# Combining Statistical Clustering with Hydraulic Modeling for Resilient Reduction of Water Losses in Water Distribution Networks: Large Scale Application Study in the City of Patras in Western Greece

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data and Study Area

^{2}, which corresponds to the entire city center and the most important part of the urban fabric of Patras, and serve approximately 58,000 consumers (based on data from the Hellenic Statistical Authority and the Municipality of Patras), with more than 44,000 active hydrometers (see Table 1). An important point regarding the four PMAs is that they share similar characteristics regarding population and building densities, land uses (which are mostly commercial and residential), and topography, as they lie along the coastline of the gulf of Patras.

## 3. Methodology

#### 3.1. Real Losses (RL, Leakages) Allocation

_{i}is the simulated total head at node i = 1, …, n (i.e., the sum of the nodal elevation and the pressure head), and h

_{i}

^{*}is the minimum threshold head at node i (i.e., the sum of the nodal elevation and the minimum required pressure head). The hydraulic simulation is repeated until the desired water losses converge.

#### 3.2. Minimum Night Flow (Bottom-Up) Approach

_{r}, see Equation (2)) corresponds to the ratio of the surplus of the available power delivered to the consumers to the maximum power that can be delivered by the designed network under the current topology:

_{i}

^{*}is the demand (sum of user’s consumption, apparent losses, and real losses) at node i, and Q

_{r}and H

_{r}are the total flows (i.e., including users’ consumption, apparent losses, and real losses) and heads, respectively, at the inlets r = 1, …, R of the study area (i.e., PMA). Although Todini’s index has been applied by many researchers to a number of water distribution systems (see [50,95,96,97,98,99,100,101]), some authors proposed different variants (see [87,93,102,103]) primarily due to the fact that, according to Equation (2), real losses contribute positively to the resilience of the network [93].

_{r,s}(see Equation (3)) of the original resilience index in Equation (2), which accounts for the leakages and nodal heads in pressure-driven and mixed pressure-demand ways, respectively, and apply it using the iterative procedure described in Section 3.1:

_{r}and H

_{r}are defined identically to Equation (2), corresponding to the total flows (i.e., including users’ consumption, apparent losses, and real losses) and heads, respectively, at the inlets r = 1, …, R of the study area (i.e., PMA), and q

_{i}denotes the sum of the users’ consumption and apparent losses at node i (i.e., contrary to q

_{i}

^{*}in Equation (2), q

_{i}in Equation (3) does not include real losses or leakages). Apparent losses are introduced by unauthorized consumption, illegal connections on the main WDN, metering errors at the inlets of district metered areas or pressure management areas, and incorrect estimates of billed users’ consumptions.

#### 3.3. Hierarchical Clustering Approach Based on Ward’s Method

#### 3.4. Selection of the proper clustering solution

## 4. Results

_{r}), applied pressure (P

_{r}), and hourly maximum water consumption (Q

_{r}), for each of the four PMAs studied. The hourly maximum water consumption (Q

_{r}) has been obtained using the flow-pressure time series at the PMA inlets, during the eight-month-long high consumption period of the year from 1 March to 31 October 2019. During the partitioning phase, particular care was taken when selecting the inlet pressures applied to each cluster, so that water supply disruptions at critical points of the network induced by low-pressure heads were avoided, as well as possible pipeline failures induced by high pressures. This was done by connecting the inlet of each delineated cluster to a main distribution pipe and setting its inlet pressure equal to the nodal pressure head calculated for the original PMA configuration (i.e., prior to partitioning).

_{i}

^{*}= 30 m; see Equations (2) and (3)) set by the competent Authority (i.e., DEYAP) for the city center of Patras.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Map indicating the locations of the four largest PMAs of the city of Patras in western Greece. Numbers correspond to the entries in Table 1.

**Figure 3.**Partitioning of PMA “Kentro” into two clusters based on (

**a**) nodal altitudes, and (

**b**) simulated pressures.

**Figure 4.**Clustering of original PMAs based on nodal altitudes: (

**a**) Boud (three clusters), (

**b**) Kentro (two clusters), (

**c**) Panachaiki (three clusters), and (

**d**) Prosfygika (three clusters). PMA locations are illustrated in Figure 1.

**Figure 5.**Three-dimensional plots of the location and simulated pressure heads of the original (i.e., one cluster; left column), and final network configurations (right column) of the four PMAs: (

**a**,

**b**) Boud; (

**c**,

**d**) Kentro; (

**e**,

**f**) Panachaiki, and (

**g**,

**h**) Prosfygika. Ground surface is shown in grey, while arrows indicate regions with a significant decrease of the pressure heads relative to the original network configuration (left column). PMA locations are illustrated in Figure 1.

**Table 1.**Name, total area, length of the pipeline grid, population, and number of authorized active hydrometers of the four largest pressure management areas (PMAs) of the city of Patras. Numbers indicate the locations of PMAs in Figure 1.

PMA Number and Name | Area (km^{2}) | Pipeline Length (km) | Population (cap.) | Number of Active Hydrometers |
---|---|---|---|---|

(1) Boud | 0.953 | 44,954 | 15,362 | 10,586 |

(2) Kentro | 1.207 | 62,174 | 13,992 | 16,454 |

(3) Panachaiki | 1.184 | 51,703 | 18,003 | 11,983 |

(4) Prosfygika | 0.802 | 43,246 | 10,657 | 5206 |

**Table 2.**Allocation of the system input volume (SIV) into BAC (billed authorized consumption), UAC (unbilled authorized consumption), AL (apparent losses), and RL (real losses) for the four largest pressure management areas (PMAs) of the city of Patras, for the eight-month long high consumption period from 1 March 2019 to 31 October 2019. Numbers indicate the locations of PMAs in Figure 1.

PMA Number and Name | SIV (m^{3}/d) | BAC (%) | UAC (%) | AL (%) | RL (%) |
---|---|---|---|---|---|

(1) Boud | 3456 | 44.36 | 10.00 | 4.44 | 41.20 |

(2) Kentro | 9216 | 39.23 | 10.00 | 3.92 | 46.85 |

(3) Panachaiki | 6912 | 54.87 | 10.00 | 5.49 | 29.64 |

(4) Prosfygika | 4032 | 28.27 | 10.00 | 2.83 | 58.90 |

**Table 3.**Inlet point elevation (z

_{r}), applied pressure (P

_{r}), and hourly maximum water consumption (Q

_{r}) for each of the four PMAs studied. The corresponding Q

_{r}estimates have been obtained using the available flow-pressure time series at the PMA inlets, during the eight-month-long high consumption period of the year from 1 March 2019 to 31 October 2019. Numbers indicate the locations of PMAs in Figure 1.

PMA Number and Name | z_{r} (m) | P_{r} (m) | Q_{r} (l/s) |
---|---|---|---|

(1) Boud | 24.32 | 30.00 | 60.00 |

(2) Kentro | 21.54 | 44.00 | 160.00 |

(3) Panachaiki | 39.85 | 68.90 | 120.00 |

(4) Prosfygika | 40.90 | 40.00 | 70.00 |

**Table 4.**Total number of clusters (one cluster corresponds to the original PMA configuration prior to partitioning), calculated flow rates of real losses (RL), and resilience index estimates for the four PMAs of the WDN of the city of Patras. Values in square brackets indicate percentage reduction relative to the original PMA configuration. Numbers indicate PMA locations in Figure 1.

PMA Number and Name | Number of Clusters | RL (l/s) [% Reduction] | I_{r,s}[% Reduction] |
---|---|---|---|

(1) Boud | 1 (original PMA) | 24.720 [0.00] | 0.293 [0.00] |

2 | 20.573 [−16.78] | 0.271 [−7.51] | |

3 | 17.645 [−28.62] | 0.223 [−23.89] | |

4 | 17.365 [−29.75] | 0.202 [−31.06] | |

(2) Kentro | 1 (original PMA) | 74.960 [0.00] | 0.303 [0.00] |

2 | 64.668 [−13.73] | 0.262 [−13.53] | |

3 | 64.445 [−14.03] | 0.181 [−40.26] | |

4 | 63.986 [−14,64] | 0.170 [−43.99] | |

(3) Panachaiki | 1 (original PMA) | 35.568 [0.00] | 0.565 [0.00] |

2 | 31.811 [−10.56] | 0.505 [−10.62] | |

3 | 28.721 [−19.25] | 0.469 [−16.99] | |

4 | 28.493 [−19.89] | 0.440 [−22.12] | |

(4) Prosfygika | 1 (original PMA) | 41.230 [0.00] | 0.225 [0.00] |

2 | 28.651 [−30.51] | 0.142 [−36.66] | |

3 | 24.367 [−40.90] | 0.121 [−46.10] | |

4 | 23.924 [−41.97] | 0.120 [−46.55] |

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## Share and Cite

**MDPI and ACS Style**

Serafeim, A.V.; Kokosalakis, G.; Deidda, R.; Fourniotis, N.T.; Langousis, A. Combining Statistical Clustering with Hydraulic Modeling for Resilient Reduction of Water Losses in Water Distribution Networks: Large Scale Application Study in the City of Patras in Western Greece. *Water* **2022**, *14*, 3493.
https://doi.org/10.3390/w14213493

**AMA Style**

Serafeim AV, Kokosalakis G, Deidda R, Fourniotis NT, Langousis A. Combining Statistical Clustering with Hydraulic Modeling for Resilient Reduction of Water Losses in Water Distribution Networks: Large Scale Application Study in the City of Patras in Western Greece. *Water*. 2022; 14(21):3493.
https://doi.org/10.3390/w14213493

**Chicago/Turabian Style**

Serafeim, Athanasios V., George Kokosalakis, Roberto Deidda, Nikolaos Th. Fourniotis, and Andreas Langousis. 2022. "Combining Statistical Clustering with Hydraulic Modeling for Resilient Reduction of Water Losses in Water Distribution Networks: Large Scale Application Study in the City of Patras in Western Greece" *Water* 14, no. 21: 3493.
https://doi.org/10.3390/w14213493