The extensive deployment of non-synchronous generation determines lower level of grid inertia resulting in deteriorated frequency containment performance and abnormal frequency excursions in case of contingency. This calls for identifying assets, controls, and relaying schemes capable to ensure acceptable grid frequency containment and dynamics satisfying the requirements of existing grid codes. A potential way to counterbalance this lack of inertia is to use large-scale battery energy storage systems (BESSs) since they provide large ramping rates and fast power control. As known, there are generally two main approaches to control converter-interfaced BESSs: grid-following and grid-forming controls. As BESSs may provide significant value to system frequency containment, it is of fundamental importance to quantitatively evaluate the dynamics of low-inertia power grids hosting large-scale BESSs. Within this context, it is also of importance to study the behavior of low-inertia power systems subsequent to large contingencies in order to develop appropriate under-frequency load shedding (UFLS) relaying schemes that may take advantage of nowadays distributed sensing technologies enabled by the Phasor Measurement Units (PMUs). Framed within the EU H2020 project "Optimal System-Mix Of flexibility Solutions for European electricity", the Thesis first characterizes the interplay between converter-interfaced BESSs and low-inertia power grids and, then, provides quantitative assessments of system dynamics and quantifies the benefits associated to different control strategies of BESSs. For this purpose, state-of-the-art detailed dynamic simulation models of power grids, BESS, and controls are implemented on a real-time simulator for detailed numerical analyses. At first, contingency tests are conducted. The results verify the substantial influence of inertia reduction on post-contingency dynamics of power systems and quantitatively prove that converter-interfaced BESSs can effectively limit the frequency decreasing and damp the frequency oscillations. Then, the proposed dynamic models are used for one-day-long simulations to assess the impact of converter-interfaced BESSs on the frequency containment of low-inertia power grids in normal operating conditions. For a practical operative context, a day-ahead schedule layer is considered where reserve levels for frequency containment and restoration are allocated considering the current practice required by European transmission system operators. Numerical analyses on suitably defined metrics applied to grid frequency show that the grid-forming control strategy outperforms the grid-following one, achieving better system frequency containment. As large frequency excursions are more likely to occur due to the decrease of kinetic energy stored in rotating synchronous machines, fast adaptive UFLS schemes are necessary to secure low-inertia power systems under contingency. PMUs provide an effective tool to track the network state in any node of interest with reporting rates in tens of frames per second. In this respect, the Thesis proposes and validates two new UFLS schemes suitable for low-inertia power grids. The first scheme is a centralized UFLS that leverages PMU-fed situational awareness systems and is coupled with an Optimal Power Flow (OPF) problem. The OPF problem is formulated to constrain nodal voltages and branch currents in combination with a model capable of predicting the system response.