Stochastic programming with a joint chance constraint model for reservoir refill operation considering flood risk

Reservoir refill operation modeling attempts to maximize a set of benefits while minimizing risks. The benefits and risks can be in opposition to each other, such as having enough water for hydropower generation while leaving enough room for flood protection. In addition to multiple objects, the uncertainty of streamflow can make decision making difficult. This paper develops a stochastic optimization model for reservoir refill operation with the objective of maximizing the expected synthesized energy production for a cascade system of hydropower stations while considering flood risk. Streamflow uncertainty is addressed by discretized streamflow scenarios and flood risk is controlled by a joint chance constraint restricting the occurrence probability. With the variability of flood risk level, two advancing refill scenarios for exploring operation benefit are presented. Scenario I loosens the current stagewise storage bounds conditions and allows advancing reservoir refills but keeps the flood risk level the same as the refill policies obtained under the current storage bounds. Scenario II keeps the current storage bounds unchanged but allows increases in flood risk level. The proposed methodology is applied to the Xiluodu cascade system of reservoirs in China and investigates the optimal refill policies obtained by both scenarios. Compared with the benchmark obtained under the current storage bounds and lowest flood risk level, the results show (1) the synthesized energy production can be improved by 2.13% without changing the flood risk level under Scenario I, and (2) the synthesized energy production can also be increased by 0.21% at the expense of increasing the flood risk level by 4.4% when Scenario II is employed. As Scenario I produces higher benefit and lower risk than Scenario II, it is recommended to loosen the current stagewise storage bounds but to keep the flood risk level unchanged during refill operations.