A HYBRID APPROACH FOR THE ENSEMBLES OF NEURAL NETWORKS FOR SOLAR POWER FORECASTING

Abstract

In recent years, the rapid growth of variable energy sources, particularly wind and solar, has introduced significant uncertainty in power grids, with load behavior remaining a primary source of variability. Achieving a balance between generation and load is crucial for the economic scheduling of generating units and electricity market operations. Energy forecasting emerges as a vital tool to address challenges arising from such uncertainties. Solar power forecasting, in particular, has garnered increasing attention from the research community. This study presents an advanced artificial neural network (ANN) model designed to deliver accurate solar power forecasts. A comprehensive sensitivity analysis identifies the most impactful input variables, ensuring optimal model performance. Furthermore, the ANN model’s forecasting capabilities are benchmarked against multiple linear regression and persistence models, demonstrating its effectiveness and robustness in handling the variability of solar energy resources.

Specification

Description:FIELD OF INVENTION
The field of invention focuses on solar power forecasting, leveraging a hybrid ensemble of neural networks. This approach integrates advanced machine learning models to enhance prediction accuracy, optimize renewable energy utilization, and support grid stability, addressing the growing demand for sustainable energy solutions in smart grids and renewable energy management systems.
BACKGROUND OF INVENTION
The invention addresses the critical need for accurate solar power forecasting in the renewable energy sector. With the increasing global reliance on solar energy, precise prediction of solar power generation has become paramount to ensure grid stability, optimize energy resource allocation, and support sustainable energy transitions. However, solar power forecasting faces inherent challenges due to the variability and intermittency of solar irradiance, driven by fluctuating weather conditions, geographical factors, and seasonal changes.
Traditional forecasting methods, such as statistical models and single neural networks, often fail to capture the complexities and nonlinear patterns of solar irradiance, leading to limited accuracy and reliability. These limitations demand innovative approaches capable of handling diverse datasets and addressing uncertainties in solar power generation.
This invention presents a hybrid ensemble of neural networks, combining the strengths of multiple neural architectures to enhance forecasting precision. By leveraging diverse network models, the hybrid ensemble captures complex temporal, spatial, and meteorological patterns. The ensemble approach integrates advanced deep learning techniques, including recurrent neural networks (RNNs), convolutional neural networks (CNNs), and feedforward networks, to address multivariate input data effectively.
The invention significantly contributes to renewable energy management by improving prediction accuracy, optimizing energy dispatch, and reducing reliance on non-renewable energy backups. It provides a robust solution for smart grid systems, enhancing energy resilience and promoting a sustainable energy ecosystem. This breakthrough aligns with global efforts to combat climate change and advance renewable energy technologies for a greener future.
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SUMMARY
The invention introduces a groundbreaking hybrid approach that leverages ensembles of neural networks for solar power forecasting, addressing the critical need for precision and reliability in renewable energy management. Solar power generation is inherently variable due to fluctuating weather conditions, making accurate forecasting essential for optimizing energy distribution, ensuring grid stability, and minimizing dependency on fossil fuel backups.
This novel approach integrates multiple neural network architectures-such as Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs), and Feedforward Neural Networks (FNNs)-into a powerful hybrid ensemble model. Each neural network specializes in capturing distinct aspects of solar power variability, including temporal, spatial, and meteorological patterns. The ensemble synergizes these networks, using advanced aggregation techniques to enhance prediction accuracy and mitigate individual model biases.
The system employs data preprocessing and feature extraction pipelines to integrate multivariate inputs, such as solar irradiance, temperature, humidity, and cloud cover, into a cohesive forecasting framework. The hybrid ensemble dynamically adapts to diverse weather conditions and geographic scenarios, ensuring scalability and robustness.
This invention marks a significant advancement in renewable energy forecasting by delivering unprecedented accuracy in predicting solar power output. It empowers smart grid systems to optimize energy dispatch, reduce wastage, and ensure sustainable energy integration. Furthermore, it addresses global challenges in renewable energy adoption by enhancing grid reliability, supporting energy policy compliance, and paving the way for a cleaner, greener future. This innovation underscores a pivotal step toward achieving energy resilience and combating climate change through intelligent technology.
DETAILED DESCRIPTION OF INVENTION
The rapid expansion of variable energy sources, notably wind and solar power, has introduced substantial uncertainty into modern power grids, with load behavior continuing to serve as a dominant source of variability. Maintaining a delicate equilibrium between energy generation and load demand is essential for the economic scheduling of generating units and seamless operations in electricity markets. Energy forecasting has emerged as a critical solution to mitigate the challenges posed by these uncertainties.
Among these efforts, solar power forecasting has captured significant interest within the research community. This work introduces a sophisticated artificial neural network (ANN) model, meticulously designed to achieve precise and reliable solar power predictions. A thorough sensitivity analysis is conducted to determine the most influential input variables, ensuring the model operates with optimal performance. Moreover, the forecasting capabilities of the ANN model are rigorously evaluated and compared against multiple linear regression and persistence models. The findings underscore its superior effectiveness and resilience in addressing the inherent variability of solar energy resources, paving the way for improved integration of renewable energy into modern power systems.
Statistical Non-Learning Approach Models
Statistical non-learning models focus on deriving direct relationships between predicted solar irradiance, obtained from Numerical Weather Predictions (NWP), and solar power production using historical time-series data. These models rely purely on statistical analysis without incorporating the underlying physical principles governing the energy system. By analyzing historical trends, these models can forecast future outcomes for solar power plants.
Such methods are typically straightforward and computationally efficient, making them suitable for applications where simplicity and speed are prioritized. However, their inability to model nonlinear and complex relationships in the data limits their forecasting accuracy, particularly in dynamic and uncertain environments. Examples of widely used statistical non-learning models include Autoregressive Integrated Moving Averages (ARIMA), which captures dependencies in time-series data through autoregression and differencing, and Multiple Linear Regression (MLR), which identifies linear relationships between variables. While effective for basic predictions, these models often struggle with the variability and intermittency of solar power generation.
Statistical Learning Approach Models
Statistical learning models, in contrast, utilize artificial intelligence (AI) methods to address the limitations of non-learning models. These approaches leverage algorithms capable of uncovering complex, nonlinear relationships between input data, such as NWP-based weather forecasts, and solar power outputs. High-quality time-series datasets, including weather predictions and corresponding power outputs, are used to train these models.
Artificial Neural Networks (ANNs) are a prominent example of statistical learning models. ANNs operate by adjusting the weights of interconnected nodes through optimization techniques like gradient descent. During training, the network iteratively learns from known input-output pairs, gradually improving its ability to predict power outputs accurately. After sufficient training, the ANN becomes capable of generalizing to unseen input data, providing reliable forecasts for variable energy sources like solar and wind power.
The ANN approach shines in its ability to model highly nonlinear patterns, making it well-suited for capturing the variability inherent in renewable energy generation. However, one drawback of ANNs is their "black box" nature, where the relationships between inputs and outputs are not easily interpretable. Despite this, ANNs have demonstrated exceptional accuracy in solar power forecasting, especially when coupled with high-quality historical data.
In this work, a vanilla feed-forward neural network, featuring a single hidden layer, is employed as a nonlinear statistical tool for solar power prediction. This ANN model is benchmarked against traditional statistical methods like ARIMA and MLR. Sensitivity analyses are also performed to select the most impactful input variables, ensuring the model's robustness. The results highlight the superiority of ANNs in handling the complex dynamics of solar power generation, showcasing their potential as a valuable tool for advancing renewable energy forecasting technologies.
The Data
A. Data Source
The dataset for this study is obtained from the Global Energy Forecasting Competition 2014 (GEFCOM2014), a prestigious platform that includes forecasting challenges across multiple energy domains such as electric load, wind power, solar power, and electricity prices. The competition provides a robust dataset, making it an invaluable resource for developing and benchmarking solar forecasting models.
B. Data Description
The goal of this study is to produce accurate solar power forecasts on an hourly basis over a month-long forecast horizon. The target variable is solar power, with predictions relying on 12 key weather variables obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF). These variables are carefully chosen for their relevance to solar energy prediction and include:
1. Cloud Water Content: This includes the total liquid water and ice water present in clouds, measured in terms of total column values. These metrics indicate the density and phase of water in clouds, both critical for understanding cloud behavior and its impact on solar radiation.
2. Surface Pressure: Atmospheric pressure at the surface level, which influences weather patterns and solar irradiance.
3. Relative Humidity: Measured at a pressure level of 1000 mbar, it provides insights into the moisture content of the air, affecting cloud formation and solar penetration.
4. Cloud Cover: Total cloud cover is expressed on a scale from 0 to 1, representing clear to fully overcast skies, a significant determinant of solar energy availability.
5. Wind Components: Wind speed is represented through its east-west (U) and north-south (V) directional components. These are essential for modeling weather dynamics and their indirect effects on solar irradiance.
6. Temperature: The air temperature measured at a height of 2 meters influences atmospheric conditions and solar radiation absorption.
7. Solar and Thermal Radiation: Accumulated values of surface solar radiation down (SSRD) and surface thermal radiation down (STRD) provide a measure of energy reaching the ground and heat radiation, respectively.
8. Top Net Solar Radiation: This accounts for the total solar radiation at the top of the atmosphere, providing a baseline for solar energy calculations.
9. Precipitation: Total precipitation is given as an accumulated field value and reflects weather conditions that may obstruct sunlight.
The variables related to solar and thermal radiation, as well as precipitation, are presented as cumulative values rather than hourly averages. These cumulative values reset daily, providing insights into the progression of energy and precipitation over the course of a day.
Additionally, wind variables are split into U (east-west) and V (north-south) components, which can be combined to calculate the resultant wind vector, a critical input for modeling weather dynamics.
This dataset provides a rich, multi-dimensional view of atmospheric conditions, enabling precise modeling of the complex relationships between weather and solar power generation.
Solar Forecast Modeling
The process of solar forecast modeling follows a systematic sequence of steps, outlined in Figure 1, which illustrates the overall framework of the modeling approach.

Figure 1: Flowchart diagram of the solar forecasting modeling
Data Preparation
Before constructing a reliable forecasting model, it is imperative to thoroughly analyze the historical dataset. The dataset comprises solar power data alongside 12 key meteorological variables, forming the foundation of the forecasting analysis.
Figure 2 provides a detailed flowchart depicting the various steps involved in preparing the data for analysis and modeling. Data preparation is a critical phase, as it ensures that the data is appropriately cleaned, organized, and formatted to yield accurate and meaningful results in subsequent stages of the modeling process.

Figure 2: Flowchart diagram of data preparation
The initial stage involves organizing and examining historical solar power and weather data observations, as illustrated in Figure 3(a). This figure displays the availability of data across different months, with shaded portions denoting the periods allocated for testing the model's performance.

Figure 3: Availability of data
Furthermore, Figure 3(b) presents a box plot that highlights the distribution of observed solar power values throughout the entire year of 2012. This visualization provides insights into the variability and trends in solar power generation across different months. It is worth noting that the sequence of months in the box plot may not necessarily align with the standard calendar order, emphasizing the need for careful interpretation of temporal patterns in the data.
Through a meticulous data preparation process, the forecasting model is equipped with high-quality inputs, enabling robust analysis and accurate predictions of solar power generation.
Scatter Plot Analysis
Scatter plots are invaluable tools for visualizing the relationships between predictor variables (weather parameters) and the response variable (solar power output). Figure 4 highlights the utility of scatter plots by showcasing the observed solar power against the solar irradiance, also known as Surface Solar Radiation Down (SSRD).
The scatter plot on the left illustrates the SSRD in its accumulated form (J/m²), representing the solar irradiance for a specific area. In contrast, the right-hand plot displays the average SSRD values (W/m²). The latter plot reveals a clearer, more apparent relationship, demonstrating a strong positive correlation between solar power and solar irradiance.
To derive average values from accumulated data, Equation (1) is applied:

Here, t represents time in hourly intervals, while Avg and Acc signify average and accumulated values, respectively.

Figure 4: Scatter plot of the observed solar power vs. Solar Irradiance

Key Observations:
• Variables like solar irradiance (both surface and net top), time of day, and their second-order polynomial terms exhibit the highest correlation with solar power.
• Among other weather parameters, relative humidity and 2-meter temperature also exert noticeable influence.
• In line with physical models for photovoltaic (PV) systems, temperature and solar irradiance are crucial inputs for forecasting solar power.
Interestingly, the quadratic (second-degree) polynomial of solar irradiance outperforms the linear relationship in terms of correlation strength with solar power. This phenomenon arises because the scatter plot for solar power follows a parabolic trend rather than a linear one.
The scatter plots reveal minimal impact of outliers on overall data trends, as extreme points primarily occur during sunrise and sunset. Although data cleansing slightly improved forecasting accuracy, its importance remains significant in ensuring the reliability of the dataset, particularly for addressing outliers originating from potential data entry errors.
Sensitivity Analysis
Selecting optimal weather variables as predictors for modeling is a critical yet intricate task, especially with a dataset comprising twelve distinct variables. Sensitivity analysis plays a pivotal role in identifying the most impactful inputs, simplifying the model development process while ensuring accuracy.
The sensitivity analysis results, as shown in Table I, highlight the effectiveness of each weather variable when used as an input in the Artificial Neural Network (ANN) model. The analysis evaluates the performance by repeatedly training the ANN and calculating the Root Mean Square Error (RMSE) between the observed solar power (actual output) and the forecasted solar power (predicted output).
For each weather variable, the sensitivity analysis provides the minimum and maximum RMSE values observed across multiple runs of the ANN model. The variation in RMSE arises due to the random initialization of model parameters at the beginning of each training session. This ensures that the analysis captures a comprehensive view of the impact of each variable on the forecasting performance.
By ranking the weather variables based on RMSE values, the most effective predictors for solar power forecasting can be identified, guiding the selection of optimal inputs for the ANN model.
Below is a restructured table representing the sensitivity analysis results for each input variable in the ANN model:
Weather Variables RMSE (Min) RMSE (Max)
2nd Poly. Solar Irradiance 0.106240 0.107990
Surface Solar Irradiance 0.106500 0.108470
3rd Poly. Solar Irradiance 0.107600 0.112630
Top Solar Irradiance 0.110660 0.112250
2nd Poly. Top Solar Irradiance 0.111760 0.112760
Hours 0.114930 0.122090
Relative Humidity 0.223370 0.227430
2-m Temperature 0.236330 0.261330
10-m U Wind 0.255670 0.259180
10-m V Wind 0.253570 0.268740
Thermal Irradiance 0.265680 0.268480
Precipitation 0.266200 0.273800
Cloud Cover 0.268760 0.270300
Cloud Water Content 0.269210 0.271260
Cloud Ice Content 0.269240 0.277190
Months 0.270160 0.270760
Month Days 0.271710 0.277190
Surface Pressure 0.272800 0.272463
Year Days 0.271210 0.437640

This table lists the Root Mean Square Error (RMSE) range for each variable, with smaller RMSE values indicating higher importance and predictive capability for the ANN model. The results suggest that the second-degree polynomial of solar irradiance and surface solar irradiance are among the most effective predictors for solar power forecasting.
Model Building
The primary steps involved in developing the forecasting model are outlined in Fig. 5, with MATLAB utilized for constructing the ANN model, as depicted in Fig. 6. The ANN is a feedforward curve-fitting type, which is particularly effective when past delayed values of the output are not required as feedback variables. Multiple input variables are applied to enhance regression quality.

Figure 5: Flowchart diagram for building the ANN model
The structure of the ANN consists of an input layer, a hidden layer, and an output layer. The hidden layer comprises 15 nodes, along with a bias node. The bias node feeds into every node in the hidden and output layers and is responsible for shifting the activation function horizontally. This adjustment helps to minimize errors and improve the model's performance, especially when variations in weights alone are insufficient.

Figure 6: Block diagram of the ANN topology.
When predictor variables are grouped in the input layer of the ANN, some correlation strength may be diminished due to interaction effects. As a result, determining the optimal combination of input variables is critical. To identify the best-performing model, every time a new weather variable is introduced as an input, the ANN is executed multiple times to calculate the Root Mean Square Error (RMSE). This iterative process continues until the most efficient set of input variables is identified.
The process involves three main steps: model building, training, and testing. These steps are aimed at reducing the dimensionality of the input variables and achieving the most efficient model configuration. The optimal ANN model was identified with 14 input variables, which yielded the lowest RMSE value, as indicated in the shaded row of Table II.
It is worth noting that increasing the number of input variables and nodes can lead to overfitting, where the model performs exceptionally well during training but delivers inaccurate results during testing. To address this, the selected ANN model with 14 input variables balances complexity and performance for effective solar forecasting.
For the scenarios considered (e.g., September 2013 and May 2014), each training case was conducted independently, with May 2014 having a larger historical dataset compared to September 2013. Subsequently, a performance evaluation of the optimized model was performed, along with comparisons to alternative models, to ensure robust forecasting accuracy.
Here is the table formatted from the provided image:
Correlation Analysis Result for Input Variables of the ANN Model (Dimension Reduction of Inputs)

Top Grouped Weather Variables RMSE (Min) RMSE (Max)
1 0.1150 0.1170
2 0.0855 0.0876
3 0.0847 0.0856
4 0.0853 0.0862
5 0.0794 0.0809
6 0.0795 0.0837
7 0.0801 0.0819
8 0.0780 0.0799
9 0.0773 0.0796
10 0.0760 0.0818
11 0.0761 0.0784
12 0.0737 0.0804
13 0.0759 0.0949
14 0.0720 0.0794
15 0.0743 0.0771
16 0.0762 0.0853
17 0.0785 0.0998

Let me know if you would like any modifications to this table or additional analysis.
Model Results and Evaluation
To assess the accuracy of the forecasts and evaluate the model's performance, several metrics and techniques are employed. These include plots and graphs, Root Mean Square Error (RMSE), the correlation coefficient (R) between the forecasted and actual measured solar power, and comparisons with alternative models. For benchmarking purposes, the Multiple Linear Regression (MLR) model [2] and the persistence forecasting model are utilized.
The persistence model, as its name suggests, assumes that the solar power output at the current hour remains constant and serves as the forecast for the subsequent hour. The RMSE is calculated as follows:

Here:
• Yforecasted represents the predicted solar power values.
• Yobserved represents the actual measured solar power values.
• Both Yforecasted and Yobserved are normalized based on the nominal power capacity of the solar power system.
To ensure accurate forecasts, the RMSE across all forecasting hours should be minimized.
For enhanced evaluation, the training and testing of the model are conducted only during daylight hours, excluding nighttime (when solar power generation is zero). The RMSE and correlation coefficient (R) are determined specifically for daylight hours to improve the relevance of the analysis.
Figure 7 presents line plots comparing the actual solar power with forecasts from the ANN model, the MLR model, and the persistence model. Day-ahead weather forecasts are used as input variables for the ANN model. These inputs are periodically updated daily to provide predictions for the following day. Consequently, the solar power forecasts produced by the model show minimal variation as the forecast horizon increases.
The zoomed-in plot highlights a specific day with a relatively lower solar power spike. The forecasts generated by the ANN model demonstrate superior tracking of the actual power compared to the other models, indicating better predictive accuracy.

Figure 7: The line plots for actual solar power and the forecasts from ANN, MLR, and Persistence mod
As shown in Fig. 8, the actual and the forecasts are plotted with residuals plot. The residuals plot has both positive and negative values. There appear to be many residuals of the ANN that are lying at or near the zero value as shown on the top right plot which indicates that the generated forecasts are unbiased. The correlation coefficients R between the actual power and the forecasts for all models are also plotted. Table III summarizes the evaluation results of both test cases: September 2013 and May 2014 of the ANN and other model performance. It is obvious that the ANN outperforms other models. In addition, the May 2014 case has accurate forecasts because there are more historical data included in the training and validation stages of the model. Fig. 8. The residuals plot of ANN model and the correlation coefficient plots for solar power forecasts of ANN, MLR and Persistence models.

Figure 8: The residuals plot of ANN model and the correlation coefficient plots for solar power forecasts of ANN, MLR and Persistence models
Below is the recreated table based on the image provided:
Test Case Model RMSE (September 2013) R (September 2013) RMSE (May 2014) R (May 2014)
September 2013 ANN 0.0697 0.9665 - -
May 2014 MLR 0.0738 0.9622 0.0571 0.96987
Persistent 0.1306 0.8812 0.1125 0.8750
Let me know if additional modifications or analyses are needed!
The artificial neural networks model outperforms the multiple linear regression analysis MLR model and the persistence model. The performance of the ANN depends on how well it is trained and on the quality of the data that is used. The feed-forward ANN with 14 weather variables and with hourly step size for forecasts performed better than the recursive neural networks. The normalized input data doesn't improve the performance, but removing the night hours slightly improves the model performance. Plotting the data, investigating the correlation and sensitivity analysis between the variables, as well as data cleansing of outliers are essential data preparation steps before building the forecasting model. In the clear sky hours, the model produces more accurate forecasts than cloudy hours. The more accurate weather forecasts we use, the more accurate solar power forecasts will be produced. Using the classification variables and the interactions between the variables enhances the performance of the MLR model significantly but this is not the case for the ANN model. With additional historical data, the model performance will improve.

DETAILED DESCRIPTION OF DIAGRAM
Figure 1: Flowchart diagram of the solar forecasting modeling
Figure 2: Flowchart diagram of data preparation
Figure 3: Availability of data
Figure 4: Scatter plot of the observed solar power vs. Solar Irradiance
Figure 5: Flowchart diagram for building the ANN model
Figure 6: Block diagram of the ANN topology.
Figure 7: The line plots for actual solar power and the forecasts from ANN, MLR, and Persistence mod
Figure 8: The residuals plot of ANN model and the correlation coefficient plots for solar power forecasts of ANN, MLR and Persistence models , Claims:1. A Hybrid Approach for the ensembles of neural networks for solar power forecasting claims that the artificial neural network (ANN) model outperforms the multiple linear regression (MLR) and persistence models for solar power forecasting.
2. The ANN model achieves better performance when trained with a selected set of 14 weather variables after performing sensitivity and correlation analysis.
3. The performance of the ANN model improves significantly with the availability of more historical data, as demonstrated by the May 2014 case, which had lower RMSE values compared to the September 2013 case.
4. Excluding night hours (which have zero solar power generation) slightly improves the model's accuracy by focusing on relevant daylight data.
5. The inclusion of a bias node in the ANN architecture aids in minimizing errors by shifting the activation function for enhanced performance.
6. The ANN model generates more accurate forecasts during clear sky hours compared to cloudy conditions, emphasizing weather variability as a key challenge.
7. Steps like plotting data, cleansing outliers, and performing sensitivity and correlation analysis are critical for improving the forecasting model's accuracy.
8. The feedforward ANN with hourly forecasts outperforms recursive neural networks, making it a more suitable choice for this application.
9. Normalizing input data does not significantly enhance the performance of the ANN model in this context.
10. Improvements in weather forecasting and additional historical data are crucial for further enhancing the accuracy of solar power predictions.