## 3 POD-P Algorithms for GFM Control
### Proposed POD-P  
Based on the results presented in the previous subsection--where the washout filter exhibited a significant influence on the system's low-frequency response--a simplified POD-P method is proposed for integration into GFM control schemes. The key advantage of this approach lies in its simplicity, delivering the desired damping effect at a narrow frequency band while preserving the response across other frequency components.  
A POD structure based on a band-pass filter is proposed. Building upon the control loop depicted in Figure 2, the feedback transfer function \(H_{c}\) is modified by incorporating the aforementioned band-pass filter and an associated gain, as illustrated in Figure 11.  
To tune a second-order band-pass filter, the target frequency (band-pass center frequency, \(\omega_{n}\)) and the quality factor (Q = 1/2\(\zeta\)) have to be adjusted. The center frequency determines the frequency at which the filter has the maximum gain. Thus, if an oscillation is detected in the grid, the measured power oscillation frequency would be the target frequency.  
The quality factor affects the bandwidth of the filter: a higher Q results in a narrower and sharper peak, while a lower Q broadens the response. In the Bode plot, changing center frequency shifts the peak of the magnitude response along the frequency axis, while modifying Q alters the slope of the roll-off and the sharpness of the peak. Additionally, the phase response is also affected, becoming steeper around the center frequency as Q increases. Proper tuning is essential to ensure that the filter isolates the desired frequency range without excessive distortion or attenuation in the rear. With more localized power oscillation, higher Q factors can be used. However, it is not recommended to surpass the 200\({}^{\circ}\) phase shift mark used to limit the droop region (Figure 4).  
Figure 11: PSL control loop including a band-pass POD.  
Figure 10: \(\Delta P/\Delta\omega_{g}\) Bode plot for the base case (without POD, H = 2.5 s, \(m_{p}=0.015\), and \(T_{f}\) = 0.075) compared to the classic POD.  
In this second case study, a natural frequency of \(\omega_{n}=0.3\cdot 2\cdot\pi\) and a damping ratio of \(\zeta=0.1\) are considered. The results are again compared with the base case (i.e., without a POD structure, shown in blue), as depicted in Figure 12.  
The proposed POD structure has a very localized effect on the frequency--active power response of the GFM unit. Its influence is confined to a narrow frequency band of interest. Although a minor reduction in damping capability may be observed, the angle shows a dispersion in the rear of the objective frequency. However, larger damping can be achieved with the same droop constant and without modifying system inertia, static gain, and synchronization power.  
Several methods can enhance damping in GFM inverters by adjusting the power synchronization loop (PSL). As the power grid evolves due to demand, generation, or operator actions, its characteristics shift over time. In this context, the simplicity of the proposed POD-P method is advantageous, allowing for the easy reconfiguration of the targeted frequency band as the grid changes.