1 Introduction

In order to reduce the water consumption in agriculture, many irrigation districts have switched from old open channels distribution systems to pressurized networks. By this modernization process higher both the conveyance efficiency and the water use efficiency at field scale are achieved. In Spain, this transformation has meant a dramatic rise of the energy consumption, which has increased from 206 kWh ha−1 in 1950 to 1,560 kWh ha−1 in 2007, while the water use efficiency has risen by 21 % over the same period (Corominas 2010). Similar trends were observed in other countries such as Australia where the modernization of water distribution systems has resulted in higher energy requirements, with estimated increased up to 163 % (Jackson et al. 2010). Nevertheless, the transformation of hydraulic infrastructures has not led farmers to obtain higher profits. On the one hand, a fourfold rise in amortization and maintenance costs was reported by Rodríguez Díaz et al. (2012b). On the other hand, the rise of the energy tariffs for irrigation about 120 % since 2008 in Spain (Rodríguez Díaz et al. 2011) has also influenced the production costs. Thus, the net electricity consumption per unit of water in the Spanish irrigation systems has grown by 10 % from 2002 to 2008 (Hardy et al. 2012). The same trends were observed in other countries such as South Africa with increases in electricity tariffs of 31 % only from 2009 to 2010 (Brazilian et al. 2011).

In order to face the high costs, farmers have replaced traditional irrigated crops, with lower water requirements, by higher value crops but more water demanding (Playán and Mateos 2006; Lecina et al. 2010). Related to this, Rodríguez Díaz et al. (2012a) estimated an increase on theoretical crop evapotranspiration (ETc) around 20 % after the transformation of an irrigation district, in Southern Spain, from surface irrigation system to pressurized irrigation system.

Methodologies to improve the energy efficiency in pressurized irrigation networks have been developed (Abadia et al. 2008; Moreno et al. 2009; Lamaddalena and Khila 2012). Likewise, the Spanish Institute for Diversification and Energy Savings (IDAE) has proposed energy saving measures suitable for irrigation districts with pressurized networks. Some of these measures consisted in network sectoring by grouping hydrants with similar energy demand and in the control of critical points, which are hydrants with higher energy requirements due to their elevation or their distance to the water source (Rocamora et al. 2008).

Carrillo Cobo et al. (2011) developed the WEBSO algorithm (Water and Energy Based Sectoring Operation) which provided monthly sectoring strategies based on the hydrants’ topological characteristics. Potential energy savings of around 9 % to 27 % in two irrigation districts were achieved by WEBSO. Jiménez Bello et al. (2010) proposed a methodology to group intakes into sectors using genetic algorithms and achieving energy savings of 36 % in the studied area. Sectoring changed the operation of the network and implied the re-organization of farmers in turns according to their energy demand.

There are fewer examples of useful methodologies to detect and control critical points. Khadra and Lamaddalena (2010) developed a decision support system to identify unsatisfied hydrants although energy saving actions in these hydrants were not considered. Related to this, Rodríguez Díaz et al. (2012b) proposed an algorithm named WECP (Water and Energy optimization by Critical Points control) which detected the critical points of a network according to their hydraulic behaviour and proposed improvements to enhance their performance. Also, Rodríguez Díaz et al. (2012b) compared the obtained results of WEBSO and WECP in two Spanish irrigation districts. The algorithm WECP obtained higher energy savings than the WEBSO (between 10 and 31 %) in both irrigation districts when theoretical irrigation requirements were considered.

However, both methodologies (WEBSO and WECP) were developed for branched networks with a single water supply point and cannot be applied to networks with multiple water sources, also common in irrigation areas. The optimization of looped water networks is more complex because the pressure head in each pumping station must be estimated simultaneously. Fernández García et al. (2013) addressed this problem and proposed a useful methodology to identify the optimum sectoring strategy for this sort of networks (WEBSOM) using the multiobjective genetic algorithm NSGA-II (Non-dominated Sorting Genetic Algorithm) (Deb et al. 2002) in the optimization process. Conversely, methodologies to detect critical points when the water is supplied from several sources have not been developed yet.

In this work, a methodology based on the control of critical points for multiple source networks is developed and applied to a real irrigation district in Southern Spain. Then, the results are compared with those obtained by Fernández García et al. (2013) when sectoring was considered as energy saving strategy.

2 Methodology

2.1 Study Area

The Palos de la Frontera (PF) irrigation district is placed in the Guadiana river basin in Southern Spain (Fernández García et al. 2013) (Fig. 1). The area is mainly flat, with elevations between 5 to 48 m. The total cropped area is 3,343 ha where strawberry accounts for nearly 75 %. Other crops in the area are citrus, fruit trees and winter vegetables. The irrigation network has three pumping stations that can provide maximum pressure heads of 85 m, 45 m and 55 m, respectively. Irrigation is organized on-demand and it is monitored by a telemetry system that records in real time information related to volumes, flows and pressures (Pérez Urrestarazu et al. 2009).

Fig. 1
figure 1

Location of Palos de la Frontera irrigation district and energy saving actions in the irrigation network

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2.2 Critical Points Detection for Multiple Source Networks

The WECP algorithm, proposed by Rodríguez Díaz et al. (2012b), was modified to cope with multiple water source networks. Thus, a new algorithm, WECPM (Water and Energy optimization by Critical Points control for Multiple supply sources), was developed. WECPM included a heuristic multiobjective optimization procedure to identify the best management of the critical points.

Genetic algorithms (GA) constitute one of the most used heuristic techniques to solve problems related to the operation and design of water distribution networks (Montesinos et al. 1999, Moradi-Jalal et al. 2004; van Dijk et al. 2008; Jamieson et al. 2007). The main stages of GA are briefly described as follows. First, a random initial population is generated. Then, all individuals of the initial population are evaluated and ranked according to their values of the objective function. Finally, selection, crossover and mutation processes are carried out until the convergence criterion or the fixed number of generations is achieved (Goldberg 1989). A typical GA minimizes or maximizes a single objective function and gives a unique optimal solution. However, to solve problems with several conflicting objectives, a multiobjective genetic algorithm (MOGA) can be used. The result of a multiobjective problem is not a single solution, but a set of optimal solutions known as Pareto optimal front (Savic 2007; Chandapillai et al. 2012; Siew and Tanyimboh 2012).

The NSGA-II has been adapted to detect critical points in multiple source networks linked to the hydraulic model EPANET (Rossman 2000) by using its dynamic link library (DLL). The optimization algorithm was developed in MATLAB (Pratap 2010).

The flow chart of WECPM is shown in Fig. 2 and its main features are described next.

Fig. 2
figure 2

Schematic representation of the critical point identification

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  • Initial Population

    Firstly, the initial population was randomly generated. In this work, individuals or chromosomes that contained n v variables corresponding to the daily pressure heads of the pumping stations during the peak demand month formed this population.

  • Objective functions

    The individuals previously generated were evaluated, that is, the values of the objective functions for each individual were calculated. The objective functions used in this work were the minimization of the daily energy consumption (Eq. 1) and the minimization of the pressure deficit (Eq. 2) considering that the network was operated on demand:

    $$ F1=E{C}_{norm} $$
    (1)
    $$ F2= Pf+ CMP{D}_{norm} $$
    (2)

    Where EC norm is the normalized daily energy consumption, Pf the pressure failure percentage and CMPD norm the normalized term that shows the magnitude of the pressure deficit.

    The calculation of the term EC norm (Eq. 1) requires the previous estimation of EC (kWh day−1), that was calculated as follows:

    $$ \mathrm{EC}=\frac{1}{1000}\kern.09em \frac{1}{\eta}\cdot \gamma \cdot {\mathrm{t}}_{\mathrm{rs}}{\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{Q}}_{\mathrm{i}}\cdot {\mathrm{H}}_{\mathrm{i}}} $$
    (3)

    Where i is the pumping stations index, N the number of pumping stations, η the global efficiency of pumps (assuming a pumping efficiency of 0.8), γ water specific weight (9,800 Nm−3), Q i the pumped flow by station i (m3s−1), H i the pressure head of pumping station i (m) and t rs the daily irrigation time (h) to satisfy crop irrigation requirements estimated as described in Allen et al. (1998).

    Regarding F2, the term Pf was determined as the ratio between the number of hydrants that did not reach the service pressure and the number of operating hydrants. In this equation, CMPD norm was derived from CMPD, calculated as the difference between the pressure in the most critical hydrant and the service pressure.

    In order to compare the values of F1 and F2, the terms EC and CMPD were normalized (EC norm and CMPD norm ) by the continuous uniform distribution U(0,1). EC norm varied from 0 to 2 while Pf and CMPD norm ranged from 0 to 1, respectively.

    The constraints of this minimization problem were the physical laws of energy and mass conservation.

    To determine the objective functions and their constraints, the hydraulic simulation of the network was carried out using EPANET, a free and widely used software in the evaluation of water distribution systems (Chandapillai et al. 2012; Siew and Tanyimboh 2012). Also, the EPANET engine can be easily integrated into external programs through its Dynamic Link Library (DLL). The required data were the network’s topology, the pressure head of the N pumping stations of every individual created by NSGA-II and the hydrant base demand (Carrillo Cobo et al. 2011). The flows supplied by each pumping station and the pressures at every hydrant were obtained from the hydraulic simulator.

  • Selection, crossover- mutation, recombination

    The processes of selection, crossover- mutation and recombination were performed as described in Deb et al. (2002) for a number of generations (GEN) fixed at the beginning of the process.

  • Critical point detection

    The optimization process finished providing the set of individuals (Pareto front) whose hydrants worked at least with the service pressure and their energy consumptions were the lowest. Among the individuals in the Pareto front, the most frequent critical hydrant was identified and then, the individual that having that hydrant as critical involved the minimal energy consumption was selected. This individual contained information of the optimal pressure heads of the N pumping stations and, as result of the hydraulic simulation, the energy consumption during the maximum demand month and the pressure in the most limiting hydrant (critical point or hydrant with the lowest pressure).

    From these results, the weighted pressure head provided by the set of pumping stations when hydrant j was the most critical, H w-j , was determined by the following equation:

    $$ {\mathrm{H}}_{\mathrm{w}\hbox{-} \mathrm{j}}=\frac{{\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{Q}}_{\mathrm{i}}\cdot {\mathrm{H}}_{\mathrm{i}}}}{{\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{Q}}_{\mathrm{i}}}} $$
    (4)

    Once the first critical point was detected, all the optimization process described above was carried out again. However, in this case, the detected critical point was considered closed and its base demand was set to zero. Thus, a second critical point and its weighted pressure head were obtained. This process continued until the differences in energy consumption in several consecutive critical hydrants was negligible. Then all critical points were identified and their weighted pressure heads were calculated.

    Finally, a dimensionless coordinate (h ∗ j ) associated to each critical hydrant, was defined to characterize its hydraulic behaviour and was calculated as follows:

    $$ {h}_j^{\ast }=\frac{H_{w-j}}{H_{w- mch}} $$
    (5)

    Where H w-mch is the weighted pressure head of the first detected critical point (run 1). Thus, the maximum value of h ∗ j was 1 for the first detected critical point and it was gradually reduced for the following critical hydrants. In the end, all hydrants were ranked according to this criterion. Hydrants with highest h ∗ j were selected (critical points) and improvement measures to reduce their energy demand were proposed.

2.3 Sectoring Strategy for Multiple Source Networks

To optimize the energy demand, Fernández García et al. (2013) developed a methodology based on multiple sources networks sectoring (WEBSOM). The sector configuration was performed by grouping hydrants according to the network’s topology. Thus, two dimensionless coordinates, z ∗ j , related to the hydrant elevation, and l ∗ j , related to the distance between the source nodes and demand nodes, were proposed for every hydrant:

$$ {\mathrm{z}}_{\mathrm{j}}^{\ast }=\frac{{\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\mathrm{z}}_{\mathrm{j}}-{\mathrm{z}}_{\mathrm{i}}}{\left|{\mathrm{z}}_{\mathrm{j}}-{\mathrm{z}}_{\mathrm{i}}\right| \max }}}{\mathrm{N}} $$
(6)
$$ {\mathrm{l}}_{\mathrm{j}}^{\ast }=\frac{{\displaystyle {\sum}_{\mathrm{i}=1}^{\mathrm{N}}\frac{{\mathrm{l}}_{\mathrm{j}\hbox{-} \mathrm{i}}}{{\mathrm{l}}_{\max -\mathrm{i}}}}}{\mathrm{N}} $$
(7)

Where z j is the hydrant j elevation, z i is the pumping station i elevation and |z j -z i | max is the maximum elevation difference between each hydrant and the pumping station i (absolute value). l j-i is the distance between the hydrant j and the pumping station i, determined by the Dijkstra’s graph search algorithm (Dijkstra 1959) and l max-i is the distance between the furthest hydrant and the pumping station i.

Once the possible sectors were determined, the monthly optimal sectoring operation calendar for irrigation networks with several supply points that required the minimum energy consumption could be identified. The optimal network operation was established using a procedure based on NSGA-II.

2.4 Selection of Best Energy Saving Strategy

After the detection of the critical points and assuming that the network improvement strategies to reduce their energy demand were implemented, WECPM was run for every month of the irrigation season and the potential annual energy savings were compared with those achieved by WEBSOM. Thus, both methodologies’ results were compared and the best energy saving strategy could be selected.

3 Results and Discussion

3.1 Irrigation Water Demand

The WECPM was applied to the PF irrigation network for the peak water demand month (May) assuming that the irrigation requirements were fully satisfied. As shown in Table 1, the peak crop water requirements occurred in May (4.1 mm day−1), while January and December were the lowest water demanding months (0.7 mm day−1). Thus, the maximum daily irrigation time required per month, which directly affects the energy consumption, was 9.5 h in May.

Table 1 Monthly crop water requirements, IN, irrigated area, IA and daily irrigation time required per month, t rs
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3.2 Critical Points Detection

Three decision variables (n v  = 3) were contained in each individual since this irrigation district has three pumping stations. The minimum values of pressure head at each pumping station were 55, 50 and 45 m while the maximum values were 95, 65 and 55 m, respectively. Concerning the NSGA-II parameters, 100 individuals and 50 generations were considered in each run. The crossover probability was 0.9 and the mutation probability 0.1 (Deb et al. 2002).

Figure 3 represents the Pareto Front obtained in the first run when all hydrants were open. The minimum value of F1 was 0.52 that implies an energy consumption of 623.2 MWh. However, this value was associated to the maximum value of F2, 0.46, which indicated that 13 hydrants did not get the pressure service and the pressure in the most critical hydrant was only 18 m. In contrast, the maximum value of F1 was 0.62 (energy consumption of 744.6 MWh) corresponding to the minimum value of F2 (0). This value is related to an individual that ensured the service pressure in all hydrants. From this set of solutions, we selected the individual with F2 equal to 0. In this run, the detected critical point was hydrant 167. In order to identify the next critical point, hydrant 167 was removed and a second run was performed. Thus, in every run a new critical point was sequentially detected and removed (hydrant 428 was eliminated after the second run) and while the critical points were eliminated, the network’s pressure requirements were progressively reduced.

Fig. 3
figure 3

Pareto Front of the first run when all hydrants are considered open

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Table 2 summarizes the WECPM’s outputs for 20 consecutive runs: 20 critical points, which are ranked according to their weighted pressure head. This table also shows the corresponding pressure heads for the three pumping stations when each critical hydrant was open, the pressure in each critical hydrant, the daily pumped flow, the energy consumption and the energy consumption per unit of supplied water in each run.

Table 2 Critical hydrants, optimal pressure heads of the pumping stations H i , weighted pressure head H w-j , pressure P in the critical hydrants, pumped flow ∑Q i , energy consumption EC and energy consumption per unit of irrigation water supplied E w
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As critical points were removed from the analysis, the pumped flow was progressively reduced. Thus, to obviate the effect of the reduction in pumped flow on the decrease of energy consumption, the energy consumption per unit of supplied water was evaluated. The weighted pressure head was reduced in the consecutive runs as well as the energy consumption and the energy consumption per unit of irrigation water supplied. However, after run 8 (hydrant 155), H w-j was reasonably constant because the following critical points had similar pressure requirements. Considering the first 8 runs, H w-j was reduced from 62.8 to 52.6 m after disabling 7 critical points, which were responsible of 20 % of the energy consumption (4,794 kWh day−1). Likewise, the unit energy demand (kWh m−3) diminished from 0.21 to 0.17 when these critical hydrants were not operating.

After obtaining the H w-j for all the critical hydrants, the hydraulic dimensionless coordinate h ∗ j was calculated and plotted against both topological coordinates, z ∗ j and l ∗ j (Fig. 4). The seven detected critical points had h ∗ j values over 0.85. The two first critical hydrants (167 and 428) show low values of z ∗ j (negative values denote that the point is below the pumping stations) and medium values of l ∗ j (this indicates that the hydrants are located at an intermediate distance from the water sources). Therefore, the high values of h ∗ j are due to the existence of undersized pipes. The other critical points (99, 156, 133, 115 and 38) show high values of z ∗ j , hence these hydrants were located in the highest areas.

Fig. 4
figure 4

Dimensionless coordinates z ∗ j , l ∗ j  and h ∗ j of the critical points detected and comparison for the first seven critical hydrants before and after the proposed measures

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3.3 Improvement Actions

After analyzing the hydraulic and topological coordinates, several energy saving actions were proposed for every critical point in order to improve the network operation (Fig. 1). These measures implied changes in pipe sizes when z ∗ j was low and the installation of booster pumps for the hydrants with the highest elevations. These measures were sequentially applied in order to analize their potential impacts in the network operation. Figure 1 details the improvement actions and shows their location.

3.4 Potential Energy Savings after the Improvement Actions

To estimate the potential energy savings after the improvement actions, the new optimal pressure heads at pumping stations were recalculated using a new network’s model which included all these changes. Then, following a similar approach, the new critical points for the improved network were detected (Fig. 4). These changes affected to the coordinate h ∗ j but did not modify z ∗ j and l ∗ j , which depend on the network’s topology only.

Hydrants 167 and 38 were not identified as critical points after the improvement actions and hydrants 98 and 213, which were not in the original list, appeared in the new set of the 7 most critical hydrants. In fact, after the introduction of the four first energy saving actions, hydrant 98 (which was not in the initial list of critical points) was detected as critical point and an improvement measure was designed for this hydrant. Furthermore, the values of coordinate h ∗ j after the measures were significantly higher than before the changes and the difference between the first and the seventh critical point was smaller. This increase in h ∗ j was related to the decrease of H w-mch , which was now much closer to the H w-j values.

In order to estimate the monthly and annual energy savings achieved if these measures were adopted, a similar analysis was carried out for all the months of the irrigation season. Thus, the monthly energy requirements were included in the WECPM model and a new set of optimal pressure heads for the three pumping stations (those with the minimum value of F1 and F2 = 0) was obtained for every month. Pumping pressure heads before and after the improvement actions are shown in Table 3.

Table 3 Optimal pressure heads (m) of the three pumping stations and weighted pressure head (m) obtained with WECPM, before and after the proposed actions
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In all months, H w-j decreased after the improvement actions. The average value of H w-j was reduced from 58 to 52 m whereas the peak value of H w-j , obtained in September, decreased from 64 to 54 m. Although May is the peak demand month, September has the largest irrigated area because most of the crops coincides in the field (Table 1). It should be noted that the simultaneous operation of all hydrants, each one supplying the volume of water required to irrigate its associated area, was considered in this work. Thus, the H w-j values were very similar in the peak demand months because more crops are simultaneously in the field. However, the daily volume of pumped water was higher in May than in other peak demand months since more irrigation time was needed (Table 1). Because of this, the control of critical points is the most appropriate management measure for the highest water demand months (related to both irrigated area and irrigation requirements). In this case, months with higher H w-j (April, May, June and September) were associated to the largest irrigated area as well as irrigation needs (Table 1). Moreover, the control of critical points resulted more effective in these months because the decrease in H w-j after the actions was more significant. The minimum value of H w-j occured on July with 50 m and 48 m before and after the actions, respectively (only 16 % of irrigated area).

The annual energy consumptions obtained when the improvements actions were sequentially introduced are shown in Fig. 5. Thus, the relation between the number of improvement actions and energy savings was obtained. The three first actions entailed almost 60 % of the energy savings achieved when all measures were introduced. Hence, managers of irrigation districts can decide the number of actions to be applied taking into account the energy saving versus the investment cost linked to each of them.

Fig. 5
figure 5

Annual energy consumption after the sequential introduction of the energy saving actions

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3.5 WEBSOM vs. WECPM

Table 4 shows the monthly energy consumptions obtained when WEBSOM and WECPM strategies were adopted and compared with the monthly energy demand required for the current operation of the network. WECPM with improvement actions achieved lower energy requirements than WEBSOM in all months. In contrast to the current operation of the network, anual energy savings of 1195.4 MWh (29 %) and 1483.7 MWh (36 %) were obtained when WEBSOM and WECPM were considered, respectively. Therefore, WECPM with actions was more effective than WEBSOM in the PF irrigation district which has a flat topography with 43 m as maximum difference between hydrant elevations. Using the strategy of critical point control Rodríguez Díaz et al. (2012b) also achieved higher energy savings than with sectoring in irrigation districts with flat topography (the maximum elevation difference among hydrants was 45.6 m). Assuming the WECPM with actions, the peak energy demand month was May with an energy consumption of 640.8 MWh while the lowest energy demand occurred in July (20.3 MWh).

Table 4 Monthly energy consumption (MWh) required for the current operation of the network, after sectoring and after WECPM with and without improvement actions
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Comparing the potential energy savings of WECPM without actions versus the current operation of the network, the annual energy saving was the 28 % (1137.1 MWh). Moreover, this strategy achieved lower energy requirements than WEBSOM in some months (January, February, April, July, August) and the annual energy consumption was only 2 % higher than the obtained by WEBSOM. Additionally, the sectoring strategy implies irrigation in turns while WECPM with and without actions allows on demand irrigation. The annual energy demand optimized by WEBSOM is 10 % higher than the value obtained by WECPM with actions. A cost/benefit analysis is required before selecting the best management option for any irrigation network according to its particular conditions (e.g. availability of telecontrol systems and only its set up would be required). The investment cost of the improvement actions (e.g. pipe replacement) must be compensated with the economical value of the energy savings.

4 Conclusions

A useful methodology to detect and control critical points for multiple source networks has been proposed. This methodology is based on the algorithm WECPM, which uses the NSGA-II genetic algorithm along with a hydraulic simulation model.

The analysis of WECPM on a real irrigation network has provided a potential annual energy saving of 36 % in relation with the current operation of the network, if minor improvement measures, such as the replacement of two pipes and the installation of four booster pumps, were adopted. Even without improvement actions, WECPM could reduce 12 % of the energy consumption of the current network operation.

The strategy of controlling critical points has been compared with sectoring. The energy savings were 10 % higher compared to the results obtained by WEBSOM.

A cost/benefit analysis is required before selecting the best energy saving strategy for any irrigation network according to its particular conditions (e.g. topography, availability of telecontrol systems). Furthermore, farmers’ management preferences should also be considered. The adoption of a sectoring strategy implies the organization of the farmers in turns, losing one degree of flexibility while the control of critical points allows farmers to irrigate on demand. In contrast to sectoring, the critical points control strategy involves investment costs to perform the proposed energy saving actions. The incorporation of the energy tariff to these algorithms would help to determine which methodology achieves higher economic savings for each particular network, that is the main target for farmers and it is not always linked to the reductions in energy consumption.