High integration of rooftop photovoltaic (PV) plants in distribution systems leads to new technical challenges: reverse-active power and voltage rise in low-voltage (LV) and medium-voltage (MV) grids. These challenges limit the maximum amount of power can be produced by PVs in LV and MV grids, called the hosting capacity (HC). Battery storage systems (BSSs) have been used in many studies to decrease the reverse power and improve the HC by controlling the active power. However, the influence of a central BSS on the HC can be greatly improved by using a quadratic power control, simultaneous active, and reactive power control, and by selecting of the optimal battery size, the converter size, and the place of the central BSS. The effectiveness of the quadratic power control was not seen in previous works due to the fact that grids with one level of voltage without modeling of MV/LV transformers were simulated. This paper develops a method to select the optimal size of the battery and converter unit as well as the optimal place of an LV-central BSS having an optimal quadratic power control. The simulation results show considerable effects of the optimal selection of an LV-central BSS on the HC improvement.