## 1 Introduction
A way for adapting the parameters has also been developed, and in [25], a deep learning algorithm is proposed to adapt and optimize the system damping and inertia as much as possible. Feedback-based compensation methods typically follow a passive feedback mechanism, aiming to stabilize the system by responding to observed variations. In contrast, feedforward compensation methods adopt a more proactive strategy, acting ahead based on predicted disturbances [26]. Focusing on feedback compensation techniques, they feed angular frequency or active power variations back into the control system of the GFM inverters, counteracting oscillations in active power. In [27], the dynamic deviation between the GFM angular frequency and the grid angular frequency, measured through a phase-locked loop (PLL), is fed back to the control loop via a proportional link. Another implementation involves using a first-order low-pass filter (LPF) to extract dynamic frequency deviations, which are then reintroduced into the active power command through a proportional feedback link [9; 28]. While the POD algorithms seem effective, the impact of the POD-P on the inherent GFM's capabilities, such as inertia or synchronization power, has not been analyzed. From the system operator perspective, if a minimum inertia contribution or synchronization power is requested by an IBR, those requirements must be met in a measurable and verifiable way. Any design methodology should consider, besides the impact of POD control on damping the grids' oscillatory modes, its effect on active power dynamics (PSL + supplementary damping control based on active power). Network frequency perturbation (NFP) plots can be used to represent the device-level behavior of a grid-connected generation source during grid frequency or voltage disturbances, independently of the grid dynamics [18]. Hence, it provides an approach for measuring the characteristics of the device itself. As a result, recent grid codes have recommended NFP plots for verifying the compliance of grid-forming (GFM) plants during testing procedures [29; 30]. In this paper, the following contributions related to the damping provision by GFM control devices are addressed:  
* Analyze limits and incompatibilities of additional POD-P control loops with inherent GFM damping, inertia, and synchronization power, using NFP plots. * Taking into account the previous limitations, propose a POD-P method that increases the damping of the targeted frequency without affecting the rest of the frequency components. * Validate all theoretical and analytical results in an experimental setup in order to extract conclusions on best practices for providing damping to LFOs with GFM control. This paper is organized as follows: Section 2 presents the system description and the small-signal model for GFM inverters. Here, in different subsections, the NFP method and a base case are also presented. Section 3 is dedicated to the POD-P algorithms; the classical POD structure and proposed POD-P control loop are evaluated. In Section 4, the validation methodology, the laboratory setup, and experimental results are presented. In Section 5, a discussion of the results is carried out, while Section 6 lists the conclusions.