Analytical Design of Contributions of Grid-Forming and Grid-Following Inverters to Frequency Stability

Most of the new renewable generation in power systems is connected through Grid-Following inverters (GFL). The accompanying decline of fossil-fuelled synchronous generation reduces the grid inertia. As these two trends progress, instabilities become more likely. To allow more renewables onto the grid, the use of combinations of GFL and Grid-Forming inverters (GFM) has been proposed, however, it is unclear how to parametrise these inverters for system objectives. This paper tackles the issue of parametrizing each GFM and GFL to ensure frequency trajectories at all buses, expressed in terms of frequency deviation, Rate of Change of Frequency and settling time, are stable, recognising that local frequencies can deviate substantially from the Center of Inertia (COI). The procedure to achieve this comprises simple closed-form equations, and yields the required values of droop slopes, GFM filter bandwidth and GFL Phase-Locked Loop bandwidth. These equations are derived from an analytical formulation of swing equations for GFM and GFL which are combined to describe the behaviour of not only the COI but also each bus. The detailed EMT simulations of a modified IEEE 14-bus network demonstrate that the simplifying assumptions made in the analysis are justified by the close correspondence between simulation and analytical projections.