Prediction of Photovoltaic Module Characteristics by Machine Learning for Renewable Energy Applications

Abstract

Photovoltaic (PV) modules undergo comprehensive testing to validate their electrical and thermal properties prior to market entry. These evaluations consist of durability and efficiency tests performed under realistic outdoor conditions with natural climatic influences, as well as in controlled laboratory settings. The overall performance of PV cells is affected by several factors, including solar irradiance, operating temperature, installation site parameters, prevailing weather, and shading effects. In the presented study, three distinct PV modules were analyzed using a sophisticated large-scale steady-state solar simulator. The current–voltage (I-V) characteristics of each module were precisely measured and subsequently scrutinized. To augment the analysis, a three-layer artificial neural network, specifically the multilayer perceptron (MLP), was developed. The experimental measurements, along with the outputs derived from the MLP model, served as the foundation for a comprehensive global sensitivity analysis (GSA). The experimental results revealed variances between the manufacturer’s declared values and those recorded during testing. The first module achieved a maximum power point that exceeded the manufacturer’s specification. Conversely, the second and third modules delivered power values corresponding to only 85–87% and 95–98% of their stated capacities, respectively. The global sensitivity analysis further indicated that while certain parameters, such as efficiency and the ratio of V_oc/V, played a dominant role in influencing the power-voltage relationship, another parameter, U, exhibited a comparatively minor effect. These results highlight the significant potential of integrating machine learning techniques into the performance evaluation and predictive analysis of photovoltaic modules.

1. Introduction and State of the Art

Electricity underpins modern economic and technological progress and is deeply integrated into everyday life. As traditional energy resources gradually deplete and environmental concerns intensify, the search for renewable energy alternatives becomes increasingly urgent. Among these alternatives, photovoltaics (PV) stand out as one of the most accessible and scalable solutions for sustainable electricity generation [1]. PV systems, which capture energy from solar photons, are composed of several fundamental components including modules, inverters, batteries, cables, and safety units [2]. The construction of a typical PV module involves multiple layers: an outer glass layer with anti-reflective treatment, one or more encapsulation layers, an array of solar cells, and a back sheet. This layered architecture enables PV systems to serve diverse applications, ranging from small-scale installations powering individual devices to large solar farms generating tens of megawatts of clean energy [3]. PV cell technologies are categorized into three generations based on their underlying materials and stages of market adoption [3].

The first generation involves well-established, wafer-based crystalline silicon technology, which can be further divided into monocrystalline (M-Si) and polycrystalline (P-Si) types. This technology is highly efficient due to the inherent properties of silicon [4,5,6]. Historical benchmarks include the pioneering silicon solar cell developed by Chapin et al. in 1954 with an initial efficiency of approximately 6%, which has since improved dramatically to values around 26.1% [7,8,9]. The second generation utilizes thin-film approaches such as amorphous silicon, micromorph silicon, cadmium telluride (CdTe), and copper-based technologies (CIS/CIGS). While traditional measurement-based characterization of PV modules—using Class AAA solar simulators and laboratory I-V tracing—provides high accuracy, it is inherently time-consuming, costly, and limited to off-line scenarios. In contrast, a machine-learning (ML) approach can leverage routinely collected operating data (e.g., voltage, current, ambient and module temperatures) to infer critical module parameters in real time. Once trained, the ML model predicts temperature coefficients and power–voltage behavior within seconds, eliminating the need for repeated simulator tests. This enables rapid, in situ monitoring and scalable deployment across large PV fleets, reducing both capital and labor costs. Moreover, by incorporating data from diverse module technologies and operating conditions, the ML framework generalizes new modules without bespoke test campaigns, offering a versatile tool for performance assessment and fault diagnosis.

Although these systems offer reduced production costs, their efficiency generally lags behind that of crystalline silicon devices [7,10,11,12,13]. The third generation encompasses emerging technologies such as concentrating photovoltaics (CPVs), organic PV cells, and novel concepts including nanowires and quantum dots, which are at various stages of research and demonstration [9,14,15]. Recent reports suggest that some third-generation approaches have reached efficiencies in the vicinity of 18.9% [16]. The efficiency and longevity of PV modules are subjected to various internal and external factors. Internally, the consistency and quality of semiconductor interfaces, the configuration of multiple cell layers, and the inherent material properties directly influence conversion efficiency. Externally, factors such as solar irradiance, ambient temperature, weather conditions, and shading significantly affect output. Even slight increases in module surface temperature can result in measurable drops in performance; studies have shown that a temperature rise can reduce the maximum power output by approximately 0.4–0.5% per degree Celsius [17,18,19,20,21,22,23,24]. In addition to the intrinsic characteristics of the PV modules, the integration of modern cooling technologies has been a subject of extensive research. Approaches such as active cooling using pumps and heat sinks or passive methods involving strategically positioned acrylic sheets have shown potential in mitigating thermal losses, thereby enhancing overall module efficiency [25,26,27,28,29,30]. Innovative designs not only help maintain optimal operating temperatures but also extend the operational life span of the modules.

Existing techniques for PV module characterization can be broadly classified as follows [31,32,33]:

• Measurement-Based Methods rely on laboratory I-V tracing under STCs using high-precision solar simulators. While these methods deliver benchmark accuracy, they incur substantial equipment and labor costs and cannot be deployed in field environments.
• Physics-Based Models fit measured data to analytical device models (e.g., single-diode, double-diode). These approaches offer physical interpretability, but parameter extraction often requires iterative optimization and can be sensitive to measurement noise and incomplete datasheet information.
• Data-Driven Machine-Learning Approaches employ regression techniques—such as artificial neural networks (ANNs), support vector machines (SVMs), and random forests—to learn empirical mappings between routinely logged operating variables (e.g., Voc, Isc, module temperature) and module performance coefficients. These methods enable rapid, in situ estimation without dedicated test rigs, but suffer from black-box opacity, need extensive training datasets, and may require careful hyperparameter tuning to avoid overfitting.

The rapid evolution in PV technologies is also mirrored by advancements in artificial intelligence. AI techniques, including artificial neural networks (ANNs) and deep learning models like long short-term memory (LSTM) networks, are increasingly applied to monitor, predict, and optimize the performance of solar energy systems. These methods analyze data collected from sensors, tracking variables such as temperature, solar radiation, humidity, and even particulate accumulation, to forecast future performance and guide maintenance strategies [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54]. Recent studies demonstrate that machine-learning (ML) and deep learning (DL) models can significantly enhance predictive accuracy, offering more robust solutions in solar energy forecasting when compared to traditional statistical methods [55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73].

Recent benchmarking studies have shown that while recurrent models like LSTM capture temporal variability in irradiance, compact MLPs deliver comparable accuracy R² ≈ 0.98 with 40% fewer trainable parameters, making them more suitable for embedded, low-latency inference [74]. Hybrid CNN-MLP architectures incur only marginal MAE improvements (<0.5%) at the expense of significantly longer training times [75].

Despite promising results, prior ML applications in PV characterization exhibit notable limitations: most rely on small datasets (<100 I-V traces) prone to overfitting; they lack interpretable sensitivity analyses to reveal key drivers; and model transferability across different module technologies remains untested. Our work addresses these gaps by training on an expanded dataset spanning crystalline and thin-film modules and by coupling the MLP with a Spearman-based global sensitivity analysis. Here, we employ Spearman’s rank correlation coefficient (ρ)—a nonparametric metric ranging from −1 to +1 to assess monotonic associations between each input (e.g., Voc, irradiance) and outputs (Tc, Tp), without assuming linearity. Looking ahead, PV module degradation alters temperature coefficients and I-V curve shape over time. We plan to extend our framework by retraining the MLP on longitudinal degradation datasets and incorporating degradation-related features (e.g., encapsulant browning index) into the sensitivity analysis to predict long-term performance shifts.

Finally, beyond the technological and operational innovations, the overarching goal remains to integrate renewable energy into existing infrastructures effectively. Achieving a sustainable energy balance demands novel policy frameworks and socio-economic strategies that foster renewable energy adoption while mitigating environmental impacts, a multidisciplinary effort that continues to evolve alongside technological progress. The structure of this discussion reflects an integrated approach: initially outlining the importance of electricity and renewable energy; then detailing PV system structures and technologies across three generations; addressing the influences of environmental and operational factors; and finally, discussing the role of AI in optimizing solar energy systems. This comprehensive perspective aims to contribute novel insights into both the current state and future direction of renewable energy technologies.

2. Materials and Methods

2.1. Testing Methods for PV Modules

The rapid evolution of the photovoltaic industry since the early 2000s has necessitated the establishment of uniform standards and regulations to ensure a consistent certification process for PV modules. In European Union countries, the certification process adheres to the standards set by the International Electrotechnical Commission (IEC). Specifically, IEC 61215 [34] outlines the construction qualification and type approval requirements for photovoltaic modules intended for terrestrial applications that will operate reliably over long periods under the climatic conditions specified by IEC 60721-2-1 [35]. These tests evaluate the performance of the PV modules under standardized conditions, and the standard is applicable to both crystalline silicon and thin-film modules. Within the framework of this work, two principal test methodologies were employed:

• MQT 04—Measurement of Temperature Coefficients: This test involves quantifying the temperature coefficients of current, voltage, and peak power in accordance with PN-EN 60904-10 [34]. It aims to determine how the electrical parameters of PV modules vary with temperature, and it requires a device specifically designed to control the module’s temperature during measurement.
• MQT 06—Performance under STC and NOCT Conditions: This evaluation focuses on determining the electrical performance of the module under Standard Test Conditions (STCs) and under NOCT (Nominal Operating Cell Temperature) conditions. The STC measurement is used to verify the module’s nameplate specifications and should be conducted with either natural solar radiation or a solar simulator of BBA-class quality, or better [34].

2.2. Characteristics of the Tested PV Modules

The first module evaluated is a double-sided, monocrystalline module, referred to as “Module 1”. According to the manufacturer’s documentation, the module exhibits an efficiency of 20% and a maximum power output of 365 W. Moreover, the manufacturer offers a 30-year warranty on the additional linear power output, which is expected to retain approximately 85% of its initial performance after 30 years [36].

The second module examined is a CIGS thin-film module, designated as “Module 2”. This module exhibits an efficiency of approximately 13% and is capable of producing a maximum power output of 145 W. It features a double-glazed panel design which minimizes the risk of micro-cracking and thereby enhances the module’s overall durability. The manufacturer guarantees that the module will retain at least 80% of its rated power after a period of 25 years [37].

The third module analyzed is a monocrystalline single-sided photovoltaic module, referred to as “Module 3”. This module achieves an efficiency of about 19.3% and can deliver a maximum power of 315 watts. The developer ensures that the degradation rate of the module remains constant over a 25-year period [38]. For detailed comparison, the characteristics of all tested modules are summarized in

Table 1. Characteristics of the tested photovoltaic modules.

Parameter			PV Modules Tested
			Module 1	Module 2	Module 3
Max Power	Pmax	[W]	365	145	315
Idle voltage	Voc/V	[V]	40.7	59.5	40.53
Module efficiency	Eff	[%]	20.0	13.3	19.3
Max power voltage	Vmpp	[V]	34.1	60.4	33.2
Max power current	Impp	[A]	10.7	2.4	9.5
Short-circuit current	Isc	[A]	11.4	2.7	10.0
Open-circuit voltage	Voc	[V]	40.7	85.2	40.5

.

2.3. Experimental Description and Test Methods

The experiments were carried out using a stationary, steady-state solar simulator, Class AAA (see Figure 1), designed for measuring the performance of photovoltaic modules under tightly controlled test parameters. This device precisely replicates solar radiation according to specified conditions, enabling the measurement of the maximum power output of each photovoltaic module under standard test conditions. For each module, tests were repeated five times, and the results were averaged to estimate the performance. All PV modules tested were brand-new, meaning they had never been previously used (see Figure 2).

The measurement setup comprises a large-area, stationary steady-state solar simulator combined with a system for analyzing the current–voltage characteristics of the photovoltaic modules, along with a calibrated, accredited reference coil. The reference coil, positioned on the module under test, was utilized to obtain baseline measurements that were subsequently compared with the readings from the module itself [39].

Both the MQT 06 and MQT 04 evaluations were performed using a large-area, stationary steady-state solar simulator. For the MQT 06 procedure, the PV module’s electrical parameters were recorded under Standard Test Conditions (STCs), defined by a solar irradiance of (1000 ± 100) W/m² and an ambient cell temperature of (25 ± 2) °C. The module, fitted with a calibrated reference coil, was slid into position beneath the simulator’s lamp array prior to initiating each measurement.

In the MQT 04 sequence, ten independent readings were taken per module: five measurements were adjusted to a reference temperature of 25 °C, while the other five were left uncorrected. Module temperatures were logged immediately before and after each test run to ensure accuracy of the temperature-dependent correction. All details are shown in

Table 2. Laboratory testing conditions.

Parameter	Value	Notes
Irradiance	1000 ± 10 W/m2	Class AAA solar emulator
Module Temperature	25 ± 0.5 °C	Back-surface thermocouple
Ambient Temperature	22 ± 1 °C	Lab environmental control
Spectral Match	Class A
Voltage Scan Rate	10 mV/s	Bidirectional sweep
Replicates per Voltage Point	5	Averaged for modeling

.

A pivotal aspect of this work was constructing machine learning models to quantify and select the most impactful correlations among independent variables for numerical simulations based on the experimental dataset. The correlation coefficient, R_ij, spans from −1 to +1, where positive values indicate that an increase in variable i leads to an increase in variable j, and negative values imply an inverse relationship. To capture nonlinear dependencies, we applied Spearman’s rank correlation coefficient (ρ), which is particularly suited for assessing monotonic, nonparametric associations [40].

All model development was performed in Python 3.10 using TensorFlow 2.11 for network implementation and scikit-learn 1.2 for preprocessing and baseline methods. To determine the optimal number of hidden neurons J, we conducted a grid search over {2,4, 6,8,10} neurons, monitoring validation MSE. We partitioned the data into training (70%), validation (15%), and independent test (15%) sets to reserve a final hold-out set for unbiased evaluation. While k-fold cross-validation was used during hyperparameter tuning within the training + validation subset, the fixed hold-out test set ensures that no model selection bias influences the reported test metrics.

The MLP architecture consists of an input layer receiving four normalized features: short-circuit current (Isc), open-circuit voltage (Voc), module back-surface temperature, and irradiance and a single hidden layer of four neurons with tanh activation. The output layer comprises two linear neurons predicting the temperature coefficients of current (Tc) and power (Tp). We initialized weights using the Xavier uniform scheme to promote stable gradient flow. Prior to training, all input features were standardized (zero mean, unit variance). The dataset was randomly split into training (80%) and validation (20%) subsets using a fixed seed (42) for reproducibility. The network was trained to minimize the mean squared error (MSE) loss using the Adam optimizer (learning rate = 0.001). Training proceeded in mini-batches of 16 samples for up to 500 epochs, with early stopping triggered after 50 epochs without improvement in validation loss. Hyperparameters (hidden neurons, learning rate, batch size) were optimized via 5-fold cross-validation on the training set. The final model was selected based on the lowest average validation MSE.

Within the multilayer perceptron (MLP) framework applied here, each incoming feature x_i at the input layer is scaled by its corresponding synaptic weight w_ij, as illustrated in Figure 3. The sum of these weighted inputs is then passed through an activation function f which may be linear or one of several nonlinear forms (e.g., exponential, hyperbolic tangent, sine, or logistic) before being delivered to the output neurons. During training, the values of w_ij are iteratively adjusted using numerical optimization techniques designed to minimize the mean squared error (MSE) between the network’s predictions and the true targets

$$\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{1}{\mathrm{N}}}\cdot \sum _{\mathrm{n}=1}^{\mathrm{N}}{\left({\widehat{\mathrm{y}}}_{\mathrm{n}}-{\mathrm{y}}_{\mathrm{n}}\right)}^2,$$

(1)

where ${\mathrm{y}}_{\mathrm{n}}$ is the ground truth for the $\mathrm{n}$-th training data point, ${\widehat{\mathrm{y}}}_{\mathrm{n}}$ is the corresponding output from the neural network, $\mathrm{n}=1,\dots , \mathrm{N}$, and $\mathrm{N}$ is the number of data points in the training set. Each coordinate $\widehat{\mathrm{y}}$ of the output was calculated according to the following formula [41]:

$$\widehat{\mathrm{y}}=\sum _{\mathrm{j}=1}^{\mathrm{J}}{\mathrm{w}}_{\mathrm{j}}\cdot \mathrm{f}\left(\sum _{\mathrm{i}=1}^{\mathrm{I}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}\cdot {\mathrm{x}}_{\mathrm{i}}+{\mathrm{b}}_{\mathrm{j}}\right),$$

(2)

where $\mathrm{I}$—the number of inputs to the model, $\mathrm{J}$—the number of neurons in the hidden layer, ${\mathrm{w}}_{\mathrm{i}\mathrm{j}}$—the values of weights between the inputs and the neurons of the hidden layer, ${\mathrm{b}}_{\mathrm{j}}$—neuron loads of the hidden layer, ${\mathrm{w}}_{\mathrm{j}}$—the values of weights between neurons of the hidden layer and neuron of the output layer, $\mathrm{f}$—the activation function. At the stage of creating the MLP model, it is crucial to determine the number of neurons in the hidden layer. Widely accepted guidelines specify that the hidden layer neuron count J should satisfy j ≤ J ≤ 2j + 1, where j denotes the number of explanatory variables [42]. To avoid the overfitting of the model, Rogers and Dowl [43] suggested that the value of $\mathrm{J}$ should not be less than ${\displaystyle \frac{\mathrm{T}}{\mathrm{j}+1}}$ (where $\mathrm{T}$ is the number of data observations in the learning set). The number of neurons in the hidden layer can also be determined by a trial-and-error method minimizing the prediction error, but not allowing overlearning of the model (when with an increase in $\mathrm{J}$ the prediction error increases, there is a decrease in the generalization ability of the model). In this study, a three-layer neural network was implemented, taking as inputs the current–voltage characteristics of each PV module and yielding two outputs corresponding to the module’s power–voltage curves. The dataset was partitioned into training (70%), testing (15%), and validation (15%) subsets.

Simultaneously, a global sensitivity analysis was carried out to pinpoint which parameters most strongly influence the power-voltage relationship, with sensitivity coefficients computed to quantify each factor’s impact. To quantify the agreement between the true value ${\mathrm{y}}^{\left(\mathrm{m}\right)}$ for each coordinate of the m-th validation sample and its corresponding network prediction ${\widehat{\mathrm{y}}}^{\left(\mathrm{m}\right)}$, the following evaluation metrics were applied:

(a)

Coefficient of determinacy (${\mathrm{R}}^2$)

$${\mathrm{R}}^2={\displaystyle \frac{\sum _{\mathrm{m}=1}^{\mathrm{M}}{\left({\widehat{\mathrm{y}}}^{\left(\mathrm{m}\right)}-\overline{\mathrm{y}}\right)}^2}{\sum _{\mathrm{m}=1}^{\mathrm{M}}{\left({\mathrm{y}}^{\left(\mathrm{m}\right)}-\overline{\mathrm{y}}\right)}^2}},$$

(3)

where $\overline{\mathrm{y}}={\displaystyle \frac{1}{\mathrm{M}}}\cdot \sum _{\mathrm{m}=1}^{\mathrm{M}}{\mathrm{y}}^{\left(\mathrm{m}\right)}$.

(b)

Mean absolute error (MAE)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{M}}}\cdot \sum _{\mathrm{m}=1}^{\mathrm{M}}\left|{\widehat{\mathrm{y}}}^{\left(\mathrm{m}\right)}-{\mathrm{y}}^{\left(\mathrm{m}\right)}\right|;$$

(4)

(c)

Root mean square error (RMSE)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{M}}}\cdot \sum _{\mathrm{m}=1}^{\mathrm{M}}{\left({\widehat{\mathrm{y}}}^{\left(\mathrm{m}\right)}-{\mathrm{y}}^{\left(\mathrm{m}\right)}\right)}^2};$$

(5)

where ${\mathrm{y}}^{\left(\mathrm{m}\right)}$—the ground truth for $\mathrm{m}$-th validation data point based on the measurements; ${\widehat{\mathrm{y}}}^{\left(\mathrm{m}\right)}$—results by ML methods, $\mathrm{m}=1,\dots ,\mathrm{M}$ and $\mathrm{M}$ is the number of data points in the validation set.

The model was constructed using the dataset containing variables U, efficiency (eff), and the open-circuit voltage ratio (V_oc/V) to predict the values of T_c and T_p. A comprehensive flowchart summarizing the entire methodology is provided in Figure 4.

3. Investigation Results

For each of the three modules, five independent measurements were performed; the results were then averaged and approximated, as detailed in

Table 3. Results of module parameters obtained during measurements.

Parameter	Module 1	Module 2	Module 3
Pmax [W]	367.302	125.332	303.844
Isc [A]	11.454	2.692	9.818
Voc [V]	44.996	86.334	49.71
Impp [A]	10.654	2.166	9.192
Vmpp [V]	34.47	57.804	32.838
Filling Factor [-]	0.712	0.538	0.622

.

Under STCs, Module 1 achieved its peak power during the first measurement (Figure 5), recording 372 W, that is about 102% of the nominal 365 W specified by the manufacturer. In all but one trial, the module met or exceeded its rated maximum power. The average fill factor across measurements was approximately 0.7.

During STC testing, Module 2 reached its highest power output of 127 W in the first measurement—only 87% of its 145 W nameplate rating (Figure 6). The second measurement produced the lowest reading of 124 W, corresponding to 85% of the specified maximum. Across all trials, the average fill factor was a mere 0.54, reflecting suboptimal performance. As a CIGS thin-film module, Module 2’s efficiency was markedly lower than that of the first-generation crystalline silicon module tested.

For Module 3, the highest power point in the final round of testing occurred during the first measurement (Figure 7), reaching approximately 309 W that is about 98% of the 315 W rating specified by the manufacturer. At no point did any test exceed the declared maximum power. The mean fill factor across measurements was roughly 0.62.

In Figure 5, Figure 6 and Figure 7, the current–voltage (I-V) plots use the current in amperes (A) on the vertical axis and the voltage in volts (V) on the horizontal axis; these units are now explicitly noted in the captions.

Table 4. Dependence of current and power values with averages for tested PV modules.

Measurement	5 V	15 V	25 V	35 V	40 V
“Module 1”
Power
Measurement 1 [W]	57.8901	171.1275	275.1322	365.42124	161.8382
Measurement 2 [W]	57.6934	170.9794	274.2930	362.1189	169.96
Measurement 3 [W]	57.3698	169.8569	280.7647	361.1334	168.7743
Measurement 4 [W]	57.5227	169.8666	281.0866	359.4855	161.9976
Measurement 5 [W]	57.3990	169.6859	274.4320	354.4239	165.2108
Average [W]	57.57503	170.3033	277.1417	360.5166	165.5562
Current
Measurement 1 [A]	11.5763	11.409	11.0057	10.452	4.0459
Measurement 2 [A]	11.5389	11.399	10.9726	10.3584	4.249
Measurement 3 [A]	11.4748	11.325	11.2311	10.3311	4.2193
Measurement 4 [A]	11.507	11.3253	11.2439	10.2844	4.0499
Measurement 5 [A]	11.4799	11.3129	10.978	10.1403	4.1303
Average [A]	11.5154	11.3543	11.0863	10.3132	4.1389
“Module 2”
Power
Measurement 1 [W]	13.4401	65.8343	113.0481	119.1181	17.9283
Measurement 2 [W]	13.3214	65.1509	111.2806	114.9977	11.3292
Measurement 3 [W]	13.4363	65.8609	112.2522	116.6261	10.9828
Measurement 4 [W]	13.3855	65.2238	111.2941	115.5224	13.8337
Measurement 5 [W]	13.4530	65.9243	112.1763	115.5607	11.9393
Average [W]	13.4073	65.5988	112.0102	116.3650	13.2026
Current
Measurement 1 [A]	2.6882	2.6334	2.5122	1.8326	0.2241
Measurement 2 [A]	2.6644	2.606	2.4729	1.7692	0.1416
Measurement 3 [A]	2.6873	2.6344	2.4945	1.7942	0.1373
Measurement 4 [A]	2.677	2.609	2.4732	1.777	0.1729
Measurement 5 [A]	2.6906	2.637	2.4928	1.7778	0.1492
Average [A]	2.6815	2.624	2.4891	1.7902	0.165
“Module 3”
Power
Measurement 1 [W]	49.4636	146.4109	243.2909	296.5507	107.8788
Measurement 2 [W]	49.5614	146.6602	243.8605	286.7913	89.9354
Measurement 3 [W]	49.5627	146.8454	243.7230	288.4221	102.8483
Measurement 4 [W]	49.4132	146.5157	242.7928	281.0666	84.2467
Measurement 5 [W]	49.2112	146.1223	242.8360	283.3992	92.6678
Average [W]	49.4424	146.5109	243.3006	287.2460	95.5154
Current
Measurement 1 [A]	9.8910	9.7619	9.7318	8.4882	2.6970
Measurement 2 [A]	9.9170	9.7782	9.7545	8.2108	2.2484
Measurement 3 [A]	9.9121	9.7907	9.7494	8.2570	2.5712
Measurement 4 [A]	9.8839	9.7686	9.7121	8.0493	2.1062
Measurement 5 [A]	9.8459	9.7419	9.7138	8.1150	2.3167
Average [A]	9.8900	9.7683	9.7323	8.2241	2.3879

reports raw Spearman rank correlation coefficients (ρ) between each input feature and the predicted outputs (Tc, Tp), quantifying pairwise monotonic associations.

Table 5. Correlation coefficients of tested PV modules.

	U	Tc	Tp	Pmax	Voc/V	eff	Vmpp	Impp	Isc
U	1.00	0.73	0.25	0.33	0.33	0.33	0.33	0.33	0.33
Tc		1.00	0.29	0.79	0.33	0.79	0.33	0.79	0.79
Tp			1.00	0.44	0.31	0.44	0.31	0.44	0.44
Pmax				1.00	0.36	1.00	0.36	1.00	1.00
Voc/V					1.00	0.36	1.00	0.36	0.36
eff						1.00	0.36	1.00	1.00
Vmpp							1.00	0.36	0.36
Impp								1.00	1.00
Isc									1.00

re-orders the same ρ values to rank input sensitivities from highest to lowest, aiding quick identification of the most influential variables.

Details of the current–voltage differences and their approximations, based on the experimental study, can be found in Table 4.

To assess whether alternative regression techniques could reduce the observed prediction errors, we implemented Random Forest (RF) and Support Vector Regression (SVR) using the same input features and data splits. RF achieved R² = 0.973 with MAE ≈ 0.014 (Tc) and 0.018 (Tp), while SVR reached R² = 0.962 with MAE ≈ 0.017 and 0.022, respectively. Although RF and SVR offered competitive performance, our compact 4:4:2 MLP yielded the highest R² and lowest MAE, with minimal model complexity and inference latency. These results confirm that the chosen MLP architecture provides the best balance of accuracy, efficiency, and deployability for real-time monitoring applications.

Table 5 presents the correlation coefficients for all parameters across the tested PV modules. The analysis revealed that the most accurate predictions were achieved by an MLP configuration with four input neurons, a four-neuron hidden layer using the hyperbolic tangent activation function, and two linear output neurons.

Table 6. Fitting measures between simulation results and measurements on dependent variables.

Set	Tp			Tc
	Ke	$\mathit{M}\mathit{A}\mathit{E}$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$	$\mathit{M}\mathit{A}\mathit{E}$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$
Training	0.94	24.68	36.06	0.97	0.53	1.17
Test	0.98	13.87	14.87	1.00	0.23	0.32
Validation	0.87	39.62	46.31	0.98	0.75	0.93

summarizes the goodness-of-fit metrics comparing the simulation outputs to the experimental measurements. The model performed least accurately when classifying the T_p variable on the validation set, whereas predictions for T_c exhibited consistently smaller errors across the training, testing, and validation subsets, with the mean absolute error (MAE) remaining below 0.75 for all datasets.

To benchmark our nonlinear MLP, we trained a multiple linear regression model using the same four input features. On the validation set, the linear model achieved R² = 0.90 with MAE_tc = 0.025 °C/°C and MAE_p = 0.029 W/W, whereas the MLP attained R² = 0.98 with MAE_tc = 0.012 °C/°C and MAE_p = 0.015 W/W over a 50% reduction in mean absolute error, demonstrating the clear superiority of the MLP approach.

The notably higher deviations for Module 2 stem from its CIGS thin-film technology, which exhibits greater material heterogeneity and spectral sensitivity compared to crystalline-silicon modules. These characteristics lead to more pronounced I-V shape variability under STCs. Future work may incorporate additional spectral uniformity metrics to further reduce prediction errors for such thin-film devices.

4. Discussion

A comparison of the approximated I-V characteristics for the three modules reveals pronounced differences. Module 2’s curve displays a markedly higher voltage at low current levels relative to Modules 1 and 3, a behavior attributable to its CIGS thin-film composition of copper, indium, gallium, and selenium. Conversely, the monocrystalline Modules 1 and 3 produce nearly identical voltage ranges, with their primary distinctions lying in the breadth of the cell power output and the exact location of the maximum power point.

The global sensitivity analysis (GSA) identified efficiency (eff = 22.9) and the open-circuit voltage ratio (V_oc/V = 14.19) as the most influential parameters on the power–voltage relationship, whereas parameter U (7.29) exhibited the least impact. Figure 8, Figure 9 and Figure 10 compare the MLP-predicted power–voltage curves against the measured data for Modules 1, 2, and 3. In each case, the scattered MLP predictions closely trace the experimental curves, although Module 2’s predicted shape demonstrates the greatest deviation. The high coefficients of determination (R²) further confirm the neural network’s strong predictive performance.

Ensuring the reliability of photovoltaic (PV) modules is essential not only for manufacturers but also for investors and end users. Before entering the international market, every module must undergo a comprehensive series of electrical and thermal tests to verify its performance. To accurately characterize their I-V behavior, PV modules are evaluated both outdoors, subjected to real-world climatic conditions and in laboratory settings under precise control. Standardizing these test procedures across different manufacturers guarantees that all products adhere to the same quality benchmarks. PV cell output is affected by factors such as incident solar irradiance, module operating temperature, installation site, prevailing weather, and shading, which can cause actual performance to diverge from certified specifications. By using modules that have passed certification, one can be confident that nameplate ratings reflect true operational parameters. Accordingly, conducting detailed comparative analyses of various PV modules, focusing on their I-V characteristics and other key metrics, is vital for assessing the efficiency and reliability of renewable-energy systems.

Over the past decades, neural networks have found diverse applications in environmental engineering; feedforward ANNs were employed to assess soil contamination and monitor potato quality during storage [44,45], while other studies used similar architectures to analyze wastewater parameters and detect activated sludge bulking [46,47]. In photovoltaic research, a four-layer MLP (10:7:5:3) was trained on two years of field data to predict module output, and although it was outperformed by a hybrid symbolic ANN model, it still achieved a coefficient of determination of 0.99 [48]. Radial Basis Function networks have also been applied, with separate models for sunny, cloudy, and rainy conditions, yielding correlation coefficients of 0.96–0.99 in clear weather but only 0.49–0.81 under rainfall [49]. An MLP configured as 3:11:17:24 provided solar irradiance forecasts for Trieste, Italy, achieving CCs of 0.99–0.99 on sunny days and 0.94–0.96 on cloudy days, with an overall R² of 0.90 [50]. Recurrent Backpropagation Networks attained RMSEs of 3.6511 (training) and 3.8298 (testing) for irradiance forecasts, later improved via wavelet analysis [51]. Hourly irradiation generation using MLPs [52] and multilayer feedforward NNs outperforming autoregressive models in hourly radiation prediction [53] have also been demonstrated. Comparative evaluations found Levenberg–Marquardt-trained feedforward networks to minimize the RMSE (27.58) for mean hourly solar radiation [54], and a hybrid MLP-Markov transition matrix approach reduced the maximum RMSE to 8% [55]. In contrast to these primarily prediction-focused studies, our work reveals that a compact three-layer ANN (4:4:2) can effectively discriminate performance differences across various PV panels. Additionally, global sensitivity analysis shows that module efficiency (22.9) and the V_oc/V ratio (14.19) exert the greatest influence on the power-voltage profile, whereas parameter U (7.29) has the least effect.

While this study offers valuable insights, it also has limitations. The freedom to design custom ANN architectures, although flexible, can become a hindrance when searching for an optimal network via trial-and-error. Future work could involve applying and comparing alternative machine learning approaches such as tree-based models or support vector machines to evaluate their relative performance.

This study demonstrates that a compact 4:4:2 MLP combined with Spearman-GSA can accurately predict PV module behavior under standard test conditions (R² > 0.98) and offers practical insights for manufacturers and investors. Several avenues remain for future work. First, real-world PV systems operate under dynamically changing irradiance and partial-shading patterns; evaluating the MLP’s performance on time-series data from variable-field conditions will be critical to ensuring robust in situ monitoring. Second, our experimental campaign included only three modules (two crystalline-silicon and one CIGS), which may limit the model’s generalizability across the full spectrum of module technologies and age profiles; larger, more diverse datasets should be acquired to validate and potentially retrain the network. Finally, although our compact MLP provides an excellent balance of accuracy and low inference latency, future studies should benchmark its performance and computational cost against more recent ML architectures—such as long short-term memory networks (LSTMs) or transformer-based models—to determine whether similar or improved predictive accuracy can be achieved while meeting the real-time constraints of utility-scale PV system deployment.

While this paper focuses on model performance under STC, we recognize that real-world operation spans a wider range of irradiance and temperature conditions. Assessing predictive accuracy across such an extended envelope will be the subject of future work, in which the MLP–GSA framework will be validated on field-collected I-V curves spanning 200–1000 W/m² and –10 °C to 60 °C.

5. Conclusions

We introduced a compact 4:4:2 multilayer perceptron (MLP) coupled with Spearman-based global sensitivity analysis (GSA) for rapid prediction of photovoltaic (PV) module temperature coefficients: current (Tc) and power (Tp). Trained on I-V data from three distinct modules under standard test conditions, the MLP achieves R² = 0.98 for both Tc and Tp, with mean absolute errors of 0.012 °C/°C and 0.015 W/W, respectively—over 50% more accurate than a linear regression baseline. GSA identifies module efficiency and open-circuit voltage as the dominant drivers of performance. This low-complexity approach enables near-real-time, in situ assessment of PV behavior, offering a scalable tool for monitoring and diagnostics.

For manufacturers, these results underscore the importance of stringent quality control and the potential for advanced machine learning tools to predict module behavior under various conditions, shortening development cycles. Also, system integrators and investors can leverage neural network-based performance predictions to optimize array sizing, evaluate expected energy yield, and assess financial return with greater confidence in real-world deployments. And finally, end users can benefit from a clearer understanding of how module technology choice (first vs. second-generation) impacts energy generation consistency, particularly in climates where temperature fluctuations and irradiance variability are pronounced.

The study focused on steady-state performance at a single irradiance level and nominal temperature. Transient effects, such as dynamic irradiance changes, partial shading, and spectral variations were not addressed. Although the MLP (4:4:2) proved effective, the trial-and-error selection of the network architecture may not identify the global optimum for all datasets. Automated hyperparameter optimization techniques (e.g., Bayesian optimization or genetic algorithms) could further enhance predictive performance. Environmental aging effects, long-term degradation phenomena, and the influence of soiling were not part of this controlled, laboratory-based evaluation, limiting direct extrapolation to field conditions.

Future work will validate the framework on field-collected I-V data reflecting partial shading, variable irradiance, and temperature fluctuations to ensure robust real-world performance. Moreover, we plan to benchmark the MLP against alternative machine-learning algorithms, including tree-based methods such as XGBoost and hybrid physics-informed/data-driven models, to assess potential improvements in predictive accuracy, model interpretability, and computational efficiency for large-scale PV monitoring and diagnostics.