To manage a large amount of flexible distributed energy resources (DERs) in the distribution networks

the virtual power plant (VPP) is introduced into the industry. The VPP can optimally dispatch these resources in a cluster manner and provide flexibility for the power system operation as a whole. Most existing studies formulate the equivalent power flexibility of the aggregating DERs as deterministic optimization models without considering their uncertainties. In this paper

we introduce the stochastic power flexibility range (PFR) and time-coupling flexibility (TCF) to describe the power flexibility of VPP. In this model

both operational constraints and the randomness of the DERs' output are incorporated

and a combined model and data-driven solution is proposed to obtain the stochastic PFR

TCF

and cost function of VPP. The aggregating model can be easily incorporated into the optimization model for the power system operator or market bidding

considering uncertainties. Finally

a numerical test is performed. The results show that the proposed model not only has higher computational efficiency than the scenario-based methods but also achieves more economic benefits.