Water saving options in hydropower by means of variable speed operation: A prototype study in a mid-head Francis turbine

Abstract

Nowadays, in order to mitigate the global warming effects, there is a need of renewable energy generation for the objective of carbon neutrality. In this context, hydropower plays a key role not only because the amount of renewable energy generated but also because it is a fundamental player to ensure the stability of the electrical grid, as one of the main dispatchable sources. Nevertheless, hydropower is facing nowadays with the climato-logical problem of the extreme droughts, that are expected to be more common in the upcoming years. Therefore, it has become more important than ever to use the water flowing through the rivers properly. In this paper, the potentiality of using variable speed operation with the aim of increasing the overall efficiency of Francis turbines, which are the most widely used hydro turbines worldwide, is numerically explored. This implies to use less water to produce the same amount of electrical power. The study is based on an accurate modelling with real prototype data which has been made available for this study. It is shown that variable speed could improve the overall efficiency of the unit with respect to the constant speed generator, typically used in hydropower. While this idea has been mentioned in some previous studies, in this paper we also consider the electrical efficiency decrease of the variable speed technologies and restrictions of the unit regarding the electrical power generated. Results show that when the unit operates at some specific operating conditions, namely low heads at part load operations and high heads at maximum power, variable speed technologies could be used to save more than 2% of water with respect to the fixed speed unit. Main results and models of this paper can be used as a reference for future studies with similar type of units.

Full text

Energy Conversion and Management 291 (2023) 117296
0196-8904/© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Water saving options in hydropower by means of variable speed operation:
A prototype study in a mid-head Francis turbine
Alexandre Presas
a
,
*
, Carme Valero
a
, David Valentín
a
, M`
onica Egusquiza
a
, Pedro Diogo Pinto
b
,
Ana Gonçalves de Carvalho
c
, Alex Coronati
c
, Eduard Egusquiza
a
a
Centre de Diagn`
ostic Industrial i Fluidodin`
amica, Universitat Polit`
ecnica de Catalunya, Av. Diagonal, 647. ETSEIB. Pab. D , Pl1, 08028 Barcelona, Spain
1
b
EDP- Gest˜
ao da Produç˜
ao de Energia, S.A., Rua Of´
elia Diogo da Costa 45, 4100-085 Porto, Portugal
2
c
EDP NEW - Centre for New Energy Technologies, R. Particular `
a Rua Cidade de Goa 2, Sacav´
em, Portugal
3
ARTICLE INFO
Keywords:
Hydropower generation
Variable speed operation
Francis Turbine
Doubly Fed Induction Machine
ABSTRACT
Nowadays, in order to mitigate the global warming effects, there is a need of renewable energy generation for the
objective of carbon neutrality. In this context, hydropower plays a key role not only because the amount of
renewable energy generated but also because it is a fundamental player to ensure the stability of the electrical
grid, as one of the main dispatchable sources. Nevertheless, hydropower is facing nowadays with the climato-
logical problem of the extreme droughts, that are expected to be more common in the upcoming years. Therefore,
it has become more important than ever to use the water owing through the rivers properly.
In this paper, the potentiality of using variable speed operation with the aim of increasing the overall ef-
ciency of Francis turbines, which are the most widely used hydro turbines worldwide, is numerically explored.
This implies to use less water to produce the same amount of electrical power. The study is based on an accurate
modelling with real prototype data which has been made available for this study. It is shown that variable speed
could improve the overall efciency of the unit with respect to the constant speed generator, typically used in
hydropower. While this idea has been mentioned in some previous studies, in this paper we also consider the
electrical efciency decrease of the variable speed technologies and restrictions of the unit regarding the elec-
trical power generated. Results show that when the unit operates at some specic operating conditions, namely
low heads at part load operations and high heads at maximum power, variable speed technologies could be used
to save more than 2% of water with respect to the xed speed unit. Main results and models of this paper can be
used as a reference for future studies with similar type of units.
1. Introduction
Global warming and climate change is a serious threat for modern
society and according to many studies it is being responsible for many
natural disasters [1]. One of the main causes of the climate change and
global warming are supposed to be the fossil fuels that are being used for
electricity generation and transportation. Therefore, many international
associations and governments claim that it is necessary to achieve the
goal of carbon neutrality by 2050[2].
Hydropower is one of the main renewable energy producers and also
plays a fundamental role in the stability of the electrical grid. This is
because nowadays, hydropower is maybe the most important dis-
patchable energy source. This predominant role will be even more
important in a scenario with a very fast grow of solar and wind energy
which are also renewable energies but with the main issue that they are
unpredictable to some extent.
One of the effects of the climate change, which is present nowadays,
are the extreme droughts which have many negative environmental and
social aspects and also affect the operation of hydropower. According to
a recent report in 2022[3], in Portugal the potential hydroelectricity
stored in reservoirs is less than half of the average in the previous ve
years. Therefore, for hydropower it is becoming more important than
ever to reduce the amount of water used to produce the same amount of
* Corresponding author.
E-mail address: alexandre.presas@upc.edu (A. Presas).
1
https://cdif.upc.edu/en.
2
https://www.edp.com/en.
3
https://www.edp.com/en/innovation/edp-new.
Contents lists available at ScienceDirect
Energy Conversion and Management
journal homepage: www.elsevier.com/locate/enconman
https://doi.org/10.1016/j.enconman.2023.117296
Received 31 January 2023; Received in revised form 11 May 2023; Accepted 10 June 2023

Energy Conversion and Management 291 (2023) 117296
2
energy, or in other words to maximize the energy produced for a given
amount of water. This can be only achieved by increasing the overall
efciency of the unit. Nevertheless, hydropower has the trend to work
more and more in off-design imposed by the massive entrance of new
renewable energies, and it is well known that in such conditions, the
hydraulic efciency of the unit decreases.
One possible solution to increase the efciency is to use variable
speed generators instead of the mostly used synchronous generators. In
the present, there are few hydro turbines equipped with variable speed,
although the idea of using it to increase the overall efciency of the
turbines has been discussed in some studies [4–7]. The main concept is
that the unit can generally operate with a higher hydraulic efciency if
the rotating speed of the unit is increased/decreased with respect to the
rotating speed imposed by the synchronous generator. This will increase
the overall efciency of the unit if the gain in hydraulic efciency is
capable to compensate extra losses of the electrical components (mainly
converters) needed for variable speed generator.
In the study of Beyer about the pump storage unit in Goldistahl [4]
the idea of improving the efciency at part load conditions is only briey
mentioned. The author states that an efciency advantage of approxi-
mately 10% is achieved when compared to xed speed units (synchro-
nous generator). Nevertheless, this possible improvement is not justied
with previous references or efciency curves of prototype turbines. In
2008, P´
erez et al.[5] calculates the amount of extra energy that could be
extracted by using variable speed in an irrigation reservoir. They esti-
mated that thanks to the variable speed, the energy extracted in this
particular set-up (a reservoir where irrigation is given priority over
hydropower) could be increased by a 20%. Heckelsmueller [6] specif-
ically states that variable speed is best used when the water head is
below the design head. He estimated that speed variations about ±20%
are necessary to reach the maximum efciency within a range of ±40%
of the design head. With the model used in that study it is estimated that
an improvement of 22% of turbine efciency at 60% of the design head
can be achieved, while only 3% can be increased if the unit operates at
140% of the design head. Abubakirov et al.[7] also presents a study of
the efciency improvement by using variable speed, although not mean
values for the efciency improvement or energy gain are given.
Generally, the numbers presented in those studies may be too optimistic,
as they do not consider the fact that the electrical efciency of a variable
speed unit is lower than the electrical efciency of a xed speed unit
(synchronous generators SG). Also, in these studies it is generally sup-
posed that the electrical power can be always adjusted to reach the
optimum hydraulic efciency. Nevertheless, a more realistic situation is
to consider that the electrical power, which is imposed by the electrical
grid conditions, should be maintained constant even when the rotating
speed changes.
There are mainly two types of variable speed generators (Double Fed
Induction Generators DFIG and Full Size Frequency Converters FSFC)
with a relatively mature technology as they have been widely used in
aerogenerators [8]. Both technologies have been used in specic cases in
hydropower on the prototype scale [9–12]. According to Hildinger and
K¨
odding [9] DFIG is generally preferred for turbines over 100 MW as the
cost of a FSFC is much higher than a DFIG for large units. Nevertheless,
Schlunegger in 2014[11], documents the installation of a FSFC in
Grimsel 2 pumped storage plant, which operates at around 100 MW as a
pump and as turbine. Valavi and Nysveen in 2018[12] focus their review
in the use of variable-speed in pump storage power plants. They stated
that only 17 variable speed systems were in operation at the year of the
publication, being most of them in Japan. When comparing both tech-
nologies (FSFC and DFIG), it can be concluded that FSFC is more ver-
satile in terms of speed variation and less efcient than DFIG.
Theoretical speed variation range in FSFC is practically unlimited [13].
DFIG has the main advantage that is more efcient, as only part of the
power (slip power) passes through the converters. Nevertheless, the
speed variation range in hydropower applications is generally assumed
to be restricted to about ±10% of the nominal speed [13–17]. Further
pros and cons of both technologies are widely discussed in the extensive
reviews studies of variable speed operation in hydropower performed by
Valavi and Nysveen [12] and by Iliev et al.[13].
Besides the efciency improvement, there are another interesting
and maybe more discussed applications of variable speed in Hydro-
power. Generally, variable speed is a very interesting application in
pump-turbines where the main focus is to provide ancillary and regu-
lation services for the power grid [14,18,19]. Nicolet et al. [14] present a
simulation study showing the advantages of using a FSFC for providing
ancillary services in a 210 MW pumped storage power plant. The au-
thors show advantages such as fast transition from pump to turbine and
the possibility of using the entire range of the unit in pump mode and in
turbine mode. For units providing ancillary services, it is of paramount
importance to regulate the output power as fast as possible. Because the
time response of the electrical unit is much faster than the hydraulic
unit, the output power can be changed quickly (scale of seconds) when
FSFC or DFIG technologies are used. For example, Frades II (Portugal) is
maybe the rst large pump-turbine unit in Europe (around 400 MW)
using DFIG technology. According to a recent report [18], variable speed
clearly contributes to the stability of the Portuguese grid, as it can
provide a much faster injection of power than conventional units in grid
disturbances and a larger operating range. Furthermore, when used as a
pump, the power absorbed can be also adjusted, increasing also the
range as energy storage system [18]. This is a very interesting aspect to
Nomenclature
D diameter of the turbine
f frequency
g gravity
Hg gross head
Hn net head
N rotating speed
n number of poles
n11 speed factor
P power
Q ow rate
q11 ow rate factor
s slip factor
Greek letters
η
efciency
ρ
density of water
Acronyms and subscripts
BEP best efciency point
DFIG doubly fed induction generator
FSFC Full size frequency converter
SG synchronous Generator
c converter
e electrical
g grid
h hydraulic
lc losses in the converter
lg losses in the generator
m mechanical
r rated conditions
sl slip
st stator of the generator
A. Presas et al.

Energy Conversion and Management 291 (2023) 117296
3
consider in a country with a high penetration of non-dispatchable en-
ergy sources such as wind and solar. These aspects, more related to the
ancillary services that these units can provide to increase the exibility
of the power grid, are also discussed and analyzed in the aforementioned
references [12–14].
From the theoretical benets of using variable speed technologies,
the present study is focused on the hydraulic efciency improvement
and the potentiality of saving water in a mid-head Francis turbine unit,
which is the most widely used hydro turbine type. The study is made for
both technologies, namely FSFC and DFIG. Compared to the previous
references [4–7] considering the same topic, two main points will be
included trying to make the study closer to the real operation of pro-
totypes. On one side, the decrease of the electrical efciency with
respect to a xed speed unit will be evaluated. On the other side it will be
assumed that for a given operating condition, the unit using variable
speed has to keep the same electrical power according to the dispatching
demand, which do not necessarily imply to operate at the maximum
efciency possible.
The study has been made in a mid-head Francis unit, which is one of
the demonstrators of the XFLEX Hydro project [20]. The unit has been
accurately modelled, considering the losses in the hydraulic circuit and
also the hydraulic, mechanical and generator efciency and actual
operating ranges. It is shown that a signicant amount of water can be
saved if the unit operates out of the design head. Main results and
models used in this study may be extrapolated to Francis units with
similar specic speeds and operating heads.
2. Variable speed for improving the hydraulic efciency
maintaining the electrical power generated
In a hydraulic turbine unit, the electrical power depends mainly on
the available net head, the ow rate and the different losses occurring in
the transformation from hydraulic power to electrical power. These
include the hydraulic losses, mechanical losses and generator losses.
Hydraulic losses are by far the most important ones, especially when the
unit works in off-design conditions. The conversion from available hy-
draulic power to electrical power can be expressed as (Eq.1) [21]:
Pe=Ph•
η
=
ρ
gQHn
η
=
ρ
gQHn
η
e
η
m
η
h;
Hn≈Hg−kQ2(1)
Hn(m)is the net head, Q(m3
s) is the ow rate passing through the
turbine,
ρ
(kg
m3)is the density,g(m
s2) gravity and
η
is the global efciency of
the turbine, which may be separated as follows.
η
e is the electrical ef-
ciency which accounts for the losses in the generator,
η
m is the me-
chanical efciency which considers the friction losses on the shaft and
η
his the hydraulic efciency which considers the hydraulic losses in the
turbine runner. The net head Hn(m)can be calculated considering the
gross head Hg (difference of the head race level and tail race level) and
the losses in the hydraulic circuit, which are proportional to Q2 [21].
According to the dimensional analysis theory applied to hydraulic
machinery, the hydraulic efciency depends on the two following pa-
rameters (Eq.2)[21,22]:
n11 =ND

Hn
√
q11 =Q
D2
Hn
√
(2)
N is the rotating speed of the unit (usually in rpm), D the reference
diameter of the runner (usually expressed in m), Hn the net head (m) and
Q the ow rate (usually in l/s). Representations of the constant hydraulic
efciency curves as a function of the n11 ,q11 are known as Hill-Charts.
To represent the idea of variable speed operation, the Hill-Chart on
Fig. 1 is used. In this Hill-Chart the constant hydraulic efciency curves,
constant electric power and constant distributor position are repre-
sented. As a reference point, it is considered the operation of a specic
unit at 17 MW, with a distributor position of 20◦and hydraulic ef-
ciency
η
h=0.93 (Fig. 1). Assuming that the unit works under a rela-
tively constant Hg (which cannot be varied rapidly), the parameter n11
will remain nearby constant for a synchronous generator as N,D are
xed (a small reduction of Hn is expected when increasing Q due to
hydraulic losses in the pipes as seen in Eq.1). Then, the operating point
can be only varied by increasing/decreasing the angle of the distributor
(represented with green arrows on Fig. 1). This will move the unit to a
new operating point n11 ,q11, with a new ow rate Q, new efciency
η
h
and new generated power Pe.
The idea of using variable speed, permits to move to another oper-
ating point with the same electrical power Pe (maintaining the gross
head Hg), different ow rate Q and different efciency
η
h. Variable speed
operation is represented in Fig. 1 with black arrows. Following the black
lines in Fig. 1 results in an operating point with the same electrical
power Pe, higher hydraulic efciency
η
h and less ow rate. This is an
interesting benet, as the unit can produce the same output Pe with less
water.
3. Model of a mid-head Francis unit prototype in operation
In order to obtain the constant electrical power curves (Fig. 1) of a
real prototype, the losses in the hydraulic circuit (inlet and outlet pipes),
the hydraulic efciency of the runner, the mechanical efciency and the
electrical efciency have to be considered. For this study, a model
Fig. 1. Operation of the turbine in the q
11,n11 coordinates. Operation of the synchronous generator with constant gross head Hg. Operation with variable speed and
constant Hg and generated power..Pe
A. Presas et al.

Energy Conversion and Management 291 (2023) 117296
4
considering all these losses has been created. The inputs for the model
are the available Hg and the electrical power Pe. Three different types of
generators have been considered: xed speed unit with a synchronous
generator SG, DFIG with a limited variable speed range and a FSFC with
a full variable speed range.
For the xed speed unit, with the given inputs Hg and Pe, there is a
single operating point and thus a single Q possible. For the variable
speed units, there are many possible Q depending on the rotating speed
N. Therefore, when modelling and simulating the variable speed units, N
is also used as an input parameter, which is optimized to minimize the
ow rate. Finally, to analyze the water saving options with respect to the
synchronous machine, the ow rates obtained for the variable speed
options are compared against the synchronous generator unit. In the
following sections, the different considerations and assumptions used
for the modelling of a mid-head Francis unit are explained in detail.
3.1. Main characteristics of the prototype used for the modelling
The simulation model used in this study is based on the prototype
data of a mid-head Francis turbine located in Portugal (Caniçada) and it
is operated by Energias de Portugal (EDP). In frame of the project XFLEX
Hydro, the needed data for this study was made available. The rated
characteristics of the unit are listed on Table 1.
3.2. Relationship between Hg,Q and Hn
The available net head Hn for the turbine depends on the gross-head
Hg and the losses in the hydraulic circuit (inlet and outlet pipes), which
are almost proportional to Q2for turbulent ows [21]. During the
commissioning tests of the unit, these losses were accurately measured.
As in many mid and high head units, the gross head Hg is mainly
determined by the upstream level. This level typically follows a seasonal
trend in the year, with a maximum in spring-summer and a minimum in
autumn–winter. In the considered turbine, with a relatively long outlet
conduit, the approximated net head obtained by regression (R2=0.989)
is measured to be (Eq.3):
Hn≈Hg−0.0046Q2(3)
Note that this measured characteristic follows the form of Eq.1. Hg,
Hn are expressed in m and Q in m3/s.
3.3. Hydraulic losses and hydraulic efciency
The hydraulic losses are the most important ones and specially when
the unit operates in off-design conditions. Hydraulic losses consider the
dissipated energy of the water passing through the turbine runner, and
therefore better designed turbines will have a better efciency. At the
design point, also known as Best Efciency Point (BEP), the hydraulic
losses are minimal, and therefore the hydraulic efciency
η
h is maximal.
The whole hydraulic efciency of the present unit is represented in the
following Hill Chart (Fig. 2). Although this Hill-Chart is a particular case
of a relatively new and well-designed mid-head Francis runner (2017) it
may be representative of turbines in the same specic range and
manufacturing period according to the basic design ideas of optimal
design in turbo machinery [23].
To model the actual prototype, the information contained in Fig. 2
was digitized with the web application WebPlotDigitzer [24].
Particularly, the constant efciency curves (in green) and the constant
guide vane opening curves were obtained in the n11 ,q11 coordinates.
Then a grid consisting of 271 points in the n11 coordinate (from n11 =
45to n11 =72 with Δn11 =0.1)and 701 points in the q11 coordinate
(from q11 =250to q11 =950 with Δq11 =1) was generated. The ef-
ciency was then obtained for all the 271x701 grid points. This process
was done with the surface tting code gridt from MATLAB [25].
3.4. Friction losses and mechanical efciency
The mechanical efciency was also measured during the commis-
sioning tests. Mechanical efciency considers the mechanical losses such
as friction of the bearings, friction of the rotating structure with the
surrounding air, disk losses and other type of minor losses. In the present
unit the mechanical efciency is given by the following expression
(Eq.4):
η
m=0.004952 Pe
Pr+0.992182for Pe
Pr
∊[0.25,1.1](4)
η
m is the mechanical efciency and Pe is the electrical power gener-
ated. Pr is the rated power. In the measured range, the mechanical ef-
ciency was always higher than 99%.
3.5. Electrical losses and electrical efciency
The actual unit operates with a synchronous generator, where the
electrical efciency was also measured during the commissioning tests.
For the FSFC and DFIG this efciency is modeled based on the existing
literature.
3.5.1. Synchronous generator (SG)
The electrical efciency in a synchronous generator considers the
stray losses, friction and windage losses in the generator structure, core
losses and I2R losses [26]. The efciency curve of the SG was determined
during the commissioning tests for Pe
Pr
∊[0.25,1.1]. The measured data can
be approximated with an R2=0.9998 with the following expression
(Eq.5):
η
SG =− 0.075961(Pe
Pr)4
+0.311295(Pe
Pr)3
−0.474741(Pe
Pr)2
+0.323532(Pe
Pr)+0.894357;
η
SG,max =0.98
(5)
For further steps, it is assumed that the maximum efciency of this
generator is 0.98. It is also important to mention that this curve was
obtained for a power factor of 1. According to the historical data, this
unit always works with a power factor of 0.995, regardless of the active
power Pegenerated.
3.5.2. Model for the Full Size frequency converter (FSFC)
For a FSFC, all the generated power in the synchronous generator
passes through the converters (Fig. 3). Here we assume that the con-
verters have an efciency of 98.5% [9,14] so that the efciency curves of
the synchronous generator (Eq.5) are downshifted in the entire range by
a factor of 0.985[13], which gives the efciency in Eq.6. We also assume
that in this conguration, the range of speed variation of the rotor is not
restricted [13].
η
FSFC =
η
SG •0.985 (6)
3.5.3 Model for the Double Fed Induction generator (DFIG)
The DFIG model is represented in Fig. 4. In this conguration, only
part of the power, namely slip-power, Pslip passes through the converters.
The rst relevant parameter to be dened in the DFIG is the slip s (Eq.
(7)) [26]:
Table 1
Rated characteristics of the prototype turbine used for the model.
Rated Power Pr 32 MW
Rated Gross Head 121 m
Rated Flow rate 34 m^3/s
Rotating speed (synchronous gen.) 300 rpm
Outer diameter 2.014 m
A. Presas et al.

Energy Conversion and Management 291 (2023) 117296
5
Fig. 2. Hill- Chart of the analyzed unit.
Fig. 3. FSFC for a Francis Turbine. Figure reproduced from [9] with permit from the authors.
A. Presas et al.

Energy Conversion and Management 291 (2023) 117296
6
s=fSG −fm
fSG
withfSG •n=fgr (7)
fSGis the synchronous frequency, and for a SG it is exactly the me-
chanical rotating speed of the rotor in Hz. This number multiplied by the
pair of poles in the generator n is the grid frequency fgr . fm is the me-
chanical rotating speed of the rotor, which in case of variable speed units
can be different from fSG. In this case, we restrict fm to be in the range
[0.9fsg,1.1fsg ]according to the limitation of ±10% assumed in previous
studies [9,13,14]. If the slip is positive, the unit operates in super-
synchronous mode and if the slip is negative in sub-synchronous
mode. If the slip is zero, then the unit rotates at the synchronous fre-
quency fSG , and it is approximated with the synchronous generator ef-
ciency described in Eq. (5).
The slip power, Psl can be calculated as (Eq.8) [27]:
Psl ≈s•Pst (8)
In order to model the losses in the DFIG, the following power ow
diagram (Fig. 5) will be considered (adapted from the DFIG power ow
model shown in [28]).
This power ow relates the mechanical power on the turbine shaft
Pm,the slip power Psl, the power on the stator side of the DFIG Pst and the
electrical power generated Pe. In this model,Pst is calculated using the
approximated efciency of the synchronous generator
η
SG described in
Section 2.4.1. This relationship is expressed with Eq.10 for both oper-
ating modes:
Pst =Pm+Psl −Plg = (Pm+Psl)
η
SG = (Pm−sPst)
η
SG (10)
It is important to notice that in sub-synchronous mode, (s<0) the
combined power Pm−sPst is higher than in super-synchronous mode
(s>0) and therefore the losses in the generator Plg, which are the most
important ones, are also higher. Therefore, at sub-synchronous regimes,
the electrical efciency will be lowered [28].
The electrical power Pe can be calculated as (Eq.11):
Pe=Pst −Psl
η
c
fors <0(sub −synchronous)
Pe=Pst +Psl
η
cfors >0(sub −synchronous)
(11)
Where the efciency of the converters
η
c is assumed to be 0.985 as in
the previous section. Finally, the overall efciency of the DFIG is dened
as follows (Eq.12):
η
DFIG =Pe/Pm(12)
With the described approximated model, when s=0,
η
DFIGis
considered to be the same as the actual synchronous generator
η
SG. For
sub-synchronous regime,
η
DFIG will be substantially lower due to the
higher losses in the generator Plg and for the super-synchronous mode,
the efciency will be slightly higher. Exactly the same trend is observed
in [28].
3.6. Restrictions considered for the study
For the present study, the following restrictions based on typical
operation of hydraulic units are assumed. The main objective is to
compare the water consumption of the actual synchronous generator
against the variable speed generators technologies (FSFC and DFIG).
•The electrical power has to be maintained constant when the rotating
speed of the generator is changed.
•When changing the rotating speed, the gross head is maintained
constant as it is given by the upstream reservoir level and this level
cannot vary rapidly.
•For the synchronous generator case, the electrical power generated
by the unit can be only modied by opening/closing the guide vanes
(Fig. 1). This will increase/reduce the passing ow rate Q and
therefore the electrical Power Pe (Eq.1). This will also increase/
decrease all the efciencies described in this section. The electrical
efciency of the synchronous generator is assumed to be
η
SG
•For the FSFC, the rotating speed of the turbine can be changed, and it
is not necessarily the synchronous speed fsg. This permits to move the
Fig. 4. DFIG for a Francis Turbine. Figure reproduced from [9] with permit from authors.
Fig. 5. Operation of the DFIG. Sub-synchronous (a) and super-synchronous mode (b).
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Energy Conversion and Management 291 (2023) 117296
7
unit to many operating points in the hill-chart without changing the
electrical power (Fig. 1). The criterium is to operate always at the
minimum q11, which will minimize the ow rate Q passing through
the turbine. The efciency of the generator is assumed to be
η
FSFC
•For the DFIG the same criteria as for the FSFC are used. In this case,
the rotating speed is restricted to ±10% of the synchronous speed.
The efciency of the generator is assumed to be
η
DFIG.
4. Results
Results of this study will be normalized against the design parame-
ters of the unit operating with the SG at the synchronous speed in the
Best Efciency Point (BEP). This point corresponds to the point with the
maximum
η
h, which is represented in Fig. 6 and the corresponding pa-
rameters are listed in Table 2.
4.1. Operation with variable speed. Constant electrical power curves
The operation with variable speed is summarized in this section. In
Fig. 7a, the unit operates in the design gross head HgSG a nd optimal
power PeSG, where
η
his maximum. Constant electric power curves for the
FSFC, DFIG and evolution of the mechanical power Pm are represented.
In order to maintain the electrical power and increase/decrease the
rotating speed, the guide vanes have to be opened/closed as seen in the
gure. In this situation it is obviously not interesting to modify the
rotating speed if the objective is to minimize Q (which is equivalent to
minimize q11 )as the unit already works at BEP. It is interesting to see
that with the FSFC; the water consumption is a little bit higher, as the
electrical efciency is lower than for the DFIG at synchronous speed.
In Fig. 7b the unit operates in a higher gross head and electrical
power than before. In this situation, the unit works out of the BEP.
Nevertheless, by increasing the rotating speed (and opening the guide
vanes) a close condition to the BEP can be reached, maintaining the
electric power. For this particular design, the ow rate is slightly
reduced as the hydraulic efciency is already very high even the ma-
chine operates in off-design conditions. Again, the DFIG shows a better
performance and the limitation of the rotating speed variation for this
technology is not affecting the optimum.
The last situation (Fig. 7c) represents the unit operating in a lower
gross head and electrical power. Again, when the turbine operates with a
SG, the unit is far from the BEP. In this case, by reducing the rotating
speed and closing the guide vanes, the BEP can be reached with variable
speed and the ow rate passing through the turbine is reduced. In this
situation, the ±10% restriction for the DFIG is still not important for
reaching the optimum although it can be appreciated that by further
reducing the head (moving to a higher n11) this limitation would affect.
4.2. Increase of hydraulic efciency and reduction of ow rate with DFIG
and FSFC
Taking into account the main behavior observed in Fig. 7, in this
section the improvement of
η
h when using FSFC and DFIG technologies
has been calculated for every operating point n11,q11 . When the unit
operates with the SG and considering that its operation is restricted by a
constant gross head Hg, only some specic n11,q11 operating points can
be reached. All these points lay in a curve (which is not a vertical line
due to losses in hydraulic circuit) corresponding to the given gross head
Hg. These curves are represented for several Hg in Fig. 8a. Low head
curves correspond to high n11 and vice versa. Operating points with high
q11 corresponds to high loads (high Pe,Q and distributor more opened).
Variable speed technologies permit to move in an almost horizontal
line as seen in Fig. 7. Therefore, the areas of the Hill-Chart with close and
inclined constant efciency curves are potential areas of improvement.
These areas correspond mainly to low Hg and low load (low Pe, Q)
operation of the machine (right-bottom of the Hill-Chart) and high head
and high load operation (top-left of the Hill-Chart). This fact is
conrmed in the results shown in Fig. 8b and Fig. 8d. With variable
speed, it is possible to improve the hydraulic efciency up to a 2–3% in
these areas. Both technologies show similar capability for improvement,
as seen in the respective gures. For very extreme off-design heads, the
FSFC technology shows a better performance as it does not have the
limitation of ±10% assumed for the DFIG.
Finally, the most important result corresponds to the possible ow-
rate reduction with variable speed. To analyze this result, we need to
consider the potential improvement of
η
h but also the reduction of
η
e
with respect to the SG (discussed in Section 3.4). In this case, the dete-
rioration of
η
e is worse for the FSFC. Therefore, as seen in Fig. 8c and
Fig. 8e, the potentiality to reduce the ow rate in the unit is higher for
the DFIG unit, especially in the operating areas mentioned before (low
head and low load; high head and high load). This reduction can be
about 2–3% in the most extreme conditions (right-bottom of the Hill-
Chart).
4.3. Amount of water saved in different scenarios
Finally, some results regarding the potential reduction of water
consumed by the unit assuming different annual scenarios (in a
simplied way) are presented. It is assumed that Hg follows the typical
pattern of a maximum during spring and a minimum after 6 months
(autumn). If the unit is properly designed for the hydroelectric instal-
lation (considering the averaged levels in the upstream and downstream
reservoirs), then the design head and therefore the BEP is assumed to be
in the center of the operating area. Together with the load variation of
the unit, this will describe an operating area every half year, as repre-
sented in Fig. 9. In order to make the results more general and repre-
sentative for more units, it is assumed a uniform operation inside this
area.
Regarding the head variation, with respect to the design head HgSG ,
two different situations are assumed; ±10% of variation and a more
Fig. 6. Best Efciency Point of the Unit (BEP).
Table 2
Operating Parameters at the BEP for the turbine unit with the SG.
Gross Head (HgSG )117m q11,BEP 681l/s•m−5/2
Net Head
BEP
(HnSG )112.3m Distributor angle 18.8◦
Flow rate (QSG) 29.3m3/s
η
h 95.47%
PeSG 30MW
η
mSG 99.67%
n11,BEP 57min−1•m1/2
η
eSG 97.82%
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Energy Conversion and Management 291 (2023) 117296
8
extreme variation of ±20% with respect to HgSG . These approximate
ranges have been dened based on our previous experiences with
similar types of units (see for example the considered prototypes in
[29,30]).
Two different scenarios are also considered for the load variation. In
the present operation of the unit, the ow rate range is dened with the
following limits [0.54QSG-1.16QSG ]. These limits are dened considering
the design of the unit and, in a more general context, considering the
management of the water resources and the hydric restrictions given by
national laws. Similar Q ranges, are also found in similar type of units
[29,30]. The rst scenario considers that the unit is using for regulating
purposes, and therefore it operates around the entire range. The second
scenario is that the unit is operated in a more conservative way around
the BEP and then the range [0.8QSG -1.16QSG].
Assuming the four different operating areas represented in Fig. 9, the
amount of water saved with respect to the synchronous unit has been
calculated. For this calculation, it is considered that the synchronous
unit and the variable speed unit produce exactly the same electrical
power at every time.
Fig. 10 shows the relative difference (%) of water consumed by the
DFIG machine and the FSFC machine with respect to the synchronous
machine. These values represent an approximated averaged value of the
areas dened in Fig. 9 transposed to Fig. 8c & Fig. 8e. Positive per-
centages mean that the variable speed unit would consume less water in
that scenario than the synchronous machine. The better performance of
the DFIG is clear, and it is due to the higher electrical efciency. In fact,
in one-year average, the FSFC unit will consume more water than the
synchronous unit. Nevertheless, if FSFC is already installed for other
purposes (such as exibility of the unit [14]) it can be used to save water
in extreme off design conditions (Fig. 8).
It is also important to remark that the results for the FSFC have been
obtained considering that the converters are always connected to the
synchronous generator, and therefore they always deteriorate the elec-
tric efciency. Nevertheless, as discussed in [9] a solution to improve
this issue is to have a switch system to connect/disconnect the full power
converter when necessary. This would improve the results for the FSFC
technology.
The amount of water saved would be even larger if the operating
ranges of the unit are increased. For example, it has been checked that if
the unit would operate with 0.4ΔHgSG and 0.86 ΔQSG (instead of
0.4ΔHgSG ; 0.62 ΔQSG )the amount of water saved in a long-term opera-
tion would be doubled (0.55% vs 0.28% for the scenario a represented in
Fig. 9). Finally, it is worth to mention that in the near future it is ex-
pected that, hydropower units will have to operate with lower heads and
ow rates than they were designed for, due to extreme droughts. This
particular situation will increase the water saved with variable speed
technologies, as it is precisely the area of the Hill-Chart where the range
of hydraulic efciency improvement is maximum (see Fig. 8b and
Fig. 8d).
To nish this section, we calculate how many hm3 could save the
DFIG unit with respect to the actual prototype in the different scenarios
assumed. These results are shown in Fig. 11. When operating the unit in
scenario c and d (Fig. 8) more water is needed as the unit works with
higher ow rates (Fig. 11a). In terms of water saving, as seen in Fig. 11b,
it is estimated that between 1 and 1.5 hm3 (1 −1.5×109 liters) could be
saved with the DFIG in one year of operation for similar type of units.
This roughly represents 1% of the useful capacity of the actual dam’s
reservoir. This percentage would be further increased for larger capacity
units as the nominal ow rate is higher.
5. Conclusions
In this study, the potentiality of using variable speed technology to
save water has been investigated with accurate data of a mid-head
prototype, which is one of the demonstrators of the EU project XFLEX-
Hydro. Thanks to the information during the commissioning tests and
the Hill-Chart of the unit, a realistic model could be made. Results and
conclusions of these study may be useful for mid-head Francis units.
The two different technologies used for variable speed hydro units
have been analyzed and compared. These are the Doubly Fed Induction
Generator (DFIG) and the Full Size Frequency Converter (FSFC). It is
shown that both technologies can help to reduce the passing ow rate
Fig. 7. Operation with variable speed. DFIG and FSFC. a) Operating at
H
g/Hg−SG =1 and Pe/Pe−SG =1 b) Operating at Hg/Hg−SG =1.2 and Pe/Pe−SG =
1.26 c) Operating at Hg/Hg−SG =0.8 and..Pe/Pe−SG =0.72
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Energy Conversion and Management 291 (2023) 117296
9
with respect to the typical synchronous generator unit, especially when
the unit operates in extreme off-design conditions (higher/lower heads
than the design head). It is estimated that the hydraulic efciency can be
improved around 3% when the unit operates at very high/low heads,
with respect to the design head.
In the present study, the decrease of the electrical efciency for
variable speed technologies has been considered. In our model, which is
also in accordance to previous studies, the DFIG has a higher electrical
efciency than the FSFC. This advantage in electrical efciency of the
DFIG with respect to the FSFC can be 1% to 1.5% close to the BEP, and
reduces when the unit operates in off-design conditions. Therefore,
when considering the whole unit, the DFIG shows better water saving
options.
Four different annual-term scenarios have been simulated with
different head and load variations. It is shown, that water saving options
are higher for units working with a high variation range of head and
Fig. 8. A) hill-chart of the mid-head francis unit. lines of operation with constant H
g and synchronous machine. b& d) Improvement of hydraulic efciency (%) for
every n11 ,q11. DFIG and FSFC technologies c& e) Reduction of ow rate Q with respect to the synchronous machine (%). DFIG and FSFC technologies.
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Energy Conversion and Management 291 (2023) 117296
10
load. It is estimated that with the DFIG technology, around 0.2%-0.3% of
water could be saved in one year of operation compared to the syn-
chronous unit assuming a head variation of ±20%. For the analyzed
unit this represents 1–1.5 hm3 (1 −1.5×109 liters) or 1% of the useful
capacity of the dam’s reservoir.
Variable speed operation may become even more interesting
Fig. 9. Annual operating areas considered. a) Unit with large variation of head and load ([0.8H
gSG -1.2HgSG ]& [0.54QSG-1.16 QSG ]) b) Unit with small variation of head
and high variation load ([0.9HgSG -1.1HgSG ]& [0.54QSG -1.16 QSG]) c) Unit with large variation of head and small variation of load ([0.8HgSG -1.2HgSG ]&
[0.8QSG-1.16 QSG ]) and d) Unit with small variation of head and load ([0.9HgSG-1.1HgSG ]& [0.8QSG-1.16 QSG]).
Fig. 10. Relative saving of water for the different scenarios represented in Fig. 9 with respect to the synchronous unit. a) FSFC and b) DFIG.
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Energy Conversion and Management 291 (2023) 117296
11
considering a near future scenario with more common extreme
droughts. Under such conditions, the units already installed will have to
operate with heads and loads much lower than they were designed for.
As seen in this study, under these operating conditions, the potentiality
of saving water is maximum.
CRediT authorship contribution statement
Alexandre Presas: Conceptualization, Methodology, Formal anal-
ysis. Carme Valero: Conceptualization, Methodology, Funding acqui-
sition. David Valentín: Software. M`
onica Egusquiza: Software. Pedro
Diogo Pinto: Formal analysis. Ana Gonçalves de Carvalho: Formal
analysis. Alex Coronati: Supervision. Eduard Egusquiza: Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgements
First of all, Authors would like to acknowledge XFLEX Hydro [20].
This study is a direct output of the technologies being studied in this
project. Alexandre Presas would like to acknowledge, Nicolas Hugo from
ALPIQ, Thomas Hildinger from VOITH and Josep Bordonau from UPC
for his expertise and valuable comments regarding the FSFC and DFIG
models and also Jo˜
ao Delgado for his valuable contributions and ideas
during part of this project. Alexandre Presas and David Valentín
acknowledge the Serra Húnter program of Generalitat de Catalunya.
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Fig. 11. A) water consumed (hm
3) in one year with the different scenarios represented in Fig. 9. b) Water saved (hm3) if operating with DFIG.
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