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Functional analysis and minimum norm formulation are employed for solving the optimal long‐term problem of a hydro power system for maximum total expected benefits (benefits from energy generated by a hydro power system over the planning period plus the expected future returns from water left in storage at the end of that period). The proposed method takes into account the stochasticity of the river inflows; we assume that their probability properties are preestimated from past history. The adequate fulfillment of other system functions such as flood control and water supply is guaranteed via constraints on storage and release variables. Numerical results are presented for a real system in operation consisting of three rivers; each river has two series reservoirs.

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