# Study on the Single-Multi-Objective Optimal Dispatch in the Middle and Lower Reaches of Yellow River for River Ecological Health

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Area and Data

^{2}, and the total length of the main stream is 5464 km, which is the second longest river in China. The Xiaolangdi Reservoir has great regulation and storage capacity, and plays an important role in ecological protection of the Yellow River and sediment control in the river. This paper selects Xiaolangdi as the research object, whose location is on the main stream of the Yellow River, north of Luoyang. The location overview shown is in Figure 1. The main parameters of the Xiaolangdi reservoir are shown in Table 1.

## 3. Modeling

## 4. Methodology

#### 4.1. Single-Objective Solution

#### 4.2. Multi-Objective Solution

^{0}represents the initial water level of the reservoir, Z

_{max}represents the highest water level, and Z

_{min}represents the lowest water level.

## 5. Results and Discussion

#### 5.1. Illustrate the Effectiveness of the NSGA-Ⅱ

^{3}, which is higher than NSGA-II but lower than MOPSO.

#### 5.2. Analysis of the Impact of Ecological Goals on Dispatching Results

#### 5.3. Result Analysis of the Multi-Objective Model

^{3}, respectively; the annual variation in the annual water power generation and the comprehensive water shortage in normal year are 6.707–6.795 billion kW·h and 1.547–3.246 billion m

^{3}, respectively; and the annual variation in the annual water power generation and the comprehensive water shortage in dry year are 5.875–6.002 billion kW·h and 0–2.835 billion m

^{3}, respectively.

^{3}, which is located at the right extreme value of the Pareto-front curve; the annual generation capacity of Model 2 is 9.564 billion kW·h, and the comprehensive water shortage is 0 billion m

^{3}, which is located at the left extreme value of the Pareto-front curve.

^{3}and 1. 547 million m

^{3}, respectively.

^{3}and 0 million m

^{3}, respectively.

^{3}, and Schemes 2–5 failed to meet the ecological requirements.

^{3}increased to 2.957 billion m

^{3}.

#### 5.4. Sensitivity Analysis

_{1}); the ratio of the difference in the total water requirement and water deficit to the total water demand is defined as the ecological elastic coefficient (f

_{2}), as shown in Table 5.

_{1}and f

_{2}in each typical year is better, and the linear slopes of the typical years are 15.03, 14.70, and 22.45, respectively, showing a consistent and significant increasing trend. In response to the sensitivity of power generation and ecology, the normal year is the smallest, followed by the wet year and the dry year. That is, with the decrease in inflow, the amount of power generation, eco-elastic coefficient, and the number of ecological guarantee months are all reduced, the ecological water deficit is greatly increased, the restrictive relationship between power generation and ecological targets is strengthened, and the sensitivity between the two is enhanced. The decrease in the ecological elasticity coefficient will make the restoration of ecological environment more severe; the reservoir should take the ecological as the main goal in the dry year and take the phased measures to alleviate the ecological deterioration situation.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Installed Capacity (MW) | Guaranteed Output (MW) | Total Storage Capacity (Billion m ^{3}) | Normal Water Level (m) | Dead Water Level (m) | Ecological Guarantee Rate (%) | Maximum Overflow (m ^{3}/s) | Adjustment Performance |
---|---|---|---|---|---|---|---|

1800 | 354 | 126.5 | 275 | 230 | 90 | 1776 | Year |

Parameter | GA | MOPSO | NSGA-Ⅱ | Optimized NSGA-Ⅱ [12] |
---|---|---|---|---|

Population size | 300 | 300 | 300 | 300 |

Selection probability | 0.5 | - | 0.5 | 0.5 |

Cross probability | 0.8 | - | 0.8 | 0.8 |

Mutation probability | 0.05 | - | 0.05 | 0.05 |

Maximum number of iterations | 200 | 200 | 200 | 200 |

Algorithm | Target | 1 | 2 | 3 | 4 | 5 | Mean Value | Standard Deviation | Time | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Lower Limit | Upper Limit | Lower Limit | Upper Limit | Lower Limit | Upper Limit | Lower Limit | Upper Limit | Lower Limit | Upper Limit | Lower Limit | Upper Limit | Lower Limit | Upper Limit | |||

GA | Power generation | - | 103.15 | - | 103.17 | - | 103.15 | - | 103.15 | - | 103.13 | - | 103.15 | - | 103.15 | 1.63 |

Water shortage | - | 5.00 | - | 5.07 | - | 5.05 | - | 5.06 | - | 5.05 | - | 5.04 | - | 5.04 | ||

MOPSO | Power generation | 102.90 | 103.15 | 102.82 | 103.14 | 102.83 | 103.15 | 102.85 | 103.15 | 102.82 | 103.13 | 102.85 | 103.14 | 102.85 | 103.14 | 2.63 |

Water shortage | 0.01 | 5.06 | 0.00 | 5.04 | 0.00 | 5.09 | 0.00 | 5.16 | 0.00 | 5.01 | 0.00 | 5.07 | 0.00 | 5.07 | ||

NSGA-Ⅱ | Power generation | 102.80 | 103.17 | 102.82 | 103.06 | 102.78 | 103.16 | 102.78 | 103.17 | 102.80 | 103.13 | 102.80 | 103.14 | 102.80 | 103.14 | 2.65 |

Water shortage | 0.00 | 5.04 | 0.00 | 3.35 | 0.00 | 5.06 | 0.00 | 5.06 | 0.00 | 5.06 | 0.00 | 4.71 | 0.00 | 4.71 | ||

Improved NSGA-Ⅱ | Power generation | 102.83 | 103.14 | 102.81 | 103.17 | 102.77 | 103.16 | 102.83 | 103.15 | 102.80 | 103.13 | 102.80 | 103.15 | 102.80 | 103.15 | 2.40 |

Water shortage | 0.00 | 5.06 | 0.00 | 5.06 | 0.00 | 5.05 | 0.00 | 5.06 | 0.00 | 5.06 | 0.00 | 5.06 | 0.00 | 5.06 |

^{8}kW·h; Water shortage/10

^{8}m

^{3}; Time/s.

Wet Year | Normal Year | Dry Year | ||||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 1 | Model 2 | Model 1 | Model 2 | |

Power generation/10^{8} kW·h | 95.97 | 95.64 | 67.95 | 67.09 | 60.02 | 58.75 |

The number of guarantee ecology | 10 | 12 | 8 | 12 | 8 | 12 |

Scheme | Wet Year | Normal Year | Dry Year | |||
---|---|---|---|---|---|---|

Power Generation/10^{8}kW·h | Eco-Water Shortage/10^{8}m^{3} | Power Generation/10^{8}kW·h | Eco-Water Shortage/10^{8}m^{3} | Power Generation/10^{8}kW·h | Eco-Water Shortage/10^{8}m^{3} | |

Scheme 1 | 95.65 | 0 | 67.09 | 16.01 | 58.82 | 0.28 |

Scheme 2 | 95.76 | 1.34 | 67.51 | 19.88 | 59.04 | 3.38 |

Scheme 3 | 95.82 | 2.08 | 67.71 | 22.6 | 59.33 | 7.9 |

Scheme 4 | 95.88 | 3.05 | 67.73 | 22.98 | 59.63 | 14.32 |

Scheme 5 | 95.95 | 4.62 | 67.92 | 29.57 | 60 | 27.36 |

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## Share and Cite

**MDPI and ACS Style**

Bai, T.; Liu, X.; HA, Y.-p.; Chang, J.-x.; Wu, L.-z.; Wei, J.; Liu, J.
Study on the Single-Multi-Objective Optimal Dispatch in the Middle and Lower Reaches of Yellow River for River Ecological Health. *Water* **2020**, *12*, 915.
https://doi.org/10.3390/w12030915

**AMA Style**

Bai T, Liu X, HA Y-p, Chang J-x, Wu L-z, Wei J, Liu J.
Study on the Single-Multi-Objective Optimal Dispatch in the Middle and Lower Reaches of Yellow River for River Ecological Health. *Water*. 2020; 12(3):915.
https://doi.org/10.3390/w12030915

**Chicago/Turabian Style**

Bai, Tao, Xia Liu, Yan-ping HA, Jian-xia Chang, Lian-zhou Wu, Jian Wei, and Jin Liu.
2020. "Study on the Single-Multi-Objective Optimal Dispatch in the Middle and Lower Reaches of Yellow River for River Ecological Health" *Water* 12, no. 3: 915.
https://doi.org/10.3390/w12030915