# A Novel Real-Time PV Error Handling Exploiting Evolutionary-Based Optimization
## 3 Methodology
### Maximum Power Point Tracking  
The output power of a PV module is given by [PERSON]'s law [24] and the I-V and P-V diagrams are presented in Figures 2 and 3:  
\[P=VI, \tag{7}\]  
where P, V, and I are the output power, voltage, and current of the PV module, respectively. According to (4), (6) can be rewritten as follows:  
\[P=N_{p}I_{ph}V-N_{p}I_{s}V\left[e^{(\frac{\mu_{e}(V+IR_{s})}{\mu_{e}RTN_{s}})}-1 \right]-\frac{V^{2}+IR_{s}V}{R_{p}}, \tag{8}\] \begin{table}
\begin{tabular}{l l l l} \hline
**Parameters** & **Description** & **Unit** & **Parameter Range** \\ \hline \(N_{p}\) & No. of cells connected in & unitless & \(>\)0 \\  & parallel in a PV module & & \\ \(N_{s}\) & No. of cells connected in & & \\  & series in a PV module & unitless & \(>\)0 \\ \(I_{ph}\) & Photo-generated current & A & 0 to saturation current \\ \(I_{s}\) & Diode’s saturation current & A & \(10^{-14}\)-\(10^{-17}\) A / \(\mu\)m\({}^{2}\) \\ \(I_{d}\) & Diode’s current & A & \(-10^{-9}\) to 2 \\ \(V_{t}\) & Diode’s thermal voltage & V & 2 mV-30 mV \\ \(R_{p}\) & Parallel resistance & Ohm & 0 to smallest resistance \\ \(R_{s}\) & Series resistance & Ohm & 0.2 Ohm to 20 Ohm \\ \(k\) & Boltzmann constant & J/K & 1.381 \(\cdot 10^{-23}\) J/K \\ \(n\) & Diode’s ideality factor & unitless & 1–2 \\ \(I\) & PV’s output current & A & \(0\leq IN_{p}\leq I_{sc}N_{p}\) \\ \(V\) & PV’s output voltage & V & \(0\leq VN_{S}\leq V_{oc}N_{s}\) \\ \(P\) & PV’s output power & W & \(0\leq P_{n}N_{p}N_{s}\) \\ \(q_{e}\) & Elementary charge & C & \(1.602\cdot 10^{-19}\) C \\ \(\mu_{I_{sc}},\mu_{V_{sc}}\) & Temperature coefficients for & (\(I/^{\circ}\)C, \(V/^{\circ}\)C) & 0.04 to 0.5, \(-0.3\) to \(-0.5\) \\  & current and voltage, respectively & & \\  & Solar irradiance and irradiance & & \\ \(G,G_{ST}\) & at standard conditions (1000 W/m\({}^{2}\)) & W/m\({}^{2}\) & \(<\)1000 W/m\({}^{2}\), 1000 W/m\({}^{2}\) \\  & Temperature of PV module and standard & & \\ \(T,T_{ST}\) & test values for temperature (25 \({}^{\circ}\)C) & & 25 \({}^{\circ}\)C to 50 \({}^{\circ}\)C, 25 \({}^{\circ}\)C \\  & Voltage of PV module and standard & & \\ \(V_{oc},V_{oc,ST}\) & test values for temperature (25 \({}^{\circ}\)C) & & \(0\leq V_{oc}N_{s}\leq V_{oc},stN_{s}\) \\  & Current of PV module and standard & & \\ \(I_{sc},I_{sc,ST}\) & test values for temperature (25 \({}^{\circ}\)C) & & \(0\leq I_{sc}N_{p}\leq I_{sc},stN_{p}\) \\ \hline \end{tabular}
\end{table} 
Table 1: PV modeling parameters. The PV module's output voltage and current of the photovoltaic module have a maximum value depending on irradiance and temperature. The voltage's maximum value results when no electric loads are connected to the module's output (open-circuit situation), and the current's maximum value results when the module's output is short-circuited (short-circuit situation). The equations that connect the short circuit current (output current's maximum value) and the open circuit voltage (output voltage's maximum value) with irradiance and temperature are [25]. \[I_{sc}=I_{sc}(G,T)=\frac{G}{G_{ST}}\big{[}I_{sc,ST}+\mu_{I_{sc}}(T-T_{ST})\big{]} \tag{9}\]  
\[V_{oc}=V_{oc}(G,T)=V_{oc}(T)+nV_{t}\ln(\frac{G}{G_{ST}}), \tag{10}\]  
where  
\[V_{oc}(T)=V_{oc,ST}+\mu_{V_{oc}}(T-T_{ST}), \tag{11}\]  
where the following apply:  
* \(G_{ST}=1000\) W/m\({}^{2}\), \(T_{ST}=25\)\({}^{\circ}\)C, \(I_{sc,ST}\), \(V_{oc,ST}\) are the standard test values for irradiance, temperature, short circuit current, and open circuit voltage, respectively. * \(G\), \(T\), \(I_{sc}\), \(V_{oc}\) are the actual values for the irradiance, temperature, short circuit current, and open circuit voltage, respectively. * \(\mu_{I_{sc}}\), \(\mu_{V_{oc}}\) are the temperature coefficients for current and voltage, respectively. The power output of the photovoltaic module is maximized, according to (4). The solution has only one global maximum point, the maximum power point (MPP), and it depends on irradiance and temperature.