The high penetration of uncertain renewable energy sources (RESs) poses significant challenges to the operational flexibility of power systems. However

considering the omission of time-series correlations among RESs and the high dispatch costs of flexibility

we propose an optimal flexibility scheduling method based on a time-series convolution probabilistic model. First

based on the convolution theory

three uncertain inputs

including the wind power

photovoltaic

and load

are transformed into a net load probabilistic model with enhanced computational efficiency. Meanwhile

Gaussian Copula is newly employed to characterize the time-series correlations of net load

thereby

the errors in flexibility demand quantification resulted from ignoring time correlations are reduced. Second

to lower the dispatch costs of flexibility supply resources

a dynamic selection model for controllable loads is proposed. The operators can dynamically choose the optimal regulation strategies of controllable loads among three standard modes

achieving a trade-off between flexibility supply capability and regulation costs. Furthermore

a day-ahead optimal scheduling model considering the probabilistic power balance of system is established. Meanwhile

the flexibility regulation costs and risks are co-optimized after considering the chance-constrained programming and conditional value-at-risk theory

which can obtain an optimal and economical allocation of flexibility supply resources. Case studies demonstrate that the proposed method can be adopted to effectively enhance both system flexibility and economic performance.