Impacts of Artificial Neural Network Training Algorithms on the Accuracy of PV System Voltage and Current Predictions

This study highlights the importance of selecting the appropriate Artificial Neural Network (ANN) training algorithm-based accuracy of prediction capacities in photovoltaic (PV) systems. Accurate PV system performance prediction, particularly output voltage and current, is essential for optimising energy generation and ensuring grid stability. This study evaluates the impact of three ANN training algorithms Levenberg-Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) on the prediction of PV voltage and current. The algorithms were tested using solar radiation and temperature as inputs, to determine their effectiveness in handling varying datasets. Therefore, the results indicate that the Levenberg-Marquardt algorithm outperforms the others in terms of speed, memory efficiency, and accuracy, achieving the lowest mean square error (MSE) of 0.0957 and the highest regression value (R= 0.999946). Bayesian Regularization demonstrated strong generalization capabilities with an MSE of 0.1436. The Scaled Conjugate Gradient algorithm performed well but had a slightly higher MSE of 0.1729. besides, Error histograms for all algorithms showed minimal deviations, confirming their predictive accuracy. The findings provide valuable insights for enhancing the accuracy and efficiency of PV system modelling and forecasting, contributing to the advancement of renewable energy integration.

Introduction

Development is fundamentally dependent on energy production, consumption, and storage. Currently, fossil fuels serve as the main source of energy for development; however, their use negatively impacts both climate and air quality. As populations grow and demand for energy increases, the combustion of fossil fuels accelerates further environmental harm. Therefore, since fossil fuels are finite resources that cannot sustain long-term growth, it is crucial to explore alternative energy solutions [1].

Solar energy stands out as a more sustainable option compared to another alternative energy systems. The sun provides an abundant and reliable source of power with significant potential for meeting our future energy needs. To effectively harness this potential, accurate solar radiation data is essential for predicting solar energy availability [2].

Photovoltaic systems convert solar energy into electrical power and are environmentally friendly, easy to install, and have a low carbon footprint. Energy generation from PV systems is influenced by various environmental and operational factors, making accurate predictions crucial for grid stability [3].

Traditional manual prediction methods can be rather fast and disposed to errors. In contrast, the machine learning algorithms boost the solar energy prediction by analysing large data basis, improving accuracy through the identification of complex relationships and adaptability to changing conditions. These algorithms offer scalability and efficiency in predicting solar energy output [4]. Therefore, this study will analyse how different machine learning algorithms impact the voltage and current development of PV systems directly affecting power generation.

This study analysed and compared various training algorithms of a neural network model to identify the most effective one for predicting voltage and current in photovoltaic systems, ultimately providing recommendations based on performance metrics.

Artificial Neural Network modelling involves choosing input variables and designing the network architecture. ANNs model nonlinear relationships between external variables [5]. The structure includes input, hidden, and output layers that process data. Learning algorithms fine-tune the parameters of the ANN to minimise prediction errors [6].

The study found that the Support Vector Machine Regression (SVMR) model outperformed others, achieving a MSE of 0.038, a mean absolute error (MAE) of 0.17, and an R² value of 0.99. It emphasized the significant influence of environmental factors, as solar radiation, ambient air temperature, and relative air humidity on the power of photovoltaic modules. These findings indicate that the SVMR model is reliable for predicting solar PV system output power, crucial for optimizing performance and economic viability in solar power plants [7].

The evaluation included 24 unique machine learning (ML) algorithms for the intent of forecasting photovoltaic power generation one day ahead, based on a dataset that lasted two years from 16 PV facilities found in Hungary [8]. According to this assessment the top models, kernel ridge regression and multilayer perceptron achieved forecast skill scores up to 44.6% better than the insistence model. Forecasts based on daily average irradiance and sun position angles had only a 1.5% higher Root-Mean-Squared Error (RMSE) than the best scenario, highlighting ML’s potential in PV forecasting [8]. Additionally, a hybrid model combining ANNs with multiverse optimization (MVO) and genetic algorithms (GA) was explored to enhance predictions of PV output power, efficiency, and cell temperature. This research underscored the significant impact of environmental factors ambient temperature, wind speed, and solar irradiance on PV performance; notably, maximum efficiency occurs at 0°C due to temperature sensitivity [9].

On the other hand, the three photovoltaic power forecasting models: a convolutional neural network (CNN), a long short-term memory neural network (LSTM), and a hybrid model demonstrated higher accuracy than the individual models. Evaluation using RMSE, MAE, and MAPE shows that while CNN generally performs best, however, LSTM excels in specific cases [10]. Additionally, an RNN outperformed classical ANN in solar radiation prediction by achieving a 47% improvement in Normalized Mean Bias Error (NMBE) and a 26% improvement in Root-Mean-Squared Error [11]. A comparative analysis of machine learning models Bayesian Neural Network (BNN), Support Vector Regression (SVR), and Regression Tree revealed that BNN achieved the highest forecasting accuracy with an RMSE of 6.95% and MAPE of 6.07% for day-ahead PV power forecasting [12].

Therefore, reliable forecasting is essential for integrating photovoltaics into power grids, as solar energy’s variability due to weather can lead to voltage surges and system instability. The study highlights the importance of improved weather classification techniques for more accurate PV power forecasts, suggesting that separate models for different conditions may yield better results [13].

Lastly, this study examines the output voltage and current of PV systems by employing Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient neural network training algorithms.

Fig. 1 presents the ANN employed in the recent study predicting the voltage and current of the photovoltaic system. This diagram depicts the structure of the neural network, including its input, hidden, and output layers, which work together to process data effectively for accurate predictions. Most PV power prediction studies use neural networks with 10 hidden layers. This study employed a neural network that takes solar radiation (G) and temperature (T) as input parameters, while voltage (V) and current (I) serve as output parameters.

Fig. 1. The layer structure of the Artificial Neural Network.

In this investigation the load of the solar system was a resistor. The hidden layer of the neural network contained 10 neurons with a hyperbolic transfer function, while linear transfer functions were used for the outputs.

In this study three training algorithms were applied to predict the voltage and current of the PV system, as Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient. These algorithms were selected based on their strong predictive capabilities and their widespread application in power prediction for photovoltaic systems. Each algorithm offers unique advantages that enhance the accuracy of predictions, making them suitable choices for this research.

Levenberg-Marquardt Algorithm

The Levenberg–Marquardt method is a mathematical technique used to find optimal solutions, like to finding the best route on a map. It iteratively adjusts results for accuracy, making it useful for fitting models to data, such as predicting solar panel energy output [14]. This powerful tool effectively solves complex nonlinear equations and stabilizes solutions across various fields like engineering, physics, and data analysis [15].

Bayesian Regularization Algorithm

The purpose of Bayesian Regularization is to enhance the performance of artificial neural networks by preventing overfitting, where a model becomes too tailored to train data and struggles with new data. It adds a penalty term for large weights in the objective function, encouraging simpler models that improve generalisation [16].

Scaled Conjugate Gradient Algorithm

The Scaled Conjugate Gradient method is an optimisation technique that efficiently finds the best solution. Like finding the fastest map route, SCG navigates through data to identify optimal paths [17].

Result and Discussion

In this study, a 10 W photovoltaic module was selected to conduct experiments. Using LabVIEW software, we recorded data on voltage and current generated by the PV module. The experimental setup included a resistor to load the system, myDAQ for data acquisition, connecting wires for circuit assembly, and a computer to run the LabVIEW program and analyse the collected data. This configuration allowed us to effectively monitor and evaluate the performance of the PV module under controlled conditions. Additionally, the measurement data was collected in Gödöllő City, located in the central region of Hungary.

In artificial neural networks, regression analysis is essential for predicting continuous outcomes based on input data. Error histograms visually represent the distribution of predicted errors, helping to assess model performance. Totally, 22 data pairs were used for the prediction analysis in this study.

Fig. 2, depicts the regression values of the Levenberg-Marquardt training algorithm for predicting voltage and current in the PV system, achieving high accuracy with an overall R-value of 0.999946.

Fig. 2. Regression values of Levenberg Marquardt training algorithm.

Fig. 3, presents the error histogram for the Levenberg-Marquardt training algorithm. According to the result, the histogram reveals that errors are predominantly centred around the zero-error line, indicating that most predictions closely align with actual values. This distribution suggests high accuracy in the model’s performance, as minimal deviation from true outcomes reflects the algorithm’s effective learning and generalisation capabilities.

Fig. 3. Error histogram of Levenberg Marquardt training algorithm.

The lack of a visible validation step in Bayesian Regularization is attributed to its automatic mechanisms for managing overfitting and ensuring generalisation. This makes it particularly effective for noisy or small datasets. Consequently, Fig. 4, shows the regression values of this algorithm, demonstrating its strong predictive capabilities for output voltage and current.

Fig. 4. Regression values of Bayesian regularization training algorithm.

Besides, Fig. 5, displays the error histogram for the Bayesian Regularization training algorithm, showing that prediction errors are predominantly close to zero. This indicates high accuracy in the model’s predictions.

Fig. 5. Error histogram of Bayesian regularization training algorithm.

Fig. 6 illustrates the regression values of the Scaled Conjugate Gradient algorithm used to be predicted the output voltage and current of the PV system, resulting in accurate estimations.

Fig. 6. Regression values of Scale conjugate gradient training algorithm.

Similarly, Fig. 7 presents the error histogram in case the use of Scaled Conjugate Gradient training algorithm, revealing that prediction errors are mostly near zero, indicating high accuracy in the model’s predictions.

Fig. 7. Error histogram of scale conjugate gradient training algorithm.

Comparison of the Selected Training Algorithm

The comparison of the selected training algorithms Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient focuses on their performance in training artificial neural networks. Each algorithm has unique strengths that make it appropriate for different scenarios in neural network training.

Table I, compares the Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient methods. The Levenberg-Marquardt algorithm stands out for its superior speed, memory efficiency, and accuracy in training artificial neural networks. This makes it a preferred choice for many applications requiring optimal performance.

Table I. Comparison of ANN Training Algorithms

Algorithm	Speed	Efficiency	Accuracy	Best use case
LM	Fast	High	High	Small to medium datasets
BR	Moderate	Moderate	Very high	Small, noisy datasets
SCG	Moderate	High	Moderate	Moderate to large datasets

Similarly, Table II, shows the mean square error for Levenberg-Marquardt is the lowest, indicating that this algorithm outperforms Bayesian Regularization and Scaled Conjugate Gradient in predicting voltage and current.

Table II. Mean Square Error of the Selected Algorithms

Algorithm	Activity	Mean square error
Levenberg-Marquardt	Training	0.0957
Bayesian regularization	Training	0.1436
Scaled conjugate gradient	Training	0.1729

Conclusion

This study evaluated the performance of three Artificial Neural Network training algorithms Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient in predicting voltage and current in photovoltaic systems.

The findings revealed that LM is the most effective for small to medium datasets, achieving the fastest convergence with a mean square error of 0.0957, indicating high accuracy. Bayesian Regularization demonstrated strong predictive capabilities with an MSE of 0.1436 but was slightly slower than LM. Scaled Conjugate Gradient offered good memory efficiency and fast convergence but had a higher MSE of 0.1729.

Error histograms showed that predictions from all algorithms were centred around zero, confirming their accuracy; however, LM consistently provided the best overall performance for PV voltage and current predictions.