physics.comp-phAug 26, 2026

Energy Yield and Lifetime Climate Classification via Machine Learning for Optimizing Photovoltaic Module Design and Materials

Authors: Youri Blom, Sofia Dutto, Alexandru Costache, Rowan Richie, Ruben Pelsser, Wesley Berger, Jing Sun, Rudi Santbergen, 

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Abstract

To resiliently and sustainably meet our future energy demand, photovoltaic (PV) modules must be deployed across a broad and diverse range of geographical regions with varying operating conditions. As these conditions strongly affect both performance and optimal system design, a dedicated PV-specific climate classification can be of great use. In this work, we develop a climate classification framework tailored to PV applications using a variety of machine learning (ML) techniques. Building on previous studies, our approach incorporates both energy yield, and for the first time, also the module lifetime with climate dependent degradation. We generate an interpolated dataset containing twelve input features and two target variables (i.e. energy yield and module lifetime). Feature importance analysis shows that annual global horizontal irradiation and ambient temperature are the most influential predictors. The most accurate regression model achieves root mean square errors (RMSE) of 0.007 MWh for energy yield and 1.5 years for lifetime prediction. The calculated feature importance scores are then integrated into a hierarchical clustering framework, resulting in 6 primary climate clusters (Tropical, Desert, Continental, Temperate, Boreal, and Polar) and 15 corresponding subclusters. Our analysis shows that the low temperature continental climate offers the highest discounted lifetime energy yield. These results can support a wide range of applications, including PV module optimization, system siting decisions, and comparative performance studies.

Figures & tables

FeatureDescription
Tmean\textrm{T}_{\textrm{mean}} [ \SIUnitSymbolCelsius\mathrm{\SIUnitSymbolCelsius} ]Annual mean ambient temperature
Tmin\textrm{T}_{\textrm{min}} [ \SIUnitSymbolCelsius\mathrm{\SIUnitSymbolCelsius} ]Mean ambient temperature of coldest month
Tmax\textrm{T}_{\textrm{max}} [ \SIUnitSymbolCelsius\mathrm{\SIUnitSymbolCelsius} ]Mean ambient temperature of warmest month
Tdiff\textrm{T}_{\textrm{diff}} [ \SIUnitSymbolCelsius\mathrm{\SIUnitSymbolCelsius} ]Mean value of daily temperature variation
GHIann\textrm{GHI}_{\textrm{ann}} [ MW h m−2\mathrm{MW}\text{\,}\mathrm{h}\text{\,}{\mathrm{m}}^{-2} ]Annual received Global Horizontal Irradiance (GHI)
GHImin\textrm{GHI}_{\textrm{min}} [ kW h m−2\mathrm{kW}\text{\,}\mathrm{h}\text{\,}{\mathrm{m}}^{-2} ]Minimum monthly received GHI
Table 1: The features that are considered for the climate classification.
Figure 1: a) The geographical distribution of the simulated energy yield and module lifetime at the locations of the available weather stations. b) The interpolated values of energy yield and module lifetime for all coordinates. c) The interpolated values for all features.
Figure 2: The correlation coefficients between all features and the energy yield (a) and module lifetime (b). Their values are on the right-hand side of both diagrams. The background colors indicate regions of no significant correlation (red), some significant correlation (orange), and strong significant correlation (green).
Figure 3: An overview of the methodology used for the climate classification. Features and targets are obtained from the operating conditions and the physical models. Feature importance is then determined using ML regression models and subsequently used as input for the clustering procedure.
ML methodReferenceModifications compared to default MATLAB settings
Linear regression[ 9 ] 
Support Vector Machine[ 14 , 33 ] 
Multivariate adaptive regression spline (MARS)[ 24 , 15 ] 
Neural network[ 16 , 20 ]Changed activation function to sigmoid [ 32 ]
Gaussian process regression[ 33 ] 
Table 2: An overview of the utilized ML regression methods that are used in this work.
Figure 4: a) The highest accuracy of the different methods with number of selected features NiN_{i} using the energy yield as target. b) The selected features by the different models for the energy yield as target. A colored box indicates that the method has selected a certain feature. c) The highest accuracy of the different methods with number of selected features NiN_{i} using the lifetime as target. d) The selected features by the different models for the lifetime as target.
Figure 5: The importance score of all features considering the energy yield (a) or lifetime (b) as target. The total feature importance score (c) is obtained by taking the average of the two.
Figure 6: a) The dendrogram that is created based on the distance map and the corresponding cluster labels. b) The relative distance to the next cut-off is plotted for each value of NclustersN_{clusters} . The values of Nclusters=2N_{clusters}=2 and Nclusters=3N_{clusters}=3 (0.51 and 0.23, respectively) are not visible, since the image is cropped to clearly show the meaningful part of the graph. This figure can be used to determine where to cut-off the dendrogram.
Figure 7: The final climate classification using Nmain=6N_{main}=6 and Nsub=15N_{sub}=15 . The main climates are labelled as Tropical, Desert, Continental, Temperate, Boreal, and Polar. Subcluster are further distinguished by irradiance (I), temperature (T), or wind speed (W) levels, denoted as low (L) and high (H).
Figure 8: The box plot distribution of the discounted lifetime energy yield for the different climate zones.
Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 1: The distribution of degradation rates obtained from the degradation model and collected by the compendium of degradation rates [ 25 ] .
Figure 1: The optical performance (a) and electrical performance (b) of the considered module at standard test conditions.
MetricEquation
averaged(r,s)=1Nr⋅Ns∑i=1Nr∑j=1Ns∣∣xri−xsj∣∣2d(r,s)=\frac{1}{N_{r}\cdot N_{s}}\sum_{i=1}^{N_{r}}\sum_{j=1}^{N_{s}}||x_{ri}-x_{sj}||_{2}
centroidd(r,s)=∣∣xˉr−xˉs∣∣2d(r,s)=||\bar{x}_{r}-\bar{x}_{s}||_{2}
completed(r,s)=max⁡(∣∣xri−xsj∣∣2),i∈(1,...,Nr),j∈(1,...,Ns)d(r,s)=\max(||x_{ri}-x_{sj}||_{2}),i\in(1,...,N_{r}),j\in(1,...,N_{s})
mediand(r,s)=∣∣x~r−x~s∣∣2,xr~=12(x~p+x~q)d(r,s)=||\tilde{x}_{r}-\tilde{x}_{s}||_{2},\tilde{x_{r}}=\frac{1}{2}(\tilde{x}_{p}+\tilde{x}_{q})
singled(r,s)=min⁡(∣∣xri−xsj∣∣2),i∈(1,...,Nr),j∈(1,...,Ns)d(r,s)=\min(||x_{ri}-x_{sj}||_{2}),i\in(1,...,N_{r}),j\in(1,...,N_{s})
wardd(r,s)=2⋅Nr⋅NSNr+Ns∣∣xˉr−xˉs∣∣2d(r,s)=\sqrt{\frac{2\cdot N_{r}\cdot N_{S}}{N_{r}+N_{s}}}||\bar{x}_{r}-\bar{x}_{s}||_{2}
Appendix
Table 3: Linkage methods used in hierarchical clustering and their corresponding definitions. For all equations, d(r,s)d(r,s) is the distance between clusters rr and ss , NrN_{r} and NsN_{s} are the number of points in cluster rr and ss , and ∣∣x−y∣∣2||x-y||_{2} is the Euclidean distance between two points. It should be noted that the median and weighted metric are recursive metrics, where cluster rr is created by combining cluster pp and cluster qq .
Figure 1: Comparison of hierarchical clustering results using different linkage methods. The top figures show the resulting dendrograms. The figures below show the standard deviation of points in the cluster over the average points in the cluster, indicating the spread of all clusters.
Figure 1: The different dendrogram and cluster selection when only considering the energy yield or lifetime. (a) and (b) show the dendrogram and relative distances for the energy yield target, finding local maxima for 4 and 10 clusters.(c) and (d) show the dendrogram and relative distances for the lifetime target, finding local maxima for 6 and 14 clusters.
Figure 2: The climate classification when considering the feature scores for the energy yield targets. Main clusters are indicated with 1, 2, 3, and 4. Subclusters are indicated with a, b, and c to avoid confusion with the presented classification.
Figure 3: The climate classification when considering the feature scores for the lifetime targets. Main clusters are indicated with 1, 2, 3, 4, 5, and 6. Subclusters are indicated with a, b, c, and d to avoid confusion with the presented classification.
Figure 1: Sensitivity analysis for determining the optimal number of clusters. The top panels show the feature importance scores for the reference case (left) and three perturbed cases. The bottom panels show the corresponding dendrogram distances and the resulting optimal numbers of main clusters and subclusters.
Figure 1: Scatter plots of the relevant features of the different subclusters in each main cluster. This is used to create meaningful annotations for the subclusters. Please note that different colors have been selected to more clearly indicate the different subclusters.
Figure 1: The overlap between the generated classification and the already existing ones. The percentages indicate which fraction of the climate zone from this work is also in the climate zone from [ 3 ] or [ 13 ] . Therefore, the values in all rows equal to 100%.
Climate zoneLatitudeLongitudeCountry
Desert-LT-1930Zimbabwe
Desert-HI-21129Australia
Desert-HT842Ethiopia
Tropical2295Myanmar
Continental-HT29117China
Continental-LT45-89United States of America
Appendix
Table 1: The coordinates of the representative locations for all climate zones.

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