The electric energy sector is moving toward extensive integration of renewable and clean energy resources, energy storage units, and modern loads via highly efficient and flexible multiterminal dc grids integrated within the traditional ac grid infrastructure. A voltage-source converter (VSC) is the main technology enabling the interconnection of dc and ac grids. In such demanding applications, dc-link voltage control is crucial to maintain system stability. However, the dynamics and control of VSCs considering the instantaneous power of both ac- and dc-side filters and dc grid uncertainties are not addressed in the current literature. Furthermore, as shown in this paper, the uncertainty in the effective dc grid parameters, including filter capacitance and dc-side inductance owing to connecting/disconnecting electric devices to/from the dc grid remarkably affects the converter stability and performance. To overcome these difficulties, this paper presents 1) a detailed small-signal model of the dc-link dynamics in grid-connected VSCs considering the instantaneous power of both ac- and dc-side energy storage components, and 2) a robust optimal dc-link voltage controller. The proposed controller ensures excellent tracking performance, robust disturbance rejection, and robust performance against operating point and parameter variation with a simple fixed-parameter controller. A theoretical analysis, comparative simulation studies, and experimental results are presented to show the effectiveness of the proposed control structure.