Fundamentals and mathematical framework for hydro-solar complementary weekly regulation of cascade reservoirs based on energy balance

In order to utilize the hydropower resources with a 90% guaranteed output rate to balance the power output of photovoltaic （PV） resources with a 10% guaranteed output rate， thereby delivering new energy power to the grid with the same reliability as hydropower， this study investigated the fundamental theory of hydro-solar complementary weekly regulation of cascade reservoirs and proposed a corresponding mathematical model. A method was developed to determine PV resource characteristics， their stochastic properties， and curtailment levels. Theoretical and practical formulas describing the relationship between reservoir water level and power generation potential energy were derived. Based on these formulations， a weekly regulation model for cascade reservoir hydro-solar hybrid systems was established. Taking the renewable energy base in the upper Jinsha River as a case study， quantitative analyses of daily PV generation and curtailment were conducted for the Yebatan and Lawa seasonal regulating reservoirs with a PV installed capacity of 12，000 MW. On the basis of this simple linear weekly regulation algorithm， monthly， annual， and multi-year cascade rolling calculations can be performed to achieve large-scale spatiotemporal numerical simulations， providing a scientific foundation for the planning and demonstration of hydro-solar complementary energy bases.