A Review of the Application of Continuous-Time Scheduling Methods in the Flexible Operation of Power Systems

[Objective] To enhance the representation of intra-interval power fluctuation and the allocation of flexibility resources，this paper provides a systematic review of the applications and existing challenges of continuous-time scheduling methods for flexible power system operation. [Methods] First，the mathematical formulations and solution paradigms of discrete-time and continuous-time scheduling are compared. Then，representative applications and problems are reviewed，organized according to four key domains：generation，transmission，storage，and demand. Finally，common challenges are synthesized from a mathematical point，and potential theoretical development directions are summarized. [Conclusions] In continuous-time scheduling，decision variables are modeled as continuous trajectories，and constraints involve derivatives，integrals，and differential equations. The main solution paradigms include optimal-control-inspired methods and Galerkin-projection-based approaches. Shared difficulties mainly arise from modeling uncertainty in continuous time，solving nonconvex constraints such as unit commitment and charge-discharge exclusivity，and handling differential-equation constraints. [Conclusions] Based on these findings，this paper outlines future application trends and follow-up research topics of continuous-time scheduling in multi-timescale scheduling coordination，planning assessment，and market mechanism design.