Evaluating the marginal utility principle for long-term hydropower scheduling

The conversion of the potential energy of dammed water into hydropower depends on both reservoir storage and release, which are the major difficulties in hydropower reservoir operation. This study evaluates the marginal utility principle, which determines the optimal carry-over storage between periods, for long-term hydropower scheduling. Increasing marginal cost and decreasing marginal return are two important characteristics that determine the marginal utility principle in water supply. However, the notion of decreasing marginal return is inapplicable in hydropower scheduling. Instead, the carry-over storage from one period has an increasing marginal contribution to the power generation in the next period. Although carry-over storage incurs an increasing marginal cost to the power generation in the current period, the marginal return is higher than the marginal cost. The marginal return from the carry-over storage further increases in the multi-period case. These findings suggest saving as much carry-over storage as possible, which is bounded by the operational constraints of storage capacity, environmental flow, and installed capacity in actual hydropower scheduling. The marginal utility principle is evaluated for a case study of the Three Gorges Reservoir, and the effects of the constraints are discussed. Results confirm the theoretical findings and show that the marginal return from carry-over storage is larger than the marginal cost. The operational constraints help determine the optimal carry-over storage.