Aggregation and Uncertainty in Power Grids

: Optimising Generator Parameters for Stability

Abstract

The transition from fossil fuel power generation to renewable energy is essential but comes with challenges. Many renewable energy sources are highly variable, and renewable power generation systems often have low inertia, which can make the power system more sensitive to imbalances between supply and demand. This combination can make a power grid more susceptible to failure and thus decrease the security of the electricity supply. Methods for finding the most stable configuration of a power grid have been available for years. However, these methods often depend on aggregated models of power grids, in which multiple generators are treated as if they were a single generator, and they assume minimal or no uncertainty in the generator parameters. This thesis explores these assumptions in detail with the aim of developing new and more robust methods for improving power grid stability. The first part of this thesis explores the clustering of generators based on coherency, where coherency is defined in terms of phase angle deflection following a disturbance in the grid. We consider different mathematical formulations of coherency and develop metrics for coherency that can incorporate information from a wide variety of modelled disturbances. We use these metrics alongside different clustering approaches to illustrate that it is difficult to consistently define generator coherency for the purposes of aggregation. While certain generators behave similarly in response to disturbances, we show that it can be difficult to find clusters of generators that are consistently coherent over a wide range of disturbances. We then analyse how the modelled stability of a power grid changes when generators are aggregated, and explore how this affects the process of choosing generator parameters to optimise stability. We find that applying generator optimisation methods to grids involving aggregated “generators” can yield different results compared to applying the same optimisation methods to fully disaggregated generators. Most notably, using optimised generator parameters based on aggregated models can lead to grid stability outcomes that are worse than those predicted by the aggregated model itself. As a result, the use of aggregated models for optimisation may give the impression that the grid is more stable than it truly is Lastly, we explore methods for choosing the parameters of individual generators to optimise grid stability. We investigate how existing methods for tuning generator parameters perform in the presence of uncertainty, and we present a method that could be used to incorporate uncertainty into the optimisation process. We define robustness as the ability to maintain grid stability across a wide range of uncertain parameter values, using a quantile-based metric to evaluate performance. We find that simple optimisation methods can lead to more robust results than more sophisticated methods that do not account for uncertainty. However, our optimisation under uncertainty method achieves the best performance in the worst-case scenarios. In conclusion, this thesis demonstrates the critical roles of generator aggregation and uncertainty in analysing grid stability and how these both affect generator parameter optimisation. The approaches and insights in this thesis could be used to develop more robust and efficient power isystem models, which will be crucial for successfully developing stable and secure renewable-led power grids at scale.

Date of Award	17 Jun 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Sam Williamson (Supervisor) & Cameron Hall (Supervisor)