# Simultaneous Sensor Placement and Pressure Reducing Valve Localization for Pressure Control of Water Distribution Systems

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## Abstract

**:**

## 1. Introduction

## 2. Pressure Sensor Placement

#### 2.1. Problem Description

#### 2.2. The K-Means++ Method to Determine the Regions

- Randomly select K points as starting centers of the clusters.
- Allocate the data points to the nearest clusters based on their distance from the center.
- The mean of each of the K clusters becomes the new center.
- Repeat from step 2 until the locations of the centers do not change.

- The number of clusters needs to be given a priori, which is a difficult task in practice.

#### 2.3. Determining the Number of Clusters K

#### 2.4. The Accuracy of Representation (AOR)

#### 2.4.1. Definition of AOR

#### 2.4.2. Improving the AOR with a Partition Matrix

## 3. Localization of PRVs

#### 3.1. Pressure Analysis on the Edges of the Regions

#### 3.2. Placement of the PRVs

- Since a PRV works with its water flow only in one direction, a pipe in which the water flow direction alters during the operation should not be selected for the valve placement. Otherwise, there will be no assurance to meet the pressure demand.
- For PRV placement, the downstream elevation should be considered to ensure the pressure demand at the downstream nodes. For example, if the main source of pressure difference is from the elevation difference, and if a downstream node is lower in elevation, its pressure will usually be greater than the upstream pressure. In this case, if the PRV is placed on this link due to the large pressure difference, the pressure at the downstream nodes can be lower than the pressure demand.For example, as shown in Figure 2, the elevations at nodes 1, 2, 3, 4 and 5 are 50 m, 20 m, 40 m, 40 m and 40 m, respectively. Node 2 is the downstream node of pipe 1 and the upstream node of pipes 2, 3 and 4. A PRV may be installed on pipe 1 and its setting of the valve is determined to reduce the external pressure at node 2 so that the pressure meets the lowest pressure requirement at node 2. Then, the head of node 2 will be lowered, and therefore, the minimum pressure requirement for nodes 3, 4 and 5 may not be met. Thus, a PRV should not be installed on pipe 1, in spite of its high pressure difference.
- Pipes directly connected to a water tank or a pump should not be selected as candidates for placing PRVs. This is due to the fact that the elevation generated by a water tank or a pump is the only energy source ensuring the consumer demands. Installing a valve there may degrade proper delivery of the water to some consumers.

#### 3.3. Determining the Setting Values for PRVs

- Partially opened (active mode): water flows through the valve and the downstream pressure is reduced to the setting value of the PRV, when the upstream pressure is above the setting value.
- Fully open (open mode): the PRV is entirely open and acts as if it is not present, when the upstream pressure is below the setting value.
- Fully closed (closed mode): the PRV closes completely and acts as a check valve, when the pressure on the downstream side exceeds that on the upstream side, or if reverse flow in the pipe is incipient.

## 4. Implementation of the Proposed Approach

## 5. Case Studies

#### 5.1. Case Study 1: Jilin Network

#### 5.2. Case Study 2: A Benchmark WDS

#### 5.3. Case Study 3: Sensor and PRV Localization for EXNET

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Jilin Network [42].

**Figure 5.**The pressure curves of the Jilin Network. (

**a**) The original system; (

**b**) with 1 PRV; (

**c**) with 2 PRVs; (

**d**) with 3 PRVs; (

**e**) with 4 PRVs; (

**f**) with 5 PRVs.

No. of PRVs | Total Pressure (m) | Min. Pressure (m) | Setting Value of PRVs | No. of PSs | AOR |
---|---|---|---|---|---|

0 | $2.4519\times {10}^{4}$ | 20.1063 | 6 | 93.04% | |

1 | $2.3037\times {10}^{4}$ | 20.0160 | 29.93 | 6 | 84.46% |

2 | $2.2976\times {10}^{4}$ | 20.0123 | 32.01; 27.83 | 6 | 82.72% |

3 | $2.2333\times {10}^{4}$ | 20.0489 | 35.65; 24.3; 32.91 | 7 | 80.67% |

4 | $2.2054\times {10}^{4}$ | 20.2887 | 35.32; 37.26; 28.43; 34.55 | 7 | 84.35% |

5 | $1.9999\times {10}^{4}$ | 20.2836 | 33.44; 28.06; 29.70; 38.7; 23.41 | 9 | 81.27% |

No. of PRVs | Link IDs [Current Study] | Link IDs [26] | Link IDs [25] |
---|---|---|---|

1 | 11 | 11 | 11 |

2 | 11,9 | 11,20 | 11,20 |

3 | 11,9,20 | 11,20,21 | 11,20,1 |

4 | 11,9,20,21 | 11,20,21,1 | 1,11,20,21 |

No. of PRVs | Total Pressure (m) |
---|---|

1 | $1.7608\times {10}^{4}$ |

2 | $1.7427\times {10}^{4}$ |

3 | $1.7271\times {10}^{4}$ |

4 | $1.5441\times {10}^{4}$ |

No. of PRVs | Link IDs [Current Study] | Link IDs [24] | Link IDs [26] |
---|---|---|---|

2 | 11,10 | 1,11 | 1,11 |

3 | 11,10,20 | 11,21,29 | 11,20,21 |

4 | 11,10,20,21 | 1,8,11,20 | 1,11,20,29 |

5 | 11,10,20,21,18 | 1,8,11,21,29 | 1,11,20,21,29 |

6 | 11,10,20,21,18,16 | 1,5,11,8,20,21 | 1,11,20,21,29,31 |

No. of PRVs | Total Pressure (m) | No. of PSs | AOR |
---|---|---|---|

0 | $2.1328\times {10}^{4}$ | 11 | 98.07% |

1 | $1.7851\times {10}^{4}$ | 11 | 81.27% |

2 | $1.7846\times {10}^{4}$ | 13 | 84.81% |

3 | $1.7725\times {10}^{4}$ | 11 | 70.36% |

4 | $1.7095\times {10}^{4}$ | 13 | 66.33% |

5 | $1.7087\times {10}^{4}$ | 13 | 59.83% |

6 | $1.6958\times {10}^{4}$ | 9 | 55.27% |

No. of PRVs | Total Pressure (m) | Min. Pressure (m) | Link IDs |
---|---|---|---|

1 | 3.4560$\times {10}^{6}$ | 25.2948 | 3026 |

2 | 3.4493$\times {10}^{6}$ | 25.1376 | 3026; 2490 |

3 | 2.8942$\times {10}^{6}$ | 8.0330 | 3026; 2490; 2341 |

4 | 2.7625$\times {10}^{6}$ | 8.0398 | 3026; 2490; 2341; 4908; |

5 | 2.7585$\times {10}^{6}$ | 8.2901 | 3026; 2490; 2341; 4908; 2714; |

6 | 2.7404$\times {10}^{6}$ | 8.1232 | 3026; 2490; 2341; 4908; 2714; 2512; |

7 | 2.7431$\times {10}^{6}$ | 8.2778 | 3026; 2490; 2341; 4908; 2714; 2512; 4854; |

8 | 2.7124$\times {10}^{6}$ | 8.1086 | 3026; 2490; 2341; 4908; 2714; 2512; 4854; 4898 |

Burst Scene | Without Burst | Place 1 | Place 2 | Place 3 | Place 4 | Place 5 |
---|---|---|---|---|---|---|

AOR | 80.63% | 79.89% | 80.51% | 80.49% | 80.49% | 79.94% |

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**MDPI and ACS Style**

Cao, H.; Hopfgarten, S.; Ostfeld, A.; Salomons, E.; Li, P.
Simultaneous Sensor Placement and Pressure Reducing Valve Localization for Pressure Control of Water Distribution Systems. *Water* **2019**, *11*, 1352.
https://doi.org/10.3390/w11071352

**AMA Style**

Cao H, Hopfgarten S, Ostfeld A, Salomons E, Li P.
Simultaneous Sensor Placement and Pressure Reducing Valve Localization for Pressure Control of Water Distribution Systems. *Water*. 2019; 11(7):1352.
https://doi.org/10.3390/w11071352

**Chicago/Turabian Style**

Cao, Hao, Siegbert Hopfgarten, Avi Ostfeld, Elad Salomons, and Pu Li.
2019. "Simultaneous Sensor Placement and Pressure Reducing Valve Localization for Pressure Control of Water Distribution Systems" *Water* 11, no. 7: 1352.
https://doi.org/10.3390/w11071352