Analytical approximations and decision-making techniques for power systems under uncertainty

Abstract

The integration of distributed energy resources and increasing adoption of electric vehicles continue to drive uncertainty in power systems to an unprecedented level.In view of reduced applicability of traditional analysis and decision-making methods, this dissertation aims to address the need for new approaches, by attempting to solve three di↵erent sets of problems.This dissertation first proposes an analytical power flow approximation and develops a closed-form power flow framework. The thesis proposes a novel framework using Gaussian process regression to learn node voltage as a closed-form function of e↵ective bus load or injection vector. The proposed approximation is valid over a subspace of load, where the 'subspace' is used to describe a hypercube within which uncertain loads/injections lie. The approximation framework explains the system's behavior under uncertainty via Gaussian process hyper-parameter based interpretability. The proposed method achieves low mean absolute error of order 10 5 (per unit) in voltage magnitude and 10 4 (rad.) in angle when tested on 33-Bus and 56-Bus systems. Also, the proposed framework is used to develop an optimal steady-state voltage control framework using a linear voltage-power relationship. Simulation results on the 69-Bus system have shown the independence of approximation error with system loading and uncertainty levels. Therefore, control mechanisms developed based on the proposed analytical approximation are suitable under uncertainty. The framework also addresses the challenges posed by independent entity integration (e.g., peer-to-peer energy trading), as independent operational decisions of prosumers a↵ect the entire network. The proposed probabilistic feasibility set construction method-for privacy-preserving feasibility assessment-is tractable and handles non-parametric injection uncertainties by applying the worst-case performance analysis theorem over the proposed closed-form power flow approximation. The developed method's ability to capture the variations in probabilistic feasibility set for storage connected at a node in a 33-Bus network is shown via numerical simulations under di↵erent levels of total renewable penetration and uncertainty.xviiContents Statement of Originality iii