A Dirichlet-multinomial mixture model-based approach for daily solar radiation classification

Abstract

A challenging problem in the classification of daily solar radiation is the selection of the appropriate model complexity and size that best describe the data. This paper introduces a new nonparametric Bayesian method for automatic classification of daily clearness index, by assuming Dirichlet process as a nonparametric prior on the model parameters. Nonparametric methods are free from the parametric model assumptions, and there is no need to specify any parametric specifications, or to restrict the number of classes. Our approach relies on the inference of the posterior distributions using the collapsed Gibbs sampler. The proposed method is tested using measurements from 2003 to 2016, at the Silver Lake monitoring station in the USA (121º3'W, 43º7'N), with a 5-min logging interval. By applying our classification algorithm, three classes of daily clearness index distributions are identified, corresponding to three types of sky cloudiness, namely cloudy, partially cloudy, and clear sky. The proposed classification framework can facilitate the design of solar radiation conversion systems.

Assessing Evidence for Weather Regimes Governing Solar Power Generation in Kuwait

“…Many have examined the use of statistical methods to improve solar forecasting, but limited attention has been paid to the use of finite mixture distributions. Often, those applications utilizing finite mixture models have employed Dirichlet multinomial distributions on prepartitioned, subdaily data [20,32], and neglected the influence of larger-scale processes on the subdaily fluctuations. Apart from the drawback of selecting an appropriate bin interval to describe continuous data with discrete distributions, we consider that an objective classification of the overall sky condition is more likely to lead to improved forecasts.…”

“…Of these, deterministic irradiance forecasts often combine clustering analyses to classify the sky state [12][13][14][15], followed by a machine-based learning algorithm to develop forecasts [16][17][18][19]. However, clustering analyses are subjective and can result in model overfitting [20]. Approaches that combine clustering with machine learning can challenge the principle of parsimonious modelling by requiring additional estimation to achieve accurate forecasts [21].…”

“…To date, finite mixture models have tended to employ Dirichlet multinomial distributions on prepartition, subhourly data to forecast solar irradiance from sky clearness indices [20,32]. A drawback of the Dirichlet method is the assumption that sky clarity is adequately described by a discrete distribution, yet the continuous nature of sky clarity can render it sensitive to the choice of data bins [33].…”

Nonparametric Bayesian-based recognition of solar irradiance conditions: Application to the generation of high temporal resolution synthetic solar irradiance data

“…The nonparametric method prescribes the use of an infinite-dimensional parameter space rather than a fixed dimension. Furthermore, a common practice is to combine the Bayesian approach with the nonparametric framework to provide more robust models based on the prior knowledge (Frimane et al, 2018), which can be of interest for different climates and geographical differences at various sites around the world.…”

“…The main advantage of using the MGD come from the fact that it is a more flexible in terms of co-variance, and thus it can be rotated, scaled and adapted easily. Moreover, it does not depend on any intrinsic properties of the measurements, then, it does not suffer from the samples size alignment or from the sampling rate compared to the multinomial distribution for example in Frimane et al (2018). Mathematically, the key benefit of the MGD choice over other distributions is that it can represent a valuable estimate of the data distribu-tion because of the central limit theorem.…”