Abstract Heating electrification powered by distributed renewable energy generation is considered among potential solutions towards mitigation of greenhouse gas emissions. Roadmaps propose a wide deployment of heat pumps and photovoltaics in the residential sector. Since current distribution grids are not designed to accommodate these loads, potential benefits of such policies might be compromised. However, in large-scale analyses, often grid constraints are neglected. On the other hand, grid impact of heat pumps and photovoltaics has been investigated without considering the influence of building characteristics. This paper aims to assess and quantify in a probabilistic way the impact of these technologies on the low-voltage distribution grid, as a function of building and district properties. The Monte Carlo approach is used to simulate an assortment of Belgian residential feeders, with varying size, cable type, heat pump and PV penetration rates, and buildings of different geometry and insulation quality. Modelica-based models simulate the dynamic behavior of both buildings and heating systems, as well as three-phase unbalanced loading of the network. Additionally, stochastic occupant behavior is taken into account. Analysis of neighborhood load profiles puts into perspective the importance of demand diversity in terms of building characteristics and load simultaneity, highlighting the crucial role of back-up electrical loads. It is shown that air-source heat pumps have a greater impact on the studied feeders than PV, in terms of loading and voltage magnitude. Furthermore, rural feeders are more prone to overloading and under-voltage problems than urban ones. For large rural feeders, cable overloading can be expected already from 30% heat pump penetration, depending on the cable, while voltage problems start usually at slightly higher percentages. Additionally, building characteristics show high correlations with the examined grid performance indicators, revealing promising potential for statistical modeling of the studied indicators. Further work will be directed to the assessment of meta-modeling techniques for this purpose. The presented models and methodology can easily incorporate other technologies or scenarios and could be used in support of policy making or network design.