# Energy Efficient Operation of Variable Speed Submersible Pumps: Simulation of a Ground Water Well Field

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^{2}

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## Abstract

**:**

## 1. Introduction

#### Optimization Using Genetic Algorithms

- Initialization (initial population): An initial population is created. This population is generated, in principle, randomly and can be of the desired size, from a couple of individuals to thousands.
- Cost evaluation (aptitude): Each member of the population is evaluated and the adjustment or aptitude for that individual is calculated. The adjustment value is calculated based on how well the individual are adjusted to the established requirements.
- Selection: This procedure is executed to constantly improve the population. The selection discards bad solutions in a way that keeps the best individuals in the population.
- Crossing: During crossing, new individuals are created by combining aspects of the individuals selected in the previous stage.
- Mutation: It is required to add some randomness to the genetics of the population; otherwise, every combination of solutions that could be created would be in the initial population, that is, it would be trapped in a local optimum.
- Iteration/convergence: Once there is a new generation, the process starts from step two until a stopping criterion is reached.

## 2. Materials and Methods

#### 2.1. Hydraulic Modeling of Groundwater Abstraction and Transport

^{2}), ρ is the density of the fluid (kg/m

^{3}), g is the gravitational constant (m/s

^{2}) and z is the elevation (m).

_{D}(mm).

_{i}), the relationships among flow (Q

_{i}), head (H

_{i}) and power (P

_{i}) at different pump rotational speed can be described by the affinity laws (Equation (4)–(6)).

_{1}and n

_{2}will be constant. An alternative relationship has been proposed by Sárbu and Borza [18].

_{P,i}is the specific energy demand needed for pumping and η

_{i}is the efficiency for a submersible well pump i.

#### 2.2. Optimization Through Genetic Algorithms Using Evolver

^{®}corporation (Ithaca, NY, USA) for Microsoft Excel

^{®}(Redmond, WA, USA) [13]. It allows addressing several optimization problems in a more efficient way in comparison to the default embedded optimization tools in Excel (e.g., Solver). It operates with Genetic Algorithms, and once it is installed in MS Excel, it provides a series of adaptation possibilities. The general idea is to model the problem with all the tools available in MS Excel, including MS Visual Basic for applications (VBA) and then to establish the optimization requirements (number of iterations, initial population, restrictions, objective function, etc.) through the embedded graphical interface provided by Evolver. This offers an easy-to-handle operational framework, which allows the implementation of a heuristic based optimization tool without requiring advanced programming skills.

#### 2.3. Case Study: Well Field Tegel-Ost

#### 2.4. Monitoring Campaign

## 3. Results and Discussion

#### 3.1. Simulation of Different Operational Scenarios Using Variable Speed Submersible Pumps in a Well Field

^{3}/h, represented by the black dot in the upper right of Figure 4. By gradually turning off the well pumps with the highest specific energy demand, the other points of the upper curve, representing 100% pump speed, are simulated. In all simulations, the last well in the well field remained active to ensure flow through the collection pipe.

^{3}/h, can either be realized by five active pumps operating 100% speed or by six pumps at 95% speed, as well as by seven pumps at 80% speed. For well field flows lower than the full capacity, operation of more pumps at reduced speed reduces the specific energy demand required to abstract groundwater and transport it to the water treatment plant, compared to operation of fewer pumps at full speed. For flows lower than 900 m

^{3}/h, a pump speed of approximately 75% seems to be optimal, since the simulation of pumps at 70% speed leads to higher specific energy demand.

#### 3.2. Analysis of Seasonal Variations in Groundwater Abstraction

^{3}/h, the median flow amounts to only 600 m

^{3}/h. Based on these data, a typical low load scenario was defined corresponding to a total volumetric flow of 430 m

^{3}/h. Accordingly, the moderate flow scenario corresponds to a total volumetric flow rate of 740 m

^{3}/h.

#### 3.3. Simulation of Typical Operational Scenarios and Optimal Pump Speed

^{3}/h and 740 m

^{3}/h, respectively. The specific energy demand in the reduced pump speed scenario is 0.08 kWh/m

^{3}in both the low flow and the moderate flow scenario. In both cases, the specific energy demand in the reduced pump speed scenario is significantly lower than in the scenarios with 100% pump speed. The pump speed settings determined by the optimization procedure are very close to the roughly estimated optimal pump speed of approximately 75% (cf. Section 3.1) and confirm these results.

^{3}/h to 56 m

^{3}/h, the head decreases from 22.7 mwc to 18.8 mwc. On the efficiency curve, the operating point is shifted closer to the optimum, resulting in an efficiency increase from 59.6% to 65.4%. In the moderate flow scenario, a very similar behavior can be observed. At 100% pump speed, the operating point is to the right of the last point of the efficiency curve, resulting in a non-optimal efficiency. In the reduced speed scenario, flow is reduced from 172 m

^{3}/h to 87 m

^{3}/h and the head from 25.9 mwc (meter of water column) to 20.2 mwc. The efficiency is shifted from 63.9% right to its optimum of 70.4%. This illustrates that, for low and moderate loads, the chosen pumps in the well field will operate out of their optimal range if operated at 100% speed. Instead, lower speed settings lead to optimal efficiency.

#### 3.4. Comparison of Simulation and Measurements

^{3}as compared to the simulated value of 0.10 kWh/m

^{3}. At reduced pump speed, the measured and simulated specific energy demand have the same value of 0.08 kWh/m

^{3}. For the low flow scenario, the lower energy demand at reduced pump speeds as compared to 100% pump speed corresponds to potential savings of 20%. In the moderate flow scenario, the measured mean specific energy demand of 0.13 kWh/m

^{3}at 100% pump speed is higher than the simulated value of 0.11 kWh/m

^{3}. At reduced pump speed, the measured mean specific energy demand is 0.09 kWh/m

^{3}, slightly higher than the simulated value of 0.08 kWh/m

^{3}. Based on the measured data, the saving potential is approximately 31%.

^{3}/h, which corresponds to a pump speed of approximately 74–88%. This is close to the optimal speed projected by model simulations. Energy savings are only achievable in systems characterized by a small static head and always depend on well field system and pump characteristics.

## 4. Conclusions

- The combination of hydraulic simulation models such as EPANET and genetic algorithm optimization can be used to determine the best efficiency scenario of variable speed pump operation in a groundwater well field.
- Simulation results show that, using speed control, significant energy savings can be achieved. For the simulated well field, the total specific energy demand required for pumping was 20–30% lower at reduced pump speed than at nominal pump speed.
- Depending on the well field, transport pipe system and pump characteristics, significant energy savings can be achieved, especially in systems characterized by low static head.
- The simulation results were compared to real world operation of variable speed pumps and the projected reduction in specific energy demand was confirmed.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flowchart and pseudo-code of Genetic Algorithms based on [16].

**Figure 2.**Schematic overview on well field simulation using EPANET, MS Excel and optimization using a genetic algorithm.

**Figure 4.**Simulated specific energy demand required to abstract ground water in a well field of 13 wells vs. total volumetric flow rate.

**Figure 5.**Cumulative frequency of the total volumetric flow in the well field Tegel-Ost (daily mean values).

**Figure 6.**(

**a**) Pump curve of Well Pump 1 in the low flow scenario; (

**b**) pump curve of Well Pump 2 in the moderate flow scenario; (

**c**) efficiency curve of Well Pump 1 in the low flow scenario; and (

**d**) efficiency curve of Well Pump 2 in the moderate flow scenario. Pump and efficiency curves in black lines represent nominal (100%) speed, grey lines represent 75% (low flow) and 73% speed (moderate flow). Simulated operating points are shown in red.

**Table 1.**Pump speed settings and simulation results for total well field flow and specific energy demand for low and moderate flow scenarios.

Low Flow Scenario | Moderate Flow Scenario | |||||||
---|---|---|---|---|---|---|---|---|

Nominal Speed | Variable Speed | Nominal Speed | Variable Speed | |||||

Pump | Pump Speed (rpm) | Pump Speed (%) | Pump Speed (rpm) | Pump Speed (%) | Pump Speed (rpm) | Pump Speed (%) | Pump Speed (rpm) | Pump Speed (%) |

1 | 3000 | 100 | 2250 | 75 | - | - | 2280 | 76 |

2 | 2160 | 72 | 3000 | 100 | 2190 | 73 | ||

3 | 2130 | 71 | 2190 | 73 | ||||

4 | 3000 | 100 | ||||||

5 | 2220 | 74 | ||||||

6 | 2130 | 71 | 2280 | 76 | ||||

7 | 2850 | 100 | ||||||

8 | 2220 | 74 | ||||||

9 | 2160 | 72 | 2220 | 74 | ||||

10 | 3000 | 100 | ||||||

11 | ||||||||

12 | 3000 | 100 | 2250 | 75 | ||||

13 | 2850 | 100 | 2052 | 72 | 2850 | 100 | 2109 | 74 |

Total well field flow (m^{3}/h) | 432 | 432 | 744 | 740 | ||||

Specific energy (kWh/m^{3}) | 0.10 | 0.08 | 0.11 | 0.08 |

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**MDPI and ACS Style**

Sperlich, A.; Pfeiffer, D.; Burgschweiger, J.; Campbell, E.; Beck, M.; Gnirss, R.; Ernst, M.
Energy Efficient Operation of Variable Speed Submersible Pumps: Simulation of a Ground Water Well Field. *Water* **2018**, *10*, 1255.
https://doi.org/10.3390/w10091255

**AMA Style**

Sperlich A, Pfeiffer D, Burgschweiger J, Campbell E, Beck M, Gnirss R, Ernst M.
Energy Efficient Operation of Variable Speed Submersible Pumps: Simulation of a Ground Water Well Field. *Water*. 2018; 10(9):1255.
https://doi.org/10.3390/w10091255

**Chicago/Turabian Style**

Sperlich, Alexander, Dino Pfeiffer, Jens Burgschweiger, Enrique Campbell, Marcus Beck, Regina Gnirss, and Mathias Ernst.
2018. "Energy Efficient Operation of Variable Speed Submersible Pumps: Simulation of a Ground Water Well Field" *Water* 10, no. 9: 1255.
https://doi.org/10.3390/w10091255