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Power system flexibility refers to the ability to respond to changing net loads within a predefined timeframe. The main causes of flexible demand are resource and load uncertainties. The joint interaction of resource and load uncertainty makes flexible demand more complex. Accurately assessing the power system flexibility and promoting flexible supply are important for maintaining grid safety and stability. In this study, a joint probability distribution for intermittent renewable energy sources (IRES) output and load forecast deviation is proposed. Subsequently, an optimal dispatch model that considers flexible demand and hydropower flexible supply is built to improve the operation scheme of flexible resources. A hydropower dispatch model that does not consider the probability of IRES output and load forecast deviation is used as the contrast model. A comparison of the results shows that the optimal dispatch model is more beneficial for maintaining grid safety and stability. The results show that the maximum upward adjustment flexible (UAF) margin of the optimal dispatch model of the Yalong River Downstream is 376 MW, whereas the maximum downward adjustment flexible (DAF) margin is 197 MW. This implies that a greater UAF supply is required in the case study to satisfy the power system flexible demand. • A quantitative method for power system flexibility is proposed. • A joint probability distribution considering resource and load uncertainties is presented. • An optimal dispatch model considering flexible margins is proposed. [ABSTRACT FROM AUTHOR]