In this paper, a detailed mathematical model of a grid-connected micro-grid including wind-turbine, photo voltaic cells, CHP and Fuel Cell with respective uncertainties in electrical loads, thermal loads, PV and wind outputs are presented. Moreover, the effects of the considered uncertainties on the micro-grid’s operation cost are modeled as risk and this risk is reduced using Monte-Carlo simulation through the battery and heat storage systems, separated into dynamic and static capacities. The dynamic capacity reduces the operation cost risk and the static capacity reduces the main (or expected) operation cost.