## 5 Control Algorithm and Numerical Analysis  
In Figure 4, the total system control diagram is reported consistently with the technique discussed in the previous paragraphs. As the measurement of the capacitor voltage is influenced by the modulation and contains oscillations linked to the switching frequency, a low pass filter is implemented for the processing of \(v_{c}\). This additional signal processing is needed in order to avoid false detections of hysteresis thresholds crossing. The control strategy of the proposed system has been tested by performing an extensive numerical analysis in the Matlab Simulink TM environment. The parameters' values used in the simulation are reported in Table 2.  
Figure 4: Control diagram of a grid connected PV generation system via an interleaved inverter. In this context, the ideal voltage/current characteristic of the PV array has been replaced by a real one based on the commercial multicrystal modules: KIOCERA KC175 GHT-2 (see Figure 5). Moreover, a detailed dynamic model of the chosen IGBTs has been implemented (SEMIKRON SKM400 GB176D). The Simulink model of the whole controlled system is reported in Figure 6, where it is possible to distinguish between four main sections: the PV array, the interleaved converter, the electric grid, and the control algorithm. Except for the electric grid, for which a standard Simulink block has been used, the other subsystems have been implemented by means of C-language S-Functions. In particular, for the models of the PV cells and forthe IGBTs, continuous states of S-Functions have been used, while the control algorithm has been implemented as a discrete S-Function, which is computed at the sampling rate of 200 us. The whole time window simulation results are reported in Figure 7. The simulation interval (225 s) can be split into four sub-intervals, which are as follows:  
* With a solar radiance kept constant at 1000 W/m\({}^{2}\), the control of the converter is activated at \(t=0\). * At \(t=110\) s, the solar radiance starts decreasing linearly with a slope of 50 W/m\({}^{2}\)s\({}^{-1}\), until it reaches 250 W/m\({}^{2}\). * At \(t=150\) s, a fault occurs in the lower module of the two channel interleaved converter. * At \(t=170\) s, the solar radiance starts increasing linearly with a slope of 50 W/m\({}^{2}\)s\({}^{-1}\), until it reaches 1000 W/m\({}^{2}\)  
Figure 7a shows the PV power \(P_{p}\), the grid power \(P_{s}\), and the solar radiation \(P_{sr}\) in the whole time range of the numerical analysis. It can be seen that the PV power follows the MPP with good transient behavior, either in correspondence of the standard condition (1000 W/m\({}^{2}\)) or during the fast varying shading conditions. After the fault event, the grid power \(P_{s}\) remains practically constant, except for a really quick transient induced by the dynamic of the operating converter, whose currents have to compensate for the faulted one. Finally, when the solar radiation starts to increase, the steady state condition is reached at a value of power that is lower than the MPP, as the power limit has been activated on the remaining converter. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Description** & **Symbol** & **Value** & **Description** & **Symbol** & **Value** \\ \hline Inverter rated power & \(P_{c,R}\) & 200 kW & PV filter capacitance & \(C\) & 14 mH \\ Phase to phase rated grid voltage & \(V_{s,R}\) & 400 V & PV filter inductance & \(L\) & 400 uH \\ Rated grid frequency & \(f\) & 50 Hz & Modulation period & \(T_{m}\) & 400 us \\ Interlaced converter inductance & \(L_{R}\) & 1 mH & Sampling time & \(T_{s}\) & 200 us \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main parameters of the system. Figure 5: Characteristic of the chosen PV module. In Figure 7b, the capacitor voltage variation with respect to 700 V is shown (\(\Delta v_{c}=v_{c}-700\)), together with the capacitor voltage time derivatives.