A double decomposition-based modelling approach to forecast weekly solar radiation

Highlights

• A double decomposition based solar radiation forecasting model incorporating climate drivers.

• Multivariate decomposition splits climate drivers into intrinsic mode functions (IMF).

• Singular value decomposition reduces dimensionality to pertinent features from a pool of IMFs.

• Random Forest (RF) algorithm used to design newly integrative hybrid model.

• Hybrid model provides significant energy management implications.

Abstract

To meet the future energy demand and avert any looming crises, efforts are being carried out to utilize sustainable and renewable energy resources. In this paper, the naturally occurring non-linearity and non-stationarity deficiencies within the climatological predictors to forecast solar radiation (Rdn) are resolved via a multivariate empirical mode decomposition method (MEMD). First, a set of antecedent weekly lags at timescale (t-1) of input datasets were collated and then were divided into training and testing subsets. The MEMD method is restricted to dissolve the training and testing climatic data independently into intrinsic modes functions (IMFs). As the numbers of total IMFs were very large, the singular value decomposition (SVD) algorithm is accustomed for dimensionality reduction simultaneously capturing the most relevant oscillatory features embedded within the IMFs. Finally, the random forest (RF) model is applied to forecast Rdn at selected solar-rich regions in Australia. The resulting hybrid MEMD-SVD-RF model was established as a consequence of the aforementioned modelling strategy. The results are benchmarked with other comparative models. The hybrid MEMD-SVD-RF model generates better and reliable forecasts having significant implications for renewable and sustainable energy applications and resources management.

Introduction

Under the Sustainable Development Goal 7 (SDG 7), the world is committed to increase electricity generations from renewable sources and to meet a country-driven target by the year 2030. Consequently, Australia is also committed to this global challenge, and the Australian energy market is changing with the key focus to increase the electricity generation via renewable sources. However, in ensuring affordability, reliability and modern energy facilities (SDG 7.1) from renewable sources, the world including Australia is falling short of meeting the targets [1]. With high economic pressures from businesses and industries, Australia has committed to developing the smart grid-smart city display project costing up to $AUD100 million, in association with the energy companies and firms [2]. Such initiatives require accurate short-term (such as weekly) monitoring and conjectures of solar radiation (Rdn) for integrated photovoltaic (PV) grid systems and concentrated solar power technologies to maintain an optimal generation mix for stable grid supply. Hence, for effective and optimized generation mix forecasting tools become essential to bring the supply on par with the demand in implementation of smart-grid systems.

The use of regression-based autoregressive models are the common forecasting technique on solar radiation forecasting, yet the autoregressive models are disadvantages as it does not consider the past disturbances in determining the current output. In addition, the empirical models have the advantage of simplicity; however, they lack generalizations [3]. Furthermore, the physical radiative transfer models do offer better generalization and accuracy, yet, such models are very complex and require a large amount of input data, which are not always available [3]. On the other hand, machine learning models have low computational complexity and are point-based that could be developed for specific sites, which complements the generation of renewable electricity that essentially are site-specific. Fundamentally, the machine learning algorithms are capable of ‘learning’ many of the entrenched features within the historical data in emulating future Rdn values, and could aptly be applied in smart grid technologies [4]. A solar irradiation data processing via estimator matrices (SIMS) was developed in Portugal [5]. Weather and Research Forecasting (WRF) model was integrated with Data Assimilation (DA) technique to forecast solar radiation in Singapore [6]. Yet, the stochastic nature of Rdn time series due to the natural variability of solar irradiance compounded by environmental factors (such as cloud cover), atmospheric conditions (such as particulate matter and dust), latitude and season makes the ‘learning’ more challenging. Hence, to increase the forecast precision of machine learning modelling approaches, data pre-processing via multi-resolution analysis (MRA) needs to be incorporated. To ameliorate this issue, a data-dependent demarcation technique is more suited in comparison to the conventional wavelet techniques [7] which is known as Empirical Mode Decomposition (EMD) pioneered by Huang, Shen [8]. The variants of EMD including, Ensemble EMD (EEMD) [9], complete ensemble EMD with adaptive noise (CEEMDAN) [10] and improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) [11] has been progressively developed to address the shortcomings of their respective predecessors. The EMD and its variants have been preferred due to their self-adaptability making it completely data-dependent in extracting salient predictive information without loss of underpinning features [7,12]. Further, the EMD based decomposition preserves the physical configurations of the temporal input data [13].

Despite such progressive evolution of the remarkable MRA tool, the EMD based decomposition techniques can only be applied to decompose a single input data series at a time [7,[9], [10], [11],14]. For instance, only the significant historical lags of weekly Rdn could be used to forecast the prospective weekly Rdn values, which a major issue with EMD, since as aforementioned, Rdn is contingent upon a number of key predictors. In such a multiple inputs case, a sequential decomposition needs to be adopted following Prasad, Deo [15], which though is a promising approach, yet, in sequential decomposition approach, some pertinent information may not be lucid since each EMD demarcation is carried out in isolation. To overcome this challenge and incorporate multiple predictor inputs with simultaneous decomposition an advanced and versatile version of EMD viz., multivariate empirical mode decomposition (MEMD) is being applied to resolve the entrenched sub-frequency components of respective inputs. The MEMD is a direct multichannel data analysis that performs concurrent time-frequency analysis to address non-linearity and non-stationarity of input signals [16]. In addition to performing an accurate investigation of composite and non-linear processes, the MEMD overcomes the mode alignment issues that are realized in the joint analysis of multidimensional data [17]. A few studies pertaining to MEMD has been detailed in literature with forecasting of the water content of soil [18], price of crude oil [19], evapotranspiration [20], and more recently standardized precipitation index [21]. So far only one study in the forecasting of solar radiation at monthly timescale has been noted [22]. These studies ascertain the suitability of MEMD as a multichannel MRA utility, yet the application of the algorithm in the short-term such as weekly Rdn forecasting has not been piloted so far.

Furthermore, this study also utilizes a robust feature optimization procedure via singular valued decomposition (SVD) [23]. The SVD is able to aptly decompose the input data series into a matrix whilst reducing its dimensionality [24]. Through this technique, the SVD conveniently extracts the characteristics more closely [25,26]. The successful studies of SVD include diagnostic analysis of meteorological fields [27], reversing engineered gene networks [28] and partitioning in the bi-plot analysis of multi-environment scenarios [29]. However, the SVD has not been applied for dimensionality reduction in Rdn forecasting studies in Australia. Additionally, the powerful random forest (RF) forecasting model which is a bootstrapped-aggregated regression tree approach has proven to have good forecasting accuracy in forecasting of energy-related variables including, wind energy [30], solar radiation [22,31], temperature variations [32] together with environmental variables like soil moisture [7,33] and standardized precipitation index [34]. However, RF has not been extensively studied for Rdn forecasting and thus has been adopted in this study. Moreover, to avoid the common issues identified by Quilty and Adamowski [35] in previous decomposition-based modelling approaches, this study partitions the data before advancing to the development of the MEMD-SVD-RF model for weekly Rdn forecasts.

This paper develops a novel hybrid model that addresses non-stationarity issues in multiple predictor inputs using self-adaptive approach whilst generating accurate forecasts of short-term, i.e., weekly solar radiation, which can have better potential of practical applications. To achieve this goal, the multichannel multiresolution analysis method, MEMD was utilized to concurrently transform the weekly time series of 8 meteorological predictor inputs into respective IMFs and residual components. Then the hybrid MEMD-SVD-RF model was developed and evaluated at three sites within sunshine-state, Queensland, Australia. Finally, the hybrid MEMD-SVD-RF model was benchmarked against multivariate adaptive regression splines (MARS) model (i.e., MEMD-SVD-MARS) and multiple linear regressions (MLR) (i.e., MEMD-SVD-MLR) equivalent models. The following section presents the theories of the machine learning algorithms, followed by MEMD decomposition technique, methods and data description, and the results. Then, the challenges and prospects of short-time to real-time Rdn forecasting using this novel MEMD-SVD-RF approach is presented and the paper is closed with concluding remarks.