## 4 Case Study  
The Wujiang multireservoir system is in the Wujiang Basin, and the Wujiang River is in southwest China. The area of this basin is 87,900 km\({}^{2}\), and the precipitation rate for this basin varies from 900 to 1400 mm. This system is one of 13 global systems that produce hydropower, and there are four hydropower reservoirs in this system. The water level reflects the reservoir storage, and thus the variation of outflow is affected by the fluctuation of the water level. When the water level was determined, the storage capacity could be calculated, and hence the outflow (water release) from the reservoir could be computed by continuity and the state equation. Figure 2 shows the multireservoir system where \(q_{1}\), \(q_{2}\), and \(q_{3}\) represent the inflow for each reservoir. Figure 1: Crow flowchart algorithm. The SFY reservoir has small regulatory storage. Thus, the optimization process was implemented on other reservoirs. Table 1 presents various characteristics for all reservoirs in this study, such as the normal water level, dead water level, total storage, regulation storage, and power efficiency. It is noticeable that there is different regulation storage in the presented reservoirs: SFY has daily regulation, DF and WJD are regulated seasonally, while there is multiyear regulation for HJD. The main duty of the DF reservoir is hydropower generation, where the normal water level is 345 m, and the dead water level is 936 m. The efficiency of this hydropower plant is 8.35. The SFY reservoir has a storage of approximately 0.2 billion m\({}^{3}\) and is downstream of the DF reservoir: The hydraulic head of the DYF is 936 m due to low storage in the reservoir. The capacity for the WJD hydropower plant is 1250 MW: The normal water level for this reservoir is 502 m, and the dead water level for this reservoir is 720 m. The total hydropower output from the system should be 680 MW to guarantee downstream demands. The inflow value for the reservoirs and the interzone for different climate conditions (wet, normal, and dry) are mentioned in Table 2. Additionally, the outflow for the WJD reservoir should be more than 100 m\({}^{3}\)/s due to navigation safety. The power coefficient in Table 1 was used to determine the efficiency of the entire turbine power system. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reservoir Item**} & \multicolumn{3}{c}{**Wet Year (m\({}^{3}\)/s)**} & \multicolumn{3}{c}{**Normal Year (m\({}^{3}\)/s)**} & \multicolumn{3}{c}{**Dry Year (m\({}^{5}\)/s)**} \\ \cline{2-11}  & **HJD** & **H-D** & **  
Dry years (May 1963-April 1964), wet years (May 1951-April 1952), and normal years (May 1985-April 1986) were considered different scenarios in the operation of the multireservoir system. The aim of the problem was to maximize hydropower production for the multireservoir system. Three years for each scenario were considered to examine the performance of the proposed algorithm for different conditions, because it was important that the method could manage the basin for the years with a scarcity of water resources. The generated hydropower is dependent on the hydraulic head and turbine release, and both parameters were computed by determining the water level of the reservoirs. The outflows for the reservoirs were computed when the upstream water level was determined, and Equation (6) was used for computing the outflow when considering the spillway and turbine release. The outflow from each reservoir was considered to be the inflow into the downstream reservoir: When the outflow increased, the water level increased downstream, which caused a lower hydraulic head. The objective function was computed based on Equation (7) [26]:  
\[ \begin{array}{l}V_{m,t+1}=V_{m,t}+\eta(I_{m,t}-Q_{m,t})\\ I_{m+1,t}=IQ_{m+1,t}+Q_{m,t-\tau_{m}}\end{array}