Model order reduction (MOR) has demonstrated its robustness and wide applicability in simulating large-scale mathematical models in the engineering research domain. In this paper, MOR techniques are applied to quantify relevant reliability metrics of power distribution systems and the impact associated with the integration of different smart grid technologies. To the best of the authors' knowledge, this is the first application of MOR techniques of balanced truncation to derive reliability models of electricity networks, which exhibit a reduced number of equivalent components and thus simplify the complexity for network analysis. The extensive case studies presented, based on both radial and meshed systems, demonstrate that the proposed technique allows for a faster reliability assessment through Monte Carlo simulation while preserving high accuracy. The proposed methodology can also be applied to systems endowed with photovoltaic and energy storage technologies, emphasising that this approach represents a promising starting point for reliability analysis of more complex systems, which are normally characterised by a large penetration of these distributed energy resources.