Abstract
Some hydropower reservoirs are operated under different constraint levels. For these reservoirs, a multi-level (ML) dependent-chance (DC) model is established. In the model, only when the higher-level constraints are satisfied are the lower-level constraints or system benefits considered. The multi-level dependent-chance (MLDC) model is specified by two models. One is based on existing reliability-constrained (RC) dynamic programming (DP), in which the soft constraints are addressed using reliability constraints of 1, and the priorities are reflected using the order of magnitudes of Lagrange multipliers. The other is the explicit dependent-chance reasoning in the DP recursive function, in which each soft constraint is represented as an objective function of negative expected failure time and the optimum is the solution with a larger value for all higher-level objective functions. The proposed models are applied to derive long-term operation rules for the hydropower system on the middle-lower Lancang River. The results show the feasibility and performances of the explicit graded constraint control of the proposed model and the solution methods.