AbstractUnderstanding the trade-offs associated with the two operation stages of hydropower generation is critical for guiding efficient reservoir operations. Previous studies showed that the marginal return in Stage 2 is always higher than the marginal cost in Stage 1 if variations in tailwater levels are ignored. However, the tailwater level often raises faster than the reservoir water level, and thus reduces the net hydraulic head of the reservoirs with reaction turbines, especially in large-scale and low-head reservoirs. Therefore, this study considers the variations in tailwater levels and theoretically evaluates the marginal utility of the total power generation (TPG) in the two stages. It is found that the variation of TPG presents diminishing marginal utility and is closely related to the topography characteristics of the reservoir and downstream channels, as well as the relationship between releases in the two stages. The marginal return in Stage 2 might be lower than the marginal cost in Stage 1 when the release in Stage 2 exceeds that in Stage 1 for the reservoirs in which the tailwater level is sensitive to discharge and hydraulic head. This suggests that the carryover storage equalizing the marginal utility in the two stages is optimal, i.e., satisfying the marginal utility principle. Otherwise, the marginal return is always higher than the marginal cost, which suggests that as much carryover storage as possible should be saved. Following these findings, the reservoir states, represented by the storage difference and the total inflow in the two stages, that satisfy the marginal utility principle are identified. Further, the optimal carryover storage under different levels of inflow and storage difference is derived. The theoretical findings are verified with four hydropower plants in China. Results confirm the theoretical findings and show that two-stage hydropower generation coupled with operating rules can greatly improve the performance of hydropower generation.

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