Stable water supply to end users is the most important element in water supply systems (WSSs). The portion of energy used by the water distribution system is up to 40% of the total energy consumed by WSSs. To save energy cost for pumping systems, a number of attempts have been made. Especially, an optimization scheme for scheduling the water-pumping operation has attracted the interest of water engineers. In this paper, a binary integer program was applied to optimize pumping schedule of a WSS in Polonnaruwa, Sri Lanka based on the hourly water demands for the next day. The water demands were forecasted by a combined model consisting of an autoregressive integrated moving average (ARIMA) model and an error compensation routine based on exponential smoothing technique. The result showed that the optimization system could reduce the operation cost of the WSS by minimizing electricity for water pumping; electricity cost for pump operation could be reduced by 55%.

## INTRODUCTION

Water supply and distribution systems consume a significant amount of energy in the process of treating and supplying water to end users. Most of the energy consumed by the system is used while it pumps drinking water through the piping network. About 3–4% of the energy consumed in the world is used by water treatment and supplying systems for urban and industrial purposes (Barry 2007). Especially, the pumping cost is a major financial expense in a water supply system (WSS) (Coelho & Andrade-Campos 2014). Energy price has increased significantly over the past decades. As a result, a number of attempts have been made to reduce the energy consumption in WSSs.

Energy consumption can be reduced by control of water leaks in a WSS. Water demand forecasting followed by optimization of pumping schedule or water levels of reservoirs for balancing water demand and supply can be implemented to save energy (Coelho & Andrade-Campos 2014). Recently, renewable energy sources, such as solar energy, wind power, and small hydropower have been utilized for reducing energy consumption in WSSs (Ramos & Ramos 2009). Renewable energy may be used to supply power only for a small WSS, because a large WSS often requires much more energy.

One of the most popular approaches to save energy in WSSs is to optimize pumping operation based on water demand forecasting. In order for operation and management of a WSS to be effective, an accurate forecasting of short-term water demand should be realized (Herrera *et al.* 2010; Donkor *et al.* 2014).

For the past decades, a few forecasting methods have been applied to optimize pumping schedules of WSSs (Adamowski *et al.* 2012). They include stochastic process models utilizing moving average, exponential smoothing, univariate time-series analysis, or autoregressive integrated moving average (ARIMA). Models utilizing time-series regression, fuzzy logic technique, and artificial neural networks (ANN) also have been applied to forecast water demands. Among them, ARIMA models have been widely applied especially for short-term water demand forecasting (Maity *et al.* 2010; Wong *et al.* 2010). However, it often produces large errors especially when there is a drastic change in water demand. Recently, a hybrid model which is a combination of two or three different modelling techniques has been used for more accurate water demand forecasting (Caiado 2009).

An optimization of pumping schedule has been addressed mainly in the operation research field. A variety of optimization methods to reduce the energy cost of a pumping system have been reported in the literature. Błaszczyk *et al.* (2012) presented the optimal pump scheduling for a large-scale water distribution system by applying linear programming. Integer programming (IP) was also applied by Kim *et al.* (2007) to optimize the operating schedule of the pumping system in the Seoul Metropolitan area. They used a multiple regression model to forecast hourly water demands. Bragalli *et al.* (2012) proposed a method to design optimal distribution reservoirs and their operation using non-linear programming. Genetic algorithm also has been applied for minimization of pumping cost through intermittent water pumping in a WSS (Wang *et al.* 2013). For WSSs that are located where different electricity rates are applied depending on the time when electricity is used, optimal pumping schedule may bring them with more significant saving in operational cost.

In this study, we optimized the pumping schedule for a WSS in Polonnaruwa, Sri Lanka. Specifically, the pump operation for distributing drinking water in Gallella region, Polonnaruwa was optimized. In the region, drinking water is supplied via an elevated water reservoir tower; water is pumped from a local water treatment plant (WTP) to the water tower and is distributed to consumers by gravity. Therefore, it was tried to fully take advantage of the water reservoir tower. For this purpose, an IP was formulated, based on a model forecasting hourly water demands for the next day. To predict the hourly water demands for the next day, an ARIMA model was formulated. In addition, errors from the ARIMA model were compensated by the exponential smoothing technique. Electricity costs for the pumping system before and after the application of the optimization program were compared.

## MATERIAL AND METHODS

### Study area

This study was performed with a WSS in the Gallella region, Polonnaruwa, Sri Lanka. The region is located at 7 ° 56′N 81 ° 0′E, and the average elevation is 35 m (GeoView Info 2014). In the Gallella area, approximately 450 m^{3} d^{−1} water is supplied. An average occupancy of the region is 2.2 per household, and per capita water consumption is estimated at 130 L (Ravihansa 2011). The population of the area is approximately 3,000.

The WSS in Gallella has a pumping station and an elevated water reservoir tower. Figure 1 depicts a schematic diagram of the WSS and the Gallella water tower in the study area. The water tower can hold water up to 1,000 m^{3}. The pumping system can supply 150 m^{3} h^{−1} water for the tower. For obtaining hourly water demand data, a flow meter was installed at the outlet of the elevated water tower. In addition, a level meter was installed to monitor the hourly volume of water stored in the tower. The outgoing flow rate and water level data are transferred to a local supervisory control and data acquisition (SCADA) system once every hour, where the data are used to predict hourly water demands for the next day and to optimize the pumping schedule.

### Water demand forecasting

*α*was set at 0.9 to more rapidly respond to the current error between model prediction and real data (Gardner 2006). Water usage data from October 2013 to March 2014 were used in the development of the forecasting model.

### Setting-up of optimization problem

In this section, we formulate the optimization program to reduce the electricity cost for the pumping system of the study area. Equations (2)–(4) show the objective function and constraints of the optimization problem. Since the pumping system is operated only by the on/off control scheme, the binary IP optimization technique is applied (Bagirov *et al.* 2013).

#### Binary IP program

*t*is time interval,

*c*is the electricity cost for the time step

_{t}*t, x*is the binary variable to determine pump operation state (

_{t}*x*= 0 or 1),

_{t}*V*is the volume of water for the time step

_{t}*t, V*

_{min}is the minimum volume of water tower (i.e., 100 m

^{3}), and

*V*

_{max}is the maximum volume of water tower (i.e., 900 m

^{3}).

The WTP is supplied with electricity by the Sri Lanka Electric Power Corporation, and the electricity price varies depending on the time when electricity is used, as shown in Table 1.

Hour . | Electricity cost (Sri Lanka $ kW^{−1})
. |
---|---|

5am to 6pm | 11.3 |

6pm to 10pm | 21 |

10pm to 5am | 7 |

Hour . | Electricity cost (Sri Lanka $ kW^{−1})
. |
---|---|

5am to 6pm | 11.3 |

6pm to 10pm | 21 |

10pm to 5am | 7 |

*is the amount of water pumped into the water tower for the time step*

_{t}*t*(pumping flow: 150 m

^{3}h

^{−1}), and Out

*is the amount of water flowing out from the water tower for the time step*

_{t}*t*.

### Procedure to apply optimization scheme

Figure 2 describes how the proposed optimization scheme is applied. Using the hourly outgoing flow rate data collected from the water tower, the hourly water demands for the next day in the region were forecasted using the combined model of the ARIMA and exponential smoothing. The pumping schedule for the next day was then determined using the binary IP. Finally, the pump was turned on or off by the SCADA system following the schedule provided by the optimization scheme.

## RESULTS AND DISCUSSION

### Water demand forecasting using ARIMA and exponential smoothing

Since the study area is a typical rural one, the water demand pattern of the area was monotonous. Therefore, only the ARIMA model was initially chosen to forecast short-term future water demands. The model parameters, that is, *p*, *d*, and *q* were manually determined; the values of *p*, *d*, and *q* were 1, 1, and 2, respectively. In general, the model could well predict the hourly water demands for the next day of the region (Figure 3(a)). However, the model showed relatively large errors when the water demands were low (circles in Figure 3(a)). These mismatches are due to the drastic changes in water demand and have also been reported by others (Zhang 2003; Ömer Faruk 2010; Khashei & Bijari 2011). In this study, therefore, the mismatches in water demand forecasting made by the ARIMA model were compensated by the exponential smoothing technique.

The combined model turned out to be more accurate than the ARIMA-alone model (Figure 3(b)). The mismatches, especially, which were observed when only the ARIMA model was applied could not be observed; especially when water demands were low. The forecasting performance of the proposed model was compared with that of the ARIMA-alone model by calculating correlation between the predicted water demands and the observed ones for 280 h (Table 2). The average error between the observed water demand and forecasting made by the combined model was only 6%, while the one made by ARIMA was as much as 24%. This result clearly shows that difference that is generated by the ARIMA model can be compensated by the exponential smoothing method. Other statistical indexes presented in Table 2 also show that the combined model is superior over the ARIMA-alone model. In particular, the Nash Sutcliffe efficiency index (*E*; Nash & Sutcliffe 1970), which is another tool to assess the goodness-of-fit of a model, was evaluated.

Accuracy index . | ARIMA . | ARIMA + exponential smoothing . |
---|---|---|

R^{2} | 0.83 | 0.90 |

r | 0.91 | 0.95 |

E | 0.80 | 0.88 |

RMSE | 6.21 | 5.26 |

Accuracy index . | ARIMA . | ARIMA + exponential smoothing . |
---|---|---|

R^{2} | 0.83 | 0.90 |

r | 0.91 | 0.95 |

E | 0.80 | 0.88 |

RMSE | 6.21 | 5.26 |

*R*^{2}, coefficient of determination; *r*, correlation coefficient; *E*, Nash Sutcliffe efficiency index; RMSE, root mean square error.

### Application of binary IP to optimize pumping schedule

After the model predicting hourly water demands for the next day was developed, the binary IP was applied to optimize the schedule of the pumping system. The objective of the binary IP was to minimize energy cost associated with the water pumping. Water demand for the next day was predicted using the combined model at 20:00 each day based on the hourly water flow rates measured by the meter for the past eight days. The optimization program was then run to determine the pumping schedule for the next day.

In this optimization problem, the operation running space of the water tower was considered as a constraint; running space was set between 15 and 90%.

To implement the proposed IP-based optimization scheme, the SCADA system was modified as shown in Figure 4; the pump optimization based on the water demand forecasting was included as a module in the SCADA system of the WTP.

The optimization module for pumping schedule provided in Figure 4 consists of four components: (a) hourly water demand measured by the meter (dot symbol), and hourly water demand forecasted by the model in the previous day (line), (b) hourly flow rate of water pumped into the water tower, (c) hourly measured water level of the tower, and (d) daily pumping schedule set by the optimization scheme.

Since the volume of the water tower is much larger than the daily water demand of the area, two operation modes were applied; in the first mode, it was assumed that the optimization program be operated once a day, while in the second it was assumed that the optimization be run once every other day.

Figure 5 shows hourly flow rate of pumped water and the fraction of the tower volume filled with water before and after the optimization was applied. Before the optimization was applied, the water reservoir tower was operated based on the level, which is often witnessed in developing countries; the volume fraction of the tower filled with water was maintained at 0.4 to 0.5 (Figure 5(b)). In order to maintain the water level, the water supply pump was frequently run during daytime when the electricity rate is high (Figure 5(a)).

After the optimization scheme was applied, however, the operation running space of the water tower was significantly increased. When the optimization was applied once a day, the utilized volume fraction of the tower ranged from 0.13 to 0.65 (Figure 5(d)). When the optimization was run once every other day, the fraction ranged from 0.15 to 0.9 (Figure 5(f)). From the result, the latter case utilized a larger volume of the elevated water distribution tower than the former. Regarding pump-operation hour, when the IP was run once a day, the pump was typically operated for 3–4 h at night (when the electricity rate is the lowest) to fill the tower with water to be used for the next day (Figure 5(c)). Conversely, when the IP was run once every 48 h, the pump was operated for 6 h at night on the first day, and for 1 h on the second day (Figure 5(e)). In the long run, it turned out that in the latter case more electricity could be saved.

The electricity consumed before and after the application of the pumping optimization is given along with its associated cost in Table 3. Before the optimization was applied, the pumping system was manually controlled by an operator. In short, it was found that the electricity cost associated with the pumping system under study could be reduced by about 55% when the proposed optimization scheme was applied (Table 3).

Case . | Electricity consumed (kW) . | Electricity cost (Sri Lanka $) . |
---|---|---|

Normal operation (October 2013) | 3,620 | 42,436 |

Optimized operation (December 2013) | 2,573 | 18,874 |

Case . | Electricity consumed (kW) . | Electricity cost (Sri Lanka $) . |
---|---|---|

Normal operation (October 2013) | 3,620 | 42,436 |

Optimized operation (December 2013) | 2,573 | 18,874 |

## CONCLUSION

In this paper, an IP to optimize pumping schedule of a WSS based on the hourly water demands for the next day forecasted by a combined model consisting of an ARIMA model and an error compensation routine based on exponential smoothing technique. This optimization program has been applied to a WSS in Polonnaruwa, Sri Lanka. The result showed that the optimization system could reduce the operation cost of the WSS by minimizing electricity for water pumping; electricity cost for pump operation could be reduced by 55%.

## ACKNOWLEDGEMENTS

This research was supported by the Korea Ministry of Environment as ‘The Eco-Innovation project’ (Global Top project; GT-SWS-11-02-007-8). We also appreciate two peer reviewers of our manuscript. Owing to their valuable comments, the quality of our manuscript has been improved, which is greatly appreciated.