The limited predictability and high variability of renewable generations has brought significant challenges on the real-time operation of bulk power systems. This paper proposes the concept of real-time dispatchability (RTDA) of power systems with variable energy resources, which focuses on investigating the impact of operating constraints and the cost of corrective actions on the flexibility of real-time dispatch. RTDA is the largest region in the uncertainty space, such that all the elements in it will not cause infeasibility while deploying a corrective action. This paper proposes a closed polyhedral form of RTDA. Moreover, an adaptive constraint generation algorithm is proposed to compute the boundaries of RTDA. Three potential applications are suggested. Case studies on the IEEE 118-bus system illustrate the RTDA concept and demonstrate the validity and efficiency of the proposed method in practical applications.