Uncertainties of renewable power generation, load, and electricity price imposes serious challenges in optimal scheduling of microgrids (MGs). To cope with this issue, advanced models should be developed to optimize scheduling problem of MGs under uncertainties. However, the optimality and robustness of solutions as well as the computational burden are still a matter of concern when applied to scheduling of a practical MG. To provide a model which is adjustably robust and computationally tractable and also financial effective at the same time, this paper proposes a novel uncertainty handling framework based on stochastic p-robust optimization method for day-ahead scheduling of MGs including renewable and non-renewable distributed generations, combined heat and power systems, energy-storage systems, as well as demand response providers. The objective is to find optimal scheduling of MG in a way that the expected profit is maximized while the regret in each scenario is bounded. The effectiveness of the proposed model is tested on a MG test system thorough different case studies. Simulation results demonstrate that the robustness of the scheduling results is enhanced significantly without substantial decrease in the expected profit of MG. (C) 2019 Elsevier Ltd. All rights reserved.