System Restoration for Low-Inertia Power Systems Incorporating Fast Frequency Response via Distributionally Robust Optimization

The high share of renewable energy sources (RESs) in power system creates inertia shortfalls, posing challenges in system restoration after a major outage due to lower system inertia and high RES uncertainty. In this paper, the restorability of low-inertia power systems is studied. A rolling horizon methodology is derived to construct restoration strategies by performing sequential decision-making to optimize blackstart, grid energization, wind power re-connection, and load pickup. Notably, wind power re-connection will introduce time-varying exogenous uncertainty for other restoration actions. To decouple exogenous uncertainty, a bi-level optimization model is built, where the upper-level determines the set of non-blackstart units and increment of grid-accommodable wind capacity, considering Minimum System Inertia Constant (MSIC) and Fast Frequency Response (FFR). The lower-level yields a secure operating point ensuring power balance and System Non-Synchronous Penetration (SNSP). The former is formulated as a look-ahead deterministic optimization model, while the latter as a distributionally robust optimization model considering wind uncertainty. Steady-state and dynamics simulation using the IEEE 14-bus system and 118-bus system are provided, demonstrating that RES can perform system restoration safeguarded by MSIC and SNSP, and FFR can accelerate restoration by providing extra inertia support for systems with up to 50% share of wind capacity.