In weak power systems experiencing significant generation/load fluctuations (e.g., high renewable penetration, fast charging), voltage deviations at critical points threaten stability. While diesel generators provide essential backup, their slow response and coarse power regulation often exacerbate voltage issues. This work proposes a novel energy storage converter control scheme that synergistically works with diesel resources to rapidly suppress voltage deviations, enhancing grid resilience and enabling cost-effective integration of renewables in remote or fragile grids. A mathematical model of the generator under a synchronous rotating coordinate system is established, yielding step-response expressions for output voltage and rotational speed. Building on this foundation, a coordinated power supply scheme is proposed, connecting an energy storage converter in parallel with the diesel generator set. This scheme aims to suppress fluctuations in output voltage magnitude and frequency caused by sudden load changes. The energy storage converter provides the total reactive power required and the active power demand during load transients, thereby improving the system's dynamic power quality. Methods for generating reactive power and dynamic active power reference setpoints are introduced. Corresponding simulation results demonstrate that with the inclusion of the energy storage converter, all reactive power is supplied by the converter and the voltage quality is significantly improved under step power changes.