# Influence of Power Operations of Cascade Hydropower Stations under Climate Change and Human Activities and Revised Optimal Operation Strategies: A Case Study in the Upper Han River, China

^{*}

## Abstract

**:**

^{3}and 5 million kWh, respectively. This study has practical significance for the efficient operation of cascade hydropower stations and is helpful for developing reservoir operation theory under changing environments.

## 1. Introduction

_{2}emissions caused by coal power generation [11]. Additionally, hydropower is also responsible for regulating the safety of power grid systems in future energy structures [12]. Take the current Chinese energy structure as an example, the hydropower installed capacity had exceeded 300 GW, about 50% of the total installed power capacity, up to 2015, and about half of total power generation was hydropower from 2000–2015 [13]. However, hydropower is vulnerable to climate change and human activities [14]. As an important input to the hydropower generation system, runoff and water distribution changes under the influences of climate change and human activities would directly impact the operation of power stations. Therefore, researching the influences of climate change and human activities on hydrological systems and establishing efficient coping strategies are of great significance for cascade power stations.

## 2. Study Area and Data

#### 2.1. The Upper Han River

^{2}. The upper Han River is in an area with a subtropical humid climate. The annual rainfall distribution in this area is uneven and most runoff recharge is surface runoff from rainfall. The main flood season is from July–September; however, some small floods also occur from mid–late April [24].

#### 2.2. Cascade Hydropower Stations

#### 2.3. The Project

^{3}of water from the Han River to the Guanzhong region, including important cities, counties, and industrial parks. The Project consists of two water source areas connected by a water transfer tunnel. The Huangjinxia reservoir (HJX) in the main stream has abundant water with no regulation ability, and the Sanhekou reservoir (SHK) in a tributary has pluriennal regulation capacity with less water.

^{3}, it means that the amount of water transferred by the Project accounts for 15% of the inflow of the Shiquan reservoir.

#### 2.4. Data Collection

## 3. Materials and Methods

#### 3.1. Variation of Runoff

#### 3.2. Hydroelectric Operation Charts

#### 3.3. Model Construction and Parameters

#### 3.3.1. Simulation Model

**Step one**: Calculate the regulated flow during the dry season and determine the guaranteed output according to formulae (1)–(9).

**Step two**: Assume an initial power generation flow and calculate the initial reservoir storage based on the water balance formula and the upstream water level as follows:

**Step three**: Compare the power plant output ${N}^{\prime}\left(t\right)$ with ${N}_{g}$. Then adjust the outflow with $\Delta q$ and return to step two:

**Step four**: If formula (12) is successfully calculated, then go ahead to step five, otherwise adjust the outflow and return to step two:

**Step five**: If formula (13) is successfully calculated, then stop, otherwise adjust the outflow and return to step two.

#### 3.3.2. Optimal Model of Cascade Hydropower Joint Operation

^{8}kWh. $T$ and $M$ represent the length of the operation cycle and the number of reservoirs, followed by Shiquan, Xihe, and Ankang. $\overline{{h}_{m}}\left(t\right)$ represents the water head of the m reservoir at time t, ${k}_{m}$ represents the power coefficient of the m power station.

- 1)
- Water balance$${V}^{m}\left(t+1\right)-{V}^{m}\left(t\right)=\left({Q}_{i}^{m}\left(t\right)-{Q}_{o}^{m}\left(t\right)\right)\xb7\Delta t$$
- 2)
- Water level$${Z}_{min}^{m}\le {Z}_{}^{m}\left(t\right)\le {Z}_{max}^{m}\left(t\right)$$
- 3)
- Maximum overflow$${Q}_{o}^{m}\left(t\right)\le {Q}_{max}^{m}\left(t\right)$$
- 4)
- Output of power station$${N}_{}^{m}\left(t\right)\le {N}_{ins}^{m}$$$${N}_{dry}^{m}\left(t\right)\le {N}_{g}^{m}$$
- 5)
- Operation lines are not allowed to be intersected in the operation chart optimization.$$D{Z}_{k-1}^{m}\left(t\right)\le D{Z}_{k}^{m}\left(t\right),\text{}t=1,2,\dots ,T,\text{}k=1,2,\dots ,K$$

#### 3.3.3. Parameter Setting and Evaluation Indicators

_{a}

_{w}(m

^{3}/k·Wh)

#### 3.4. Calculation Schemes

_{a}, P, and P

_{w}were used to quantitatively analyze the impacts.

## 4. Results and Discussion

#### 4.1. Analysis of Runoff Variation Point

_{k}and UF

_{k}crossed in 1990, which may indicate that the runoff begins to change in this year.

- (1)
- Initial natural runoff (1954–1990)
- (2)
- Only climate change: Natural runoff (1991–2010)
- (3)
- Only human activities: Natural runoff (1954–1990) minus transferred process (1954–1990)
- (4)
- Combined climate change and human activities: natural runoff (1991–2010) minus the transferred process (1991–2010)

#### 4.2. Influences of Climate Change and Human Activities on Hydropower Operation

^{8}kWh (16.67%), 1.45 × 10

^{8}kWh (20.48%), and 2.73 × 10

^{8}kWh (38.56%), respectively. Additionally, the same decreasing trend occurs in Xihe, which decreases by 0.2 × 10

^{8}kWh (4.04%), 0.3 × 10

^{8}kWh (6.06%), and 0.37 × 10

^{8}kWh (7.47%) and Ankang, which decreases by 5.73 × 10

^{8}kWh (20.78%), 2.59 × 10

^{8}kWh (9.39%), and 7.68 × 10

^{8}kWh (27.85%), respectively

^{3}in the upper Han River area.

#### 4.3. Coping Hydropower Operation Charts under the Influence of Climate Change and Human Activities

#### 4.3.1. Chart 1: Modified Regular Single Reservoir Operation Chart

#### 4.3.2. Chart 2: Modified Optimal Single Reservoir Operation Chart

_{p}is slightly low compared with Figure 6b. All these changes are used to increase the power generation of the power stations.

#### 4.3.3. Chart 3: Modified Optimal Cascade Reservoir Operation Chart

#### 4.4. Optimal Operation of the Project

^{3}and power generation would increase by 5 million kWh. (2) The Project would reduce the water level pressure for the downstream reservoirs before the flood season, and the abandoned water of Shiquan, Xihe, and Ankang power stations would decrease by 5.19%, 6.67%, and 5.33%, respectively. (3) The abandoned water from Shiquan and Xihe reservoirs always occurs at the same time, and the largest amount of abandoned water is July. These three reservoirs occur abandoned water in June and September at the same time, and Ankang reservoir has the largest abandoned water before the flood season (June).

## 5. Conclusions

^{3}, and the abandoned water of Shiquan, Xihe, and Ankang power stations would decrease by 5.19%, 6.67%, and 5.33%, respectively, which could increase power generation by 5 million kWh. The Project can also reduce the water level pressure before the flood season for the downstream power stations.

## 6. Supplementary Material

#### 6.1. The Multi-Objective Optimal Model for the Project

_{pump}represents the total energy consumption of two pump stations in an operation series, E

_{power}represents the total power generation of two power stations in an operation series, W represents the transferred water quantity. T, M, and Δt represent the same as in the simulated operation model; ${P}_{pump}^{m}\left(t\right)$ represents the power from pump station m consumed in the period t, ${q}_{pump}^{m}\left(t\right)$ represents the water flow of pump station m transferred in the period t, ${\eta}_{pump}^{m}$ represents the efficiency of pump station m, g represents gravity; ${N}_{power}^{m}\left(t\right)$ represents the power generation of power station m generated in the period t, ${Q}_{power}^{m}\left(t\right)$ represents the power flow of power station m used in the period t, $h\left(t\right)$ represents the water head of reservoir m in the period t, and k represents the power coefficient of power station m.

- 1)
- Water balance$${V}^{m}\left(t+1\right)-{V}^{m}\left(t\right)=\left[{Q}_{I}^{m}\left(t\right)-{Q}_{O}^{m}\left(t\right)-{Q}_{S}^{m}\left(t\right)\right]\xb7\Delta t$$
- 2)
- Water level$${Z}_{min}^{2}\le {Z}^{2}\left(t\right)\le {Z}_{max}^{2}\left(t\right)$$
- 3)
- Transferable water quantity$$\sum}_{m=1}^{M}{Q}_{S}^{m}\left(t\right)\xb7\Delta t\le {W}_{max}^{qty}\left(t\right)$$
- 4)
- Maximum overflow$${Q}_{power}^{m}\left(t\right)\le {Q}_{max}^{m}$$$${Q}_{}^{tunnel}\left(t\right)\le {Q}_{max}^{tunnel}$$
- 5)
- Output of power station$${N}_{}^{m}\left(t\right)\le {N}_{installed}^{m,max}$$$${N}_{dry}^{1}\left(t\right)\ge {N}_{firm}^{1}$$
- 6)
- Power of pump station$${P}_{}^{m}\left(t\right)\le {P}_{installed}^{m,max}$$
^{m}$\left(t\right)$ represents storage capacity of the m reservoir in t period (10^{8}m^{3}); ${Q}_{I}^{m}\left(t\right)$, ${Q}_{O}^{m}\left(t\right)$, and ${Q}_{S}^{m}\left(t\right)$ represent the inflow runoff, outflow runoff, and water transferred flow of the reservoir m in period t, respectively (m^{3}/s); Z^{2}(t) represents the water level of the SHK reservoir in period t, ${Z}_{min}^{2}$ represents the dead water level and ${Z}_{max}^{2}$(t) represents the highest water level, including the flood control level during flooding season and the normal high water level during non-flooding seasons (m); ${W}_{max}^{qty}$(t) represents the maximum transferable water quantity of the Han River in period t (10^{8}m^{3}); Q^{m}$\left(t\right)$ represents the outflow of the power station m in period t, ${Q}_{max}^{m}$ represents the maximum outflow of the power station m (m^{3}/s); Q^{tunnel}(t) represents the average transferred flow in the Qinling tunnel in period t, ${Q}_{max}^{tunnel}$ represents the maximum water transfer capability of the Qinling tunnel (m^{3}/s); N^{m}(t) represents the output of power station m in period t, ${N}_{installed}^{m,max}$ represents the installed capacity of power station m, ${N}_{dry}^{1}\left(t\right)$ and ${N}_{firm}^{1}$ represent the output in the dry season and the firm power of HJX power station, respectively; P^{m}(t) represents the power consumption of the pump station m in period t, ${P}_{installed}^{m,max}$ represents the installed capacity of pump station m. All variables were non-negative.

#### 6.2. The Original Interpretation of the Operation Chart for the Project

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**distribution map of power stations and reservoirs in the upper Han River, the blue area is water resource areas of the Project, the brown area is intake areas of the Project and the gray area is power stations in the downstream of the Project.

**Figure 2.**Conventional hydroelectric operation charts for Shiquan (

**a**) and Ankang (

**b**). The red line and green line are the upper basic line and lower basic line, respectively. The blue line and the purple line are the 1.2 Ng and 0.8 Ng line, respectively.

**Figure 3.**Flow chart for generating the optimal operation charts under climate change and human activities. See Section 3.2 in the main text for definition of the different parts. MK = Mann-Kendall test.

**Figure 4.**Mann-Kendall test results of inflow of Shiquan reservoir, UBk and UFk are time statistics.

**Figure 5.**Operating parameters (E, N

_{g}, P, P

_{w}, and P

_{a}) of the hydropower stations in the conventional operation chart under the four schemes. The blue, green, yellow, and red curve are in turn scheme 1 to 4.

**Figure 6.**Modified hydropower operation charts for Shiquan (

**a**) and Ankang (

**b**) to address the effects of climate change and human activities. The solid and dashed lines indicate the modified and traditional operation lines, respectively. The red line and green line are the upper basic line and lower basic line, respectively. The blue line and the purple line are the 1.2 Ng and 0.8 Ng line, respectively.

**Figure 7.**The monthly average change process of water abandoned of the Shiquan, Xihe, and Ankang reservoirs in condition of the Project optimized. The upper right part is the multi-year average change of abandoned water when the operation of Project is optimized or not.

**Figure 8.**The modified operation chart for the Sanhekou reservoir of the Project. The original interpretation of the operation chart is listed in the supplementary material.

**Table 1.**The characteristics of the cascade reservoirs of Shiquan, Xihe, and Ankang hydropower stations.

Index | Unit | Shiquan | Xihe | Ankang |
---|---|---|---|---|

Average annual discharge | m^{3}/s | 308.3 | 378 | 621 |

Normal water level | m | 410 | 362 | 330 |

Dead water level | m | 400 | 360 | 305 |

Regulation storage | 10^{8}m^{3} | 1.8 | 0.22 | 14.72 |

regulation performance | / | seasonal | Daily | incomplete yearly |

Installed capacity | MW | 225 | 180 | 852.5 |

Guaranteed output (Ng) | MW | 32 | 21.8 | 175 |

Annual average power generation | 10^{8}kW·h | 6.06 | 4.92 | 27.48 |

Maximum head | m | 47.5 | 32.5 | 88 |

Minimum head | m | 26.3 | 13 | 57 |

Maximum power flow | m^{3}/s | 677.5 | 811 | 1500 |

Parameters | CS Algorithm |
---|---|

Decision variable | Water level |

Number of operation lines | 4 |

Number of decision variables | 48 |

Population size | 400 |

Generation | 5000 |

Discovery probability | 0.25 |

Scheme | Operation Scenario | Operation Mode | Coping Strategy |
---|---|---|---|

1 | Initial natural runoff (1954-Y) | Single reservoir operation in conventional operation charts | Chart 1 |

2 | Only climate change: natural runoff (Y-2010) | ||

3 | Only human activities: 1954-Y, natural runoff (1954-Y) minus transferred process (1954-Y) | ||

4 | Combined climate change and human activities: natural runoff (Y-2010) minus transferred process (Y-2010) | ||

5 | Combined climate change and human activities: natural runoff (Y-2010) minus transferred process (Y-2010) | Single reservoir optimization | Chart 2 |

6 | Cascade reservoir optimization | Chart 3 |

**Table 4.**Operating results of hydropower station under the influence of climate change and human activities (Scheme 1, Scheme 2, Scheme 3, and Scheme 4).

Scheme | 1: Initial Runoff (1954~1989) | 2: Climate Change (1990~2009) | 3: Human Activities (1954~1989) | 4: Climate Cange and Human Activities (1990~2009) | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Station | E | Ng | P (%) | Pw | Pa (%) | E | Ng | P (%) | Pw | Pa (%) | E | Ng | P (%) | Pw | Pa (%) | E | Ng | P (%) | Pw | Pa (%) |

Shiquan | 7.08 | 35 | 88 | 10.4 | 28.10 | 5.9 | 28 | 64 | 10.40 | 27.30 | 5.63 | 27 | 59 | 10.6 | 26.34 | 4.45 | 25 | 50 | 10.7 | 25.24 |

Xihe | 4.95 | 23 | 91 | 14.3 | 22.42 | 4.75 | 20 | 80 | 14.3 | 22.11 | 3.91 | 18 | 75 | 14.8 | 21.34 | 3.71 | 16 | 65 | 15.1 | 20.37 |

Ankang | 27.58 | 185 | 81 | 5.8 | 15.01 | 21.85 | 159 | 74 | 6.2 | 13.56 | 24.99 | 170 | 69 | 6.3 | 13.92 | 19.26 | 165 | 67 | 6.3 | 12.21 |

Cascade stations | 39.61 | 243 | 87 | 10.17 | 21.84 | 32.5 | 207 | 73 | 10.30 | 20.99 | 34.53 | 215 | 68 | 10.57 | 20.53 | 27.42 | 206 | 61 | 10.70 | 19.27 |

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## Share and Cite

**MDPI and ACS Style**

Wu, L.; Bai, T.; Huang, Q.; Zhang, M.; Mu, P.
Influence of Power Operations of Cascade Hydropower Stations under Climate Change and Human Activities and Revised Optimal Operation Strategies: A Case Study in the Upper Han River, China. *Water* **2019**, *11*, 895.
https://doi.org/10.3390/w11050895

**AMA Style**

Wu L, Bai T, Huang Q, Zhang M, Mu P.
Influence of Power Operations of Cascade Hydropower Stations under Climate Change and Human Activities and Revised Optimal Operation Strategies: A Case Study in the Upper Han River, China. *Water*. 2019; 11(5):895.
https://doi.org/10.3390/w11050895

**Chicago/Turabian Style**

Wu, Lianzhou, Tao Bai, Qiang Huang, Ming Zhang, and Pengfei Mu.
2019. "Influence of Power Operations of Cascade Hydropower Stations under Climate Change and Human Activities and Revised Optimal Operation Strategies: A Case Study in the Upper Han River, China" *Water* 11, no. 5: 895.
https://doi.org/10.3390/w11050895