Reservoir Scheduling Using a Multi-Objective Cuckoo Search Algorithm under Climate Change in Jinsha River, China
Abstract
:1. Introduction
2. Methods
2.1. Estimating Climate Change Impacts on Hydropower
2.2. Improved Multi-Objective Cuckoo Search Algorithm
2.2.1. NGSA-II
- (1)
- Randomly generate an initial population of size N. Then, sort the initial population using the non-dominated method.
- (2)
- Generate new subpopulations through selection, crossover, and mutation operations of the evolutionary algorithm.
- (3)
- Merge the parent and child populations and select the most fit individuals to form the next-generation population based on a dominance relationship and crowding degree.
- (4)
- Repeat the above processes until the termination condition is met.
2.2.2. Improved Cuckoo Search
- (1)
- Dynamic parameter adjustment strategy
- (2)
- Differential strategy for Lévy flight
- (3)
- Revised solution
Algorithm 1. Improved cuckoo search |
Objective function |
Initialize default parameters |
Generate initial population of n host nests |
While (t < MaxEvaluation) or (stop criterion) |
Select two solution from host nests randomly |
For d=1,…, D do |
End for |
If |
Replace xi by the new solution |
End if |
If |
Init the worst nest |
End if |
End while |
2.2.3. Multi-Objective Cuckoo Search
- (1)
- Generate a random initial population, and classify the individuals using the non-dominated sorting method. A new population can then be generated using the ICS algorithm.
- (2)
- Merge the parent and child populations, employ a fast, non-dominated sorting and crowding degree calculation in the mixed population, and select the most fit individuals to form the next generation.
- (3)
- Repeat the processes above until the termination conditions are met.
2.3. Gradient Multi-Objective Cuckoo Search for Reservoir Scheduling
2.3.1. Power Generation Objective
2.3.2. Residual Load Variance Objective
2.3.3. Constraints
- (1)
- Hydraulic connection (Equation (7)):
- (2)
- Water-balance constraint (Equation (8)):
- (3)
- Water-level constraints (Equations (9) and (10)):
- (4)
- Outflow constraint (Equation (11)):
- (5)
- Output constraint (Equation (12)):
- (6)
- Boundary condition (Equation (13)):
2.3.4. Solution Encoding and Initialization
2.3.5. Gradient Search Strategy
2.3.6. Single Entry External Archive
2.3.7. Self-Tuning Divergent Operator Strategy
2.3.8. Procedures of Solving MLTHG with Gradient Based MoCS
- (1)
- Set the initial conditions of the MLTHG model, including incoming water, water level of each hydropower station in the initial time period and the end time period.
- (2)
- Set up the constraints of the MLTHG model, including the maximum outflow, minimum outflow, maximum water level, minimum water level, and water level variation in each period of each hydropower station. The setting of water level constraints needs to consider the flood control requirements in the flood season.
- (3)
- Set the parameters of the GMoCS algorithm.
- (4)
- Generate a random individual according to Equations (14) and (15), calculate its objective values and check whether it meets all constraints. If the constraints are met, added it to the initial population. Generate other new individuals using the same method until the population size is reached.
- (5)
- Generate new individual by Lévy flight.
- (6)
- Calculate objective values of the new individual and check whether it meets all constraints. If the new individual does not meet the constraints, try to adjust the water level to make it meet the constraints.
- (7)
- Mix the old and new populations. Perform non-dominated sorting and crowding calculations on the mixed population. Select better individuals to form the next generation population.
- (8)
- Select the individual with the largest power generation and perform gradient search for the power generation objective. Then, select the individual with the smallest residual load variance, and perform gradient search for the residual load variance objective.
- (9)
- Select non-dominated individuals from the next generation population. Insert the non-dominated individuals into the external archives one by one, while replacing the worst individual with a better random individual with a certain probability.
- (10)
- Repeat steps 3–9 until the termination condition is met.
- (11)
- Select non-dominated individuals from the external archive set as the Pareto optimal frontier. Export time series data of these individuals, including water level, outflow, power output, etc.
2.4. MLTHG in Jinsha River
2.4.1. The Projection of Streamflow in the Context of Climate Change
2.4.2. Modeling of MLTHG in Jinsha River
3. Results and Discussion
3.1. Performance of GMoCS
3.2. Climate Change on Multi-Objective Scheduling of Cascade Hydropower Stations
3.2.1. Power Generation Objective
3.2.2. Residual Load Variance Objective
3.2.3. Combination of the Two Objectives
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameters | Wudongde | Baihetan | Xiluodu | Xiangjiaba |
---|---|---|---|---|
Dead water level (m) | 945 | 765 | 540 | 370 |
Normal water level (m) | 977 | 825 | 600 | 380 |
Flood limit water level (m) | 952 | 785 | 560 | 370 |
Installed capacity (104 kw) | 1020 | 1600 | 1260 | 600 |
Total capacity (108 m3) | 74.08 | 206.27 | 126.7 | 51.63 |
Minimum outflow (m3·s−1) | 906 | 905 | 1500 | 1500 |
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Feng, Y.; Xu, J.; Hong, Y.; Wang, Y.; Yuan, Z.; Wang, C. Reservoir Scheduling Using a Multi-Objective Cuckoo Search Algorithm under Climate Change in Jinsha River, China. Water 2021, 13, 1803. https://doi.org/10.3390/w13131803
Feng Y, Xu J, Hong Y, Wang Y, Yuan Z, Wang C. Reservoir Scheduling Using a Multi-Objective Cuckoo Search Algorithm under Climate Change in Jinsha River, China. Water. 2021; 13(13):1803. https://doi.org/10.3390/w13131803
Chicago/Turabian StyleFeng, Yu, Jijun Xu, Yang Hong, Yongqiang Wang, Zhe Yuan, and Chao Wang. 2021. "Reservoir Scheduling Using a Multi-Objective Cuckoo Search Algorithm under Climate Change in Jinsha River, China" Water 13, no. 13: 1803. https://doi.org/10.3390/w13131803