Energy Cost Optimization for Water Distribution Networks Using Demand Pattern and Storage Facilities

: Energy consumption in water supply systems is closely connected with the demand for water, since energy is mostly consumed in the process of water transport and distribution, in addition to the energy that might be needed to pump the water from its sources. Existing studies have been carried out on optimizing the pump operations to attain appropriate pressure and on controlling the water level of storage facilities to transfer the required demand and to reduce the energy cost. The idea is to reduce the amount of the water being supplied when the unit price of energy is high and to increase the supply when the unit price is low. To realize this scheme, the energy consumption of water supply systems, the amount of water transfer, the organization of energy cost structure, the utilization of water tanks, and so forth are investigated and analyzed to establish a model of optimized water demand management based on the application of water tanks in supplied areas. In this study, with the assumption that energy cost can be reduced by the redistribution of a demand pattern, a numerical analysis is conducted on transferring water demand at storage facilities from the peak energy cost hours to the lower energy cost hours. This study was applied at the Bupyeong 2 reservoir catchment, Incheon, Korea.


Introduction
These days, it is always necessary to make big efforts to save energy costs. In addition, energy savings in South Korea are always an important matter. Nationwide, South Koreans were reminded of this issue after suffering traumatic damage from a major blackout throughout the country in 2011. In addition, energy issues relating to climate change and emission reductions are currently treated as part of the national competitiveness strategy (IEA, Paris, France, 2012) [1].
In terms of water distribution networks (WDNs), water saving strategies (e.g., water demand control and water efficient design) are generally implemented as part of energy saving efforts by water saving company projects, water saving utilities, and different campaigns. These programs are favorably progressing since water use is naturally connected with energy consumption.
Previous studies on demand management have established various data sets on water consumption patterns for different purposes of water use. Furthermore, several strategies have emerged and have been tested in previous studies [2][3][4][5][6][7]. In addition, Kim et al. (2007) and Kanakoudis and Tsitsifli (2013) monitored water demand patterns and their side effects in terms of hours in without (or partially) using the main water supply [9]. Furthermore, WDNs with different WTPs might have distinct differences, and each WDN has its own storage facilities. Therefore, energy cost can be minimized through optimal operations of demand pattern control, WTPs, and storage facilities [25,26]. Although the price of water supply does not vary with time, the minimized, by optimization, energy cost can affect the improvement of water pricing policy [27].

Water Storage Facilities
Water supply by WDNs is occasionally operated by different supply methods, such as (1) direct water supply (i.e., water coming directly from the water supply); (2) indirect water supply (i.e., through storage facilities such as a tank); and (3) combinations of direct-indirect water supplies. In general, storage facilities are used to ensure a stable water supply with constant water supply through securing water pressure. Table 2 presents the current state of installed water storage facilities in Incheon metropolitan city. Most of the storage facilities are installed in the apartments or in large buildings with areas greater than 2000 m 2 . The storage facilities are operated by individual buildings, and there is no special code on storage facility operations; therefore, the operation of facilities occasionally depend on the practically based rule of meeting water demand. Kwak et al. (2005) studied the hydraulic characteristics of water storage facilities [16]. In their study, downtime averaged 0.3-3.9 days and the water level average was 37.6% of height. At this level, and operating inefficiently, less than 40% of the storage facility is being used. However, water demand is typically less than 40% of the capacity of a water storage facility, and the rest (60% of storage) of the capacity can be used as research capacity for this study.

EPANET
Since the EPANET model was developed by the US Environment Protection Agency in 1994, hydraulic simulations of WDNs have been routinely implemented. EPANET has been extensively used as a tool for research implementation in terms of network design optimization [28,29]. EPANET can be used through a graphical user interface (GUI) as standalone software or can be used through a toolkit library using open source user-specific software. The library and source code can be called through external programming language [29]. In this study, the MATLAB toolkit for the EPANET model was used [30]. MATLAB allows connections to external software libraries, which can help researchers use tools and simulators developed originally in a different language. The EPANET source code was originally formulated in C language.

Genetic Algorithms
GAs are widely used for the optimization of water-related problems [28,[31][32][33]. This optimization technique searches for a solution with minimum costs given as the objective goal of the target problem [33]. Prasad et al. (2003) presented a GA with multivariable functions for an optimal design of WDNs using a Pareto-optimal approach [34]. Prasad and Park (2004) outlined a multi-objective GA for an optimal WDN design [35]. Deb and Jain (2014) developed a nondominated sorting approach for Multi-objective Genetic Algorithm (MOGA) for multi-objective optimization [36]. The considered objectives minimize the error among real and simulated values and maximize reliability. In this study, a GA was selected and coded by simple revision. The GA, based on Deb and Jain's (2014) work [36], included the following considerations: (1) minimum and maximum values for mutation and cross-over; (2) the EPANET model as its variable; (3) many variables with multiple objectives; and a (4) simultaneously fixed bug at mutation with 10+ variables. The GA model was applied for emitter calibration by minimizing errors because the number of variables to be calibrated in WDN was the same as the number of junctions in the network. The EPANET model was applied as the general solver for variables to be calibrated in conjunction with GA. The Pareto front (known as the nondominated solution set) is the fully optimal solution in a multi-objective sense, and the GA is a robust optimization approach for multi-objective purposes with the Pareto front [37].

Objective Function
A formula was developed based on the concept of energy costs for water transfer in WDNs. Energy costs are closely related to water flow and its unit energy cost, and water flow is generated based on water consumption, which has occasionally similar patterns in terms of the energy cost hourly patterns. A possible assumption is that the energy cost could be minimized by redistributing pattern within the concept of GA optimization. The basic concept for optimization is described in Figure 1.
As shown in Figure 1, the demand pattern is considered as a variable, and they become input variables for EPANET to produce the variation of water flow rate. Produced water flow rate as an hourly pattern becomes a new water consumption pattern, and the calculation is iterated through GA optimization. In addition, the energy cost by each pattern is calculated, and the iteration continues until the tool finds the minimum cost as specified.
The water consumption at peak cost time can be classified by consumption through a direct water supply or an indirect water supply (by tank). A direct water supply cannot control the consumption pattern, while an indirect water supply can control it by storage operation. A water supply with high-cost pumping energy during peak price hours can be moved to low-cost hours through tank storage operations. Thus, the daily water supply can be expressed through the summation of a controllable water supply and an uncontrollable water supply, and the energy cost is the summation of hourly water supply multiplied by hourly energy cost, as depicted in Equations (1) and (2): where Q day is the daily total water consumption, Q n is the daily water consumption by direct water supply (without a storage facility), Q u is the daily water consumption by the indirect water supply (with a water storage facility), P n (i) is the dimensionless pattern of water consumption for the direct water supply (uncontrollable) at time step i and can be determined through hourly water consumption by direct water supply divided by the Q n , P u (i) is the dimensionless pattern of water consumption for the indirect water supply (controllable) at time step i and can be determined by hourly water consumption (indirect with a water storage facility) divided by Q u , and E cost (i) is the energy cost for water transfer at time step i. P n and P u are dimensionless hourly patterns of daily water consumption and they vary within a range from zero to one and the sum of 24 h value should be one, respectively. In Equations (1) and (2), Q n and Q u are fixed daily value and P n is also a fixed value; therefore, Q n , Q u and P n are variables out of design space while P u is a variable that varies within the range from zero to one. In addition, unit cost of electricity also varies with time and season. Therefore, the water consumption designed by the P u and the energy cost designed by the unit price of electricity were used as the bi-objective Pareto front objective function. By Equations (1) and (2), the objective function for optimization can be defined as Equation (3): where D i is the water consumption at time step i, and C i is the unit price of electricity at time step i. The energy cost optimization should also consider the stability of water consumption by securing the necessary water pressure; therefore, there must be two constraints. In the optimization model, we tried to find the lowest objective function value as the energy cost for the water supply through designing a P u variable. However, some of chromosomes that are produced through GA can lead to unexpected or infeasible values. Previous studies on GA recommend defining a penalty for them to guide algorithms to avoid infeasible values through defining penalty functions [38,39]. Therefore, the first constraint applies a penalty function throughout the WDNs at junctions, and the other constraint defines the pressure range constraint at specified junctions. Therefore, the penalty function is defined as Equation (4): where P t (i) is the pressure at all junctions within total WDNs, and α is a coefficient to determine relativeness among OF and PF. The value of α is zero when the pressure at the junction is in the range of specified minimum and maximum pressure by user specification. Thus, the OF can be revised within the consideration of PF as Equation (5):  The water consumption at peak cost time can be classified by consumption through a direct water supply or an indirect water supply (by tank). A direct water supply cannot control the consumption pattern, while an indirect water supply can control it by storage operation. A water supply with high-cost pumping energy during peak price hours can be moved to low-cost hours through tank storage operations. Thus, the daily water supply can be expressed through the summation of a controllable water supply and an uncontrollable water supply, and the energy cost is the summation of hourly water supply multiplied by hourly energy cost, as depicted in Equations (1) and (2): where is the daily total water consumption, is the daily water consumption by direct water supply (without a storage facility), is the daily water consumption by the indirect water supply (with a water storage facility), ( ) is the dimensionless pattern of water consumption for the direct water supply (uncontrollable) at time step and can be determined through hourly water consumption by direct water supply divided by the , ( ) is the dimensionless pattern of water consumption for the indirect water supply (controllable) at time step and can be determined by hourly water consumption (indirect with a water storage facility) divided by , and ( ) is the energy cost for water transfer at time step . and are dimensionless hourly patterns of daily water consumption and they vary within a range from zero to one and the sum of 24 h value should be one, respectively. In Equations (1) and (2), and are fixed daily value and is also a fixed value; therefore, , and are variables out of design space while is a variable that varies within the range from zero to one. In addition, unit cost of electricity also varies with time and season. Therefore, the water consumption designed by the and the energy cost designed by the unit price of electricity were used as the bi-objective Pareto front objective function. By Equations (1) and (2), the objective function for optimization can be defined as Equation (3):

Study Area
In this study, the study area is chosen in the effluence area of Bupyeong's second water supply reservoir since there are several different types of storage facilities and different types of land use (e.g., residential, commercial, public, and an apartment complex). In addition, data about WDNs, electricity, and hydraulic data (flow rate and pressure) could be secured. Figure 2a shows the boundary and land use data of the study area, and Figure 2b shows the pipeline on the block.
where is the water consumption at time step , and is the unit price of electricity at time step . The energy cost optimization should also consider the stability of water consumption by securing the necessary water pressure; therefore, there must be two constraints. In the optimization model, we tried to find the lowest objective function value as the energy cost for the water supply through designing a variable. However, some of chromosomes that are produced through GA can lead to unexpected or infeasible values. Previous studies on GA recommend defining a penalty for them to guide algorithms to avoid infeasible values through defining penalty functions [38,39]. Therefore, the first constraint applies a penalty function throughout the WDNs at junctions, and the other constraint defines the pressure range constraint at specified junctions. Therefore, the penalty function is defined as Equation (4): where ( ) is the pressure at all junctions within total WDNs, and is a coefficient to determine relativeness among OF and PF. The value of is zero when the pressure at the junction is in the range of specified minimum and maximum pressure by user specification. Thus, the OF can be revised within the consideration of PF as Equation (5):

Study Area
In this study, the study area is chosen in the effluence area of Bupyeong's second water supply reservoir since there are several different types of storage facilities and different types of land use (e.g., residential, commercial, public, and an apartment complex). In addition, data about WDNs, electricity, and hydraulic data (flow rate and pressure) could be secured. Figure 2a shows the boundary and land use data of the study area, and Figure 2b shows the pipeline on the block.  In the study area, the daily maximum water supply is 46,000 m 3 /day, and the water supply is generally coming from Bupyeong's second water supply reservoir, which has 20,000 m 3 of capacity, 59.5 m at the high-water level, and 55 m at the low-water level. The maximum water use pattern occurs between 6:00 p.m. and 7:00 p.m., and the water use pattern for the high energy cost time frame (peak hours) and the intermediate high cost time frame (mid hours) is high while the pattern for the low energy cost time frame (low hours) is low. Thus, it is possible to lower energy costs by redistributing the water use pattern. The water use pattern is shown in Figure 3.
In the study area, the daily maximum water supply is 46,000 m 3 /day, and the water supply is generally coming from Bupyeong's second water supply reservoir, which has 20,000 m 3 of capacity, 59.5 m at the high-water level, and 55 m at the low-water level. The maximum water use pattern occurs between 6:00 p.m. and 7:00 p.m., and the water use pattern for the high energy cost time frame (peak hours) and the intermediate high cost time frame (mid hours) is high while the pattern for the low energy cost time frame (low hours) is low. Thus, it is possible to lower energy costs by redistributing the water use pattern. The water use pattern is shown in Figure 3. In Figure 3, the water demand pattern is high during peak cost and intermediate cost hours, while the pattern is low during low energy cost hours. In this study, we assumed that the high water demand pattern can be moved to the low energy cost hours by using the water storage facilities (which are not actively used), and the use of facility can be determined by the optimization process.
The study area has 122 storage facilities and 11,321 m 3 of capacity in total storage facilities. The total capacity of the storage facilities is approximately 24% of the daily maximum water supply (46,000 m 3 /day). Seven storage facilities have greater than 500 m 3 of capacity, and they represent about half the total capacity of all the storage facilities, as shown in Table 3. The official GIS provided from Incheon city authorities was used as the major input for EPANET modeling, and the water use pattern data was included in the model for an extended period simulation. The completed set of EPANET data was validated by test simulation and added as a variable of Matlab GA optimization. Table 4 shows the summarized parameters for GA optimization.  In Figure 3, the water demand pattern is high during peak cost and intermediate cost hours, while the pattern is low during low energy cost hours. In this study, we assumed that the high water demand pattern can be moved to the low energy cost hours by using the water storage facilities (which are not actively used), and the use of facility can be determined by the optimization process.
The study area has 122 storage facilities and 11,321 m 3 of capacity in total storage facilities. The total capacity of the storage facilities is approximately 24% of the daily maximum water supply (46,000 m 3 /day). Seven storage facilities have greater than 500 m 3 of capacity, and they represent about half the total capacity of all the storage facilities, as shown in Table 3. The official GIS provided from Incheon city authorities was used as the major input for EPANET modeling, and the water use pattern data was included in the model for an extended period simulation. The completed set of EPANET data was validated by test simulation and added as a variable of Matlab GA optimization. Table 4 shows the summarized parameters for GA optimization.
The parameters were determined through several test implementations. Moreover, the main variable for optimization was the WDN's pipe network problem, which was also quite complicated to solve. The length of chromosome was set as 24 since there were 24 real number coding for each hour pattern (24/day). The population was set as 50 after several practice runs. The linear ranking was selected as 1.7 for higher selective pressure. In addition, random selection for crossover and a 0.1 mutation ratio were selected. The model simulation consisted of five different cases for each season. The first case shows the current state of operation without any application of energy saving strategies. The second, third, and fourth cases depict the redistribution of water demand to the low energy cost hours at 60%, 80%, and 100% of water use, respectively. The last case applies the GA optimization. Table 5 shows detailed descriptions of the simulation cases.

Model Sensitivity and Convergence
To choose the value of α, a coefficient to determine relativeness among objective function and penalty function as described in Equation (4), the sensitivity of α was examined. The result is shown in Figure 4.
The pattern of P u (i) (the dimensionless pattern of water consumption for the indirect water supply, which is controllable, at time step i) in Figure 4 is similar to all cases since the GA is calculated based on the rank of the generated population, and the extreme values in the population are excluded due to their low rank. However, the higher value of α distributes homogeneous pressure, which could provide less fluctuation since the penalty function reflects the pressure in the pipe network. In addition, the simulation time, from start to convergence, with the value of higher α was shorter than lower or the zero value of α. To summarize, the penalty function affected the convergence in determining the optimized value of the objective function; however, the sensitivity itself was not high. The value of α was determined as 10% by the analysis. The convergence of the objective function with the value of α as 10% is shown in Figure 5.  The convergence was tested with the result of the objective function value in the summer season. The convergence was completed at the 22nd generation. Fast convergence can show the lack of diversity; however, this fast convergence could be made by the effect of the penalty function, which can provide a strong exploration capacity for the model. The total number of pipe networks with iterations was 1100 times, and the convergence made a slow improvement, which can be appropriate for optimization. In addition, the convergence patterns in the other seasons were similar to the example of the summer season.
To optimize the energy cost, we examined cases by uniform distribution and optimization in different seasons; however, the spring and autumn seasons were treated as the same case since the energy cost in the spring and autumn are the same. The classification of cases is shown in Table 5.

Summer Season
In the summer season, the flow rate between 10:00 a.m. and 11:00 p.m. (peak and mid hours) is high, while water consumption for the low energy cost hours is comparably low, as shown in Figure  6.  The convergence was tested with the result of the objective function value in the summer season. The convergence was completed at the 22nd generation. Fast convergence can show the lack of diversity; however, this fast convergence could be made by the effect of the penalty function, which can provide a strong exploration capacity for the model. The total number of pipe networks with iterations was 1100 times, and the convergence made a slow improvement, which can be appropriate for optimization. In addition, the convergence patterns in the other seasons were similar to the example of the summer season.
To optimize the energy cost, we examined cases by uniform distribution and optimization in different seasons; however, the spring and autumn seasons were treated as the same case since the energy cost in the spring and autumn are the same. The classification of cases is shown in Table 5.

Summer Season
In the summer season, the flow rate between 10:00 a.m. and 11:00 p.m. (peak and mid hours) is high, while water consumption for the low energy cost hours is comparably low, as shown in Figure  6. The convergence was tested with the result of the objective function value in the summer season. The convergence was completed at the 22nd generation. Fast convergence can show the lack of diversity; however, this fast convergence could be made by the effect of the penalty function, which can provide a strong exploration capacity for the model. The total number of pipe networks with iterations was 1100 times, and the convergence made a slow improvement, which can be appropriate for optimization. In addition, the convergence patterns in the other seasons were similar to the example of the summer season.
To optimize the energy cost, we examined cases by uniform distribution and optimization in different seasons; however, the spring and autumn seasons were treated as the same case since the energy cost in the spring and autumn are the same. The classification of cases is shown in Table 5.

Summer Season
In the summer season, the flow rate between 10:00 a.m. and 11:00 p.m. (peak and mid hours) is high, while water consumption for the low energy cost hours is comparably low, as shown in Figure 6. In Case S1, water consumption from the storage facilities was increased during the low energy cost hours, while it decreased during peak and mid hours. Bigger variations occurred in Case S2 and S3, with an almost reversed pattern from the current state. In addition, the results of S1, S2, and S3 showed different scales of variations by the different proportions of storage usage but showed similar variation patterns since the distribution method was almost the same. In the case with GA optimization (SGA), the pattern was between the patterns of S1 and S2 during the low energy cost hours, while the pattern was similar to the S3 pattern during peak hours. It is clear that the water demand during peak hours and mid hours was transferred and distributed for low cost hours, as shown in Table 6.  1761  1497  1335  1173  1552  264  426  587  209  11  1854  1538  1376  1215  1577  316  478  640  278  12  Peak  1794  1574  1412  1251  1255  220  382  543  539  13  Mid  1799  1568  1406  1244  1465  232  394  555  334  14   Peak   1634  1598  1436  1274  1397  37  198  360  238  15  1535  1493  1331  1169  1338  42  204  365  197  16  1567  1451  1289  1127  1247  117  278  440  320  17  1584  1403  1241  1080  1169  181  342  504  415  18  Mid  1500  1402  1241  1079  1206  97  259 421 294 In Case S1, water consumption from the storage facilities was increased during the low energy cost hours, while it decreased during peak and mid hours. Bigger variations occurred in Case S2 and S3, with an almost reversed pattern from the current state. In addition, the results of S1, S2, and S3 showed different scales of variations by the different proportions of storage usage but showed similar variation patterns since the distribution method was almost the same. In the case with GA optimization (SGA), the pattern was between the patterns of S1 and S2 during the low energy cost hours, while the pattern was similar to the S3 pattern during peak hours. It is clear that the water demand during peak hours and mid hours was transferred and distributed for low cost hours, as shown in Table 6.  As shown in Table 6, the transferred water from intermediate hours to low hours is higher in cases S1, S2, and S3 than for SGA, while the transferred water from peak hours to low hours is higher in the SGA case than in the rest of the cases. Therefore, in the cases for the summer season, the SGA case shows higher efficiency for energy savings. Figure 7 shows the transferred water demand from the peak and mid hours to the low hours. As shown in Table 6, the transferred water from intermediate hours to low hours is higher in cases S1, S2, and S3 than for SGA, while the transferred water from peak hours to low hours is higher in the SGA case than in the rest of the cases. Therefore, in the cases for the summer season, the SGA case shows higher efficiency for energy savings. Figure 7 shows the transferred water demand from the peak and mid hours to the low hours. In Figure 7, the water demand transferred from peak hours to low hours in cases S1, S2, and S3 was approximately 27-33%, while it was approximately 60% in the SGA case, as the GA tries to give priority for water demand during peak hours. The saving effect in case S1 and SGA was approximately 33.3%. In Figure 7, the water demand transferred from peak hours to low hours in cases S1, S2, and S3 was approximately 27-33%, while it was approximately 60% in the SGA case, as the GA tries to give priority for water demand during peak hours. The saving effect in case S1 and SGA was approximately 33.3%.

Winter Season
In the winter season, unlike the summer, the flow rate is very high in the evening time, especially between 6:00 p.m. and 9:00 p.m. and 10:00 p.m. and 11:00 p.m., as shown in Figure 8. In cases W1, W2, and W3, the variations of water demand pattern from the current state were similar to the cases for the summer season. In addition, the pattern revised by case W1 was similar to the WGA case. W1, W2, and W3 at 11:00 p.m. were close to one another, with the highest variations in the day. Demand pattern changes in the W1, W2, and W3 cases were similar to the results of the summer season in S1, S2, and S3, respectively, with the reversed demand, while the WGA case showed very low demand between 5:00 p.m. and 6:00 p.m. and at 11:00 p.m. It is clear that the water demand during the peak and mid hours was transferred and distributed to the low hours, as shown in Table 7.  −248  10  Mid  1935  1817  1655  1493  2213  118  280  441  −278  11  2130  1867  1705  1544  1671  263  425  587  459  12  Peak  1868  1809  1647  1486  1751  59  220  382  117  13  Mid  1921  1870  1708  1547  1971  51  213  374  −50  14   Peak   1898  1849  1687  1526  2016  49  210  372  −118  15  1904  1751  1590  1428  1572  153  315  477  333  16  1940  1701  1539  1378  1585  239  401  563  355  17  1700  1709  1547  1386  1599  −9  153  314  101  18  Mid  1722  1773  1611  1449  1482  −50  112  273  241  19  1880  1833  1672  1510  1907  47 209 371 −26 In cases W1, W2, and W3, the variations of water demand pattern from the current state were similar to the cases for the summer season. In addition, the pattern revised by case W1 was similar to the WGA case. W1, W2, and W3 at 11:00 p.m. were close to one another, with the highest variations in the day. Demand pattern changes in the W1, W2, and W3 cases were similar to the results of the summer season in S1, S2, and S3, respectively, with the reversed demand, while the WGA case showed very low demand between 5:00 p.m. and 6:00 p.m. and at 11:00 p.m. It is clear that the water demand during the peak and mid hours was transferred and distributed to the low hours, as shown in Table 7.  As shown in Table 7, the transferred water from mid hours to low hours is higher in the W1, W2, and W3 cases than the WGA, while the transferred water from peak hours to low hours is higher in the WGA case than in the rest of the cases, which was similar to the case for the summer season. Therefore, in the cases for the winter season, the WGA case shows higher efficiency for energy savings. Figure 9 shows the transferred water demand from the peak and mid hours to the low hours. Figure 9. Flow rate transferred to low cost hours by the winter season simulation.
In Figure 9, the water demand transferred from the peak hours to the low hours in cases W1, W2, and W3 was approximately 40%, while it was approximately 60% in the WGA case, as the GA tries to give priority for water demand during peak hours. The saving effect by cases W (1, 2, and 3) and WGA was approximately 33.3%. In Figure 9, the water demand transferred from the peak hours to the low hours in cases W1, W2, and W3 was approximately 40%, while it was approximately 60% in the WGA case, as the GA tries to give priority for water demand during peak hours. The saving effect by cases W(1, 2, and 3) and WGA was approximately 33.3%.

Spring and Autumn Seasons
In the spring and autumn seasons, unlike the summer or winter seasons, the flow rate was high during the daytime and continuous in the evening, as shown in Figure 10. are comparably small because of a fairly constant demand pattern in the current state. A comparison of energy costs is summarized in Table 8.   In the spring and autumn seasons, the shapes of the curves in Figure 10 are very different between the current state and the simulation cases. In the current case, no significant variation is observed between 9:00 a.m. and 9:00 p.m., while the simulation cases show an hourly varying curve as high demand during the morning and evening. F1, F2, and F3 show a similar variation as the S1, S2, and S3, respectively. However, the F1 and F2 cases do not show the reversed demand pattern in the morning and evening, while F3 shows a reversed pattern from the morning to evening. In terms of the FGA case with GA optimization, the curve is quite close to the SGA since the hourly energy cost in spring, summer, and autumn is constant. The differences between the current state and SGA are comparably small because of a fairly constant demand pattern in the current state. A comparison of energy costs is summarized in Table 8.
As shown in Table 8, the transferred water from the mid hours to the low hours is higher in cases F1, F2, and F3 than in FGA, while the transferred water from the peak hours to the low hours is higher in the FGA case than in the rest of the cases, similar to the case for the summer season. Therefore, in the cases for the winter season, the FGA case shows higher efficiency for energy savings. Figure 11 shows the transferred water demand from the peak and mid hours to the low hours. As shown in Table 8, the transferred water from the mid hours to the low hours is higher in cases F1, F2, and F3 than in FGA, while the transferred water from the peak hours to the low hours is higher in the FGA case than in the rest of the cases, similar to the case for the summer season. Therefore, in the cases for the winter season, the FGA case shows higher efficiency for energy savings. Figure 11 shows the transferred water demand from the peak and mid hours to the low hours. Figure 11. Flow rate transferred to the low cost hours in the spring-autumn season simulation.
In Figure 11, the water demand transferred from the peak hours to the low hours in cases F1, F2, and F3 were approximately 35%, while it was approximately 50% in the FGA case, as the GA tries to give priority for water demand during peak hours. The saving effect in cases W(1, 2, and 3) and FGA was approximately 30%. In Figure 11, the water demand transferred from the peak hours to the low hours in cases F1, F2, and F3 were approximately 35%, while it was approximately 50% in the FGA case, as the GA tries to give priority for water demand during peak hours. The saving effect in cases W(1, 2, and 3) and FGA was approximately 30%.

Energy Cost Savings
As discussed in the previous chapter, only 37.6% of the storage facilities are being used in the current state. Therefore, the realistic, available capacity to be used for energy cost optimization is approximately 60% of total storage facilities, and only the S1, W1, and F1 cases could be considered close to the real world scenario. The current seasonal simulations (S1, W1, and F1) and optimization cases (SGA, WGA, and FGA) compared in this chapter are summarized in Table 9. In terms of the energy cost in the summer season, the cost reductions would be 4.22% for S1, 6.33% for SGA, 4.06% for W1, and 4.69% for WGA from the 3.92 USD/m 3 cost at the current state. For spring and autumn, F1 and FGA can be reduced by 4.71% and 5.51%, respectively. It means that the energy efficiency reduction is best in the summer season, while the winter season does not show significant differences.
In this study, only WDNs were applied to reduce the energy cost in a water supply system; however, the cost reduction ratio could be applied to the whole process in the water supply system, including the water supply pump from the WTP to the reservoir, the intake pump, and the boost pump from the intake to the WTP. The monthly reduction ratio is determined as the reducing ratio of energy cost from SGA, WGA, and FGA, and the estimated reductions are summarized in Table 10.

Conclusions
In a water distribution system, the proportion of energy costs from using pumps at the WDN is high for the total cost. Energy cost (electricity) varies according to the season of year and the hours of a day. The water demand pattern is similar to the hourly energy cost curve, so high water demand occurs during high energy cost hours. In this study, under the assumption that energy cost reduction is possible through redistributing the demand pattern, a numerical analysis was conducted on transferring the water demand at peak energy cost hours to low energy cost hours by the storage facilities. This study was applied to a real facility, the Bupyeong 2 reservoir catchment, and produced the following conclusions.
The demand pattern was optimized using several methods, and the optimization was applied for the summer, winter, and spring-autumn seasons. The maximum energy cost savings from the optimization was 6.33% for the summer season. Only 37.6% of the total capacity of the storage facilities was being used, and 60% of storage capacity was still available for this study. This study confirms that it is possible to reduce energy costs by using electricity during the low-cost hours to fill storage facilities to be used during peak hours. In this study, the real capacity of the storage facilities in the study area was applied to redistribute the water demand from the peak hours to the low hours. The result of the energy cost reduction could be generalized throughout the water supply system and applied to the major procedures involved, such as pumping the water supply from the water treatment plant to the reservoir, using the water intake pump, and powering the boost pump to move water from the intake to the water treatment plant. In total, approximately 5.36% of energy cost could be reduced.
This study applied water demand patterns, pipe networks, storage facilities, and hourly varying electricity prices in a study area without special characteristics. An energy cost changes over time in many regions of the world and there are many water storage facilities that are not actively being used. Therefore, it is possible to apply this research to the other regions as a worldwide application for studies on energy savings, improvement of the water billing system or smart water grids. In addition, we studied energy costs and water demand among the water supply costs and, in further study, water tariffs can be an additional variable for energy savings since the low price of water tariffs can trigger over use of water. Seongjoon Byeon collected data and Yungyu Chang generated the result. All authors read and approved the final manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.