Climate change threatens the economic prosperity of future generations, which makes it urgent to strive for sustainable economic growth. This is in fact one of the key priorities within the UK Sustainable Development Strategy, which has been drawn up as a response to Agenda 21 of the United Nations. Mathematics and statistics play a key role in tackling this challenge and can deliver the reliable, urgently needed tools for risk assessment.
The ultimate objective of my PhD is to develop new methods of stochastic modelling and statistical inference to reliably quantify risk and uncertainty related to renewable sources of energy production. The project aims to tackle this challenge through a collaborative effort with EDF, who provide expert advice from the perspective of the world-leading power company.
Renewables are often regarded as unreliable due to their highly random and unpredictable behaviour. However, in order to achieve sustainable economic growth, investments in renewable sources of energy are needed. The question big energy suppliers are facing is which investment decision will result in a reliable energy supply for the population while minimising risk at the same time. They need to know the corresponding prices of electricity and how they depend on the supply and the variations of renewable sources of energy.
I focus on deriving suitable stochastic models for wind energy prices characterised by two criteria. First, while they need to be flexible enough to accurately describe the random evolution of renewables over time, they also have to allow for efficient calibration. Second, they have to be analytically tractable, so that futures prices of electricity generated from renewable sources of energy can be computed in explicit form, which allows operational decision making based on such models.
I already introduced a three-factor model for electricity spot prices, consisting of a deterministic seasonality and trend function as well as short- and long-term stochastic components, and derived a formula for futures prices. I further modified the model by including the information about the wind energy production as an exogenous variable. I fitted the models to German and Austrian data including spot and futures prices as well as the wind energy production and total load data. Empirical studies revealed that taking into account the impact of the wind energy generation on the prices improved the goodness of fit.
The new challenge is to model the wind energy generation directly by describing two horizontal components of wind separately and taking into account any dependencies between them. As the final part of my PhD I am going to feed these results into the model for electricity prices in order to propose a full model that could be used in practice by EDF and other energy providers.