With the dual-carbon strategy, the increasing penetration of renewable energy has led to a reduction in the rotational inertia of power systems. Synchronous machine characteristics such as inertia and voltage support capabilities have become important requirements for grid-connected converters. To address this, a power-controlled static synchronous machine control strategy based on a grid-following framework is proposed. This strategy simulates the voltage and frequency support characteristics of a synchronous machine through a reference power point tracking loop combined with a dual-loop control of voltage and current. A state-space model of the power-controlled static synchronous machine system is then established to analyze the influence of control parameters on system stability. The operational characteristics and application scenarios of the proposed control strategy are compared with classic grid-following, grid-forming, and virtual inertia control based on measuring the rate of change of frequency (RoCoF). Finally, an electromagnetic transient simulation model based on PSCAD/EMTDC is developed to verify the effectiveness of the proposed control strategy.