The seven (7) parameter model is also called 2M7P.

The photovoltaic cell is represented by the following electric circuit (Figure 1), which consists of a current source modeling the luminous flux, two diodes for the polarization of the cell, a shunt resistor and a resistor series.

· Intensity of the current supplied by the cell

I p υ = I L − I D 1 − I D 2 − I s h (3.1)

I L = I p h : photon current;

I D 1 : diode current 1;

I D 2 : diode current 2;

I s h : shunt resistor current.

I s h = V p υ + I p υ R S R S H (3.2)

I D 1 = I S 1 ( exp ( q β 1 k T ( V p υ + I p υ R S ) ) − 1 ) (3-3)

I D 2 = I S 2 ( exp ( q β 2 k T ( V p υ + I p υ R S ) ) − 1 ) (3-4)

Equations (3.2), (3.3) and (4) in Equation (3.1) yield Equation (3.5)

I p υ = I L − I S 1 ( exp ( q ( V p υ + I p υ R S ) β 1 k T ) − 1 )       − I S 2 ( exp ( q ( V p υ + I p υ R S ) β 2 k T ) − 1 ) − V p υ + I p υ R S R S H (3-5)

The parameters that go into Equation (3.5) are:

I S 1 et I S 2 : reverse saturation currents;

β 1 et β 2 : the successive quality factors of diode 1 and diode 2;

R S : resistance in series;

R S H : shunt resistor.

The photovoltaic cell is represented by the electrical circuit (Figure 2), which consists of a current source modeling the luminous flux (illuminance), two diodes for the polarization of the cell and a series resistor. To pass from the model with seven (7) parameters to the model with six (6) parameters, we formulate the hypothesis that the cell is made in such a way that the losses by thermal leaks are negligible. Such an assumption in the modeling of the equivalent circuit means that the shunt resistor has a value which time towards infinity.

The photo-current I p υ produced by the current source depends on the illumination and the series resistance R S .

· Intensity of the current supplied by the cell

In the 2M6P we have R S H → ∞ ⇒ I s h = 0

Equations (3.1) and (3.5) become:

I p υ = I L − I D 1 − I D 2 (3.6)

I p υ = I L − I S 1 ( exp ( q ( V p υ + I p υ R S ) β 1 k T ) − 1 ) − I S 2 ( exp ( q ( V p υ + I p υ R S ) β 2 k T ) − 1 ) (3.7)

This model is obtained when we consider that the model with two (2) diodes is ideal, that is to say that we do not take into account the losses by leakage and the losses by Joule effect. These hypotheses result in a photo-current produced by a current source which depends on the illumination and the temperature.

· Intensity of the current supplied by the cell

We have:

R S H → ∞ ⇒ I s h = 0 et R S = 0

Equations (3.1) and (3.5) become:

I p υ = I L − I D 1 − I D 2 (3.8)

I p υ = I L − I S 1 ( exp ( q V p υ β 1 k T ) − 1 ) − I S 2 ( exp ( q V p υ β 2 k T ) − 1 ) (3.9)

The photovoltaic cell is represented by the electric circuit (Figure 4). This is the most classic model in the literature. The model is also called a real diode model, it involves a current generator for modeling the incident light flux, a diode for the physical phenomena of polarization and two resistors (series and shunt).

These resistors will have some influence on the I-V characteristic of the solar cell:

1) The series resistance is the internal resistance of the cell; it mainly the resistance of the semiconductor used, the contact resistance of the collector grids and the resistivity of these grids.

2) The shunt resistance is due to a leakage current at the junction; it depends on how it was done.

· Intensity of the current supplied by the cell

The model is a diode so I D 2 = 0

ID2 = 0 in equation (3.1) gives:

I p υ = I L − I D 1 − I s h

The current generated by the photovoltaic cell is given by:

I p υ = I L − I S 1 ( exp ( q ( V p υ + I p υ R S ) β 1 k T ) − 1 ) − V p υ + I p υ R S R S H (3.10)

The four-parameter model treats the PV cell as a current source, dependent on irradiance, connected in parallel with a diode in series with a series resistance R_s. The (Figure 5) models the equivalent circuit of the photovoltaic cell with four parameters to a diode.

The model is called 1M4P or one diode model without shunt resistance, it is a simple empirical electrical model, in the literature we are told that it is the closest model to the photovoltaic generator. It is a model that is currently widely used because of the quality of the results obtained.

This model makes use of the PV module specifications offered by the manufacturers, so it offers a very simple way to calculate the power produced by the PV modules.

· Intensity of the current supplied by the cell

The model is a diode so I D 2 = 0 ,

and we have R S H → ∞ ⇒ I s h = 0 .

So we get I p υ = I L − I D 1 .

The current generated by the photovoltaic cell is given by:

I p υ = I L − I S 1 ( exp ( q ( V p υ + I p υ R S ) β 1 k T ) − 1 ) (3.11)

It is the model of the ideal solar cell, the solar cell is a semiconductor component which delivers a current by exciting the latter by photons, so in first approximation we have a current source, which is short-circuited by a diode (because the solar cell is a p-n junction). This model is very idealistic, among the working conditions, diffusion phenomena are not taken into account. The equivalent diagram of the ideal photovoltaic cell includes a current generator which models the illumination and a diode in parallel which models the PN junction.

· Intensity of the current supplied by the cell

The model is a diode so I D 2 = 0 ,

R S H → ∞ ⇒ I s h = 0 and R S = 0

So we get I p υ = I L − I D 1 .

The current generated by the photovoltaic cell is given by:

I p υ = I L − I S 1 ( exp ( q V p υ β 1 k T ) − 1 ) (3.12)

The equivalent circuit is shown in Figure 6.

Under illumination, the current generated is expressed by:

I p υ = I L − I S 1 ( exp ( q ( V p υ + I p υ R S ) β 1 k T ) − 1 )       − I S 2 ( exp ( q ( V p υ + I p υ R S ) β 2 k T ) − 1 ) − V p υ + I p υ R S R S H