Stochastic and Private Energy System Optimization

Abstract

Modern energy systems are undergoing the green transition towards renewable-based operations. This transition promises an emission-neutral and equal-access energy supply that finds tremendous public and governmental support. To succeed, the responsible parties must account for a range of engineering, economic and ethical challenges arising from the uncertain nature of renewables and utilization of vast amounts of data required to facilitate this transition. This thesis addresses those challenges using mathematically rigorous methods of optimization and privacy preservation. There is a growing consensus that the methods from stochastic optimization are critical enablers of this transition. By leveraging the probabilistic information on uncertainty, they produce control and market signals that ensure secure operations and competitive energy trading. In this thesis, we utilize those methods to develop new operational and market policies that enumerate the contributions of various actors to uncertainty and variability control. While guiding energy systems towards secure operations, these policies enable a stochastic market settlement to price energy under uncertainty and variability. To immunize the desired market properties of this settlement against any uncertainty realizations, this thesis develops stochastic approximations to trade cost efficiency for the satisfaction of market properties. To complete stochastic market settlements, we provide market redesign solutions to accommodate private forecasts in energy market clearing and to satisfy individual stochastic preferences of market participants. This thesis improves conventional data protection practices in energy systems by providing strong privacy guarantees to data owners, thus addressing the ethical challenges in utilizing vast amounts of energy data. These guarantees originate from rendering the standard optimization algorithms as differentially private mechanisms – the mechanisms that add a calibrated noise to computations to obfuscate the input optimization datasets when querying optimization results. By calibrating the noise to the privacy preferences of energy system users, these mechanisms encourage information sharing across energy systems without exposing sensitive data attributes, such as energy load patterns. The differentially private optimization mechanisms are designed for distributed and centralized optimization methods and allow for trade-offs between the level of privacy and the utility of noisy optimization outcomes.