## 4 Results
The residuals, obtained after applying the MEMD algorithm to PMU measurements of speed deviation at generator terminals following a simulated active power imbalance disturbance of 0.05 (p.u.) and 0.1 (p.u. ), respectively, are depicted in Figure 4.  
If the magnitude of the disturbance is accurately known, it becomes possible to estimate the total system inertia. In addition, by applying the MEMD method to the speed deviation signals during disturbances, Col RoCoF values are determined for all three simulated experiments. Knowing the value of Col RoCoF and the imposed magnitude of disturbance using Equation (18), the inertia values of the power system were established. The results are presented in Table 4. The table displays both the actual inertia values obtained by subtracting the share of inertia of the generating units that tripped, causing an imbalance in the active power in the power system. Additionally, the table also presents the error in percentages. \begin{table}
\begin{tabular}{c c c} \hline  & _MSE_ & _MAE_ \\ \hline MEMD & 5.30659 \(\times\) 10\({}^{-5}\) & 0.00538 \\ DigSILENT & 0.000118 & 0.00766 \\ \hline \end{tabular}
\end{table} 
Table 2: Mean square error and mean absolute error. \begin{table}
\begin{tabular}{c c c} \hline  & **MEMD** & **DigSILENT** \\ \hline Error (\%) & 0.57 & 0.73 \\ \hline \end{tabular}
\end{table} 
Table 3: Estimation error (%). During another disturbance, different wind penetration levels were examined to assess the impact of renewable integration on inertia distribution. The results, depicted in Figure 5, highlight the outcomes across various wind penetration percentages under a scenario of active power imbalance of 0.05 (p.u.). The CoI location undergoes a significant excursion because of the installation of wind plants. For validating the simulation model, the effects of wind generation on system frequency responses are analyzed by modeling diverse levels of renewable generation penetration. The selected penetration rates include 10%, 15%, and 20%, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Disturbance Scenario \(\Delta\)P (p.u.)** & **H(s), Actual Value** & **H(s), Estimated** & **Error (\%)** \\ \hline
0.05 & 7.57 & 7.50 & 0.92 \\
0.1 & 7.32 & 7.42 & 1.73 \\
0.108 & 6.93 & 7.14 & 3.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimated inertia for different disturbance scenarios. Figure 4: Speed deviation and residuals obtained via the MEMD approach: (**a**) disturbance magnitude 0.05 (p.u. ); (**b**) disturbance magnitude 0.1 (p.u.). Figure 5: Frequency response after the occurrence of disturbances at different levels of renewable energy integration. The MEMD approach was employed to analyze the frequency response data depicted in Figure 5. It identified the average modal function and residue across the entire signal set. The residue predominantly represents the slowing trend of the power system following the imbalance in active power. The observed trend illustrates a substantial decrease in the system's frequency response as the penetration rate of renewable generation increased. For instance, at a 10% renewable penetration rate, the RoCoF measured 0.242 Hz/s. This value escalated to 0.235 Hz/s with a 15% penetration scenario and reached 0.258 Hz/s with a 20% share of RESs. A notable increase in RoCoF is evident, particularly at the 20% RES penetration level, compared to scenarios without renewable generation, where the CoI RoCoF value amounted to 0.2 Hz/s. The nadir frequencies were 58.57 Hz, 58.79 Hz, and 59.06 Hz for 15%, 10%, and 20% renewable penetration, respectively. Furthermore, there was a significant drop of 0.48 Hz observed at nadir frequencies. These outcomes emphasize the necessity for the precise estimation and distribution of inertia, appropriate assessment of inertia requirements, and the implementation of additional strategies to mitigate the issue of declining frequency response, especially in systems with higher RES penetration levels.