High-voltage direct current (HVDC) systems linked to AC grids with converters are promising energy transmission systems. These systems present complex AC- and DC-side dynamic interactions. Impedance-based stability studies have recently been proposed to assess DC-side dynamics from DC-side characterization of voltage source converters (VSCs) considering AC-side dynamics. However, the existing approaches used for stability studies in VSC-HVDC systems do not completely model VSCs because they do not consider together the VSC delay, the grid voltage feedforward filter, and all the d- and q-reference current controls. Moreover, these approaches are analytically characterized from dq-real space vectors (less related to circuit theory than dq-complex space vectors), and some work with simple AC grids. The main contribution of this paper is a detailed and complete DC admittance model of VSCs from dq-complex space vectors, which considers the VSC delay, feedforward filter, and d- and q-reference current controls, and also a general AC grid. The proposed model can be used for DC-side stability studies in VSC-HVDC systems considering AC grid dynamics. The capabilities and drawbacks of impedance-based stability methods for DC-side stability assessment were analyzed, and the positive-net-damping criterion was validated as a robust approach. The model was validated by PSCAD/EMTDC simulations and applied to a stability study in a VSC-HVDC system.