With the rising concerns about climate change and technological developments, the deployment of low carbon technologies (LCT) is gaining importance for reliable and sustainable power system operation. To decarbonize the heat and transportation sectors, LCTs such as heat pumps (HP) and electric vehicles (EV) are integrated into the power system from the low voltage (LV) distribution network, where predominantly end-users are connected. However, the increasing penetration of EVs and HPs, together with distributed photovoltaic (PV) systems on the demand side, can cause technical challenges in LV distribution networks, such as under/over voltages at the far end of the feeders. Therefore, the hosting capacity of a grid for LCTs is limited due to network constraints such as line ampacity, bus voltage, and frequency. In this paper, voltage-constrained management approaches for LCTs are proposed to improve the grid hosting capacity in a real large-scale distribution network. Moreover, HPs, PVs, battery energy storage systems (BESS), and EVs as well as their vehicle-to-grid (V2G) feature are evaluated as LCTs. The uncertain behavior of these technologies is taken into consideration for more realistic analyses. In addition, the charging and discharging interactions of BESSs are controlled by following the power consumption profiles from the economic point of view. Furthermore, the hourly carbon data is used to control BESSs from an emission-sensitive aspect. To demonstrate the effectiveness of the proposed algorithms, a series of tests is conducted on a real distribution network model. The results show that the hosting capacity of the considered LV network can be increased from 35% to 50% using the proposed algorithms. The promising results obtained in this study pave the way for future active LCT management studies to improve hosting capacity in urban networks, and pilot demonstrations in the field.