The increasing penetration of renewable energy in active distribution networks introduces severe power fluctuations and uncertainties. This challenges traditional scheduling methods that rely on conservative and static capacity boundaries of converter-interfaced equipment. This paper proposes a multi-time-scale secure and economic dispatch framework that explicitly integrates the dynamic operating characteristic constraints of grid-forming converters. First, a spatial correlation model based on Copula theory is established to handle wind power uncertainties via scenario generation and reduction for the day-ahead and intra-day scheduling phases. This formulation aims to minimize the comprehensive operational costs of the system. For the real-time rolling optimization phase, the short-term overload potential of grid-forming converters, which is unlocked by electro-thermal coupling optimization and discontinuous pulse width modulation phase-shift clamping, is mathematically abstracted into a generalized dynamic elliptical active and reactive power capability envelope. This cross-scale mapping mechanism allows the system to utilize transient thermal margins for enhanced local reactive power support without violating device junction temperature limits. Furthermore, the non-convex scheduling model is transformed into a mixed-integer second-order cone programming problem using convex relaxation techniques to guarantee global optimality and computational efficiency. Comprehensive case studies on the modified IEEE 33-bus and 69-bus systems demonstrate that the proposed strategy reduces tie-line power fluctuations and operational costs under extreme conditions. The results achieve a favorable economic trade-off between brief power quality degradation and global physical stability.
Liu et al. (Thu,) studied this question.