Continuous and Distribution-Free Probabilistic Wind Power Forecasting: A Conditional Normalizing Flow Approach

We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow (CNF). In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches) and can directly yield continuous probability densities, hence avoiding quantile crossing. It relies on a base distribution and a set of bijective mappings. Both the shape parameters of the base distribution and the bijective mappings are approximated with neural networks. Spline-based conditional normalizing flow is considered owing to its non-affine characteristics. Over the training phase, the model sequentially maps input examples onto samples of base distribution, given the conditional contexts, where parameters are estimated through maximum likelihood. To issue probabilistic forecasts, one eventually maps samples of the base distribution into samples of a desired distribution. Case studies based on open datasets validate the effectiveness of the proposed model, and allows us to discuss its advantages and caveats with respect to the state of the art.

I. Introduction

As An essential tool to assess and accommodate wind power generation uncertainty, short-term probabilistic wind power forecasting (PWPF) has gained increasing interest in recent decades. It generally takes numerical weather prediction and historical values as input features, in order to model and communicate the probability density of wind power generation at some time in the future. Such densities may be for a unique lead time and location (hence, univariate), or jointly for several lead times and/or locations (referred to as multivariate) [1]. It has become common now to decouple the estimation of the marginal probability density function of each variable and of the interdependence structure in the multivariate PWPF [2]. In other words, univariate PWPF is usually recognized as the cornerstone of PWPF problems.