## 2 Review of PV Model and MPPT Control Methods
### Review of MPPT Control Methods
#### 2.2.4 Artificial Neural Network (ANN)  
An artificial neural network (ANN) is a form of machine learning algorithm that mimics the structure and function of the human brain. Neural networks are built using input layers of cells (neurons), output layers, and several hidden layers of densely interconnected neurons. Each neuron has a variable activation gain, or weight, given by a non-linear function, that is tuned during the learning (training) process. As a result, some neurons are more active than others in the inputs, hidden layers, and outputs, resulting in distinct output signals according to the tuning obtained from the applied training. Therefore, one of the most significant aspects of neural networks is the quantity and quality of the existing training data, which influence the quality of the neural network outcomes after training.  
In MPPT, neural networks can be used in a variety of ways [19; 20; 21; 22]. They can be trained using irradiance and temperature datasets [19; 22] or datasets generated via alternative methods, such as P&O or FL [20; 21].  
Implementations based on irradiance and temperature are very accurate in simulation, but they have several drawbacks in practice. For each PV model, the neural network must be trained in order to tune the neuron gains. Additionally, irradiance and temperature sensors are expensive and difficult to calibrate [41]. Another disadvantage can occur if the PV is dusty or shadowed while the irradiance sensor is not, or vice versa. In this case, the irradiance- and temperature-trained ANN has reduced performance, since the sensor data do not correspond to the actual panel irradiance.  
The work conducted in [21] represents an example of training using the P&O approach, while [20] presents an ANN trained using the fuzzy logic method. These approaches often do not require additional sensors, instead employing the sensors from the DC/DC converter (current and voltage), which contributes to cost savings.  
The number of neurons and hidden layers of a neural network is often determined empirically [42], as it depends on the problem's complexity. The number of hidden layers should be balanced, because while more hidden layers can increase the performance of the neural network, too many layers may result in the network reaching a local minimum rather than a global minimum [42].  
As approaches based on irradiance and temperature are frequently investigated in the literature [19; 22], a neural network trained with a dataset based on these parameters  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fuzzy Rule**} & \multicolumn{6}{c}{**S(k)**} \\ \cline{2-7}  & **NB** & **NS** & **ZE** & **PS** & **PB** \\ \hline \multirow{4}{*}{\(\Delta\)**S(k)**} & **NB** & ZE & PB & PS & ZE & NB \\  & **NS** & PB & PS & ZE & ZE & NB \\  & **ZE** & PB & PS & ZE & NS & NB \\  & **PS** & PB & ZE & NZ & NS & NB \\  & **PB** & PB & ZE & NS & NB & ZE \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fuzzy rule table based on [5].  
Figure 6: Fuzzy logic membership functions.  
(ANN (G, T)) was evaluated in this work. The dataset was created using only MPP PV current values, for irradiances between 0 W/m\({}^{2}\) and 1000 W/m\({}^{2}\) with steps of 50 W/m\({}^{2}\), and at temperatures between 0 \({}^{\circ}\)C and 80 \({}^{\circ}\)C with steps of 5 \({}^{\circ}\)C. Although the PV equations produce non-linear I-V and P-V characteristics, the current values in the MPP have a linear relationship with irradiance and temperature (Figure 7), making the problem straightforward. In this case, only one hidden layer with 10 neurons was needed. This implementation achieved good results.