## 3 POD-P Algorithms for GFM Control  
### Classic POD and GFM  
The classic POD method is based on the inclusion of an additional high-level control loop, which typically uses the angle difference--or a variable related to it--as the input signal to detect power oscillations. Based on this detection, and after appropriate signal  
Figure 8: \(\Delta P/\Delta P^{*}\) Bode plots for different \(m_{p}\) values (H = 2.5 s): base case (solid line) compared to the PSL modified to increase bandwidth (dotted line).  
processing, an output reference (voltage, reactive power, or active power) is generated for the lower-level control loops.  
As a first approach to implementing a POD-P algorithm in a GFM IBR, the same procedure and control structure as the classic POD is used. The control scheme consists of a washout filter, an optional number of lead-lag compensators, and a gain. The time constant of the washout filter ensures that the POD operates only at low frequencies and removes any DC component from the input signal. Lead-lag compensators, if included, allow for the adjustment of the phase angle at the target frequency. In this initial implementation, however, no lead-lag compensators are used.  
To analyze this first case, power oscillations are detected directly from the active power. Since lead-lag compensators are not considered in this first approach, the small-signal model of the system corresponds to the one shown in Figure 9.  
Figure 9 builds upon Figure 2, where the feedback transfer function \(H_{\text{c}}\) is modified by introducing the classic POD structure (without lead-lag components). The NFP Bode plot of the system is derived using Equation (5), with parameters \(K_{p}=1\) and \(\tau_{w}=1.6\) s. The results, shown in Figure 10, compare the base case (GFM without POD, blue line) with the case including the POD (red line). It can be observed that at very low frequencies, the POD does not affect the frequency response due to the presence of the washout filter. Similarly, at high frequencies, both configurations behave almost identically, effectively filtering out perturbations.  
However, in the inertia region, although the GFM inverter provides increased damping--i.e., more injected active power for the same frequency variation--there is a significant impact on the phase angle. More critically, the inertia behavior of the GFM inverter is completely altered, and the intrinsic damping of the inverter is degraded (see Figure 10).  
When the classic POD is implemented in a GFL structure, the injected active power is independent of frequency variation. The phase-locked loop (PLL) provides a stable reference for low- and medium-low frequency variations, while the active power loop (typically implemented with a PI controller) offers sufficient bandwidth. As a result, the only contribution to frequency-dependent behavior comes from the POD algorithm. These assumptions, however, no longer apply in GFM systems, where the natural response to frequency variations must be preserved.  
In the case of the POD-P structure implemented within a GFM, the use of second-order band-pass or band-stop filters is recommended. These filters help mitigate the impact of the POD on the synthesized inertia and damping, confining its effect to a specific frequency band. This approach is analyzed in detail in the following section.  
Figure 9: PSL control loop including classic POD.