# Competitive Relationship between Flood Control and Power Generation with Flood Season Division: A Case Study in Downstream Jinsha River Cascade Reservoirs

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. The Joint Optimal Operation Model of Reservoir Model

#### 3.1. Model Construction

#### 3.1.1. Objective Function

^{3}/s); $T$ is the number of periods (d).

#### 3.1.2. Constraints

^{3}); ${Q}_{i,t}$ is the inflow of the i-th reservoir during t-th period (m

^{3}/s); ${Q}_{\mathrm{r}i,t}$ is the local inflow of the i-th reservoir during t-th period (m

^{3}/s).

^{3}/s);${q}_{i,t}^{min}\text{}\mathrm{and}\text{}{q}_{i,t}^{max}$ are the lower limit and the upper limit of the discharge volume of the i-th reservoir during the t-th period, respectively (m

^{3}/s)

^{3}/s); ${q}_{i,t+1}$ is the discharge volume of the i-th reservoir during the t+1-th period (m

^{3}/s); $\nabla q$ is the upper limit of the discharge variation (m

^{3}/s).

^{3}/s); and ${H}_{i,t}$ is the average water head of the i-th reservoir during the t-th period (m).

#### 3.2. Input

#### 3.2.1. Measured Flood

#### 3.2.2. Design Flood

#### 3.3. Model Solution

#### 3.4. Discrimination of Competitive Relations

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Multi-objective Pareto curve for flood control and power generation with different inflow.

Reservoir | Lower Bound of Water Level (m) | Upper Bound of Water Level (m) | Lower Bound of Discharge (m^{3}/s) | Upper Bound of Discharge (m^{3}/s) | Installed Capacity (MW) | Maximum Allowable Water Discharge Variation Rate (m^{3}/(s·d)) |
---|---|---|---|---|---|---|

Wudongde | 952 | 972 | 883 | 30,000 | 10,200 | 2000 |

Baihetan | 785 | 825 | 700 | 30,000 | 16,000 | 2000 |

Xiluodu | 560 | 600 | 1060 | 30,000 | 13,860 | 2000 |

Xiangjiaba | 370 | 380 | 830 | 30,000 | 6000 | 2000 |

Name | Clayton Copula | Frank Copula | Gumbel Copula |
---|---|---|---|

Inflow of Wudongde | 0.0620 | 0.0589 | 0.0579 |

Interval inflow of Baihetan | 0.0825 | 0.0759 | 0.0753 |

Interval inflow of Xiluodu | 0.0735 | 0.0678 | 0.0676 |

Interval inflow of Xiangjiaba | 0.0848 | 0.0686 | 0.0723 |

Name | Co-occurrence and Return Period = 100 y | |
---|---|---|

Peak Flow (m^{3}/s) | 3D volumes (m^{3}/s·d) | |

Inflow of Wudongde | 26,000 | 73,700 |

Interval inflow of Baihetan | 763 | 1530 |

Interval inflow of Xiluodu | 1540 | 4550 |

Interval inflow of Xiangjiaba | 797 | 1030 |

Obj1 | Upward Trend | No Apparent Trend | Downward Trend | ||
---|---|---|---|---|---|

Competitive Relationship | |||||

Obj2 | |||||

Upward trend | strong | weak | no | ||

No apparent trend | weak | weak | weak | ||

Downward trend | no | weak | strong |

Scenario | $\mathit{\eta}1$ | $\mathit{\eta}2$ |
---|---|---|

1-1 | $8.2\times {10}^{9}$ | $6.6\times {10}^{7}$ |

1-2 | $5.1\times {10}^{9}$ | $7.3\times {10}^{7}$ |

2-1 | $6.5\times {10}^{9}$ | $2.0\times {10}^{9}$ |

2-2 | $5.2\times {10}^{9}$ | $--$ |

3-1 | $1.1\times {10}^{9}$ | $9.0\times {10}^{7}$ |

3-2 | $6.4\times {10}^{8}$ | $--$ |

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**MDPI and ACS Style**

Yao, H.; Dong, Z.; Jia, W.; Ni, X.; Chen, M.; Zhu, C.; Li, D. Competitive Relationship between Flood Control and Power Generation with Flood Season Division: A Case Study in Downstream Jinsha River Cascade Reservoirs. *Water* **2019**, *11*, 2401.
https://doi.org/10.3390/w11112401

**AMA Style**

Yao H, Dong Z, Jia W, Ni X, Chen M, Zhu C, Li D. Competitive Relationship between Flood Control and Power Generation with Flood Season Division: A Case Study in Downstream Jinsha River Cascade Reservoirs. *Water*. 2019; 11(11):2401.
https://doi.org/10.3390/w11112401

**Chicago/Turabian Style**

Yao, Hongyi, Zengchuan Dong, Wenhao Jia, Xiaokuan Ni, Mufeng Chen, Cailin Zhu, and Dayong Li. 2019. "Competitive Relationship between Flood Control and Power Generation with Flood Season Division: A Case Study in Downstream Jinsha River Cascade Reservoirs" *Water* 11, no. 11: 2401.
https://doi.org/10.3390/w11112401