Multi-Objective Optimal Operations Based on Improved NSGA-II for Hanjiang to Wei River Water Diversion Project, China
2. Study Area and Data
2.1. Study Area
2.2. The Hanjiang to Wei River Water Diversion Project
2.3. Data Situation
3. Modeling and Methodology
3.1. Simulated Operation Model of Water Quantity
3.2. Multi-Objective Optimization Operation Model
- Water balance
- Water level
- Transferable water quantity
- Maximum overflow
- Output of power station
- Power of pump station
3.3. Feasible Search Space
3.4. Steps of the Solution and Settings of the Schemes
3.5. Drafting the Operation Chart of Water Supply
- The maximum storage capacity: this is determined by design data of the maximum water level in flood season and maximum water level in non-flood season.
- The minimum storage capacity: this is decided by design data of dead water level.
- The hedging rule curve for abandoned water: this is decided by the outsourcing line composed of the initial water level for each month in the abandoned water year during long time series data.
- The hedging rule curve for combined water supply: this is determined by the outsourcing line composed of the initial water level of each month in the year of SHK pump stations operation involved during long time series data.
- The hedging rule curve for basic water supply: this is decided by the outsourcing line composed of the initial water level of each month in the year, in this situation, water demand can’t be satisfied and only the SHK reservoir supplies.
4. Results and Discussion
4.1. Simulation Model (Scheme 1)
4.2. Improvement in NSGA-II (Schemes 2 and 3)
- In the design of the Project, if the average annual transferred quantity of water is 1.5 billion, the best water transferred ratio is one where the HJX reservoir transferred approximately 0.8–0.9 billion m3 and the SHK reservoir approximately 0.6–0.7 billion m3.
- The HJX reservoir should undertake the main task of transferring water in flood season to the intake area and the SHK reservoir, and the pumping flow of the HJX pump station is better controlled at around 50 m3/s if the adjustable water is sufficient in volume.
- The SHK pump station is better at reducing operating frequencies and time to save energy. Once the SHK pump station begins operating, it meant the HJX pump station has consumed energy to lift water to the SHK reservoir. The highest volume of water transferred from HJX to SHK is 0.05–0.08 billion m3.
- The SHK reservoir should increase water supply to reduce abandoned water in flood season and avoid drastic fluctuations in the water level.
4.3. Feasible Search Space in I-NSGA-II (Schemes 3~9)
4.4. Operation Chart of the Project
- The simulation results show that the operational framework in this paper is superior to other models designed under the same initial conditions. Therefore, it can be applied to subsequent research.
- Setting a reasonable feasible search space with the NSGA-II can help find better optimal solutions. With the same influence of the initial populations of the algorithm and limited computing ability, the qualified rate of the I-NSGA-II is much higher than that of the NSGA-II.
- It is determined that 10 m3/s is the most suitable search step size value for the feasible search space in this case study. Power generation, energy consumption, rate of guaranteed water supply and the WSI of intake area should all be regarded as factors of evaluation to determine the search step size. A very large or too small feasible search space affects the optimization results.
- It is useful to manage water resources of large-scale IBWT projects in combination with the specific characteristics of the projects, especially under strict constraints of government regulation and the interests of all parties. If the Project operates as shown in Figure 10, it can both meet the demand for water and ensure the optimal conversion of energy in the system according to the needs of the decision makers.
Conflicts of Interest
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|Reservoir||Power Station||Pump Station||Reservoir||Power Station||Pump Station|
|Regulating storage||108 m3||0.92||-||-||7.10||-||-|
|Regulation ability||-||Daily||-||-||Multi-year regulating||-||-|
|Normal high water level||m||450||-||-||643||-||-|
|Flood control level||m||448||-||-||642||-||-|
|Dead water level||m||440||-||-||558||-||-|
|Scheme||Δq b||Search Space||Method||Objects|
|1||-||All feasible space||Simulated||Water quantity (15) a|
|2||-||NSGA-II||Energy consumption Power generation|
|3||Δq = 5||reference Equations (14) and (15)||I-NSGA-II|
|4||Δq = 10|
|5||Δq = 20|
|6||Δq = 30|
|7||Δq = 40|
|8||Δq = 50|
|9||Δq = 60|
|Number of decision variables||672|
|Number of objective functions||3|
|to Intake Area||to SHK||to Intake Area||to SHK|
|Objectives||Model||Simulated||Multi Objective Optimized||Relative Change Rate|
|Water Supplying a||HJX to intake area||9.32||7.91||8.52||−15.13%||−8.58%|
|HJX to SHK||0.47||0.51||0.58||+8.51%||+23.40%|
|SHK to intake area||5.21||6.58||5.90||+26.3%||+13.24%|
|Power generation c||HJX power station||3.70||3.90||3.78||+5.41%||+2.16%|
|SHK power station||1.46||1.53||1.55||+4.79%||+6.16%|
|Energy consumption c||HJX pump station||3.88||3.50||3.78||−9.79%||−2.58%|
|SHK pump station||0.19||0.20||0.23||+5.26%||+21.05%|
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Wu, L.; Bai, T.; Huang, Q.; Wei, J.; Liu, X. Multi-Objective Optimal Operations Based on Improved NSGA-II for Hanjiang to Wei River Water Diversion Project, China. Water 2019, 11, 1159. https://doi.org/10.3390/w11061159
Wu L, Bai T, Huang Q, Wei J, Liu X. Multi-Objective Optimal Operations Based on Improved NSGA-II for Hanjiang to Wei River Water Diversion Project, China. Water. 2019; 11(6):1159. https://doi.org/10.3390/w11061159Chicago/Turabian Style
Wu, Lianzhou, Tao Bai, Qiang Huang, Jian Wei, and Xia Liu. 2019. "Multi-Objective Optimal Operations Based on Improved NSGA-II for Hanjiang to Wei River Water Diversion Project, China" Water 11, no. 6: 1159. https://doi.org/10.3390/w11061159