Statistical analysis of multi‐day solar irradiance using a threshold time series model

Abstract

The analysis of solar irradiance has important applications in predicting solar energy production from solar power plants. Although the sun provides every day more energy than we need, the variability caused by environmental conditions affects electricity production. Recently, new statistical models have been proposed to provide stochastic simulations of high-resolution data to downscale and forecast solar irradiance measurements. Most of the existing models are linear and highly depend on normality assumptions. However, solar irradiance shows strong nonlinearity and is only measured during the day time. Thus, we propose a new multi-day threshold autoregressive model to quantify the variability of the daily irradiance time series. We establish the sufficient conditions for our model to be stationary, and we develop an inferential procedure to estimate the model parameters. When we apply our model to study the statistical properties of observed irradiance data in Guadeloupe island group, a French overseas region located in the Southern Caribbean Sea, we are able to characterize two states of the irradiance series. These states represent the clear-sky and non-clear sky regimes. Using our model, we are able to simulate irradiance series that behave similarly to the real data in mean and variability, and more accurate forecasts compared to linear models.

Subordinated Gaussian processes for solar irradiance

“…In fact, markedly missing from the literature in this subject are models that can unconditionally generate multiple days of realistic GHI data simulations at the 1 s time scale, a method for which we present here. While studies like (Zhang et al, 2022) or (Euán et al, 2022) are successful, we feel that, because the problems they tackle (conditional downscaling and forecasting, respectively) are different enough from ours, direct comparison is not justifiable. Additionally, particularly at fine temporal resolution, GHI data tend to have intermittent high frequency variability and are highly non-Gaussian, which challenges the assumptions of most traditional time series models.…”

“…Even if closed‐form likelihoods were available, we would be working in a high‐dimensional parameter space, which would be a computational burden that the approach we propose avoids. Due to these limitations, we propose a multi‐step procedure, which is not uncommon in the solar irradiance forecasting and modeling literature (Euán et al, 2022; Zhang et al, 2022). See Figure 4 for a summary overview of the steps of the estimation procedure.…”

“…One final difference is that, similar to other papers in the literature, this model is built for the 1 min time scale, which has different variability than the 1 s level. Recent work from (Euán et al, 2022) does address high‐frequency GHI simulation at the 1 s level using a self‐exciting threshold autoregressive (SETAR) model to quantify and replicate the variability of daily irradiance time series for use in short term (1‐ and 5‐step ahead) forecasting. While this has been shown to be quite effective for these short term time horizon forecasts, it has not been tested on the task of full‐day one second resolution GHI simulations.…”

Pointwise data depth for univariate and multivariate functional outlier detection

“…This fluctuation can seriously affect PV systems; for example, short‐term variations (a few seconds) might cause local voltage flickering, and a longer‐term time scale change can impact the storage system (Kleissl, 2013). As a result, improper detection of such fluctuations in daily performance might result in many disruptions and damages to PV production (Euán et al, 2022; Mallor et al, 2017).…”