Mathematical Modelling of Electrical Power System Stability – Looking Towards a Zero Carbon Future

Cooke, Christian (2023). Mathematical Modelling of Electrical Power System Stability – Looking Towards a Zero Carbon Future. PhD thesis The Open University.



Lightning hit a transmission powerline outside London, England on 9 August 2019. There followed a loss of power from a cascade of generator outages that exceeded contingency reserves, leading to an exceptional fall in grid frequency causing widespread transport disruptions and the disconnection of over 1m households.

The power outage raised questions about the ability of the GB electricity grid to withstand rapid changes in frequency caused by outages and surges on the network. Grid inertia has been changing in recent years due to the emergence of renewable generation as a significant contributor to the energy mix.

As part of climate change mitigation efforts, there has been an acceleration in the deployment of distributed renewable generation replacing conventional thermal power plants in grids across the world. As a result, there has been a change in the aggregate and regional inertial capacity, with consequences for the stability of these networks and their ability to withstand large variations in frequency. Measures to mitigate the consequences of this change to grid stability need to be evaluated and the level of investment required to prevent a reoccurrence of an event such as that of 9 August quantified.

Simulating frequency events on the GB grid using a single-bus model involves a system of differential equations representing the overall generation and load present at the time. The standard model based on the swing equation assumes unlimited capacity in aggregated resources, the availability of these services for the duration of the frequency excursion and a homogeneous response without local variation.

In simulating the effect of outages on the GB Grid frequency on 9 August 2019 and other events in the period 2018--2019, the effect of limiting these services to the capacity of resources engaged during the event is examined. Taking resource limitations into account enables the approximation of the frequency trace for documented network perturbations. Enhancing this model so that it represents a networked grid using an algebraic differential system of equations facilitates the simulation of the effects of localized variation in inertia and frequency response services on the propagation of transients across a network.

Using this model, the effects of varying responses to transients can be investigated, and grids of varying scales and topologies can be compared to determine differences in their response to outages.

The propagation of disturbances across domains within the network that have different frequency response characteristics can thereby be examined with a view to drawing conclusions about the optimal deployment of frequency response services, and their relative cost-effectiveness in delivering a stable supply as the proportion of renewable generation in the energy mix grows.

The model is demonstrated to be generalizable by its application to simulating an outage on the Italian grid, with the results compared to similar results on that network. This demonstrates the facility of applying the model to examining power systems of different topologies and characteristics, and evaluating plans for their migration to zero-carbon generation.

Insight is gained into the responses of various characteristics of the grid and how they interact with unplanned generation imbalances. Using this adapted model, events on the GB grid are examined to validate the influence of these features and evaluate the anticipated response to similar events in the future using energy-mix scenario projections. With the effectiveness of the model validated, novel mitigating measures to preserve the stability of a low-inertia grid can be evaluated.

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