Service Pressure and Energy Consumption Mitigation-Oriented Partitioning of Closed Water Distribution Networks
Abstract
:1. Introduction
2. Case Study
3. Materials and Methods
- Partitioning (clustering and dividing) of the WDN;
- Optimization of the hourly settings of the pumping stations present in the WDN.
3.1. WDN Partitioning
3.1.1. Clustering
- Construction of a configuration of the first attempt with the desired number M of clusters;
- Refinement of the configuration by means of an algorithm inspired by simulated annealing to search for a configuration with a better value of Q, the number M of clusters being the same.
3.1.2. Dividing
3.2. The Optimization of Pump Settings
4. Results
4.1. Results of WDN Partitioning
4.1.1. Results of Clustering
4.1.2. Results of Dividing
4.2. Results of the Optimization of Pump Settings
5. Discussion
- The modelled service pressure remained above the threshold of 20 m for full demand satisfaction.
- The rate of leakage in the real WDN is currently small.
- The number of nodes in the WDN layout is high, meaning that demand is always modelled close to its associated user along the pipe.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Station ID | Station Name | Number of Pumps | Qmax (L/s) | Hmax (m) |
---|---|---|---|---|
1 | Villalunga | 1 | 50 | 80 |
2 | Nord | 4 | 144 | 47 |
3 | Libertà | 1 | 38 | 85 |
4 | Borgo Ticino | 1 | 38 | 85 |
5 | Mirabello | 1 | 50 | 80 |
6 | Est | 4 | 144 | 47 |
Solution | Weights | nb (-) | H1 (-) | H2 (-) | H3 (-) |
---|---|---|---|---|---|
1 | α1 = 0.1; α2 = 0.0; α3 = 1.9 | 53 | 0.0112 | 0.2351 | 0.0315 |
2 | α1 = 0.5; α2 = 0.0; α3 = 1.5 | 50 | 0.0105 | 0.1668 | 0.0468 |
3 | α1 = 1.0; α2 = 0.0; α3 = 1.0 | 46 | 0.0097 | 0.1643 | 0.0478 |
4 | α1 = 1.5; α2 = 0.0; α3 = 0.5 | 42 | 0.0089 | 0.1642 | 0.0494 |
Time (h) | Setting in Station 1 | Setting in Station 2 | Setting in Station 3 | Setting in Station 4 | Setting in Station 5 | Setting in Station 6 |
---|---|---|---|---|---|---|
0–1 | 0.648 | 0.607 | 0.754 | 0.770 | 0.717 | 0.571 |
1–2 | 0.646 | 0.607 | 0.760 | 0.776 | 0.708 | 0.569 |
2–3 | 0.648 | 0.606 | 0.756 | 0.774 | 0.715 | 0.569 |
3–4 | 0.648 | 0.606 | 0.756 | 0.774 | 0.715 | 0.569 |
4–5 | 0.646 | 0.615 | 0.750 | 0.764 | 0.780 | 0.569 |
5–6 | 0.707 | 0.729 | 0.678 | 0.710 | 0.680 | 0.728 |
6–7 | 0.880 | 0.893 | 0.943 | 0.665 | 0.643 | 0.909 |
7–8 | 0.884 | 0.939 | 0.890 | 0.790 | 0.673 | 0.943 |
8–9 | 0.880 | 0.893 | 0.943 | 0.665 | 0.643 | 0.909 |
9–10 | 0.769 | 0.774 | 0.786 | 0.656 | 0.740 | 0.798 |
10–11 | 0.769 | 0.774 | 0.786 | 0.656 | 0.740 | 0.798 |
11–12 | 0.777 | 0.795 | 0.806 | 0.725 | 0.888 | 0.831 |
12–13 | 0.717 | 0.751 | 0.738 | 0.663 | 0.725 | 0.765 |
13–14 | 0.707 | 0.729 | 0.678 | 0.710 | 0.680 | 0.728 |
14–15 | 0.672 | 0.667 | 0.702 | 0.702 | 0.663 | 0.631 |
15–16 | 0.699 | 0.686 | 0.761 | 0.779 | 0.658 | 0.648 |
16–17 | 0.714 | 0.707 | 0.646 | 0.721 | 0.671 | 0.703 |
17–18 | 0.717 | 0.751 | 0.738 | 0.663 | 0.725 | 0.765 |
18–19 | 0.694 | 0.716 | 0.729 | 0.717 | 0.708 | 0.706 |
19–20 | 0.653 | 0.659 | 0.734 | 0.734 | 0.638 | 0.610 |
20–21 | 0.652 | 0.647 | 0.730 | 0.740 | 0.702 | 0.597 |
21–22 | 0.636 | 0.619 | 0.748 | 0.756 | 0.791 | 0.572 |
22–23 | 0.640 | 0.613 | 0.758 | 0.769 | 0.736 | 0.571 |
23–24 | 0.649 | 0.605 | 0.730 | 0.733 | 0.719 | 0.571 |
Time (h) | Setting in Station 1 | Setting in Station 2 | Setting in Station 3 | Setting in Station 4 | Setting in Station 5 | Setting in Station 6 |
---|---|---|---|---|---|---|
0–1 | 0.648 | 0.606 | 0.756 | 0.769 | 0.716 | 0.571 |
1–2 | 0.658 | 0.604 | 0.760 | 0.778 | 0.713 | 0.569 |
2–3 | 0.649 | 0.605 | 0.760 | 0.776 | 0.721 | 0.569 |
3–4 | 0.649 | 0.605 | 0.760 | 0.776 | 0.721 | 0.569 |
4–5 | 0.642 | 0.615 | 0.750 | 0.758 | 0.773 | 0.571 |
5–6 | 0.829 | 0.730 | 0.765 | 0.763 | 0.763 | 0.729 |
6–7 | 0.873 | 0.890 | 0.886 | 0.860 | 0.786 | 0.979 |
7–8 | 0.944 | 0.938 | 0.976 | 0.985 | 0.744 | 0.999 |
8–9 | 0.873 | 0.890 | 0.886 | 0.860 | 0.786 | 0.979 |
9–10 | 0.766 | 0.792 | 0.832 | 0.811 | 0.639 | 0.820 |
10–11 | 0.766 | 0.792 | 0.832 | 0.811 | 0.639 | 0.820 |
11–12 | 0.754 | 0.823 | 0.697 | 0.723 | 0.649 | 0.922 |
12–13 | 0.735 | 0.763 | 0.839 | 0.745 | 0.659 | 0.776 |
13–14 | 0.829 | 0.730 | 0.765 | 0.763 | 0.763 | 0.729 |
14–15 | 0.662 | 0.667 | 0.705 | 0.715 | 0.765 | 0.607 |
15–16 | 0.670 | 0.692 | 0.739 | 0.803 | 0.665 | 0.623 |
16–17 | 0.742 | 0.713 | 0.824 | 0.849 | 0.683 | 0.648 |
17–18 | 0.735 | 0.763 | 0.839 | 0.745 | 0.659 | 0.776 |
18–19 | 0.696 | 0.727 | 0.815 | 0.890 | 0.639 | 0.669 |
19–20 | 0.677 | 0.656 | 0.804 | 0.798 | 0.815 | 0.592 |
20–21 | 0.674 | 0.651 | 0.732 | 0.740 | 0.715 | 0.601 |
21–22 | 0.637 | 0.623 | 0.768 | 0.764 | 0.791 | 0.572 |
22–23 | 0.645 | 0.612 | 0.758 | 0.764 | 0.742 | 0.571 |
23–24 | 0.648 | 0.606 | 0.756 | 0.769 | 0.716 | 0.571 |
Station | Benchmark | Solution 3 | Solution 4 |
---|---|---|---|
Station 1 | 29.62 | 11.40 | 12.10 |
Station 2 | 138.95 | 66.17 | 67.29 |
Station 3 | 19.71 | 9.00 | 9.92 |
Station 4 | 19.25 | 7.49 | 9.84 |
Station 5 | 30.22 | 13.45 | 12.24 |
Station 6 | 145.64 | 67.62 | 71.69 |
Total | 383.40 | 175.13 | 183.08 |
Results | Solution 3 | Solution 4 | Solution Based on Clustering [27] |
---|---|---|---|
hmean (m) | 28.88 | 30.09 | 30.83 |
Total Energy (KW) | 175.13 | 183.08 | 213.21 |
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Creaco, E.; Giudicianni, C.; Tosco, A. Service Pressure and Energy Consumption Mitigation-Oriented Partitioning of Closed Water Distribution Networks. Water 2023, 15, 3218. https://doi.org/10.3390/w15183218
Creaco E, Giudicianni C, Tosco A. Service Pressure and Energy Consumption Mitigation-Oriented Partitioning of Closed Water Distribution Networks. Water. 2023; 15(18):3218. https://doi.org/10.3390/w15183218
Chicago/Turabian StyleCreaco, Enrico, Carlo Giudicianni, and Alessandro Tosco. 2023. "Service Pressure and Energy Consumption Mitigation-Oriented Partitioning of Closed Water Distribution Networks" Water 15, no. 18: 3218. https://doi.org/10.3390/w15183218