# Optimal Operation of Complex Flood Control System Composed of Cascade Reservoirs, Navigation-Power Junctions, and Flood Storage Areas

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/s for designed floods with different return periods, which increased by about 333~1498 m

^{3}/s in comparison with the conventional operation. Considering that the maximum water level of reservoirs using DP-POA and the conventional operation is the same, this indicated that DP-POA can make full use of the reservoirs’ flood control storage to reduce downstream flood peaks. In addition, the flood diversion volume of the flood storage area using DP-POA ranged from 0.33 × 10

^{8}to 1.79 × 10

^{8}m

^{3}for designed floods with 200-year, 300-year, and 500-year return periods, which is smaller than that using the conventional operation.

## 1. Introduction

## 2. Optimization Model and Methodology

#### 2.1. Optimization Model of Complex Flood Control System

_{i}(t), q

_{i}(t), V

_{i}(t) are the discharge, inflow, and water storage of the ith water project during time period, t, respectively; τ

_{i}is the time-lags of discharge from the ith water project flood routing to the jth flood control point; Q

_{j}(t) is the streamflow of the jth flood control point during time period, t; Δq

_{j}(t) is the local flow of the jth flood control point during time period, t; R

_{s}(t) is the flood diversion volume of the sth flood storage area during time period, t; ψ

_{i}(·) is the flood control operation rule of the ith water projects; φ

_{j}(·) is the flood routing function between the ith water project and the jth flood control point; ρ

_{s}(·) is the flood control operation rule of the sth flood storage area.

#### 2.1.1. Objective Function

_{i}is the weight coefficient for the jth flood control point; Qp

_{j}is the flood peak at the jth flood control point without flood control operation; and Qf

_{j}is the flood peak at the jth flood control point using optimal flood control operation.

#### 2.1.2. Constraints

- (1)
- Water balance equation:$$[\frac{{q}_{i}(t)+{q}_{i}(t+1)}{2}-\frac{{Q}_{i}(t)+{Q}_{i}(t+1)}{2}]\Delta t={V}_{i}(t+1)-{V}_{i}(t),$$
_{i}(t) and q_{i}(t + 1) are the inflow of the ith reservoir during time period, t and t + 1, respectively; Q_{i}(t) and Q_{i}(t + 1) are the discharge of the ith reservoir during time period, t and t + 1, respectively; Δt is the time interval; and V_{i}(t) and V_{i}(t + 1) are the initial and final storage of the ith reservoir at time period, t. - (2)
- Reservoir water level limits:$${Z}_{i}^{\mathrm{min}}\le {Z}_{i}(t)\le {Z}_{i}^{\mathrm{max}},$$
_{i}^{min}and Z_{i}^{max}are the minimal and maximal water level of the ith reservoir during the operation period, respectively; Z_{i}(t) is the water level of the ith reservoir during the time period, t. - (3)
- Boundary conditions:$${Z}_{i}(1)={Z}_{i,start},{Z}_{i}(T+1)={Z}_{i,end},$$
_{i}_{,start}is the water level of the ith reservoir at the initial time period; Z_{i}_{,end}is the water level of the ith reservoir at the final time period. - (4)
- Reservoir discharge limits:$${Q}_{i}^{\mathrm{min}}\le {Q}_{i}(t)\le {Q}_{i}^{\mathrm{max}}[{Z}_{i}(t)],$$
_{i}^{max}[Z_{i}(t)] is the maximal discharge of the ith reservoir when the water level of the ith reservoir is Z_{i}(t) during time period, t. Q_{i}^{min}is the minimum discharge of the ith reservoir. - (5)
- Discharge variation limits:$$|{Q}_{i}(t+1)-{Q}_{i}(t)|\le \Delta {Q}_{i},$$
_{i}is the allowable discharge variation of the ith reservoir between adjacent time periods. - (6)
- Flood routing constraints using the Muskingum method:$${Q}_{hd}^{m}(t+1)={C}_{0}^{m}{I}_{hd}^{m}(t+1)+{C}_{1}^{m}{I}_{hd}^{m}(t)+{C}_{2}^{m}{Q}_{hd}^{m}(t)+{Q}_{q}^{m}(t),$$
_{hd}^{m}(t) is the streamflow of the down section of the mth sub-river during the time period, t; I_{hd}^{m}(t) is the streamflow of the upper section of the mth river during the time period, t; Q_{q}^{m}(t) is the local flow of the mth sub-river; C_{0}^{m}, C_{1}^{m}, C_{2}^{m}means the Muskingum method coefficients of the mth sub-river, respectively. - (7)
- Other water projects’ constraints:Other water projects such as navigation-power junctions and flood storage areas, affect flood routing by flood detention. This study simulates their operation according to their flood control rules for these constraints.
- (a)
- Constraints of navigation-power junctions:Navigation-power junctions do not function as flood control for the lack of flood control storage capacity. However, to reduce the submergence loss in the reservoir area, the navigation-power junctions are required to lower the water level and open all the discharge gates when encountering large flood events. The flood control operation rules of navigation-power junctions can be generalized into four stages as follows:
- (I)
- Power generation stageWhen the inflow is small, the main purpose of the navigation-power junction is power generation, and discharge is equal to the inflow. This can be calculated as:$$\begin{array}{l}{q}_{nj,k}(t)={Q}_{nj,k}(t),\\ {Z}_{nj,k}(t)={Z}_{nl,k}\end{array}$$
_{nj}_{,k}(t) and q_{nj}_{,k}(t) are inflow and discharge of the kth navigation-power junction during time period, t, respectively; Z_{nj}_{,k}(t) is the water level of the kth navigation-power junction during time period, t; Z_{nl}_{,k}is the normal pool level of the kth navigation-power junction. - (II)
- Water level reduction stageWhen the inflow continues increasing, the outflow is increased gradually, which can be calculated as:$${q}_{nj,k}(t)=\mathrm{min}\{{Q}_{nj,k}(t)+\Delta {Q}_{d,k},{q}_{nj,k}^{\mathrm{max}}\},$$
_{d}_{,k}is discharge increment of the kth navigation-power junction and q_{nj}_{,k}^{max}is the maximal discharge volume of the kth navigation-power junction when all the discharge gates are opened, which can be calculated as:$$\{\begin{array}{l}{V}_{nj,k}(t+1)={V}_{nj,k}(t)+[\frac{{Q}_{nj,k}(t)+{Q}_{nj,k}(t+1)}{2}-\frac{{q}_{nj,k}(t)+{q}_{nj,k}(t+1)}{2}]\Delta t\\ {Z}_{nj,k}(t+1)={\phi}_{nj,k}[{V}_{nj,k}(t+1)]\\ {Z}_{nj,k}^{\ast}=\mathrm{max}\{{Z}_{nj,k}(t+1),{Z}_{nj,k}^{\mathrm{min}}\}\\ {q}_{nj,k}^{\mathrm{max}}={\psi}_{nj,k}({Z}_{nj,k}^{\ast})\end{array},$$_{nj}_{,k}^{min}is the minimum water level of the kth navigation-power junction during the flood control operation period; φ_{nj}_{,k}(·) is the relationship curve of water level and reservoir capacity of the kth navigation-power junction;ψ_{nj}_{,k}(·) is the relationship curve of water level and discharge of the kth navigation-power junction, which is similar to the relationship of water level and streamflow in the natural river channel. - (III)
- All discharge gates opened stageWhen the inflow of the navigation-power junction is too large, all the discharge gates are opened, and the water level is close to that of the natural river, which can be calculated as:$$\begin{array}{l}{q}_{nj,k}(t)={Q}_{nj,k}(t),\\ {Z}_{nj,k}(t)={f}_{nj,k}[{q}_{nj,k}(t)]\end{array}$$
_{nj}_{,k}[q_{nj}_{,k}(t)] is the relationship of water level and streamflow in the natural river channel. - (IV)
- Water storage stage

In the falling limb, the water level will rise to the normal pool level, which can be calculated as:$${q}_{nj,k}(t)={Q}_{nj,k}(t)-\Delta {Q}_{r,k},$$_{r}_{,k}is the discharge reduction of the kth navigation-power junction. - (b)
- Constraints of the flood storage area:

The flood control operation of flood storage areas can be generalized as follows:$${Q}_{d,s}(t)={Q}_{u,s}(t)-{\rho}_{s}({Q}_{u,s}(t)),$$$${\rho}_{s}({Q}_{u,s}(t))=\{\begin{array}{cc}0\hfill & {Q}_{u,s}(t)\le L\text{}\mathrm{or}\text{}W(t){W}_{\mathrm{max}}\hfill \\ {Q}_{u,s}(t)-L\hfill & L{Q}_{u,s}(t)\le {Q}_{\mathrm{max}}\text{}\mathrm{and}\text{}W(t)\le {W}_{\mathrm{max}}\hfill \\ {Q}_{\mathrm{max}}\hfill & {Q}_{u,s}(t){Q}_{\mathrm{max}}\text{}\mathrm{and}\text{}W(t)\le {W}_{\mathrm{max}}\hfill \end{array},$$$$W(t)={\displaystyle \sum _{t=1}^{T-1}[\frac{{Q}_{u,s}(t)+{Q}_{u,s}(t+1)}{2}-\frac{{Q}_{d,s}(t)+{Q}_{d,s}(t+1)}{2}]}\Delta t,$$_{d}_{,s}(t) and Q_{u}_{,s}(t) are streamflow of the sth flood storage area before and after flood diversion during time period, t; ρ_{s}(Q_{u}_{,s}(t)) means flood diversion streamflow according to flood control rules of the sth flood storage area during time period, t; L is the indicative flow for the use of the sth flood storage area; W(t) is the water storage volume of the sth flood storage area during time period, t; Q_{max}and W_{max}are the maximum flood diversion discharge and maximum water storage volume, respectively. - (8)
- Non-negative constraints:All the variables are non-negative.

#### 2.2. Optimization Methods

_{i}(t) is the release of the ith reservoir during the time period, t; T = the number of the time periods. Constraints are similar to Equations (3)–(7).

_{1}(1),…, Z

_{i}(t + 1),…, Z

_{i}(T + 1),…, Z

_{M}(1),…, Z

_{M}(T + 1)} is obtained. Here, M is the total number of reservoirs. Set iteration k = 1 and the reservoir number i = 1.

^{*}= {Z

_{1}

^{*}(1),…, Z

_{i}

^{*}(t + 1),…, Z

_{i}

^{*}(T + 1),…, Z

_{M}

^{*}(1),…, Z

_{M}

^{*}(T + 1)}. Replace the initial solution u with u

^{*}. Then the iteration k = k + 1.

^{*}, and the optimization is completed.

## 3. Study Area and Data

#### 3.1. Study Area

^{2}(Figure 3). This basin is situated in the subtropical humid monsoon climate zone with mean annual discharge of 2130 m

^{3}/s and mean annual precipitation of approximately 1400–1800 mm [43]. Runoff in the flood season from April to June, accounts for more than half of the annual runoff [44]. The Ganjiang River has a great influence on the social and economic development of Jiangxi Province, China. However, flood disasters frequently happen in the middle and lower reaches of the Ganjiang River, which harm human lives and property and threaten the safety of society. In addition, more and more water projects have been built in the middle and lower reaches of Ganjiang River, making the hydraulic connection complex and it is worth researching on optimal flood control operation to reduce the loss of flood disasters.

^{8}m

^{3}[45]. Xiajiang reservoir is the second largest reservoir in the Jiangxi province with a storage capacity of 11.87 × 10

^{8}m

^{3}. Quangang flood storage area, with a storage capacity of 8.35 × 10

^{8}m

^{3}, located in the lower reaches of Ganjiang River, helps protect flood control points Shishang and Waizhou through flood diversion. The two navigation-power junctions, Jinggangshan and Shihutang, are situated between Wan’an reservoir and Ji’an flood control point. The other navigation-power junctions, Xingan and Longtoushan, are located between the Xiajiang reservoir and Shishang flood control point. The skeleton of the middle and lower reaches of Ganjiang River flood control system is shown in Figure 4. The characteristic parameters of these reservoirs and navigation-power junctions are listed in Table 1.

#### 3.2. Input Data

## 4. Results

#### 4.1. Flood Peak Reduction of Flood Control Points

^{3}/s and its discharge is equal to inflow. For the same designed return period floods, the flood peak reduction of the Wan’an reservoir using DP-POA was larger than that using conventional flood control operation, which means optimization method can make full use of flood control capacity to reduce flood peak. Table 5 shows that the flood peak reduction of the Xiajiang reservoir increases as designed return periods increase from 50 years to 200 years. While for designed floods with 300-year and 500-year return periods, the flood peak reduction of the Xiajiang reservoir decreased from 1819 to 1339 m

^{3}/s. This is because flood peak reduction listed in Table 5 and Table 6 is the average value of six years. When flood peak is larger, greater storage of the reservoir is used to detain the inflow without exceeding the acceptable safety level of the reservoir. However, the flood peaks of some designed floods were too large for the Xiajiang reservoir and the discharge was equal to the inflow for the safety of the reservoir, which means that flood peak reduction was zero. For example, the flood peak reduction of the Xiajiang reservoir was zero only for “1961” designed floods with 300-year return periods, while for designed floods with 500-year return periods, the flood peak reduction of “1961”, “1968”, and ”1994” was zero. Therefore, the average flood peak reduction of the Xiajiang reservoir for designed floods with 500-year return periods was less than that for designed floods with 300-year return periods.

^{3}/s while it increases by 1041~1498 m

^{3}/s using DP-POA. The Shishang flood control point is located in the downstream of Xiajiang reservoir and its flood peak is mainly reduced by the operation of the Wan’an-Xiajiang cascade reservoirs and Quangang flood storage area. Comparing with the conventional operation, DP-POA can increase flood peak reduction of Shishang flood control point by 584~1151 m

^{3}/s. The Waizhou flood control point is the outlet of the Ganjiang River. DP-POA can decrease its flood peak by 1080~4809 m

^{3}/s while the conventional operation can decrease the flood peak by 747~4063 m

^{3}/s. Considering that the maximal water level using DP-POA is equal to that using the conventional operation, these results indicate that DP-POA is more efficient in making full use of the flood control capacity of reservoirs to reduce the flood peak of flood control points.

^{3}/s whenever using conventional or optimal operation. Except for that, other flood peaks of three flood control points using DP-POA were smaller than those using the conventional operation.

#### 4.2. Flood Diversion Volume of the Flood Storage Area

^{8}to 2.49 × 10

^{8}m

^{3}. Comparing with the conventional operation, the flood diversion volume using DP-POA was smaller. For typical floods and designed floods with 20-year, 50-year, and 100-year return periods, the flood diversion volume of the optimal operation was zero. For designed floods with 200-year, 300-year, and 500-year return periods, the flood diversion volume turned from 0.33 × 10

^{8}m

^{3}to 1.79 × 10

^{8}m

^{3}. This means that DP-POA can retain more storage capacity and it is safe for operation in the Quangang flood storage area.

#### 4.3. Flood Control Operation Process of Reservoirs

^{3}/s, which occurs at the 53rd time period. However because DP-POA optimizes the discharge of the Wan’an reservoir, the maximal inflow peak of the Xiajiang reservoir using DP-POA was reduced to 21,060 m

^{3}/s, which is even smaller than the discharge of the Xiajiang reservoir using the conventional operation. In addition, DP-POA did not reduce the inflow peak of the Xiajiang reservoir. Comparing the occurrence time of inflow peak with that of discharge peak, it is shown that DP-POA delays the occurrence time of flood peak from the 46th time period to the 50th time period. This indicates that DP-POA can consider the downstream local flow and delay occurrence time of the discharge peak to avoid encountering downstream flood peak.

## 5. Discussions and Limitations

## 6. Conclusions

^{3}/s, its discharge is equal to its inflow and the flood diversion volume of the Quangang flood storage area is zero. This means flood peaks of downstream flood control points are mainly reduced by operation of the Wan’an reservoir. For larger floods, such as designed floods with 50-year, 100-year, 200-year, 300-year, and 500-year return periods, the joint flood control operation of the Wan’an-Xiajiang cascade reservoirs and Quangang flood storage area can greatly reduce flood peak of downstream flood control points.

^{3}/s, respectively for typical floods and designed floods with 20-year, 50-year, 100-year, 200-year, 300-year, and 500-year return periods, which is a great progress comparing with the conventional operation. Considering that the maximal water level of Wan’an–Xiajiang cascade reservoirs during the periods of conventional and optimal operation is the same, this means DP-POA was more efficient in making full of flood control storage of reservoirs.

^{8}m

^{3}, while the corresponding value of DP-POA was only 1.79 × 10

^{8}m

^{3}. The greater the storage retained, the safer it is for the operation of the flood storage area.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**The location of reservoirs, navigation-power junctions, and flood control points in the Ganjiang River.

**Figure 4.**The skeleton of the middle and lower reaches of Ganjiang River basin flood control system.

**Figure 8.**The average flood diversion volume of the Quangang flood storage for typical and design floods.

**Figure 9.**Conventional flood control operation of the Wan’an–Xiajiang cascade reservoirs: (

**a**) discharge of the Wan’an reservoir; (

**b**) discharge of the Xiajiang reservoir.

**Figure 10.**Optimal flood control operation of the Wan’an–Xiajiang cascade reservoirs: (

**a**) discharge of the Wan’an reservoir; (

**b**) discharge of the Xiajiang reservoir.

Reservoir | Wan’an | Xiajiang | Jinggangshan | Shishutang | Xingan | Longtoushan |
---|---|---|---|---|---|---|

Basin area (km^{2}) | 36,900 | 62,710 | 40,937 | 43,770 | 64,776 | 72,810 |

Mean annual runoff (m^{3}/s) | 947 | 1640 | 1050 | 1160 | 1690 | 1890 |

Dead water level (m) | 85 | 44 | 67.7 | 56.2 | 32 | 23.7 |

Flood limited water level (m) | 85 | 45 | - | - | - | - |

Flood control highwater level (m) | 93.6 | 49 | - | - | - | - |

Normal pool level (m) | 96 | 46 | 68 | 56.5 | 32.5 | 24.2 |

Regulation ability | Seasonal | Seasonal | Daily | Daily | Daily | Daily |

Stream Segment | Muskingum Coefficients | Sub-River Number | Δt/h | ||
---|---|---|---|---|---|

C_{0} | C_{1} | C_{2} | |||

1 | 0.2308 | 0.5385 | 0.2308 | 1 | 6 |

2 | 0.2857 | 0.4286 | 0.2857 | 1 | 6 |

3 | 0.2857 | 0.4286 | 0.2857 | 1 | 6 |

4 | 0.2857 | 0.4286 | 0.2857 | 1 | 6 |

5 | 0.3333 | 0.3333 | 0.3333 | 1 | 6 |

6 | 0.3333 | 0.3333 | 0.3333 | 1 | 6 |

7 | 0.3333 | 0.3333 | 0.3333 | 2 | 6 |

8 | 0.5000 | 0 | 0.5000 | 4 | 6 |

Condition | Inflow (m^{3}/s) | Reservoir Water Level (m) | Discharge (m^{3}/s) |
---|---|---|---|

Rising limb | q ≤ 8800 | 85 < Z ≤ 93.6 | Q = q |

8800 < q ≤ 9550 | Q = 8800 | ||

9550 < q ≤ 12,000 | Q = q − 750 | ||

q > 12,000 | Q = q − 4000 | ||

- | Z > 93.6 | Open discharge | |

Falling limb | q > 8000 | Z > 88 | Open discharge |

Z < 88 | Q = q | ||

4000 < q ≤ 8000 | Z > 88 | Q = 8800 | |

Z < 88 | Q = q | ||

2800 < q ≤ 4000 | Z > 88 | Q = 4000 | |

Z < 88 | Q = q | ||

q ≤ 2800 | Z > 88 | Q = 2800 | |

Z < 88 | Q = q |

Condition | Inflow (m^{3}/s) | Reservoir Water Level (m) | Outflow (m^{3}/s) |
---|---|---|---|

Rising limb | 20,000 < q ≤ 21,500 | 45 < Z < 48.4 | Q = q |

21,500 < q ≤ 23,500 | Q = 20,000 | ||

q ≥ 23,500 | Q = 22,000 | ||

q ≤ 22,000 | 48.4 < Z < 49 | Q = q | |

22,000 < q ≤ 24,000 | Q = 22,000 | ||

q > 24,000 | Q = 24,000 | ||

q < 26,600 | Z > 49 | Q = q | |

q ≥ 26,600 | Open discharge | ||

Falling limb | q > 19,000 | - | Open discharge |

Q ≤ 19,000 | - | Q = 19,000 |

Return Periods (Year) | Wan’an Reservoir | Xiajiang Reservoir | ||
---|---|---|---|---|

Maximal Water Level (m) | Flood Peak Reduction (m^{3}/s) | Maximal Water Level (m) | Flood Peak Reduction (m^{3}/s) | |

Typical | 88.62 | 271 | 45.00 | 0 |

20 | 90.09 | 53 | 45.00 | 0 |

50 | 91.35 | 382 | 45.41 | 323 |

100 | 91.87 | 663 | 46.48 | 1044 |

200 | 92.44 | 783 | 47.86 | 2004 |

300 | 92.66 | 937 | 48.29 | 1819 |

500 | 93.43 | 1215 | 48.75 | 1339 |

Return Periods (Year) | Wan’an Reservoir | Xiajiang Reservoir | ||
---|---|---|---|---|

Maximal Water Level (m) | Flood Peak Reduction (m^{3}/s) | Maximal Water Level (m) | Flood Peak Reduction (m^{3}/s) | |

Typical | 88.62 | 481 | 45.00 | 0 |

20 | 90.09 | 827 | 45.00 | 0 |

50 | 91.35 | 1120 | 45.41 | 100 |

100 | 91.87 | 1092 | 46.48 | 324 |

200 | 92.44 | 1649 | 47.86 | 1058 |

300 | 92.66 | 1649 | 48.29 | 1195 |

500 | 93.43 | 1771 | 48.75 | 1161 |

Return Periods (Year) | Designed Flood Peak (m^{3}/s) | Operation | Reduction (m^{3}/s) | Rate (%) |
---|---|---|---|---|

Typical | 16,032 | Convention | 365 | 2.28 |

DP-POA | 1491 | 9.30 | ||

20 | 17,748 | Convention | 598 | 3.37 |

DP-POA | 2059 | 11.60 | ||

50 | 20,235 | Convention | 993 | 4.91 |

DP-POA | 2491 | 12.31 | ||

100 | 21,950 | Convention | 1274 | 5.80 |

DP-POA | 2425 | 11.05 | ||

200 | 23,665 | Convention | 1328 | 5.61 |

DP-POA | 2583 | 10.91 | ||

300 | 24,608 | Convention | 1351 | 5.49 |

DP-POA | 2629 | 10.68 | ||

500 | 25,808 | Convention | 1500 | 5.81 |

DP-POA | 2541 | 9.85 |

Return Periods (Year) | Designed Flood Peak (m^{3}/s) | Operation | Reduction (m^{3}/s) | Rate (%) |
---|---|---|---|---|

Typical | 18,059 | Convention | 482 | 2.67 |

DP-POA | 1102 | 6.10 | ||

20 | 19,856 | Convention | 627 | 3.16 |

DP-POA | 1629 | 8.20 | ||

50 | 22,637 | Convention | 1194 | 5.27 |

DP-POA | 2345 | 10.36 | ||

100 | 24,556 | Convention | 1961 | 7.98 |

DP-POA | 3088 | 12.57 | ||

200 | 26,474 | Convention | 3336 | 12.60 |

DP-POA | 4171 | 15.75 | ||

300 | 27,529 | Convention | 4081 | 14.82 |

DP-POA | 4665 | 16.95 | ||

500 | 28,873 | Convention | 4575 | 15.85 |

DP-POA | 5359 | 18.56 |

Return Periods (Year) | Designed Flood Peak (m^{3}/s) | Operation | Reduction (m^{3}/s) | Rate (%) |
---|---|---|---|---|

Typical | 18,839 | Convention | 747 | 3.96 |

DP-POA | 1080 | 5.73 | ||

20 | 20,700 | Convention | 912 | 4.40 |

DP-POA | 1527 | 7.38 | ||

50 | 23,600 | Convention | 1370 | 5.81 |

DP-POA | 2090 | 8.86 | ||

100 | 25,600 | Convention | 2076 | 8.11 |

DP-POA | 2920 | 11.41 | ||

200 | 27,600 | Convention | 3085 | 11.18 |

DP-POA | 3833 | 13.89 | ||

300 | 28,700 | Convention | 3449 | 12.02 |

DP-POA | 4228 | 14.73 | ||

500 | 30,100 | Convention | 4063 | 13.50 |

DP-POA | 4809 | 15.98 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhu, D.; Mei, Y.; Xu, X.; Chen, J.; Ben, Y. Optimal Operation of Complex Flood Control System Composed of Cascade Reservoirs, Navigation-Power Junctions, and Flood Storage Areas. *Water* **2020**, *12*, 1883.
https://doi.org/10.3390/w12071883

**AMA Style**

Zhu D, Mei Y, Xu X, Chen J, Ben Y. Optimal Operation of Complex Flood Control System Composed of Cascade Reservoirs, Navigation-Power Junctions, and Flood Storage Areas. *Water*. 2020; 12(7):1883.
https://doi.org/10.3390/w12071883

**Chicago/Turabian Style**

Zhu, Di, Yadong Mei, Xinfa Xu, Junhong Chen, and Yue Ben. 2020. "Optimal Operation of Complex Flood Control System Composed of Cascade Reservoirs, Navigation-Power Junctions, and Flood Storage Areas" *Water* 12, no. 7: 1883.
https://doi.org/10.3390/w12071883