A machine-learning surrogate model for optimising photovoltaic-thermal deployment in complex urban morphologies

Building-integrated and urban power generation

Several studies focus on predicting power generation within the built environment, using Building-Integrated Photovoltaics (BIPV) and standard rooftop systems. Shin et al. (2022) utilised an ANN combined with PVsyst^® and Solar^® Pro software to model BIPV generation, achieving a high accuracy with an R² of 0.92. Similarly, Serrano-Luján et al. (2022) applied Genetic Algorithms (GA) and Differential Evolution (DE) for BIPV power prediction, using measured ambient temperature and solar irradiation as key variables.

For general building power generation, Sulaiman et al. (2024) achieved an RMSE of 0.7 using a Neural Network (NN), while Mohana et al. (2021) compared multiple models including LASSO, RF, and XGBoost, reaching an MSE of 0.9. Kassem and Othman (2022) explored specialised architectures like MFFNN and RBFNN in Matlab, attaining an impressive RMSE of 0.0021. In the context of urban power generation, Patel et al. (2022) used Linear Regression to achieve a MAPE of 1.40%. Other research by Pham and Tran (2023) incorporated structural data like rooftop dimensions alongside weather variables, testing various models such as KNR and GBR to reach an RMSE of 0.60.

PV and PVT efficiencies

A subset of the literature emphasises the thermal and electrical efficiency of specialised modules. Yousif and Kazem (2021) applied an ANN to PVT systems with a best accuracy of 0.11 NMSE. Chaibi et al. (2021) also utilised ANNs to model building electrical and thermal efficiencies, reporting a very low MAE of 0.0078%. Efficiency modelling was further advanced by Cao et al. 2022 who used ANFIS and LS-SVR models to achieve an R² of 0.95, focusing on radiation intensity and coolant materials as variables. More recently, Gharaee et al. (2024) studied PVT module efficiency using MLP and RF, identifying mass flow rate and fluid inlet temperature as critical inputs to achieve an R² of 0.76.

Module-level power and performance

Predicting the specific output of individual modules is a frequent theme. Zazoum (2022) employed SVM and Gaussian Process Regression (GPR) to model module power generation, reaching an R² of 0.98 based on panel and ambient temperatures. Zhang et al. (2021) focused on the impact of evaporation and wind speed using a Neural Network, yielding an MSE of 0.01. Alghamdi et al. (2023) achieved the highest precision recorded in the sources (MSE of 3.34E-08) using a Deep Neural Network (DNN) to model module power based on cell type.

Methodological trends

Across these studies, ANN and RF are among the most frequently cited algorithms for their robustness in handling non-linear weather data. The most common validation strategy is the train/test split, though k-fold cross-validation was notably used by Mohana et al. (2021). The primary variables driving these models consistently include solar irradiance (or radiation), ambient temperature, and humidity. Additionally, Rojek et al. (2023) demonstrated the utility of ML in predicting not only power but also CO₂ reduction, highlighting the environmental impact of these technological applications.

Research gaps

Several limitations in previous research (Table 1) identified regarding solar power prediction:

• Focus on Single Parameters: Prior research often focuses on a single indicator, typically exclusively on PV electricity production (EP), while neglecting other vital outputs such as environmental impacts.

• Reliance on Historical Performance Data: Most existing studies rely on datasets of actual, historical PV panel performance rather than predictive modelling for specialised systems.

• Neglect of Thermal Outputs: Despite the dual nature of PVT systems, many studies fail to integrate predictive models for both electrical and thermal outputs simultaneously.

• Climate-Centric Variables: Much of the existing literature uses climatic indicators (such as humidity, wind speed, or ambient temperature) as the primary variables, often overlooking the impact of geometric installation conditions and urban morphology.

• Limited Environmental Integration: There is a lack of comprehensive analysis that combines energy yield with integrated environmental impacts, such as CR, in an urban context.

Research contributions

This study introduces a multi-faceted approach to address these deficiencies:

• Integrated multi-output modelling: Unlike previous studies, this research differentiates itself by integrating predictive models for three distinct indicators: electricity production (EP), hot water production (HWP), and CR.

• Focus on Installation Patterns: Instead of focusing solely on weather data, this study examines the effect of 1,575 different installation configurations, including horizontal/vertical angles, panel-to-panel distance, and elevation from the roof.

• Impact of Urban Morphology: The study models these configurations across three unique urban districts in Tehran, which has cold semi-arid climate, with varying building heights and densities (from low-rise/high-density to high-rise/low-density) to account for shading effects in a dynamic urban environment.

• AI-Driven Optimisation: By leveraging and comparing ANN and RF, the study identifies that the RF algorithm provides superior performance for this integrated modelling, achieving an R² accuracy of 0.91 and significantly faster learning times.

• Development of a Non-Expert Framework: The research culminates in a four-step software framework that integrates GIS data and AI. This tool is designed to facilitate decision-making for non-experts, allowing them to optimise PVT installations based on specific urban areas and panel properties.

• Comprehensive Environmental Assessment: The study explicitly calculates the environmental benefits by correlating electricity and hot water production (HWP) with specific carbon emission reduction metrics.

Context

To create the dataset, Tehran, was chosen which is divided into 22 distinct urban areas (Figure 2), each with unique characteristics. Three selected regions are central to this research, with the selection criterion focusing on variations in elevation and population density across the city.

Figure 2

Three morphologically distinct regions were selected: Region 1 (high-rise/dense) Figure 3, Region 2 (mid-rise/dispersed) Figure 4, and Region 16 (low-rise/dense packed) Figure 5.

Figure 3

Figure 4

Figure 5

Dataset creation and modelling

To standardise calculations and ensure comparability of results, a specific type of thermal photovoltaic panel was utilised. The chosen model is the PV-MLE275HD2, manufactured by Mitsubishi. This panel is equipped with monocrystalline silicon photovoltaic cells, with 120 cells per panel. With a power output of 275 watts and a maximum voltage supply of 32.1 volts, these cells demonstrate an overall efficiency rating of 16.6%.

To construct a robust dataset for the ML surrogate model, 1,575 unique installation configurations were systematically generated (Table 2). These configurations represent the «potential states» of the system, defined by five primary variable parameters that directly influence both electrical and thermal performance within dense urban environments.

• Geometric Variables: The Horizontal Angle and Vertical Angle were adjusted to optimise solar azimuth and tilt, thereby minimising angular losses relative to specific geographic position. Furthermore, Panel Elevation was incorporated to account for convective cooling, a critical factor in maintaining PV cell efficiency by preventing overheating.

• Spatial Configuration: The Distance Between Panels serves as a vital parameter for assessing self-shading effects within the array. This variable allows the model to learn the critical trade-off between maximising panel density on a limited roof area and minimising inter-row shading losses.

• Urban Morphology: To ensure the model remains accurate across diverse cityscapes, these configurations were modelled across three distinct urban districts.

To initiate modelling of urban maps GIS files for regions were obtained from the Tehran Municipality. Utilising ArcGIS software, a shapefile file was generated for the designated urban blocks. The shapefile format serves as a straightforward and indirect method for storing geometric and geographic feature information.

In next step for solar radiation analysis, the Ladybug plugin within the Grasshopper software was utilised. This plugin, powered by the EnergyPlus engine, was employed to perform PVT output calculations. The solar radiation analysis algorithm was designed using Tehran’s epw file for 2020, providing essential meteorological data. Then, surfaces with an average annual radiation exceeding 1,500 kWh/m²/yr were identified and compiled into a list. This threshold is derived from the findings of Biyik et al. (2017). Surfaces with radiation below 1,500 kWh/m²/yr, wouldn’t be efficient for installing PV cells. Then the focus shifts to the installation of thermal photovoltaic panels on surfaces identified as optimal for radiation reception in previous stages. To facilitate this process, an algorithm was developed within the Grasshopper environment.

Panel geometry was parametrically varied across all 1,575 configurations using the Colibri plugin in Grasshopper, which iteratively evaluated all parameter combinations to generate the thermal, electrical, and environmental outputs. Upon specifying the desired parameters and installing the panels, the thermal and electrical outputs of each panel are calculated. Additionally, environmental outputs are generated to provide a comprehensive assessment of the system›s performance and sustainability.

For the environmental impact assessment, a life-cycle approach was adopted to quantify the net CR potential of the PVT system. This calculation accounts for the carbon emissions offset by both the electrical and thermal yields of the panels. In the context of Tehran, where residential water heating is almost exclusively powered by natural gas, the thermal energy produced by the PVT panels directly offsets the domestic gas load. It is assumed that each unit of thermal energy generated by the system displaces an equivalent amount of fossil fuel consumption. Consequently, the CR is calculated by estimating the volume of natural gas that would otherwise be burned to meet this heating demand, thereby determining the resultant greenhouse gas (GHG) emissions avoided on an annual basis. Furthermore, the electricity generated by the panels contributes to carbon mitigation by displacing grid-supplied electricity, which carries a specific carbon intensity per kilowatt-hour (kWh) based on the local power plant mix. To ensure a balanced assessment, these gains are weighed against the ‘carbon debt’ of the system; specifically, the embodied carbon emissions associated with the manufacturing and production of each PVT panel. By determining the total number of panels utilised in each urban configuration, the net carbon benefit is calculated by subtracting the production-related emissions from the total annual avoided emissions (displaced gas and electricity). To quantify the net annual CR, the following equation was applied:

Where EP is annual electricity production (kWh), HWP is annual hot water production (kWh), N is the number of panels, α is the grid electricity carbon intensity (0.183 kgCO₂/kWh), β is the natural gas displacement emission factor (0.185 kgCO₂/kWh thermal), and γ is the embodied carbon per panel (kgCO₂/panel). The value of α is consistent with Iran’s national grid emission factor, while β reflects the CO₂ equivalent of natural gas combustion for domestic water heating. CR is expressed in kg CO₂ per year. Figure 6 illustrates the steps of creating dataset.

Figure 6

ML algorithm development

Following the simulation phase, a comprehensive dataset comprising 1,575 distinct scenarios was generated based on the parametric variables defined in Table 2. The resulting PVT performance data were curated and formatted to serve as the foundational input for the ML stage. In this research, the employed ML framework utilised supervised learning and regression analysis, specifically invoking ANN and RF algorithms.

These two algorithms were selected to develop a high-speed “surrogate model” capable of providing instantaneous performance predictions. The objective was to create a data-driven tool that could bypass the need for computationally intensive physical simulations when evaluating new urban installation configurations. Each algorithm is characterised by its unique set of hyperparameters, the external configuration settings that govern the model’s structure and the efficiency of the learning process. For the ANN, this involved tuning variables such as the number of hidden layers and neurons to capture complex non-linear relationships. For the RF, hyperparameters included the number of decision trees and the maximum depth of each tree, which are essential for ensuring model stability and preventing overfitting.

Initially, a specific range was assigned to each hyperparameter; through a systematic optimisation process, the configurations that yielded the highest predictive accuracy were identified (Table 3).

To ensure the computational efficiency and stability of the training process, the input parameters were normalised using the Min-Max scaling method. This ensured that all parameter values were scaled to a range between 0 and 1, which is instrumental in accelerating convergence and improving the accuracy of the gradient-based learning algorithms. The formula utilised for this normalisation is defined as follows:

To develop and verify the predictive models, the dataset was systematically partitioned into distinct subsets for training and testing. Specifically, a test set comprising 20% of the total data was initially held out; this data was not utilised during any part of the training or hyperparameter optimisation phases, serving as an “unseen” benchmark to check for signs of overfitting and to reduce the likelihood of evaluation bias.

The remaining 80% of the data was then further segmented: approximately 90% was allocated for model training, while 10% was reserved for internal validation during the learning process. This stratified approach ensures the model is exposed to a vast majority of the simulated scenarios while maintaining rigorous subsets for ongoing performance assessment. By keeping the distribution of these sets consistent, the framework ensures that the final accuracy metrics are representative of the model’s true generalisation capability across diverse urban configurations. To ensure full reproducibility, a fixed random seed of 10 was applied to all data partitioning operations. No stratification was applied during splitting, as the target variables are continuous and the dataset was generated through systematic parametric sampling, ensuring an inherently balanced distribution of input configurations across all subsets.

Sensitivity analysis

Statistics involves comprehending the interrelationships among variables within a dataset and determining the extent to which these relationships are influenced by one another. In the context of this study, a sensitivity analysis was conducted on the dataset of 1,575 simulated scenarios to evaluate the impact of installation parameters, specifically inter-panel distance, horizontal/vertical angles, and panel elevation, on the target outputs: EP, thermal energy HWP, and CR.

By examining the performance trends within the urban blocks of Tehran, it was observed that the data for these specific indicators changes linearly relative to the input features. Consequently, correlation calculation methods tailored for linear data with consistent performance are applicable. The most prevalent methods in this domain are the Pearson and Spearman coefficients (Gonçalves et al. 2020). In this research, the Pearson correlation coefficient was specifically employed to quantify the sensitivity of the performance indicators to each geometric and contextual variable. Pearson correlation was selected because inspection of the simulation outputs confirmed that the target indicators (EP, HWP, and CR) vary approximately linearly with respect to the input parameters within the defined ranges of this study, satisfying the key assumption of the Pearson method and making it an appropriate and interpretable choice for this dataset. This allowed for the identification of which parameters, such as shading-induced distance or tilt angle, exerted the most significant influence on the system’s dual-output efficiency.

Accuracy measurement

Accuracy measurement indices are vital for evaluating the performance and training of machine learning models. These indices compare the predicted values with the values obtained in the simulation. Common accuracy measurement indices include root mean square error (RMSE), percentage error (PE), recognition coefficient index (R²), and mean square error (MSE) (Willmott and Matsuura 2005).

In this research, three error measurement indicators, RMSE, R², and MAE are utilised. The calculation formulas for each are as follows:

Root Mean Square Error (RMSE):

Recognition Coefficient Index (R²):

Mean Absolute Error (MAE):

Electricity production simulation results

The highest numerical amount of EP was recorded in region 16 with low-rise buildings (Figure 7), while the lowest was observed in region 1 which includes high-rise buildings. In terms of average annual EP, panels in region 16 outperformed those in region 2 by approximately 38% and exceeded the production in region 1 by about 52%. These differences are directly attributable to inter-building shading, with Region 16’s lower-rise morphology allowing significantly greater solar access to rooftop surfaces. Figures 7 and 8, show simulation results of EP for training and test data in 3 different regions respectively.

Figure 7

Figure 8

Hot water production simulation results

Region 2 recorded the highest numerical HWP (Figures 9 and 10), while Region 1 exhibited the lowest. In terms of average annual HWP, the performance of panels in region 16 surpasses that of region 2 by approximately 36% and exceeds that of region 1 by about 50%. The same shading mechanism governs thermal output, though the effect is less pronounced than for electricity production, as the thermal collector is less sensitive to partial shading than the PV cells. Furthermore, in regions characterised by more uniform building heights, (Region 16), HWP results are relatively consistent. In contrast, regions with varied building heights show significant differences in HWP, underscoring the impact of building height variability on system performance.

Figure 9

Figure 10

Carbon reduction simulation results

On average, the highest amount of CR occurred in region 16 while region 1 exhibited the lowest average CR rate. Numerically, the highest amount of CR was observed in region 2, while the lowest was in region 1. Region 16 achieved a 56% higher CR compared to region 2, and approximately 90% higher compared to region 1 (Figures 11 and 12).

Figure 11

Figure 12

Selecting optimal ML algorithm

The optimisation and validation of learning models should be conducted separately for each of the three study regions, using two ML algorithms, and for all target indicators. This process would require 30 iterations (3 areas × 2 algorithms × 5 indicators).

Given that hyperparameter optimisation is computationally intensive, this process was performed exclusively on Region 1 data. This approach is justified on two grounds. First, all three regions share an identical feature space – the same five input variables (horizontal angle, vertical angle, inter-panel distance, roof elevation, and urban block), meaning the underlying data structure and complexity are consistent across regions. Second, a preliminary inspection of the simulation outputs confirmed that the statistical distributions of the target indicators across the three regions are comparable in range and variance, suggesting that the optimal model configuration identified for one region is transferable to the others. The hyperparameters identified for Region 1 were therefore applied directly to Regions 2 and 16, with validation metrics confirming their suitability (Tables 6 and 7).

Table 4 compares the two learning models based on the data from Region 1, across various indicators and using the optimal hyperparameters.

Validation of learning models

At this stage, each model was trained and validated using the optimal hyperparameters for region 1. The accuracy evaluation metrics for each target indicator are presented in Table 5. Additionally, the time required for model training, as well as the target indicators for each model, have been compared.

Based on the comparison between the neural network and RF models using the R² recognition coefficient index and the time required for learning, it’s evident that the RF model slightly outperforms the neural network model in terms of R². Additionally, the RF model demonstrates significantly better performance in terms of learning time compared to the neural network model. Therefore, based on these findings, the RF algorithm is applied in this research.

At this stage, each of the models has been trained and validated with optimal hyperparameters for region 2. Each of the accuracy evaluation indicators for each of the target indicators is displayed in Table 6. Also, the time required to learn the model has been measured in each target index. The duration of learning among the indicators varied from 0.05 to 0.09, and the recognition coefficient index among the target indicators was at least 0.99.

At this stage, each of the models has been trained and validated with optimal hyperparameters for region 16. Each of the accuracy evaluation indicators for each of the target indicators is displayed in Table 7. Also, the time required to learn the model has been measured in each target index. The duration of learning among the indicators was different from 0.05 to 0.95 and the recognition coefficient index was at least 0.99 among the target indicators.

Machine learning results

The results of the simulation and the values predicted by the RF algorithm for each of the target indicators for each region have been compared and are presented in Figure 13.

Figure 13

Sensitivity analysis results

The correlation values between different data are visually represented in Figure 14, allowing for a clear understanding of the relationships between the variables. Each numerical value of the coefficients is clearly displayed, providing valuable insights into the strength and direction of the correlations observed in the data.

Figure 14

The correlation values shown in Figure 14, shed light on the factors influencing various aspects of the study:

• HWP: The most significant factor impacting HWP is the distance between panels, with a coefficient of -0.75. This indicates that decreasing the distance between panels (increasing panel density) leads to higher HWP. The density and height of buildings in the study region (coefficient: 0.42) also play a notable role. Additionally, the vertical angle of the panels (coefficient: 0.074) contributes to HWP, while the horizontal angle and distance of panels from the ceiling have lesser impacts.

• EP: The study region (coefficient: 0.96) is the most influential factor in EP, followed by the vertical angle of the panels (coefficient: 0.093). Other factors, such as the horizontal angle, distance of panels from the ceiling, and distance between panels, also contribute to EP, albeit to a lesser extent.

• Number of Panels: The distance between panels has the highest impact on the number of panels, with a coefficient of -0.78, indicating that increasing panel density reduces the number of panels required. The study region (coefficient: 0.43) is the next significant factor, followed by the vertical angle of the panels. The horizontal angle and distance of panels from the ceiling have minimal effects on the number of panels.

• Amount of CR: The distance between panels (coefficient: -0.75) has the greatest impact on CR, with higher panel density resulting in lower CR. The study region (coefficient: 0.48). Additionally, the vertical angle of the panels influences CR, while the horizontal angle and distance from the ceiling have minimal effects.

Proposed framework

The proposed framework (Figure 15) functions as a high-speed surrogate model designed to bypass the computational delays of traditional building performance simulations. It begins with the generation of a large-scale parametric dataset using GIS-based urban modelling and physical simulations, which captures the complex relationships between installation geometry and urban shading. This framework allows non-expert users to input specific urban configurations and receives near-instantaneous predictions for EP, HWP, and CR. Ultimately, it transforms a slow, specialist-led simulation process into a rapid, automated decision-support tool for optimising PVT deployments in dense city environments.

Figure 15

Integrated performance modelling

A significant contribution of this research is the integration of electrical, thermal, and environmental indicators into a single predictive framework. While much of the existing literature, such as Shin et al. (2022) and(Sulaiman et al. (2024) focuses primarily on building-level EP, this study expands the scope to include HWP and CR. By doing so, it addresses a gap identified in the literature where studies often prioritise single parameters. The results indicate that the RF algorithm is exceptionally well-suited for this multi-output task, achieving an R² accuracy of 0.91 to 1.0 across different indicators (Table 5).

Algorithmic efficiency and selection

The comparison between ANN and RF highlights critical trade-offs in ML applications for renewable energy. While both models demonstrated high predictive accuracy (R² ≥ 0.91), the RF algorithm was chosen as the superior model primarily due to its significantly shorter learning time. For instance, in Region 1 (high-rise buildings), the RF model’s learning time for HWP was a mere 0.08 seconds, compared to 63.26 seconds for the ANN. This efficiency is vital for the proposed four-step software, which aims to facilitate decision-making for non-experts by providing rapid, data-driven results for urban PVT installations. Although this study focuses on Tehran, the proposed surrogate framework is transferable to other dense urban contexts, including European cities facing similar rooftop solar deployment challenges under the Energy Performance of Buildings Directive (EPBD) and the EU Renovation Wave policy frameworks (Hamdy et al. 2013; Pompei et al. 2026).

The role of urban morphology

The findings underscore that urban density and building height are the most critical environmental determinants of PVT performance. The simulation results across Tehran’s regions revealed that Region 16 (low-rise, high density) outperformed Region 1 (high-rise) by approximately 52% in EP and 50% in HWP. This disparity is directly attributed to shading effects caused by taller structures, confirming the findings of Wang et al. (2021) regarding the necessity of shading mitigation. Furthermore, sensitivity analysis showed that the study region itself had a 0.96 correlation coefficient with EP, indicating that the physical urban context is the single most influential factor for power generation.

Optimisation of installation parameters

Beyond urban context, the study identifies specific installation variables that can be optimised to enhance system yield. Sensitivity analysis revealed that the distance between panels (density) is the most influential factor for HWP (coefficient: -0.75) and CR (coefficient: -0.75). This suggests that increasing panel density is a highly effective strategy for maximising thermal and environmental benefits. Additionally, while many studies in the literature review, such as Kassem and Othman (2022) rely on climatic variables like humidity and wind speed, this research demonstrates that geometric installation parameters (vertical/horizontal angles and roof elevation) are sufficient for high-accuracy performance modelling when integrated with urban GIS data.