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

Youri Blom, Sofia Dutto, Alexandru Costache, Rowan Richie, Ruben Pelsser, Wesley Berger, Jing Sun, Rudi Santbergen, Olindo Isabella, Malte Ruben Vogt

arXiv:2608.25448v1physics.comp-phcs.LG

TL;DR

PV modules face diverse operating conditions that affect efficiency, degradation, and design customization. This paper combines machine learning, interpolated global data, and hierarchical clustering to classify climates by energy yield and lifetime, identifying six main clusters and the highest discounted lifetime energy yield in Temperate-LT.

  • Problem

    PV operating conditions vary geographically and affect module efficiency, degradation, and design customization, motivating climate groups for location-specific PV design.

  • Method

    The study interpolates global environmental and performance data, applies multiple machine-learning regression methods for feature importance, and uses hierarchical clustering for classification.

  • Results

    Six main climate clusters and fifteen subclusters were defined, with the highest discounted lifetime energy yield observed in the Temperate-LT climate zone.

  • Takeaways & Limitations

    The classification supports optimized PV module and bill-of-materials design, PV system siting decisions, and comparative studies across PV technologies.

  • Takeaways & Limitations

    The dendrogram is sensitive to small changes in feature-importance scores, so the number of optimal clusters may change.

Abstract

from arXiv · show

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.

1. Introduction

PV deployment across diverse climates requires classification methods that account for location-dependent module performance and degradation. This work develops an ML-based classification focused on c-Si module energy yield and lifetime to identify relevant environmental parameters and cluster similar locations.

  • Motivation: 25% annual growth in global PV capacity is needed over the next decade to meet future energy demand resiliently and sustainably.
  • Motivation: Varying regional operating conditions influence PV-module operating efficiency, performance, behavior, and degradation rates.
  • Background: PV-specific climate classification can reduce location-by-location customization to a limited number of module types optimized for particular climate zones.
  • Related work: Existing adaptations omit parameters such as wind speed and ultraviolet irradiance and may not be fully optimal because the original Köppen–Geiger classification did not focus on solar energy.
  • Contribution: The proposed ML-based classification combines methods of varying complexity to identify relevant environmental parameters and cluster locations based on c-Si module energy yield and lifetime performance.

2. Dataset

The dataset combines globally sourced hourly environmental data with physically modeled PV energy yield and module lifetime, then corrects spatial sampling imbalance through interpolation. Correlation analysis identifies key feature–target relationships, while acknowledged limitations motivate advanced machine-learning feature-importance methods.

  • Dataset construction: Meteonorm hourly weather-station data define 12 environmental features and two PV-performance targets for worldwide climate classification.Hourly data are selected because they enable accurate calculation of both targets.
  • Target generation: The targets are annual energy yield and module lifetime, generated with PVMD Toolbox physical simulations for c-Si modules worldwide.No global dataset of measured energy yield and module lifetime is available.
  • Target generation: Module lifetime is defined as the time until degradation reduces module performance to 80% of its initial performance.PVMD Toolbox degradation analysis enables this lifetime calculation.
  • Spatial interpolation: Three-neighbor nearest-neighbor interpolation produces a more spatially uniform dataset by applying correction to all features and targets.The correction addresses bias from uneven global distribution of simulated locations.
  • Feature relevance: GHIann has the strongest energy-yield correlation, while Tmean is most strongly correlated with lifetime; correlation limitations motivate advanced ML-based feature-importance analysis.AMeff shows a similar-magnitude, opposite-sign lifetime correlation consistent with its inverse relationship with Tmean.

3. Methodology

The methodology ranks environmental features using multiple machine-learning regressors and then applies their importance scores to agglomerative hierarchical clustering for transparent, adjustable climate classification.

  • Methodology overview: The workflow preprocesses operating-condition features and physical-model targets, estimates feature importance with machine-learning regression, and clusters locations using the most relevant environmental characteristics.Feature importance scores are subsequently used as clustering inputs.
  • Feature importance analysis: Five diverse regression methods provide a more robust, model-independent assessment of feature relevance than reliance on a single model.The models span linear, kernel-based, spline-based, probabilistic, and neural-network approaches.
  • Feature importance analysis: Feature subsets are exhaustively evaluated as Ni varies from 1 to Nfeat, and the lowest-error combination is selected for each Ni.For each feature j, the importance score Sj uses model error, the maximum observed target error, and binary selection function K(j, Ni, k).
  • Regression evaluation: 85% training data, 15% test data, and RMSE evaluate each model, while fixed hyperparameters replace exhaustive optimization because 212 feature combinations are computationally impractical.The importance boost reflects performance improvement relative to the previous feature-count iteration and is distributed across selected features.
  • Hierarchical clustering: Agglomerative hierarchical clustering uses Euclidean distances and Ward linkage to form a dendrogram, enabling nested classifications whose detail can be adjusted by selecting its cut-off point.Ward linkage was chosen because it produced the most balanced cluster structure among tested linkage methods.

4. Results

Gaussian Process Regression achieved the strongest predictive accuracy, while feature-importance analysis identified GHIann and Tmean as the most influential parameters. Weighted hierarchical clustering produced six main climate clusters and 15 subclusters, with temperate-LT offering the highest lifetime energy yield.

  • Regression accuracy: 0.007 MW h and 1.5 year were the RMSE values achieved by Gaussian Process Regression for energy yield and lifetime, respectively.Nonlinear models outperformed linear regression and Support Vector Machines, whose RMSE values were highest.
  • Feature importance: GHIann and Tmean emerged as the two most influential parameters after averaging energy-yield and lifetime feature-importance scores.GHIann ranked highest for energy yield, while Tmean ranked highest for lifetime.
  • Climate classification: 6 main climate clusters and 15 subclusters were selected from local maxima in the hierarchical dendrogram distances.The resulting main climates were Tropical, Desert, Continental, Temperate, Boreal, and Polar.
  • Classification limitation: Small changes in feature-importance scores can alter the number of optimal clusters because the dendrogram is sensitive to computed distances.The study identifies analysis of this sensitivity as a topic for future research.
  • Lifetime energy yield: The highest LEY values occurred in the temperate-LT climate, and LT subclusters consistently outperformed HT counterparts across all main climates.Lower temperatures reduce degradation rates and extend module lifetime.
  • Applications: The classification can guide climate-specific PV module design, PV system site allocation, and comparisons across locations without evaluating many sites.It highlights regions with high lifetime performance and supports fair comparative studies.

5. Conclusion · Appendix A. Definition of features

The study develops a PV-specific climate classification using interpolated environmental data, machine-learning predictions of energy yield and lifetime, and hierarchical clustering. Its appendix defines the weather-derived features used in the analysis, including temperature, irradiance, air-mass, humidity, wind, and ultraviolet measures.

  • 5. Conclusion: The framework combines twelve environmental features, two performance targets, spatial interpolation, and five machine-learning regression methods for PV climate classification.Spatial interpolation addresses the raw data’s non-uniform geographical distribution.
  • 5. Conclusion: 0.007 MW h and 1.5 years are the Gaussian process RMSE values for energy yield and lifetime, respectively.Linear regression and Support Vector Machines perform worst, while model performance saturates beyond six features.
  • 5. Conclusion: Six main climate clusters and fifteen subclusters are defined as Tropical, Desert, Continental, Temperate, Boreal, and Polar, with further differentiation by temperature, irradiance, or wind speed.Discounted lifetime energy yield is evaluated across all clusters, with the highest values observed in the Temperate-LT climate.
  • Appendix A. Definition of features: The feature set is derived from Meteonorm hourly weather data covering ambient temperature, GHI, DNI, DHI, sun position, wind speed, and relative humidity.These measurements provide the underlying weather variables for the PV-oriented analysis.
  • Appendix A. Definition of features: Tmean, Tmin, Tmax, GHIann, GHImin, GHImax, WSmean, and RHmean use annual means, monthly extrema, or sums of hourly values.Most features are obtained through these direct aggregations.
  • Appendix A. Definition of features: Tdiff represents average daily temperature fluctuation, using Ndays, Tamb(t), and the hours within each day.Ndays denotes the number of days in the year, while Tamb(t) is ambient temperature at hour t.
  • Appendix A. Definition of features: DNIshare measures the direct-irradiance share of total irradiance using DNI(t), GHI(t), and sun altitude ϕsun(t).The quantities are evaluated at time t.
  • Appendix A. Definition of features: AMeff denotes the effective air mass at which irradiance is received, while UVann is annual ultraviolet irradiance below 400 nm.UVann is computed directly by the PVMD Toolbox.

Appendix B. Validation lifetime calculation · Appendix C. Considered module

The appendices validate the lifetime model against reported degradation rates and describe the simulated monofacial silicon heterojunction module and location-specific irradiance optimization. Simulated lifetimes use an 80%-performance threshold, while discrepancies reflect differences between modeled and reported conditions.

  • Appendix B. Validation lifetime calculation: Lifetime is defined as the time required for module performance to decrease to 80% of its initial value.Some simulated lifetimes exceed the commonly expected module lifetime of 30/40 years under this definition.
  • Appendix B. Validation lifetime calculation: Temperature is the dominant degradation stress factor, causing consistently low-temperature regions to exhibit high simulated lifetimes.
  • Appendix B. Validation lifetime calculation: The degradation model is validated by comparing its predicted degradation-rate distribution with rates compiled globally by Jordan et al..Figure B.1 presents the relative distributions from the model and compendium.
  • Appendix B. Validation lifetime calculation: Although simulated and reported degradation rates differ noticeably, their overall ranges are comparable, indicating that the simulated lifetimes are not unrealistic.Remaining discrepancies are attributed to module technologies, installation characteristics, and geographical sampling.
  • Appendix C. Considered module: The dataset’s energy-yield and lifetime targets are simulated using a monofacial silicon heterojunction module with 144 half-cut cells and a G12 wafer size.The module uses an EVA encapsulant and PET backsheet.
  • Appendix C. Considered module: The considered module’s optical and electrical performance are shown at standard test conditions.Full module and lifetime-simulation parameters are provided in previous work.
  • Appendix C. Considered module: For each location, module tilt and azimuth are selected to maximize received irradiance.The resulting values are available in the supplementary information.

Appendix D. Comparison distance metrics

Appendix D compares linkage methods for hierarchical clustering using Euclidean sample distances and evaluates their influence on dendrogram structure and climate classification. Method selection is based on how evenly points are distributed across clusters, quantified by a normalized standard-deviation ratio.

  • Distance and linkage methods: Euclidean distance is used between samples, while alternative linkage methods are evaluated to construct the hierarchical-clustering dendrogram.The linkage method defines distances between clusters.
  • Distance and linkage methods: MATLAB provides several linkage definitions, with median and weighted methods specified recursively through merged clusters.For the definitions, d(r, s) denotes intercluster distance, N_r and N_s cluster sizes, and ||x−y||_2 Euclidean sample distance.
  • Metric sensitivity: The linkage method strongly influences dendrogram structure, while different distance metrics can substantially alter its shape and the resulting climate classification.The comparison seeks a dendrogram with data points distributed as evenly as possible across clusters.
  • Uniformity criterion: A lower std(P_i)/mean(P_i) ratio indicates a more even distribution of points across clusters and is used to compare linkage methods across dendrogram levels.P_i denotes the number of points in cluster i, and the ratio is computed from the standard deviation and mean cluster sizes.

Appendix E. Classifications for separate targets

Applying the clustering procedure to energy yield or lifetime alone changes feature weighting, dendrograms, and resulting climate classifications. The separate classifications contain 4 main clusters and 10 subclusters for energy yield, and 6 main clusters and 14 subclusters for lifetime.

  • Method: Separate-target clustering weights feature values using energy-yield-only or lifetime-only importance scores, altering the dendrogram and climate classification.The corresponding dendrograms are presented in Figures E.1a and E.1c.
  • Separate classifications: 4 main clusters and 10 subclusters result from the energy-yield-only classification.The same selection criteria as in the main analysis are applied.
  • Separate classifications: 6 main clusters and 14 subclusters result from the lifetime-only classification.The resulting classifications are shown in Figures E.2 and E.3, respectively.
  • Labeling: The alternative classifications use numerical labels for main clusters and alphabetical labels for subclusters because their regions differ substantially from the main study.Future work may assign meaningful descriptive labels when separate-target classifications are needed for specific applications.

Appendix F. Sensitivity to changes in feature importance score · Appendix G. Labeling of subclusters

Appendix F shows that minor perturbations to feature-importance scores can change the dendrogram and optimal cluster counts, despite preserving the ranking of the three most important features. Appendix G explains that subcluster labels are assigned from feature-separation plots, with high and low values interpreted relative to each main cluster.

  • Appendix F. Sensitivity to changes in feature importance score: Considering energy yield alone identifies local maxima at 4 and 10 clusters, whereas lifetime alone identifies local maxima at 6 and 14 clusters.The appendix compares dendrograms and relative distances separately for the two target variables.
  • Appendix F. Sensitivity to changes in feature importance score: Energy-yield feature scores produce 4 main clusters, while lifetime feature scores produce 6 main clusters with differently labeled subclusters.The corresponding classifications use numeric main-cluster labels and lettered subcluster labels for presentation.
  • Appendix F. Sensitivity to changes in feature importance score: Small feature-importance perturbations preserve the ranking of the three most important features but can alter dendrogram structure and optimal cluster numbers.Each score is modified by adding a random value uniformly drawn from [−0.5, 0.5].
  • Appendix F. Sensitivity to changes in feature importance score: Three independent perturbation realizations produce different optimal numbers of clusters and subclusters, demonstrating sensitivity in the clustering outcome.Figure F.1 presents the feature-importance scores, dendrogram distances, and resulting cluster selections for the reference and perturbed cases.
  • Appendix G. Labeling of subclusters: Subclusters are labeled by relative high or low temperature, irradiance, or wind-speed values within their respective main clusters.The labels use H or L indicators for temperature (T), irradiance (I), and wind speed (W).
  • Appendix G. Labeling of subclusters: Selected-feature scatter plots justify subcluster names by showing clear separation between subclusters within each main cluster.For each main cluster, the plotted feature pair is chosen to distinguish its subclusters.

Appendix H. Overlap with existing classifications

The developed PV climate classification substantially overlaps existing classifications, while significant differences indicate the value of the new framework.

  • >70% overlap occurs for multiple clusters between the developed classification and classifications from Ascencio-Vásquez et al. and Triana de las Heras et al.The comparison is presented using the maps in Figure 7 and Figure H.1.
  • Significant differences between the classifications highlight the need for the classification developed in this work.

Appendix I. Definition discounted lifetime energy yield · Appendix J. Representative locations for all climate zones

The appendices define discounted lifetime energy yield using module lifetime, annual energy yield, and a 7% discount rate while accounting for degradation. They also identify representative locations by selecting locations closest to feature-importance-weighted climate-zone means.

  • Appendix I. Definition discounted lifetime energy yield: Discounted lifetime energy yield is evaluated across all climate zones using the module lifetime and annual energy yield.
  • Appendix I. Definition discounted lifetime energy yield: 7% is the discount rate used in the discounted lifetime energy yield calculation.
  • Appendix I. Definition discounted lifetime energy yield: Module lifetime accounts for degradation-induced reductions in energy yield throughout the module’s operating life.
  • Appendix I. Definition discounted lifetime energy yield: The degradation assumption is linear and targets 80% module performance at the end of the module lifetime.
  • Appendix J. Representative locations for all climate zones: A single representative location is identified for each climate zone to enable consistent global comparisons.
  • Appendix J. Representative locations for all climate zones: For each climate zone, the mean weighted value of each feature is computed using feature importance scores.
  • Appendix J. Representative locations for all climate zones: The representative location is the location whose feature values are closest to the corresponding mean weighted feature values.
  • Appendix J. Representative locations for all climate zones: Table J.1 summarizes the geographic coordinates of the representative locations identified for each climate zone.
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