**4.1. Optimization of the pumps' schedule in the Fátima system**

The drinking system of Fátima is composed of 22 water sources, 10 treatment plants, 36 pump-stations and 64 tanks. The water is distributed to the consumers through 1111 km by a supply and distribution network system. Nowadays, the system is managed by the com‐ pany Veolia – Águas de Ourém, which is responsible for the catchment, water treatment and distribution (Figure 7).

**Figure 7.** Drinking system of Cascalheira's tank

The supply system chosen for this case study supplies the tank Fazarga with an elevation of 402 m. This tank is responsible for the service to the demands of the region of Fátima and other close locations. This supply system has a pump station (PS) located in the proximi‐ ties of the tank Cascalheira (elevation: 375 m). This last one is supplied by EPAL (Portu‐ guese Lisbon Water Company) and provides water, by gravity, to the locations of Aljustrel and Fontainhas.


In the ANN code running, the process of training and simulation for each system character‐ istic is analysed. In the training mode is introduced the configuration parameters. Those pa‐ rameters are standard limits (max and min), number of neurons on the hidden layer, limit number of epochs, final error desired, validation rate and activation function used in the hidden layer. With the best ANN configuration for each possible hybrid system and new da‐ ta set for inputs, a validation process is made and the results are verified in terms of correla‐

The drinking system of Fátima is composed of 22 water sources, 10 treatment plants, 36 pump-stations and 64 tanks. The water is distributed to the consumers through 1111 km by a supply and distribution network system. Nowadays, the system is managed by the com‐ pany Veolia – Águas de Ourém, which is responsible for the catchment, water treatment and

The supply system chosen for this case study supplies the tank Fazarga with an elevation of 402 m. This tank is responsible for the service to the demands of the region of Fátima and other close locations. This supply system has a pump station (PS) located in the proximi‐

tion and relative error among the values of CES base model and the ANN.

**4.1. Optimization of the pumps' schedule in the Fátima system**

**Table 4.** Input data set for the best economic configuration used in ANN.

90 Water Supply System Analysis - Selected Topics

**4. Case studies**

distribution (Figure 7).

**Figure 7.** Drinking system of Cascalheira's tank

According to former description, the water storage of the tank Cascalheira is done by EPAL. The cost attributed to Veolia by this supply is related only to the effluent volume from this tank and it is not dependent of any alteration in the operation of the pump-station between tanks of Cascalheira and Fazarga. The reduction of this cost would only be possible with the implementation of water loss control by leakage. The level of the tank Cascalheira is always maintained close to the maximum limit in a way that it increases the reliability of the sys‐ tem. Thus, in the optimization model, it was chosen to consider only the variation of the lev‐ el of the tank Fazarga at downstream of the pump-station.

The tank of Cascalheira has the storage capacity of 4000 m³ of water, whereas Fazarga has a total volume of 347 m³ and operates with the initial, minimum and maximum levels of 2.0 m, 0.3 m and 2.3 m, respectively. The pump-station comprises two pumps of Grundfos NK65-250 type which work for an average flow of 42 1/s with an efficiency of 65%.

The average time variation of the consumption in the region of Fátima during the day was obtained from the sensors located at the exit of the tank Fazarga. The period analyzed was from March to September, 2007. The water consumption in this year is more noticeable for comprising spring and summer. Figure 8 presents the average time variation calculated.

The hours with the pump working are considered as regular and discrete intervals by the optimization algorithm. Thus, for this case study, a day in which the pumps remained switched-on, in intervals similar to the format considered in the optimization model, were chosen. The hydraulic model of the system was built, in which the tanks Cascalheira and Fa‐ zarga were considered as reservoir and storage tank, respectively.

The variation in the level of the tank of Fazarga during the day calculated by the hydraul‐ ic simulator was similar to the real values. The maximum number of pump start-ups (Na max) used by Veolia was three (pump 1) and the level of the tank at the end of the opera‐ tional time is very close to the initial one (Figure 9). The variation of the energy rate is presented in Table 5.


**Table 5.** Hour vs Energy Tariff (€/kWh) for Fátima system

Both GA models presented in this analysis were implemented to determine the best opera‐ tional strategy with a reduced energy cost in the system Cascalheira/Fazarga. Figure 10 presents the evolution of the objective function with the computational time, in minutes.

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It is possible to evaluate the efficiency of the HGA model. Only with the feasible solutions obtained with 20 generations, from the repair algorithms and from the specialized local search system, it is possible to find a local optimal solution in about 5 minutes, whereas the SGA took a little more than 33 minutes to find a good solution, with also a bit higher energy cost when compared to the solution found by the HGA. The difficulty for GA to find a good feasible solution can quickly be confirmed. Such behaviour occurs due to the high level of randomness existent in GA models. The alterations of the solutions provided by the genetic operators diversify the type of answer without a guarantee of the evolution in each genera‐ tion. Among all possible solutions, the probability of extracting, for each pump, a solution with at most three start-ups is 0.0173. Now, it is possible to confirm the difficulty of obtain‐ ing a feasible solution, because besides the determination of a solution it is necessary the other constraints (pressure limits, water levels in tanks and power pumps start-ups) be satisfied. These constraints are dependent on the complexity of the drinking system to be evaluated.

The energy cost due to the operation was 22.22 euros (date: 07 (day)/12 (month)/07 (year)). The pumps remained switched-on during 12 hours. A period of two hours (13h and 22h) be‐ longs to the period with the most expensive energy tariff (Figure 11). The variation in the

**Figure 10.** Convergence of the fitness functions

**Figure 8.** Pattern demand of Fátima system

**Figure 9.** Control pump strategy

Both GA models presented in this analysis were implemented to determine the best opera‐ tional strategy with a reduced energy cost in the system Cascalheira/Fazarga. Figure 10 presents the evolution of the objective function with the computational time, in minutes.

**Figure 10.** Convergence of the fitness functions

**Figure 8.** Pattern demand of Fátima system

92 Water Supply System Analysis - Selected Topics

**Figure 9.** Control pump strategy

It is possible to evaluate the efficiency of the HGA model. Only with the feasible solutions obtained with 20 generations, from the repair algorithms and from the specialized local search system, it is possible to find a local optimal solution in about 5 minutes, whereas the SGA took a little more than 33 minutes to find a good solution, with also a bit higher energy cost when compared to the solution found by the HGA. The difficulty for GA to find a good feasible solution can quickly be confirmed. Such behaviour occurs due to the high level of randomness existent in GA models. The alterations of the solutions provided by the genetic operators diversify the type of answer without a guarantee of the evolution in each genera‐ tion. Among all possible solutions, the probability of extracting, for each pump, a solution with at most three start-ups is 0.0173. Now, it is possible to confirm the difficulty of obtain‐ ing a feasible solution, because besides the determination of a solution it is necessary the other constraints (pressure limits, water levels in tanks and power pumps start-ups) be satisfied. These constraints are dependent on the complexity of the drinking system to be evaluated.

The energy cost due to the operation was 22.22 euros (date: 07 (day)/12 (month)/07 (year)). The pumps remained switched-on during 12 hours. A period of two hours (13h and 22h) be‐ longs to the period with the most expensive energy tariff (Figure 11). The variation in the reservoir level is the main factor in the decision making the operation and the variation of the energy tariff is the second reason.

depend on the water company priorities, economic and social impacts, and performance or

Energy Efficiency in Water Supply Systems: GA for Pump Schedule Optimization and ANN for Hybrid Energy Prediction

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Real Water Level Water Level (EPANET-HGA)

Espite is located in Ourém and it is a small system that distributes water to Couções and Arneiros do Carvalhal villages and the average flow in this pipe system is approximately 7 l/s. This system is hydraulically analysed to determine the best hydro solution. Then ANN is applied to establish the best economical hybrid solution, employing the same data set used to developed ANN model. A simplified scheme of Espite water drinking system is present‐

> Demand point Carvalhal 1

Node 3 Node 4

Demand point

Turbine

Carvalhal 2 Demand point

Tank Carvalhal

Node 5 Node 6

Pump Carvalhal 1

Pump Carvalhal 2

Couções

Tank Couções

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feasibility factors.

0

ed in Figure 13.

Reservoir 01

Pump R01

**Figure 12.** Water level of Fazarga tank

Tank ASJ

**Figure 13.** Scheme of Espite water distribution system

Pump R02

Node 1

Reservoir 02

Node 2

**4.2. Prediction of hybrid energy solutions in Espite system**

0,3

0,6

0,9

1,2

Water Level (m)

1,5

1,8

2,1

2,4

The best solution obtained by HGA, in each iteration step, is selected from a set of solutions containing only individuals hydraulically feasible. The objective function for this case is the total energy cost. For SGA while the model does not find a feasible solution, the objective function starts to be the sum between the energy cost and the penalty function. The opera‐ tional strategy found by the HGA and the variations of the water level in the Fazarga tank for the real situation and the solution with reduced energy cost are shown at Figures 11 and 12. From Figures 9, 11 and 12 it is possible to make a comparison between the operational strategies presently adopted by the water manager company and the one obtained by HGA optimization model. The variation of the energy tariff was well explored in the solution with an important reduction of the energy cost (HGA). It is possible to observe a significant dif‐ ference from the strategies, being noticeable that the pumps do not work in hours with ener‐ gy tariff more expensive. With the implementation of the optimization model an economy of 31% was achieved for the period chosen for the analysis.

**Figure 11.** Control pump strategy (HGA).

In operational terms, the strategy obtained from the HGA can be considered more daring. In the critical time (1:00 p.m.) the level of the tank in the present operation by the water company achieved values superior to 1m. However based on former mentioned, the mini‐ mum water level in the Fazarga tank is 0.30m. In case of desirable an economic solution with higher levels in the tanks, it is easy to increase the minimum limit of the water level in the constraints of the HGA developed model. The importance between the minimum water level attained in the tank and the energy costs to be paid by the water company will depend on the water company priorities, economic and social impacts, and performance or feasibility factors.

**Figure 12.** Water level of Fazarga tank

reservoir level is the main factor in the decision making the operation and the variation of

The best solution obtained by HGA, in each iteration step, is selected from a set of solutions containing only individuals hydraulically feasible. The objective function for this case is the total energy cost. For SGA while the model does not find a feasible solution, the objective function starts to be the sum between the energy cost and the penalty function. The opera‐ tional strategy found by the HGA and the variations of the water level in the Fazarga tank for the real situation and the solution with reduced energy cost are shown at Figures 11 and 12. From Figures 9, 11 and 12 it is possible to make a comparison between the operational strategies presently adopted by the water manager company and the one obtained by HGA optimization model. The variation of the energy tariff was well explored in the solution with an important reduction of the energy cost (HGA). It is possible to observe a significant dif‐ ference from the strategies, being noticeable that the pumps do not work in hours with ener‐ gy tariff more expensive. With the implementation of the optimization model an economy of

In operational terms, the strategy obtained from the HGA can be considered more daring. In the critical time (1:00 p.m.) the level of the tank in the present operation by the water company achieved values superior to 1m. However based on former mentioned, the mini‐ mum water level in the Fazarga tank is 0.30m. In case of desirable an economic solution with higher levels in the tanks, it is easy to increase the minimum limit of the water level in the constraints of the HGA developed model. The importance between the minimum water level attained in the tank and the energy costs to be paid by the water company will

the energy tariff is the second reason.

94 Water Supply System Analysis - Selected Topics

**Figure 11.** Control pump strategy (HGA).

31% was achieved for the period chosen for the analysis.
