# Flood Control Optimization of Reservoir Group Based on Improved Sparrow Algorithm (ISSA)

^{*}

## Abstract

**:**

^{3}, and the peak cutting rate is 48%. The optimization effect is obviously better than the other two algorithms. This study provides a new and effective way to solve the problem of flood control optimization of reservoir groups.

## 1. Introduction

## 2. Reservoir Joint Flood Control Dispatching Model

#### 2.1. Objective Function

#### 2.2. Condition of Constraint

- (1)
- Water balance constraint:$${V}_{t}={V}_{t-1}+(({Q}_{t}+{Q}_{t+1})/2-({q}_{t}+{q}_{t+1})/2)\mathrm{\Delta}t$$

- (2)
- Constraints on reservoir water level:$${\mathrm{Z}}_{\mathrm{min},k}\le {\mathrm{Z}}_{\mathrm{k}}\le {\mathrm{Z}}_{\mathrm{max},k}(k=1,2)$$

- (3)
- Letdown flow constraint:$$0\le {q}_{k}\le {q}_{\mathrm{max},k}(k=1,2)$$

- (4)
- Initial water level constraint:$${Z}_{0}={Z}_{\mathrm{min},k}(k=1,2)$$

- (5)
- Terminal water level constraint:$${Z}_{end}={Z}_{\mathrm{min},k}(k=1,2)$$

## 3. Sparrow Optimization Algorithm

#### 3.1. Basic Sparrow Search Algorithm (SSA)

^{−1}. When i > n/2, it indicates that the i-th finder with low fitness value has not got food and is in a very hungry state. At this time, it needs to fly to other places to forage for more energy.

#### 3.2. Improved Sparrow Algorithm (ISSA)

- (1)
- Sin chaos initialization population

- (2)
- Dynamic adaptive weight

- (3)
- An improved formula for updating the position of the watchman$${\mathrm{X}}_{i,j}^{t+1}=\left\{\begin{array}{l}{X}_{best}^{t}+\beta ({X}_{i,j}^{t}-{X}_{best}^{t}),{f}_{i}\ne {f}_{g}\\ {X}_{best}^{t}+\beta ({\mathrm{X}}_{worst}^{t}-{X}_{best}^{t}),{f}_{i}={f}_{g}\end{array}\right.$$

- (4)
- Fusion of Cauchy Variation and Reverse Learning Strategy

## 4. Model Analysis

#### 4.1. Solution Method of Flood Control Operation Model

- (1)
- Initialization parameters, such as population number N, maximum iteration number $ite{r}_{\mathrm{max}}$, discoverer proportion PD, joiner proportion SD, alert threshold R
_{2}and initialization of sparrow population using the Sin chaotic map of Equation (12) according to the calculation period given by flood flow. The sparrow is constructed with the discharge of each reservoir at the end of each cycle as the control variable. The flood lasts 78 periods and has two reservoirs, so the vector dimension is 156. Then, the matrix form of sparrow population:$$Y(0)=[{Z}_{1}(0),{Z}_{2}(0),\dots {X}_{n}(0)]=\left(\begin{array}{cccc}{z}_{1,1}(0)& {z}_{1,2}(0)& \dots & {z}_{1,n}(0)\\ {z}_{2,1}(0)& {z}_{2,2}(0)& \cdots & {z}_{2,n}(0)\\ \vdots & \vdots & \vdots & \vdots \\ {z}_{156,1}(0)& {z}_{156,2}(0)& \cdots & {z}_{156,n}(0)\end{array}\right)$$ - (2)
- Calculate the fitness value of each sparrow and find out the current optimal fitness value, the worst fitness value, and the corresponding position.
- (3)
- From the sparrows with better fitness values, select some sparrows as the discoverers, and update their positions according to Formula (14).
- (4)
- The remaining sparrows will be the participants, and their positions will be updated in the original way.
- (5)
- Randomly select some sparrows from the sparrows as watchers and update their positions according to Formula (15).
- (6)
- According to probability ${\mathrm{P}}_{s}$, the Cauchy mutation perturbation strategy and reverse learning strategy are selected to perturb the current optimal solution to generate a new solution.
- (7)
- Determine whether to update the location according to the greedy rule (21).
- (8)
- Judge whether the end conditions are met. If the end conditions are met, proceed to the next step; otherwise, skip to step (2).
- (9)
- The program ends and the optimal result is output.

#### 4.2. Study Area of Flood Control Operation Model

^{2}. The Yellow River basin has many tributaries and developed water system, which also leads to frequent floods in the Yellow River basin. The water system of the Yellow River basin is shown in Figure 3.

^{2}, accounting for 91.49% of the total drainage area. Sanmenxia Reservoir is a large comprehensive reservoir focusing on flood control and considering irrigation and power generation. Xiaolangdi Reservoir is 130 km away from Sanmenxia Reservoir. The total storage capacity of the reservoir is 12.65 billion cubic meters, and the controlled drainage area is 694,000 km

^{2}, accounting for 92.3% of the total area of the Yellow River basin. It is the only large-scale comprehensive water conservancy project with large storage capacity in the middle and lower reaches of the Yellow River except Sanmenxia. See Table 1 for the current situation of Sanmenxia Xiaolangdi Reservoir.

#### 4.3. Interval Water Supply Analysis of Flood Control Operation Model

_{1}, the interval flow between Sanmenxia and Xiaolangdi is Q

_{2}, and the interval flow between Xiaolangdi Reservoir and Huayuankou is Q

_{3}. It is assumed that the discharge of Sanmenxia Reservoir is q

_{1}, and the discharge will evolve into q

_{2}through the river channel. The sum of interval flow Q

_{2}and flow q

_{2}of Sanmenxia Reservoir and Xiaolangdi Reservoir is the inflow flow of Xiaolangdi Reservoir. The outflow flow q

_{3}of Xiaolangdi reservoir evolves into flow q

_{4}through the river, and the sum of q

_{4}and flow Q

_{3}is used as the flood flow at Huayuan Estuary of the control point. The flood routing process of the flood control system is shown in Figure 5.

## 5. Results and Discussion

^{3}/s, respectively, meeting the flood control requirements of 22,000 m

^{3}/s for this section. When the ISSA algorithm is used to solve the model, the peak clipping rate of the Huayuankou control point is 48%, which is significantly higher than that of the other two algorithms. Additionally, the flood process of the Huayuankou control point is more stable when the ISSA algorithm is used to solve the problem. It shows that the ISSA algorithm is superior to the other two algorithms in solving the joint flood control operation problem of reservoirs.

## 6. Conclusions

- (1)
- From the solution results of the model, it can be seen that the construction of this model not only guarantees the flood control safety of the reservoir itself when encountering the flood with the return period of 1000 years, but also guarantees the flood control safety of the downstream, indicating the rationality and applicability of the model.
- (2)
- In this paper, ISSA, SSA and POS algorithms are used to study the flood control operation of tandem cascade reservoirs including Sanmenxia Reservoir and Xiaolangdi Reservoir on the Yellow River mainstream. The comparison of the solution results of the three optimization algorithms shows that the ISSA algorithm is more efficient than the conventional SSA algorithm and POS algorithm and can fully play the role of reservoir capacity compensation to achieve the best flood control effect. The results show that the ISSA algorithm can effectively solve the flood control optimal operation problem of cascade reservoirs. It provides a new method to solve the problem of joint flood control operation of cascade reservoirs. It also provides a reference for the ISSA algorithm to be applied to other research fields.
- (3)
- Without the regulation of Sanmenxia Reservoir and Xiaolangdi Reservoir, the maximum flood peak flow at the Huayuankou control point is 24,325 m
^{3}/s, far exceeding the flood control requirement of 22,000 m^{3}/s at the Huayuankou control point section. Through the joint flood control operation of Sanmenxia Reservoir and Xiaolangdi Reservoir, the flood peak of the Huayuankou control point is reduced, making the maximum peak flow of the Huayuankou control point 11,676.3 m^{3}/s, ensuring the flood control safety of the Huayuankou control point when encountering the millennium flood. This shows that it is necessary to study the joint flood control operation of Sanmenxia Reservoir and Xiaolangdi Reservoir, and further explains the significance of this study.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Reservoir | Sanmenxia Reservoir | Xiaolangdi Reservoir |
---|---|---|

Control watershed area | 688,400 km^{2} | 694,000 km^{2} |

Flood control limited water level | 305 m | 220 m |

Flood control high water level | 335 m | 275 m |

Total reservoir capacity | 16,200,000,000 m^{3} | 12,650,000,000 m^{3} |

Name of River Section | Flood Propagation Time | Number of Flood Routing Sections | K | x | Δt |
---|---|---|---|---|---|

Sanmenxia–Xiaolangdi | 8 h | 2 | 3.875 | 0.2 | 4 h |

Xiaolangdi–Huayuankou | 12 h | 3 | 4.576 | 0.3 | 4 h |

Algorithm | Population Quantity (N) | Maximum Iterations (Itemax) | Maximum Peak Flood Discharge | Peak Clipping Rate |
---|---|---|---|---|

ISSA | 50 | 1000 | 11,676.3 m^{3}/s | 48% |

SSA | 100 | 1000 | 12,673.65 m^{3}/s | 45% |

POS | 80 | 1000 | 12,408.23 m^{3}/s | 44% |

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**MDPI and ACS Style**

He, J.; Liu, S.-M.; Chen, H.-T.; Wang, S.-L.; Guo, X.-Q.; Wan, Y.-R. Flood Control Optimization of Reservoir Group Based on Improved Sparrow Algorithm (ISSA). *Water* **2023**, *15*, 132.
https://doi.org/10.3390/w15010132

**AMA Style**

He J, Liu S-M, Chen H-T, Wang S-L, Guo X-Q, Wan Y-R. Flood Control Optimization of Reservoir Group Based on Improved Sparrow Algorithm (ISSA). *Water*. 2023; 15(1):132.
https://doi.org/10.3390/w15010132

**Chicago/Turabian Style**

He, Ji, Sheng-Ming Liu, Hai-Tao Chen, Song-Lin Wang, Xiao-Qi Guo, and Yu-Rong Wan. 2023. "Flood Control Optimization of Reservoir Group Based on Improved Sparrow Algorithm (ISSA)" *Water* 15, no. 1: 132.
https://doi.org/10.3390/w15010132