PV conversion model

Overview

The PV conversion model simulates the transformation of sunlight and temperature into DC electrical output at each inverter input, serving as a crucial bridge between the optical simulation and the rest of the electrical system. This model includes:

• Generation of IV curves for each PV cell using the Single Diode Model, which incorporates key module parameters and real-time environmental inputs (irradiance, temperature).

• Calculation of cell temperature, considering factors such as air temperature, irradiance, wind speed, and module-specific adjustments.

• Modeling of module degradation over its operational lifetime, including higher first-year losses and stabilized long-term decline.

• Numerical aggregation of IV curves through the system’s hierarchy—cells to modules, modules to strings, strings to inverter inputs—resulting in the complete DC-side electrical representation for each inverter.

Altogether, this approach provides a detailed, hierarchical simulation of how irradiance and temperature data result in the final DC electrical characteristics used for further conversion and grid integration.

PV conversion model methodology

For each time interval, the PV conversion model uses the current Global Tilted Irradiance (GTI) and temperature heat-map to calculate the current-voltage (IV) characteristics on the DC side for each inverter input.

Figure 1: PV conversion - general process.

This calculation involves two main steps:

• Generating the IV curve for each PV cell using the Single Diode Model.

• Aggregating these IV curves numerically—first combining cell-level curves into module curves, then into string curves, DC combiner box curves, and ultimately producing the IV curve at every inverter input.

Figure 2: PV conversion process in detail.

Single Diode Model

A PV cell is essentially a p-n junction diode designed to efficiently convert sunlight into electrical energy. This conversion process can be represented using the Single Diode Model, as described by W. De Soto.

Figure 3: Single Diode Model.

In this schematic, several electrical quantities are considered:

• I_L: Current generated by incident light (photocurrent)

• I_D: Current flowing through the diode

• R_sh: Parallel resistance, representing leakage currents across the junction

• R_S: Series resistance, accounting for resistive losses in the current path

For any given GTI and temperature, the model calculates I_D and I_L currents using key PV module parameters from the product catalog, including:

• The photocurrent at reference conditions

• The diode reverse saturation (dark) current at reference conditions

• The open-circuit voltage at reference conditions

• The reference ideality factor

• The module’s short-circuit current temperature coefficient

These parameters, combined with the parallel and series resistances, fully define the Single Diode Model. The Lambert W function by Darko Veberic is used to accurately simulate the diode’s behavior in this context.

With these inputs, the model determines the output current and voltage for each cell, according to the GTI and temperature provided by the optical simulation.

Cell temperature model

The cell temperature is determined by considering several key factors:

• Air temperature: The ambient temperature surrounding the module.

• Global Tilted Irradiance (GTI): The amount of solar energy received on the cell surface.

• Thermal inertia: The history of the module’s average temperature, accounting for how quickly or slowly the module responds to temperature changes.

In addition, the model uses several module-specific parameters to capture environmental and material influences:

• Nominal Operating Cell Temperature (NOCT): Indicates the typical cell temperature under standard reference conditions.

• Thermal Model Correction Coefficient: Adjusts the model for the unique conditions at the site.

• Wind Speed Empirical Constant: Reflects the cooling effect of wind on the module, based on observed data.

• Module efficiency at 25°C: Specifies the panel’s performance under standard testing conditions.

• Module type factor: Differentiates between various PV technologies, such as crystalline silicon (CSi) and cadmium telluride (CdTe).

• Emissivity coefficient approximation: Estimates the module’s ability to release heat as thermal radiation.

By combining these environmental inputs and module-specific parameters, the model accurately predicts cell temperature under real-world conditions.

Module degradation

The Solargis implementation of the Single Diode Model accounts for module degradation over time. Typically, PV modules have a lifespan of 25 to 30 years, during which their power output gradually decreases due to aging and environmental effects.

Degradation is modeled in two main phases:

• First-year degradation: In the initial year, modules usually lose about 1% of their efficiency. This higher loss is mainly caused by light-induced degradation (LID) and the settling of module materials.

• Long-term degradation: After the first year, the degradation rate stabilizes at approximately 0.5% per year. This steady decline is attributed to ongoing exposure to ultraviolet (UV) radiation, temperature variations, and mechanical stresses.

By considering these factors, the model provides a realistic estimate of the module’s performance throughout its operational life.

Single diode model output

For each cell, the model uses the GTI and temperature data from the optical simulation to calculate current values across the full range of possible voltages. This process generates the cell’s electrical characteristics in the form of an IV curve (current-voltage), which illustrates how the current varies with voltage under the given conditions (Figure 4).

Figure 4: Cell’s IV curve.

IV Curve aggregation

The model replicates the electrical structure of the energy system by aggregating IV curves at each level:

• It combines individual cell IV curves to form the IV curve of a PV module.

• Module IV curves are then grouped to create string IV curves.

• Finally, string IV curves are aggregated to produce the IV curve at each inverter input.

This process, known as numerical IV curve aggregation (or IV curve superposition), ensures that the overall system behavior reflects how all components work together.

Example (Figure 5):

Inside a PV module, cells are grouped into submodules, with each submodule protected by a bypass diode. These submodules are connected in series to form the full module. If a submodule (e.g., Submodule 1 shown in red) is shaded and delivers less current, the series configuration means all submodules share the same current. The overall module voltage is the sum of the submodules' voltages, resulting in the module’s IV curve (shown in blue in Figure 5).

Figure 5: IV curve aggregation on PV module.

DC losses

DC losses in the direct current path from PV modules to inverters are a crucial factor in energy yield simulations. These losses occur due to the electrical resistance in the DC combiner boxes and DC cables.

Note: Solargis Evaluate provides a default value of 2% for DC cable losses. Users can adjust this value based on specific project requirements.

IV Curve aggregation output

As the IV curves are progressively aggregated through strings, DC cables, and DC combiner boxes, the process ultimately generates the IV curve at the inverter input (Figure 6). This final IV curve represents the combined electrical behavior of all upstream components as calculated by the PV conversion model. In systems with multiple shaded areas, the resulting inverter input IV curve can display more complex shapes, reflecting the varying contributions from different parts of the PV array.

Figure 6: Example of inverter input IV curve.

Further reading

• “Improvement and validation of a model for photovoltaic array performance” by W. De Soto.

• “Lambert W Function for Applications in Physics” by Darko Veberic.