A large amount of renewable energy generation (REG) has been integrated into power systems, challenging the operational security of power networks. In a real-time dispatch, system operators need to estimate the ability of the power network to accommodate REG with a limited reserve capacity. The real-time dispatchable region (RTDR) is defined as the largest range of a power injection that the power network can accommodate in a certain dispatch interval for a given dispatch base point. State-of-the-art research on the RTDR adopts a DC power flow model regardless of the voltage profiles and reactive power, which can overlook potentially insecure operational states of the system. To address this issue, this paper proposes an AC power flow based RTDR model simultaneously considering the reactive power and voltage profiles constraints. The nonlinear constraints in our model are approximated using a linear power flow model together with a polytope approximation technique for quadratic constraints. An adaptive constraint generation algorithm is used to calculate the RTDR. Simulation results using the IEEE 5-bus and 30-bus systems illustrate the advantages of the proposed model.