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.
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, Irec, a refinement in the model that can be set to zero if the parameters required to determine the current (μ, τeff, di, Vbi) are not provided in the module definition input file.
Figure 35. One-Diode Equivalent Electric Circuit Model of a PV Module
1.) Solve the following transcendental equation that relates the module’s output current i and output voltage υ to the photocurrent Iph, and the 1-diode parameters corrected for the temperature and irradiance level (I0, Rsh, Rs, 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, νoc,g], where νoc,g is the guess for the open-circuit voltage, and can be found by setting the I to zero in the above equation (neglecting Irec):
4.) Find the maximum power point diode voltage using the Newton-Raphson method by iteratively solving the following equation until the difference between Vd,n+1 and νd,n is arbitrarily small.
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/m2), compute the temperature and irradiance-corrected parameters at the actual module temperature Tm and the available solar energy GT,Eff. 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.
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
1.) Given the effective available insolation GT,Eff and module temperature Tm, 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 ay,by,cy,dy = 0, then correct it for the module temperature as follows:
The temperature dependence on voltage is also computed, but not used elsewhere in the simulation. Note that μΙsc ≅ αIph, given in 1/°C.
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.