Hydro generation scheduling: non-linear programming and optimality conditions
A mathematical analysis based on hydroelectric plant characteristics, i.e. reservoir and tailrace geometry, is the central chapter's subject. Deterministic mid-short term scheduling planning could be solved to optimality if generation function is at least biconcave, i.e. a discontinuous reservoir and a uniform tailrace. Although the formulation is not proved to be unimodal, a B&B method based on concave envelope relaxation converges to global optimum. In a broader sense, increasing property is established for hydro-generation function. As the formulation is linearly constrained, i.e. only linear inequalities, special algorithms could exploit boundary of the feasible set (a polytope) to find a global optimum. Unimodularity property could also be studied in general case, i.e. arbitrary reservoir and tailrace height.