## 5 Discussion  
This study introduced an approach designed for systems with the integration of converter-interfaced generation to calculate the inertia constant, focusing primarily on accounting for the impact of frequency response dispersion. This discussion centers on the working hypotheses:  
1. According to the outcomes of the IEEE 39 bus test system simulation, when the distribution of inertia becomes more uneven, there is a possibility of the RoCoF being excessively restricted within the low-inertia systems. 2. The proposed method introduced a decomposition technique MEMD for extracting low-frequency components from the signal and signal trends. The MEMD method was applied to time series data of frequency deviation following disturbances. The resulting residual indicates the pattern of the signal under analysis and is expected to be effective in evaluating the RoCoF. The residue primarily signifies the decreasing trend in the power system after an active power imbalance. This is supported by the results obtained for both the mean square error and mean absolute error, with the mean square error calculated at 5.30659 \(\times\) 10\({}^{-5}\) and the mean absolute error at 0.00538. 3. The MEMD can generate the average modal function and residue for the entire signal set, facilitating the simultaneous processing of multiple signals and providing a comprehensive resolution covering all signals and their residual components. This simultaneous decomposition of PMU measurement data with MEMD identifies common scales among various signals, enabling thorough analysis across multiple signals. This characteristic is utilized to resort to estimating the CoI RoCoF. The MEMD estimation results of the frequency deviations represent the average gradient of the residual representing the center of inertia frequency on the observed time interval (\((((x_{(i+1)}-xi))/\Delta t)\), \(\Delta t=0.01\) s). During the estimation of CoI RoCoF, errors ranging from 0.42% to 1.35% were identified, depending on the imposed imbalance in active power. For an imbalance of 0.108 (p.u. ), a percentage error of 0.57% was identified in estimating the CoI RoCoF. Such low values of percentage errors indicate a promising potential for applying the MEMD approach to estimate CoI RoCoF in modern power systems. 4. When accurately known disturbance magnitudes are present, estimating the total system inertia H becomes feasible. Additionally, when the MEMD method is applied to speed deviation signals during disturbances, CoI RoCoF values are determined for simulated experiments. Knowledge of the CoI RoCoF value and the imposed dis  
Figure 6: Estimated and actual inertia constant: (**a**) different disturbance magnitude without RESs; (**b**) disturbance magnitude 0.05 (p.u.) with 10 (%), 15 (%) and 20 (%) RES penetration. turbance magnitude allows the establishment of the power system's inertia constant. The calculated percentage errors of the estimated inertia constant compared to the actual inertia constant ranged from 0.92% to 3.03%. 5. To validate the simulation model, the impact of wind generation on system frequency responses was analyzed. This involved modeling various levels of renewable generation penetration, specifically focusing on penetration rates of 10%, 15%, and 20%, respectively. The aim was to understand how different levels of renewable energy integration affect the system's frequency responses. The frequency response of the system showed a notable decrease as renewable generation penetration increased and there was a significant increase in the RoCoF compared to scenarios without renewables. Additionally, there was a considerable drop in nadir frequency with wind generation increase. In these conditions, the inertia constant of the system was estimated using the MEMD approach, and the percentage errors of the estimation were recorded. The errors ranged from 0.57(%) to 12.6(%). These results emphasize the advantage of using the MEMD approach for precise inertia estimation and allocation.