To meet ambitious upcoming state renewable portfolio standards (RPSs), respond to customer demand for “green” electricity choices and to move towards more renewable, domestic and clean sources of energy, many utilities and power producers are accelerating deployment of wind, solar photovoltaic and solar thermal generating facilities. These sources of electricity, particularly wind power, are highly variable and difficult to forecast. To manage this variability, utilities can increase availability of fossil fuel-dependent backup generation, but this approach will eliminate some of the emissions benefits associated with renewable energy. Alternately, energy storage could provide needed ancillary services for renewables. Energy storage could also support other operational needs for utilities, providing greater system resiliency, zero emission ancillary services for other generators, faster responses than current backup generation and lower marginal costs than some fossil fueled alternatives. These benefits might justify the high capital cost associated with energy storage. Quantitative analysis of the role energy storage can have in improving economic dispatch, however, is limited. To examine the potential benefits of energy storage availability, a generalized unit commitment model of thermal generating units and energy storage facilities is developed. Initial study will focus on the city of Austin, Texas. While Austin Energy’s proximity to and collaborative partnerships with The University of Texas at Austin facilitated collaboration, their ambitious goal to produce 30-35% of their power from renewable sources by 2020, as well as their continued leadership in smart grid technology implementation makes them an excellent initial test case. The model developed here will be sufficiently flexible that it can be used to study other utilities or coherent regions. Results from the energy storage deployment scenarios studied here show that if all costs are ignored, large quantities of seasonal storage are preferred, enabling storage of plentiful wind generation during winter months to be dispatched during high cost peak periods in the summer. Such an arrangement can yield as much as $94 million in yearly operational cost savings, but might cost hundreds of billions to implement. Conversely, yearly cost reductions of $40 million can be achieved with one CAES facility and a small fleet of electrochemical storage devices. These results indicate that small quantities of storage could have significant operational benefit, as they manage only the highest cost hours of the year, avoiding the most expensive generators while improving utilization of renewable generation throughout the year. Further study using a modified unit commitment model can help to narrow the performance requirements of storage, clarify optimal storage portfolios and determine the optimal siting of this storage within the grid. / text

In optimization problems involving uncertainty, probabilistic constraints are an important tool for defining safety of decisions. In Energy management, many optimization problems have some underlying uncertainty. In particular this is the case of unit commitment problems. In this Thesis, we will investigate probabilistic constraints from a theoretical, algorithmic and applicative point of view. We provide new insights on differentiability of probabilistic constraints and on convexity results of feasible sets. New variants of bundle methods, both of proximal and level type, specially tailored for convex optimization under probabilistic constraints, are given and convergence shown. Both methods explicitly deal with evaluation errors in both the gradient and value of the probabilistic constraint. We also look at two applications from energy management: cascaded reservoir management with uncertainty on inflows and unit commitment with uncertainty on customer load. In both applications uncertainty is dealt with through the use of probabilistic constraints. The presented numerical results seem to indicate the feasibility of solving an optimization problem with a joint probabilistic constraint on a system having up to 200 constraints. This is roughly the order of magnitude needed in the applications. The differentiability results involve probabilistic constraints on uncertain linear and nonlinear inequality systems. In the latter case a convexity structure in the underlying uncertainty vector is required. The uncertainty vector is assumed to have a multivariate Gaussian or Student law. The provided gradient formulae allow for efficient numerical sampling schemes. For probabilistic constraints that can be rewritten through the use of Copulae, we provide new insights on convexity of the feasible set. These results require a generalized concavity structure of the Copulae, the marginal distribution functions of the underlying random vector and of the underlying inequality system. These generalized concavity properties may hold only on specific sets.

In recent years, the share of renewable energy sources (RESs) has been increasing in the electricity generation mix with a mandate to reduce greenhouse gas emissions that are released from burning fossil fuels. Indeed, a large share of electricity from renewable resources is required to de-carbonize the electricity sector. With the evolution of smart grids and microgrids, effective and efficient penetration of renewable generation such as wind and solar can possibly be attained. However, the intermittent nature of wind and solar generation makes microgrid operation and planning a complex problem and there is a need for a flexible grid to cope with the variability and uncertainty in their generation profiles. This research focuses on the coordination of distributed energy resources, such as energy storage systems (ESSs) and demand response (DR) to present an efficient solution towards improving the flexibility of microgrids, and supporting high levels of renewables generation. The overall goal of this research is to examine the influence of coordinated operation of ESS and DR on microgrid operations in the presence of high penetration levels of renewable generation. Deterministic and stochastic short-term operational planning models are developed to analyze the effects of coordinating ESS and DR, vis-à-vis their independent operation, on microgrids with high renewable generation. Special focus is on operation costs, scheduling and dispatching of controllable distributed generators, and levels of renewable generation. A set of valid probabilistic scenarios is considered for the uncertainties of load, and intermittency in wind and solar generation sources. The numerical results considering a benchmark microgrid indicate that coordinated operation of ESS and DR is beneficial in terms of operation costs, vis-à-vis their independent presence in the microgrid, when there is sufficient renewable generation. The coordinated operation reduces the risk in scheduling and increases the flexibility of the microgrid in supporting high levels of renewable generation.

Wind power installations are growing rapidly throughout the world due to environmental concerns associated with electric power generation from conventional generating units. Wind power is highly variable and its uncertainty creates considerable difficulties in system operation. Reliable operation of an electric power system with significant wind power requires quantifying the uncertainty associated with wind power and assessing the capacity value of wind power that will be available in the operating lead time. This thesis presents probabilistic techniques that utilize time series models and a conditional probability approach to quantify the uncertainty associated with wind power in a short future time, such as one or two hours. The presented models are applied to evaluate the risk of committing electric power from a wind farm to a power system. The impacts of initial wind conditions, rising and falling wind trends, and different operating lead times are also assessed using the developed methods. An appropriate model for day-ahead wind power commitment is also presented. Wind power commitment for the short future time is commonly made equal to, or a certain percentage, of the wind power available at the present time. The risk in meeting the commitment made in this way is different at various operating conditions, and unknown to the operator. A simplified risk based method has been developed in this thesis to assist the operator in making wind power commitments at a consistent level of risk that is acceptable to the system. This thesis presents a methodology to integrate the developed short-term wind models with the conventional power generation models to evaluate the overall operational reliability of a wind integrated power system. The area risk concept has been extended to incorporate wind power, evaluate the unit commitment risk and the well- being indices of a power system for a specified operating lead time. The method presented in this thesis will assist the operator to determine the generator units and the operating reserve required to integrate wind power and meet the forecast load for a short future time while maintaining an acceptable reliability criterion. System operators also face challenges in load dispatch while integrating wind power since it cannot be dispatched in a conventional sense, and is accepted as and when present in current operational practices. The thesis presents a method to evaluate the response risk and determine the unit schedule while satisfying a specified response risk criterion incorporating wind power. Energy storage is regarded as an effective resource for mitigating the uncertainty of wind power. New methods to incorporate energy storage with wind models, and with wind-integrated power system models to evaluate the wind power commitment risk and unit commitment risk are presented in this thesis. The developed methods and the research findings should prove useful in evaluating the operating risks to wind farm operators and system operators in wind integrated power systems.

Recently, the concept of Microgrids (MG) has been introduced in the distribution network. Microgrids are defined as small power systems that consist of various distributed micro generators that are capable of supplying a significant portion of the local demand. Microgrids can operate in grid-connected mode, in which they are connected to the upstream grid, or in isolated mode, where they are disconnected from the upstream grid and the local generators are the only source of power supply. In order to maximize the benefits of the resources available in a microgrid, an optimal scheduling of the power generation is required. Renewable resources have an intermittent nature that causes uncertainties in the system. These added uncertainties must be taken into consideration when solving the generation scheduling problem in order to obtain reliable solutions. This research studies the scheduling of power generation in a microgrid that has a group of dispatchable and non-dispatchable generators. The operation of a microgrid during grid-connected mode and isolated mode is analyzed under variable demand profiles. Two mixed integer linear programming (MILP) models for the day-ahead unit commitment problem in a microgrid are proposed. Each model corresponds to one mode of operation. Uncertainty handling techniques are integrated in both models. The models are solved using the General Algebraic Modeling System (GAMS). A number of study cases are examined to study the operation of the microgrid and to evaluate the effects of uncertainties and spinning reserve requirement on the microgrid’s expenses.

abstract: This research develops heuristics for scheduling electric power production amid uncertainty. Reliability is becoming more difficult to manage due to growing uncertainty from renewable resources. This challenge is compounded by the risk of resource outages, which can occur any time and without warning. Stochastic optimization is a promising tool but remains computationally intractable for large systems. The models used in industry instead schedule for the forecast and withhold generation reserve for scenario response, but they are blind to how this reserve may be constrained by network congestion. This dissertation investigates more effective heuristics to improve economics and reliability in power systems where congestion is a concern. Two general approaches are developed. Both approximate the effects of recourse decisions without actually solving a stochastic model. The first approach procures more reserve whenever approximate recourse policies stress the transmission network. The second approach procures reserve at prime locations by generalizing the existing practice of reserve disqualification. The latter approach is applied for feasibility and is later extended to limit scenario costs. Testing demonstrates expected cost improvements around 0.5%-1.0% for the IEEE 73-bus test case, which can translate to millions of dollars per year even for modest systems. The heuristics developed in this dissertation perform somewhere between established deterministic and stochastic models: providing an economic benefit over current practices without substantially increasing computational times. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2015

abstract: This dissertation carries out an inter-disciplinary research of operations research, statistics, power system engineering, and economics. Specifically, this dissertation focuses on a special power system scheduling problem, a unit commitment problem with uncertainty. This scheduling problem is a two-stage decision problem. In the first stage, system operator determines the binary commitment status (on or off) of generators in advance. In the second stage, after the realization of uncertainty, the system operator determines generation levels of the generators. The goal of this dissertation is to develop computationally-tractable methodologies and algorithms to solve large-scale unit commitment problems with uncertainty. In the first part of this dissertation, two-stage models are studied to solve the problem. Two solution methods are studied and improved: stochastic programming and robust optimization. A scenario-based progressive hedging decomposition algorithm is applied. Several new hedging mechanisms and parameter selections rules are proposed and tested. A data-driven uncertainty set is proposed to improve the performance of robust optimization. In the second part of this dissertation, a framework to reduce the two-stage stochastic program to a single-stage deterministic formulation is proposed. Most computation of the proposed approach can be done by offline studies. With the assistance of offline analysis, simulation, and data mining, the unit commitment problems with uncertainty can be solved efficiently. Finally, the impacts of uncertainty on energy market prices are studied. A new component of locational marginal price, a marginal security component, which is the weighted shadow prices of the proposed security constraints, is proposed to better represent energy prices. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016

Dans un marché électrique concurrentiel, EDF a adapté ses outils de gestion de production pour permettre une gestion optimale de son portefeuille, particulièrement sur les horizons journaliers et infra-journaliers, derniers leviers pour une gestion optimisée de la production. Et plus l'horizon d'optimisation s'approche du temps réel, plus les décisions prises aux instants précédents deviennent structurantes voire limitantes en terme d'actions. Ces décisions sont aujourd'hui prises sans tenir compte du caractère aléatoire de certaines entrées du modèle. En effet, pour les décisions à court-terme, la finesse et la complexité des modèles déjà dans le cas déterministe ont souvent été un frein à des travaux sur des modèles tenant compte de l'incertitude. Pour se prémunir face à ces aléas, des techniques d'optimisation en contexte incertain ont fait l'objet des travaux de cette thèse. Nous avons ainsi proposé un modèle robuste de placement de la production tenant compte des incertitudes sur la demande en puissance. Nous avons construit pour cette fin un ensemble d'incertitude permettant une description fine de l'aléa sur les prévisions de demande en puissance. Le choix d'indicateurs fonctionnels et statistiques a permis d'écrire cet ensemble comme un polyèdre d'incertitude. L'approche robuste prend en compte la notion de coût d'ajustement face à l'aléa. Le modèle a pour objectif de minimiser les coûts de production et les pires coûts induits par l'incertitude. Ces coûts d'ajustement peuvent décrire différents contextes opérationnels. Une application du modèle robuste à deux contextes métier est menée avec un calcul du coût d'ajustement approprié à chaque contexte. Enfin, le présent travail de recherche se situe, à notre connaissance, comme l'un des premiers dans le domaine de la gestion optimisée de la production électrique à court terme avec prise en compte de l'incertitude. Les résultats sont par ailleurs susceptibles d'ouvrir la voie vers de nouvelles approches du problème. / Robust Optimization is an approach typically offered as a counterpoint to Stochastic Programming to deal with uncertainty, especially because it doesn't require any precise information on stochastic distributions of data. In the present work, we deal with challenging unit-commitment problem for the French daily electricity production under demand uncertainty. Our contributions concern both uncertainty modelling and original robust formulation of unit-commitment problem. We worked on a polyhedral set to describe demand uncertainty, using statistical tools and operational indicators. In terms of modelling, we proposed robust solutions that minimize production and worst adjustment costs due to uncertainty observation. We study robust solutions under two different operational contexts. Encouraging results to the convex unit-commitment problems under uncertainty are thus obtained, with intersting research topics for future work.

Les contraintes en probabilité constituent un modèle pertinent pour gérer les incertitudes dans les problèmes de décision. En management d’énergie de nombreux problèmes d’optimisation ont des incertitudes sous-jacentes. En particulier c’est le cas des problèmes de gestion de la production au court-terme. Dans cette Thèse, nous investiguons les contraintes probabilistes sous l’angle théorique, algorithmique et applicative. Nous donnons quelques nouveaux résultats de différentiabilité des contraintes en probabilité et de convexité des ensembles admissibles. Des nouvelles variantes des méthodes de faisceaux « proximales » et « de niveaux » sont spécialement mises au point pour traiter des problèmes d’optimisation convexe sous contrainte en probabilité. Ces algorithmes gèrent en particulier, les erreurs d’évaluation de la contrainte en probabilité, ainsi que son gradient. La convergence vers une solution du problème est montrée. Enfin, nous examinons deux applications : l’optimisation d’une vallée hydraulique sous incertitude sur les apports et l’optimisation d’un planning de production sous incertitude sur la demande. Dans les deux cas nous utilisons une contrainte en probabilité pour gérer les incertitudes. Les résultats numériques présentés semblent montrer la faisabilité de résoudre des problèmes d’optimisation avec une contrainte en probabilité jointe portant sur un système de environ 200 contraintes. Il s’agit de l’ordre de grandeur nécessaire pour les applications. Les nouveaux résultats de différentiabilité concernent à la fois des contraintes en probabilité portant sur des systèmes linéaires et non-linéaires. Dans le deuxième cas, la convexité dans l’argument représentant le vecteur incertain est requise. Ce vecteur est supposé suivre une loi Gaussienne ou Student multi-variée. Les formules de gradient permettent l’application directe d’un schéma d’évaluation numérique efficient. Pour les contraintes en probabilité qui peuvent se réécrire à l’aide d’une Copule, nous donnons de nouveau résultats de convexité pour l’ensemble admissibles. Ces résultats requirent la concavité généralisée de la Copule, les distributions marginales sous-jacents et du système d’incertitude. Il est suffisant que ces propriétés de concavité généralisée tiennent sur un ensemble spécifique. / In optimization problems involving uncertainty, probabilistic constraints are an important tool for defining safety of decisions. In Energy management, many optimization problems have some underlying uncertainty. In particular this is the case of unit commitment problems. In this Thesis, we will investigate probabilistic constraints from a theoretical, algorithmic and applicative point of view. We provide new insights on differentiability of probabilistic constraints and on convexity results of feasible sets. New variants of bundle methods, both of proximal and level type, specially tailored for convex optimization under probabilistic constraints, are given and convergence shown. Both methods explicitly deal with evaluation errors in both the gradient and value of the probabilistic constraint. We also look at two applications from energy management: cascaded reservoir management with uncertainty on inflows and unit commitment with uncertainty on customer load. In both applications uncertainty is dealt with through the use of probabilistic constraints. The presented numerical results seem to indicate the feasibility of solving an optimization problem with a joint probabilistic constraint on a system having up to 200 constraints. This is roughly the order of magnitude needed in the applications. The differentiability results involve probabilistic constraints on uncertain linear and nonlinear inequality systems. In the latter case a convexity structure in the underlying uncertainty vector is required. The uncertainty vector is assumed to have a multivariate Gaussian or Student law. The provided gradient formulae allow for efficient numerical sampling schemes. For probabilistic constraints that can be rewritten through the use of Copulae, we provide new insights on convexity of the feasible set. These results require a generalized concavity structure of the Copulae, the marginal distribution functions of the underlying random vector and of the underlying inequality system. These generalized concavity properties may hold only on specific sets.

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