The safety and stability of modern power systems are undergoing various challenges, introduced by the integration of fluctuating renewable generation. In this paper, we present a hierarchical model predictive power dispatch and control strategy for a class of modern power systems with price-elastic controllable loads (CLs) in energy Internet. In the upper-level optimization, a generalized multiperiod economic dispatch (GMPED) problem is organized within an electricity market environment aiming at maximizing the social welfare. Specifically, the price-elastic CLs are aggregated in controllable load aggregators (CLAs) to participate in the market competition. A novel utility function of the price-elastic CLAs is proposed for market demand response. By solving GMPED, the power setpoints of plants over the further periods are produced, as well as the real-time price for the optimal response of price-elastic CLAs. In the second-level operation, two types of model predictive control-based controllers for both the supply and demand sides are designed for power tracking control by considering the model of the power system and aggregated thermostatically controlled loads. Finally, two case studies are performed on the IEEE 14- and 39-bus system, respectively, which shows that the system-frequency deviation and system cost are reduced significantly with the proposed methods.