# Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Basis of the Model

#### 2.2. Discharge Optimization Model for a Single Pumping Station

- (1)
- Decision Variables

- (2)
- Constraints

- (3)
- Objective function

- (4)
- Optimization algorithm

#### 2.3. Head Optimization Model for Cascade Pumping Stations

## 3. Application and Results

#### 3.1. Study Area

^{3}/s. However, as the storage capacities of the channels and the discharges of the pumping stations are adjustable over a small range, there may be mismatches in the discharges for these cascade pumping stations. To be able to address this issue, VFDs are equipped with two pumping units at each pumping station. Under normal operating conditions, three pumps are running simultaneously at each pumping station, and one pump is used as a standby. However, it is difficult to control the discharge of the pump equipped with a VFD, and because of this, it is difficult to ensure an efficient operation of the water diversion project utilizing cascade pumping stations based on personal experience. Therefore, it is significant to obtain the optimal discharge distribution scheme of each pumping station equipped with a VFD in the Tuancheng Lake–Huairou Reservoir section. Table 1 provides the basic parameters of each pumping station. Note that one pumping unit is equipped with only one VFD, and the adjustable speed ratio is in the range of 0.7–1.

#### 3.2. Discharge Optimization for Single Pumping Station

^{3}/s and 0.01 m, respectively, and the discharge distribution under each condition is calculated based on the discharge optimization model for a single pumping station. The optimization and energy-saving potential of a single pumping station with the addition of VFDs are analyzed, and the influence of the number of VFDs is also discussed.

#### 3.2.1. Discharge Range

^{3}/s, and for the same reason, one VSBAP unit in combination with two BAP units can be used for the non-operable area corresponding to the discharge range of 13.5~15 m

^{3}/s. It is noted that when two VFDs are equipped, almost all the non-operable areas shown in Figure 3a become operable by combining VSBAP and BAP units. Thus, the use of three VFDs would lead to no further increase in the non-operable area. For the BAP unit equipped with a VFD, the discharge range of the unit can be expanded by changing the combination of blade angle and speed, thus increasing the number of operable conditions of the pumping station.

#### 3.2.2. Energy Consumption

^{3}/s). That is, the optimal efficiency can be obtained when a single VSBAP unit is used for water transfer. Over the discharge range of 6.5–11.5 m

^{3}/s, the optimal efficiency distribution is basically the same for the pumping station equipped with two and three VFDs. The efficiency of the pumping station is higher under the combination of two VSBAP units compared to that under the combination of one VSBAP unit and one BAP unit. Similarly, over the discharge range of 11.5–20 m

^{3}/s, the optimal efficiency is obtained with the use of three VSBAP units.

#### 3.3. Head Optimization Model for Cascade Pumping Stations

^{3}/s over the range of 10–20 m

^{3}/s, and the inlet water level of the first pumping station (Tundian) and the outlet water level of the last pumping station (Xitaishang) are taken as the design values. It is assumed that the number of VFDs is the same across pumping stations. The head distribution scheme under the above conditions is obtained based on the head optimization model.

^{3}/s and 17.9–20 m

^{3}/s, accounting for only 22% of the total conditions, and the efficiency is generally lower than 55%. When one VFD is equipped in each pumping station, the number of operable conditions is increased sharply by 3 times, and the efficiency is in the range of 50–60%; while when two VFDs are equipped in each pumping station, the number of operable conditions is further increased by 3.8 times, accounting for 85% of the total conditions, and the efficiency is generally above 60%. However, further increasing the number of VFDs in each pumping station does not increase the proportion of operable conditions, but the average efficiency is increased to 65.84%.

^{3}/s, and therefore the two curves are overlapped in this discharge range, as shown in Figure 5.

## 4. Discussion

- (1)
- The influence of VFD cost on the total investment

- (2)
- The influence of running time on the effect of VFDs

^{3}/s. As shown in Figure 7, there is no need to install three VFDs within 5 years, irrespective of the cost of the VFDs. As the cost of the VFDs increases, the optimal number of VFDs is changed from two to one, and, in some cases, there may even be no need to install a VFD. As the running time increases, the optimal number of VFDs under different VFD costs is closer to two. That is, the longer the running time, the more energy is saved with the use of two VFDs. To sum up, it is desirable to install two VFDs in the Tuancheng Lake–Huairou Reservoir section for the long-term operation of the cascade pumping stations in an economically profitable way.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Tuancheng Lake–Huairou Reservoir section of the Miyun Reservoir Regulation and Storage Project.

**Figure 3.**Optimal operation of pumping units under different conditions of discharge and head for a pumping station equipped with 0–3 VFDs, and it is represented by four subgraphs (

**a**–

**d**). V represents VSBAP, and P represents BAP.

**Figure 4.**Efficiency of the pumping station corresponding to the optimal operation of pumping units. Subfigures (

**a**), (

**b**), (

**c**) and (

**d**) respectively show the optimization results when the pumping station is equipped with different numbers of VFDs.

**Figure 5.**Optimal efficiency of each pumping station equipped with different numbers of VFDs corresponding to each operable condition.

**Figure 6.**Optimal total investment of the optimal scheme for each daily discharge under different VFD costs in 1 year.

**Table 1.**General information about the pumping stations in the Tuancheng Lake–Huairou Reservoir section.

Pumping Station Name | Design Head (m) | Rated Speed (r/min) | Pump Parameter | |
---|---|---|---|---|

Discharge Range (m^{3}/s) | Head Range (m) | |||

Tundian | 1.71 | 245 | 5.3–8.2 | 0.07–1.5 |

Qianliulin | 2.21 | 245 | 4.7–7.4 | 0.67–2.2 |

Niantou | 2.83 | 245 | 4.45–6.64 | 1.05–2.45 |

Xingshou | 2.58 | 245 | 4.67–6.86 | 0.18–2.21 |

Lishishan | 2.21 | 245 | 4.9–7.4 | 0.25–2.04 |

Xitaishang | 6.18 | 290 | 4.8–10.3 | 4.13–8.18 |

Number of VFDs | Discharge Range | Average Proportion of Operable Conditions | Relative Increment |
---|---|---|---|

0 | 4.45–19.92 m^{3}/s | 42.80% | - |

1 | 3.115–19.92 m^{3}/s | 80.14% | 87.24% |

2 | 3.115–19.92 m^{3}/s | 98.35% | 129.8% |

3 | 3.115–19.92 m^{3}/s | 98.46% | 130% |

Number of VFDs | Efficiency | Average Efficiency | Average Absolute Increase | Average Relative Increase |
---|---|---|---|---|

0 | 23.91–63.56% | 45.16% | - | - |

1 | 27.25–65.1% | 52.25% | 8.75% | 19.38% |

2 | 32.03–65.1% | 57.69% | 12.94% | 28.65% |

3 | 43.33–65.1% | 61.09% | 15.86% | 35.12% |

Operating Conditions | Number of VFDs | Discharge (m^{3}/s) | Speed Ratio | Blade Angle (°) | Pumping Station Efficiency (%) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1# | 2# | 3# | 1# | 2# | 3# | 1# | 2# | 3# | |||

Discharge = 6 m^{3}/s; head = 1.45 m | 0 | 6 | 1 | −3.46 | 33.86 | ||||||

1 | 6 | 0.84 | 2 | 57.7 | |||||||

2 | 6 | 0.84 | 2 | 57.7 | |||||||

3 | 6 | 0.84 | 2 | 57.7 | |||||||

Discharge = 10.1 m^{3}/s; head = 2.41 m | 0 | 5.05 | 5.05 | 1 | 1 | −3.92 | −3.92 | 50.21 | |||

1 | 3.46 | 6.64 | 0.81 | 1 | −2.71 | 1.19 | 60.58 | ||||

2 | 5.05 | 5.05 | 0.86 | 0.86 | 1.21 | 1.21 | 63.35 | ||||

3 | 5.05 | 5.05 | 0.86 | 0.86 | 1.21 | 1.21 | 63.35 | ||||

Discharge = 16 m^{3}/s, head = 2.05 m | 0 | 5.33 | 5.33 | 5.33 | 1 | 1 | 1 | −3.93 | −3.93 | −3.93 | 44.39 |

1 | 3.11 | 6.44 | 6.44 | 0.74 | 1 | 1 | −2.9 | −0.43 | −0.43 | 54.4 | |

2 | 4.68 | 4.68 | 6.64 | 0.8 | 0.8 | 1 | 1.22 | 1.22 | 0.2 | 59.89 | |

3 | 5.33 | 5.33 | 5.33 | 0.83 | 0.83 | 0.83 | 2 | 2 | 2 | 65.09 |

Number of VFDs | Number of Conditions in which the Head Can Be Distributed | Average Efficiency | Absolute Efficiency Gain |
---|---|---|---|

0 | 22 | 50.37% | - |

1 | 68 | 55.57% | 7.47% |

2 | 85 | 61.52% | 12.04% |

3 | 85 | 65.84% | 15.09% |

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**MDPI and ACS Style**

Du, M.; Zhang, Z.; Chen, Y.; Qu, X.; Yan, P.; Wang, H.
Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project. *Water* **2023**, *15*, 3571.
https://doi.org/10.3390/w15203571

**AMA Style**

Du M, Zhang Z, Chen Y, Qu X, Yan P, Wang H.
Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project. *Water*. 2023; 15(20):3571.
https://doi.org/10.3390/w15203571

**Chicago/Turabian Style**

Du, Mengying, Zhao Zhang, Yichao Chen, Xieyu Qu, Peiru Yan, and Hao Wang.
2023. "Economic Operation of Variable Speed and Blade Angle-Adjustable Pumping Stations of an Open-Channel Water Transfer Project" *Water* 15, no. 20: 3571.
https://doi.org/10.3390/w15203571