# Data-Driven Voltage Control in Isolated AC Microgrids Subject to Sensor Saturation
## 4 Simulation Results
### Quantitative Performance Analysis and Discussion  
To provide a rigorous statistical evaluation of the proposed DAILC method, we introduce several quantitative performance metrics as suggested: Root Mean Square Error (RMSE) for steady-state voltage tracking, convergence time after a disturbance, and robustness assessed by steady-state error fluctuation under measurement noise. We compare the performance of our DAILC method against a conventional distributed PI controller, which serves as a baseline. The results are summarized in Table 3.  
The quantitative analysis, summarized in Table 3, reveals the superior performance of the DAILC method across several key metrics. Regarding tracking accuracy, the DAILC method consistently achieves a significantly lower Root Mean Square Error (RMSE)--0.08 V, 0.11 V, and 0.09 V across the three scenarios--compared to the PI controller's 0.25 V, 0.32 V, and 0.28 V. In terms of transient performance, the DAILC method also excels in convergence time, which measures the duration for the system voltage to settle within a \(\pm\)0.5% tolerance band of the reference after a major disturbance. In Case 4.2 and Case 4.3, the DAILC method's convergence times of 0.18 s and 0.21 s are more than twice as fast as the PI controller, highlighting its superior adaptive response. Moreover, the DAILC's robustness against noise was demonstrated by its ability to maintain a steady-state error fluctuation range of only \(\pm\)0.15 V when white Gaussian noise was injected, whereas the PI controller exhibited larger fluctuations of \(\pm\)0.40 V. Finally, to confirm the statistical significance of these findings, 20 Monte Carlo runs for Case 4.1 established a tight 95% confidence interval (CI) of [0.076, 0.084] for the DAILC method's RMSE, which is distinctly separate from the PI controller's CI of [0.241, 0.259], thereby validating that its superior performance is statistically significant. The proposed DAILC method is demonstrably superior to conventional PI control in terms of accuracy, speed, and robustness. To address the crucial question of scalability, we analyze the communication and computational demands of the DAILC algorithm when applied to larger systems (e.g., 20+ DREGUs). The algorithm's distributed nature is key to its scalability. The communication burden on an individual DREGU is determined by its number of direct neighbors (the  
Figure 7: System performance when topological change. (a) Output voltage amplitude. (b) Output voltage error. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Metric** & **Case** & **DAILC** & **PI** \\ \hline \multirow{3}{*}{RMSE (V)} & 4.1: Sensor Saturation & 0.08 & 0.25 \\  & 4.2: Variable Load & 0.11 & 0.32 \\  & 4.3: Topology Change & 0.09 & 0.28 \\ \hline \multirow{3}{*}{Convergence Time (s)} & 4.2: Load Added & 0.18 & 0.45 \\  & 4.3: DG4 Removed & 0.21 & 0.52 \\ \hline \multirow{3}{*}{Robustness under Noise (Error Fluctuation)} & \(\pm\)0.15 V & \(\pm\)0.40 V \\ \cline{1-1} \cline{2-4} RMSE (95\% CI) & Case 4.1 (20 runs) & [0.076, 0.084] & [0.241, 0.259] \\ \hline \end{tabular}
\end{table} 
Table 3: Quantitative performance analysis. node's degree in graph G), not the total number of DREGUs (N) in the microgrid. For instance, in a ring or line topology, each node only communicates with two neighbors, regardless of whether N is 4 or 40. This contrasts sharply with centralized approaches where communication traffic to a central controller scales with N. Furthermore, as highlighted in Remark 7, the computational load per DREGU is exceptionally low. The control law update (9) and PPD estimation (11) involve only a few scalar algebraic operations. The memory and processing requirements for each agent remain constant and independent of the overall system size. This inherent O(1) complexity per node ensures that the DAILC algorithm can be efficiently deployed on low-cost microcontrollers, making it highly scalable and practical for large, heterogeneous microgrids.