**2. Mathematical modelling of PV system**

The following mathematical models of electrical characteristics are considered to design 20 kW photovoltaic module and simulated using MATLAB environment:

#### **2.1. Open-circuit voltage**

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

$$V = \frac{\text{NKT}}{\text{Q}} \cdot \text{in} \frac{I\_{\text{L}} - I\_{\text{s}}}{I\_{\text{s}}} + 1 \text{ Volt} \tag{1}$$

**2.5. Irradiation**

G = radiation W/m2

(**Figures 1** and **2**).

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

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

**3. Maximum power point tracking (MPPT) for photovoltaic system**

power generation at various weather conditions.

for 20 kW PV system.

Renewable energy sources play an important role in meeting consumer power demand due to their abundant availability and lesser impact on the environment [5]. The main hurdle in PV energy expansion is the investment cost of the PV power system implementation. PV energy generation is not constant throughout the day due to the changes in weather. The efficiency of power generation is very low (the range of efficiency is only 9–17% in low irradiation regions). Therefore, MPPT technologies have an important role in PV power generation for optimal

Fuzzy Controller-Based MPPT of PV Power System http://dx.doi.org/10.5772/intechopen.80065 63

In this chapter, we have discussed and analysed fuzzy logic controller-based MPPT controller

The proposed fuzzy-based MPPT block diagram is shown in **Figure 3**. **Figure 4** presents the structure of the fuzzy controller that has two inputs and one output. The fuzzy membership function has been designed by trapezoidal method for both input and output membership values. The defuzzification of proposed fuzzy controller has been used for centre of gravity. The MPPT fuzzy controller has two inputs such as PV voltage and PV current shown in **Figures 5** and **6**, respectively. The MPPT fuzzy controller generates a duty cycle based on input of fuzzy controller and is fed into boost converter shown in **Figure 7**. Finally, the fuzzy interference rules are designed based on changes in PV voltage

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

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

$$\mathbf{I}\_{\perp} = \frac{\mathbf{G}}{\mathbf{G}\_{nd}} \ast \left(\mathbf{I}\_{\perp nd} + \alpha\_{\text{loc}} (\mathbf{T}\_c - \mathbf{T}\_{cnd})\right) \tag{2}$$

where G is the radiation (W/m2 ), Gref is the radiation under standard condition 1000 W/m2 , 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 current (A/K) = 0.0065/K, and IL is the light-generated current (radiation).

#### **2.3. Reverse saturation current**

$$\mathbf{I}\_o = \mathbf{I}\_{ox} \* (\mathbf{\bar{\cdot}} \mathbf{\bar{\cdot}} \mathbf{\bar{\cdot}})^3 \exp\left(\frac{(\mathbf{\bar{\cdot}} \mathbf{\bar{\cdot}})^\*(\mathbf{\bar{\cdot}} \mathbf{\bar{\cdot}})}{(\mathbf{\bar{\cdot}} \mathbf{\bar{\cdot}})^\*}\right) \tag{3}$$

$$\mathbf{I}\_{\rm om} = \frac{\rm{Isc}}{\exp^{(\ell\_{\rm e}\,\prime\prime)}}\tag{4}$$

where Io is the reverse saturated current, Ior is the saturation current, N is the ideality factor 1.5, and Eg is the band gap for silicon 1.10 eV.

#### **2.4. Short-circuit current**

Ish = IL. It is the extreme value of the current produced by a PV cell. It is formed by the short circuit-situation: V = 0.

$$\mathbf{I}\_{\rm sh} = \mathbf{I}\_{\rm l} - \mathbf{I}\_{\rm o} \left( \left( \exp^{\left( \mathbf{Q}\_{\rm NKT}^{V \rm R} \right)} - 1 \right) \right) \tag{5}$$
