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Short-term Solar Irradiation forecasting based on Dynamic Harmonic Regression

Authors:
Juan R. Trapero at University of Castilla-La Mancha
Juan R. Trapero
Nikolaos Kourentzes at University of Skövde
Nikolaos Kourentzes
Alberto Martín García at Agencia Estatal de Meteorología
Alberto Martín García
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Solar power generation is a crucial research area for countries that suffers from high dependency on external energy sources and is gaining prominence with the current shift to renewable sources of energy. In order to integrate this generated energy into the grid, solar irradiation must be forecasted, where deviations of the forecasted value involve significant costs. The present paper proposes a univarivate Dynamic Harmonic Regression model set up in a State Space framework for short-term (1 to 24 hours) solar irradiation fore-casting. Time series hourly aggregated as the Global Horizontal Irradiation and the Direct Normal Irradiation will be used to illustrate the proposed approach. This method provides a fast automatic identification and estima-tion procedure based on the frequency domain. The recursive algorithms applied offer adaptive predictions and, since the method is based on unob-served components models, explicit information about trend, seasonal and irregular behaviour of the series can be extracted. The good forecasting per-formance and the rapid adaptability of the model to fast transient conditions of solar radiation are illustrated with minutely solar irradiance measurements collected from ground-based weather stations located in Spain.
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Supplementary resource (1)

TraperoKourentzes 1v1
Data
July 2015
Juan R. Trapero · Nikolaos Kourentzes · Alberto Martín García
... In this sense, several methodologies were used to estimate solar irradiance through different time horizons. The most commons approaches used are Numerical Weather Prediction (NWP) [3], [4], time series analysis [5], [6], image processing applications [7]- [9] and ML algorithms [10]- [13]. ...
... This was also confirmed in [5], [30] where models that use decision trees were the ones that obtained the best accuracies. Another conclusion obtained in [5], [30] that converges with what was found here was the positive influence on the performance of the models that the information extracted from the images present. ...
... This was also confirmed in [5], [30] where models that use decision trees were the ones that obtained the best accuracies. Another conclusion obtained in [5], [30] that converges with what was found here was the positive influence on the performance of the models that the information extracted from the images present. ...
Dimensional reduction for solar irradiance forecasting problem using principal components analysis and Turk-Pentland strategy
Conference Paper
Full-text available
  • Jun 2024
In this work, a preprocessing procedure was performed in a dataset consisting of signals acquired from light dependent resistor (LDR) sensors and statistical descriptors extracted from sky images captured by a simple camera. The sensors integration was performed using a Raspberry Pi 3 system. At first, the Principal Components Analysis (PCA) and descriptive statistics were used to reduce dataset dimensionality, i. e., a controlled decrease in the number of predictors of the dataset. Thereafter, the Turk-Pentland strategy was then employed to reduce computational costs on the execution of PCA. Finally, forecasting solar irradiance for 30-minutes ahead was performed using Machine Learning (ML) algorithms, namely: Support Vector Regression (SVR), Ridge regression, LASSO, Principal Components Regression (PCR) and Multilayer Layer Perceptron (MLP). The best results were achieved by SVR and LASSO, reaching values for Root Mean Squared Error (RMSE) of 161.54 W/m² and 166.60 W/m², respectively. The PCR allowed the reduction of the original dataset dimensionality by 50% without major decreases in accuracy when compared to the best result achieved, reaching RMSE equal to 170.26 W/m² (5.40% higher when compared to SVR). Thus, the achieved results show that less powerful computational processing may be needed to perform real-time solar irradiance applications reliably.
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... al., 2022. NWP models typically operate over various time scales, from hours to several days, making them suitable for short-term and medium-term forecasting (Du et al., 2018;Trapero et al., 2015;Hashimoto and Yoshimoto, 2023) The basic equation governing NWP models is derived from the laws of fluid dynamics and thermodynamics, specifically through the application of partial differential equations (PDEs). These equations describe the motion and thermodynamic processes of the atmosphere, allowing for the simulation of weather phenomena. ...
EFFICIENT METHOD FOR FORECASTING SOLAR IRRADIANCE - A REVIEW
Article
Full-text available
  • Dec 2024
Efficient solar irradiance forecasting is essential for optimizing solar energy systems and integrating renewable energy sources into power grids. This review aims to evaluate the effectiveness of various forecasting methods to inform energy management and grid integration strategies. It compares physical models, statistical approaches, machine learning techniques, and hybrid models, using specific criteria such as accuracy, computational efficiency, and data requirements. Physical models like Numerical Weather Prediction (NWP) provide detailed atmospheric simulations but are computationally intensive. Statistical models, such as ARIMA, are simpler yet struggle with non-linear data. Machine learning methods, particularly Artificial Neural Networks (ANNs) and Long Short-Term Memory (LSTM) networks, effectively capture complex data relationships but require substantial datasets and computing power. Hybrid models, which combine physical and machine learning approaches, achieve high accuracy and are suitable for real-time applications despite increased computational costs. One of the key findings indicates that hybrid models offer high accuracy but demand significant computational resources and offer the best balance between accuracy and computational efficiency. However, challenges such as data quality, geographic and temporal variability, and model complexity persist. Emerging technologies like artificial intelligence, big data, and quantum computing present promising solutions for enhanced irradiance forecasting. The review highlighted the models’ limitations and strengths to facilitate informed decision making and concluded with recommendation of the adoption of hybrid models, investment in data acquisition and sharing technologies, balancing model complexity with practicality as steps towards improved irradiance forecasting for grid integration and stability to ensure sustainable yet cost-effective energy solutions.
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... Short-term forecasts are needed for operational planning, switching sources, programming backup, and short-term power purchases, as well as for planning for reserve usage, and peak load matching. There are many approaches as summarized by Trapero, Kourentzes & Martin (2015): The diversity of solar radiation forecasting methodologies can be classified according to the input data and the objective forecasting horizon. For instance, NWP (Numerical Weather Prediction) models, which are based on physical laws of motion and conservation of energy that govern the atmospheric air flow, are operationally used to forecast the evolution of the atmosphere from about 6 h onward. ...
Solar energy production: Short-term forecasting and risk management
Preprint
  • Feb 2016
Electricity production via solar energy is tackled via short-term forecasts and risk management. Our main tool is a new setting on time series. It allows the definition of "confidence bands" where the Gaussian assumption, which is not satisfied by our concrete data, may be abandoned. Those bands are quite convenient and easily implementable. Numerous computer simulations are presented.
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... In this sense, technologies that provide reliable forecasts of solar and wind resources for different time horizons act as a tool to aid the operator's decision-making, thus allowing a better management of the network. In the context of solar resource forecasting, Numerical Weather Prediction (NWP) models stand out for long-term forecasts (Marquez and Coimbra, 2011), as do statistical and machine learning models for short-term forecasts (Pedro and Coimbra, 2015;Dong et al., 2013;Trapero et al., 2015;Young et al., 1999). ...
Forecasting Global and Direct Solar Irradiance with Machine Learning Algorithms: Insights from Recursive Feature Selection and SHAP Analysis
Preprint
Full-text available
  • Aug 2024
In the present work, forecasts of Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI) were obtained for the sequence of forecast horizons from 5 min to 30 min in steps of 5 min, using state-of-the-art machine learning algorithms, namely: Group Method Handling Data, Extreme Gradient Boosting Method and Light Gradient Boosting Method using the FOLSOM Benchmarking database. In addition, an analysis of the importance of variables was carried out from a global point of view using Recursive Feature Selection, as well as from a local point of view applying SHAP analysis. Performance evaluation was carried out using the error metrics Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Coefficient of Determination (R²). The best predictive performances were obtained for GHI forecasts in the 5min ahead horizon, by the XGBoost and LightGBM models with RMSE values of 47.25 W/m² and 47.49 W/m², respectively.
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... Dynamic harmonic regression was utilized to forecast short-term solar irradiation in a separate study. The fi ndings indicated that this method resulted in the lowest relative mean squared error, particularly at approximately 30% and 47% for GHI during a 24-hour prediction (Trapero et al., 2015). The evaluation of high-frequency irradiance fl uctuations and geographic smoothing, revealed that smaller scattering factors result in greater reductions in variability compared to the model at longer time scale (Lave et al., 2012;Sha & Aiello, 2020;Behr et al., 2021;Syed & Khalid, 2021;Elfeky et al., 2023). ...
Quantifying the Variability of Solar Energy Fluctuations at High–Frequencies through Short-Scale Measurements in the East–Channel of Mozambique Conditions
Article
Full-text available
  • Apr 2024
The solar power output of a solar plant is directly affected by changes in solar energy. To enhance the accuracy, durability, and efficiency of solar projections, it was necessary to quantify the rapid fluctuations in solar energy on a short–scale in the conditions of eastern Mozambique. An analytical approach was utilized to measure the high–frequency variations in the clear–sky index (K*t) and its increments (∆K*t). The results indicate that the K*t fluctuations in the nine stations along the eastern–channel of Mozambique ranged from 0.0001 to 0.9999, with a probability density (PDF) of fluctuations limited to 0.9991. Through statistical analysis, it was determined that ∆K*t reaches its maximum value near zero. Days with intermediate–sky conditions exhibited high PDF values of approximately 1.0 and greater deviation, while clear and cloudy–sky days displayed consistent solar energy frequencies and a lower tendency for K*t deviation. In conclusion, the correlation between high–fluctuation variability diminishes rapidly for shorter intervals. Furthermore, high–frequencies of fluctuations are observed during the hot and rainy season, whereas low frequencies are observed during the cold and dry season.
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Parametric Forecast of Solar Energy over Time by Applying Machine Learning Techniques: Systematic Review
Article
Full-text available
  • Mar 2025
To maximize photovoltaic (PV) production, it is necessary to estimate the amount of solar radiation that is available on Earth’s surface, as it can occasionally vary. This study aimed to systematize the parametric forecast (PF) of solar energy over time, adopting the validation of estimates by machine learning models (MLMs), with highly complex analyses as inclusion criteria and studies not validated in the short or long term as exclusion criteria. A total of 145 scholarly sources were examined, with a value of 0.17 for bias risk. Four components were analyzed: atmospheric, temporal, geographic, and spatial components. These quantify dispersed, absorbed, and reflected solar energy, causing energy to fluctuate when it arrives at the surface of a PV plant. The results revealed strong trends towards the adoption of artificial neural network (ANN), random forest (RF), and simple linear regression (SLR) models for a sample taken from the Nipepe station in Niassa, validated by a PF model with errors of 0.10, 0.11, and 0.15. The included studies’ statistically measured parameters showed high trends of dependence on the variability in transmittances. The synthesis of the results, hence, improved the accuracy of the estimations produced by MLMs, making the model applicable to any reality, with a very low margin of error for the calculated energy. Most studies adopted large time intervals of atmospheric parameters. Applying interpolation models can help extrapolate short scales, as their inference and treatment still require a high investment cost. Due to the need to access the forecasted energy over land, this study was funded by CS–OGET.
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Short-term solar irradiance forecasting using exponential smoothing state space model
Article
  • Jun 2013
  • ENERGY
We forecast high-resolution solar irradiance time series using an exponential smoothing state space (ESSS) model. To stationarize the irradiance data before applying linear time series models, we propose a novel Fourier trend model and compare the performance with other popular trend models using residual analysis and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) stationarity test. Using the optimized Fourier trend, an ESSS model is implemented to forecast the stationary residual series of datasets from Singapore and Colorado, USA. To compare the performance with other time series models, autoregressive integrated moving average (ARIMA), linear exponential smoothing (LES), simple exponential smoothing (SES) and random walk (RW) models are tested using the same data. The simulation results show that the ESSS model has generally better performance than other time series forecasting models. To assess the reliability of the forecasting model in real-time applications, a complementary study of the forecasting 95% confidence interval and forecasting horizon of the ESSS model has been conducted.
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Statistical approaches to modelling and forecasting time series.
Chapter
  • Jan 2002
There are numerous statistical approaches to forecasting, from simple, regression-based methods to optimal statistical procedures formulated in stochastic state-space terms. This chapter tries to distil, from this large mixture of models and methods, those that the authors feel have most significance in theoretical and practical terms within the specific context of economic forecasting. Most of the statistical forecasting methods referred to in the chapter are model-based, in the sense that the forecasting operation is carried out subsequent to the statistical identification and estimation of a suitable (usually stochastic) mathematical model based on the available time-series data.
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