Convex Capacity Expansion Planning Under Inertial Response Constraints

Future low-carbon energy systems will show reduced generation from synchronous generators. The resulting loss of inertia can lead to a high rate of change of frequency after a disturbance and, thus, to potentially unrecoverable system states. Yet, inertial response constraints are rarely considered in large-scale capacity expansion planning models investigating decarbonization pathways. We thus present a convex formulation of a coordinated capacity expansion problem for generator, transmission, and storage expansion. Next to a unit commitment relaxation, the formulation includes linearized rate of change of frequency constraints that model the inertial response to a priori defined disturbances such as a large power injection deficit or a system split. In a numerical experiment, we solve model instances that cover the European power system at high spatial and temporal resolution and, moreover, consider the inertial responses from synchronous generators and inverter-based resources. Our results show that inertia provision from battery energy storage systems with grid-forming inverters is already valuable today due to enabling decreased conventional generation. Moreover, we find that future low-carbon energy systems can ensure sufficient capacities for inertial response by equipping a share of battery energy storage systems with grid-forming inverters at a negligible system cost increase.