Dynamic frequency-robust restoration for renewable-penetrated transmission systems: A McCormick convex envelope-based optimization framework

• A dynamic frequency-robust restoration strategy with an MCE-based optimization framework is proposed. • The MCE+PBC method reduces linearization error by 20% and speeds convergence by 90%. • A two-stage robust method jointly handles RG uncertainty in power balance and frequency stability. • The method prevents 60% frequency-instability events and ensures simultaneous power and frequency robustness. Renewable generation (RG) has been empirically validated as both technically essential and operationally viable for active participation in power system restoration processes. However, the large-scale integration of RG poses significant challenges to system restoration due to the inherent characteristics of the RG, including the low inertia, weak frequency regulation and randomness, which are not comprehensively addressed in the traditional restoration method. For this purpose, this paper proposes a dynamic frequency- robust restoration strategy for renewable-penetrated transmission systems with a McCormick Convex Envelope (MCE)-based optimization framework. First, nonlinear frequency dynamics are reformulated through a customized MCE method embedded with progressive boundary contraction (PBC) approach, which can improve linearization accuracy and computational efficiency. Subsequently, RG uncertainty is modeled via polyhedral sets with adjustable robustness budgets, enabling joint robustness in steady-state power balance and transient frequency security through a two-stage robust method. Extensive numerical tests on modified IEEE 24-bus and 118-bus systems demonstrate: 1) improved MEC + PBC linearization accuracy (20% (0.017 Hz) reduction in frequency error) and computational efficiency (90% (340 min) faster convergence) compared to existing methods, and 2) simultaneous robustness in power balance and dynamic frequency stability (preventing 60% (24) frequency-instability time steps concerning RG randomness).