This paper presents a generic storage model (GSM) inspired by the scheduling of hydraulic reservoirs. The model for steady state short-term operational studies interlaces with the long-term (LT) energy scheduling through a piecewise-linear future cost function (FCF). Under the assumption that a stochastic dual dynamic programming approach has been used to solve the energy schedule for the LT, the FCF output from that study will be processed to obtain an equivalent marginal opportunity cost for the storage unit. The linear characteristic of a segment of the FCF will allow a linear modeling of the storage unit production cost. This formulation will help to coordinate the renewable resource along with storage facilities in order to find the optimal operation cost while meeting end-point conditions for the LT plan of the energy storage. The generic model will be implemented to represent a battery storage and a pumped-hydro storage. A stochastic unit commitment with the GSM will be formulated and tested to assess the day-ahead scheduling strategy of a virtual power plant facing uncertainties from production, consumption, and market prices.