This article deals with DC voltage dynamics of Multi-Terminal HVDC grids (MTDC) with energy-based controlled Modular Multilevel Converters (MMC) adopting the commonly used power-voltage droop control technique for power flow dispatch. Special focus is given on the energy management strategies of the MMCs and their ability to influence on the DC voltage dynamics. First, it is shown that decoupling the MMC energy from the DC side, causes large and undesired DC voltage transient after a sudden power flow change. This occurs when this energy is controlled to a fixed value regardless of the DC voltage level. Second, the Virtual Capacitor Control technique is implemented in order to improve the results. However, its limitations on droop-based MTDC grids are highlighted. Finally, a novel energy management approach is proposed to improve the performance of the later method. These studies are performed with detailed MMC models suitable for the use of linear analysis techniques. The derived MTDC models are validated against time-domain simulations using detailed EMT MMC models with 400 sub-modules per arm.