Modern power systems must deal with a greater degree of uncertainty in power flow calculation due to variations in load and generation introduced by new technologies. This scenario poses new challenges to power system operators which require new tools for an accurate assessment of the system state. This paper presents an interval load flow (ILF) approach for dealing with uncertainty in power system analysis. A probabilistic load flow (PLF), based on Monte Carlo Simulation (MCS), was also implemented for comparative purposes. The ILF and PLF are used to estimate the network states. Both methods were implemented in Python® using the IEEE 34-bus, IEEE 69-bus and 192-bus Brazilian distribution system. The results with the proposed ILF on the aforementioned benchmark test systems proved to be compatible with that of the MCS, evidencing the robustness and applicability of the proposed approach.