Incident irradiance

In this document

We explore how modern solar simulation tools leverage advanced models to improve the calculation of irradiance on photovoltaic (PV) panels under a variety of conditions. We will discuss the distinct strengths and applications of each method, highlighting their suitability for both preliminary estimations and detailed analyses.

Overview

To calculate the total incident irradiance on a power plant's PV modules, it is essential to determine how the sky's irradiance is redistributed onto tilted surfaces. This process begins with modeling the sky's irradiance, which can be approached using different methods. The Isotropic Model divides the sky into distinct regions, offering a simplified yet effective estimation, while the Anisotropic Model provides a continuous and detailed representation of sky luminance, better capturing variations under different weather conditions.

Next, spatial relationships and surface orientation must be incorporated to accurately compute light interactions. For more precise analyses, Ray Tracing Models simulate light interactions in 3D, capturing details such as accurate reflections. In Solargis, an advanced sky model is paired with the path tracing method to provide more accurate simulations.

Additional steps in irradiance calculations include modeling Angular Losses, which account for reductions in usable light due to the angle of incidence, and applying Spectral Corrections to adjust for atmospheric effects on the solar spectrum. Together, these models enable precise and reliable irradiance predictions required for optimal PV system design.

*Diagram showing ray tracing algorithm applied to a PV plant*

Sky irradiance

The Sky irradiance models are designed to estimate the irradiation from various parts of the sky, enabling the calculation of tilted irradiance on each PV cell at a later stage. We utilize two different anisotropic models:

The Solargis GTI Simulator utilizes the simple Perez sky model in combination with the View Factor.
Solargis PV Simulator utilizes an All-weather Perez sky model in combination with path tracing.

Simple Perez model

All-weather Perez model

Based on the simple Perez anisotropic model, the core of this model is the internal coefficient matrix, referred to as the Perez sky diffuse irradiance model coefficients. Multiple versions of these coefficient sets exist, making it important to distinguish between them. This model is used to simulate simple GTI Energy systems.

Derived from the all-weather Perez model, this model estimates the relative luminance distribution of the sky dome using sky brightness and clearness parameters. This model is particularly suited for raytracing light simulations, providing a more detailed representation of diffuse shadows on PV modules. The model is employed in complete PV Energy system simulations to calculate GTI and, subsequently, PVOUT.

Ray tracing

The Ray Tracing model calculates the incident irradiance after the PV plant’s full 3D scene is known. The model simulates the path of individual light rays as they interact with surfaces and objects, including PV modules, buildings, obstacles, and terrain. This model traces rays from the sun to the PV module, taking into account reflection, refraction, and shading by surrounding objects. It provides a more detailed and accurate representation of shading effects and the spatial distribution of sunlight on the PV panel.

Solargis’s ray tracing method uses Monte Carlo backward path-tracing, tracing rays from the cell to the light source. The model considers multiple bounces until the light source is reached. Path tracing yields more accurate energy predictions for PV panels by considering the full complexity of light interactions within the scene, making it particularly effective in scenarios with complex shading or reflective surfaces. It is computationally intensive, requiring detailed geometric information about the scene and precise calculations for each ray, making simulations slower and more resource-intensive.

The process involves four main steps:

Step 1: Direct illumination calculation

Methodology: Each PV cell is covered with multiple sample points. At these points, the algorithm determines whether they are in direct sunlight or shaded. If a cell is partially shaded, a shadow ratio is calculated as a fraction.
Purpose: This step ensures accurate accounting of direct solar radiation on each cell, which is crucial for calculating the overall energy yield.

Step 2: Diffuse radiation calculation

Methodology: A grid of sampling points is placed over the PV module table. At each point, multiple rays are generated in random directions and traced through the 3D simulation scene. The direction of rays at the PV module surface is recorded for angular loss calculations.
Reflection handling: Each intersection of a ray with an object in the scene is treated as a Lambertian reflection, attenuating the ray's power proportionally to the surface's albedo. If a ray hits the sky, its brightness is calculated using the Sky irradiance model.
Termination criterion: The probability of terminating the path tracing increases as the ray's power weakens due to multiple reflections.

Step 3: Post-processing

Denoising: The diffuse radiation values are denoised to get clearer ray tracing results. This ensures consistent power output calculations.
Resampling and summation: The diffuse radiation is resampled per cell and summed with the direct radiation to obtain the final Global tilted irradiance (GTI) for each cell.

Step 4: Implementation and validation

Applicability: This ray tracing method is implemented for both fixed-mounted PV modules (monofacial or bifacial) and trackers with various tracking strategies.
Validation: The algorithm has been validated against the Bifacial Radiance software by NREL and ground measurements of GTI, ensuring its accuracy and reliability.

For a visual comparison, refer to the image showing the rear GTI spatial distribution from Solargis simulations versus results from the NREL bifacial radiance tool at locations in Saudi Arabia and Finland.

Figure 2: Comparison of rear GTI spatial distribution from Solargis simulations (SG, top) with results obtained using NREL Bifacial Radiance tool (BF, bottom) at locations in Saudi Arabia (left) and Finland (right)

Comparison with View Factor model
For applications that require quick estimations and preliminary design studies, it is a common approach to use the View Factor model. Unlike Ray tracing, View Factor model evaluates the radiation exchange between surfaces based on their geometric relationship and orientation. It uses mathematical formulas or algorithms to determine the fraction of radiation emitted by one surface that is intercepted by another. However, this model does not accurately capture complex shading effects, particularly in situations with irregular or non-uniform shading patterns.

Angular losses

Angular loss, also known as IAM (incidence angle modifier), refers to the reduction in usable irradiation for a solar panel due to the angle at which light strikes its surface.

We use the Martin-Ruiz model, which quantifies the amount of light that penetrates the surface—e.g., does not reflect off it—using an angular factor with a value range between 0 and 1. This relationship is non-linear. The coefficient affects the shape of the angular loss curve, ensuring that the model accurately accounts for the surface characteristics of the PV modules.

Incidence angle dependency: At an incidence angle of 0 degrees from the surface normal vector, there is no angular loss. However, as the incidence angle increases towards 90 degrees, the loss increases, reaching a complete (100%) loss at 90 degrees.
Factors influencing accuracy: The accuracy of angular reflectivity loss calculations depends on the cleanliness and specific properties of the module surface, such as antireflection coatings and texture.

Comparison with other software

Angular reflection losses are accounted for similarly in other solar simulation software:

Software	Parameter name	Notes
Solargis Prospect	Angular reflectivity	Modeled by the same model as in Solargis Evaluate (Martin & Ruiz).
Solargis Evaluate	Angular reflectivity	Angular reflection losses model by Martin & Ruiz.
PVsyst	IAM factor on global	Custom IAM, ASHRAE, Fresnel or Fresnel with anti-reflective coating, depending on user settings.
SAM (NREL)	Reflection (IAM)	According to IEC 61853 model: standard glass or glass with anti-reflective coating (page 63).
SolarFarmer (DNV)	Incidence Angle Modifier	ASHRAE, CIEMAT, Fresnel normal glass, Fresnel anti-reflective coated glass, Custom IAM, depending on settings.

Spectral correction

As light travels through the atmosphere, its solar spectrum changes. Spectral correction adjusts for the differences in spectral response between PV modules. Solargis Evaluate uses the Lee & Panchula model for this purpose, which is also known as the First Solar spectral correction model. The coefficients for this correction vary depending on the module type, such as CSI (Crystalline Silicon) versus CdTe (Cadmium Telluride).

The specific intensity of the spectral responsivity correction depends on two key atmospheric factors:

Air mass: This represents the optical path length of sunlight through the Earth's atmosphere. It increases as the Sun's position moves closer to the horizon, affecting the spectral distribution of sunlight.
Precipitable water content: This refers to the total amount of water vapor present in a column of the atmosphere.

Both air mass and precipitable water content influence the spectral distribution of sunlight reaching the Earth's surface, which in turn affects the spectral response and output of PV modules.