**2.5. Irradiation**

**2. Mathematical modelling of PV system**

62 Fuzzy Logic Based in Optimization Methods and Control Systems and Its Applications

*V* = \_\_\_\_\_\_\_\_\_\_ *NKT*

**2.2. Light-generated current (radiation)**

IL <sup>=</sup> \_\_\_G

where G is the radiation (W/m2

**2.3. Reverse saturation current**

**2.4. Short-circuit current**

circuit-situation: V = 0.

Io = Ior ∗ ( <sup>T</sup>⁄ Tref)3 exp((

Iorn <sup>=</sup> \_\_\_\_\_\_\_\_ Isc

Ish <sup>=</sup> IL <sup>−</sup> Io((exp(QV−IR \_s

1.5, and Eg is the band gap for silicon 1.10 eV.

**2.1. Open-circuit voltage**

The following mathematical models of electrical characteristics are considered to design

The open-circuit voltage, VOC, is the extreme voltage offered from a PV cell, and this happens at zero current. The open-circuit voltage links to the amount of forward bias on the PV cell

where V is the open-circuit voltage, N is diode ideality constant, K is the Boltzmann constant (1.381\*10^-23 J/K), T is temperature in Kelvin, Q is electron charge (1.602\*10^-19 c), IL is the

ILref is the photoelectric current under standard condition 0.15 A, TCref is module temperature under standard condition 298 K, αISC is the temperature coefficient of the short-circuit

where Io is the reverse saturated current, Ior is the saturation current, N is the ideality factor

Ish = IL. It is the extreme value of the current produced by a PV cell. It is formed by the short

QE \_\_\_\_g KN )∗( \_\_1 Tr −\_\_1

+ 1 Volt (1)

∗ (ILref + αIsc(Tc − Tc ref)) (2)

<sup>T</sup>)) (3)

exp(Vocn <sup>⁄</sup> NVtn) (4)

NKT ) − 1)) (5)

,

), Gref is the radiation under standard condition 1000 W/m2

*<sup>Q</sup> in I <sup>L</sup>* <sup>−</sup> *<sup>I</sup>* \_\_\_\_*<sup>o</sup> I o*

light-generated current same as Iph (A), and Io is the saturation diode current (A).

Gref

current (A/K) = 0.0065/K, and IL is the light-generated current (radiation).

20 kW photovoltaic module and simulated using MATLAB environment:

due to the bias of the PV cell junction with the light-generated current [5, 6]:

G = radiation W/m2 (**Figures 1** and **2**).

**Figure 1.** PV—Voltage vs. current characteristics.

**Figure 2.** PV—Power vs. voltage characteristics.
