The increasing amount of renewable power generation systems is a challenging issue for the control and operation of the electrical networks. One of the main issues is their lack of inertia, which is becoming a greater problem as much as the share of the power plants based on traditional synchronous generators gets reduced. In this regard, the new grid codes ask these plants to provide new functionalities such as the frequency support and inertia emulation. In this paper, a synchronous power controller for grid-connected converters is proposed as a good solution for the renewable generation systems with energy storage. It provides inertia, damping, and flexible droop characteristics. Different from the faithful replication of the swing equation of synchronous machines, an alternative control structure is proposed, by which the damping and inherent droop slope can be configured independently to meet the requirements in both dynamics and frequency regulations. Analysis and experimental results are both shown to validate the proposed controller.