# Module I(V) Curve

A complete module I(V) curve is computed under ambient conditions for the current time step. The “One-Diode” parameters are defined in the module file. The one-diode model uses an equivalent electrical circuit model and the governing diode equation to generate an explicit, continuous current vs. voltage function.

# One-Diode Model

Given the 1-diode model parameters for the module, this routine computes the module’s current-voltage characteristics. **Figure 35** shows the equivalent circuit of a PV cell. The following algorithm includes the recombination current, I_{rec}, a refinement in the model that can be set to zero if the parameters required to determine the current (μ, τ_{eff}, *di*, V_{bi}) are not provided in the module definition input file.

### Figure 35. One-Diode Equivalent Electric Circuit Model of a PV Module

## Inputs

## Outputs

## Algorithm

1.) Solve the following transcendental equation that relates the module’s output current *i* and output voltage υ to the photocurrent *I*_{ph}, and the 1-diode parameters corrected for the temperature and irradiance level (I_{0}, *R*_{sh}, *R*_{s}, γ).

The parameter b, given in the module parameter definition, combines the following terms:

Expanded, the transcendental function for the output current becomes:

2.) The current should be solved for diode voltages in the interval [0, ν_{oc,g}], where ν_{oc,g} is the guess for the open-circuit voltage, and can be found by setting the I to zero in the above equation (neglecting *I*_{rec}):

*i*and ν to 0, respectively.

4.) Find the maximum power point diode voltage using the Newton-Raphson method by iteratively solving the following equation until the difference between *V*_{d,n+1} and ν_{d,n} is arbitrarily small.

## Reference

Mermoud, A., Conception et dimensionnement de systèmes photovoltaïques : Introduction des modules PV en couches minces dans le Logiciel PVsyst. Université de Genève, 2005.

# One-Diode Model Temperature Correction

Given the 1-diode model parameters defined for the module under STC conditions (25 °C, 1000 W/m^{2}), compute the temperature and irradiance-corrected parameters at the actual module temperature *T _{m}* and the available solar energy

*G*. The default temperature correction of all 1-diode parameters is linear. If a non-linear temperature correction of the diode ideality factor is desired, the then a set of additional parameters (polynomial coefficients) is available to affect this correction.

_{T,Eff}This non-linear response is illustrated in **Figure 36** for a family of I(V) curves with a module temperature range of 8 °C to 75 °C. This data was measured in the laboratory using the module temperature control system and a Spire long-pulse solar simulator.

### Figure 36. Non-Linear Module Power Temperature Response using a Third-Order Polynomial Correction to the Diode Ideality Factor γ

## Inputs

## Outputs

## Algorithm

1.) Given the effective available insolation *G*_{T,Eff} and module temperature *T*_{m}, find the corrected 1-diode shunt and series resistance.

2.) If the linear correction to the diode ideality factor is desired, or all non-linear coefficients *a _{y},b_{y},c_{y},d_{y}* = 0, then correct it for the module temperature as follows:

*a*γ is referring to the y1 non-linear temperature coefficient in PlantPredict and

*b*γ is referring to y2,

*c*γ is referring to y3 and

*d*γ is referring to y4

*R*

_{s}. As a result, the junction still experiences a voltage bias and there are currents flowing through both the recombination path and through

*R*

_{sh}when the terminal voltage of the device is zero, i.e. the recombination term does not go to zero in the short circuit condition. Therefore the photocurrent,

*I*

_{ph}must be greater than

*I*

_{sc}in order to supply parasitic currents as well as the external current which has the rated

*I*

_{SC,ref}value. Find the actual

*I*

_{ph}as follows:

The temperature dependence on voltage is also computed, but not used elsewhere in the simulation. Note that μΙ_{sc} ≅ α_{Iph}, given in 1/°C.

## Reference

Schwieger, M., Michalksi, S., Non-Linearity of Temperature Coefficients, Equivalent Cell Temperature and Temperature Behaviour of Different PV-Module Technologies. TÜV Rheinland Energie und Umwelt, Cologne, Germany. Proceedings from the 28th EU PVSEC.