A stochastic linear programming model for maximizing generation and firm output at a reliability in long-term hydropower reservoir operation - Chen, Cheng; Feng, Suzhen; Liu, Shuangquan; Zheng, Hao; Zhang, Hong; Wang, Jinwen (Journal of hydrology (Amsterdam), 2023)
•A modeling framework to express complex probabilistic constraints by assigning an unknown probability for a decision made at a state.•A stochastic linear programming (SLP) model to explicitly incorporate the reliability in ensuring an unknown firm output to be maximized.•Superiority of the SLP numerically demonstrated over the SDP in ensuring a firm output at a higher reliability. The firm output, usually determined in the design stage of a hydroplant to serve as a threshold to measure system reliability, can be regarded as an unknown parameter to be explored to its maximum in long-term hydropower reservoir operation (LHRO). An unknown firm output to be ensured at certain reliability, however, will make the problem much more nonlinear and then complicate the modeling. This work presents a stochastic linear programming (SLP-1) model that can explicitly incorporate reliability in ensuring an unknown firm output to be maximized by using a probability variable to represent a decision at a state and introducing binary variables to decide whether the decision will ensure the unknown firm output. The present SLP-1 is improved on 1) another previous SLP model (SLP-0) that must have a firm output prespecified at certain reliability, and compared with 2) the stochastic dynamic programming (SDP) model that can only manage to estimate the firm output at a reliability with trial and error. Case studies show the superiority of the present SLP to the SDP that can hardly make the reliability any closer to what the SLP can achieve, especially in ensuring a high firm output, with gaps to desired reliability ranging up to 42.33% for Xiaowan and 31.8% for Nuozhadu. Indeed, the SLP-1 will encounter the dimensional difficulty that needs further efforts to overcome when applied to cascaded reservoirs.