Chance-constrained co-optimization for day-ahead generation and reserve scheduling of cascade hydropower-variable renewable energy hybrid systems

The rapid development of variable renewable energy (VRE), such as wind and solar energy, has stimulated the complementary operation of VRE with flexible cascade hydropower stations in China. Due to the uncertainties of VRE power generation and complex constraints of cascade hydropower stations, formulating reliable day-ahead generation and reserve scheduling plans is a real challenge in the actual operation stage of the cascade hydropower-VRE hybrid systems (CHVHS). In this paper, we propose a tractable chance-constrained co-optimization model for day-ahead generation and reserve scheduling of a CHVHES. First, compared with existing models, the relationship between the hydropower reserve capacities and water-electricity conversion efficiency is finely modeled. Accordingly, the economic allocation of total VRE reserve requirements among cascade hydropower stations is for the first time considered in our proposed model. This can save more water resources for cascade hydropower stations when compensating for VRE, further improving hydro-VRE complementary profits. Second, we propose a solution approach for chance constraints by incorporating the nonparametric probabilistic forecasting of VRE power based on quantile regression into the chance-constrained model, ensuring that the stochastic dependence between VRE power output and its point forecast can be effectively captured. Importantly, this solution approach does not require prior knowledge or any probability distribution assumptions of VRE power and does not introduce any additional computational burden. With the help of three-dimensional interpolation technology for nonlinear constraints, the proposed scheduling model is finally cast as a mixed-integer linear programming model that is computationally tractable. Numerical tests implemented on a real CHVHES located in Southwest China verify the effectiveness and advantages of the proposed methods.