Environmental concerns have led to the displacement of fossil-fuel-fired Synchronous Generators (SG) by renewable energy in the form of Inverter-Based Resources (IBR). The rise of IBR has created new threats to grid stability, and this thesis focuses on frequency stability following a sudden large power imbalance. Frequency stability traditionally relied on the inertia and damping of SGs, but now IBR features dominate, and local frequencies can deviate substantially from the system frequency, called Centre-of-Inertia (CoI).

With carefully chosen simplifications, a cohesive set of swing equations for two main types of IBRs, Grid-Forming Inverters (GFMI) and Grid-Following Inverters (GFLI), is developed to model the local frequency trajectories. Combining these, the aggregate CoI frequency trajectory is also modelled. Further analysis has yielded closed-form formulas for frequency stability indicators, namely: settled frequency deviation, Rate of Change of Frequency (RoCoF) and minimum settling time.

The contributions of IBRs to frequency stability are uncovered from the analysis. GFMIs can provide inertia and damping to limit the frequency deviation and local RoCoFs, respectively. GFLIs can directly contribute to the system damping, but only indirectly help reduce the local RoCoF and CoI settling time.

A procedure based on the stability indicators is proposed to design IBR contributions to frequency stability and set the local and global frequency trajectories. The procedure guides the parameterization of IBR droop slopes and controller bandwidths. Because it relies on closed-form formulas, the procedure is quick and simple and could be applied at every settlement period to choose the IBR generation mix.

The analysis and procedure are validated with modified IEEE 14-bus and 68-bus networks. Simulations show that, despite the simplifications, the swing equations and indicators are reliable to evaluate the frequency stability of the system, and thanks to the simplicity of the procedure, IBR contributions are easily designed to guarantee frequency stability.