# On Transient Stability Problems in DC Microgrids
## 4 Experimental Verifications  
This section provides experimental results for validation purposes. The experimental setup, as shown in Figure 7, consists of a grid-tied DC-DC converter that is powered by a lithium battery module comprising 15 cells. The converter is regulated by a DSP (TI LAUNCHXL-F28379D) (Texas Instruments, Dallas, TX, USA), ensuring efficient and reliable operation. The experimental parameters of DC microgrids are listed in Table 1. While the experiment employed a lithium battery module as the power source, the underlying principles and the theoretical framework of this article are not inherently limited to this particular type of DC source. The key aspects that govern the transient stability, such as the power-transfer limitations, equilibrium points, and the influence of different control strategies, are largely independent of the specific DC source technology. To evaluate the performance of PI power-controlled DC generators, two equilibrium points were identified based on (5). These equilibrium points are \(v_{\text{c1\_d  
Figure 6: \(\text{d}v_{\text{c}}/\text{d}t\) as a function of \(v_{\text{c}}\) with droop control. \(\
u_{\text{c2\_PI}}=8.23\) V, respectively. Additionally, the minimum power injection was found to be \(p_{\text{c\_min}}=-75\) W according to (6). In contrast to the PI power-controlled DC generators, droop-controlled DC generators exhibited different characteristics. The two equilibrium points for this type of generator were determined based on (9) as \(v_{\text{c1\_droop}}=26.83\) V and \(v_{\text{c2\_droop}}=-26.83\) V, respectively, showcasing their ability to maintain voltage stability under varying load conditions. Furthermore, the minimum power injection \(p_{\text{c\_min}}=-300\) W achieved by droop-controlled DC generators was calculated based on (10). These experimental findings provide valuable insights into the performance and capabilities of both PI-power-controlled and droop-controlled DC generators in grid-tied systems with lithium battery modules. By comparing their respective equilibrium points and minimum power injections, researchers can gain a deeper understanding of how these control strategies impact system dynamics. Moving on to Figure 8, it presents the experimental results of another PI power-controlled DC generator. The focus here was on examining its ability to handle disturbances in \(v_{\text{c}}\), specifically small and large disturbances. The findings revealed that while the generator could ride through a small \(v_{\text{c}}\) disturbance, it failed to undertake a large \(v_{\text{c}}\) disturbance. This suggests that there are limitations in terms of handling significant fluctuations in voltage for this particular control strategy. In contrast, Figure 9 illustrates the experimental results of a droop-controlled DC generator under similar conditions as before but with an enlarged stable region due to its unique control mechanism. When subjected to the same large \(v_{\text{c}}\) disturbance as in previous experiments, this droop-controlled DC generator remained stable throughout. These results align well with theoretical analysis and highlight the advantages offered by droop control in terms of stability during voltage disturbances. Figure 10 shows the experimental waveforms of the converter voltage ( \(v_{\text{c}}\)), current (\(i_{c}\)), and power of a PI power-controlled DC generator with \(p_{\text{c\_ref}}\) changing from \(-60\) W to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Descriptions** & **Symbols** & **Values** \\ \hline DC grid voltage & \(v_{\text{g}}\) & \(30\) V \\ Converter voltage reference & \(v_{\text{c\_ref}}\) & \(30\) V \\ Line resistance & \(R_{c}\) & \(3\)\(\Omega\) \\ Active power reference & \(p_{\text{c\_ref}}\) & \(-60/-80\) W \\ Power P gain & \(k_{\text{PP}}\) & \(0.1\) V/W \\ Power I gain & \(k_{\text{RI}}\) & \(0.1\) V/J \\ Droop coefficient & \(k_{\text{droop}}\) & \(0.1\) V/W \\ Cut-off frequency & \(\omega_{\text{c}}\) & \(10\) rad/s \\ \hline \hline \end{tabular}
\end{table}