The future of the electric grid requires advanced control technologies to reliably integrate high level of renewable generation and residential and small commercial distributed energy resources (DERs). Flexible loads are known as a vital component of future power systems with the potential to boost the overall system efficiency. Recent work has expanded the role of flexible and controllable energy resources, such as energy storage and dispatchable demand, to regulate power imbalances and stabilize grid frequency. This leads to the DER aggregators to develop concepts such as the virtual energy storage system (VESS). VESSs aggregate the flexible loads and energy resources and dispatch them akin to a grid-scale battery to provide flexibility to the system operator. Since the level of flexibility from aggregated DERs is uncertain and time varying, the VESSs’ dispatch can be challenging. To optimally dispatch uncertain, energy-constrained reserves, model predictive control offers a viable tool to develop an appropriate trade-off between closed-loop performance and robustness of the dispatch. To improve the system operation, flexible VESSs can be formulated probabilistically and can be realized with chance-constrained model predictive control. The large-scale deployment of flexible loads needs to carefully consider the existing regulation schemes in power systems, i.e., generator droop control. In this work first, we investigate the complex nature of system-wide frequency stability from time-delays in actuation of dispatchable loads. Then, we studied the robustness and performance trade-offs in receding horizon control with uncertain energy resources. The uncertainty studied herein is associated with estimating the capacity of and the estimated state of charge from an aggregation of DERs. The concept of uncertain flexible resources in markets leads to maximizing capacity bids or control authority which leads to dynamic capacity saturation (DCS) of flexible resources. We show there exists a sensitive trade-off between robustness of the optimized dispatch and closed-loop system performance and sacrificing some robustness in the dispatch of the uncertain energy capacity can significantly improve system performance. We proposed and formulated a risk-based chance constrained MPC (RB-CC-MPC) to co-optimize the operational risk of prematurely saturating the virtual energy storage system against deviating generators from their scheduled set-point. On a fast minutely timescale, the RB-CC-MPC coordinates energy-constrained virtual resources to minimize unscheduled participation of ramp-rate limited generators for balancing variability from renewable generation, while taking into account grid conditions. We show under the proposed method it is possible to improve the performance of the controller over conventional distributionally robust methods by more than 20%. Moreover, a hardware-in-the-loop (HIL) simulation of a cyber-physical system consisting of packetized energy management (PEM) enabled DERs, flexible VESSs and transmission grid is developed in this work. A predictive, energy-constrained dispatch of aggregated PEM-enabled DERs is formulated, implemented, and validated on the HIL cyber-physical platform. The experimental results demonstrate that the existing control schemes, such as AGC, dispatch VESSs without regard to their energy state, which leads to unexpected capacity saturation. By accounting for the energy states of VESSs, model-predictive control (MPC) can optimally dispatch conventional generators and VESSs to overcome disturbances while avoiding undesired capacity saturation. The results show the improvement in dynamics by using MPC over conventional AGC and droop for a system with energy-constrained resources.

abstract: Breeding seeds to include desirable traits (increased yield, drought/temperature resistance, etc.) is a growing and important method of establishing food security. However, besides breeder intuition, few decision-making tools exist that can provide the breeders with credible evidence to make decisions on which seeds to progress to further stages of development. This thesis attempts to create a chance-constrained knapsack optimization model, which the breeder can use to make better decisions about seed progression and help reduce the levels of risk in their selections. The model’s objective is to select seed varieties out of a larger pool of varieties and maximize the average yield of the “knapsack” based on meeting some risk criteria. Two models are created for different cases. First is the risk reduction model which seeks to reduce the risk of getting a bad yield but still maximize the total yield. The second model considers the possibility of adverse environmental effects and seeks to mitigate the negative effects it could have on the total yield. In practice, breeders can use these models to better quantify uncertainty in selecting seed varieties / Dissertation/Thesis / Masters Thesis Industrial Engineering 2019

<div>Stochastic programs are standard models for decision-making under uncertainty and have been extensively studied in the operations research literature. In general, stochastic programming involves minimizing an expected cost function, where the expectation is with respect to fully specified stochastic models that quantify the aleatoric or `inherent' uncertainty in the decision-making problem. In practice, however, the stochastic models are unknown but can be estimated from data, introducing an additional epistemic uncertainty into the decision-making problem. The Bayesian framework provides a coherent way to quantify the epistemic uncertainty through the posterior distribution by combining prior beliefs of the decision-makers with the observed data. Bayesian methods have been used for data-driven decision-making in various applications such as inventory management, portfolio design, machine learning, optimal scheduling, and staffing, etc.</div><div> </div><div>Bayesian methods are challenging to implement, mainly due to the fact that the posterior is computationally intractable, necessitating the computation of approximate posteriors. Broadly speaking, there are two methods in the literature implementing approximate posterior inference. First are sampling-based methods such as Markov Chain Monte Carlo. Sampling-based methods are theoretically well understood, but they suffer from various issues like high variance, poor scalability to high-dimensional problems, and have complex diagnostics. Consequently, we propose to use optimization-based methods collectively known as variational inference (VI) that use information projections to compute an approximation to the posterior. Empirical studies have shown that VI methods are computationally faster and easily scalable to higher-dimensional problems and large datasets. However, the theoretical guarantees of these methods are not well understood. Moreover, VI methods are empirically and theoretically less explored in the decision-theoretic setting.</div><div><br></div><div> In this thesis, we first propose a novel VI framework for risk-sensitive data-driven decision-making, which we call risk-sensitive variational Bayes (RSVB). In RSVB, we jointly compute a risk-sensitive approximation to the `true' posterior and the optimal decision by solving a minimax optimization problem. The RSVB framework includes the naive approach of first computing a VI approximation to the true posterior and then using it in place of the true posterior for decision-making. We show that the RSVB approximate posterior and the corresponding optimal value and decision rules are asymptotically consistent, and we also compute their rate of convergence. We illustrate our theoretical findings in both parametric as well as nonparametric setting with the help of three examples: the single and multi-product newsvendor model and Gaussian process classification. Second, we present the Bayesian joint chance-constrained stochastic program (BJCCP) for modeling decision-making problems with epistemically uncertain constraints. We discover that using VI methods for posterior approximation can ensure the convexity of the feasible set in (BJCCP) unlike any sampling-based methods and thus propose a VI approximation for (BJCCP). We also show that the optimal value computed using the VI approximation of (BJCCP) are statistically consistent. Moreover, we derive the rate of convergence of the optimal value and compute the rate at which a VI approximate solution of (BJCCP) is feasible under the true constraints. We demonstrate the utility of our approach on an optimal staffing problem for an M/M/c queue. Finally, this thesis also contributes to the growing literature in understanding statistical performance of VI methods. In particular, we establish the frequentist consistency of an approximate posterior computed using a well known VI method that computes an approximation to the posterior distribution by minimizing the Renyi divergence from the ‘true’ posterior.</div>

L'objectif de ce travail de thèse est de poser, d'analyser et de résoudre le problème multidisciplinaire et multi-objectif de la conception d'avions plus écologiques et plus économiques. Dans ce but, les principaux drivers de l'optimisation des performances d'un avion seront: la géométrie de l'avion, son moteur ainsi que son profil de mission, autrement dit sa trajectoire. Les objectifs à minimiser considérés sont la consommation de carburant, l'impact climatique et le coût d'opération de l'avion. L'étude sera axée sur la stratégie de recherche de compromis entre ces objectifs, afin d'identifier les configurations d'avions optimales selon le critère sélectionné et de proposer une analyse de ces résultats. L'incertitude présente au niveau des modèles utilisés sera prise en compte par des méthodes rigoureusement sélectionnées. Une configuration d'avion hybride est proposée pour atteindre l'objectif de réduction d'impact climatique. / The objective of this PhD work is to pose, investigate, and solve the highly multidisciplinary and multiobjective problem of environmentally efficient aircraft design and operation. In this purpose, the main three drivers for optimizing the environmental performance of an aircraft are the airframe, the engine, and the mission profiles. The figures of merit, which will be considered for optimization, are fuel burn, local emissions, global emissions, and climate impact (noise excluded). The study will be focused on finding efficient compromise strategies and identifying the most powerful design architectures and design driver combinations for improvement of environmental performances. The modeling uncertainty will be considered thanks to rigorously selected methods. A hybrid aircraft configuration is proposed to reach the climatic impact reduction objective.