Scheduling hydrothermal power systems with cascaded and head-dependent reservoirs

An optimization-based algorithm is presented for scheduling hydrothermal power systems with cascaded and head-dependent reservoirs. Within the Lagrangian relaxation framework, the hydro river catchment subproblems are difficult to solve because of the continuous reservoir dynamics and constraints, discontinuous operating regions, discrete operating states and hydraulic coupling of cascaded reservoirs. The head-dependent water-power conversion adds another dimension of difficulty since the objective functions of hydro subproblems are no longer stage-wise additive with respect to water discharge. It is difficult to solve the subproblems by relaxing the reservoir limits or the hydraulic coupling among units as in previous work A new algorithm with a novel relaxation structure is presented in this paper to solve hydro river catchment subproblems. The key idea is to use another set of multipliers to relax capacity and minimum generation constraints of individual hydro units. A river catchment subproblem can be further decomposed into two sets of subproblems: a continuous-variable optimization problem determining the generation levels of all units in the entire river catchment, and a number of pure integer problems determining the hydro commitment states, one for each unit. The continuous problem is solved by a nonlinear network flow algorithm, and the integer problems are solved by dynamic programming with a small number of states and well-structured transitions. The two sets of subproblems are coordinated through the multipliers that are updated at the intermediate dual level by using a modified subgradient algorithm. After the dual problem converges, the feasible hydro schedule is obtained by using the same network flow algorithm with operating states obtained in the dual solution and possibly adjusted by heuristics. Numerical testing based on the data sets of a practical system shows that this method is efficient and effective to deal with hydrothermal systems with cascaded and head-dependent reservoirs, and discrete hydro constraints. The results indicate that near-optimal schedules are obtained.