Decarbonisation efforts are making power (electricity) systems - which require a continuous matching of supply and demand across time and throughout a network known as the grid - increasingly weather-dependent. Historically, this balance was maintained by adjusting dispatchable (mostly fossil fuel) generation. However, as fossil fuels are displaced by weather-dependent renewables such as solar and wind, neither supply nor demand can be fully controlled. This complicates the maintenance of supply-demand balance, known informally as "keeping the lights on".

Power system planning models are simplified representations of electricity systems used to inform investment strategy, such as whether to build a wind farm, solar farm, gas plant, transmission line or battery. They involve an optimisation problem that minimises the sum of install and subsequent operation costs. Their outputs depend on demand and weather patterns, which enter the model as time series of e.g. demand levels, wind speeds and solar irradiances.

The use of relatively short demand and weather time series (e.g. a single year) in power system planning studies has recently been criticised. This is because many conclusions - such as whether a 100% renewable power system is feasible and affordable - depend on the choice of sample; picking an unrepresentative one provides an unrealistic impression of cost or reliability. At the same time, computing resources usually prevent the consideration of longer samples, since planning problems take too much time or memory to solve.

In this thesis, we introduce subsampling methods to reduce and quantify the impact of demand and weather sampling uncertainty in power system planning models. Our algorithms compress long time series into shorter data sets - enhancing computational efficiency - and provide uncertainty bounds on model outputs. They help prevent incorrect conclusions by (1) allowing the consideration of larger amounts of data, reducing sampling uncertainty, and (2) indicating to users whether their outputs are statistically robust or a result of the particular demand and weather sample.

We combine and extend techniques from the power systems, statistics and optimisation literature. This is because power system planning models involve optimisation problems solved across demand and weather time series, which we view - as is common in statistics - as samples from an underlying distribution. Our contributions are statistical subsampling methods, such as importance sampling and the bootstrap, adapted to power system optimisation problems.