When large-scale

uncertain

centralized

and distributed renewable energy sources are connected to a power system

separate dispatch of the transmission power system (TPS) and the active distribution network (ADN) will compromise the network and frequency security of the system. To address these problems

this paper proposes a frequency-constrained coordinated stochastic economic dispatch (FC-CSED) model for an integrated transmission and distribution (ITD) system. In this model

the dynamic frequency and network security constraints of the ITD system are constructed

and joint chance constraints are adopted to handle the uncertainty. Then

the control parameters of inverter-based resources

the base point power

and the regulation reserve of all dispatchable resources in the ITD system are jointly optimized to minimize operating cost. TPS and ADNs can deliver base point power bidirectionally and provide frequency regulation support bidirectionally

which extends the existing reserve assumption in ITD dispatch and enhances the operational security of the ITD system. Moreover

based on the alternating direction of the multiplier algorithm

a two-layer distributed optimization framework is proposed to solve the FC-CSED model. Case studies show the FC-CSED model can fully utilize the potential of multiple regulation resources to improve the security performance of the ITD system

and TPS and ADNs can be coordinated efficiently through the proposed distributed optimization framework.