Forecasting offshore wind energy: Online learning, bounds and missing data

Forecasting is of the utmost importance to the integration of renewable energy into power systems and electricity markets. Indeed, to get electricity from conventional generators such as fuel-based or nuclear power plants, one is in charge of the production, whereas renewable energy sources are fundamentally variable and weather-dependent. Full benefits from their integration can only be reaped if one is given reliable, trustworthy forecasts and therefore the opportunity to accommodate the actual renewable power generation in an optimal way. In this thesis, we focus on offshore wind power short-term forecasting, as wind power fluctuations at horizons of a few minutes ahead particularly affect the system balance and are the most significant offshore. Those very short-term lead times are not only crucial but also the most difficult to improve the forecasts for, especially compared to the simple but very effective persistence benchmark.

Forecasts characterize but do not eliminate uncertainty. Therefore, they ought to be probabilistic, taking the form of distributions. Wind power generation is a stochastic process which is double-bounded by nature, by zero when there is no production and by the nominal power for high-enough wind speeds. It is non-linear and non-stationary. For short-term forecasting, statistical methods have proved to be more skilled and accurate. However, they often rely on stationary, Gaussian distributions, which cannot be appropriate for wind power generation. We start by extending previous works on generalized logit-normal distributions for wind power generation. First, we develop a rigorous statistical framework to estimate the full parameter vector of the distribution through maximum likelihood inference. Then, we derive the corresponding recursive maximum likelihood estimation and propose a recursive algorithm which can track the full parameter of the distribution in an online fashion.

From the observation that bounds are always assumed to be fixed when dealing with bounded distributions, which may not be appropriate for wind power generation as curtailment actions happen, we develop new statistical frameworks where the bounds of a distribution are allowed to vary without being observed. First, we address the bounds as additional parameters of the distribution and propose an online algorithm for quasiconvex functions which is able to track a new bound parameter over time along with the original parameters of the distribution. Alternatively, to account for the uncertainty in the bounds as well, we propose to introduce them in the statistical model as discrete latent variables. To deal with these additional, missing, variables, we suggest batch and online algorithms based on the expectation-maximization method.

The algorithms developed during this thesis were run on both synthetic and real power generation data. We question the k-nearest neighbors imputation method we implicitly used to deal with missing data in historical records. To address a common shortcoming in such non-parameteric methods, which is to overlook the distances between the neighbors themselves, we propose to explicitly acknowledge the structure of the wind farm by considering it as a graph. Then, we design an augmented imputation method which combines spectral graph theory and online learning to exploit information from both the wind farm layout and the data already collected.