Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls for new control methods to increase the efficiency and coordination of systems, to both lower energy needs, and offer consumption flexibility as a service to the grid. One key feature for the acceptance of those new control methods, which often rely on the availability of data and some form of data-driven modeling, is the guarantee of constraint satisfaction, either operational or related to, e.g., user comfort. This thesis considers the problem of guarantees in data-driven control, focusing on the robust setting. It covers a spectrum from a more general learning perspective to a more application-driven perspective, targeting energy systems. The first part of the thesis discusses kernel methods for function approximation, such as Kernel Ridge Regression or Support Vector Regression. Being non-parametric, these methods offer a way to approximate functions, such as the response of a dynamical system, with varying complexity, based on the choice of hyperparameters and the available data samples. Depending on assumptions on the complexity of the ground truth function, deterministic error bounds of the approximations are developed, bounding the difference of the approximation to the true function, under noisy sampling. These bounds are further improved by formulating the bounding problem as an infinite-dimensional variational problem and reformulating it into a finite-dimensional version, using representer-theorem arguments. The tightness of those bounds is demonstrated through different simulation examples.In the second part of the thesis, an open-source tool for controller benchmarking is introduced, to bridge the gap between the general control setting, and the specific application of building control. This Python library, called Energym, collects different building models from the simulation tools EnergyPlus and Modelica and interfaces them for direct usage in Python. Through an API that resembles the one of the reinforcement learning benchmarking library Gym, control signals can be sent to the individual models, and performance can be evaluated based on predefined metrics.In the third part, a method to estimate the consumption flexibility potential of individual buildings is presented. By learning the parameters of a virtual battery model and expressing uncertainties as parameter uncertainties, this method combines robust estimation and its application to buildings. The flexibility potential of individual buildings is represented by flexibility envelopes, which are used in the formulation of a coordination problem of a pool of buildings. By solving a mixed-integer problem, a schedule of activation is fixed, while the actual flexibility requests are dispatched by a heuristic algorithm. This coordination is demonstrated in large-scale simulations, using building models from Energym, for the scenarios of self-consumption and peak reduction.