# Risk Control in Optimization of Cascade Hydropower: Considering Water Abandonment Risk Probability

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Description of WARP

#### 2.2. TEM of WARP Based on Runoff Forecasting Error

#### 2.2.1. WARP of the Head Hydropower Station

^{3}/s; ${q}_{gen}$ and ${q}_{dis}$ are the maximum generation discharge and the average water abandonment discharge, respectively, during the period, with the units m

^{3}/s;${V}_{t}$ and ${V}_{t+\Delta t}$ are the water storage of the reservoir at time $t$ and $t+\Delta t$, m

^{3}, respectively; and $\Delta t$ is the length of the period.

^{3}/s; $\epsilon $ is the runoff forecasting error between ${Q}_{fore}$ and the actual inflow value $Q$ in m

^{3}/s; and $F\left(\epsilon \right)$ is the CDF of the runoff forecasting error.

#### 2.2.2. WARP of the Downstream Hydropower Station

- (1)
- The expected release of each cascade reservoir

- (2)
- WARP calculation based on the expected release of the upstream reservoir

^{3}/s; ${\overline{q}}_{i-1,out}$ is the expected release of the (i−1)-th reservoir in m

^{3}/s; ${S}_{i}$ is the interval inflow between the i-th reservoir and the (i−1)-th reservoir in m

^{3}/s; ${q}_{i,gen}$ and ${q}_{i,dis}$ are the maximum generation discharge and the average water abandonment discharge, respectively, of the i-th hydropower station during the period, with the units m

^{3}/s; and ${V}_{i,t+\Delta t}$ and ${V}_{i,t}$ are the water storage of the i-th reservoir at time $t+\Delta t$ and $t$, respectively, with the unit m

^{3}.

^{3}/s; $\epsilon $ is the runoff forecasting error between ${S}_{i,fore}$ and the actual interval inflow value ${S}_{i}$ in m

^{3}/s; and $F\left(\epsilon \right)$ is the CDF of the runoff forecasting error.

#### 2.3. Cascade Hydropower Optimal Operation Model under WARP

#### 2.3.1. Objective Function

#### 2.3.2. Constraints

- (1)
- General constraints

^{3}/s; ${V}_{t+1}^{i}$ and ${V}_{t}^{i}$ are the water storage of the i-th reservoir at period t + 1 and period t, respectively, with the unit m

^{3}; ${Z}_{i,t}^{min}$ and ${Z}_{i,t}^{max}$ are the minimum and maximum water levels, respectively, of the i-th reservoir at period t, with the unit m; ${Q}_{r,i,t}^{min}$ and ${Q}_{r,i,t}^{max}$ are the minimum and maximum outflow, respectively, of the i-th reservoir at period t; and ${N}_{i,t}^{min}$ and ${N}_{i,t}^{max}$ are the minimum power output and the installed capacity, respectively, of the i-th hydroelectric plant at period t.

- (2)
- WARP water level constraints

#### 2.3.3. Solution

#### 2.4. Entire Solution Process

## 3. Case Study

#### 3.1. Study Area and Data

^{2}. The main purpose of Wujiang River hydropower system is not only to maximize the total cascade power generation but also to ensure the safety of the downstream area during the flood season. In actual operation, the flood season for Wujiang River is from June to September every year, when due to multiple reasons, most of the water abandonment occurs.

#### 3.2. Results and Discussion

#### 3.2.1. The Probability Distribution of Runoff Forecast Errors

#### 3.2.2. Hydropower Optimal Operation Strategy

#### 3.2.3. Water Abandonment

#### 3.2.4. WARP

#### 3.2.5. Efficient Utilization of Medium and Small Flood Resources

## 4. Conclusions

- (1)
- The optimal scheme ensures an invariable water level at the beginning and end of the operation period, while the water level is higher than the historical scheme during most of the operation period due to the addition of WARP water level constraints (water climbing constraints for a certain period);
- (2)
- Water abandonment, especially in the downstream hydropower stations with small reservoir capacity caused by runoff uncertainties and forecast errors, can be flexibly alleviated and controlled to efficiently utilize flood resources. In the case study, compared with the historical scheme, the total amount of water abandonment in DHS, GLQ and DHS-GLQ decreases by 11.69%, 47.69% and 28.27%, respectively;
- (3)
- Adopting the appropriate WARP water level constraints can effectively guide the head hydropower station with a large reservoir capacity to function as a flood storage at the early stage to stagger the downstream flood peak. In the case study, the flood peak in the GLQ optimal scheme is reduced by 21.6% compared with that in the historical scheme;
- (4)
- The output may be reduced appropriately to meet the requirement to increase the water level at the early stage but improved with greater head efficiency at the later stage, and thereby the system generation profits of the whole operation period can be improved.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Ren, D. Outlook for renewable energy development of 13th Five Year Plan. Sci. Technol. Rev.
**2016**, 34, 133–138. [Google Scholar] - China Renewable Energy Engineering Institute. China Renewable Energy Development Report; China Renewable Energy Engineering Institute: Beijing, China, 2021. [Google Scholar]
- Hall, W.A.; Butcher, W.S.; Esogbue, A. Optimization of the operation of a multiple-purpose reservoir by dynamic programming. Water Resour. Res.
**1968**, 4, 471–477. [Google Scholar] [CrossRef] - Keckler, W.G.; Larson, R.E. Dynamic programming applications to water resource system operation and planning. J. Math. Anal. Appl.
**1968**, 24, 80–109. [Google Scholar] [CrossRef] - Mizyed, N.R.; Loftis, J.C.; Fontane, D.G. Operation of large multireservoir systems using optimal-control theory. J. Water Resour. Plan. Manag.
**1992**, 118, 371–387. [Google Scholar] [CrossRef] - Russell, S.O.; Campbell, P.F. Reservoir operating rules with fuzzy programming. J. Water Resour. Plan. Manag.
**1996**, 122, 165–170. [Google Scholar] [CrossRef] - Alcamo, J.; Flörke, M.; Märker, M. Future long-term changes in global water resources driven by socio-economic and climatic changes. Hydrol. Sci. J.
**2007**, 52, 247–275. [Google Scholar] [CrossRef] - Simonovic, S.P.; Burn, D.H. An improved methodology for short-term operation of a single multipurpose reservoir. Water Resour. Res.
**1989**, 25, 1–8. [Google Scholar] [CrossRef] - Xie, M.; Zhou, J.; Li, C.; Zhu, S. Long-term generation scheduling of Xiluodu and Xiangjiaba cascade hydro plants considering monthly streamflow forecasting error. Energy Convers. Manag.
**2015**, 105, 368–376. [Google Scholar] [CrossRef] - Zhao, T.; Yang, D.; Cai, X.; Zhao, J.; Wang, H. Identifying effective forecast horizon for real-time reservoir operation under a limited inflow forecast. Water Resour. Res.
**2012**, 48, 1–15. [Google Scholar] [CrossRef] - Tan, Q.; Fang, G.; Wen, X.; Lei, X.; Wang, X.; Wang, C.; Ji, Y. Bayesian stochastic dynamic programming for hydropower generation operation based on copula functions. Water Resour. Manag.
**2020**, 34, 1589–1607. [Google Scholar] [CrossRef] - Yuan, L.; Zhou, J. Self-optimization system dynamics simulation of real-time short term cascade hydropower system considering uncertainties. Water Resour. Manag.
**2017**, 31, 2127–2140. [Google Scholar] [CrossRef] - Schultz, G.A.; Plate, E.J. Developing optimal operating rules for flood protection reservoirs. J. Hydrol.
**1976**, 28, 245–264. [Google Scholar] [CrossRef] - Sigvaldson, O. A simulation model for operating a multipurpose multireservoir system. Water Resour. Res.
**1976**, 12, 263–278. [Google Scholar] [CrossRef] - Karamouz, M.; Vasiliadis, H.V. Bayesian stochastic optimization of reservoir operation using uncertain forecasts. Water Resour. Res.
**1992**, 28, 1221–1232. [Google Scholar] [CrossRef] - Ahmed, I. On the Determination of Multi-Reservoir Operating Policy under Uncertainty. Ph.D. Thesis, The University of Arizona, Tucson, AZ, USA, 2001. [Google Scholar]
- Yamout, G.M.; Hatfield, K.; Romeijn, H.E. Comparison of new conditional value-at-risk-based management models for optimal allocation of uncertain water supplies. Water Resour. Res.
**2007**, 43, 1–13. [Google Scholar] [CrossRef] - You, J.; Cai, X. Hedging rule for reservoir operations: 1. A theoretical analysis. Water Resour. Res.
**2008**, 44, 1–9. [Google Scholar] [CrossRef] - You, J.; Cai, X. Hedging rule for reservoir operations: 2. A numerical model. Water Resour. Res.
**2008**, 44, 1–11. [Google Scholar] [CrossRef] - Piantadosi, J.; Metcalfe, A.; Howlett, P. Stochastic dynamic programming (SDP) with a conditional value-at-risk (CVaR) criterion for management of storm-water. J. Hydrol.
**2008**, 348, 320–329. [Google Scholar] [CrossRef] - Xu, W.; Zhang, C.; Peng, Y.; Fu, G.; Zhou, H. A two stage Bayesian stochastic optimization model for cascaded hydropower systems considering varying uncertainty of flow forecasts. Water Resour. Res.
**2014**, 50, 9267–9286. [Google Scholar] [CrossRef] - Datta, B.; Houck, M.H. A stochastic optimization model for real-time operation of reservoirs using uncertain forecasts. Water Resour. Res.
**1984**, 20, 1039–1046. [Google Scholar] [CrossRef] - Ji, C.; Li, R.; Tian, K.; Zhang, Y.; Li, C. A coupling model of load adjustment for cascade hydropower stations based on inflow uncertainty: A case study of Jinping-guandi cascade hydropower stations. J. Hydraul. Eng.
**2017**, 48, 1–12. [Google Scholar] - Wen, Q.; Xue, N. Study on the spill electricity price of central china power net. Autom. Electr. Power Syst.
**2001**, 25, 48–51. [Google Scholar] - Shuai, W. The problems and countermeasures about abandoned water in China southwest hydropower station. Electr. Power
**2017**, 50, 171–175. [Google Scholar] - Tan, Q.; Wen, X.; Sun, Y.; Lei, X.; Wang, Z.; Qin, G. Evaluation of the risk and benefit of the complementary operation of the large wind-photovoltaic-hydropower system considering forecast uncertainty. Appl. Energy
**2021**, 285, 116442. [Google Scholar] [CrossRef] - Windsor, J.S. Optimization model for the operation of flood control systems. Water Resour. Res.
**1973**, 9, 1219–1226. [Google Scholar] [CrossRef] - Wu, Z.; Hu, C.; Wang, B.; Liu, H. Risk analysis on limited water level of reservoirs in flood season and flood control system in midstream and downstream of Yellow River. J. Hydraul Eng.
**2006**, 37, 641–648. [Google Scholar] - Xiao, Y. Research on optimal scheduling based on abandoned water probability. Express Water Resour. Hydropower
**2015**, 36, 22–24. [Google Scholar] - Zhang, C. Research on Risk Analysis and Control method of Spillage for Cascade Reservoirs in Wujiang River Basin. Master’s Thesis, Dalian University of Technology, Dalian, China, 2019. [Google Scholar]
- Sun, X.; Dong, S.; Xu, X. The Minimum Abandoned Water Optimization Model of Reservoir and Its Application. In Proceedings of the 2009 Fifth International Conference on Natural Computation, Tianjin, China, 14–16 August 2009; pp. 131–135. [Google Scholar]
- He, Y. Research on the cascade reservoirs surplus water risk control methods for frequent flood. China Rural. Water Hydropower
**2019**, 9, 162–170, 180. [Google Scholar] - Yang, X.S. Cuckoo search and firefly algorithm: Overview and analysis. In Cuckoo Search and Firefly Algorithm; Springer: Berlin/Heidelberg, Germany, 2014; pp. 1–26. [Google Scholar]

**Figure 2.**The frequency distribution histograms of runoff forecasting relative error of various forecast periods (

**a**) 1h. (

**b**) 2h. (

**c**) 3h. (

**d**) 4h. (

**e**) 5h. (

**f**) 6h.

Name | DHS | GLQ | Location Diagram of the Two Reservoirs |
---|---|---|---|

Watershed flow concentration area (km^{2}) | 4328 | 4735 | |

Annual average runoff (m^{3}/s) | 75 | 82 | |

Reservoir regulation capacity | incomplete annual | daily | |

Unit maximum overflow (m^{3}/s) | 165 | 202.6 | |

Normal water level (m) | 868.00 | 719.00 | |

Flood control level (m) | 868.00 | 719.00 | |

Dead water level (m) | 845.00 | 709.00 | |

Installed capacity (MW) | 2 × 100 | 2 × 75 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Fang, G.; Ye, J.; Liu, J.; Wen, X.; Wu, C.
Risk Control in Optimization of Cascade Hydropower: Considering Water Abandonment Risk Probability. *Sustainability* **2022**, *14*, 10911.
https://doi.org/10.3390/su141710911

**AMA Style**

Zhang X, Fang G, Ye J, Liu J, Wen X, Wu C.
Risk Control in Optimization of Cascade Hydropower: Considering Water Abandonment Risk Probability. *Sustainability*. 2022; 14(17):10911.
https://doi.org/10.3390/su141710911

**Chicago/Turabian Style**

Zhang, Xinyi, Guohua Fang, Jian Ye, Jin Liu, Xin Wen, and Chengjun Wu.
2022. "Risk Control in Optimization of Cascade Hydropower: Considering Water Abandonment Risk Probability" *Sustainability* 14, no. 17: 10911.
https://doi.org/10.3390/su141710911