A comprehensive review and analysis of solar forecasting techniques

doi:10.1007/s11708-021-0722-7

Front. Energy

2022, Vol. 16

Issue (2) : 187-223 https://doi.org/10.1007/s11708-021-0722-7

REVIEW ARTICLE

A comprehensive review and analysis of solar forecasting techniques

Pardeep SINGLA¹(

), Manoj DUHAN¹, Sumit SAROHA²

¹. Department of ECE, Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Sonepat 131039, India
². Department of Printing Technology (Electrical Engineering), Guru Jambheshwar University of Science and Technology, Hisar 125001, India

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Abstract

In the last two decades, renewable energy has been paid immeasurable attention to toward the attainment of electricity requirements for domestic, industrial, and agriculture sectors. Solar forecasting plays a vital role in smooth operation, scheduling, and balancing of electricity production by standalone PV plants as well as grid interconnected solar PV plants. Numerous models and techniques have been developed in short, mid and long-term solar forecasting. This paper analyzes some of the potential solar forecasting models based on various methodologies discussed in literature, by mainly focusing on investigating the influence of meteorological variables, time horizon, climatic zone, pre-processing techniques, air pollution, and sample size on the complexity and accuracy of the model. To make the paper reader-friendly, it presents all-important parameters and findings of the models revealed from different studies in a tabular mode having the year of publication, time resolution, input parameters, forecasted parameters, error metrics, and performance. The literature studied showed that ANN-based models outperform the others due to their nonlinear complex problem-solving capabilities. Their accuracy can be further improved by hybridization of the two models or by performing pre-processing on the input data. Besides, it also discusses the diverse key constituents that affect the accuracy of a model. It has been observed that the proper selection of training and testing period along with the correlated dependent variables also enhances the accuracy of the model.

Keywords forecasting techniques hybrid models neural network solar forecasting error metric support vector machine (SVM)

Corresponding Author(s): Pardeep SINGLA

Online First Date: 03 March 2021 Issue Date: 25 May 2022

Cite this article:

Pardeep SINGLA,Manoj DUHAN,Sumit SAROHA. A comprehensive review and analysis of solar forecasting techniques[J]. Front. Energy, 2022, 16(2): 187-223.

URL:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-021-0722-7
https://academic.hep.com.cn/fie/EN/Y2022/V16/I2/187

Fig.1 Installed solar PV capacity (MW) of five countries from 2015 to 2018 (adapted with permission from Refs. [7,10,13–15]).

Fig.2 Types of forecasting techniques based on data processed and their structure.

Fig.3 Hierarchy of ARIMA for forecasting (adapted with permission from Ref. [6]).

Fig.4 Markov process for three states (adapted with permission from Ref. [6]).

Fig.5 Architecture of ANN (adapted with permission from Ref. [32]).

Fig.6 Basic structure of SVM (adapted from Ref. [95] under CC BY).

Fig.7 Architecture of deep learning.

Ref.	YOP	Region/place	Lat/Long	Time ahead	Training period	Testing period	Input variable	Output variable	Technique	Error parameters	Error/%
[76]	2005	Turkey	36°/42°		4 years, train 9 station	3 station	Lat, Long, Al, M, MSD, T_m	SR	ANN with SCG, CGP, LM	MAPE, R²	MAPE<6.78%, R² = 99.7768%
[113]	2005	Helwan, Egypt			1 year	1 year	RH, T, WS, WD, CC	UV, IR, GI	ANN	RMSE	RMSE: IR= 5.02%, UR= 7.46%, GI= 3.97%
[90]	2009	India: Ahmadabad, Nagpur, Mumbai, Vishakhapatnam			10 stations in India	10 stations in India	Lat, Long, Al, t, M, T, RH, R, WS, LW	CI	ANN-FFBP	RMSE	RMSE= 4.5%
[32]	2010	Dezful, Iran	32°.16′N 48°.25^′ E	24 h	1398 d	214 d	DAT_m, RH, SD, E WS	DGSR	MLP, RBF	MAPE	MAPE= 5.21%
[77]	2011	Mediterrane, Anatolia, Turkey	36°.43′ –37°.46′ /30°.17′ –36°.55′		1 year	1 year	Lat, Long, Al, M, CC, T_a, H_a, WS_a, SD	SR	ANN	R², RMSE	RMSE= 0.0358, R² = 0.9974
[88]	2012	Central Queensland, Australia	23°.38′/150°.58^′	3 h	4 m	1 m	AT, WS, WD, SR, RH, R, VWSP, WS, WD, WG, E,	WE, SE	ANN	R	R = 0.96399
[89]	2012	Istanbul	-	3–40 min	1 m	1 m	SI, AT,CT	PV_o	ANN-LMBP	RMSE,R²	Stable forecast 3–40 min, Augest, stable 5–35 min forecast, April
[98]	2012	South China		1 d	Historic	10 m	Weather+ Historic	Solar PV power	SVM	RMSE, MRE	RMSE= 2.10 MW, MRE= 8.64%
[128]	2012	China		24–72 h	80% of data	20% of data	3rd order difference of SI, T_mday, normalized discrete difference, T_a	SR	ANN with statistical parameter selection	RMSE, MAPE, MABE	MAPE= 9.09%–26.7%, RMSE= 42.29–84.65 (W/m²), MABE= 31.10–64.6 (W/m²)
[97]	2013	US		1–6 h	1 year	1 year	Meteorological variables	Solar power	SVM, RBFNN AR	MAE, MAPE, R²	SVM>RBFNN>AR
[55]	2013	Gurgaon, India			750 d	165 d	AT, RH, AP, WS, WD, SR	SR	HMM and GFM	RMSE, MAPE	RMSE= 7.9124, MAPE= 3.4255
[116]	2013	NEA, Singapore		1 h–1 d	17280 data	4320 data	T, SKI, SR	SR	Fuzzy and ANN	MAPE	MAPE= 6.03%–9.65%
[145]	2013	Algeria, Oran		Hourly	2.6 years	6 m	Time series	GSR	k-means cluster and NAR	RMSE, nRMSE	RMSE= 60.24 (W/m²), nRMSE= 0.1985
[68]	2014	Owabi, Ghana,	6°.45′ N/1°.43′ W		11 m	Monthly	T, RH, AP, R, DR, SMP, SHF, WS	GSR	Sunshine and air temperature based empirical model	MBE, MPE, RMSE	Sunshine: MPE= 0.0585%, MBE= -0.0102 (MJ/(m²·d)), RMSE= 0.0338 (MJ/(m²·d))
[68]	2014	Owabi, Ghana,	6°.45′ N/1°.43′ W		11 m	Monthly	T, RH, AP, R, DR, SMP, SHF, WS	GSR	Sunshine and air temperature based empirical model	MBE, MPE, RMSE	Air temp: MPE= 1.707%, MBE= –2.973(MJ/(m²·d)), RMSE= 0.985(MJ/(m²·d))
[47]	2015			1–3 step ahead			Time series	SR	ARMA, ARIMA with LLF	MAPE	ARMA_MAPE= 71.67%, ARIMA_MAPE= 32.07%
[49]	2015	Spain	38°.67′ N/4°.15′ W	1–24 h	1 year	Monthly	Aggregated hourly SR	DHI and DNI	DHR	rMBE, rRMSE	GHI: rMBE= 0.21, rRMSE= 29.66
[49]	2015	Spain	38°.67′ N/4°.15′ W	1–24 h	1 year	Monthly	Aggregated hourly SR	DHI and DNI	DHR	rMBE, rRMSE	DNI: rMBE= 3.82, rRMSE= 46.79
[62]	2015			1 h to 1 d	1 year	1 year	NWP, meteorological	SI	Multi/step linear regression	RMSE, MAE	MOS-MLR>MOSP5
[86]	2016	Florida		15 m, 1h, 24 h			t, time lag, PM energy MT	PV energy	ANN and SVR	RMSE, MAE, MBE	ANN>SVR
[87]	2016	Tehran, Iran	51°.23^′ N/35°.44′ E		1 year	1 year	Molde-1: T_max, T_min, RH, WS, PM, Model-2: T_max, T_min, RH, WS,	GSR	ANN	MAPE, RMSE, R²	MAPE= 3.13, RMSE= 0.077, R² = 0.97
[96]	2016	Malaga, Spain	36°.42′ N/4°.28^′ W		4 years	4 years	AT, RH, AP, GHI	GSR	DT and ANN, DT and SVM, -R, SVM-C and SVM-R, SVM-C and ANN	rMAE, RMSE, S%	rMAE= 15.2%, RMSE= 22.9%, S= 43.9%
[99]	2016	North East Asia		60 min	4 years		Satellite image	SI	AVM+ SVM	RMSE, MRE, R²	RMSE= 44.1390 (W/m²), MRE= 7.7329%, R² = 0.9420
[56]	2016	Nakhon Pathom station, Thailand	13°.81′ N/100°.04′ E	Hourly	3 years	1 year	GSR, DSR, Al, CI, ESR	GSR	Markov transition matrix	RMSD	Second order>First order
[69]	2016	Ibadan	7°.4^′ N/3°.5′ E		9 years	Daily and monthly	daily avg. GSR daily SD, daily avg. T_max, daily avg.T_min	Daily and monthly vg. GSR,	Angstrom Prescott model, Garcia model, Hargreaves-Sammani model	RMSE, MAE, MAPE, R²	Daily avg. GSR RMSE= 2.70 (MJ/(m²·d)), MAE= 1.86(MJ/(m²·d)), MAPE= 9.34%, R² = 0.68
[69]	2016	Ibadan	7°.4^′ N/3°.5′ E		9 years	Daily and monthly	daily avg. GSR daily SD, daily avg. T_max, daily avg.T_min	Daily and monthly vg. GSR,		RMSE, MAE, MAPE, R²	Monthly avg. GSR RMSE= 0.0909 (MJ/(m²·d)), MAE= 0.0733(MJ/(m²·d)), MAPE= 0.5174%, R² = 0.9974
[119]	2016	Gran Canaria Island (Spain)	28°.75^′ /–16°	1 to 6 h	1 year		Meteorological data, NWP, Satellite data	GHI	ANN, ANN and SATANN and ECMWF, ANN and ECMWF and NWP	RMSE, % skill	RMSE= 83.58%–147.88%, %S= 9.67%–35.19%
[120]	2016	Kerman, Iran	25°.55^′–32°/ 30°.29^′–57°.06^′		5 years	2 years	CI	GHI	SVM and WT	MABE, RMSE, R	MABE= 0.5757 (MJ/m²), RMSE= 0.69 (MJ/m²), R = 0.96
[75]	2017	Kuwait: Wafra, Kuwait, International Airport, Abdaly, Rabyah, Sulaibiya			3 years	1 year	Time series data	SR	Gradient descent algo, LM algo	MAPE	GDE MAPE= 86.3, LM MAPE= 85.6
[79]	2017	10 cities, India		Hourly	90% of 2 years	10% of 2 years	T_min, T_max, T_avg, WS, RH, P, ESR, SD	DGSR	ANN and unity feedback, RBF and LR	MAPE	Average MAPE= 14.84%–16.32%
[83]	2017	Singapore	1°.34′ N, 103°.96′ E		3 m	1 m	T, DP, WD, WS, WG, irradiance (clear sky), error (BP)	SI	FF-ANN, BP-ANN, Fuzzy preprocessing, Error correction of past 5 min output	MAPE	ANN and Fuzzy and error correction= 29.6%, ANN and Fuzzy= 43.1%, ANN= 46.3%
[84]	2017	Italy: Lombardy, Calabria, Sicily		72 h ahead	2 years	3 m to 1 year	GHI, CC, T, Azimuth Elevation	Solar power	Analog ensemble and ANN	RMSE	RMSE= 8.09%
[85]	2017	9 plants in Taipei, China		60 min	4 h with 5 min interval		Past GSI, T, RH,WS, WD	GSI	K-NN and ANN	RMSE, MABE	RMSE= 242 (W/m²), MABE= 42 (W/m²)
[50]	2017	9 cities in Indian	NA	Hourly, Montly	data sets of 7 cities	data set of 2 cities	SD, API, Lat/Long	DGSR`	Linear, quadratic, explinear, expquadratic regression	RMSE, MAPE, r	RMSE= 3.08 (W/m²), MAPE= 0.1342%, R = 0.3790
[57]	2017	Afyonkarahisarand Antalya, Turkey		Hourly	75% of 4 years	25% of 4 years	Time series	GSR	Mycielski-Markov	RMSE, MABE, R²	RMSE= 13.49(W/m²), MABE= 10.7554%, R² = 0.8320
[58]	2017	Fort Peck, Montana, desert Rock, Navada, Bondville, Illinois Penn State Univ, Pensylvania	48°.30^′ N/105°.10^′ W 36°.62^′ N/116°.01^′ W 40°.05^′ N/88°.37^′ W 40°.72^′ N/77°.93^′ W	Seasonal			Historical data	TSRY	Discrete Markov chain	% average error	Max % Error= 10%, Min % Error= 6%
[70]	2017	Adrar, Ghardaïa, Tamanrasset, Algeria	27°.88^′/–0.27^′ 32°.36^′/ 3°.81^′ 22°.78^′/ 5°.51^′		3 years	3 years	SD, AT, RH	DSR	Sunshine based empirical, CI based sunshine and clearness	MPE, RMSE, U95, R, t-statistics	Sunshine and clearness index>All
[144]	2017	Le-Raizet, France	16°.26^′ N/ 61°.5^′ W	1 h	1 year	1 year	Time series	GSR	WD-hybrid, EEMD-hybrid, EMD-hybrid	rRMSE, rMBE, rMAE	rRMSE= 3.80%–8.31%, rMBE= –2.06%–0.02%, rMAE= 2.76%–6.64%
[28]	2018	12 locations, Iran		1 d ahead	70%	30%	M, atmosphere insolation, AP, AT, T_max, T_min, RH, WS, Lat, long	DGSR	GMDH, ANFIS, ANFIS-PSO, ANFIS-GA, ANFIS-ACO	RMSE, MAPE	GMDH>MLFFNN>ANFIS-PSO>ANFIS-GA>ANFIS-ACO>ANFIS
[81]	2018	Data Euskalmet			Six years	Seasonal	SI, AP, RH, AT	SI	ANN with delays	RMSE	RMSE= 0.03%–1.64,
[41]	2018	UMASS Trace Repository		5 min to 2 days	2 years	2 m	T, RH, DP, WS, P	SI	TMLM and GABP and ALHM	MAPE	MAPE= 8.66%
[100]	2018	Beijing, China		1 d	2 years	1 year	MSD, T_max, T_min, PM_2.5, PM₁₀, SO₂, NO₂, CO, O₃, AQI	GSR, DSR	SVM	RMSE_DSR, RMSE_GSR	RMSE_DSR= 1.432 MJ/(m²·d), RMSE_GSR= 2.947 MJ/(m²·d)
[63]	2018	Singapore	2°/140°	1 d	2 years	1 year	NWP	SI	NWP and PCA	RMSE, rMSE, MAE, rMAE, MBE, rMBE	RMSE= 169 (W·m²), rRMSE= 35.7%, MAE= 193 (W/m²), rMAE= 28.1% MBE= –14 (W/m²), rMBE= 2.9%
[105]	2018	Santiago, Cape Verde	NA	1 d	2 years and 10 years	6 m, 1 year	M, day, t, T, DP, RH, V, WS	GHI	LSTM	RMSE	RMSE= 76.245 (W/m²)
[107]	2018	Global Energy Forecasting Competiton 2014 and ECMRWF			2 years and 8 d	1 m and 10 d	Time series, T, CC TCLW, IW, SP, RH, UWC, SSRD, STRD, GHI, P	PV power	k-means and GRU	RMSE_avg	RMSE_avg = 0.036
[110]	2018	Kalipi, Andhra-Pradesh, India	13°.99′ / 77°.45′		1 year	Day	GHI, DHI, T, P, WS, AP, SD, RH, Surface Temp.	PV power	ANN ANFIS	% Error	ANN>ANFIS
[122]	2018	Tamanrasset (Algeria), Madina(Saudi Arabia)	22°.79′/5°.52′ 24°.55′/39°.70′	5 min to 3 h ahead	Tamanrassrt 11 years, Madina 1 year		Time series	GHI	WMIM and ELM	MAPE	MAPE= 7.4%–10.77
[127]	2018	Ghardaia, Algeria	32°.6′ /3°.8′	10 steps	1 year	1.5 year	D, T_min, T_max, RH, P, Max. elevation, declination angle, day duration, SD, sunshine ratio	GHR, DHR	WGPR-CFA, WGPR-PFA	RMSE, r²	RMSEGHR= 3.18 (MJ/m²), r²GHR= 85.85%, RMSEDHR= 5.23 (MJ/m²), r²DHR= 56.21%
[130]	2018	Syracuse		Monthly	1 year	Monthly	Sun angle, SI, T, visibility, CC, RH	Solar power	EMD and PSO and SVR	nRME MAPE	Avg nRMSE= 0.95%, Avg MAPE= 14.55%
[132]	2018	Beijing, China		1 d	1 year	Seasonal	SR, T, CC, RH, AP, WS, SCADA	Solar PV Power	Wavelet-PSO-SVM	MAPE	MAPE= 4.22%
[135]	2018	3 PV site in Australia	149°.06′E/35°.16′ S		2 years		CC, CW, IC, SI, P, AT, WS, RH AP	Ramp events	RF with loss functions	NA	NA
[143]	2018	Colorado	39°.74′/105°.1′	1 h	75% of 1 year	25% of 1 year	GHI, GHIclr, CSI, DNI, DHI, T, RH, AP, WS, WD	GHI	OCCUR and SVM and M3	nRMSE, nMAE	UC-M3>UC-GBM
[19]	2019	AUTH, Central Macedonia, AMIN, West Macedonia	40°.37′ N/22°.57′ E 40°.36′ N/ 21°.39′ E	d	1 year	Daily	T_max, T_min, T_avg, Radiation, TD, $TD$ , RH_avg	R_s	Empirical, ANN, MLR	RMSE, R	For AUTH, RMSE= 3.344 MJ/(m²·d), R= 1; For AMIN, RMSE= 3.166 MJ/(m²·d), R= 1
[78]	2019	Atlanta New York Hawaii	33°.77′/84°.98′ 43°.13′/75°.90′ 19°.33′/155°.58′	1 h to 1d	3 year	1 year	GHI, CSK, GHI, CC, DP, PW, RH, SZA, WS, WD, T	GHI	LSTM	RMSE, MAE, R²	RMSE= 41.37–66.69 (W/m²), MAE= 30.19–46.04 (W/m²), R² = 0.95–0.97
[80]	2019	Algiers	36°.8′ N/3°.170′ E	5 min	2 years	Monthly	T, RH, WS,WD, P, SD, AP, SZA, ESI	GHI, DNI	ANN	RMSE, nRME, MAE, nMAE	RMSE= 126.65–157.2 (Wh/m²), nRMSE= 28.08%–34.85%, MAE= 112.60–118.59 (Wh/m²), nMAE= 24.96%–26.28%
[44]	2019	Reese Research Center, Lubbock, TX			1 year	30 days	Time series	Daily solar energy	ARIMA	MAPE	MAPE= 17.70%
[45]	2019	Seoul, South Korea	37°.34′ N/126°.5′ E	Monthly and daily	3 years		Time series	Daily and monthly SR	SARIMA	RMSE and R²	Daily: RMSE= 104.26, R² = 68%; Monthly: RMSE= 33.18, R² = 79%
[46]	2019	Jamia Millia Islamia, New Delhi	28°.56′ N/77°.28′ E	Monthly	34 years	Monthly	Time series	SR	SARIMA	MPE	MPE= 1.402
[48]	2019	Mauritius	20°.3′ S/57°.6′ E	Monthly	29 years	10 years	SD, T, ER, RH	GSR	Sayigh Universal formula	MAPE, RMSE	MAPE= 5.07%–7.49%, RMSE= 0.96–1.57 MJ/(m²·d)
[101]	2019	6 sites in China		Daily	70% of 3 years	30% of 3 years	T_m, T_max, T_min, AP, RH, SD, N WS, AQI	DGSR	SVR	RMSE	RMSE= 0.00036–0.1910 MJ/m²
[54]	2019	Naresuan University, Thailand		1 h	6 m		GSR, AT, WS	PV power	HMM, GA-HMM	MAPE, nRME	nRMSE= 2.33%, MAPE= 6.27%
[64]	2019	Netherland		Hourly	2 year	Seasonal	T, RH, SR, CC, R, aerosols, CSK, CI, lat, long, VIAE, VIO	Deterministic and Proba-bilistic forecast	Parametric regression, Quantile regression, Quantile regression, RF, GBDT	RMSE, RMSE_SS, CRPSS
[67]	2019	Amravati, Maharashtra	20°.93′/77°.77′		5 years		DGSR, ESR, SD, SD_max monthly average DSI, T, RH	GSR, DSR	Empirical model	MAPE, RMSE, R²	GSR: MAPE= 2.50%, RMSE= 0.58 (MJ/m²), R² = 0.98; MDR: MAPE= 13.506%, RMSE= 1.11 (MJ/m²), R² = 0.94
[108]	2019	Nanao, Japan	NA		90% of 8735 data points	10% of 8735 data points	GHI, T, WS, WD, Ep, Ei	Solar PV power	GRU	nRMSE	nRMSE= 9.64%
[111]	2019	University of Queensland, Australia		1 d	1 year	Seasonal	PV power, SI, WS, T	PV power	WT and PSO and NNE	Error-variance	Seasonal variations, 0.1723–0.3103
[125]	2019	Kunming, China; Denver, USA	24°.51′/102°.51′ 39°.44′/105°.1′	Monthly	2 years	1 year	Time series	GHI	WT and ENN	RMSE, nRME, FS	RMSE= 25.83 (W/m²), nRMSE= 14.17%, FS= 0.7590
[126]	2019	NSRDB	W97°/N33°W107°/N143°	3 h ahead	1 year	Monthly	GHI, SZA, T, DP, RH, PWWD, WS,	GHI	ConvGRU-VB	RMSE, MEA, NSE	RMSE= 69.5, MEA= 34.8, NSE= 0.929
[112]	2019	Odeillo, France	42°.29′ /2°.01′	1 to 6 h ahead	80% of 3 years	20% of 3 year	SR time series	GHI, BNI, DHI	SP, ANN, RF	nRME, RMSE, MAE, nMAE	nRMSE_GHI= 19.65%–27.78%, nRMSE_BNI= 34.11%–49.08%, nRMSE_DHI= 35.08%–49.14%
[114]	2019	Favignana Island, Italy	37°.55′/12°.19′	Monthly	1 year	Seasonal	WS and solar data	Wind power, solar power	GMDHNNFOA	MAPE, AME, RMSE, R²	MAPE= 1.770%, MAE= 0.015, RMSE= –0.017868
[117]	2019	5 cites in China		1 h to 24 h	1 year	Monthly	Time series	DSR	DFT-PCA-Elman	RMSE, MAE	RMSE= 72.95–191.33, MAE= 39.46–118.67
[118]	2019	Toledo, Spain	39°.53′ N/4°.02′ N	Hourly	80% of each month	20% of each month	Reflectivity, CSK, CI	GSR	ELM	RMSE	RMSE= 60.60 W/m²
[129]	2019	GEFcom2014		1 to 3 step ahead	3 m	10% of data	t, RH, SP, CC, WS, P, T, R, SR	PV power	PCA and k-means and HGWO and RF	RMSE, MAE	RMSE= 8.88%–9.82%, MAE= 4.76%–5.80%
[134]	2019	8 sites in Xinjiang Uygur Autonomous Region, China		1 h	1 year	1 year	SZA, P, T, WD, WS, RH, AP	GSR	RS and SRSCAD and FF	MAPE, RMSE, TIC, CC, R²	MAPE= 0.066, RMSE= 20.21 W/m², TIC= 0.06, CC= 3.40 s, R² = 0.98
[137]	2019	IIT Gandhinagar		20 to 60 min	1 year		Time series	SR	SARIMA-RVFL	?MAPE, ?R², ? RMSE, ?MASE	MAPE= 6.376, RMSE= 3.497, MASE= 6.452, R² = –0.649
[139]	2019	Shaoxing, China	120°.23′ E/29°.72′ N	7.5 min to 60 min	3 years	2 years	PV power, T	PV power output	ALSTM	RMSE, MAPE, MAE	ALSTM>PM>ARIMAX>LSTM>MLP>
[140]	2019	MMMUT, Gorakhpur, India	26°.43′/83°.26′	1 d to 6 d	Monthly	Daily	T_min, T_max, T_avg, WS,R, DP, GSR, AP, SZ	Solar PV output	MARS, CART, M5, RF	MBE, RMSE, MAE	RF>M5>MARS>CART
[141]	2019	Galicia, Spain		Monthly	70% of data	30% of 1 year data	Flow, SR, Lower and upper panel T	Solar energy	ML with BR, SCG, RB, GDX, LM algo	NMSE	RBFN, MLP>MLR, MN-LR
[131]	2019	Salto, Uruguay	31°.28′/57°.92′	1 to 10 min			Sky images	GHI	Cloud detection and motion estimation	FS	FS= 11.4%
[133]	2019	Victoria, Australia		Hourly	80% of 278 days	20% of 278 d	PV power, SI, AT	PV power	GASVM	RMSE, MAPE	RMSE= 11.226 W, MAPE= 1.7052%
[142]	2019	Australia		Daily	5 years	Daily, weekly, monthly	WS, T, RH, GHI, DHI, WD	PV output	Ensemble with recursive arithmetic average	RMSE, MAPE, MAE	Ensemble>SVM>MLR>MARS
[146]	2019	Australia		1 d	60743 data points	23 to 5077 data points	Time series	GSR	CNN and LSTM	rRMSE, MAPE, APE	rRMSE= 1.515%, MAPE= 4.672%, APE= 1.233%
[147]	2019	90 stations in China		Hourly	1 year	Hourly, daily, monthly	MTSAT images, long, lat, Al	GSR	CNN and MLP	RMSE	RMSE_hourly = 0.30 MJ/m², RMSE_daily = 1.92 MJ/m², RMSE_monthly = 1.08 MJ/m²
[148]	2019	Shagaya, Kuwait Cocoa, USA			255 to 330 data points	32 to 38 data points	GHI, GTI, WS, WD, AT, RH, P, CT	Solar power	Theta and MLSHM	nMAE, nMSE	nMAE= 0.0317–0.0877, nMSE= 0.00197–0.0168
[106]	2020	Barmer, Jaisalmer, Bikaner, Jodhpur	25°.75^′ N/71°.38^′ E 26°.90^′ N/70°.90^′ E 28°.02^′ N/73°.31^′ E 26°.23^′ N/73°.02^′ E	3/6/24 h	70% of 5 years	30% of 5 years	DHI, DNI, DP, WD, RH, T	GSR	LSTM	MAPE, RMSE	MAPE= 6.69%–10.47%, RMSE= 0.099–0.181
[121]	2020	American Meteorological Society 2013–2014			10 years	2 years	P, DLWF, DSWF, AP,P, RH, total column-integrated condensate ULWRs, CC	Solar irradiation	GA/PSO and CNN	MSE, MAE, RS, AER	MSE= 4.268·10¹², MAE= 1.5153 (MJ/m²), RS= 70.89%, AER= 0.14208
[136]	2020	Oak Ridge National Laboratory		1 to 50min	1 year		past PV power Past PV+ CC	Solar radiation, PV power	Uncertainty bias and Kalman filter	nRMSE MAPE	nRME= 7.43%–26.13% MAPE= 5.72%–25.75%
[138]	2020	Wuhan, Beijing, Lhasa, and Urumqi, China	30°.37′/114°.08′ 39°.48′/116°.28′ 29°.40′/91°.08′ 43°.47′/87°.39′		10 years	10 years	CI, sunshine ratio, T_avg, RH_avg	SR	SVM, CNQR, Empirical model	RMSE, R², MABE, MBE	SVM>CNQR>Empirical model

Tab.1 Summary of investigated studies

Fig.8 Time horizon based solar irradiation forecasting models (adapted with permission from Ref. [52]).

ACF	Autocorrelation function
ACO	Ant colony optimization
AIC	Akaike information criteria
ALHM	Adaptive learning hybrid model
ALSTM	Attention mechanism with multiple LSTM
ANFIS	Adaptive neuro-fuzzy inference system
ANN	Artificial neural network
APE	Absolute percentage error
AR	Auto regression
ARIMA	Auto regressive integrated moving average
ARIMAX	Auto-regressive integrated moving average model with exogenous variable
ARMA	Auto regression and movie average
AVM	Atmospheric motion vectors
BIC	Bayesian information criteria
BR	Bayesian regularization
BRT	Boosted regression trees
BNI	Beam normal irradiance
CART	Classification and regression trees
CDER	Renewable energies development centre
CDSWR	Clear sky down welling short wave radiation
CGP	Pola-Ribiere conjugate gradient
CNFRRM	Cooperative network for renewable resources measurement
CNN	Convolution neural network
CNQR	Copula-based nonlinear quantile regression
CRPSS	Continuous ranked probability skill score
CSRIO	Commonwealth scientific and industrial research organization
DL	Deep learning
DFT	Discrete Fourier transform
DGSR	Daily global solar radiation
DHI	Direct horizontal irradiance
DHR	Dynamic harmonic regression
DNI	Direct normal irradiance
DNN	Deep neural network
DSI	Diffuse solar irradiance
DSR	Daily solar radiation
DT	Decision trees
ECMWF	European centre for medium-range weather forecasts
EEMD	Ensemble empirical mode decomposition
ELM	Extreme learning machine
ELNN	Elman neural network
EMD	Empirical mode decomposition
ESR	Extraterrestrial solar radiation
FF	Firefly algorithm
FFBP	Feed forward back propagation
FOA	Fruit fly optimization algorithm
FS	Forecast skill
GA	Genetic algorithm
GABP	Genetic algorithm back propagation neural network
GBDT	Gradient boosting decision trees
GDX	Gradient descent with adaptive learning rates and momentum
GFS	Global forecast system
GHI	Global horizontal irradiance
GMDHNN	Group method of data handling neural network
GMDH	Group method of data handling
GPI	Global performance indicator
GRU	Gate recurrent unit
GSI	Global solar irradiance
GSR	Global solar radiation
HGWO	Differential evolution grey wolf optimize
HIS	Hybrid intelligent system
HMM	Hidden Markov model
ICP	Interval coverage probability
IEA	International energy agency
IMD	Indian meteorological department
K-NN	K-nearest neural network
KSI	Kolonogorov-Smirnov integral
LLF	Log-likelihood function
LASSO	Least absolute shrinkage and selection operator
LR	Linear regression
LM	Levenberg-Marquardt
LMBP	Levenberg Marquardt back propagation
LSTM	Long short-term memory
LS-SVM	Least square support vector machine
MABE	Mean absolute biased error
MAD MAE	Mean absolute deviation Mean absolute error
MAID	Mean absolute interval deviation
MAPE	Mean absolute percentage error
MBD	Mean bias deviation
MBE	Mean bias error
MARS	Multivariate adaptive regression splines
MFOA ML	Modified fruit fly optimization Machine learning
MLFFN	Multilayer feed-forward neural network
MLP	Multi-layer perceptron
MLR	Multi linear regression
MNRE	Ministry of New and Renewable Energy
MOS	Model output statistics
MRE	Mean relative error
MTM	Markov transition method
NAR	Nonlinear autoregressive
NCEP	National Centers for Environmental Prediction
NCMRWF	National Center for Medium Range Weather Forecasting
nE	Normalized error
nMAE	Normalized mean absolute error
NMSC	National Meteorological Satellite Center
NNE	Neural network ensemble
NNFOA	Neural network modified fruit fly optimization
nRMSE	Normalized root mean square error
NSE	Nash-Sutcliffe efficiency
NWP	Numerical weather prediction
OCCUR	Optimized cross-validated clustering
PACF	Partial autocorrelation function
PCA	Principal component analysis
PEV	Potential economic value
PINAW	Prediction interval normalized average width
PSO	Particle swarm optimization
PV	Photo voltaic
RB	Batch training with bias and weight learning rules
RBF	Radial basis function
RDI	Ramp detection index
RF	Random forest
RM	Ramp magnitude
RS	Random subspace
RSM	Response surface method
RVFL	Random vector functional link
SARIMA	Seasonal auto regressive integrated moving average
SCADA	Supervisory control and data acquisition
SCG	Scaled conjugate gradient
SP	Smart persistence
SRSCAD	Square root smoothly clipped absolute deviation
SVM	Support vector machine
TIC	Theil inequality coefficient
TMLM	Time-varying multiple linear model
TSRY	Typical solar radiation year
TMY	Typical meteorological year
WD	Wavelet decomposition
WGPR	Weighted Gaussian process regression
WGPR-CFA	Weighted Gaussian process regression – cascade forecasting architecture
WGPR-PFA	Weighted Gaussian process regression – parallel forecasting architecture
WI	Wilmot’s index
WMIM	Wrapper mutual information methodology
WRF	Weather research and forecasting
WT	Wavelet transform

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