This paper presents a novel mixed-integer second-order cone programming model for the robust multi-stage substation expansion planning problem considering stochastic demand. The stochastic nature of the demands is considered through a robust model that uses chance constraints to guarantee that the substation capacity limits are satisfied within a given robustness probability. Furthermore, a multi-objective formulation that takes into account the total expected expansion planning cost and the robustness probability related to the violation of the substation capacity limits is proposed. The optimal solution of the proposed model is guaranteed by the convexity of the formulation, when classical optimization techniques are used in its solution. The results found (construction of new substations, reinforcement of existing substations, and service area of each substation) for two test systems demonstrate the efficiency and robustness of the proposed model. Additionally, Monte Carlo simulations were carried out in order to evaluate the extent to which the solutions found were able to satisfy the substation capacity limits.