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Real-Time Data-Driven Optimization Algorithms for Modern Power Systems
Power systems have experienced significant transformations in recent years driven by the integration of new technologies, such as renewable generation and distributed energy resources (DERs). However, the variability of renewable generation and uncontrollable loads, along with the increasing grid-to-user interactions, pose severe challenges to the grid operation. Therefore, ensuring a reliable, safe, and optimal real-time operation of modern power systems requires new scalable optimization approaches that can cope with uncertainty and learn models in real-time. Towards this end, this dissertation presents contributions to the field of time-varying optimization, focusing on applications where renewable generation and controllable DERs interact with the grid.
The dissertation is divided into two parts. Part I (Chapter 2 and 3) investigates time-varying optimization problems associated with a physical system and human-in-the-loop interactions. In this part, we study two settings. First, we consider a cost comprising a partially known time-varying function capturing performance metrics of the system, as well as unknown functions associated with users interacting with the physical system. Second, we feature an optimization problem where the objective is to minimize cost functions related to the individuals’ preferences, subject to timevarying constraints that capture the physical or operational limits of the network. Based on these time-varying optimization problems, we develop learning-based distributed online optimization algorithms. Our focus lies in the synthesis of first-order online methods, where feedback from the user is leveraged to learn the unknown functions concurrently with the execution of the online algorithm, and measurements of the output of the system are used to estimate the gradient and evaluate the partially known engineering functions.
Part II (Chapter 4 - 7) focuses on optimization and control techniques for different applications where power systems interact with controllable DERs. First, we present an application of the theoretical framework of Part I to the real-time management of DERs. Second, we present a demand response application on commercial buildings. In this case, we introduce a predictive controller for a grid-interactive multi-zone building where the temperature dynamics are learned via a supervised learning technique. This controller uses the learned dynamics to solve a multi-objective problem to guarantee occupants’ comfort and energy efficiency during normal conditions and demand response events. Third, we study the estimation of sensitivity matrices in power grids with applications in transmission and distribution systems. By leveraging a low-rank approximation of certain classes of sensitivity matrices, we propose an online proximal-gradient algorithm based on a robust nuclear norm minimization problem to estimate linear sensitivities from measurements. Finally, we address a problem related to the charging schedule of electric vehicles (EVs). We consider a scenario where a ride-service provider utilizes a 100%-EV fleet to serve customers, while a power utility company aims to maximize the utilization of renewable generation at specific charging stations. To achieve this, we propose a novel mechanism that encourages EV charging during hours of high renewable generation while minimizing the impact on the quality of service for the ride-service provider.</p