# A State-of-Art-Review on Machine-Learning Based Methods for PV
## 6 The Latest Research on MPPT in PV

Table 6: \(Cont.\)methods have been proposed for better transient and steady-state performance. Intelligent techniques (i.e., FL and ANN-based MPPT methods) are more efficient and they have fast responses, but they are more complex compared to the conventional techniques that are generally simple, cheap and less efficient [91]. ANN-based methods have shown their advantages under rapidly varying irradiance [92], especially regarding response efficiency. However, despite their higher efficiency, these advanced heuristic approaches are much more complex compared to the conventional techniques. The performance of the ML approaches is heavily dependent on the accuracy of the trained model that is determined by the quality of training data, and frequent calibration is needed as the system evolves. In Table 7, several papers that use ML approaches to improve MPPT performance have been analyzed. They have been ordered based on the year of publication. In particular, the table is useful to underline the ML method that has been used most frequently and the results that the different approaches allow to obtain. Unfortunately, results are not always presented in such a way they can be compared with other similar papers. In particular, some papers present results comparing the value of the power that the proposed solution allows reaching with the value of the power of the global MPP [77; 93; 94; 95]. In these cases, to compare results obtained in the different papers, the ratio between the reached power, \(P_{\textit{reached}}\), and that one that should be obtained, \(P_{\textit{GMPP}}\), has been calculated as:  
\[MPP\_ratio=\frac{P_{\textit{reached}}}{P_{\textit{GMPP}}}\cdot 100 \tag{1}\]  
In some papers, other statistical errors have been used to compare the reached power with that one at MPP: the Mean Error (\(ME\) in Equation (2)) [96], the Mean Square Error (\(MSE\) in Equation (3)) [96], the Standard Deviation error (\(\sigma\) in Equation (4)) [96], the Root Mean Square Error (\(RMSE\) in Equation (5)) [76; 97], means absolute error (\(MAE\) in Equation (6)) [97], the overall power tracking efficiency (\(\eta\) in Equation (7)) [98] and a quality indicator that provides information about the ability of the ANN to predict the MPP (\(QI1\) in Equation (8)) [99]:  
\[ME=\frac{1}{N}\cdot\sum_{i=1}^{N}(P_{\textit{GMPP}}-P_{\textit{reached}}) \tag{2}\]  
\[MSE=\frac{1}{N}\cdot\sum_{i=1}^{N}(P_{\textit{GMPP}}-P_{\textit{reached}}) ^{2} \tag{3}\]  
\[\sigma=\sqrt{\frac{1}{N}\cdot\sum_{i=1}^{N}(P_{\textit{GMPP}}-\mu)^{2}} \tag{4}\]  
\[RMSE=\sqrt{\frac{1}{N}\cdot\sum_{i=1}^{N}(P_{\textit{GMPP}}-P_{\textit{ reached}})^{2}} \tag{5}\]  
\[MAE=\frac{1}{N}\cdot\sum_{i=1}^{N}|P_{\textit{GMPP}}-P_{\textit{reached}}| \tag{6}\]  
\[\eta=\frac{\int_{0}^{t}P_{\textit{reached}}(t)\cdot dt}{\int_{0}^{t}P_{ \textit{GMPP}}(t)\cdot dt}\cdot 100 \tag{7}\]  
\[\text{QI1}=1-\frac{1}{N}\cdot\sum_{i=1}^{N}\frac{P_{\textit{reached}}}{P_{ \textit{GMPP}}} \tag{8}\]  
\[EI=\frac{1}{N}\cdot\sum_{i=1}^{N}\frac{P_{\textit{GMPP}}-P_{\textit{reached }}}{P_{\textit{GMPP}}} \tag{9}\]  
where \(N\) is the number of tests and \(\mu\) is the average of the reached values.