Multi-Horizon Forecasting of Global Horizontal Irradiance Using Online Gaussian Process Regression: A Kernel Study

Abstract

In the present paper, global horizontal irradiance (GHI) is modelled and forecasted at time horizons ranging from 30 min to 48 h, thus covering intrahour, intraday and intraweek cases, using online Gaussian process regression (OGPR) and online sparse Gaussian process regression (OSGPR). The covariance function, also known as the kernel, is a key element that deeply influences forecasting accuracy. As a consequence, a comparative study of OGPR and OSGPR models based on simple kernels or combined kernels defined as sums or products of simple kernels has been carried out. The classic persistence model is included in the comparative study. Thanks to two datasets composed of GHI measurements (45 days), we have been able to show that OGPR models based on quasiperiodic kernels outperform the persistence model as well as OGPR models based on simple kernels, including the squared exponential kernel, which is widely used for GHI forecasting. Indeed, although all OGPR models give good results when the forecast horizon is short-term, when the horizon increases, the superiority of quasiperiodic kernels becomes apparent. A simple online sparse GPR (OSGPR) approach has also been assessed. This approach gives less precise results than standard GPR, but the training computation time is decreased to a great extent. Even though the lack of data hinders the training process, the results still show the superiority of GPR models based on quasiperiodic kernels for GHI forecasting.

Evaluating the Potential of Gaussian Process Regression for Solar Radiation Forecasting: A Case Study

“…This diminishes the effect of short term variability in atmospheric conditions. As Tolba et al [20] point out, the effect of short-term variability is an important consideration when constructing a kernel. To illustrate the effect of sampling interval on data characteristics, wind speed data from the Stellenbosch weather station was sampled at different intervals, ranging from 1 h to 12 h. A Gaussian process regression was done for each of the wind speed data sets.…”

“…This means that the Gaussian process regressor was trained on a multi-dimensional array of input data, but that interpolation and prediction was only done for a single output, namely GHI. Alternative structures for a Gaussian process regression model include online Gaussian process regression (OGPR) and online sparse Gaussian process regression (OSGPR), both of which have been investigated within the context of GHI forecasting by Tolba et al [20].…”

“…The root-mean-squared (RMS) error was used to quantify the goodness-of-fit for the interpolation. The RMS error was also employed by [20].…”

“…Tolba et al [20] used Online Gaussian Process Regression and Online Sparse Gaussian Process Regression to forecast global horizontal irradiance (GHI) over time horizons ranging between 30 min and 48 h. By carefully considering kernel selection, Tolba et al [20] have furthermore compared the performance of different kernels (simple as well as compound kernels) for application in GHI data modelling. A thorough investigation into the effect of different kernels on the performance of the model was done.…”

“…A thorough investigation into the effect of different kernels on the performance of the model was done. Tolba et al [20] have found that quasi-quadratic kernels are particularly useful for modelling and forecasting GHI data and suggest that a periodic component should be present in a kernel for modelling the global structure of GHI data, while a random component should be used for modelling local variation due to atmospheric disturbances. This result of Tolba et al [20] has been confirmed in the current paper.…”