# Short-Term Peak-Shaving Operation of Head-Sensitive Cascaded Hydropower Plants Based on Spillage Adjustment

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Formulation

#### 2.1. Objective Function

#### 2.2. Constraints

^{3}), respectively; ${Q}_{d,t}^{\mathrm{min}}$ and ${Q}_{d,t}^{\mathrm{max}}$ are the minimum and maximum power generation outflows of plant d during period t (m

^{3}/s), respectively; ${U}_{d,t}^{\mathrm{min}}$ and ${U}_{d,t}^{\mathrm{max}}$ are the minimum and maximum water releases of plant d during period t (m

^{3}/s), respectively; and ${N}_{d,t}^{\mathrm{min}}$ and ${N}_{d,t}^{\mathrm{max}}$ are the minimum and maximum power outputs of plant d during period t (MW), respectively.

^{3}/s); ${U}_{d,t}$ is the water release of plant d during period t (m

^{3}/s); and ${\tau}_{d}$ is the water delay, i.e., the time until the discharge of upstream plant d-1 reaches downstream plant d (h).

^{3}), respectively; and $\mathsf{\Delta}t$ is the time interval (h).

^{3}/s).

^{3}/s).

## 3. Methods

#### 3.1. Automatically Dividing Peak and Valley Periods via FCA

#### 3.2. Strategy of Releasing Water Spillage in Advance(SRSA)

#### 3.3. Steps for SRSA

- Step 1:
- The plant currently being adjusted for water spillage is recorded as b, and the total number of plants with water spillage is recorded as B.
- Step 2:
- The most upstream plant b = 1, and its original water spillage is recorded as $W{S}_{b,t}^{*},t\in T$ (obtained from AS).
- Step 3:
- For plant b, divide the peak periods’ water spillage equally into the valley periods according to Equation (29) to calculate the adjusted water spillage, $W{S}_{b,t},t\in T$, and the original water spillage of plant b + 1, $W{S}_{b+1,t}^{*},t\in T$, by the proposed model.
- Step 4:
- If $b<B$, $b=b+1$ and jump to Step 3, otherwise go to Step 5.
- Step 5:
- End the adjustment process.

#### 3.4. Linearization of Hydropower Output Function Based on SOS2

#### 3.5. Overall Solution Process

## 4. Application in the Hongshui River Basin

^{3}, respectively, meaning rich hydropower resources. There are 10 hydropower plants that are expected to be built in the Hongshui River, including 1 multiyear regulating hydropower plant, 2 annually regulating hydropower plants, 6 daily regulating hydropower plants, and 1 run-of-river hydropower plant. Currently, all hydropower plants except Datengxia are operational and generating some quantity of water spillage.

## 5. Results and Discussion

#### 5.1. Identification of Peak, Flat, and Valley Periods

#### 5.2. Case 1—Single Plant

#### 5.3. Case 2—Cascaded System

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Cheng, C.T.; Yan, L.Z.; Mirchi, A.; Madani, K. China’s Booming Hydropower: Systems Modeling Challenges and Opportunities. J. Water Resour. Plan. Manag.
**2017**, 143, 02516002. [Google Scholar] [CrossRef] - National Energy Administration. Available online: http://www.nea.gov.cn/2020-01/20/c_138720881.htm (accessed on 10 November 2020).
- Feng, Z.K.; Niu, W.J.; Cheng, C.T. China’s large-scale hydropower system: Operation characteristics, modeling challenge and dimensionality reduction possibilities. Renew. Energy
**2019**, 136, 805–818. [Google Scholar] [CrossRef] - Cheng, C.T.; Wang, J.Y.; Wu, X.Y. Hydro Unit Commitment with a Head-Sensitive Reservoir and Multiple Vibration Zones Using MILP. IEEE Trans. Power Syst.
**2016**, 31, 4842–4852. [Google Scholar] [CrossRef] - XINHUANET. Available online: http://www.xinhuanet.com/energy/2019-01/30/c_1124061943.htm (accessed on 14 October 2020).
- ESCN. Available online: http://www.escn.com.cn/news/show-699676.html (accessed on 13 November 2020).
- SOHU. Available online: https://www.sohu.com/a/231139439_550183 (accessed on 14 October 2020).
- Ding, N.; Duan, J.H.; Xue, S.; Zeng, M.; Shen, J.F. Overall review of peaking power in China: Status quo, barriers and solutions. Renew. Sustain. Energy Rev.
**2015**, 42, 503–516. [Google Scholar] [CrossRef] - Blokhuis, E.; Brouwers, B.; Putten, E.V.D.; Schaefer, W. Peak loads and network investments in sustainable energy transitions. Energy Policy
**2011**, 39, 6220–6233. [Google Scholar] [CrossRef] - Wang, X.X.; Virguez, E.; Xiao, W.H.; Mei, Y.D.; Patino-Echeverri, D.; Wang, H. Clustering and dispatching hydro, wind, and photovoltaic power resources with multiobjective optimization of power generation fluctuations: A case study in southwestern China. Energy
**2019**, 189, 116250. [Google Scholar] [CrossRef] - Gu, Y.J.; Xu, J.; Chen, D.C.; Wang, Z.; Li, Q.Q. Overall review of peak shaving for coal-fired power units in China. Renew. Sustain. Energy Rev.
**2016**, 54, 723–731. [Google Scholar] [CrossRef] - Simopoulos, D.N.; Kavatza, S.D.; Vournas, C.D. An enhanced peak shaving method for short term hydrothermal scheduling. Energy Convers. Manag.
**2007**, 48, 3018–3024. [Google Scholar] [CrossRef] - Xie, M.F.; Zhou, J.Z.; Li, C.L.; Lu, P. Daily Generation Scheduling of Cascade Hydro Plants Considering Peak Shaving Constraints. J. Water Resour. Plan. Manag.
**2016**, 142, 04015072. [Google Scholar] [CrossRef] - Su, C.G.; Cheng, C.T.; Wang, P.L. An MILP Model for Short-term Peak Shaving Operation of Cascaded Hydropower Plants Considering Unit Commitment. In Proceedings of the IEEE International Conference on Environment and Electrical Engineering (EEEIC)/IEEE Industrial and Commercial Power Systems Europe (I&CPS Europe), Palermo, Italy, 12–15 June 2018; pp. 1–5. [Google Scholar]
- Wu, X.Y.; Cheng, C.T.; Shen, J.J.; Luo, B.; Liao, S.L.; Li, G. A multi-objective short term hydropower scheduling model for peak shaving. Int. J. Elect. Power Energy Syst.
**2015**, 68, 278–293. [Google Scholar] [CrossRef] - Shen, J.J.; Cheng, C.T.; Zhang, J.; Lu, J.Y. Peak Operation of Cascaded Hydropower Plants Serving Multiple Provinces. Energies
**2015**, 8, 11295–11314. [Google Scholar] [CrossRef] [Green Version] - Su, C.G.; Cheng, C.T.; Wang, P.L.; Shen, J.J. Optimization Model for the Short-Term Operation of Hydropower Plants Transmitting Power to Multiple Power Grids via HVDC Transmission Lines. IEEE Access
**2019**, 7, 139236–139248. [Google Scholar] [CrossRef] - Rao, A.R.; Srinivas, V.V. Regionalization of watersheds by fuzzy cluster analysis. J. Hydrol.
**2006**, 318, 57–79. [Google Scholar] [CrossRef] - Goyal, M.; Gupta, V. Identification of Homogeneous Rainfall Regimes in Northeast Region of India using Fuzzy Cluster Analysis. Water Resour. Manag.
**2014**, 28, 4491–4511. [Google Scholar] [CrossRef] - Wang, Y.T.; Chen, L.H. Multi-view fuzzy clustering with minimax optimization for effective clustering of data from multiple sources. Expert Syst. Appl.
**2017**, 72, 457–466. [Google Scholar] [CrossRef] [Green Version] - Yan, M.H.; Yao, X.P.; Wang, L.; Jiang, L.X.; Zhang, J.F. An analysis of the applicability of fuzzy clustering in establishing an index for the evaluation of meteorological service satisfaction. J. Trop. Meteorol.
**2020**, 26, 103–110. [Google Scholar] - Bou-Fakhreddine, B.; Abou-Chakra, S.; Mougharbel, I.; Faye, A.; Pollet, Y. Short-term hydro generation scheduling of cascade plants operating on Litani River project—Lebanon. In Proceedings of the 3rd International Conference on Renewable Energies for Developing Countries (REDEC), Beirut, Lebanon, 13–15 July 2016; pp. 1–6. [Google Scholar]
- Nabavi-Pelesaraei, A.; Bayat, R.; Hosseinzadeh-Bandbafha, H.; Afrasyabi, H.; Chau, K.W. Modeling of energy consumption and environmental life cycle assessment for incineration and landfill systems of municipal solid waste management—A case study in Tehran Metropolis of Iran. J. Clean. Prod.
**2017**, 148, 427–440. [Google Scholar] [CrossRef] - Siu, T.K.; Nash, G.A.; Shawwash, Z.K. A practical hydro, dynamic unit commitment and loading model. IEEE Trans. Power Syst.
**2001**, 16, 301–306. [Google Scholar] [CrossRef] - Zhao, T.T.G.; Zhao, J.S.; Yang, D.W. Improved Dynamic Programming for Hydropower Reservoir Operation. J. Water Resour. Plan. Manag.
**2014**, 140, 365–374. [Google Scholar] [CrossRef] - Feng, Z.K.; Niu, W.J.; Cheng, C.T.; Wu, X.Y. Optimization of hydropower system operation by uniform dynamic programming for dimensionality reduction. Energy
**2017**, 134, 718–730. [Google Scholar] [CrossRef] - Hota, P.K.; Barisal, A.K.; Chakrabarti, R. An improved PSO technique for short-term optimal hydrothermal scheduling. Electr. Power Syst. Res.
**2009**, 79, 1047–1053. [Google Scholar] [CrossRef] - Yuan, Y.B.; Yuan, X.H. An improved PSO approach to short-term economic dispatch of cascaded hydropower plants. Kybernetes
**2010**, 39, 1359–1365. [Google Scholar] [CrossRef] - Bi, W.; Dandy, G.C.; Maier, H.R. Improved genetic algorithm optimization of water distribution system design by incorporating domain knowledge. Environ. Model Softw.
**2015**, 69, 370–381. [Google Scholar] [CrossRef] - Yazdi, J.; Moridi, A. Multi-Objective Differential Evolution for Design of Cascade Hydropower Reservoir Systems. Water Resour. Manag.
**2018**, 32, 4779–4791. [Google Scholar] [CrossRef] - Madani, K.; Lund, J.R. A Monte-Carlo game theoretic approach for Multi-Criteria Decision Making under uncertainty. Adv. Water Resour.
**2011**, 34, 607–616. [Google Scholar] [CrossRef] - Ji, C.M.; Jiang, Z.Q.; Sun, P.; Zhang, Y.K.; Wang, L. Research and application of multidimensional dynamic programming in cascade reservoirs based on multilayer nested structure. J. Water Resour. Plan. Manag.
**2015**, 141, 04014090. [Google Scholar] [CrossRef] - Mandal, K.K.; Chakraborty, N. Parameter study of differential evolution based optimal scheduling of hydrothermal systems. J. Hydro-Environ. Res.
**2013**, 7, 72–80. [Google Scholar] [CrossRef] - Li, X.; Li, T.J.; Wei, J.H.; Wang, G.Q.; Yeh, W.W.G. Hydro Unit Commitment via Mixed Integer Linear Programming: A Case Study of the Three Gorges Project, China. IEEE Trans. Power Syst.
**2014**, 29, 1232–1241. [Google Scholar] [CrossRef] - Conejo, A.J.; Arroyo, J.M.; Contreras, J.; Villamor, F.A. Self-scheduling of a hydro producer in a pool-based electricity market. IEEE Trans. Power Syst.
**2002**, 17, 1265–1271. [Google Scholar] [CrossRef] - Rodríguez, J.A.; Anjos, M.F.; Côté, P.; Desaulniers, G. MILP Formulations for Generator Maintenance Scheduling in Hydropower Systems. IEEE Trans. Power Syst.
**2018**, 33, 6171–6180. [Google Scholar] [CrossRef] - Babayev, D.A. Piece-wise linear approximation of functions of two variables. J. Heuristics
**1997**, 2, 313. [Google Scholar] [CrossRef] - Kang, C.X.; Chen, C.; Wang, J.W. An efficient linearization method for long-term operation of cascaded hydropower reservoirs. Water Resour. Manag.
**2018**, 32, 3391–3404. [Google Scholar] [CrossRef] - Shen, J.J.; Cheng, C.T.; Cheng, X.; Lund, J.R. Coordinated operations of large-scale UHVDC hydropower and conventional hydro energies about regional power grid. Energy
**2016**, 95, 433–446. [Google Scholar] [CrossRef] - Cai, Q.; Le, L. Renewable Electricity Pricing Mechanism Formation Mechanism Model Prediction. In Proceedings of the 3rd International Conference on Applied Engineering, Wuhan, China, 22–25 April 2016; pp. 1243–1248. [Google Scholar]
- Kang, C.X.; Guo, M.; Wang, J.W. Short-Term Hydrothermal Scheduling Using a Two-Stage Linear Programming with Special Ordered Sets Method. Water Resour. Manag.
**2017**, 31, 3329–3341. [Google Scholar] [CrossRef]

**Figure 1.**The Hongshui River cascade structure: Scale 1 is the scale of the map; Scale 2 is the scale of the river.

**Figure 3.**Linearization sketch of the hydropower output function. (

**a**) Discretization of the hydropower output function; (

**b**) weights of discretized values.

**Figure 4.**Overall solution process; SOS2 is a special ordered set of type two, T is the total number of periods, t is the period index, B is the total number of plants, and b is the plant index.

**Figure 5.**Identification of peak, flat, and valley periods. (

**a**) Dynamic clustering graph; (

**b**) division results of peak, flat, and valley periods.

**Figure 6.**The results of SPM and AS. (

**a**) Power output; (

**b**) water spillage and forebay water level; (

**c**) tailrace water level and water head.

**Figure 8.**Comparison results of the cascaded system of SPM and AS. (

**a**) Pingban water spillage and forebay water level; (

**b**) Pingban tailrace water level and water head; (

**c**) Bailongtan water spillage and forebay water level; (

**d**) Bailongtan tailrace water level and water head; (

**e**) Letan water spillage and forebay water level; (

**f**) Letan tailrace water level and water head; (

**g**) Qiaogong water spillage and forebay water level; (

**h**) Qiaogong tailrace water level and water head.

Items | Pingban | Dahua | Bailongtan | Letan | Qiaogong |
---|---|---|---|---|---|

Maximum forebay water level (m) | 440.00 | 155.00 | 130.00 | 112.00 | 84.00 |

Minimum forebay water level (m) | 437.50 | 153.00 | 127.00 | 111.00 | 82.00 |

Maximum storage (Mm^{3}) | 211.76 | 393 | 86.3 | 402 | 191 |

Minimum storage (Mm^{3}) | 184.42 | 356 | 73.7 | 356 | 164 |

Maximum generation flow (m^{3}/s) | 1320 | 3076 | 2580 | 3432 | 3680 |

Ecological flow (m^{3}/s) | 62 | 189 | 190 | 209 | 214 |

Maximum output of plant (MW) | 405 | 566 | 192 | 600 | 456 |

Minimum output of plant (MW) | 200 | 320 | 90 | 280 | 150 |

Constant delay time (h) | / | / | 2 | 5 | 2 |

Natural inflow (m^{3}/s) | / | / | 0 | 171 | 0 |

Items | Pingban | Dahua | Bailongtan | Letan | Qiaogong |
---|---|---|---|---|---|

Adjustable storage (Mm^{3}) | 27.34 | 37 | 12.6 | 46 | 27 |

Time (h) | 5.75 | 3.34 | 1.36 | 3.72 | 2.04 |

**Table 3.**Comparison results of Pingban on scheduling with the proposed method (SPM), actual scheduling (AS), and scheduling achieved only by solving the objective function (SAF); WSR = water spillage ratio.

Items | SPM | AS | SAF |
---|---|---|---|

Daily total power generation (10^{4} kWh) | 830.73 | 839.08 | 684.09 |

Peak period power generation (10^{4} kWh) | 464.09 | 454.50 | 464.09 |

Peak-shaving capacity (MW) | 39.81 | 0 | 160.08 |

Object value (MW) | 7064.21 | 7075.97 | 6998.02 |

Ratio of water spillage to water release (%) | 10.8 | 10.8 | 27.1 |

Average of WSRs (%) | 100 | / | / |

Items | Dahua | Bailongtan | Letan | Qiaogong | Cascade | |
---|---|---|---|---|---|---|

Daily total power generation (10^{4} kWh) | SPM | 1129.39 | 422.40 | 1082.13 | 850.75 | 3484.66 |

AS | 1183.60 | 422.40 | 1089.23 | 893.43 | 3588.66 | |

SAF | 1015.94 | 337.47 | 1030.02 | 731.76 | 3115.19 | |

Peak period power generation (10^{4} kWh) | SPM | 657.63 | 237.85 | 659.45 | 553.03 | 2107.97 |

AS | 641.12 | 228.80 | 590.00 | 483.94 | 1943.86 | |

SAF | 663.94 | 238.47 | 722.02 | 566.76 | 2191.19 | |

Peak-shaving capacity (MW) | SPM | 146.91 | 26.06 | 262.52 | 258.85 | 668.77 |

AS | 0 | 0 | 0 | 0 | 0 | |

SAF | 226.26 | 100.76 | 279.61 | 288.63 | 885.87 | |

Object value (MW) | SPM | / | / | / | / | 6892.28 |

AS | / | / | / | / | 7075.98 | |

SAF | / | / | / | / | 6672.58 | |

Ratio of water spillage to water release (%) | SPM | 25.0 | 37.1 | 19.6 | 13.8 | 23.7 |

AS | 25.0 | 37.1 | 19.6 | 13.8 | 23.7 | |

SAF | 35.4 | 50.8 | 27.3 | 31.8 | 31.8 | |

Average of WSRs | SPM | 55.8 | 0 | 51.4 | 100 | / |

AS | / | / | / | / | / | |

SAF | / | / | / | / | / |

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**MDPI and ACS Style**

Liao, S.; Zhang, Y.; Liu, B.; Liu, Z.; Fang, Z.; Li, S.
Short-Term Peak-Shaving Operation of Head-Sensitive Cascaded Hydropower Plants Based on Spillage Adjustment. *Water* **2020**, *12*, 3438.
https://doi.org/10.3390/w12123438

**AMA Style**

Liao S, Zhang Y, Liu B, Liu Z, Fang Z, Li S.
Short-Term Peak-Shaving Operation of Head-Sensitive Cascaded Hydropower Plants Based on Spillage Adjustment. *Water*. 2020; 12(12):3438.
https://doi.org/10.3390/w12123438

**Chicago/Turabian Style**

Liao, Shengli, Yan Zhang, Benxi Liu, Zhanwei Liu, Zhou Fang, and Shushan Li.
2020. "Short-Term Peak-Shaving Operation of Head-Sensitive Cascaded Hydropower Plants Based on Spillage Adjustment" *Water* 12, no. 12: 3438.
https://doi.org/10.3390/w12123438