Electronic Capacitors (ECs) are two-terminal "plug-and-play"active devices, typically utilized to replace bulk DC link electrolytic capacitance in grid-connected power conversion systems. An EC consists of a bidirectional power converter, terminated by small auxiliary capacitor, and a feedback control system, forcing the system to emulate a large finite capacitance at the output terminals, based on local measurements only. Typically, DC link voltage regulation is carried out by the outer loop controller of grid-connected converter, tuned to a specific value of DC-link capacitor. Therefore, accurate emulation of this specific capacitance by an EC is essential to preserve prescribed DC link voltage dynamics, which directly influences grid-side current quality. However, due to finite capacitance employed, steady-state DC link ripple is always present in grid-connected power systems. The paper proposes a modification of EC control structure, allowing to achieve near-zero DC-link ripple (i.e. emulating infinite capacitor in steady-state) while maintaining accurate transient dynamics of a specific finite-valued capacitance.