# Investigation on Water Levels for Cascaded Hydropower Reservoirs to Drawdown at the End of Dry Seasons

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## Abstract

**:**

## 1. Introduction

_{2}emission from the power systems. It can be targeted by keeping the forebay water level as high as possible to improve the generation efficiency and properly regulating the storage to reduce spillages. In California, for instance, single-purpose reservoirs are predominantly located at high elevations to take advantage of higher water heads to generate more hydropower [10]. Additionally, as demonstrated by Lu et al. [11] with case studies, a joint operation of two large upstream reservoirs could increase the electricity production of the mainstream run-off hydropower plants at the lower reaches by regulating the upstream reservoirs to reduce spillages from the downstream reservoirs. Additionally, compared with conventional coal power plants, hydropower prevents the emission of about 3 GT CO

_{2}per year, representing about 9% of global annual CO

_{2}emissions [12].

## 2. Problem Formulation

_{i}= weights assigned to the objectives, with ${W}_{i}\gg {W}_{i+1}$ to prioritize the objectives; V

_{it}= storage volume of reservoir i at the beginning of time-step t; ${\mathsf{\Omega}}_{i}$= the set of reservoirs immediately upstream of reservoir i; Q

_{it}= release in m

^{3}/s from reservoir i in time-step t; I

_{im}= local inflow in m

^{3}/s of reservoir i in time-step t; Δt = length of time-step t; ${V}_{i}^{\mathrm{dead}}$ and ${V}_{i}^{\mathrm{normal}}$= dead and normal storages of reservoir i, respectively; ${V}_{i}^{\mathrm{flood}}$= flood control storage of reservoir i in time-step t; ${Q}_{it}^{\mathrm{navi}},{Q}_{i}^{\mathrm{envn}},{Q}_{i}^{\mathrm{comp}}$= release required at least, respectively for downstream navigation, environmental and comprehensive purposes that may include industrial, agricultural and municipal water supplies; ${Q}_{i}^{\mathrm{safe}}$= outflow needed at most for the safety of downstream river banks of reservoir i in time-step t; ${h}_{it},{n}_{it}$= the water head and maintenance rate in time-step t of hydro-plant i, respectively; ${G}_{i}({h}_{it},{n}_{it})$= capacity of hydropower output of hydro-plant i; ${P}_{it}$,${\widehat{E}}_{it}$= the power output and contracted electricity hydro-plant i in time-step t, respectively; $U$= the time-step when the flood seasons end; ${V}_{i}^{\mathrm{draw}}$= the storage to be targeted for reservoir i at the end of flood seasons; ${h}_{it}$= water head of reservoir i in time-step t; ${f}_{i}(\cdot )$= a function of storage and release; ${\eta}_{i}(\cdot )$ is a function of water head (${h}_{it}$).

## 3. Solution Strategy

#### 3.1. Solution Method

#### 3.2. Simulation Strategy

## 4. Case Studies

#### 4.1. Engineering Background

#### 4.2. Assessment of Optional Drawdown Levels

#### 4.3. Simulation Results of the 7th Option

## 5. Conclusions

- (1)
- The preferential drawdown water levels should be between 1185–1214 m for the OY07 and 774–791 m for OY10 as it is in favor of both the total hydropower production and the firm third-monthly hydropower output.
- (2)
- Targeting higher drawdown levels of the OY07 and OY10 will lead to more hydropower production during the flood season, mainly attributable to higher water heads that contribute to higher generation efficiency.
- (3)
- The hydropower productions during dry season will be less when targeting higher drawdown levels. The hydropower production during the year, as well as the firm hydropower output, goes up first and then down when elevating the drawdown water levels of the over-year reservoirs, with the maximums in total hydropower production and firm hydropower output achieved by drawing the OY07 and OY10’s water levels down to (774 m, 791 m) and (1185 m, 1214 m), respectively.
- (4)
- Targeting higher drawdown water levels at the end of dry seasons has, if any, minimal impact on the upstream reservoirs of the OY07 in the hydropower curtailment due to the generating capacity, but will result in a more significant curtailment in the downstream hydro-plants due to a smaller storage capacity available to reduce spillages.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**The third-monthly results by simulating the 8th option over the years 1953–2002. (

**a**) OY07; (

**b**) OY10.

**Figure 6.**The distribution of the water level over space and time within a year. (

**a**) OY07; (

**b**) OY10.

Number | Name | Annual Inflow (m ^{3}/s) | Installed Capacity (MW) | Dead Water Level (m) | Normal Water Level (m) | Operability |
---|---|---|---|---|---|---|

1 | D01 | 744 | 990 | 1901 | 1906 | Daily |

2 | D02 | 758 | 420 | 1814 | 1818 | Daily |

3 | S03 | 902 | 1900 | 1586 | 1619 | Seasonal |

4 | D04 | 923 | 920 | 1472 | 1477 | Daily |

5 | W05 | 960 | 1400 | 1398 | 1408 | Weekly |

6 | D06 | 1010 | 900 | 1303 | 1307 | Daily |

7 | OY07 | 1210 | 4200 | 1166 | 1240 | Over-year |

8 | S08 | 1230 | 1670 | 988 | 994 | Seasonal |

9 | S09 | 1330 | 1350 | 887 | 899 | Seasonal |

10 | OY10 | 1740 | 5850 | 765 | 812 | Over-year |

11 | W11 | 1810 | 1750 | 591 | 602 | Weekly |

Option | Water Level (m) | Hydropower Production (TW) | Curtailment (TW) | Full-Refilling Rate | ||||||
---|---|---|---|---|---|---|---|---|---|---|

OY07 | OY10 | Annu. | Dry | Flood | Firm | Up | Down | OY07 | OY10 | |

1 | 1166 | 765 | 102.17 | 48.63 | 53.54 | 1.54 | 4.86 | 0.76 | 38% | 54% |

2 | 1176 | 770 | 102.9 | 48.23 | 54.67 | 1.56 | 4.85 | 0.87 | 40% | 64% |

3 | 1185 | 774 | 103.54 | 47.51 | 56.03 | 1.56 | 4.85 | 1.06 | 46% | 76% |

4 | 1193 | 779 | 104.06 | 46.87 | 57.19 | 1.54 | 4.85 | 1.30 | 52% | 90% |

5 | 1201 | 783 | 104.47 | 46.23 | 58.24 | 1.52 | 4.85 | 1.54 | 64% | 92% |

6 | 1207 | 787 | 104.75 | 45.43 | 59.33 | 1.50 | 4.85 | 1.80 | 64% | 98% |

7 | 1214 | 791 | 104.82 | 44.09 | 60.73 | 1.45 | 4.85 | 2.12 | 78% | 100% |

8 | 1219 | 794 | 104.64 | 42.53 | 62.12 | 1.38 | 4.85 | 2.59 | 82% | 100% |

9 | 1225 | 798 | 104.32 | 40.88 | 63.45 | 1.31 | 4.85 | 2.59 | 88% | 100% |

10 | 1231 | 801 | 103.74 | 39.09 | 64.65 | 1.22 | 4.85 | 3.86 | 94% | 100% |

11 | 1236 | 804 | 103.24 | 37.39 | 65.84 | 1.14 | 4.85 | 4.56 | 100% | 100% |

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**MDPI and ACS Style**

Liu, S.; Luo, X.; Zheng, H.; Zhang, C.; Wang, Y.; Chen, K.; Wang, J. Investigation on Water Levels for Cascaded Hydropower Reservoirs to Drawdown at the End of Dry Seasons. *Water* **2023**, *15*, 362.
https://doi.org/10.3390/w15020362

**AMA Style**

Liu S, Luo X, Zheng H, Zhang C, Wang Y, Chen K, Wang J. Investigation on Water Levels for Cascaded Hydropower Reservoirs to Drawdown at the End of Dry Seasons. *Water*. 2023; 15(2):362.
https://doi.org/10.3390/w15020362

**Chicago/Turabian Style**

Liu, Shuangquan, Xuhan Luo, Hao Zheng, Congtong Zhang, Youxiang Wang, Kai Chen, and Jinwen Wang. 2023. "Investigation on Water Levels for Cascaded Hydropower Reservoirs to Drawdown at the End of Dry Seasons" *Water* 15, no. 2: 362.
https://doi.org/10.3390/w15020362