Robust control by a novel two-step successive solution approach to mitigate emergency frequency sag in power systems with modeling uncertainties

This paper presents a robust emergency frequency control framework that leverages coordinated rapid regulation by wind turbines and loads to pre-generate control strategies for large hypothetical frequency sag faults and activate control to stabilize system frequency during faults. The underlying optimization problem considers multi-type resources with discrete and continuous control modes, while capturing uncertainties from environmental and modeling errors, nonlinearities, and non-analytical computations. Accordingly, this paper proposes a two-step successive solution approach to address the formulated mixed-integer nonlinear robust optimization problem efficiently. In step one, uncertainties are temporarily ignored, and the resulting mixed-integer nonlinear and non-analytical problem is solved using proposed simplified methods, such as differential discretization, which serves as a warm start for the original problem. In step two, the solution from step one is treated as a reference, and trajectory sensitivities are used to quantify the impact of uncertainties on frequency security and other constraints. The original problem is ultimately reformulated as a bi-level mixed-integer linear optimization with independent decision variables, enabling efficient solution. Finally, simulations on the modified IEEE 39-bus and 118-bus systems demonstrate that incorporating rapid regulation of wind turbines and loads significantly reduces control costs. Additionally, the proposed method ensures high solving efficiency and reliable control effects against modeling uncertainties.