High penetrations of renewable energy sources (RES) in distribution grids lead to new challenges in voltage regulation. These challenges are not just limited to the steady-state voltage rise, but they are extended to rapid voltage changes due to wind speed variations and moving clouds, casting shadows on photovoltaic panels. According to EN50160 in low-voltage (LV) grids, the steady-state voltage should not exceed 1.1 pu (static characteristic), and rapid voltage changes should be kept less than 0.05 pu (dynamic characteristic). These two characteristics may limit the maximum amount of RES that can be installed in LV grids, called, respectively, the static hosting capacity (SHC) and dynamic hosting capacity (DHC). Although existing research just evaluated SHC in distribution grids, high-penetrated RES grids can be faced with such large voltage changes, which cause a smaller DHC than the SHC. This paper studies both SHC and DHC in distribution grids and proposes an adaptive controller for static synchronous compensators to regulate the steady-state and dynamic voltage while avoiding the unnecessary increase in the reactive power. The simulation results in some German distribution grids show considerable effects of the proposed adaptive controller on improving both SHC and DHC.