Pumping regimes for water distribution systems have been established to reduce pump operation costs. Optimization of water reservoir networks has been studied extensively for operating pumps efficiently. According to research, optimization reduces pump operation costs by approximately 10–20%. However, comparing economic benefits per country would be too complex because the effects of optimization differ depending on the power cost estimation system of each country and the existing operations. This study presents an optimization algorithm to minimize the operating costs of an entire system via the application of dynamic programming. Case studies were conducted to apply the algorithm to real values in four scenarios. By setting cost minimization as an objective, an optimum water pump operation plan was derived that encompasses operating conditions, variations in water demand, and energy costs. Results showed that operating a standby pump in an existing system can increase the system's efficiency. In addition, even if hourly water consumption remains constant, each case requires its own operating method, because each case has different operational costs. By considering various conditions such as those mentioned in this study, future pump operation schedules can be optimized and stabilized to maintain economic water supply.

INTRODUCTION

The purpose of a water supply system is to provide customers with a reliable source of water under sufficient hydraulic pressure (Nitivattananon et al. 1996). To improve infrastructure maintenance efficiency, optimization of the interconnection between reservoirs and pump stations has been suggested for optimal control of the water distribution system (McCormick & Powell 2003). In particular, it is necessary to reduce the amount of electricity required to operate water pumps, because pumping systems represent a major operational expenditure and they account for the largest consumption of energy (Lehar 1991).

This study presents an optimization algorithm to minimize the operating costs of the entire water supply system. The Civil Society Urban Development Program (CSUDP), which is based on dynamic programming (DP) developed by Labadie (1999), was selected as the optimization algorithm, and City YangJu (YJ) was selected as the target region for the study. With cost reduction as the objective, an optimal water pump operation plan is derived that encompasses both variations in water demand and energy costs.

METHODS

Study process

The goal of this study was to schedule the operation of pumps over a specific time period in such a way that the system constraints and boundary conditions are satisfied while operational cost is minimized. Figure 1 contains a flow chart representing the sequence of steps planned for the study.

Figure 1

Flow chart of this study.

Figure 1

Flow chart of this study.

These four steps are described briefly as follows:

  • Step 1.

    Select study area. To optimize multiple water reservoirs, City YJ was selected as the study region. In addition, pump scheduling was determined based on a few factors, which had a significant impact on the efficiency of the pump operation. These factors included pump operating conditions, power cost fluctuations, and changes in the water level of each reservoir (RJózsef 2010).

  • Step 2.

    Designate objective functions, including the power cost of the pump, the maximum change value of the pump water, and the water level of the reservoir to define DP. Restrictions were determined to be the capacity limit of the pump, conveyance of pipe, water level and changes in the reservoir, ON/OFF switch count, and power cost of pump. In this study, minimization of electrical cost was established as an objective (Lansey & Awumah 1994).

  • Step 3.

    Establish pump operation scenarios. Four scenarios, including different operating conditions, were established to determine the optimum pump operation schedule in this study.

  • Step 4.
    Schedule optimal operation for each scenario by applying DP, especially the CSUDP program based on DP developed by Labadie (1999).
    Figure 2

    The structure of DP.

    Figure 2

    The structure of DP.

Dynamic programming

The sequential analysis procedure should be considered through the general DP algorithm. However, because the optimum value to the next step (n + 1) is unknown, the optimal value is determined by separating the upper and lower limits of the state variable Sn−1 and Sn via division (Bellman 1957; Chun 2001).

Figure 2 shows the forward DP method, which calculates the optimal solution of the next step by separating each step starting from the first to the last, where Sn−2 in step (n − 1) is the primary state variable of (n − 1), and Sn−1 of the next step is determined by the decision variable Xn−1. Formula (1) is the recurrence equation, which is the basic concept of finding the optimal value of the next step in forward DP 
formula
1
 
formula
Here, fn(Sn, Xn) is the objective function, which is the solution of the problem, and it has an independent relationship with the objective functions estimated in the other steps. It can be determined by calculating Xn with Sn−1 or Qn in step n, or by using the equation Rn (Xn), which estimates the output value corresponding to step n from the input value. Thus, in DP, the recurrence equation of each of the separated values is determined in the last step by recalling the value of the previous step that represents the optimal value of each of the separated values, and by following the remembered value and backtracking to the first step, the optimal state variable Sn* and the decision variable Xn* can be determined to find the optimal solution.

Network description of the study area

Y pump station located in City YJ is the primary supply system for the local waterworks, and it has been supplying water to some parts of city D as well. Pump station Y is divided into Y and B systems and serves a total of 105,000 tons/day. This study was carried out only for system Y (total capacity: 64,000 tons/day). Pressurized water going to system Y is distributed to reservoirs DJ, Y, and K and SP, respectively. In case of reservoir SP, water is supplied from reservoir SY which is in another system due to pipe communication (Figure 3).

Figure 3

Pipe network diagram and the present state of the reservoirs in pump station Y.

Figure 3

Pipe network diagram and the present state of the reservoirs in pump station Y.

Model development

Pump specification

Pump station Y is mainly fed by system Y and it consists of four pumps, as shown in Table 1. Four pumps from system Y are operated 24 hours a day. The fourth, with the smallest pump quantity, is a standby pump. The total pump station capacity is 64,000 m3/day, and it is increased to 89,000 m3/day when utilizing standby pumps.

Table 1

Pump specifications in pump station Y

Building test
Pump station YPump station capacity [m3/day] (+ standby pump)Pump quantity [m3/h]Height [m]Efficiency [%]Power [kWh/m3]
64,000 (89,000) 1,086 105.0 79.1 0.3667 
1,086 105.9 79.7 0.3688 
1,086 104.7 79.5 0.3610 
4 (standby pump) 534 101.2 70.0 0.3987 
Building test
Pump station YPump station capacity [m3/day] (+ standby pump)Pump quantity [m3/h]Height [m]Efficiency [%]Power [kWh/m3]
64,000 (89,000) 1,086 105.0 79.1 0.3667 
1,086 105.9 79.7 0.3688 
1,086 104.7 79.5 0.3610 
4 (standby pump) 534 101.2 70.0 0.3987 

Electric power unit cost

In Korea, electricity tariff is priced lower during off-peak hours, which are determined by seasonal or hourly demand (Kim 1989). According to the actual electricity tariff recorded in November 2011, summarized in Table 2, the unit cost system is divided into three sections by season (summer, spring/fall, winter) and by time of day (night, day, evening). The cost for the night period was lowest regardless of season, daytime cost was highest during the summer, and the cost for the evening period was highest during the winter. Since the night period tariff is approximately 36% of peak power, operating more pumps during the night can reduce operation cost. However, this feature makes it difficult to cope with the large scale of water demand when the reservoir capacity is low. In addition, it can cause problems with regard to high water level due to a sudden rise in the water level. Therefore, differences in the electricity tariff should be taken into account to determine the water supply schedule in order to minimize the overall operation costs.

Table 2

Seasonal electricity surcharge charge (contract 300–1,000kW)

Unit cost (won/kWh)
Spring/Fall
Basic rate (won/kW)TimeSummer (July–August)(June)(March–May, September–October)Winter (November–February)
6,410 Night 49.50 49.50 49.50 54.30 
Daytime 120.00 82.30 68.70 89.10 
Evening 82.40 68.70 82.30 107.20 
Unit cost (won/kWh)
Spring/Fall
Basic rate (won/kW)TimeSummer (July–August)(June)(March–May, September–October)Winter (November–February)
6,410 Night 49.50 49.50 49.50 54.30 
Daytime 120.00 82.30 68.70 89.10 
Evening 82.40 68.70 82.30 107.20 

Objective function and restriction

In this study, 2010 operating data were used in order to evaluate the possible range of operating costs by optimizing the pump plan. DP was also applied to achieve optimization. Initial reservoir storage values from August 6, 2010 and October 23, 2010 were used based on the fact that there is no difference in water demand with regard to season or day of the week. This decision was similar to that of Yu et al. (2005), and the objective function, which was determined to be minimizing operating cost, can be stated as follows: 
formula
2
where the following notation is employed: = electricity usage fee in k month; t time period; = pump unit cost (kWh/m3) of j pump; = volume in t time period of j pump (m3); M = number of pumps; T = time (in this study, 24 h).
The inlet flow quantity is applied as an upper restriction, which limits the designed flow of the reservoir inlet. The minimum water level should be able to guarantee the storage capacity for 3 h or longer for emergency supply. In addition, the maximum water level does not exceed the specified range in order to restrict the working volume to within 90% of overall capacity. 
formula
3
 
formula
4
where the following notation is employed: = volume in t time period of j pump (m3); = maximum daily pumping capacity; = conveyance of pipes; T = time (in this study, 24 h).
The restriction, which is applied in the reservoirs, can be stated as follows: 
formula
5
 
formula
6
 
formula
7
where the following notation is employed: = supply demand in t time period in l reservoir; , = operating restriction of reservoir storage capacity; , = pipe (from pump station to reservoir) conveyance restriction.

Scenarios

Four scenarios were assumed to confirm how pump operating conditions and electricity cost fluctuations influence the optimal pump schedule. Scenarios 1 and 3 simulated the cost of power consumption in the current operating condition, and scenarios 2 and 4 compared the electricity cost savings effect regarding operating conditions with added pre-pumps to previous operating performances by applying and simulating the patterns for August, which has the maximum water consumption rate, and for October, which has a different electricity unit price. Patterns for August, included in scenarios 1 and 2, represent the period of the year in which water consumption peaks, and patterns for October were assumed to represent the period in which water consumption is average; the scenario was established as shown in Table 3.

Table 3

Set scenarios to compare the present condition

ScenarioCapacity (m3/day)Application pattern
Scenario 1
(Optimization of present condition) 
64,000 August pattern 
Scenario 2
(Optimization of standby pump operation) 
89,000  
Scenario 3
(Optimization of present condition) 
64,000 October pattern 
Scenario 4
(Optimization of standby pump operation) 
89,000  
ScenarioCapacity (m3/day)Application pattern
Scenario 1
(Optimization of present condition) 
64,000 August pattern 
Scenario 2
(Optimization of standby pump operation) 
89,000  
Scenario 3
(Optimization of present condition) 
64,000 October pattern 
Scenario 4
(Optimization of standby pump operation) 
89,000  

RESULTS AND DISCUSSION

Optimization according to standby pump usage

In this subsection, a comparison, in terms of energy efficiency, between current and optimized operation is considered in pump station Y. Optimizing in accordance with the availability of the standby pump was performed via DP by applying the August pattern.

While existing operation patterns in system Y are shown irregularly, as illustrated in Figure 4, optimized operation patterns according to scenarios 1 and 2 showed a regular pattern basis to maximized supply during the night period, as can be seen in Figures 5 and 6, respectively.

Figure 4

Present operation patterns in system Y (August).

Figure 4

Present operation patterns in system Y (August).

Figure 5

Optimal operation patterns in system Y (scenario 1 August).

Figure 5

Optimal operation patterns in system Y (scenario 1 August).

Figure 6

Optimal operating pattern in system Y (scenario 2 August).

Figure 6

Optimal operating pattern in system Y (scenario 2 August).

Here, pump operation means number of pumps operating and inflow rate indicates total inflows to four reservoirs (reservoir K, DJ, Y, SP). In the case of Figure 4, pump operation was decreased between 8 p.m. and 9 p.m., but inflow rate was increased. Because in the study area water demand was increased at that time, reservoir SP was supplied water from reservoir SY by pipe communication.

Moreover, it can be observed in Figure 6 that operating a standby pump with existing pumps is more effective, since it enables reservoirs to be filled during the cheap period of electricity surcharge charge.

The energy-consumption cost-reducing effect in scenario 2, which operates all facilities including the standby pump, is larger compared to the current operation scenario 1, since pumping as much water as possible during the night period takes full advantage of the electricity tariffs system. Compared with the initial cost (1,539,981 won/day), savings of 6.3% in scenario 1 (1,442,841 won/day) and of 19.2% in scenario 2 (1,244,110 won/day) are obtained under the upper limit constraints, which secure the minimum reservoir level as 3 h.

Optimization according to electricity cost fluctuation

Electricity unit cost has an enormous effect on pump operation scheduling. As shown in Table 2, the unit cost system is divided into season and time. Night period is 10 p.m.–8 a.m., daytime is 8 a.m.–6 p.m., and evening period is 6 p.m.–10 p.m. Night period cost was lowest regardless of season, and it was usually cheaper by approximately 49.1–65.7%. In this subsection, August and October water patterns, which have different unit costs but similar water demand, are compared in order to determine the impact of unit cost. Figures 5, 6, 7, and 8 show calculated optimized values for scenarios 1, 2, 3, and 4, respectively. As illustrated in Figures 5,678, four results are derived from the optimum schedule of pumping the largest amount of water during the night period.

Figure 7

Optimal operation patterns in Y system (scenario 3 October).

Figure 7

Optimal operation patterns in Y system (scenario 3 October).

Figure 8

Optimal operation patterns in Y system (scenario 4 October).

Figure 8

Optimal operation patterns in Y system (scenario 4 October).

As to the results, amount of pumping flow is small in August when the power cost was the most expensive (8 a.m.–6 p.m.); conversely, amount of pumping flow is small in October during the evening time (6 p.m.–10 p.m.). The reduced cost effects for each scenario are given in Table 4. Results showed that there was a 5.2–10.3% cost difference between scenario optimizations. In other words, it is essential to take into account the cost unit fluctuation when deriving optimum schedules even when water demand is the same.

Table 4

Electricity cost per scenario (change of electricity unit)

Energy cost (won/day)
SectionExisting conditionOptimization of present conditionOptimization after adding standby pump operation
Application of time pattern in Aug (a) 1,539,981 Scenario 1 Scenario 2 
1,442,841 1,244,110 
Application of time pattern in Oct (b) 1,297,457 Scenario 3 Scenario 4 
1,068,230 984,230 
Reduced cost (a–b) 242,524 374,611 259,880 
15.7% 26.0% 20.9% 
Energy cost (won/day)
SectionExisting conditionOptimization of present conditionOptimization after adding standby pump operation
Application of time pattern in Aug (a) 1,539,981 Scenario 1 Scenario 2 
1,442,841 1,244,110 
Application of time pattern in Oct (b) 1,297,457 Scenario 3 Scenario 4 
1,068,230 984,230 
Reduced cost (a–b) 242,524 374,611 259,880 
15.7% 26.0% 20.9% 

CONCLUSIONS

The aim of this study was to optimize multiple water reservoirs. City YJ was selected as the area of study. Pump scheduling was determined based on a few factors that had a significant impact on the efficiency of pump operation. These factors included pump operating conditions, power cost fluctuations, and changes in the water level of the reservoir.

DP was used as a methodology to obtain an exact solution, and case studies were conducted for four different scenarios. To define DP, cost minimization was designated as the objective, and restrictions were determined to be the capacity limit of the pump, the conveyance of the pipe, the water level and changes in the reservoir, and the power cost of the pump.

Results showed that operating a standby pump with existing pumps is more effective. The energy consumption cost-reducing effect, which impacts all facilities including the standby pump, is larger compared to the current operation, since pumping as much water as possible during the night period takes full advantage of the electricity surcharge system. Compared with the initial cost, savings of 6.3% in scenario 1, which optimizes the current condition, and 19.2% in scenario 2, which includes standby pump operation, are obtained. In addition, the optimization results according to demand levels show that it is necessary to operate pumps more flexibly than the current schedule in order to reduce cost. Moreover, it was found that optimized patterns varied by electricity unit cost even when the water demand was similar, because unit cost systems differ depending on season and time.

From the results, a better optimized pump schedule can be used for future maintenance. However, since this study only focused on minimizing operational cost, other advanced techniques, which take into account not only cost but also water quality stability, need to be studied.

ACKNOWLEDGMENT

This study was supported by the Korea Ministry of Environment under ‘Projects for Developing Eco-Innovation Technologies (GT-11-G-02-001-1)’.

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