An optimization-based algorithm for scheduling hydrothermal power systems with cascaded reservoirs and discrete hydro constraints

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An optimization-based algorithm is presented for the short-term scheduling of hydrothermal power systems using the Lagrangian relaxation technique. This paper concentrates on the solution methodology for hydro subproblems with cascaded reservoirs and discrete hydro constraints. Continuous reservoir dynamics and constraints, discontinuous operating regions, discrete operating states and hydraulic coupling of cascaded reservoirs are considered in an integrated fashion. The key idea is to substitute out the reservoir dynamics and to relax the reservoir level constraints by using another set of multipliers, making a hydro subproblem unit-wise and stage-wise decomposable. The optimal generation level for each operating state at each hour can be obtained simply by minimizing a single variable function. Dynamic programming is then applied to optimize the operating states across the planning horizon with a small number of well structured transitions. A modified subgradient algorithm is used to update multipliers. After the dual problem converges, the feasible solution to the hydropower subsystem is obtained by using a network flow algorithm, with operating states obtained in the dual solutions, and possibly adjusted by heuristics. Numerical testing based on practical system data sets show that this method is efficient and effective for dealing with hydrothermal power systems with cascaded reservoirs and discrete hydroelectric constraints.