biosystems engineering 102 (2009) 95105

Available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/issn/15375110

Research Paper: SWdSoil and Water

Development of a new methodology to obtain the

characteristic pump curves that minimize the
total cost at pumping stations
M.A. Moreno*, P. Planells, J.I. Corcoles, J.M Tarjuelo, P.A. Carrion
Centro Regional de Estudios del Agua, Castilla-La Mancha University, 02071 Albacete, Spain

article info
In this paper, a new methodology to obtain the optimal characteristic and efficiency curves
Article history:

(QH and Qh) at pumping stations is presented. The design flow, the design pressure head,

Received 25 February 2008

and the discharge distribution throughout the irrigation season are the three main

Received in revised form

parameters to design pumping stations. The purpose of this study is to develop a decision

6 August 2008

support tool to obtain the theoretical characteristic and efficiency curves of the pumps, the

Accepted 29 September 2008

number of pumps, and the number of frequency speed drives that minimize the total cost

Available online 28 November 2008

(investment and operation costs) for a specific pumping station demand (design flow,
pressure head, and frequency of the discharges). The results obtained in this paper make
evident that the optimal shape (slope) of the QH curve varies depending on the discharge
distribution throughout the irrigation season, mainly when there are few pumps installed
at the pumping station. When there is a high frequency of low discharges, the desired slope
of the QH curve is higher. In cases when the discharge distribution is unknown, increasing
the number of pumps ensures high energy efficiency. When installing a pump with an
optimal characteristic curve, it is not necessary to increase the number of frequency speed
drives.
2008 IAgrE. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

The design of a collective pressurized on-demand irrigation

network can be summarized in five stages (Labye et al., 1988):
optimum network layout in order to minimize the total cost of
the network (Bhave and Lam, 1983; Awumah et al., 1989;
Granados, 1990); calculation of the hydrant discharge
according to plot sizes (Planells et al., 2001); determination of
design flow per pipeline (associated with a determined supply
guarantee) (Clement and Galand, 1979; Pulido-Calvo et al.,
2003a; Moreno et al., 2007a); calculation of the optimum pipe
size diameters, minimizing the investment and energy cost
(Labye et al., 1988; Lansey and Mays, 1989; Perez et al., 1996;

DIOPRAM, 2003); and analysis of the network performance

under different operating conditions (Aliod et al., 1997; Rossman, 1997) to determine the possible supply failure situations
of the network or of the pumping plant (Lamaddalena and
Sagardoy, 2000).
One of the main problems in the design of water distribution networks is obtaining the type of pump that best fits the
water demand under specific pressure head requirements.
Different algorithms for minimizing the total cost of pumping
stations (investment and operation costs) have been developed (Moradi-Jalal et al., 2003; Pulido-Calvo et al., 2003a;
Moradi-Jalal et al., 2004; Planells et al., 2005). These algorithms
consider characteristic curves of existing pumps. However,

* Corresponding author.
E-mail address: miguelangel.moreno@uclm.es (M.A. Moreno).
1537-5110/$ see front matter 2008 IAgrE. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.biosystemseng.2008.09.024

96

biosystems engineering 102 (2009) 95105

Nomenclature
CRF
fi
Hd
hi
Hi
hj
hmax
n
Nabs
PLC
Qd
Qi
Qmax
r
RDDC
t
a

capital recovery factor ()

frequency of the discharge Qi (fraction)
design pressure head (m)
average pumping station efficiency for each
flow Qi (%)
pressure head (m)
efficiency of the pump j that supplies a flow Qj
(%)
maximum efficiency of the pump (%)
number of pumps of the pumping station ()
average absorbed power (kW)
programmable logic controller ()
design discharge (m3 s1)
average flow for the flow interval i (m3 s1)
maximum discharge of the pump (m3 s1)
interest rate (%)
Random Daily Demand Curve Methodology ()
useful life of the project (year)
relative speed of the pump (fraction)

none of them proposes an algorithm to obtain the desirable

types of the characteristic and efficiency curves.
Several methodologies have been developed to obtain the
design flow in each pipe of a network. The Clement methodology (Clement, 1966) is the most commonly used model
because it is easy to implement. Recent studies have shown
that this methodology does not fit properly with the real
network behaviour. Thus, a new methodology, named
Random Daily Demand Curves (RDDC) Method, was developed
to obtain the flow rate in each pipe, and therefore in the main
pipe (Moreno et al., 2007a). RDDC was shown to have a better
fit with the measured data than the Clement methodology,
which underestimated the design flow by 3540% in some of
the studied networks.
The main required parameters to design pumping stations
are the design flow and the pressure head. In addition, the
discharge distribution throughout the irrigation season is an
essential parameter for carrying out a proper energy study of
pumping stations. The determination of the discharge distribution throughout the irrigation season has been the subject of
several studies, from simple soil moisture balance (Lamaddalena, 1997; Khadra, 2004) to the utilization of complex forecasting tools such as neural networks (Pulido-Calvo et al.,
2003b). Moreno et al., 2007b obtained the discharge distribution
of a pumping station by measuring the electrical parameters,
which resulted in a better approximation than other methodologies. Usually, only the design flow and the pressure heads
are considered when designing pumping stations, without
taking into account remaining discharges. However, it has
been found that the majority of pumping stations supply
mostly low or medium discharges and not maximum
discharges (Moreno et al., 2007b). Thus, it is necessary to
improve the efficiency for low and medium discharges, and not
only for high discharges (design flow). Different standard
distributions can be used to simulate the effect on the pumping
station efficiency of different types of flow demand. A model
called ENE was developed, which utilizes the discharge

distribution at the pumping station in order to obtain the

average absorbed power and the average efficiency.
The main goal of this study is to develop a decision support
tool to obtain the theoretical characteristic and efficiency
curves of the pumps, the number of pumps, and the number
of frequency speed drives that minimize the total cost for
a specific pumping station requirement (design flow, pressure
head, and frequency of the discharges).

2.

Materials and methods

2.1.

The case study

This methodology was applied to the irrigable area of La

Pinada (Cuenca, Spain). This irrigation society covers an irrigable area of 170 ha. The primary irrigation system is drip
irrigation for vineyards and olive tree crops. The pumping
station is composed of four pumps (36 kW each), two of which
have frequency speed drives and the remainder have electronic starters. A manometric regulation is carried out with
51 m pressure head, which was obtained by using the
hydraulic model implemented in EPANET 2.0 (Fig. 1).
In order to achieve manometric regulation of the pumping
station, a pressure transducer is installed in the pumping
collector. This pressure transducer sends a current of between
4 and 20 mA, corresponding to a pressure of 010 bar. This
signal is received by a programmable logic controller (PLC)
that activates the different pumps to keep a pressure head of
51 m (in this case). In this on-demand network, a pressure of
25 m at hydrant level is required. Several demand scenarios
were studied to determine the pressure head that warrants
25 m at hydrant, in most of the cases. The utilized hydraulic
network was calibrated by using the methodology developed
by Moreno et al., 2008.

2.2.
Calculation of the design parameters of the
pumping station
To properly design a pumping station it is necessary to carry
out an exhaustive analysis of the network behaviour and its

Fig. 1 Irrigation network implemented in EPANET 2.0.

biosystems engineering 102 (2009) 95105

97

management. The three main parameters to design pumping

stations are design flow, pressure head, and discharge distribution throughout the irrigation season.
Different statistical distributions will be used to determine the effect of the discharge distribution on the final
result. In addition, the real discharge distribution in the
studied network will be compared with the standard
distributions. The discharge distributions considered in this
study were four types of Poisson distributions [Eq. (1)] and
the discharge distribution measured at the pumping station
in the 2007 irrigation season (Figs. 2 and 3, respectively).
Each type of Poisson distribution (A, B, C, and D) corresponds with the following lambda values of Eq. (1): 2.5, 3.0,
4.0, and 7.5.
p Fxjl el

x
X
li
i0

i!

(1)

Fig. 3 shows a higher frequency of low and medium

discharges, and an absence of high discharges. Thus, the
pumping station must operate with a proper efficiency for
low and medium discharges.

2.3.
Development of the model for analysis of energy
efficiency at pumping stations (ENE)
Once all of the design parameters were obtained, it was then
necessary to simulate the behaviour of the pumping station. A
simulation model was required to analyze the energy efficiency of the pumping station. The developed model simulates the pumping station behaviour when a variable demand
of flow and pressure head is required by the network.
The model, which was implemented in MatLab 7.4,
requires the following input data: head and efficiency curves
of the pumps, QH and Qh (theoretical or measured if they are
available), number of pumps, pressure head, and the
discharge distribution throughout the irrigation season
(measured, if it is available, or following different standard
distributions). The model simulates the behaviour of the
variable-speed pumps by using affinity laws and the working
points for the fixed pumps. Thus, the model calculates the

Fig. 2 Utilized standard distribution (

Poisson A,
Poisson B,
Poisson C, d Poisson D).

Fig. 3 Discharge distribution of La Pinada for the 2007

irrigation season.

dischargeefficiency relation for the entire discharge range of

the pumping station.
The average efficiency of the pumping station can be
calculated by Eq. (2).
Pn
j1 hj Qi;j
for j 1; ::; n and for all i
(2)
hi
Qi
where hi is the average pumping station efficiency for each
flow Qi, m3 s1; Qi is the average flow for the flow interval i in
which the flow range has been divided into, m3 s1; hj is the
efficiency of the pump j that supplies a flow Qj; and n is the
number of pumps in the station.
The sum of the discharges of each pump (Qj) is equal to Qi
[Eq. (3)].
Qi

n
X

Qi;j

for j 1; ::; n and for all i

(3)

j1

When measured discharges throughout an irrigation season

are available, ENE calculates the frequency of discharges by
introducing the discharge data as a text file. If measured data
are not available, ENE permits the user to select different
standard distributions (Poisson A, B, C, and D; random
uniform; or others). The user should select the standard
distribution that best fits the real discharge distribution based
on previous experience or based on different algorithms that
can be found in the literature (Lamaddalena, 1997; PulidoCalvo et al., 2003a; Khadra, 2004). In order to evaluate the
effect of the discharge distribution on the final result, different
standard distributions can be studied. Thus, the most appropriate distribution, considering the available information, can
be applied.
Based on the results obtained in previous studies (Planells
et al., 2005; Moreno et al., 2007b) three regulation types of the
pumping station were implemented in ENE, although any
other type of regulation can be also implemented: one variable-speed pump with the remainder as fixed pumps; two
variable-speed pumps activated simultaneously and with the
remainder as fixed pumps; two variable-speed pumps activated sequentially and with the remainder as fixed pumps. In

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biosystems engineering 102 (2009) 95105

this study the first and third options were considered because
the first option is the most commonly used and the third has
been shown to improve the energy efficiency in some cases
(Moreno et al., 2007b).
The average absorbed power (Nabs) was calculated by
considering the discharge distribution and the corresponding
pumping station efficiency. To obtain the most efficient
regulation type, ENE calculates the value of the average
absorbed power [Eq. (4)].
Nabs

n
X
9:81Qi Hi
i1

hi

fi

n
X


NQi fi

(4)

i1

where fi is the frequency of the discharge Qi, fraction, Hi is the

pressure head, m corresponding to the flow interval i (constant
for manometric regulation), and hi is the total average
pumping station efficiency for the discharge Qi, fraction.

2.4.

Optimization of the pump characteristic curves

The optimization process of the characteristic and efficiency

curves will be applied to fixed speed pumps. Once the optimal
characteristic and efficiency curves are known, the study of
the efficiency for variable-speed pumps can be done by
utilizing the affinity laws.
The characteristic and efficiency curves of the pumps (QH
and Qh) are approximated by Eqs. (5) and (6) for fixed pumps
and by Eqs. (7) and (8) for variable-speed pumps, by using
affinity laws.
H a bQ cQ 2

(5)

h eQ fQ 2

(6)

H a2 a abQ cQ 2

(7)

e
f
h Q 2Q2
a
a

(8)

where a is the relative speed of the pump and the coefficients

a, b, c, e, and f determine the shape of the curves. In this study,
the coefficient b was considered to be zero, which means that
the maximum head of the QH curve is obtained when Q is
zero. This is a desirable characteristic in order to avoid double
working points. Jeppson (1977) proposed a variable change [Eq.
(9)] to remove the coefficient b.
b
Q0 Q
2c

Fig. 4 Variable transformation to remove coefficient

b from characteristic curve.

(4)]. The coefficients e and f can be written as functions of the

coefficients a and c. Fig. 5 shows the relation between the head
and efficiency curve.
The operating point (Qd, Hd) is defined by the intersection of
the pump characteristic curve and the system curve. With the
discharge Qd and the efficiency curve, the efficiency hd can be
calculated. However, when the commercial pumps are
selected, the head curve of all the pumps of the pumping
station can intersect the system curve above the operating
point (Qd, Hd), causing small pressure excess if the pumps are
properly selected.
When H and h are equal to zero and considering Eqs. (5) and
(6) with b 0:
 0:5
a
(12)
Qmax
c

2
eQmax fQmax

(13)

Thus, the coefficient e is defined in the next equation as:

 a0:5
(14)
e f 
c
In addition, the relation between the coefficient f and the
coefficients a and c is obtained, considering the maximum
efficiency as follows:
dh
2fQ e 0
dQ

(15)

e
Q
2f

(16)

(9)

With Eqs. (5) and (9) the characteristic curve of the pump is
the following:
H a0 cQ 02

(10)
0

and the coefficient a is:

a0 a 

b2
4c

(11)

Fig. 4 shows the effect of this variable transformation that

permits coefficient b to be removed.
The objective function to minimize is the average absorbed
power by the pumping station during an irrigation season [Eq.

Fig. 5 Scheme of the characteristic curves of the pumps.

biosystems engineering 102 (2009) 95105

99

With all pumps being equal, the most common case in this
type of pumping station in which the variable-speed and fixed
pumps can be switched to have the same level of wear, from
Eq. (5), with b 0, the following relation can be established:
 2
Qd
(19)
a Hd  c
n

Fig. 6 Design flow by utilizing RDDC methodology.

With Eqs. (6) and (15) the following equation can be

obtained:

2 

e
e
e2
(17)
e 

hmax f 
4f
2f
2f
Considering Eq. (14) and (16):
f

4hmax
a=c

(18)

where Hd design pressure head, Qd design discharge, and

n number of pumps installed at the pumping station.
When Eq. (19) could not be used because of, for example,
having different pump sizes in the pumping station, the
optimization process would be more complex because of
having the coefficients a and c as variables. In this case,
convergence problems in the optimization process have been
found.
The maximum efficiency can be determined from manufacturer information. In this study, a theoretical maximum
pump efficiency of 80% was considered. Thus, the optimization variable is only c. The optimization was carried out by
using the Downhill Simplex Method (Nelder & Mead, 1965). For
each number of pumps considered, the optimal characteristic
and efficiency curves for the design condition were obtained.
Once the optimal characteristic curve and the optimal
number of pumps were obtained for the design condition,
a cost analysis was developed considering the energy and
investment costs. Thus, the proper number of pumps is
selected from an economic point of view. In the application,
the annual cost is calculated by multiplying the initial cost by
the capital recovery factor (CRF):

Fig. 7 Generation of the maximum and minimum demand curve (left) and generation of the demand curve for the 96% of
warranty of supply (right).

100

CRF

biosystems engineering 102 (2009) 95105

r1 rt
1 rt 1

(20)

where t useful life of the project, year; and r interest rate

considered, %.
In the case study, t 10 years and r 5%, and therefore
CRF 0.13. Operating cost is determined for an energy rate of
0.08 V kW h1.

2.5.

Determination of the design flow and pressure head

RDDC methodology was used to obtain the design flow at the

pumping station. To obtain the demand curve, different

methodologies can be utilized (Lamaddalena and Sagardoy,

2000; Moreno, 2005; Planells et al., 2005). In this study, the
methodology proposed by Lamaddalena and Sagardoy (2000)
was implemented. Software in MatLab 7.4 environment was
developed that uses the EPANET calculation engine by using
the EPANET toolkit. This software calculates the required
pressure head for each demanded discharge, taking into
account different scenarios of open hydrants and a minimum
pressure at hydrant level (25 m in the case study). Thus, for
each demanded discharge, there are different values of
required pressure head depending on the location of the open
hydrants. A maximum and a minimum curve of demand can
be obtained as well as a curve considering a specific guarantee

Fig. 8 Efficiency curve for varied number of pumps, taking into account the measured discharge distribution (A 2 pumps,
- 3 pumps, : 4 pumps, 3 5 pumps, 6 pumps, C 7 pumps).

biosystems engineering 102 (2009) 95105

of supply (96% in the case study). Once the demand curve is

obtained, the pressure head can be calculated with an
understanding of the design flow. To obtain an accurate
demand curve, the hydraulic model of the network should be
calibrated with pressure measurements (Moreno et al., 2008).

3.

Results

The design flow obtained by the RDDC methodology was

178 l s1, for a 96% of guarantee of supply (Fig. 6).
The discharge distribution throughout the 2007 irrigation
season was measured and it validated the RDDC methodology
because the measured discharge for a 96% rate of guarantee of

101

supply was 173 l s1, which is very close to that obtained with
the RDDC methodology.
The pressure head corresponding to a design flow of
178 l s1 was 51 m (Fig. 7).
The optimal characteristic and efficiency curves, which
fulfil the discharge and pressure head requirements and take
into account the measured discharge distribution, for
a different number of pumps, are presented in Fig. 8.
When the number of pumps increases, the steepness of the
curve also increases. In addition, when the number of pumps
is high, the working point is closer to the zone of maximum
efficiency than when the number of pumps is low.
The discharge distribution throughout the irrigation
season has an important effect on the shape of the optimal

Fig. 9 QH and efficiency curves when 2 pumps are installed and different discharge distributions are considered
(A measured, - Poisson A, : Poisson B, 3 Poisson C, Poisson D).

102

biosystems engineering 102 (2009) 95105

characteristic and efficiency curves of the pumps. Fig. 9

shows the QH and efficiency curves, respectively, considering two pumps and different Poisson discharge distributions together with the measured distribution during the
irrigation season.
When there are few pumps at the pumping station, the
optimal characteristic curves are different depending on the
discharge distribution that is considered (Fig. 9). When there is
a higher frequency of low discharges (Poisson A and B), the
optimal QH curve is steeper than when the discharges are
more uniform (Poisson C, D, and the measured distribution).
When the QH pump is steeper, the working point (defined by
a pressure head of 51 m and the characteristic curves) is in the
descendent zone of the efficiency curve. If the curve QH is

flatter, which corresponds with more uniform discharge

distributions in the range of discharges, the working point is
in the zone of maximum efficiency. In none of the cases is the
working point in the ascending zone of the efficiency curve.
Therefore, when selecting the pumps, the working point
should be in the zone of maximum efficiency or in the
descendent zone of the efficiency curve, but never in the
ascending zone of the efficiency curve.
If the number of pumps increases, these differences are
minimal, the optimal characteristic and efficiency curves
having the same shape for all the discharge distributions
(Fig. 10). Thus, if the discharge distribution throughout the
irrigation season is not known, increasing the number of
pumps and optimizing the characteristic curves can ensure

Fig 10 Efficiency curves when 7 pumps are installed and different discharge distributions are considered (A measured,
- Poisson A, : Poisson B, 3 Poisson C, Poisson D).

biosystems engineering 102 (2009) 95105

103

Fig. 11 Relation between the number of pumps and the average absorbed power for different discharge distributions using
1 variable-speed pump (1VSP) (A Poisson A, : Poisson B, Poisson C, and D Poisson D, and d the measured) or 2 variablespeed pumps (- PoissonA, 3 Poisson B, C Poisson C, and d Poisson D, and > the measured).

proper energy efficiency. In addition, the working point of the

pumps is in the zone of maximum efficiency.
In order to determine the optimal number of pumps, it is
necessary to carry out energy and cost analyses. From
the energy point of view, Fig. 11 shows the relation between
the number of pumps and the average absorbed power for the
four standard distributions studied, and that measured in the
irrigation season 2007. The effect of installing a second variable-speed pump (2VSP) is also shown in Fig. 11.
Fig. 11 illustrates that the number of pumps that makes
Nabs the minimum is seven, in the studied irrigation network.
However, the slight differences indicate that the range of
reasonable number of pumps is between 3 and 10. When the
pump selection is performed correctly, there are not significant differences in the average absorbed power when using
one variable or two variable-speed pumps activated sequentially. However, when the pumps are not properly selected or
when the variables on which the selection of the pumps was
based are changed, the installation of a second frequency
speed drive usually improves the energy efficiency (Moreno
et al., 2007b).

In the case study, the average absorbed power in 2007 was

69.14 kW, and the pumping station had 4 pumps. If the pumps
had been selected by using the proposed methodology, the
average absorbed power would have been 46.8 kW (Fig. 11,
considering 4 pumps and the measured discharge distribution). Therefore, an energy saving in the pumping station of
32.3% would have been obtained.
A cost analysis was carried out to determine the number of
pumps that minimized the total cost at the pumping station
(investment and operation costs). Results of the energy cost
analysis, when the actual operation time (315 hours year1)
was considered, are shown in Fig. 12.
In the case in which the pumping station is working for
a few hours a year, the minimum cost is obtained with the use
of only two pumps. This is due to the higher price of installing
a greater number of pumps (more valves, pipes, and other
elements), which is not compensated by higher energy efficiency. However, the actual operation time of this irrigation
network is low and not representative of the rest of the irrigable areas. Therefore, Fig. 13 shows the relation between the
number of hours of operation and the number of pumps that

Fig. 12 Relation between number of pumps and the total cost for different discharge distributions (A Poisson A,
: Poisson B, Poisson C, and D Poisson D, and d the measured), considering 1 variable-speed pump (1VSP).

104

biosystems engineering 102 (2009) 95105

Fig. 13 Operation time in hours versus the number of pumps that minimizes the total cost.

minimizes the total cost. When the operation time of the

pumping station in the irrigation season is long, the number of
pumps that minimizes the total cost is higher. This is due to
the higher energy cost when the number of operating hours is
higher, and due to the improvement of the energy efficiency
when there is a high number of pumps in the pumping station
(Figs. 8 and 11). To obtain the minimum total cost with seven
pumps, which is the number of pumps that best minimizes
energy consumption (Fig. 11), the operation time should be
2390 h. This operation time is too long for the actual operation
condition in the majority of the irrigable areas.

4.

Conclusions

In this paper, a new methodology to obtain the optimal

characteristic and efficiency curves (QH and Qh) at pumping
stations is presented. It considers the design flow, the design
pressure head, and the discharge distribution throughout the
irrigation season.
The optimal shape (slope) of the QH curve varies
depending on the discharge distribution throughout the irrigation season, mainly when there are few pumps installed at
the pumping station. For high frequency of low discharges,
the recommended QH curve is steeper than for high
frequency of medium and high discharges. These differences
are negligible when a large number of pumps are installed.
Therefore, when the discharge distribution is not known,
increasing the number of pumps can improve the energy
efficiency. Because the discharge distribution is not usually
known, increasing the number of pumps can help to decrease
the negative effect of choosing an inappropriate pump.
However, when the operation time is lower, the number of
pumps that minimizes the total cost (investment
exploitation) is also lower.
If the pumps are properly chosen, no improvement of the
energy efficiency is found by installing a second variablespeed pump. This and the price of this equipment make its
installation unprofitable. However, if the pumps have not
been adequately chosen, a second variable-speed pump can

help to improve the energy efficiency at the pumping station,

if it is correctly operated.

Acknowledgment
This research was funded by the Consejera de Educacion y
Ciencia de Castilla-La Mancha within the project PCI08-0117
and the Regional Agency of Energy in Castilla-La Mancha
(AGECAM) within the project Auditoras energeticas en Castilla-La Mancha.

references

Aliod R; Eizaguerri A; Estrada C; Perna E (1997). Dimensionado y

analisis hidraulico de redes de distribucion a presion en riego
a la demanda: Aplicacion del programa GESTAR. Riegos y
Drenajes XXI, 92, 2238.
Awumah K; Bhatt S K; Goulter I C (1989). An integer programming
model for layout design of water distribution networks.
Engineering Optimization, 15, 5770.
Bhave P R; Lam C F (1983). Optimal layout for branching
distribution networks. Journal of Transportation Engineering,
109, 534547.
Clement R (1966). Calcul des debits dans le reseaux dirrigation
fonctionnant a la demande. La Houille Blanche, 5, 553575
(in French).
Clement R; Galand A (1979). Irrigation par aspersion et reseaux
collectifs de distribution sous pression. Eyrolles, Paris.
ptimo de Redes Ramificadas 3.0.
DIOPRAM, 2003. Diseno O
Manual de Usuario. Grupo Multidisciplinar de Modelacion de
Fluidos, Universidad Politecnica de Valencia, Valencia.
Granados A (1990). Infraestructura de regados. Redes colectivas
de riego a presion (2a edicion). Escuela Tecnica Superior de
Ingenieros de Caminos Canales y Puertos, Universidad
Politecnica, Madrid.
Jeppson R W (1977). Analysis of Flow in Pipe Network. Ann Arbor
Science, Ann Arbor, Michigan.
Khadra R (2004). Development of an Integrated Tool for the
Analysis of Irrigation Systems under Water Scarcity
Conditions. Dipartamento di Scienze della Produzion Vegetali,
Universitat degli Studi di Bari, Bari, Italy.

biosystems engineering 102 (2009) 95105

Labye Y; Olson M A; Galand A; Tsourtis N (1988). Design and

optimisation of irrigation distribution network. Irrigation and
Drainage Paper 44. FAO, Rome.
Lamaddalena N (1997). Integrated simulation modelling for
design and performance analysis of on-demand pressurised
irrigation systems. Ph.D. Dissertation, Universidade Tecnica
de Lisboa, Instituto Superior de Agronoma, Lisboa, Portugal.
Lamaddalena N; Sagardoy J A (2000). Performance analysis of ondemand pressurized irrigation systems. In: Proceedings of
FAO Irrigation and Drainage, Rome.
Lansey K E; Mays L W (1989). Optimization model for water
distribution system design. Journal of Hydraulic Engineering,
115, 14011418.
Moradi-Jalal M; Marino M A; Afshar A (2003). Optimal design and
operation of irrigation pumping stations. Journal of Irrigation
and Drainage Engineering, 129(3), 149154.
Moradi-Jalal M; Rodin S I; Marino M A (2004). Use of genetic
algorithm in optimization of irrigation pumping stations.
Journal of Irrigation and Drainage Engineering, 130(5), 357365.
Moreno M A (2005). Analisis hidraulico y energetico de redes de
riego a la demanda. Ph.D. Dissertation, Centro Regional de
Estudios del Agua, Universidad de Castilla-La Mancha
(in Spanish)
Moreno M A; Planells P; Ortega J F; Tarjuelo J M (2007a). New
methodology to evaluate flow rates in on-demand irrigation
networks. Journal of Irrigation and Drainage Engineering,
133(4), 298306.
Moreno M A; Carrion P; Planells P; Ortega J F; Tarjuelo J M (2007b).
Measurement and improvement of the energy efficiency at
pumping stations. Biosystems Engineering, 98, 479486.

105

Moreno M A; Planells P; Ortega J F; Tarjuelo J M (2008). Hydraulic

networks models calibration. Journal of Irrigation and
Drainage Engineering, 134(1), 3642.
Nelder J A; Mead R (1965). A simplex method for function
minimization. Computation Journal, 7(4), 308313.
Perez R; Andreu M; Izquierdo J (1996). Diseno de redes de
distribucion. In: Curso de ingeniera hidraulica aplicada
a los sistemas de distribucion de agua (Cabrera E; Espert V;
Garca-Serra J; Martinez F; Andris M; Garca M eds), pp.
653727. Universidad Politecnica de Valencia, Valencia,
Spain.
Planells P; Tarjuelo J M; Ortega J F; Casanova M I (2001). Design of
water distribution networks for on-demand irrigation.
Irrigation Science, 20, 189201.
Planells P; Carrion P A; Ortega J F; Moreno M A; Tarjuelo J M
(2005). Pumping selection and regulation for water
distribution networks. Journal of Irrigation and Drainage
Engineering, 131(3), 273281.
Pulido-Calvo I; Roldan J; Lopez-Luque R; Gutierrez-Estrada J C
(2003a). Water Delivery Planning Considering Irrigation
Simultaneity. Journal of Irrigation and Drainage Engineering,
129(4), 247255.
Pulido-Calvo I; Roldan J; Lopez-Luque R; Gutierrez-Estrada J C
(2003b). Demand forecasting for irrigation water distribution
systems. Journal of Irrigation and Drainage Engineering,
129(6), 422431.
Rossman L A (1997). EPANET: User Manual. Risk Reduction
Engineering Laboratory Office of Research and
Development. United States Environmental Protection
Agency, Cincinnati, OH.