Long-Term Hydropower Generation Scheduling of Large-Scale Cascade Reservoirs Using Chaotic Adaptive Multi-Objective Bat Algorithm
Abstract
:1. Introduction
2. Mathematical Modeling of the CHRO Problem
2.1. Objective Function
- (1)
- Maximizing the annual power generation of the hydropower system:
- (2)
- Maximizing the firm power output:
2.2. Constraints
- (1)
- Reservoir water balance equation:
- (2)
- Reservoir storage conversion:
- (3)
- Reservoir water head:
- (4)
- Reservoir water level constraint:
- (5)
- Reservoir outflow constraint:
- (6)
- Power output constraint:
3. Overview of the Multi-Objective Bat Algorithm
4. Implementation of CAMOBA for solving the CHRO problem
4.1. External Archive Set Maintenance and Updating Operation
- (1)
- If EAS ( ) is vacant, put into EAS( ) directly.
- (2)
- Compare with other solutions in EAS( ). If is not dominated by any solution in EAS ( ), add into EAS ( ) and delete the solution dominated by in EAS( ).
- (3)
- If the number of individuals in EAS( ) exceeds the NE, a crowding distance comparison is performed for each new solution addition. In this process, the solution with the smallest crowding distance is eliminated. Non-dominated solutions are ranked based on one of the objective functions. The boundary solutions (the smallest and largest solutions of the function values) are given a larger distance value to maintain the diversity of the external archive set [23]. The crowding distance can be expressed as:
4.2. Initial Population Generation
4.3. Self-Adaptive Local Search Strategy
4.4. Mutation Operation
4.5. Procedures of CAMOBA for Solving the CHRO Problem
5. Case Study
5.1. Case Study Description
5.2. Parameter Settings
5.3. Results and Discussion
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Hydrological Years | Objective | Method | Max ↑ | Improve (%) | Mean ↑ | Improve (%) | Std ↓ | Improve (%) |
---|---|---|---|---|---|---|---|---|
Wet year | Annual power generation | CAMOBA | 115.6408 | 0.082% | 115.5407 | 0.048% | 0.0408 | 3.702% |
MOBA | 115.5694 | 0.021% | 115.4885 | 0.003% | 0.0414 | 2.172% | ||
NSGA-II | 115.5456 | - | 115.4851 | - | 0.0423 | - | ||
Firm power output | CAMOBA | 560.6503 | 3.368% | 539.3225 | 5.774% | 22.6059 | 31.829% | |
MOBA | 550.5622 | 1.508% | 525.0124 | 2.967% | 26.9268 | 18.798% | ||
NSGA-II | 542.3833 | - | 509.8830 | - | 33.1604 | - | ||
Normal year | Annual power generation | CAMOBA | 72.8236 | 0.005% | 72.8125 | 0.054% | 0.0173 | 67.544% |
MOBA | 72.8227 | 0.004% | 72.7947 | 0.029% | 0.0415 | 22.043% | ||
NSGA-II | 72.8199 | - | 72.7735 | - | 0.0532 | - | ||
Firm power output | CAMOBA | 483.0351 | 7.237% | 431.6210 | 9.679% | 29.5803 | 19.650% | |
MOBA | 461.8928 | 2.543% | 409.1474 | 3.968% | 30.5043 | 17.140% | ||
NSGA-II | 450.4362 | - | 393.5319 | - | 36.8142 | - | ||
Dry year | Annual power generation | CAMOBA | 56.0700 | 0.002% | 56.0621 | 0.046% | 0.0145 | 47.405% |
MOBA | 56.0697 | 0.001% | 56.0582 | 0.040% | 0.0203 | 26.570% | ||
NSGA-II | 56.0690 | - | 56.0360 | - | 0.0276 | - | ||
Firm power output | CAMOBA | 338.1704 | 5.592% | 299.2050 | 4.398% | 20.4751 | 11.893% | |
MOBA | 326.3672 | 1.906% | 288.7327 | 0.744% | 22.2445 | 4.279% | ||
NSGA-II | 320.2625 | - | 286.6007 | - | 23.2388 | - |
Hydrological Years | Algorithm | SP | HV | Time(s) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Max ↓ | Mean ↓ | Min ↓ | Std ↓ | Max ↑ | Mean ↑ | Min ↑ | Std ↓ | |||
Wet year | CAMOBA | 0.0247 | 0.0220 | 0.0190 | 0.0017 | 0.8183 | 0.8114 | 0.7949 | 0.0075 | 511.2 |
MOBA | 0.0729 | 0.0662 | 0.0618 | 0.0042 | 0.7367 | 0.7220 | 0.7124 | 0.0085 | 461.4 | |
NSGA-II | 0.0245 | 0.0221 | 0.0165 | 0.0028 | 0.7320 | 0.7211 | 0.7057 | 0.0093 | 759.6 | |
Normal year | CAMOBA | 0.0194 | 0.0148 | 0.0112 | 0.0027 | 0.8147 | 0.8038 | 0.7812 | 0.0107 | 515.4 |
MOBA | 0.0681 | 0.0626 | 0.0519 | 0.0048 | 0.7821 | 0.7449 | 0.7123 | 0.0252 | 456.8 | |
NSGA-II | 0.0398 | 0.0345 | 0.0298 | 0.0039 | 0.7414 | 0.7150 | 0.6968 | 0.0158 | 741.3 | |
Dry year | CAMOBA | 0.0223 | 0.0204 | 0.0187 | 0.0011 | 0.8979 | 0.8852 | 0.8732 | 0.0080 | 509.7 |
MOBA | 0.1940 | 0.1748 | 0.1658 | 0.0076 | 0.8165 | 0.8007 | 0.7826 | 0.0111 | 457.6 | |
NSGA-II | 0.0384 | 0.0359 | 0.0317 | 0.0023 | 0.5525 | 0.5283 | 0.5213 | 0.0094 | 753.7 |
Scheme | f1 (108 kWh) | f2 (MW) | Scheme | f1 (108 kWh) | f2 (MW) | Scheme | f1 (108 kWh) | f2 (MW) |
---|---|---|---|---|---|---|---|---|
1 | 72.8236 | 189.1719 | 11 | 72.7347 | 374.6256 | 21 | 72.5535 | 452.4976 |
2 | 72.8232 | 225.4624 | 12 | 72.7227 | 390.1868 | 22 | 72.5333 | 460.2505 |
3 | 72.8217 | 241.1590 | 13 | 72.7082 | 402.6378 | 23 | 72.5109 | 467.7229 |
4 | 72.8200 | 256.8327 | 14 | 72.6925 | 405.8924 | 24 | 72.4848 | 470.2905 |
5 | 72.8177 | 273.0836 | 15 | 72.6864 | 418.7940 | 25 | 72.4680 | 471.5678 |
6 | 72.8134 | 285.7809 | 16 | 72.6620 | 425.8439 | 26 | 72.4475 | 472.9724 |
7 | 72.8007 | 304.9514 | 17 | 72.6352 | 427.0217 | 27 | 72.4238 | 473.4131 |
8 | 72.7871 | 324.6124 | 18 | 72.6088 | 438.4034 | 28 | 72.3926 | 477.6139 |
9 | 72.7668 | 343.0365 | 19 | 72.5878 | 443.0313 | 29 | 72.3594 | 478.6686 |
10 | 72.7623 | 357.0580 | 20 | 72.5694 | 444.8507 | 30 | 72.3189 | 483.0351 |
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Su, L.; Yang, K.; Hu, H.; Yang, Z. Long-Term Hydropower Generation Scheduling of Large-Scale Cascade Reservoirs Using Chaotic Adaptive Multi-Objective Bat Algorithm. Water 2019, 11, 2373. https://doi.org/10.3390/w11112373
Su L, Yang K, Hu H, Yang Z. Long-Term Hydropower Generation Scheduling of Large-Scale Cascade Reservoirs Using Chaotic Adaptive Multi-Objective Bat Algorithm. Water. 2019; 11(11):2373. https://doi.org/10.3390/w11112373
Chicago/Turabian StyleSu, Lyuwen, Kan Yang, Hu Hu, and Zhe Yang. 2019. "Long-Term Hydropower Generation Scheduling of Large-Scale Cascade Reservoirs Using Chaotic Adaptive Multi-Objective Bat Algorithm" Water 11, no. 11: 2373. https://doi.org/10.3390/w11112373