## 7 Experimental Investigation
### Results  
The experiments are divided into two stages--preliminary testing and comparative testing. In the preliminary testing stage, experiments were conducted to derive the relationships between \(\mathrm{K_{PU}}\) and \(\mathrm{V_{in}}\) as well as \(\mathrm{K_{PL}}\) and \(\mathrm{V_{in}}\) for the online tuning module as described in Section 4. The selection of \(\mathrm{K_{PU}}\) and \(\mathrm{K_{PL}}\) was made in a manner that would balance the capacitor voltages at a given \(\mathrm{V_{in}}\) that is adjusted between 0 V and 300 V. In order to carry out this selection, a trial-and-error method was adopted. This approach is preferred because it involves actual measurement of the output current THD using a power analyzer for a given \(\mathrm{V_{in}}\) to derive the optimum values of \(\mathrm{K_{PU}}\) and \(\mathrm{K_{PL}}\). The optimum values refer to \(\mathrm{K_{PU}}\) and \(\mathrm{K_{PL}}\) values that are associated with the lowest output current THD measured for every \(\mathrm{V_{in}}\). The use of actual measurement improves the accuracy and credibility of the \(\mathrm{K_{PU}}\) and \(\mathrm{K_{PL}}\) selected since no ideal condition is assumed, and thus, the error that is due to the assumptions and estimation made in an ideal condition can be minimized. In addition, when the optimum \(\mathrm{K_{PU}}\) and \(\mathrm{K_{PL}}\) are used, the controller is able to run at the optimum operating point, which in turn enables the best output performance of the inverter to be retained. This is critical since in most cases, changes in \(\mathrm{V_{in}}\) would likely cause the controller to deviate from its optimum operating point since the reference voltages for the capacitors also change. As a result, the performance of the multilevel inverter may deteriorate. While the values of \(\mathrm{K_{PU}}\) and \(\mathrm{K_{PL}}\) are varied, the values of \(\mathrm{K_{LU}}\) and \(\mathrm{K_{IL}}\) are not required to be changed. This helps reduce complexity in the proposed tuning scheme. By using the MATLAB curve-fitting tool, the relationships between \(\mathrm{K_{PU}}\) and \(\mathrm{V_{in}}\) as well as \(\mathrm{K_{PL}}\) and \(\mathrm{V_{in}}\) are formed. Based on the established relationships, five equations are derived for \(\mathrm{K_{PU}}\) in the upper part of the buck-boost converter at every \(\mathrm{V_{in}}\) change between 0 V and 300 V, as explained in Section 4. A similar method applies to the lower part of the converter. Hence, with the application of online tuning mechanism, the proposed PI controller attempts to keep \(\mathrm{V_{1}}\), \(\mathrm{V_{2}}\), \(\mathrm{V_{3}}\) and \(\mathrm{V_{4}}\) balanced via the adjustment of the proportional gain only without modifying the integral gain and the anti-windup parameters. In the comparative testing stage, the performance of the proposed controller and the conventional controller are analyzed and compared. Here, two experimental conditions have been assessed. In the first condition, experiments with the proposed controller were performed. On the other hand, the conventional controller was applied for the second condition. Similar parameters were used in both conditions, as displayed in Table 1. Figure 13 displays the step response and steady-state performances when the online tuning mechanism is applied. The results show that the proposed online tuning mechanism is able to maintain all capacitor voltages around their reference values between 15 V and 50 V when \(\mathrm{V_{in}}\) changes between 60 V and 200 V. The rise time, peak time and settling \begin{table}
\begin{tabular}{c c} \hline
**Component** & **Values** \\ \hline DC-link capacitor & 2200 μF \\ Inductor of buck-boost converter & 12 mH \\ R load & 120 \(\Omega\) \\ L load & 69 mH \\ \hline \end{tabular}
\end{table} 
Table 1: Values of circuit components. time are recorded as 6, 8 and 12 ms, respectively. For the step-down response, the fall time is measured as 6 ms. The percent overshoot is calculated as 6%.