## 4 Simulation and Results  
In this section, a simulation study using PSIM software (2024.1) is presented to validate both the design procedure of the series resonant converter and the proposed ESC algorithm  
Figure 10: The overall control diagram of the system with the series resonant converter and the extremum-seeking controller. formulated for the series resonant converter. The characteristics of the PV panel shown in Figure 11 are the ones used for this design case. The PV panel has I_V curves under different irradiance levels, as shown in Figure 11 and Table 1.  
The battery was represented with a simple model that consisted of a voltage source and a series resistance, and the voltage source was changed for different simulation cases. For a 24 V battery, a minimum voltage of 24 V was considered and a series resistor of 0.05 \(\Omega\) was included. A maximum voltage of 28 V could be considered for simulating a high state of charge (SOC). These values can be adjusted for specific battery specifications, but for a 24 V battery pack, they are typically representative. The design procedure in Figure 9 can now be applied using the system parameters shown in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Irradiance** & **VMPP** & **IMPP** & **PMPP** \\
**W/m\({}^{2}\)** & **(V)** & **(A)** & **(W)** \\ \hline
1000 & 34 & 6.03 & 205 \\
800 & 34 & 4.85 & 165 \\
700 & 34 & 4.26 & 145 \\
300 & 33.5 & 1.82 & 61 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PV panel MPPs under different irradiance levels. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\mathbf{P_{PVmin}}\approx\mathbf{61}\)**W** & \(\mathbf{P_{PVmax}}\approx\mathbf{205}\)**W** \\ \hline \(V_{BATmin}\) & & 24 & \\ \(V_{BATmax}\) & & 28 & \\ \(V_{PV}\) & 33 V min & & 34 V max \\ \(M_{MAX}\) & & 0.8484 & \\ \(M_{MIN}\) & & 0.7647 & \\ \(F_{n}\) & & 1–1.2 & \\ \(Q_{min}\) & & 3 & \\ \(Q_{max}\) & & 13 & \\ \(L_{r}\) & & 122.7 uH & \\ \(C_{r}\) & & 82.5 nF & \\ \(\omega_{r}\) & & \(314.16\times 10^{3}\) rad/s & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: System and simulation parameters. Figure 11: I_V characteristics of simulated PV panel. For the given PV parameters and a battery voltage of 26 V, the expected operating points of the designed system when tracking maximum power are shown in Figure 12. It can be seen that the change in the switching frequency required to match the desired voltage gain is well within the specified range of 20%, and the required voltage gain is also achievable. These parameters can now be simulated, and different scenarios can be implemented to validate the operation of the converter and the algorithm. The first case shows the system at a 1000 W/m\({}^{2}\) irradiance level, and the battery voltage is at its minimum level of 26 V. It can be seen in Figure 13 that the converter is successfully tracking and extracting the maximum available power with stable output. The irradiance level is then stepped down to 800 W/m\({}^{2}\) at 0.075 s, and the converter responds appropriately, continuing to track and extract the new available power, which is around 165 W.  
The converter in this case is operating at a frequency higher than the resonant frequency and zero-voltage switching is achieved, as seen in Figure 14.  
The next case (Figure 15) shows a starting irradiance level of 700 W/m\({}^{2}\) and an MPP of 142 W, where the resonant converter is tracking well. Then, at 0.15 s the irradiance level is stepped up to 1000 W/m\({}^{2}\). It can be seen that the converter is following the reference in both step-up and step-down scenarios. In addition to stepping the irradiance, a step increase to the battery voltage was introduced to check whether the converter would track the MPPT under load-side variations. The battery voltage was stepped from 26 to 27.5 volts and the converter exhibited a quick adjustment in output voltage to maintain maximum power at the same level. Figure 16 shows the step increase at 0.15 s.