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In the Apulian-35 network, six independent optimizations were performed to obtain the optimal design and operation of different operational robustness levels. Pareto optimal solutions are plotted in Figure 5. As expected, the total cost increased as the required daily maximum pressure difference decreased (i.e., required operational robustness level increased). A sharp increase in the total cost was observed when the maximum pressure difference was less than 10 m (14.2 psi). The difference between the maximum and minimum pressures was about 25 m (35.5 psi) for the solution that did not consider robustness. Interestingly, only the PCC increased in the Apulian-35 network, while the POCs of the solutions stayed constant (Figure 5 and Table 3). Therefore, the proportion of the POC to the total cost decreased from 71% for the least-cost solution to 53% for the most robust solution, while that of the PCC increased from 29 to 47%. The POCs were around 4.2 million USD regardless of whether or not robustness was considered. However, the PCC of the most robust solution were about 2 million USD higher than the investment required by the least-cost solution (Table 3).
Figure 5

Total cost and daily maximum pressure difference of Pareto optimal solutions for pump optimization of the Apulian-35 network.

Figure 5

Total cost and daily maximum pressure difference of Pareto optimal solutions for pump optimization of the Apulian-35 network.

Table 3

Austin network's pump design and scheduling solutions with the original tank capacity (tank volume = 3,779 tons)

Daily maximum pressure difference (m)Pump capacity (kW)Number of pumpsPOC (%)PCC (%)Total cost (USD)
24.3 75 4,200,470 (71) 1,756,790 (29) 5,957,260 
10.0 55 4,136,083 (67) 2,061,125 (33) 6,197,208 
9.0 45 4,149,892 (60) 2,719,809 (40) 6,869,701 
8.0 45 4,291,177 (61) 2,719,808 (39) 7,010,985 
7.0 45 4,240,651 (55) 3,442,135 (45) 7,682,786 
6.6 45 4,342,599 (53) 3,779,396 (47) 8,121,995 
Daily maximum pressure difference (m)Pump capacity (kW)Number of pumpsPOC (%)PCC (%)Total cost (USD)
24.3 75 4,200,470 (71) 1,756,790 (29) 5,957,260 
10.0 55 4,136,083 (67) 2,061,125 (33) 6,197,208 
9.0 45 4,149,892 (60) 2,719,809 (40) 6,869,701 
8.0 45 4,291,177 (61) 2,719,808 (39) 7,010,985 
7.0 45 4,240,651 (55) 3,442,135 (45) 7,682,786 
6.6 45 4,342,599 (53) 3,779,396 (47) 8,121,995 
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