This paper presents a mixed-integer conic programming model (MICP) and a hybrid solution approach based on classical and heuristic optimization techniques, namely matheuristic,to handle long-term distribution systems expansion planning (DSEP) problems. The model considers conventional planning actions as well as sizing and allocation of dispatchable/renewable distributed generation (DG) and energy storage devices (ESD).The existing uncertainties in the behavior of renewable sources and demands are characterized by grouping the historical data via the ${k}$ -means. Since the resulting stochastic MICPis a convex-based formulation, finding the global solution of the problem using a commercial solver is guaranteed while the computational efficiency in simulating the planning problem of medium- or large-scale systems might not be satisfactory. To tackle this issue, the subproblems of the proposed mathematical model are solved iteratively via a specialized optimization technique based on variable neighborhood descent (VND) algorithm. To show the effectiveness of the proposed model and solution technique, the 24-node distribution system is profoundly analyzed, while the applicability of the model is tested on a 182-node distribution system.The results reveal the essential requirement of developing specialized solution techniques for large-scale systems where classical optimization techniques are no longer an alternative to solve such planning problems.