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We consider the problem of controlling the frequency of low-inertia power systems via inverter-based resources (IBRs) that are weakly connected to the grid. We propose a novel grid-forming control strategy, the so-called frequency shaping control, that aims to shape the frequency response of synchronous generators (SGs) to load perturbations so as to efficiently arrest sudden frequency drops. Our solution relaxes several existing assumptions in the literature and is able to navigate tradeoffs between peak power requirements and maximum frequency deviations. Finally, we analyze the robustness to imperfect knowledge of network parameters, while particularly highlighting the importance of accurate estimation of these parameters.

This paper considers a nonconvex optimization problem that evolves over time, and addresses the synthesis and analysis of regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized primal-dual gradient methods are implemented in a running fashion, in the sense that the underlying optimization problem changes during the iterations of the algorithms. For a problem with twice continuously differentiable cost and constraints, and under a generalization of the Mangasarian-Fromovitz constraint qualification, sufficient conditions are derived for the running algorithm to track a KKT trajectory. Further, asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory) are obtained. A continuous-time version of the algorithm, framed as a system of differential inclusions, is also considered and analytical convergence results are derived. For the continuous-time setting, a set of sufficient conditions for the KKT trajectories not to bifurcate or merge is proposed. Illustrative numerical results inspired by a real-world application are provided.

As buildings account for approximately 40% of global energy consumption and associated greenhouse gas emissions, their role in decarbonizing the power grid is crucial. The increased integration of variable energy sources, such as renewables, introduces uncertainties and unprecedented flexibilities, necessitating buildings to adapt their energy demand to enhance grid resiliency. Consequently, buildings must transition from passive energy consumers to active grid assets, providing demand flexibility and energy elasticity while maintaining occupant comfort and health. This fundamental shift demands advanced optimal control methods to manage escalating energy demand and avert power outages. Reinforcement learning (RL) emerges as a promising method to address these challenges. In this paper, we explore ten questions related to the application of RL in buildings, specifically targeting flexible energy management. We consider the growing availability of data, advancements in machine learning algorithms, open-source tools, and the practical deployment aspects associated with software and hardware requirements. Our objective is to deliver a comprehensive introduction to RL, present an overview of existing research and accomplishments, underscore the challenges and opportunities, and propose potential future research directions to expedite the adoption of RL for building energy management.