In practice, electrification of remote and islanded communities with no connection to the main grid is entangled with many techno-economic issues. These technical and more importantly economical challenges often justify the use of Micro-Grids (MGs) as self-sufficient electrical networks with a group of controllable/non-controllable consumers and producers in remote and islanded areas. However, the optimal design of sustainable MGs, even in small communities, is a complex optimisation problem due to the uncertain nature of load consumption and renewable production as well as the non-convex characteristics of network constraints. In this paper, we propose a model to design sustainable MGs using the notion of Distributionally Robust Optimisation (DRO) to handle the uncertainties arising from forecast data wherein the non-convex AC power flow equations are reformulated into convex constraints. Furthermore, a three-step approach is introduced to recast the tri-level DRO-based model into a tractable single-stage Mixed-Integer Linear Programming (MILP) problem. The proposed approach is tested on a modified Europrean CIGRE 18-bus test network and its performance is compared with the stochastic optimisation approach.