# Online Learning-Based ANN Controller for a Grid-Interactive Solar PV System
## 3 DC Link Voltage of the VSC from the Solar PV System  
Solar PV distributed generation systems generate DC voltage and are dependent on climatic conditions such as temperature and irradiance. As these climatic conditions vary frequently, PV panels also generate variable DC voltages, which are not suitable for any application. It needs to be stabilized by generating constant voltage. This can be accomplished by tracking the maximum power from the sun, irrespective of climatic conditions. For that purpose, DC-DC boost converters are required. They not only boost the voltage levels, but they also maintain constant, irrespective of temperature and irradiances of the sun. Different DC-DC boost converters are discussed in this paper, as shown in Figure 2, and it was concluded that the performance of the super-lift positive Luo converter was better than the other two converters, as shown in Figure 3. P&O and incremental conductance methods were used to track maximum power and between them, the incremental method was considered the best.  
Figure 3: _Cont_.  
Figure 2: Different DC–DC boost converters and MPPT techniques.  
The circuit diagram of the super-lift Luo DC-DC converter, as shown in Figure 4a, was analyzed in detail using the state model. During the ON state, as shown in Figure 4b, inductor L and capacitor C1 are charged, as diode D1 is in forward bias. Capacitor C2, which is already charged, delivers the current to the load R. During the OFF state, as shown in Figure 4c, diode D1 is off and diode D2 is on. L and C1 discharge through C2 and address the load demand.  
Figure 4: _Cont._  
Figure 3: (**a**) Efficiency of three converters; (**b**) voltage gain of three converters.  
The differential equations representing the ON state are:  
\[\frac{\mathrm{di_{L}}}{\mathrm{dt}}=-\frac{\mathrm{r_{L}}}{\mathrm{L}}\mathrm{i_ {L}}+\frac{1}{\mathrm{L}}\mathrm{v_{in}} \tag{1}\]  
\[\frac{\mathrm{d}\mathrm{v_{C1}}}{\mathrm{dt}}=-\frac{1}{(\mathrm{r_{C1}C_{1}}) }\mathrm{v_{C1}}+\frac{\mathrm{v_{in}}}{\mathrm{r_{C1}C_{1}}} \tag{2}\]  
\[\frac{\mathrm{d}\mathrm{v_{C2}}}{\mathrm{dt}}=-\frac{1}{(\mathrm{R+r_{C2}}) \mathrm{C_{2}}}\mathrm{v_{C2}} \tag{3}\]  
\[\mathrm{v_{o}}=-\frac{\mathrm{R}}{(\mathrm{R+r_{C2}})\mathrm{C_{2}}}\mathrm{v _{C2}} \tag{4}\]  
The differential equations representing the OFF state are:  
\[\frac{\mathrm{di_{L}}}{\mathrm{dt}}=-\frac{1}{\mathrm{L}}\bigg{(}\mathrm{r_{L }}+\mathrm{r_{C1}}+\frac{\mathrm{r_{C2}R}}{\mathrm{R+r_{C2}}}\bigg{)}\mathrm{i_ {L}}+\frac{1}{\mathrm{L}}\mathrm{v_{C1}}-\frac{\mathrm{R}}{\mathrm{L}(\mathrm{ R+r_{C2}})}\mathrm{v_{C2}}+\frac{1}{\mathrm{L}}\mathrm{v_{in}} \tag{5}\]  
\[\frac{\mathrm{d}\mathrm{v_{C1}}}{\mathrm{dt}}=-\frac{1}{\mathrm{C_{1}}}\mathrm{ i_{L}} \tag{6}\]  
\[\frac{\mathrm{d}\mathrm{v_{C1}}}{\mathrm{dt}}=-\frac{1}{\mathrm{C_{1}}}\mathrm{ i_{L}} \tag{7}\]  
\[\mathrm{v_{o}}=\frac{\mathrm{r_{C2}R}}{(\mathrm{R+r_{C2}})}\mathrm{i_{L}}+ \frac{\mathrm{R}}{(\mathrm{R+r_{C2}})}\mathrm{v_{C2}} \tag{8}\]  
Three state variables were considered, i.e., the current through the inductor and the voltages across the two capacitors. State equations were formulated and the transfer function of the converter was obtained, as shown in the equations.  
\[\frac{\hat{v}_{o}(s)}{\hat{v}_{in}(s)}=\frac{495s^{2}+6.93\times 10^{6}s+9.28 \times 10^{9}}{s^{3}+3819s^{2}+7.22\times 10^{6}s+3.52\times 10^{9}} \tag{9}\]  
Using the transfer function approach, stability analysis of the super-lift converter was performed using the Bode plot method, which is a frequency domain testing method. As shown in Figure 5, it was observed from the plot that the gain margin and phase margin were positive, meaning the system was stable in nature; hence, the positive-lift Luo converter was used to boost the voltage from the solar panel and given as the DC link voltage for the grid-interactive VSC.  
Figure 4: (**a**) Circuit diagram of the super-lift Luo Converter; (**b**) circuit when S is ON; (**c**) circuit when S is OFF