# Decision Support for the Design and Operation of Variable Speed Pumps in Water Supply Systems

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## Abstract

**:**

## 1. Introduction

## 2. Model

## 3. Evaluation of Operation States

## 4. Speed Control

## 5. Optimisation Process

#### 5.1. Operation with Finite Number of Speed Control Options

#### 5.2. Operation on Single Pumps with Variable Speed Control

#### 5.3. Operation on Pumps Running in Parallel with Variable Speed Control

## 6. Decision Support Process

## 7. Examples

#### 7.1. Decision Support for Pump Operation

#### 7.2. Decision Support for the Design of the Water Supply System

## 8. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Branching for the pump operation $(n=2)$ in the second time step after pump ${p}_{1}$ has been operated in the first time step. The colors red, blue and no color represent pumps ${p}_{1}$ and ${p}_{2}$ and no pump.

**Figure 2.**Branching for the pump operation $(n=2)$ with two speed control options ${v}_{1}$ and ${v}_{2}$. The colors red, blue and no color represent pumps ${p}_{1}$ and ${p}_{2}$ and no pump. Faded nodes represent duplicates.

**Figure 3.**The characteristic curve in (

**a**) and the efficiency curve in (

**b**) are both scaled down from speed $v=1$ to speed $v=0.7$.

**Figure 4.**Solution tree traversal with jumps: After choosing to operate pump ${p}_{1}$ at speed ${v}_{1}$ at operating time step ${s}_{i}$, the operation is continued until the operation is no longer feasible at step ${s}_{j+1},1\le i<j<m$, i.e., the storage container overflows, or the intermediate solution can be compared to previously computed solutions.

**Figure 5.**Variable speed optimization comparison for the pump operation $(n=2,m=4)$.

**On the left hand side**, each schedule $s\in S$ is optimized with respect to at most $n\xb7m=8$ variables for speed $v\in V$.

**On the right hand side**, optimization is performed at each colored node with respect to, at most, $n=2$ variables. In both cases, the same number of optimization problems has to be solved (255), but, the problems to solve are simpler on the right hand side (two instead of eight variables). Red, blue and no color represent pumps ${p}_{1}$ and ${p}_{2}$ and no pump, respectively.

**Figure 6.**Comparison to speed control. Red solutions operate pumps with a nominal speed. Green solutions operate pumps at speed of 0.9.

**Figure 8.**Decision support system for pump operation: The software presents the best solutions concerning the specific energy (blue circle) and number of switches (red circle). Inferior solutions are filtered out.

**Figure 9.**Pump schedule with pumps running at a nominal speed (upper panel) compared to the pump schedule resulting from speed optimization (second panel). In the lower panel, the optimized speeds of the pumps in the second panel are shown.

Operation at Nominal Speed | Operation at Optimized Speed | |
---|---|---|

specific energy ($\mathrm{kWh}/{\mathrm{m}}^{3})$ | 0.24855 | 0.21525 (86.6%) |

total energy (kWh) | 4.471 | 3.872 (86.6%) |

Control Simulation | Cont. Speed Optimization | Pump One Fixed at Speed 0.85 | Discrete Speed Optimization for a New Pump | |
---|---|---|---|---|

specific energy ($\mathrm{kWh}/{\mathrm{m}}^{3})$ | 0.24453 | 0.22325 (91.3%) | 0.22393 (91.6%) | 0.19963 (81.6%) |

total energy (kWh) | 1.659.387 | 1.513.923 (91.2%) | 1.518.704 (91.5%) | 1.354.214 (81.6%) |

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nowak, D.; Krieg, H.; Bortz, M.; Geil, C.; Knapp, A.; Roclawski, H.; Böhle, M.
Decision Support for the Design and Operation of Variable Speed Pumps in Water Supply Systems. *Water* **2018**, *10*, 734.
https://doi.org/10.3390/w10060734

**AMA Style**

Nowak D, Krieg H, Bortz M, Geil C, Knapp A, Roclawski H, Böhle M.
Decision Support for the Design and Operation of Variable Speed Pumps in Water Supply Systems. *Water*. 2018; 10(6):734.
https://doi.org/10.3390/w10060734

**Chicago/Turabian Style**

Nowak, Dimitri, Helene Krieg, Michael Bortz, Christian Geil, Axel Knapp, Harald Roclawski, and Martin Böhle.
2018. "Decision Support for the Design and Operation of Variable Speed Pumps in Water Supply Systems" *Water* 10, no. 6: 734.
https://doi.org/10.3390/w10060734