More and more wind and solar are installed to limit the global warming. Demand side management is often seen as a tool to allow more renewables to be integrated. The renewable generation such as photovoltaic (PV) power and wind power generation and load in the microgrid may have considerable forecast errors with uncertainties of solar radiation, wind speed and local demands. In this paper, scenarios are selected corresponding to a specified confidence interval by mathematical formulation of duration curves methodology in energy mix optimization for considering the uncertainty. The methodology to reflect the degree of uncertainties of renewable generation and load according to their patterns using the duration curves of the forecasted generation and load is presented when a stochastic solution is achieved by energy mix optimization. Through the case study for a microgrid with uncertainties, it is shown that this stochastic methodology can be applied effectively for optimal operation of a microgrid with uncertainties through the case study.