Global Horizontal Irradiance Data Research Articles

DWT-BILSTM-based models for day-ahead hourly global horizontal solar irradiance forecasting

AbstractAccurate forecasting of electricity generation from renewable energy sources is crucial for the operation, planning and management of smart grids. For reliable planning and operation of photovoltaic (PV) systems in grid-connected or islanded utilities, an hourly day-ahead forecast of PV output is critical. The forecast of PV power can be done indirectly by estimating solar irradiance. For forecasting day-ahead hourly global horizontal irradiance (GHI), two forecasting models with different multivariate inputs are proposed in this paper, and the results are compared. These models use a hybrid algorithm of discrete wavelet decomposition and bidirectional long short-term memory (BILSTM). The inputs of the first model contain GHI and weather type data. The other model allows for observation of the effect of meteorological values including GHI, temperature, humidity, wind speed, and weather type data. The forecasting performance of deep learning algorithms which contain recurrent neural network (RNN), long short-term memory (LSTM), and BILSTM algorithms for day ahead hourly solar irradiance forecasting problems are also compared. To evaluate the performance of proposed models, two datasets are used for Model 1 and one dataset is used for Model 2. An experiment is also done to demonstrate that the proposed Model 1 is applicable in datasets collected in the vicinity of the city of Trabzon. On the other hand, BILSTM algorithm outperforms RNN and LSTM algorithms. It is seen that the test successes of both proposed models are better than the results given in the literature.

Estimation of maximum photovoltaic cover ratios in greenhouses based on global irradiance data

In this study, a method for estimating the maximum PV (photovoltaic) cover ratio for plastic greenhouses based on various years of global horizontal irradiance (GHI) data is presented and illustrated with an exemplary site in southeastern Spain. CAMS (Copernicus Atmosphere Monitoring Service) GHI data from 2005 to 2023 were analyzed to estimate the DLI (daily light integral) inside the greenhouses for various PV coverage ratios with East-West or North-South orientation. The conversion from GHI to photosynthetically active radiation is performed with the usage of a regression model from literature based on satellite and measurement data. The shading effect of the PV cover is estimated with a regression model from literature based on radiation distribution simulations in different greenhouse types. The maximum PV cover ratio was derived for different minimal DLI thresholds, corresponding to different crops. The proposed methodology has been tested for the Almería region in southeastern Spain which is characterized by high solar irradiance and can be applied also to other regions with similar climatic conditions. With a required DLI of at least 12 mol/m2/day, a theoretical maximum PV coverage of about 44% is acceptable even in December at the studied site for East-West orientation, while it reaches up to 100% (June) during the year. Further, the maximum PV cover ratios for a DLI threshold range have been calculated and compared with experimental results for plastic greenhouses from literature. In 87.2% of the case studies analyzed from literature, the proposed method showed an agreement in the estimation of the effect of PV shading ratios on marketable crop yields. The study indicates that significant PV cover ratios are theoretically possible even for light demanding crops considering DLI thresholds only and can help to select a useful PV cover ratio in PV greenhouses.

Ultra-short-term solar forecasting with reduced pre-acquired data considering optimal heuristic configurations of deep neural networks

<abstract> <p>Forecasting solar irradiance, particularly Global Horizontal Irradiance (GHI), has drawn much interest recently due to the rising demand for renewable energy sources. Many works have been proposed in the literature to forecast GHI by incorporating weather or environmental variables. Nevertheless, the expensive cost of the weather station hinders obtaining meteorological data, posing challenges in generating accurate forecasting models. Therefore, this work addresses this issue by developing a framework to reliably forecast the values of GHI even if meteorological data are unavailable or unreliable. It achieves this by leveraging lag observations of GHI values and applying feature extraction capabilities of the deep learning models. An ultra-short-term GHI forecast model is proposed using the Convolution Neural Network (CNN) algorithm, considering optimal heuristic configurations. In addition, to assess the efficacy of the proposed model, sensitivity analysis of different input variables of historical GHI observations is examined, and its performance is compared with other commonly used forecasting algorithm models over different forecasting horizons of 5, 15, and 30 minutes. A case study is carried out, and the model is trained and tested utilizing real GHI data from solar data located in Riyadh, Saudi Arabia. Results reveal the importance of employing historical GHI data in providing precise forecasting outcomes. The developed CNN-based model outperformed in ultra-short-term forecasting, showcasing average root mean square error results across different forecasting horizons: 2.262 W/m<sup>2</sup> (5min), 30.569 W/m<sup>2</sup> (15min), and 54.244 W/m<sup>2</sup> (30min) across varied day types. Finally, the findings of this research can permit GHI to be integrated into the power grid and encourage the development of sustainable energy systems.</p> </abstract>

Global horizontal irradiance prediction model considering the effect of aerosol optical depth based on the Informer model

Accurate and reliable global horizontal irradiance (GHI) prediction helps respond to the volatility of solar power output in advance. Aerosol optical depth (AOD) is the primary factor affecting the GHI in clear skies. In this study, the Informer model was first used to predict the GHI over the next 8 h by considering the AOD, meteorological parameters, and historical GHI data of Beijing as input variables, and the prediction of the GHI without AOD as a feature was calculated. The comparison results showed that the prediction errors of the models that considered AOD were lower than those of the models that did not. Moreover, when the AOD of the predicted day was larger, the difference in the mean absolute percentage error values between the two models was more significant. Hence, we proposed Planck's average AOD as a feature input to the GHI prediction model and found that the accuracy of the model improved regardless of the AOD size on the prediction day. The applicability of the developed model was verified using Golden's data. Overall, these findings indicate that this model can improve computational efficiency while maintaining good predictive performance.

Global Horizontal Irradiance Prediction using the Algorithm of Moving Average and Exponential Smoothing

To reduce the discrepancy between the results of the expected data and the actual data, prediction is a procedure that is calculated systematically based on owned historical and present information. For the creation of solar energy projects and for decision-making in other connected domains, solar radiation intensity prediction is essential. This study aims to create a predictive model on monthly global horizontal irradiance data. The method used is the Simple Moving Average algorithm, Exponentially Weighted Moving Average and Single Exponential Smoothing. The stages carried out in this study include data collection, data preprocessing, testing of predictive models, interpretation of data visualization, and performance evaluation. The results of calculating the error value and correlation produce an evaluation of the performance of the prediction model. The SES method, which obtained an MAE value of 7.13, a MAPE of 0.02%, an MSE of 88.07, an RMSE of 9.38, and an R2 of 0.94, was determined to be the best prediction model by the calculation of the prediction model performance evaluation. A MAE value of 9.45, a MAPE of 0.02%, an MSE of 150.16, an RMSE of 12.25, and an R2 of 0.91 were obtained by the EWMA method, which is also the method that produced the second-best result. A MAE value of 14.38, a MAPE of 0.04%, an MSE of 367.59, an RMSE of 19.17, and an R2 of 0.77 were obtained by the SMA method, which is the third-best result.

SIZING AND IMPLEMENTATION OF A STANDALONE SOLAR PHOTOVOLTAIC SYSTEM FOR A THREE-PHASE SUBMERSIBLE PUMPING MACHINE CONSIDERING THE TECHNO-ECONOMICS PERSPECTIVES: A CASE OF SUPER FARM ILORIN

The solar photovoltaic system is an alternative power supply source that could aid the economic growth of a nation. However, improper sizing of the system leads to a high installation cost and a low level of penetration in the energy mix. This paper focused on the appropriate sizing and implementation of a standalone solar system for a three-phase pump machine in a farm in Ilorin, Nigeria. The pump rating was determined manually as 20HP, with a flow rate of 180,000 L/h. Consequently, the daily load and solar global horizontal irradiance data were acquired and used for sizing the PV system using HOMER Pro software. Fifty-six solar panels with a total area of 120.4 m2 were proposed and installed to achieve a total power of 22.4 kW required for the machine's operation. The levelised cost of energy is 0.4007 $/kWh as against the cost of energy when the farm was running on generators with an energy cost of 4.170 $/kWh. The economic analysis of the system for the farm shows the NPC and COE of the system configuration are $28,341.91 and 0.4007 $/kWh, respectively.

Comparative Analysis of Photosynthetically Active Radiation Models Based on Radiometric Attributes in Mainland Spain

The aims of this work are to present an analysis of quality solar radiation data and develop several hourly models of photosynthetically active radiation (PAR) using combinations of radiometric variables such as global horizontal irradiance (GHI), diffuse horizontal irradiance (DHI), and direct normal irradiance (DNI) from their dimensionless indices atmospheric clearness index (kt), horizontal diffuse fraction (kd), and normal direct fraction (kb) together with solar elevation angle (α). GHI, DHI, and DNI data with 1-minute frequencies in the period from 2016 to 2021 from CEDER-CIEMAT, in a northern plateau, and PSA-CIEMAT in the southeast of the Iberian Peninsula, were used to compare two locations with very different climates according to the Köppen—Geiger classification. A total of 15 multilinear models were fitted and validated (with independent training and validation data) using first the whole dataset and then by kt intervals. In most cases, models including the clearness index showed better performance, and among them, models that also use the solar elevation angle as a variable obtained remarkable results. Additionally, according to the statistical validation, these models presented good results when they were compared with models in the bibliography. Finally, the model validation statistics indicate a better performance of the interval models than the complete models.

Validating global horizontal irradiance estimated by McClear model under clear-sky and all-sky conditions in Pakistan

The availability of accurate and reliable solar radiation data is very important to explore solar energy potential for commercial power plants. This study presents the validation of global horizontal irradiance (GHI) from McClear model under clear-sky and all-sky conditions against measured data for complex topography of Pakistan. The McClear GHI shows good agreement with measured GHI under clear-sky conditions for nine stations and good correlation was achieved with correlation coefficient ranging from 0.972 to 0.992. The relative mean bias error (rMBE) and relative root mean square error (rRMSE) using GHI data having temporal resolution of 10 minutes was ranging from −2.3 to 6.4% and 3.6 to 7.8% respectively. A seasonal statistical analysis shows variation of errors during seasons, significant variation of errors was observed for monthly statistical analysis, the overall errors for all stations were maximum in January and minimum in June. Cloud fraction (CF) from three state-of-the-art datasets (ERA-5, MERRA-2 and MODIS) was incorporated into McClear clear-sky GHI (GHIMC,clear-sky) to derive commercially resourceful all-sky GHI data (GHIMC,all-sky) using a noval approach. The rMBE of GHIMC,all-sky using CF from ERA-5, MERRA-2 and MODIS ranges from 0.1 to 8.4%, 0.1 to 14.1% and 0.2 to 16.8% respectively. The application of ERA-5 cloud fraction shows good correlation with correlation coefficient ranging from 0.871 to 0.966 and gave best results as rMBE for all stations is less than 4% except one station, the long-term GHIMC,all-sky data can be used for the solar resource assessment of Pakistan in the absence of measured data.

Comparison of Satellite-Based and Ångström–Prescott Estimated Global Horizontal Irradiance under Different Cloud Cover Conditions in South African Locations

The study compares the performance of satellite-based datasets and the Ångström–Prescott (AP) model in estimating the daily global horizontal irradiance (GHI) for stations in South Africa. The daily GHI from four satellites (namely SOLCAST, CAMS, NASA SSE, and CMSAF SARAH) and the Ångström–Prescott (AP) model are evaluated by validating them against ground observation data from eight radiometric stations located in all six macro-climatological regions of South Africa, for the period 2014-19. The evaluation is carried out under clear-sky, all-sky, and overcast-sky conditions. CLAAS-2 cloud fractional coverage data are used to determine clear and overcast sky days. The observed GHI data are first quality controlled using the Baseline Surface Radiation Network methodology and then quality control of the HelioClim model. The traditional statistical benchmarks, namely the relative mean bias error (rMBE), relative root mean square error (rRMSE), relative mean absolute error (rMAE), and the coefficient of determination (R2) provided information about the performance of the datasets. Under clear skies, the estimated datasets showed excellent performance with maximum rMBE, rMAE, and rRMSE less than 6.5% and a minimum R2 of 0.97. In contrast, under overcast-sky conditions there was noticeably poor performance with maximum rMBE (24%), rMAE (29%), rRMSE (39%), and minimum R2 (0.74). For all-sky conditions, good correlation was found for SOLCAST (0.948), CMSAF (0.948), CAMS (0.944), and AP model (0.91); all with R2 over 0.91. The maximum rRMSE for SOLCAST (10%), CAMS (12%), CMSAF (12%), and AP model (11%) was less than 13%. The maximum rMAE for SOLCAST (7%), CAMS (8%), CMSAF (8%), and AP model (9%) was less than 10%, showing good performance. While the R2 correlations for the NASA SSE satellite-based GHI were less than 0.9 (0.896), the maximum rRMSE was 18% and the maximum rMAE was 15%, showing rather poor performance. The performance of the SOLCAST, CAMS, CMSAF, and AP models was almost the same in the study area. CAMS, CMSAF, and AP models are viable, freely available datasets for estimating the daily GHI at South African locations with quantitative certainty. The relatively poor performance of the NASA SSE datasets in the study area could be attributed to their low spatial resolution of 0.5° × 0.5° (~55 km × 55 km). The feasibility of the datasets decreased significantly as the proportion of sky that was covered by clouds increased. The results of the study could provide a basis/data for further research to correct biases between in situ observations and the estimated GHI datasets using machine learning algorithms.

Short-term solar irradiance forecasting based on a novel Bayesian optimized deep Long Short-Term Memory neural network

Accurate forecasting is indispensable for improving solar renewables integration and minimizing the effects of solar energy's intermittency. Existing research on time series solar forecasting confronts challenges such as determining the accurate hyperparameters and flexibility in considering meteorological parameters. This study proposes a novel deep learning model, namely an optimized stacked Bi-directional Long Short-Term Memory(BiLSTM)/ Long Short-Term Memory(LSTM) model to forecast univariate and multivariate hourly time series data by integrating stacked LSTM layers, drop out architecture, and LSTM based model. The performance of the model is enhanced by Bayesian optimization with the tuning of six relevant hyperparameters. To evaluate the model, standard Global Horizontal Irradiance (GHI) and observed Plane of Array (POA) irradiance with meteorological real-world solar data from Sweihan Photovoltaic Independent Power project in Abu Dhabi, UAE, and NREL solar data for year-round data are forecasted. Furthermore, the performance of the proposed algorithm is also evaluated under weather uncertainty for different climate types. The forecasting accuracy is evaluated based on various performance metrics and it is observed that the proposed model offered the best R2 values, 0.99 for univariate as well as multivariate models using GHI data and 0.97 using POA data. The findings suggest that the proposed model is a reliable technique for solar prediction due to its comparable performance with both GHI and POA in terms of accuracy.

A cyclostationary model for temporal forecasting and simulation of solar global horizontal irradiance

AbstractAs part of Saudi Vision 2030, a major strategic framework developed by the Council of Economic and Development Affairs of Saudi Arabia, the country aims to reduce its dependency on oil and promote renewable energy for domestic power generation. Among the sustainable energy resources, solar energy is one of the leading resources because of the endowment of Saudi Arabia with plentiful sunlight exposure and year‐round clear skies. This essentializes to forecast and simulate solar irradiance, in particular global horizontal irradiance (GHI), as accurately as possible, mainly to be utilized by the power system operators among many others. Motivated by a dataset of hourly solar GHIs, this article proposes a model for short‐term point forecast and simulation of GHIs. Two key points, that make our model competent, are: (1) the consideration of the strong dependency of GHIs on aerosol optical depths and (2) the identification of the periodic correlation structure or cyclostationarity of GHIs. The proposed model is shown to produce better forecasts and more realistic simulations than a classical model, which fails to recognize the GHI data as cyclostationary. Further, simulated samples from both the models as well as the original GHI data are used to calculate the corresponding photovoltaic power outputs to provide a comprehensive comparison among them.

Probabilistic post-processing of gridded atmospheric variables and its application to site adaptation of shortwave solar radiation

Site adaptation refers to procedures for correcting systematic errors in an extended period of gridded modeled data using a short period of ground-based measurements used as unbiased reference. Traditionally, site adaptation leverages a single gridded product and issues point predictions. Currently, remote-sensed and reanalysis data are available from different sources providing multiple versions of estimates of a same atmospheric variable, for any location on Earth. These datasets allow what is called an ensemble prediction. In this regard, this contribution proposes a probabilistic site-adaption framework, and describes how one can use parametric and nonparametric techniques within the framework. On top of the stand-alone probabilistic site-adaption methods, heuristics are optionally used to combine quantiles, to further improve the accuracy of site adaptation. To exemplify the framework, global horizontal irradiance data from 26 sites worldwide with different climate characteristics and weather regimes are used to side-adapt the corresponding predictions from up to 5 satellite-derived databases and 2 reanalyses spanning various periods, collectively. It is found that the proposed site-adaptation methods using multiple gridded products are able to attain, on average, a 5 W/m2 reduction in continuous ranked probability score than that leveraging just a single product.

Assessment of solar radiation data quality in typical meteorological years and its influence on the building performance simulation

Solar radiation along with other weather variables are commonly processed on typical meteorological years (TMYs) to be applied in the design of various energy systems. However, in several regions of the world, solar radiation data usually lacks a suitable and/or representative measurement, which leads to its modeling and prediction to properly fill this information in the databases. Consequently, the accuracy of these models can influence the viability and proper design of such energy systems. Within this context, the present contribution aims to assess the quality of solar radiation data included in the most recent TMY databases with Brazilian data and how that quality can influence the selection of months that create TMYs as well as the building performance simulation (BPS) results. Because two different approaches to generate the solar radiation data are used, we evaluate the global horizontal irradiation data in the two latest versions of recent Brazilian TMY databases against the corresponding satellite-derived ones obtained from the POWER database (NASA). Simultaneously, as another alternative approach, global solar radiation data are calculated for the same studied locations and period through the modeling method used to generate the current version of the International Weather for Energy Calculations (IWEC2), and its performance is also compared against the corresponding reanalysis data (POWER). Finally, a set of case studies applying the local building performance regulations are exhaustively analyzed to quantify the impact of the uncertainty of solar radiation models on BPS results throughout Brazil. The results indicate that the accuracy of solar radiation models can highly influence the resulting TMY configurations. These changes can drive differences up to 40% on the prediction of the ideal annual loads of the residential buildings while, regardless of design performance, differences lower than 10% are found for the commercial case studies in most locations. Conversely, the prediction of peak loads for cooling shows to be more sensitive to the climate data changes in the commercial buildings than in the residential ones.

Twenty-Four-Hour Ahead Probabilistic Global Horizontal Irradiance Forecasting Using Gaussian Process Regression

Probabilistic solar power forecasting has been critical in Southern Africa because of major shortages of power due to climatic changes and other factors over the past decade. This paper discusses Gaussian process regression (GPR) coupled with core vector regression for short-term hourly global horizontal irradiance (GHI) forecasting. GPR is a powerful Bayesian non-parametric regression method that works well for small data sets and quantifies the uncertainty in the predictions. The choice of a kernel that characterises the covariance function is a crucial issue in Gaussian process regression. In this study, we adopt the minimum enclosing ball (MEB) technique. The MEB improves the forecasting power of GPR because the smaller the ball is, the shorter the training time, hence performance is robust. Forecasting of real-time data was done on two South African radiometric stations, Stellenbosch University (SUN) in a coastal area of the Western Cape Province, and the University of Venda (UNV) station in the Limpopo Province. Variables were selected using the least absolute shrinkage and selection operator via hierarchical interactions. The Bayesian approach using informative priors was used for parameter estimation. Based on the root mean square error, mean absolute error and percentage bias the results showed that the GPR model gives the most accurate predictions compared to those from gradient boosting and support vector regression models, making this study a useful tool for decision-makers and system operators in power utility companies. The main contribution of this paper is in the use of a GPR model coupled with the core vector methodology which is used in forecasting GHI using South African data. This is the first application of GPR coupled with core vector regression in which the minimum enclosing ball is applied on GHI data, to the best of our knowledge.

A Comparative Study of Machine Learning-Based Methods for Global Horizontal Irradiance Forecasting

The proliferation of photovoltaic (PV) power generation in power distribution grids induces increasing safety and service quality concerns for grid operators. The inherent variability, essentially due to meteorological conditions, of PV power generation affects the power grid reliability. In order to develop efficient monitoring and control schemes for distribution grids, reliable forecasting of the solar resource at several time horizons that are related to regulation, scheduling, dispatching, and unit commitment, is necessary. PV power generation forecasting can result from forecasting global horizontal irradiance (GHI), which is the total amount of shortwave radiation received from above by a surface horizontal to the ground. A comparative study of machine learning methods is given in this paper, with a focus on the most widely used: Gaussian process regression (GPR), support vector regression (SVR), and artificial neural networks (ANN). Two years of GHI data with a time step of 10 min are used to train the models and forecast GHI at varying time horizons, ranging from 10 min to 4 h. Persistence on the clear-sky index, also known as scaled persistence model, is included in this paper as a reference model. Three criteria are used for in-depth performance estimation: normalized root mean square error (nRMSE), dynamic mean absolute error (DMAE) and coverage width-based criterion (CWC). Results confirm that machine learning-based methods outperform the scaled persistence model. The best-performing machine learning-based methods included in this comparative study are the long short-term memory (LSTM) neural network and the GPR model using a rational quadratic kernel with automatic relevance determination.

Short-Term Solar Power Forecasting Using Genetic Algorithms: An Application Using South African Data

Renewable energy forecasts are critical to renewable energy grids and backup plans, operational plans, and short-term power purchases. This paper focused on short-term forecasting of high-frequency global horizontal irradiance data from one of South Africa’s radiometric stations. The aim of the study was to compare the predictive performance of the genetic algorithm and recurrent neural network models with the K-nearest neighbour model, which was used as the benchmark model. Empirical results from the study showed that the genetic algorithm model has the best conditional predictive ability compared to the other two models, making this study a useful tool for decision-makers and system operators in power utility companies. To the best of our knowledge this is the first study which compares the genetic algorithm, the K-nearest neighbour method, and recurrent neural networks in short-term forecasting of global horizontal irradiance data from South Africa.

The Performance Assessment of Six Global Horizontal Irradiance Clear Sky Models in Six Climatological Regions in South Africa

This study assesses the performance of six global horizontal irradiance (GHI) clear sky models, namely: Bird, Simple Solis, McClear, Ineichen–Perez, Haurwitz and Berger–Duffie. The assessment is performed by comparing 1-min model outputs to corresponding clear sky reference 1-min Baseline Surface Radiation Network quality controlled GHI data from 13 South African Weather Services radiometric stations. The data used in the study range from 2013 to 2019. The 13 reference stations are across the six macro climatological regions of South Africa. The aim of the study is to identify the overall best performing clear sky model for estimating minute GHI in South Africa. Clear sky days are detected using ERA5 reanalysis hourly data and the application of an additional 1-min automated detection algorithm. Metadata for the models’ inputs were sourced from station measurements, satellite platform observations, reanalysis and some were modelled. Statistical metrics relative Mean Bias Error (rMBE), relative Root Mean Square Error (rRMSE) and the coefficient of determination (R2) are used to categorize model performance. The results show that each of the models performed differently across the 13 stations and in different climatic regions. The Bird model was overall the best in all regions, with an rMBE of 1.87%, rRMSE of 4.11% and R2 of 0.998. The Bird model can therefore be used with quantitative confidence as a basis for solar energy applications when all the required model inputs are available.

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

The proliferation of solar power systems could cause instability within existing power grids due to the variable nature of solar power. A well-defined statistical model is important for managing the supply-and-demand dynamics of a power system that contains a significant variable renewable energy component. It is furthermore important to consider the inherent uncertainty in the data when modeling such a complex power system. Gaussian process regression has the potential to address both of these concerns: the probabilistic modeling of solar radiation data could assist in managing the variability of solar power, as well as provide a mechanism to deal with uncertainty. In this paper, solar radiation data was obtained from the Southern African Universities Radiometric Network and used to train a Gaussian process regression model which was developed especially for this purpose. Attention was given to constructing an appropriate Gaussian process kernel. It was found that a carefully constructed kernel allowed for the successful interpolation of global horizontal irradiance data, with a root-mean-squared error of 82.2W/m2. Gaps in the data, due to possible meter failure, were also bridged by the Gaussian process with a root-mean-squared error of 94.1 W/m2 and accompanying confidence intervals. A root-mean-squared error of 151.1 W/m2 was found when forecasting the global horizontal irradiance with a forecasting horizon of five days. These results, achieved in modeling solar radiation data using Gaussian process regression, could open new avenues in the development of probabilistic renewable energy management systems. Such systems could aid smart grid operators and support energy trading platforms, by allowing for better-informed decisions that incorporate the inherent uncertainty of stochastic power systems.

Intelligent techniques, harmonically coupled and SARIMA models in forecasting solar radiation data: A hybridization approach

The unsteady and intermittent feature (mainly due to atmospheric mechanisms and diurnal cycles) of solar energy resource is often a stumbling block, due to its unpredictable nature, to receiving high-intensity levels of solar radiation at ground level. Hence, there has been a growing demand for accurate solar irradiance forecasts that properly explain the mixture of deterministic and stochastic characteristic (which may be linear or nonlinear) in which solar radiation presents itself on the earth’s surface. The seasonal autoregressive integrated moving average (SARIMA) models are popular for accurately modelling linearity, whilst the neural networks effectively capture the aspect of nonlinearity embedded in solar radiation data at ground level. This comparative study couples sinusoidal predictors at specified harmonic frequencies with SARIMA models, neural network autoregression (NNAR) models and the hybrid (SARIMA-NNAR) models to form the respective harmonically coupled models, namely, HCSARIMA models, HCNNAR models and HCSARIMA-NNAR models, with the sinusoidal predictor function, SARIMA, and NNAR parts capturing the deterministic, linear and nonlinear components, respectively. These models are used to forecast 10-minutely and 60-minutely averaged global horizontal irradiance data series obtained from the RVD Richtersveld solar radiometric station in the Northern Cape, South Africa. The forecasting accuracy of the three above-mentioned models is undertaken based on the relative mean square error, mean absolute error and mean absolute percentage error. The HCNNAR model and HCSARIMA-NNAR model gave more accurate forecasting results for 60-minutely and 10-minutely data, respectively.
 Highlights
 
 HCSARIMA models were outperformed by both HCNNAR models and HCSARIMA-NNAR models in the forecasting arena.
 HCNNAR models were most appropriate for forecasting larger time scales (i.e. 60-minutely).
 HCSARIMA-NNAR models were most appropriate for forecasting smaller time scales (i.e. 10-minutely).
 Models fitted on the January data series performed better than those fitted on the June data series.

The Ångström–Prescott Regression Coefficients for Six Climatic Zones in South Africa

The South African Weather Service (SAWS) manages an in situ solar irradiance radiometric network of 13 stations and a very dense sunshine recording network, located in all six macroclimate zones of South Africa. A sparsely distributed radiometric network over a landscape with dynamic climate and weather shifts is inadequate for solar energy studies and applications. Therefore, there is a need to develop mathematical models to estimate solar irradiation for a multitude of diverse climates. In this study, the annual regression coefficients, a and b, of the Ångström–Prescott (AP) model, which can be used to estimate global horizontal irradiance (GHI) from observed sunshine hours, were calibrated and validated with observed station data. The AP regression coefficients were calibrated and validated for each of the six macroclimate zones of South Africa using the observation data that span 2013 to 2019. The predictive effectiveness of the calibrated AP model coefficients was evaluated by comparing estimated and observed daily GHI. The maximum annual relative Mean Bias Error (rMBE) was 0.371%, relative Mean Absolute Error (rMAE) was 0.745%, relative Root Mean Square Error (rRMSE) was 0.910%, and the worst-case correlation coefficient (R2) was 0.910. The statistical validation metrics results show that there is a strong correlation and linear relation between observed and estimated GHI values. The AP model coefficients calculated in this study can be used with quantitative confidence in estimating daily GHI data at locations in South Africa where daily observation sunshine duration data are available.