## 1 Introduction  
On a global scale, the installed capacity of wind turbines alongside photovoltaic (PV) installations experienced significant growth. This is a clear indication of the increasing importance of renewable energy sources (RESs), with a clear stance that their share in total production in the future should become even larger. Reducing the share of synchronous generator production in favor of non-synchronous production from RESs leads to a decrease in the overall inertia in the power system, and it is precisely the system's inertia that is responsible for the stable frequency response (higher system inertia provides less sensitivity to the immediate mismatch between production and consumption). Due to electro-mechanical coupling, the rotating masses of generators provide kinetic energy to the grid (but also draw from it) in case of frequency deviation. The grid frequency is directly linked to the speed of rotation of the synchronous generator rotor and hence to the balance of active power, varying within acceptable limits, and monitored within the system through the so-called rate of change of frequency (RoCoF). Reduced inertia will increase the RoCoF when the system is exposed to sudden disturbances, such as a decrease or increase in consumption or a decrease or increase in production. With insufficient inertia, frequency changes can be too rapid, causing uncontrolled failures of consumers, generators, and interconnectors, potentially leading to a partial or complete system breakdown [1; 2]. In the process of decarbonization of the electric power system (EPS), the widespread adoption of RESs plays a key role. According to the report [3], in order to achieve the goals set in the Paris Agreement, the global share of electricity produced by wind should be 21% by 2030, and 35% by 2060. The most commonly used wind turbines operate at variable speeds to enhance the efficiency of wind energy conversion. However, this variable speed operation leads to a decoupling between the generator rotation speed and the grid frequency, managed by a converter. The variability of the primary energy source has positioned wind farms to negatively impact the frequency stability of the electric power system [4]. Due to the increased proportion of RESs, units connected to the grid via power electronic converters will replace many conventional sources that previously used electromechanical conversion with standard synchronous machines directly connected to the power system. As management and protection concepts for traditional power systems are based on the static and dynamic characteristics of synchronous generators, their absence poses a risk of unreliable and unstable system operation [5]. Numerous approaches for estimating power system inertia can be found in the literature, including model-based and measurement-based methods [6]. Model-based inertia estimation includes a single synchronous generator (SG) estimation [7] and regional system inertia estimation [8]. Ambient data-based inertia estimation [9] and large disturbance-based estimation methods [10; 11] belong to measurement-based inertia estimation approaches. However, they rely on accurate models and may struggle with virtual inertia estimation for converter-interfaced generators (CIGs) lacking replicated dynamics or known control schemes. The review [12] encapsulates various inertia estimation techniques, highlighting their respective advantages and limitations. These include measurement-based methods, which, while capable of utilizing actual system data, face issues with data reliability due to noise and nonlinear variables. Transient signal-based methods are noted for their applicability in both offline and online settings, yet they suffer from limitations like sample deficiency, cost, and time constraints. The paper also discusses Artificial Neural Network (ANN)-based models, which offer fast computation and robustness against noise but are complex and face challenges in multi-area interconnected systems.