Bi-level hybrid game model for optimal operation of multi-function reservoir considering integrated water resource management

Damming can promote flood control, water supply, power generation, and shipping but often changes the downstream hydrological regimes, producing adverse externality effects. Maximizing downstream social and ecological benefits will inevitably reduce upstream power generation. This study presents two novel bi-level hybrid game models, called the non-cooperative hybrid game model (NCHG) and the cooperative hybrid game model (CHG), to facilitate integrated water resource management in reservoir systems. The performance index of propensity to disrupt is applied to evaluate the stability of CHG, and an improved reliability index and Gini coefficient are adopted to evaluate the reliability and equity of both two models. The Three Gorges Reservoir and its adjacent cities were chosen as a case to inspect the two models' performance. A range of scheduling schemes was derived by proposed bi-level hybrid game models in wet, normal, and dry years. Results reveal that (i) the RI values of the watershed system obtained by the CHG are less than those in NCHG in three typical years (for example, 0.1201 VS 0.1930 in the wet year), showing higher systemic reliability. The Gini coefficients of the watershed system obtained by the CHG are all less than those obtained by the NCHG in all typical years (for example, 0.1016 VS 0.1020 in the wet year), which shows better performance of CHG on fairness for the allocation results; (ii) in the case of a multi-function reservoir system, the CHG generates favorable allocation schemes with higher systemic characteristic values by 32.43, 34.39, and 33.54 in wet, normal, and dry years, respectively, than those in NCHG (32.03, 33.16, and 31.42 in wet, normal, and dry years, respectively); (iii) compared with NCHG, the economic benefits obtained by CHG decreased by 0.98%, 1.04%, and 5.42% in wet, normal, and dry years, respectively; the social negative benefits decreased by 3.49%, 9.84%, and 28.69%; and the ecological negative benefits decreased by 1.77%, 5.65%, and 5.59%, respectively. It indicates that a minor sacrifice of the reservoir benefit could significantly improve the welfare at the system level by the CHG. The developed CHG can provide optimal water scheduling schemes in balancing inter-regional water conflicts and can be widely used to produce an equilibrium management strategy for a multi-function reservoir system.