequilibrada en múltiples microrredes virtuales (MV) balanceadas, considerando la potencia suministrada por GD y la flexibilidad proporcionada por los dispositivos de almacenamiento y respuesta a la demanda (DR). El tercer eje aborda los esquemas emergentes de energía transactiva en RDs con alta penetración de RED a nivel residencial a través de dos enfoques estocásticos para modelar un comercio de energía Peer-to-peer (P2P). Para ello, se evalúa la capacidad de un esquema de comercialización de energía P2P para operar en diferentes mercados como el mercado diario, intradiario, de flexibilidad y de servicios complementarios, a la vez que se desarrolla un algoritmo para gestionar la información de los usuarios bajo un esquema descentralizado.Postprint (published version