Renewable Energy 35 (2010) 2639e2648
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ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
Wave energy plants: Control strategies for avoiding the stalling behaviour in the
Wells turbine
Modesto Amundarain
*
, Mikel Alberdi, Aitor J. Garrido, Izaskun Garrido, Javier Maseda
Dept. of Automatic Control and Systems Engineering, EUITI Bilbao, University of the Basque Country, Plaza de la Casilla 3, 48012 Bilbao, Spain
a r t i c l e i n f o
Article history:
Received 16 October 2009
Accepted 10 April 2010
Available online 6 May 2010
Keywords:
Wave energy
Oscillating water column
Wells turbine
Double-fed induction generator
Control
a b s t r a c t
This study analyzes the problem of the stalling behaviour in Wells turbines, one of the most widely used
turbines in wave energy plants. For this purpose two different control strategies are presented and
compared. In the
first
one, a rotational speed control system is employed to appropriately adapt the
speed of the double-fed induction generator coupling to the turbine, according to the pressure drop
entry. In the second control strategy, an airflow control regulates the power generated by the turbine
generator module by means of the modulation valve avoiding the stalling behaviour. It is demonstrated
that the proposed rotational speed control design adequately matches the desired relationship between
the slip of the double-fed induction generator and the pressure drop input, whilst the valve control using
a traditional PID controller successfully governs the
flow
that modulates the pressure drop across the
turbine.
Ó
2010 Elsevier Ltd. All rights reserved.
1. Introduction
The use of distributed energy resources is increasingly being
pursued as a supplement and an alternative to large conventional
central power stations
[1].
Therefore, the control of the power
delivered to the grid is becoming an important topic, especially as
the number of distributed power generation systems increases.
In this context, the ocean composes an enormous and predict-
able source of renewable energy with the potential to satisfy an
important percentage of the worldwide electricity supply. It has
been estimated that 0.02% of the renewable energy available within
the oceans would satisfy the present world demand for energy
[2].
There exist different forms of renewable energy available in the
oceans: waves, currents, thermal gradients, salinity gradients, tides
and others. During the last years, there has been a worldwide
resurgent interest for wave energy. Harnessing the immense wave
power of the world’s oceans can be part of the solution to our
energy problems. Conversion of the wave resource alone could
supply a substantial part of electricity demand of several countries
in Europe, such as Ireland, UK, Denmark, Portugal, Spain and others.
The Electric Power Research Institute has estimated the wave
energy along the U.S. coastline at 2100 Twh per year, which
represents half the total U.S. consumption of electricity. Ocean
*
Corresponding author. Tel.:
þ34
946014503; fax:
þ34
946014300.
E-mail address:
molty.amundarain@ehu.es
(M. Amundarain).
0960-1481/$
e
see front matter
Ó
2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.renene.2010.04.009
waves arise from the transfer of energy from the sun to the wind
and then to the water. Solar energy creates wind which then blows
over the ocean, converting wind energy to wave energy. Once this
conversion has taken place, wave energy can travel thousands of
miles with little energy loss. Most importantly, waves are a regular
source of power with an intensity that can be accurately predicted
several days before their arrival.
There exist many different technologies to convert ocean wave
power into electricity and, nowadays, it remains unclear what the
winning technical approach is. This is reflected by several different
technical approaches and different methods and systems for con-
verting this power into electrical power, such as oscillating water
columns (OWC), hinged contour devices such as the Pelamis,
overtopping devices such as the wave dragon and the Archimedes
wave
[3].
However, the oscillating water column type wave energy
harnessing method is considered as one of the best techniques to
convert wave energy into electricity. As shown schematically in
Fig. 1,
the OWC consists of a partially submerged, hollow structure,
which is open to the sea below the water line. This structure
encloses a column of air on top of a column of water. As waves
impinge upon the device, they cause the water column to rise and
fall, which alternatively compresses and depressurises the air
column. If this trapped air is allowed to
flow
to and from the
atmosphere via a turbine generator, energy can be extracted from
the system and used to generate electricity.
As indicated in Ref.
[4],
two different turbines are currently in
use; the Wells turbine
[5e8]
and the impulse turbine
[9].
Both
2640
M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648
2. Theoretical analysis and modelling
In this section we will present the necessary theoretical analysis to
model the different components of the systems, i.e.: wave model,
oscillating water column, Wells turbine, and the induction generator.
2.1. Wave theories. Power per meter of wave front
The
first
objective of our analysis is to
find
the power per
meter of wave front (or wave crest) to model the input to the
system. The mathematical description of periodic progressive
waves is not a trivial issue. Some well-known works of authors,
such as Muir Wood (1969), Le Mahaute (1969) and Korma (1976)
recommended ranges of application for the various wave theories
[15].
Therefore, a number of regular wave theories of diverse
degree of complexity have been developed to describe the water
particle kinematics associated with ocean waves. These would
include linear or Airy wave theory, Stokes second order and other
higher order theories, stream-function and cnoidal wave theories,
amongst others. Fortunately, the earliest (and simplest) descrip-
tion, attributed to Airy in 1845, is generally accurate enough for
many engineering purposes and specifically for control design
purposes
[16].
Linear (or Airy) wave theory describes ocean waves
as simple sinusoidal waves. Surfaces waves can be classified
according to the ratio of the wavelength (L) to the water depth (h),
as follows:
Deep-water:
h/L
>
0.25.
Transitional water: 0.25
!
h/L
>
0.05.
Shallow-water: 0.05
!
h/L.
NEREIDA MOWC is a project involving the integration of an OWC
system with Wells turbines in the new rockfill breakwater at the
harbour in Mutriku, located in the Basque coast of Spain. The
technical solution adopted in this case consists of 16 OWCs, to give
an active collector length of close to 100 m. The breakwater is
located in 7 m (h) of MWL or SWL (mean water level or still water
level)
[17].
The average height of waves in the Cantabrian coast is
less than 2 m with a period between 8 and 12 s
[18].
According to
these data, the most suitable approach in our case is to use the
linear wave theory for transitional water.
In
Fig. 2
is shown a wave with its characteristic parameters. The
part of the wave profile with the maximum elevation above the still
water level (SWL) is called the wave crest and the part of the wave
Fig. 1.
Scheme of OWC.
these turbines are currently in operation in different power plants
in Europe, India, Japan, Korea, and so forth
[10].
The Wells turbine,
which was developed by Prof. Alan Wells in 1976, has been
extensively researched over the last 30 years. This turbine, converts
the bi-directional airflow into mechanical energy in the form of
unidirectional shaft power, which is in turn used to move the
wound rotor induction machine.
The use of double-fed induction generator, DFIG, has a huge
potential in the development of distributed renewable energy
sources
[11,12].
DFIG is essentially an asynchronous machine, but
instead of the rotor windings being shorted (as in a
“squirrel-cage”
induction machine), it is arranged to allow an AC current to be
injected into the rotor, via the power converter. By varying the
phase and frequency of the rotor excitation it is possible to optimise
the energy conversion
[13].
The frequency converter only has to
process the generator’s slip power fraction, which is generally no
more than 30% of the generator rated power. This reduced rating for
the frequency converter implies an important cost saving,
compared to a fully rated converter.
Several prototypes of OWCs have been built, such as, Toft-
stalen, Norway, 1985; Trivandrum, India, 1990; Pico, Portugal,
1999; Limpet, UK, 2000; Port Kembla, Australia, 2005
[14].
The
Basque Energy Board (EVE) was created by the Basque Govern-
ment in 1982 and has been the main agent of energy policy in the
Basque Country. The NEREIDA MOWC project is intended to
demonstrate the successful incorporation of the OWC technology
with Wells turbine power take-off into a newly constructed
rubble mound breakwater in the Basque location of Mutriku, in
the northern coast of Spain. This demo project aims to demon-
strate the viability of this technology for future commercial
projects. In this context, the objectives of the present work are
twofold: on one hand, to present and compare two different
control strategies for avoiding the stalling behaviour in the Wells
turbine and, on the other hand, to particularize these results to
the case of Mutriku.
The paper is organized as follows: in Section
2
is presented
a theoretical analysis and modelling of the waves, OWC, Wells
turbine, and DFIG. In Section
3,
the problem of the stalling behav-
iour in the Wells turbine and the uncontrolled case drawbacks are
described. Section
4
presents the control strategies for avoiding the
stalling behaviour in Wells turbine in two different ways. Results
and discussions comparing the uncontrolled and controlled cases
are presented in Section
5.
Finally, concluding remarks are given in
Section
6.
Fig. 2.
Ocean wave.
M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648
2641
profile with the lowest depression is the wave trough. The distance
from the SWL to the crest or the trough is the amplitude of the wave
and the wave height (H) is defined as the total distance from the
trough to the crest.
The wavelength of a regular wave at any depth is the horizontal
distance between successive points of equal amplitude and phase
for example from crest to crest or trough to trough and is defined
according to the linear theory as:
Therefore, since a wave resource is typically described in terms
of power per meter of wave front, it can be computed by multi-
plying the energy density by the wave front velocity as expressed in
Eq.
(8) [19].
P
wavefront
¼
nCE
density
¼
C
g
E
density
;
with
C
¼
L
T
(8)
gT
2
L
¼
tanhð2
p
h=LÞ
2
p
where:
L:
wavelength (m).
g:
gravitational constant (9.81 m/s
2
).
T:
wave period (s).
h:
water depth (distance from ocean
floor
to SWL) (m).
P
wavefront
¼
(1)
r
w
gH
2
L
16T
4
p
h=L
1
þ
ðW=mÞ
sinhð4
p
h=LÞ
(9)
2.2. Oscillating water column
The OWC energy equations are similar to those used for wind
turbines. Eq.
(10)
expresses the power available from the airflow in
the OWC’s chamber.
P
in
¼
2
p
þ
r
V
x
=2
V
x
a
(10)
The equation describing the free surface as a function of time
t
and horizontal distance
x
for a simple sinusoidal wave can be
shown to be:
where:
P
in
: pneumatic incident power (W).
p:
pressure at the turbine duct (Pa).
r
: air density (kg/m
3
).
V
x
: airflow speed at the turbine (m/s).
a:
area of turbine duct (m
2
).
h
¼ ðH=2Þ
cosðð2
p
x=LÞ
À ð2
p
t=TÞÞ
where:
(2)
h
: elevation of the water surface relative to the SWL (m).
H:
wave height (m).
The propagation speed or celerity of a regular wave is given by:
2.3. Turbo-generation equipment
The equation for the system turbo-generator can be written as:
gT
C
¼
L=T
¼
tanhð2
p
h=LÞ
2
p
(3)
The total average wave energy per unit surface area is called the
specific energy or energy density and is given by:
v
u
J
vt
¼
T
t
À
T
g
(11)
where:
J:
moment of inertia of the system (kg m
2
).
u
: angular velocity of rotor (rad/s).
T
t
: torque produced by the turbine (N m), calculated below.
T
g
: torque imposed by the generator (N m), calculated below.
E
density
¼
r
gH
2
E
¼
w
L
8
(4)
The energy density of a wave, shown in Eq.
(4),
is defined as the
mean energy
flux
crossing a vertical plane parallel to a wave’s crest.
The energy per wave period represents the wave’s power density.
Eq.
(5)
shows how the wave power density can be found by dividing
the energy density by the wave period.
P
density
¼
where:
E
density
r
gH
2
¼
w
T
8T
(5)
2.3.1. Wells turbine
The input to the Wells turbine is the pulsating pressure drop
across the turbine rotor which is generated due to the airflow from
the OWC chamber. The equations for the turbine are:
i
h
2
u
t
Þ
2
dP
¼
C
a
Kð1=aÞ V
x
þ ðr
2
(12)
(13)
(14)
(15)
(16)
E
density
: wave energy density (J/m ).
P
density
: wave power density (W/m
2
).
The rate at which wave energy propagates is directly dependent
on the group velocity of the wave. The group velocity is given by:
i
h
2
T
t
¼
C
t
Kr V
x
þ ðr
u
t
Þ
2
À1
T
t
¼
dPC
t
C
a
ra
C
g
¼
nC
where:
C
g
: celerity (wave front velocity) (m/s).
C:
wave celerity (m/s).
n:
constant determined by:
(6)
f
¼
V
x
ðr
u
t
Þ
À1
Q
¼
V
x
a
h
turbine
¼
T
t
u
t
ðdPQ Þ
À1
¼
C
t
ðC
a
phyÞ
À1
(7)
K
¼
r
b
ln=2
(17)
1
4
p
h=L
1
þ
n
¼
2
sinhð4
p
h=LÞ
(18)
2642
M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648
14
12
Ca (Power Coefficient)
10
8
6
Fig. 3.
Dynamic d-q equivalent circuit of DFIG d axis circuit.
4
where:
dP:
pressure drop across the rotor (Pa).
C
a
: power coefficient.
K:
constants (kg/m).
a:
cross sectional area (m
2
).
V
x
: airflow velocity (m/s).
r:
mean radius (m).
u
t
: turbine angular velocity (rad/s).
C
t
: torque coefficient.
f
:
flow
coefficient (can be expressed as angle).
b:
blade height (m).
l:
blade chord length (m).
n:
number of blades.
2.3.2. Double-fed induction generator (DFIG)
Figs. 3 and 4
show the d-q dynamic model equivalent circuits. As
it is well-known, the main advantage of the d-q dynamic model of
the machine, also know as vector control or
field
oriented control is
that all the sinusoidal variables in stationary frame appear as DC
quantities referred to the synchronous rotating frame
[13].
Hence,
the equations for the generator are simplified to:
2
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Flow Coefficient
Fig. 5.
Power coefficient vs
flow
coefficient.
and the
flux
linkage expressions in terms of the currents can be
written as follows:
j
qs
¼
L
s
i
qs
þ
L
m
i
qr
;
j
ds
¼
L
s
i
ds
þ
L
m
i
dr
;
L
s
¼
L
ls
þ
L
m
;
where:
j
qr
¼
L
r
i
qr
þ
L
m
i
qs
j
dr
¼
L
r
i
dr
þ
L
m
i
ds
(24)
(25)
(26)
L
r
¼
L
lr
þ
L
m
v
qs
¼
R
s
i
qs
þ
d
j
þ
u
e
j
ds
dt
qs
d
j
À
u
e
j
qs
dt
ds
d
j
þ ð
u
e
À
u
r
Þ
j
dr
dt
qr
(19)
v
ds
¼
R
s
i
ds
þ
(20)
R
s
,
L
ls
: stator resistance and leakage inductance (U).
R
r
,
L
lr
: rotor resistance and leakage inductance (U).
L
m
: magnetizing inductance (H).
L
s
,
L
r
: total stator and rotor inductances (H).
v
qs
,
i
qs
: q axis stator voltage and current (V, A).
v
qr
,
i
qr
: q axis rotor voltage and current (V, A).
v
ds
,
i
ds
: d axis stator voltage and current (V, A).
v
dr
,
i
dr
: d axis rotor voltage and current (V, A).
j
qs
,
j
ds
: stator q and d axes
fluxes
(Wb).
j
qr
,
j
dr
: rotor q and d axes
fluxes
(Wb).
v
qr
¼
R
r
i
qr
þ
(21)
0.6
v
dr
d
¼
R
r
i
dr
þ
j
dr
À ð
u
e
À
u
r
Þ
j
qr
dt
(22)
0.5
Ct (Torque Coefficient)
3
P
j
ds
i
qs
À
j
qs
i
ds
T
e
¼
2 2
(23)
0.4
X: 0.3
Y: 0.34
0.3
0.2
0.1
0
-0.1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Flow Coefficient
Fig. 4.
Dynamic d-q equivalent circuit of DFIG q axis circuit.
Fig. 6.
Torque coefficient vs
flow
coefficient.
M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648
7000
2643
6
6000
x 10
4
Stalling behabior
5
5000
Pressure drop (Pa)
4
4000
Turbine power (W)
3
3000
2
2000
1
1000
0
0
0
10
20
30
40
50
60
70
80
90
100
Average value (21.554kw)
-1
0
10
20
30
40
50
60
70
80
90
100
time (s)
Fig. 7.
dP
¼ j7000
sinð0:1
p
tÞj
Pa:
time (s)
Fig. 9.
Pt vs time for
dP
¼ j7000
sinð0:1
p
tÞj
Pa:
u
e
: stator supply frequency (rad/s).
P:
number of poles of the machine.
u
r
: rotor electrical speed
¼
u
(P/2) (rad/s).
T
e
: electromagnetic torque (N m).
3. Problem formulation: stalling behaviour in the
Wells turbine
The performance of the Wells turbine is limited by the onset of
the stalling phenomenon on the turbine blades. In order to explain
the nature of the stalling behaviour it is recommendable to intro-
duce some previous concepts regarding the operation of the
system. The torque and power developed by the turbine can be
computed based on the behaviour of the power coefficient and the
torque coefficient with respect to the
flow
coefficient
[20].
These
are the characteristic curves of the turbine under study and their
shape may be seen in
Figs. 5 and 6.
From Eq.
(15),
it may be observed that when the airflow velocity
increases, the
flow
coefficient also increases provoking the so-called
stalling behaviour in the turbine. This behaviour is also clearly
observable in
Fig. 6
when
f
approaches 0.3 (this value may change
depending on the characteristic curve of each turbine). In order to
model the waves, it is necessary to take into account the spectrum of
the wave climate, which indicates the amount of wave energy at
different wave frequencies. Considering this data and the value
T
¼
10 s
[17]
for the standard input pressure drop in our case, the
turbine may be experimentally modelled as
j7000
sinð0:1
p
tÞj
Pa; as
it may be seen in
Fig. 7.
With this input, the variation of the
flow
coefficient for the
uncontrolled system may be seen in
Fig. 8.
It can be observed that
its value is higher than 0.3, which corresponds to the stalling
behaviour threshold value for our turbine.
In this sense,
Figs. 9 and 10
show the power extracted from the
turbine and generator respectively. Please note that the negative
sign of the generator power in
Fig. 10
is due to the sign convention
used, and it just means that this power is provided to the grid. As
indicated before, it may be clearly observed that the power to be
extracted by the turbine and generator is limited by its stalling
behaviour.
In conclusion, the power to be extracted by the OWC-turbine
generator module is limited by the stalling behaviour in the Wells
turbine, composing therefore the main problem to resolve.
0.6
3
x 10
5
0.5
2.5
Flow Coefficient
0.4
Power generated (W)
2
Stalling behavior
1.5
Averaga value (-20.053kw)
1
0.3
0.2
0.5
0.1
0
0
0
10
20
30
40
50
60
70
80
90
100
-0.5
0
10
20
30
40
50
60
70
80
90
100
time (s)
Fig. 8.
Flow coefficient vs time for
dP
¼ j7000
sinð0:1
p
tÞj
Pa:
time (s)
Fig. 10.
Pg vs time for
dP
¼ j7000
sinð0:1
p
tÞj
Pa:
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