A mathematical model designs and operates a hybrid power system consisting of diesel generators, photovoltaic cells and battery storage to minimize fuel use at remote sites subject to meeting variable demand profiles, given the following constraints: power generated must meet demand in every time period; power generated by any technology cannot exceed its maximum rating; and best practices should be enforced to prolong the life of the technologies. We solve this optimization model in two phases: (i) we obtain the design and dispatch strategy for an hourly load profile, and (ii) we use the design strategy, derived in (i), as input to produce the optimal dispatch strategy at the minute level. Our contributions consist of: combining a year-long hourly optimization procurement strategy with a minute-level dispatch strategy, and using a high-fidelity battery model at the minute-level derived from electrochemical engineering principles that incorporate temperature and voltage transient effects. We solve both phases of the optimization problem to within 5% of optimality and demonstrate that solutions from the minute-level model more closely match the load, more closely capture battery and generator behavior, and provide fuel savings from a few percent to 30% over that provided by the hour-level model for the tested scenarios.