The estimation of photovoltaic (PV) capacity factors at the global scale relies on a physics-based modelling workflow inspired by Saint-Drenan et al. (2018). The approach assumes utility-scale, fixed-tilt PV installations, as these represent a significant share of the installed global PV capacity. However, the modelling framework will be open-source, allowing users to customise system configurations according to their needs.
The model implements the full simulation chain—from the downscaling of meteorological inputs to the calculation of irradiance on the tilted PV module surface and its subsequent conversion into a capacity factor. It incorporates major physical loss mechanisms (optical, thermal, and electrical), ensuring a realistic representation of PV system performance under varying environmental conditions.
Input Data and Pre-processing
The following meteorological and technical data serve as model inputs:
Gridded surface solar radiation downwards (GHI)
Gridded 2 m temperature (TA)
PV system characteristics (tilt, azimuth), derived from private plant metadata and generalised rules
Temporal Downscaling
To better represent sub-hourly variability in solar irradiance, the original gridded data is downscaled to 15-minute intervals before recomputing the PV output. This approach avoids artefacts that may occur when relying solely on hourly averages.
The hourly global horizontal irradiance (GHI) is first transformed into the clearness index \( K_t \) , defined as:
\[ K_t = \frac{GHI}{TOA} \]where \( TOA \) denotes the theoretical irradiance at the top of the atmosphere.
The \( K_t \) time series is linearly interpolated to 15-minute resolution and then reconverted to GHI using the same \( TOA \) irradiance values. Air temperature (TA) is also interpolated linearly to 15-minute intervals. This temporal refinement enables a more accurate reconstruction of irradiance variability within each hour. Once the PV conversion is completed at the 15-minute scale, the results are averaged back to hourly values.
Methodology
The model implements a complete physical simulation chain—from irradiance transposition to loss modelling and power output conversion—ensuring realistic system performance across geographies and climates.
Irradiance Decomposition and Transposition
To compute the irradiance on the tilted surface of the PV modules (GTI – Global Tilted Irradiance), the incoming solar radiation is decomposed into direct (beam), diffuse, and reflected components.
The diffuse horizontal irradiance (DHI) is estimated using the Skartveit-Olseth model (1987), which distinguishes between overcast, partially cloudy, and clear-sky regimes, based on the clearness index \( K_t \) and solar elevation.
Once the beam horizontal irradiance (BHI) and DHI are known, the total irradiance on the tilted plane is calculated as:
\[ GTI = R_b \times BHI + R_d \times DHI + R_r \times GHI \]where GHI is the surface solar radiation downwards. Each term accounts for a transposition factor:
The beam irradiance transposition factor is:
where AOI is the angle of incidence and SZA is the solar zenith angle, both computed using the SG2 algorithm (Blanc et al., 2012).
The diffuse irradiance is treated with the Klucher model:
where β is the surface tilt angle and fk corresponds to:
\[ f_k = 1- \frac{DHI}{GHI} \]The reflected irradiance assumes isotropic reflection from the ground with a fixed albedo ρ = 0.2, which is most used in the literature (Gueymard et al., 2019):
Modelling of PV Efficiency and Losses
Several conversion steps transform the plane-of-array (POA) irradiance into AC power output, taking into account system-level losses.
Optical Losses
The Martin-Ruiz model (2001, 2013) estimates reflection losses based on the incidence angle:
\[ \bar R(AOI) = \bar R(0) + \bigl(1-\bar R(0)\bigr) \times \frac{\Bigl(exp\Bigl(-\cos \frac{AOI}{a_r}\Bigr) -\exp \Bigl(-\frac{1}{a_r} \Bigr) \Bigr)}{1-\exp \Bigl(-\frac{1}{a_r} \Bigr)} \]where \( \bar R(0) \) is the normal-incidence reflectance and \( a_r \) is a surface-dependent angular loss coefficient.
Conversion Efficiency at 25°C
The PV module conversion efficiency under standard conditions (25°C) is calculated using a fourth-order polynomial (Beyer et al., 2004):
\[ \eta_{25^\circ C} = max(0, a_1 \times GTI + a_2 \times GTI^2 + a_3 \times GTI^3 + a_4 \times GTI^4 + a_5 \times GTI \times \log(GTI)) \]with parameters calibrated using French and German plant data listed in Table 2.1 below.
Table 2.1: Parameters used in the estimation of the PV generation.
| Parameter value | ||||
|---|---|---|---|---|
a1 | a2 | a3 | a4 | a5 |
1.4306 | -1.0084 | 1.0121 | 0.4401 | 0.1979 |
Thermal Losses
The module temperature \( T_{PV} \) is estimated using the Ross model (1976), which relates PV module temperature to ambient air temperature and solar irradiance. The temperature-corrected efficiency \( \eta_{eff} \) is then calculated as:
\[ \eta_{eff} = \eta_{25^\circ C} \times (1-0.0045 \times(T_{PV}-25)) \]The model assumes that ground-based installations experience greater ventilation, leading to lower PV module temperatures and thus reduced thermal losses, as outlined by Skoplaki et al. (2008). This empirical adjustment improves the realism of the estimated thermal behaviour of utility-scale PV systems, which are typically mounted on open structures allowing natural airflow.
Inverter Losses
AC power output \( P_{PV,AC} \) is estimated using the Schmidt et al. (1994) formulation, which accounts for inverter self-consumption and conversion inefficiencies:
\[ P_{PV,AC} = GTI \times \eta_{eff} \times (b_1 + b_2 \times \eta_{eff} + b_3 \times \eta^2_{eff}) \]where \( b_i \) are empirical coefficients, with \( b_1 = -0.0005 \) , \( b_2 = 1.0269 \) , and \( b_3 = -0.002217 \) .
Representation of Global Tilt and Orientation
To define representative values for panel tilt and azimuth at the global scale, metadata from hundreds of utility-scale PV installations in Germany and France was analysed. The spatial distribution of these tilt angles, each associated with plants over 1 MWp, is shown in Figure 2.1. The observed angles were compared to theoretical optimum values, defined as the tilt that maximises annual incident radiation on the module surface.
The optimal tilt was computed by simulating PV output over a 5-year period (2015–2020) using ERA5 irradiance data. For each grid cell, multiple tilt configurations were tested, and the angle yielding the maximum annual GTI (Global Tilted Irradiance) was selected. The resulting global distribution of optimal tilts is shown in Figure 2.2.
A comparison between actual and optimal tilts revealed that many installations operate with a tilt around 75% of the theoretical optimum. This trend is visualised in Figure 2.3, which shows the relationship between actual and optimal tilt values. The deviation from the optimum is likely explained by practical trade-offs, such as minimising inter-row shading or reducing installation costs.
To formalise this pattern, the ratio between actual tilt and optimal tilt was analysed alongside the azimuth angle. As shown in Figure 2.4, the tilt ratio follows a normal distribution centred around 0.75, while the azimuth angles are tightly clustered around 0°, indicating a strong preference for south-facing modules. Based on these findings, the global model adopts a south-facing orientation and assumes a tilt equal to 75% of the optimal value for each ERA5 grid cell.
Figure 2.1: Geographic distribution of tilt angles for over 300 utility-scale PV plants (>1 MWp) located in France and Germany.
Colour scale indicates tilt angle (°), highlighting spatial variation as a function of latitude and regional deployment practices.
Figure 2.2: The map shows the optimal fixed tilt (in degrees) computed for each ERA5 grid cell based on the 2015–2020 average.
This value is derived by simulating energy output across varying tilts and selecting the configuration with the highest annual GTI (Global Tilted Irradiance).
Figure 2.3. Relationship between actual tilt angles ( \( \theta \) ) and their corresponding optimal values ( \( \theta_{opt} \) ) for utility-scale PV installations in Germany and France. The red dashed line indicates the 1:1 ratio ( \( \theta = \theta_{opt} \) ), while the black line shows the 0.75 scaling ( \( \theta = 0.75 \cdot \theta_{opt} \) ) used in the global modelling approach.
Figure 2.4: Empirical distribution of tilt-to-optimal tilt ratio (
\( \theta / \theta_{opt} \)
).
Top-left: Joint 2D histogram of azimuth angle and tilt ratio.
Top-right: Histogram of tilt ratio with fitted normal distribution N(0.75, 0.17).
Bottom: Histogram of azimuth angles fitted to N(0, 7.96), confirming a strong concentration of south-facing modules.
Output Data
The final output consists of:
Gridded SPV capacity factors at hourly resolution, assuming DC installed capacity as normalisation factor.
Aggregated indicators at ADM0 and ADM1 levels in CSV format (see Spatial Aggregation Procedure) at hourly, daily, monthly, seasonal, and annual temporal resolutions, following the Temporal Aggregation Procedure.
These capacity factors reflect local climate, system losses, and realistic tilt/azimuth configurations, offering consistent comparability across regions and timescales.
References
For the references, please refer to the References section in the Product User Guide.
