# Reservoir Scheduling Using a Multi-Objective Cuckoo Search Algorithm under Climate Change in Jinsha River, China

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## Abstract

**:**

## 1. Introduction

_{2}, CH

_{4}, and N

_{2}O, the primary gaseous drivers of climate change [13]. Increases in global temperature are self-accelerating, as the melting snow in polar regions and high-altitude mountains decreases surface albedo as low-elevation snow cover, glaciers, and permafrost are in decline [14]. The melting of glaciers and snow in the polar regions, and the resulting rise in sea level, will increase oceanic area, which along with higher temperatures, will increase evaporation and correlated large-scale changes in the global water cycle. Water vapor from the ocean is converted into precipitation, and when rainfall increases or decreases in wet or dry areas, respectively, the probability of natural disasters, such as floods and droughts, increases significantly. Changes in glacial and snow-covered areas of mountains have also altered river runoff [15]; however, streamflow changes by region have neither consistently increased nor decreased.

## 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

_{a}) is a fixed value that affects the convergence speed of the algorithm. The improved solution turns p

_{a}into a dynamic adjustment using Equation (2):

- (2)
- Differential strategy for Lévy flight

_{i}and x

_{j}are randomly chosen nests, sl is the step size, and Levy(u,c) is the sample value generated by the Lévy distribution. The probability density function of Levy(u,c) is calculated according to Equation (4):

- (3)
- Revised solution

Algorithm 1. Improved cuckoo search |

Objective function $f\left(x\right),x={({x}_{1},\dots ,{x}_{d})}^{T}$ |

Initialize default parameters |

Generate initial population of n host nests ${x}_{i}\left(i=1,2,\dots ,n\right)$ |

While (t < MaxEvaluation) or (stop criterion) |

Select two solution ${x}_{i},{x}_{j}$ from host nests randomly |

For d=1,…, D do |

${x}_{i}^{d\prime}={x}_{i}^{d}+\left(sl\times Levy\left(u,c\right)\times \left({x}_{j}^{d}-{x}_{i}^{d}\right)\right)$ |

End for |

If $f\left({x}_{i}^{\prime}\right)<f\left({x}_{i}\right)$ |

Replace x_{i} by the new solution ${x}_{i}^{\prime}$ |

End if |

If $rand\left(0,1\right)<{p}_{a}$ |

Init the worst nest ${x}_{worst}$ |

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

_{1}(kW∙h) is the total energy production of the cascade hydropower system, T is the period count, N is the number of reservoirs, k

_{i}is the output coefficient of reservoir i, Q

_{i,t}(m³/s) is the generation of outflow through hydropower units of reservoir i at time t; H

_{i,t}(m) is the net water head of hydropower reservoir i at time t, and ∆t is the length of the time interval.

#### 2.3.2. Residual Load Variance Objective

_{2}(kW) is the residual load variance of the power grid, P

_{t}(kW) is the total power output of the cascade hydropower stations over period t, and $\overline{P}$ (kW) is the average power output of all periods. Notably, it is necessary to maintain a low water level during the flood season due to flood control requirements; thus, this season was not considered in the formula.

#### 2.3.3. Constraints

- (1)
- Hydraulic connection (Equation (7)):$$\{\begin{array}{c}{I}_{i,t}={O}_{i-1,t}+{R}_{i,t}\hfill \\ {O}_{i-1,t}={Q}_{i-1,t}+{S}_{i-1,t}\hfill \end{array}$$
- (2)
- Water-balance constraint (Equation (8)):$${V}_{i,t}={V}_{i,t-1}+\left({I}_{i,t}-{O}_{i,t}\right)\cdot \Delta t$$
_{i,t}(m³) is the storage of reservoir i in time t. - (3)
- Water-level constraints (Equations (9) and (10)):$${Z}_{i,t}^{min}\le {Z}_{i,t}\le {Z}_{i,t}^{max}$$$$\left|{Z}_{i,t}-{Z}_{i,t-1}\right|\le {Z}_{i,t}^{step}$$
- (4)
- Outflow constraint (Equation (11)):$${O}_{i,t}^{min}\le {O}_{i,t}\le {O}_{i,t}^{max}$$
- (5)
- Output constraint (Equation (12)):$${N}_{i,t}^{min}\le {N}_{i,t}\le {N}_{i,t}^{max}$$
- (6)
- Boundary condition (Equation (13)):$${Z}_{i,0}={Z}_{i,start},{Z}_{i,T}={Z}_{i,end}$$

#### 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

_{i}is the precipitation of the grid box i, and S

_{i}is the area of grid box i. N is the number of grid boxes in the sub-catchment.

_{A}and H

_{E}are the parameters with standard values of 0.0023 and 0.5, respectively. R

_{e}is the extraterrestrial radiation. T is the mean temperature (T = (T

_{max}+ T

_{min})/2) and ΔT is the air temperature range (ΔT = T

_{max}– T

_{min}). The daily evapotranspiration of each sub-catchment is calculated in the same way with precipitation.

#### 2.4.2. Modeling of MLTHG in Jinsha River

_{i,t}(kW∙h) is the hydropower generation of reservoir i at time t; Q

_{i,t}(m³/s) is the generation flow through the hydropower units of reservoir i at time t; k

_{i}is the comprehensive benefit coefficient of reservoir i, which reflects the hydro-generating unit efficiency; Δt is the length of time interval, and H

_{i,t}(m) is the net water head of reservoir i at time t, defined by Equation (25):

_{i,t−}

_{1}(m) and Z

_{i,t}(m) are the beginning and end water levels of reservoir i at time t, respectively; Zd

_{i,t}(m) is the water level under the dam; and ΔH

_{i}(m) is the water head loss of reservoir i.

## 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

^{8}kWh), respectively, while the uncertainty ranges were similar to each other: (−4.4%, 4.0%), (−5.2%, 3.9%), and (−4.3%, 5.4%). Figure 18b,c show the results under scenarios RCP4.5 and RCP8.5, which both displayed much larger uncertainty ratios than RCP2.6. Moreover, the average power generation in RCP2.6 was significantly larger than that in RCP8.5, and when compared with the average power generation in RCP4.5, RCP2.6 was larger for the first 20 years, but smaller following decade.

#### 3.2.2. Residual Load Variance Objective

^{8}kWh), for 2021–2030, 2031–2040, 2041–2050, respectively; while the uncertainty ranges were (13.6%, 6.0%), (6.1, 6.5%) and (−9.7%, 17.5%). Figure 19b,c show the results under scenarios RCP4.5 and RCP8.5, respectively, with relatively larger uncertainty ranges. Similar to the characteristics of power generation in the preceding section, the average residual load variance in RCP2.6 was larger than RCP8.5 at each interval, and larger than RCP4.5 for the first 20 years, but smaller following decade.

#### 3.2.3. Combination of the Two Objectives

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Mendes, C.A.B.; Beluco, A.; Canales, F.A. Some important uncertainties related to climate change in projections for the Brazilian hydropower expansion in the Amazon. Energy
**2017**, 141, 123–138. [Google Scholar] [CrossRef] - Fan, J.-L.; Hu, J.-W.; Zhang, X.; Kong, L.-S.; Li, F.; Mi, Z. Impacts of climate change on hydropower generation in China. Math. Comput. Simul.
**2020**, 167, 4–18. [Google Scholar] [CrossRef] - Gaudard, L.; Romerio, F.; Valle, F.; Gorret, R.; Maran, S.; Ravazzani, G.; Stoffel, M.; Volonterio, M. Climate change impacts on hydropower in the Swiss and Italian Alps. Sci. Total Environ.
**2013**, 493. [Google Scholar] [CrossRef] - Chang, J.; Wang, X.; Li, Y.; Wang, Y.; Zhang, H. Hydropower plant operation rules optimization response to climate change. Energy
**2018**, 160, 886–897. [Google Scholar] [CrossRef] - Zhong, W.; Guo, J.; Chen, L.; Zhou, J.; Zhang, J.; Wang, D. Future hydropower generation prediction of large-scale reservoirs in the upper Yangtze River basin under climate change. J. Hydrol.
**2020**, 588, 125013. [Google Scholar] [CrossRef] - Qin, P.; Xu, H.; Liu, M.; Du, L.; Xiao, C.; Liu, L.; Tarroja, B. Climate change impacts on Three Gorges Reservoir impoundment and hydropower generation. J. Hydrol.
**2020**, 580, 123922. [Google Scholar] [CrossRef] - Kim, K.; Jeong, H.; Ha, S.; Bang, S.; Bae, D.-H.; Kim, H. Investment timing decisions in hydropower adaptation projects using climate scenarios: A case study of South Korea. J. Clean. Prod.
**2017**, 142, 1827–1836. [Google Scholar] [CrossRef] - Boehlert, B.; Strzepek, K.M.; Gebretsadik, Y.; Swanson, R.; McCluskey, A.; Neumann, J.E.; McFarland, J.; Martinich, J. Climate change impacts and greenhouse gas mitigation effects on U.S. hydropower generation. Appl. Energy
**2016**, 183, 1511–1519. [Google Scholar] [CrossRef][Green Version] - Huang, S.; Krysanova, V.; Hattermann, F. Projections of climate change impacts on floods and droughts in Germany using an ensemble of climate change scenarios. Reg. Environ. Chang.
**2014**, 15. [Google Scholar] [CrossRef] - Mezosi, G.; Bata, T.; Meyer, B.; Blanka, V.; Ladányi, Z. Climate Change Impacts on Environmental Hazards on the Great Hungarian Plain, Carpathian Basin. Int. J. Disaster Risk Sci.
**2014**, 5, 136–146. [Google Scholar] [CrossRef][Green Version] - Hasan, M.M.; Wyseure, G. Impact of climate change on hydropower generation in Rio Jubones Basin, Ecuador. Water Sci. Eng.
**2018**, 11, 157–166. [Google Scholar] [CrossRef] - Falchetta, G.; Gernaat, D.E.H.J.; Hunt, J.; Sterl, S. Hydropower dependency and climate change in sub-Saharan Africa: A nexus framework and evidence-based review. J. Clean. Prod.
**2019**, 231, 1399–1417. [Google Scholar] [CrossRef][Green Version] - Lu, S.; Dai, W.; Tang, Y.; Guo, M. A review of the impact of hydropower reservoirs on global climate change. Sci. Total Environ.
**2020**, 711, 134996. [Google Scholar] [CrossRef] - IPCC; McDowell, G.; Barr, I. ‘High Mountain Areas’ Chapter—IPCC Special Report on the Oceans and Cryosphere in a Changing Climate (SROCC); IPCC: Geneva, Switzerland, 2019. [Google Scholar]
- Mishra, S.K.; Hayse, J.; Veselka, T.; Yan, E.; Kayastha, R.B.; LaGory, K.; McDonald, K.; Steiner, N. An integrated assessment approach for estimating the economic impacts of climate change on River systems: An application to hydropower and fisheries in a Himalayan River, Trishuli. Environ. Sci. Policy
**2018**, 87, 102–111. [Google Scholar] [CrossRef] - Feldbauer, J.; Kneis, D.; Hegewald, T.; Berendonk, T.U.; Petzoldt, T. Managing climate change in drinking water reservoirs: Potentials and limitations of dynamic withdrawal strategies. Environ. Sci. Eur.
**2020**, 32, 48. [Google Scholar] [CrossRef][Green Version] - Helfer, F.; Lemckert, C.; Zhang, H. Impacts of climate change on temperature and evaporation from a large reservoir in Australia. J. Hydrol.
**2012**, 475, 365–378. [Google Scholar] [CrossRef][Green Version] - Shu, J.; Qu, J.; Motha, R.; Xu, J.; Dong, D. Impacts of climate change on hydropower development and sustainability: A review. IOP Conf. Ser. Earth Environ. Sci.
**2018**, 163, 012126. [Google Scholar] [CrossRef] - Turner, S.W.D.; Hejazi, M.; Kim, S.H.; Clarke, L.; Edmonds, J. Climate impacts on hydropower and consequences for global electricity supply investment needs. Energy
**2017**, 141, 2081–2090. [Google Scholar] [CrossRef] - Nam, W.-H.; Kim, T.; Hong, E.-M.; Choi, J.-Y. Regional Climate Change Impacts on Irrigation Vulnerable Season Shifts in Agricultural Water Availability for South Korea. Water
**2017**, 9, 735. [Google Scholar] [CrossRef][Green Version] - Carvajal, P.E.; Li, F.G.N.; Soria, R.; Cronin, J.; Anandarajah, G.; Mulugetta, Y. Large hydropower, decarbonisation and climate change uncertainty: Modelling power sector pathways for Ecuador. Energy Strategy Rev.
**2019**, 23, 86–99. [Google Scholar] [CrossRef] - Chilkoti, V.; Bolisetti, T.; Balachandar, R. Climate change impact assessment on hydropower generation using multi-model climate ensemble. Renew. Energy
**2017**, 109, 510–517. [Google Scholar] [CrossRef] - Sample, J.E.; Duncan, N.; Ferguson, M.; Cooksley, S. Scotland׳s hydropower: Current capacity, future potential and the possible impacts of climate change. Renew. Sustain. Energy Rev.
**2015**, 52, 111–122. [Google Scholar] [CrossRef] - Pereira-Cardenal, S.; Madsen, H.; Arnbjerg-Nielsen, K.; Riegels, N.; Jensen, R.; Mo, B.; Wangensteen, I.; Bauer-Gottwein, P. Assessing climate change impacts on the Iberian power system using a coupled water-power model. Clim. Chang.
**2014**, 126, 351–364. [Google Scholar] [CrossRef] - González-Villela, R.; Martínez, M.J.M.; Sepúlveda, J.S.S. Effects of climate change on the environmental flows in the Conchos River (Chihuahua, Mexico). Ecohydrol. Hydrobiol.
**2018**, 18, 431–440. [Google Scholar] [CrossRef] - Givati, A.; Thirel, G.; Rosenfeld, D.; Paz, D. Climate change impacts on streamflow at the upper Jordan River based on an ensemble of regional climate models. J. Hydrol. Reg. Stud.
**2019**, 21, 92–109. [Google Scholar] [CrossRef] - Clifton, C.F.; Day, K.T.; Luce, C.H.; Grant, G.E.; Safeeq, M.; Halofsky, J.E.; Staab, B.P. Effects of climate change on hydrology and water resources in the Blue Mountains, Oregon, USA. Clim. Serv.
**2018**, 10, 9–19. [Google Scholar] [CrossRef] - Bhatta, B.; Shrestha, S.; Shrestha, P.K.; Talchabhadel, R. Evaluation and application of a SWAT model to assess the climate change impact on the hydrology of the Himalayan River Basin. CATENA
**2019**, 181, 104082. [Google Scholar] [CrossRef] - de Queiroz, A.R.; Faria, V.A.D.; Lima, L.M.M.; Lima, J.W.M. Hydropower revenues under the threat of climate change in Brazil. Renew. Energy
**2019**, 133, 873–882. [Google Scholar] [CrossRef] - Arango-Aramburo, S.; Turner, S.W.D.; Daenzer, K.; Ríos-Ocampo, J.P.; Hejazi, M.I.; Kober, T.; Álvarez-Espinosa, A.C.; Romero-Otalora, G.D.; van der Zwaan, B. Climate impacts on hydropower in Colombia: A multi-model assessment of power sector adaptation pathways. Energy Policy
**2019**, 128, 179–188. [Google Scholar] [CrossRef] - Zhai, M.Y.; Lin, Q.G.; Huang, G.H.; Zhu, L.; An, K.; Li, G.C.; Huang, Y.F. Adaptation of Cascade Hydropower Station Scheduling on A Headwater Stream of the Yangtze River under Changing Climate Conditions. Water
**2017**, 9, 293. [Google Scholar] [CrossRef][Green Version] - Zhang, W.; Liu, P.; Wang, H.; Lei, X.; Feng, M. Operating rules of irrigation reservoir under climate change and its application for the Dongwushi Reservoir in China. J. Hydro-Environ. Res.
**2017**, 16, 34–44. [Google Scholar] [CrossRef] - Yang, X.S.; Deb, S. Cuckoo Search via Levy Flights. Mathematics
**2010**, 210–214. [Google Scholar] - Geressu, R.; Harou, J. Reservoir system expansion scheduling under conflicting interests. Environ. Model. Softw.
**2019**, 118, 201–210. [Google Scholar] [CrossRef] - Feng, Y.; Zhou, J.; Mo, L.; Wang, C.; Yuan, Z.; Wu, J. A Gradient-Based Cuckoo Search Algorithm for a Reservoir-Generation Scheduling Problem. Algorithms
**2018**, 11, 36. [Google Scholar] [CrossRef][Green Version] - Warszawski, L.; Frieler, K.; Huber, V.; Piontek, F.; Serdeczny, O.; Schewe, J. The Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP): Project framework. Proc. Natl. Acad. Sci. USA
**2014**, 111, 3228–3232. [Google Scholar] [CrossRef][Green Version] - Hempel, S.; Frieler, K.; Warszawski, L.; Schewe, J.; Piontek, F. A trend-preserving bias correction—The ISI-MIP approach. Earth Syst. Dyn.
**2013**, 4, 219–236. [Google Scholar] [CrossRef][Green Version] - Berti, A.; Tardivo, G.; Chiaudani, A.; Rech, F.; Borin, M. Assessing reference evapotranspiration by the Hargreaves method in north-eastern Italy. Agric. Water Manag.
**2014**, 140, 20–25. [Google Scholar] [CrossRef] - Feng, Y.; Zhou, J.; Mo, L.; Yuan, Z.; Zhang, P.; Jiang, W.; Wang, C.; Wang, Y. Long-Term Hydropower Generation of Cascade Reservoirs under Future Climate Changes in Jinsha River in Southwest China. Water
**2018**, 10, 235. [Google Scholar] [CrossRef][Green Version]

**Figure 16.**Comparison between the 2nd and 49th solutions in wet year. (

**a**) Water level of Wudongde (

**b**) Power generation of Wudongde (

**c**) Water level of Baihetan (

**d**) Power generation of Baihetan (

**e**) Water level of Xiluodu (

**f**) Power generation of Xiluodu (

**g**) Water level of Xiangjiaba (

**h**) Power generation of Xiangjiaba.

**Figure 17.**Annual streamflow in Pingshan Station under IPCC climate scenarios: (

**a**) RCP2.6, (

**b**) RCP4.5, and (

**c**) RCP8.5.

**Figure 18.**Power generation projections for the next three decades under scenarios: (

**a**) RCP2.6, (

**b**) RCP4.5, and (

**c**) RCP8.5.

**Figure 19.**Residual load variance for the next three decades under scenarios: (

**a**) RCP2.6, (

**b**) RCP4.5, and (

**c**) RCP8.5.

**Figure 20.**Predicted, decadal variation ratios under different climate scenarios: (

**a**) RCP2.6, (

**b**) RCP4.5, and (

**c**) RCP8.5.

**Table 1.**Main parameters of the four cascade hydropower stations along the lower reaches of the Jinsha River.

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 (10^{4} kw) | 1020 | 1600 | 1260 | 600 |

Total capacity (10^{8} m^{3}) | 74.08 | 206.27 | 126.7 | 51.63 |

Minimum outflow (m^{3}·s^{−1}) | 906 | 905 | 1500 | 1500 |

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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Feng, 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