Uncertainties in our energy system, such as consumption and renewables, pose a challenge to system-wide planning. Deterministic approaches are thus insufficient for making techno-economically optimal decisions for the type, scale, and operations of energy supply and storage facilities. This work adopts a stochastic approach and develops a general multi-period optimization model of an energy system consisting of renewable and non-renewable energy supply sources, storage facilities, and uncertain parameters such as energy demand. It uses multi-stage stochastic programming to address multiple probabilistic scenarios for the stochastic parameters modeled as scenario trees. The model evaluates all the scenarios including the deterministic case and prescribes minimum cost options for the energy supply and storage capacities, and multi-period supply allocations to meet energy demand over a time horizon. The model enables assessment of the potential impacts of variations in demand on energy supply and storage costs and plans as demonstrated by the results of the numerical cases.