# Reservoir Operation Sequence- and Equity Principle-Based Multi-Objective Ecological Operation of Reservoir Group: A Case Study in a Basin of Northeast China

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Multi-Objective Ecological Operation Model

#### 2.1.1. Objective Function

- Maximize WSGR

^{3}) and ${W}_{i,t}$ (m

^{3}) represent the water supply and demand of the i-th calculation unit in the t-th stage, respectively.

- 2.
- Maximize EFS

^{3}/s) and ${Q}_{j,t}^{E}$ (m

^{3}/s) represent the actual flow and ecological flow of the j-th monitoring section in the t-th stage.

#### 2.1.2. Constraints

- Water balance constraint:

^{3}) and ${V}_{k,t}$ (m

^{3}) signify the storage capacity of the k-th reservoir in the t and (t + 1)-th stages, respectively. ${I}_{k,t}$ (m

^{3}/s), ${I}_{{}_{k,t}}^{D}$ (m

^{3}/s), ${O}_{{}_{k,t}}$ (m

^{3}/s), ${O}_{{}_{k,t}}^{D}$ (m

^{3}/s), and $R{S}_{k,t}$ (m

^{3}/s) are the inflow, diversion inflow, outflow, diversion outflow, and supply flow of the k-th reservoir in the t-th stage, respectively; and $\Delta t$ (s) is the scheduling stage; $R{E}_{k,t}$ (m

^{3}) and $R{F}_{k,t}$ (m

^{3}) signify the evaporation and seepage of the k-th reservoir in the t-th stage, respectively.

- 2.
- Reservoir outflow and water supply constraints:

^{3}) represents the water demand for the reservoir supply channel. $\alpha $ (dimensionless) is the failure depth factor, which represents the ratio of water shortage to water demand (in a dry year, when water supply cannot meet water demand, the water supply can be appropriately reduced, but it should not be lower than the water shortage depth allowed by each user. In this study, α of domestic, industrial, and agricultural water is 0.05, 0.10, and 0.30, respectively). ${Q}_{k,t}^{{E}_{}}$ (m

^{3}/s) and ${Q}_{\mathit{max}}$ (m

^{3}/s) signify the ecological flow in the t-th stage and overflow capacity of the corresponding river section, respectively.

- 3.
- Reservoir storage capacity constraint:

^{3}) signifies the dead capacity of the k-th reservoir and ${V}_{k,t}^{\mathit{max}}$ (m

^{3}) signifies the maximum permissible storage capacity of the k-th reservoir in the t-th stage.

- 4.
- Channel overflow capacity constraints:

^{3}/s), ${Q}_{\mathit{kmax}}^{D}$ (m

^{3}/s), and $R{S}_{\mathit{kmax}}$ (m

^{3}/s) signify the flow capacity of the water supply, diversion inflow, and diversion outflow channel, respectively.

#### 2.1.3. Reservoir Operation Sequence (ROS) and Equity Principle (EP)

- Reservoir Operation Sequence (ROS)

#### 2.2. Equity Principle (EP)

^{3}) in the t-th stage, and the water demand of each unit is ${D}_{i,t}$ (m

^{3}) (Figure 1). If $\sum _{i=1}^{n}{D}_{i,t}}>{S}_{t$, the amount of water actually obtained by each water unit from the water supply project, assumed as ${A}_{i,t}$, is allocated according to Equation (10).

#### 2.2.1. Optimisation Algorithm

#### 2.2.2. Data Input

#### 2.3. Case Study

#### 2.3.1. Study Area and Data

^{8}m

^{3}/year; the other is the Songhua River–Changchun Diversion Project (SCDP) with a designed water supply capacity of 2.67 × 10

^{8}m

^{3}/year. The YRB is a relatively water-deficient watershed, and the shortage of water resources is the main factor that restricts the social development in this region. Besides, the irrational use of water resources makes the watershed face severe ecological problems. Hence, an efficient and reasonable way of utilising water resources is particularly important.

#### 2.3.2. Calculation of Ecological Flow

#### 2.3.3. Scheduling Network Generalisation

#### 2.3.4. Scheduling Schemes Setting

## 3. Results

#### 3.1. Water Demand Prediction

^{8}m

^{3}in 2015 and 2.71 × 10

^{8}m

^{3}in 2030, respectively. Water units are divided into three categories: urban, irrigation area, and river internal (Figure 4). The water demand of urban/irrigation area/internal river was 5.89/3.85/8.36 × 10

^{8}m

^{3}in 2015, and the water demand of urban/irrigation area/internal river is 11.86/3.58/3.57 × 10

^{8}m

^{3}in 2030. The EBF of the Dehui section in flood/non-flood season is 2.63/1.87 m

^{3}/s, and the EBF of the Dehui section in flood/non-flood season is 1.27/1.14 m

^{3}/s (Figure 5a). The ESF reached its maximum in August, with 38.29 m

^{3}/s in the Dehui section and 15.37 m

^{3}/s in the Nongan section (Figure 5b).

#### 3.2. Supply-Demand Balance Analysis

^{4}m

^{3}in 2015, and the water shortage rate of them was 3.98%/4.32%/5.04% (Figure 6a). The water shortage of P1/P2/P3 is 2170/5290/8708 × 10

^{4}m

^{3}in 2030, and the water shortage rate of them is 0.8%/1.95%/3.21% (Figure 6b). In a normal year, the water shortage of P1/P2/P3 is 5448/7204/8272 × 10

^{4}m

^{3}in 2015, and the water shortage rate of them is 3.01%/3.98%/4.57% (Figure 6a). The water shortage of P1/P2/P3 is 2062/2930/6348 × 10

^{4}m

^{3}in 2030, and the water shortage rate of them is 0.76%/1.08%/2.34% (Figure 6b). In a wet year, the water shortage of P1/P2/P3 was 3150/4634/5810 × 10

^{4}m

^{3}in 2015, and the water shortage rate of them was 1.74%/2.56%/3.21% (Figure 6a). The water shortage of P1/P2/P3 is 1519/2686/4747 × 10

^{4}m

^{3}in 2030, and the water shortage rate of them is 0.56%/0.99%/1.75% (Figure 6b).

#### 3.3. Runoff of River Section

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Geographical location, DEM, weather station, river, and hydraulic engineering distribution of the study area.

**Figure 7.**Box plot of water shortage rate of different schemes in each level year: (

**a**) P1 in 2015, (

**b**) P2 in 2015, (

**c**) P3 in 2015, (

**d**) P1 in 2030, (

**e**) P2 in 2030, and (

**f**) P3 in 2030.

**Figure 8.**Plot of the Dehui section runoff of different schemes in each level year: (

**a**–

**c**) in 2015 and (

**d**–

**f**) in 2030.

**Figure 9.**Plot of the Nongan section runoff of different schemes in each level year: (

**a**–

**c**) in 2015 and (

**d**–

**f**) in 2030.

**Figure 10.**The annual cumulative water shortage rate curve for Unit 25 in Figure S1 with reservoir water supply sequences S1, S2, S3, S4, S5, and S6 after 500 iterations with the respective algorithm: (

**a**) P1 in 2015, (

**b**) P1 in 2030, (

**c**) P2 in 2015, (

**d**) P2 in 2030, (

**e**) P3 in 2015, and (

**f**) P3 in 2030. * S1 indicates the sequence of reservoir water supply (1 XLC, 2 STKM, 3 XXS), which indicates the XXS reservoir is first, the STKM reservoir is second, and the XLC reservoir is third. S2, S3, S4, S5, and S6, respectively, indicate (1 XLC, 2 XXS, 3 STKM), (1 XXS, 2 XLC, 3 STKM), (1 XXS, 2 STKM, 3 XLC), (1 STKM, 2 XXS, 3 XLC), and (1 STKM, 2 XLC, 3 XXS). The boxplot on the right shows the mean, median, outliers, and inter-quartile ranges for the annual water shortage rate of Unit 25.

Mode | Schematic Diagram * | Reservoir Operation Sequence |
---|---|---|

A | The water supply sequence is based on the utilisable reservoir storage capacity, from small to large. | |

B | The water supply sequence depends on the reservoir locations, which proceed successively from the downstream reservoir to the upstream reservoir. | |

C | The two tandem reservoirs on the right are equivalent to a reservoir, and the utilisable capacity of the equivalent reservoir is equal to the sum of the reservoir’s utilisable capacity in the series system. Thus, the equivalent reservoir forms a parallel system with the remaining reservoirs, and the water supply sequence is determined according to the operation rules of Mode A. Additionally, the water supply sequence of the series reservoirs follows Mode B. | |

D | The two upstream parallel reservoirs are equivalent to a reservoir. Thus, the equivalent reservoir forms a series system with the remaining reservoirs, and the water supply sequence of the reservoirs is determined according to the operation rules of Mode B. Additionally, the water supply sequence of the parallel reservoirs follows Mode A. |

Year | Scenario Description | Ecological Scheduling Scheme | No. |
---|---|---|---|

2015 | Before the water supply of Central Jilin Water Supply Project | Reservoir group operation not considering ecological flow | P1 |

Reservoir group operation considering ecological base flow | P2 | ||

Reservoir group operation considering ecological suitable flow | P3 | ||

2030 | After the water supply of Central Jilin Water Supply Project | Reservoir group operation not considering ecological flow | P1 |

Reservoir group operation considering ecological base flow | P2 | ||

Reservoir group operation considering ecological suitable flow | P3 |

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**MDPI and ACS Style**

Wu, X.; Shen, X.; Wei, C.; Xie, X.; Li, J.
Reservoir Operation Sequence- and Equity Principle-Based Multi-Objective Ecological Operation of Reservoir Group: A Case Study in a Basin of Northeast China. *Sustainability* **2022**, *14*, 6150.
https://doi.org/10.3390/su14106150

**AMA Style**

Wu X, Shen X, Wei C, Xie X, Li J.
Reservoir Operation Sequence- and Equity Principle-Based Multi-Objective Ecological Operation of Reservoir Group: A Case Study in a Basin of Northeast China. *Sustainability*. 2022; 14(10):6150.
https://doi.org/10.3390/su14106150

**Chicago/Turabian Style**

Wu, Xu, Xiaojing Shen, Chuanjiang Wei, Xinmin Xie, and Jianshe Li.
2022. "Reservoir Operation Sequence- and Equity Principle-Based Multi-Objective Ecological Operation of Reservoir Group: A Case Study in a Basin of Northeast China" *Sustainability* 14, no. 10: 6150.
https://doi.org/10.3390/su14106150