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Grid connection of wave energy converter in
heaving mode operation by supercapacitor
storage technology
ISSN 1752-1416
Received on 7th March 2015
Revised on 26th May 2015
Accepted on 1st July 2015
doi: 10.1049/iet-rpg.2015.0093
www.ietdl.org
Gianluca Brando1, Adolfo Dannier1, Andrea Del Pizzo1, Luigi Pio Di Noia1, Cosimo Pisani2✉
1
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Via Claudio, 21, Naples 80125, Italy
2
Department of Engineering, University of Sannio, Piazza Roma 21, Benevento 82100, Italy
✉E-mail: cosimo.pisani@unisannio.it
Abstract: European energy policy guidelines recognise renewable energy sources the main mean to contrast the rapid
fossil fuels depletion and the related global warming. Marine energy source represents an attractive and inexhaustible
reservoir from which to draw. One of the major difficulties in integrating sea wave generation systems or equivalently
wave energy converters (WECs) with existing electrical systems is the management of their generation intermittency.
This is essentially due to the inherent nature of the sea wave source. Energy storage represents an effective enabling
technology for mitigating such an effect. To this aim, this study proposes an efficient control strategy for embedded
floating buoy generation systems with energy storage technologies in order to regularise the injected grid power while
minimising the contractual power established by the distribution system operator. The control strategy has been tested
numerically on a grid connected DC microgrid formed by a DC bus at which a floating buoy generation system is
interfaced with an energy storage system, supercapacitors-based, having the purpose of smoothing the natural power
fluctuations of the WEC.
1 Introduction
European Union (EU) member states are settling their national
energy policies on the basis of three major needs: (i) to augment
the security of energy supplies by limiting the energy dependence
from foreign countries, (ii) to fulfil the targets imposed by
international regulatory frameworks coping with global warming
and (iii) to ensure global cost competitiveness [1]. Renewable
energy sources (RESs) option generally matches all the
aforementioned needs, covering actually a more and more leading
role in the EU member states energy portfolio, even due to the
rapid exhaustion of the oil resources [2, 3]. Several incentive
mechanisms have been specifically introduced to promote RES
development, such as carbon taxes, cap-and-trade systems, tax
credits and feed-in tariffs [4]. 2020 Climate and Energy package
(a.k.a. ‘20-20-20’package) sets the roadmap to follow for
achieving: (i) a 20% reduction in EU greenhouse gas (GHG)
emissions from 1990 levels; (ii) a share increase of EU’s energy
consumption covered by renewable resources to 20% and at last;
(iii) an improvement of 20% in EU’s energy efficiency, by the
year 2020 [5]. The aforementioned three items are directly linked
among them, actually it can be simply verified that an
enhancement of the RES share in EU member states energy
portfolios implies a consequent GHG emissions reduction and
often an improvement of the energy conversion processes
efficiency. For these reasons, RESs are universally recognised as
an effective tool to satisfy growing energy demand sustainable [6].
The ocean is an enormous source of energy. It is estimated that
0.1% of the energy in ocean waves could be capable of supplying
the entire world’s energy requirements five times over; currently
ocean energy covers around 0.02% of EU energy needs and it is
primarily focused on electricity production [7]. The basic energy
conversion technologies are aimed at exploiting diversified energy
forms, such as tidal and marine energy, wave energy, difference of
temperature and salinity energy. Several international initiatives are
testing these technologies around the world [8] with particular
reference to the wave and tidal/current energy systems; ocean
thermal energy and salinity gradient energy are still embryonic.
Wave energy converters (WECs), on which the present paper is
primarily focused on, have been subject of several
conceptualisations, patents, studies and in-field experimental
investigations [9–12]. WECs can be classified according different
criteria, such as the working principle (energy extraction
principle), water depth, location (shoreline, near-shore, offshore)
and size. The authors in [13] conceptualised a working-principle
based categorisation by considering the projects which actually
provided prototypes or however, those ones undergone to
extensive development efforts. From this framework, three main
WECs categories can be identified: oscillating water column,
overtopping converters and oscillating bodies. In the oscillating
water column systems, electric energy is produced by an
embedded electric generator with a turbine moved by the air flow
ducted in a column by the incident waves. In the overtopping
systems, the wave crest is captured and held at quote higher than
the surrounding water surface to transfer the inherent potential
energy to hydraulic turbines for the electric energy production. In
the oscillating bodies systems, the hydraulic motor/turbines or
linear electric generators convert the kinetic energy transmitted by
the sea waves to oscillating bodies floating or submerged.
Recently, different offshore wave generation devices have reached
the full-scale demonstration stage and they are generally
constituted by means of oscillating bodies, either floating or fully
submerged [14, 15]. Grid integration of the latter is a challenging
duty due to the impact of the power fluctuations caused by the
intermittent nature of the source on the electrical systems. Energy
storage is recognised, by academics and industrial community, an
enabling technology for mitigating the issue. Some recent studies
[11, 16–18] specifically deal with the topic for wave, current and
tidal generation systems without going deep inside architecture and
control strategies to develop for accomplishing this task. Actually,
the energy storage role is enhanced by the development of
appropriate architecture and control strategies aimed at managing
embedded sea wave generation systems with energy storage
technologies. Armed with such a vision, the present paper
proposes a simple but efficient control strategy for embedded
floating buoy generation systems with energy storage system
IET Renewable Power Generation
Research Article
IET Renew. Power Gener., pp. 1–10
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&The Institution of Engineering and Technology 2015
(ESS) supercapacitor based. The control strategy is tested on a grid
connected DC microgrid formed by a DC bus at which a floating
buoy generation system is interfaced with energy storage
technology having the purpose of smoothing the natural power
fluctuations of wave energy generation systems. The remaining of
this paper is organised as follows: Section 2 analyses all the
fundamental elements for achieving a proper ESS sizing and
technology choice, Section 3 discusses the designed control
strategy for mitigating the power fluctuations of the floating buoy
generation system, Section 4 reports numerical simulations
confirming the goodness of the conceptualised control strategy
and, at last, Section 5 provides concluding remarks.
2 ESS: sizing and technology choice
This section is devoted to analysing all the basic elements for
achieving a proper ESS sizing and technology choice: an adequate
characterisation of the wave energy source at the WEC installation
site, the sizing methodology, wave energy fundamentals for
electrical power generation and at last the technology choice criteria.
2.1 Wave energy source characterisation
An adequate characterisation of the wave energy source at the
installation site is essential for choosing the proper size of the
ESS. It is well known that such a source is widely variable on
several time-scales: from wave to wave, with sea state, and from
month to month (although patterns of seasonal variation can be
recognised). Wave energy characterisation benefits from several
investigations carried out for other purposes, such as navigation,
harbour, coastal and offshore engineering. All these studies
converged in a universally recognised powerful tool for wave
energy planning in Europe, namely WERATLAS [19]. Since this
tool provides data related to locations in the open sea, at distances
from the coast of a few hundred kilometres, some similar tools
have been specifically developed by some EU states, such as
Portugal [20] and Italy [21, 22] for near shore locations. An
installation of the floating buoy generation system in the
Mediterranean Sea, along the Sardinia’s west coasts in proximity
of Alghero, is hence here supposed. Such an installation
hypothesis is driven by the need to minimise the system payback
time. Actually the estimates provided by the wave energy potential
study for Italian coastlines [23] recognise this region one of the
most interesting, with an annual wave power from 5.1 to 12.0 kW/
m and hence annual wave energy from 51 to 110 MWh/m. In fact,
wave power is conventionally rated in terms of energy flux
crossing an imaginary deep water contour and expressed in
kilowatt/metres [24]. Analysing the assessment methodology at the
basis of the aforementioned studies is behind the scope of the
paper, nonetheless it can be useful to add to the synthetic power
estimates above a graphical analysis for the principal spectral
parameters, such as wave height (significant), peak and mean
period, and wave direction. Two different resolutions of the
spectral parameters are available: tri-hourly and half-hourly. More
specifically, the figures that follow are referred to the available
data from the wave gauge buoy of the Italian Wave Network
(IWN) installed at Alghero along a period of about seven years
(from 2001 to 2008) (Fig. 1).
The outcomes shown are the result of a preliminary processing
phase aimed at verifying the data consistency and integrity as well
as an outliers removal.
2.2 Wave energy fundamentals and procedure for WEC
electric power simulation
A rigorous description of a real sea wave would involve the
consideration of many elementary waves of different frequencies,
directions and wavelengths [8]. We consider, for instance the first
of the three aforementioned parameters; the rationale can be easily
extended for the remaining ones. The energy spectrum S(f)
measures how much energy is carried by different frequency
components in the real-sea ‘mixture’of waves. More specifically,
for a real sea wave, the average stored energy per unit area of sea
surface is
Et=
r
g1
0
S(f)df=
r
g
16 H2
s[J/m2] (1)
where ρ= 1030 kg/m is the mass density of sea water and g= 9.81
m/s
2
is the acceleration of gravity, whereas H
s
is the significant
wave height for the actual sea state, which is traditionally defined
as the average trough-to-crest height of the one-third of the
recorded waves with the highest heights [25]. E
t
is equally
subdivided between kinetic energy, as the result of the water
motion, and potential energy as the result of its position. Energy
spectrum can be derived either from a classical Fourier analysis or,
in some conditions, by using semi-empirical Pierson–Moskowitz
approximation [26] reported in the following
S(f)=5
16
f4
p
f5e−(5/4)(fp/f)4
H2
s[m2/Hz] (2)
where f
p
=1/T
p
is the peak frequency [at which S(f) has its
maximum], T
p
is the peak period. f
p
is related to the mean wind
Fig. 1 Histograms of the average wave period and height at Alghero (IT) –IWN data
IET Renew. Power Gener., pp. 1–10
2&The Institution of Engineering and Technology 2015
speed Uat a level of 19.5 m, through the following equation
fp=0.55 g
U[Hz] (3)
Fig. 2 depicts an example of energy spectrum from wind-sea
conditions for a wind velocity recorded equal to 11 m/s. The
presented tool could be valuable to overcome the lack of wave
spectral data (average wave height, frequency etc.) sampled with
shorter sampling periods with respect to the one presented in
Section 2.1 which reports long term statistics with purpose to map
the wave resource. Unfortunately, due to the recorded wind
velocities (that must be higher than 10 m/s) and the sea depth at
the installation site, it cannot be employed in our case. This
justifies the generation manner of the wave profiles introduced later.
By reformulating the approach proposed in [27], a real sea wave
acquisition along a certain time interval can be converted into an
equivalent train of sinusoidal waves having piecewise constant
amplitude A=H/2 along some subintervals (His the vertical
distance between crest and trough of the sinusoidal wave).
Generally speaking, the expression of each sinusoidal wave in the
generic subinterval as a function of the space and the time is
z
(x,t)=Acos 2
p
l
(x−vwt)
=Acos (k(x−vwt)) =Acos (kx −
v
t)
with k=2
p
l
and vw=
l
Tand
v
=2
p
T
(4)
where
l
is the wavelength in m, ωis the angular frequency in rad/s, T
is the period in s, v
w
is the wave velocity in the chosen
single-dimension reference system and kis the so-called wave
number representing the wave spatial frequency. As can be noted a
sinusoidal wave is uniquely determined by the three independent
sets (A,
l
,v
w
), (A,k,v
w
) and (A,k,ω).
Equation (1) can be characterised for the sinusoidal wave
expression above in this manner
Et=
r
g
8H2[J/m2] (5)
The half part of the stored energy is of potential type while the
remaining one is of kinetic type. A point absorber WEC, which is
the one considered in this paper, is characterised by a prevailing
dimension negligible with respect to the resource wavelength and
the motion occurs along a single axis reference system (heaving
mode).
It is well known that wave energy extraction may be considered a
phenomenon of wave interference, whereas, in case of point
absorbers, only the 50% of the stored energy can be captured [28].
To ensure this condition, Newton’s law on floating buoy has to be
formulated by considering the contribution of all the forces acting
on the WEC. The excitation force, F
w
, caused by the incident
wave has the following relationship [10]:
Fw(t)=(
r
g
p
r2−
rv
2V)
z
(0, t)
=
rp
r2(g−
v
2h)
z
(0, t) (6)
where his the point absorber submerged part, assumed cylindrical of
radius r. The radiated force term, representing the forces due to the
wave that is radiated as a result of the buoy oscillation, is here
neglected.
The hydrodynamic force, F
h
, depends on the buoy displacement
with respect to the equilibrium condition z= 0. The latter is
defined in a reference system rigidly coupled with the wave
surface at the buoy installation point x=0
Fh=−
r
g
p
r2z(7)
By neglecting viscous and friction effects, as well as the inertial force
since the buoy mass is negligible with respect to the water mass
moved, Newton’s second law can be so formulated
md2z
dt2=Fw+Fh+Fg(8)
with F
g
the force applied by the electrical generator.
The WEC control strategy for maximising the energy extraction
consists in ensuring that the mechanical power average value P
b
acting on the buoy is equal to half the average power P
w
related to
the wave motion
Pb=Pw
22r=
r
g
2rA
2vw(9)
Equation (9) takes into account that the wave power extraction is
performed by a cylindrical buoy with diameter 2r. On the other
hand, the instantaneous power P
b
(t) can be written as
Pb(t)=Fw(t)vb(t)=
rp
r2(g−
v
2h)
z
(0, t)vb(t)
=
rp
r2(g−
v
2h)Acos (
v
t)vb(t) (10)
Fig. 2 Example of an energy spectrum from wind-sea conditions (U = 11 m/s)
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Since g>ω
2h
, (10), for sake of simplicity, can be rewritten as
Pb(t)
rp
r2gA cos (
v
t)vb(t) (11)
with v
b
(t) is the buoy velocity. Naturally, energy extraction is
maximised when F
w
(t) and v
b
(t) phases are equal
vb(t)=Vbcos (
v
t) (12)
and hence
Pb(t)=Vb
rp
r2gAcos2(
v
t) (13)
then the optimum condition for the energy extraction is
1
TT
0
Pb(t)dt=
r
g
2rA
2vw(14)
that implies also that
1
2Vb
rp
r2gA=
r
g
2rA
2vw⇒Vb=A
p
rvw(15)
hence finally
vb(t)=A
p
rvwcos (
v
t)
=A
p
r
l
Tcos (
v
t)=A
p
22r
lv
cos (
v
t) (16)
From the relation above, the buoy displacement in optimum
condition has to be
z(t)=
l
p
22rAsin (
v
t) (17)
Equation (17) states that the buoy has to oscillate synchronously and
in quadrature with the wave at the installation site, with a
displacement which is proportional to the wave amplitude
according to its wavelength.
These optimality conditions are used to control the WEC which
will generate the maximum allowable power on the basis of the
assumed wave profiles. An example of the numerically built wave
profile is reported in Fig. 3.
As it can be noted, in each half hour, an equivalent train of
sinusoidal waves is generated by using the recorded parameters
and ensuring the total energy balance. In particular, the ratio
between the minimum and maximum amplitudes of the sinusoidal
wave train is fixed at 5
√in order to obtain a ratio between the
minimum and maximum WEC power peaks equal to 5. In this
condition, the ratio between the WEC instantaneous maximum
power and the WEC average power in the observation interval is
around 4.3, which represents a good approximation of the
observed wave motion variations with respect to the chosen
observation interval.
2.3 ESS technology choice
As previously pointed out ESS could represent an effective enabling
technology for (i) smoothing intermittent power fluctuations, (ii)
enhancing the reliability of the electrical distribution systems, (iii)
providing network services, such as load levelling and peak
shifting. Literature analysis [29–35] shows that the ESS
technology coupled with generation units powered by marine
source (wave, tidal and marine current) is essentially constituted
by electrochemical batteries, supercapacitors, flywheels,
compressed air energy storage, pumped-storage hydroelectricity
and so on. By making reference to the application of this paper,
the employment of some of them has to be excluded due both to
scale and technical issues. A valid help in the choice of the most
appropriate ESS technology is furnished by the Ragone diagrams
developed in [36] depicting the various technologies respectively
in the plane power-energy stored and nominal power-discharge
time. Roughly speaking the selection criteria are based upon the
ratio power-energy stored and the discharge time, which permits to
differentiate all the ESS technology, according three main
functionalities: power quality,bridging power and at last energy
management. In our application ESS performs the function of
improving the power quality at the interface bus with the main
grid, ensuring at the same time the required power not provided by
the WEC (exactly bridging power). The magnitude order of the
ESS discharge time is of from few seconds to few minutes. For
these reasons, the technologies effectively combinable with WEC
would be electrochemical batteries, supercapacitors and flywheels
individually or properly combined with them, if particular
purposes must be pursued. At the best of our knowledge, no one
real application or, however, research proposal considered until
know WEC coupled with flywheels. The motivations can be
reasonably found in the fact that the overall marine structure
dimensions would become prohibitive. By looking at a typical
time behaviour of the marine generator power profile depicted in
Fig. 3b, to mitigate the power fluctuations of the wave source,
ESS should have the following characteristics: (i) high power
density due to the high value of peak-to-average ratio, (ii) fast
dynamic in compensating the electric overproduction or
underproduction, hence fast response times in charging and
discharging stages, (iii) high lifetime and high charge/discharge
efficiencies. The aforementioned characteristics together with the
discussion argued in the section that follows justify how the
Fig. 3 Numerically built wave profile
aTrain of equivalent sinusoidal waves generated
bWEC electrical power produced
IET Renew. Power Gener., pp. 1–10
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supercapacitor technology appears the best candidate to be
integrated.
2.4 Sizing methodology
Since the aim of the ESS is to minimise the power fluctuations with
the main grid, it will continuously exchange a power quote, P
ESS
(t),
equal to the difference between the power P
WEC
(t) instantly
produced by the marine generation distribution unit and the power
P
VSR
(t) exchanged with the grid. The latter is clearly related to the
average profile of P
WEC
(t). Therefore, the objective is to make
P
VSR
(t) as constant as possible.
The size of the ESS, in terms of power and energy, can be
determined by calculating the following quantities [17]
PESS(t)=PWEC (t)−PVSR(t) (18)
EESS(Tw)−EESS (0) =Tw
0
PWEC(t)−PVSR (t)
dt(19)
where T
w
is the time interval on which P
VSR
(t) should to be kept
constant, here called the observation interval. The objective to
keep P
VSR
(t) constant is reached only if
PVSR(t)=1
TwTw
0
PWEC(t)dt=
PWEC ∀t[(0, Tw) (20)
Hence the kth element of the sinusoidal waves train provides an
average power equal to
PWEC,k=A2
k
r
gr
vl
/4
p
, (20) becomes
PVSR(t)=1
Nw
Nw
k=1
PWEC,k(21)
On the other hand, the instantaneous ESS energy in the considered
time interval is given by
EESS(t)=t
0
PWEC(
q
)−1
Nw
Nw
k=1
PWEC,k
d
q
(22)
Therefore, the sizing of the ESS is linked to the maximum E
ESS,max
of E
ESS
(t) in (0, T
w
).
Fig. 4 shows the behaviour of E
ESS,max
as a function of the number
of the elementary waves belonging to the time interval on which
P
VSR
(t) power has to be kept constant. From this figure, it can be
deduced that
†The sizing of the ESS is obviously linked to the number of
elementary waves; in particular, the behaviour is strictly dependent
on the expression of A
k
that appears as square power; E
ESS,max
is
not monotonous with respect to the considered number of elements.
†1.2 kWh rating would be sufficient for compensating the whole
sinusoidal waves train ensuring P
VSR
(t) constant on a wide T
w
(i.e.
30 min).
These considerations have to be matched with power requirements
of the ESS. Actually, the sizing power P
ESS,max
can be computed as
PESS, max =max PWEC(t)−1
TwTw
0
PWEC(t)dt
0,Tw
=max PWEC(t)
0,Tw−
PWEC (23)
that characterised for the WEC profile in Fig. 3b
max PWEC(t)
0,Tw75 kW,
PWEC 18 kW
⇒PESS, max 57 kW
⇒PESS, max
EESS, max 48 h−1(24)
It should be noted that the ratio P
ESS,max
/E
ESS,max
is the requested C
rate of the storage system. This result, together with the
considerations of the previous section, justifies that a
batteries-based ESS has to be excluded due to the well-known
reduced value of Crate, encouraging, for this application, the
installation of a supercapacitors-based ESS.
Therefore, by installing a supercapacitors-based ESS with P
ESS
=
57 kW and E
SS
= 1.2 kWh a constant power of 17 kW would be
ensured to the main grid on T
w
= 30 min. Unfortunately, this
choice is not compatible with the weight and dimensions
constraints of the embedded floating buoy generation system with
ESS. Therefore, an acceptable trade-off between the system
performances, in terms of power fluctuations reduction, and its
physical feasibility must be chosen. In particular, if the
observation interval is selected meeting the condition T
grid
≪T
w
<
T
wave
, with T
grid
is the reciprocal of the grid frequency and T
wave
is
the whole period of the sinusoidal wave train, a twofold advantage
would be obtained:
†The ESS energy requirements can be drastically reduced.
In particular for T
w
= 30 s one obtains E
ESS,max
≅80 Wh and
P
ESS,max
≅37 kW.
†The grid power fluctuations are kept at a frequency lower than
0.1 Hz.
This approach implies a rated power for the voltage source
inverter (VSR) almost equal to 37 kW. So, while the VSR power
rating increases from 17 to 37 kW, the ESS requirement decreases
from 1.2 to 80 kWh, with a sensible reduction of the overall cost.
By employing the presented sizing procedure, a 2 series-2 parallel
modules architecture is designed by considering the features of the
supercapacitors commercial solution reported in Table 1.
This configuration ensures adequate ESS capacity and a rated
voltage which can be easily adapted by a bidirectional chopper
boost to the DC-link operating voltage.
Fig. 4 E
ESS,max
as a function of the elementary waves number
Table 1 Supercapacitor module electric features
rated capacitance 5.8 F
rated voltage 160 V
rated power 26 kW
capacitance of individual cells 350 F
rated energy 21 Wh
number of cells 60
weight 5.1 kg
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3 Proposed control strategy for mitigating the
floating buoy generation system power fluctuations
The proposed control architecture of the embedded WEC with
energy storage is depicted in Fig. 5. As it can be noted, the system
is built upon a grid connected DC bus at which a floating buoy
generation system is interfaced with the supercapacitors-based
ESS. The DC side, operated at a voltage magnitude of 650 V, is
interfaced with the AC side (three-phase AC grid) by a VSR,
whose aim is to transfer the active power to the grid with unity
power factor and minimum current total harmonic distortion. On
the other hand, the ESS is connected at the DC link via a buck–
boost chopper. As explained below, the chopper should be
controlled with a constant voltage strategy whose aim is to keep
the DC-link voltage constant and equal to its reference value
V∗
c=650 V.
An AC permanent magnet machine coupled with ball-screw was
chosen for the WEC: an adequate modelling of the latter can be
found in [37]. Actually, a ball-screw system converts the linear
movement associated with the wave motion into rotating
movement of the generator machine allowing to achieve easily a
relatively high speed ratio, dependent on the chosen pitch screw.
This solution, compared with direct drive linear motors topologies,
is characterised by the highest values of power density thanks to
the high speed ratio that can be achieved with the ball-screw
technology. This approach allows therefore, to reduce the
generator size. Table 2 shows the electrical generators sizing
results obtained for two different generator types: AC brushless
with ball-screw system and tubular-linear AC brushless with direct
drive [38]. The electrical machines sizing has been performed by
using the FEM analysis software FLUX
®
.
As can be appreciated by Fig. 5, the control strategy is
characterised by two distinct logical layers that carry out two
different objectives: (i) the block maximum wave power extraction
control strategy computes the references signals for the low level
generator control in order to maximise the power available in the
incident waves according to the limits presented in Section 2.2; (ii)
the block WEC/ESS control strategy computes the reference power
for the low level VSR control in order to ensure a constant value
of power injected in the main grid on T
w
. The hierarchical control
levels are not related and hence can be executed independently.
More specifically, the maximum wave power extraction control
strategy, which is not the main focus of this work, can be
implemented according to several control paradigms. With this
regard, a very recent review of suitable control strategies for
electrical control of WECs is reported in [38]. Subsequently, the
following notable works can be identified in the relevant literature.
An observer-based control effectively implemented in wave tank
real experiments is described in [39] demonstrating how the
energy conversion rate can be improved. In [40, 41] the authors
deployed a centralised and a decentralised model predictive
controller for WEC arrays to maximise energy harvest. In each
case, an adequate WEC control requires, under the hypothesis of
only heave motion, the measurement of one of the parameters set
presented in Section 2.2. A reliable manner to accomplish this
task, without introducing too much complexity to the WEC
control algorithm, is to install a sensors network placed around the
WEC [29]. In this manner, the fundamental parameters of the
incident wave can be determined so permitting to impose the
optimal speed profile to the buoy according to the fundamentals
reported in Section 2.2.
On the other hand, the WEC/ESS control strategy, on which this
paper is primarily focused, delivers the wave energy extracted by
the WEC to the main AC grid, ensuring an instantaneous active
power equal to the average power extracted on the observation
interval T
w
. This approach allows to limit the contractual power
with the distribution system operator (DSO), since the power
fluctuation of the WEC is totally compensated by the ESS. A
further reduction of the VSR power is obtained through the choice
of the T
w
value, which guarantees a constant VSR power over
several incident waves (around 7 with respect to the statistical data
referring to H
s
= 1 m). Therefore, the role of the ESS consists
essentially in absorbing the alternating component produced by the
WEC. As the above hinted at, due to the recorded ratio between
the active power peak and its mean value on a wide time horizon,
ESS plays a bridging power functionality. The basic idea is to
Fig. 5 Schematic control architecture of the embedded floating buoy generation system with energy storage
Table 2 Comparison between ball-screw brushless generator and
tubular-brushless generator
Electrical generator
type
AC brushless with
ball-screw
Tubular-linear AC
brushless
power 20 kVA 20 kVA
maximum speed 1200 rpm 1 m/s
maximum
frequency
60 Hz 7 Hz
rated voltage 460 V 460 V
rated current 30 A 32 A
efficiency 0.93 0.82
pole pairs 3 6
external diameter 0.28 m 1.27 m
magnetic stack
length
0.15 m 0.5 m
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maintain the active power transfer level with the main grid as
constant as possible on T
w
through a proper VSR control:
supercapacitors will absorb power when the WEC generated
instantaneous power exceeds the VSR active power and vice versa
will provide power in the opposite case. During this operation, the
ESS state of charge (SOC) must be within the upper and lower
charging limits established by the manufacturers. This behaviour
can be obtained by properly computing the VSR reference power,
as explained below.
The balance of power at the DC link can be formulated as follows
1
2Cdv2
c
dt=PWEC −PESS −PVSR (25)
where v
c
is the DC-link voltage, P
ESS
is the power transferred to the
DC bus by the chopper which drives the ESS, P
WEC
is the power
generated by the wave motion and P
VSR
is the power exchanged
by the VSR with the electrical grid.
The term P
WEC
can be expressed as
PWEC =
PWEC +
˜
PWEC (26)
whereas
PWEC and
˜
PWEC are, respectively, the average and the
alternating components of P
WEC
.
Actually, by imposing that the VSR control permits to extract the
average value of the power produced by the WEC, i.e.
PVSR =
PWEC, (25) becomes
1
2Cd
dtv2
c
=
˜
PWEC −PESS (27)
The VSR control here applied is the one proposed by the authors in
[41].
The optimal control strategy of the chopper, according to an
effective paradigm like the one in [42–44], has to keep constant
the DC-link voltage since
d
dtvc=0⇒PESS =
˜
PWEC (28)
In this manner, at steady-state conditions, the ESS balances the WEC
alternating component while the VSR delivers the related average
component. Therefore, the condition V∗
c=const expresses,
synthetically, the control strategy of the chopper.
The proposed VSR control strategy hence updates the ‘main
component’P
^∗
vsr,kof the VSR reference power at the ‘update
instants’t
k
by evaluating the average active power injected in
the DC bus by the generator in the time interval [t
k−1
,t
k
] with
t
k
−t
k−1
=T
w
Pwec,k=(1/Tw)tk
tk−1
vdcidc,wec dt(29)
Therefore
P
^∗
vsr,k=
Pwec,k(30)
This approach would give good results only in case of slow WEC
power variations. Therefore, in order to considefR also highly
variable conditions (characteristic of the considered energy
source), two correction terms are added in order to compute the
VSR reference power at t
r
P∗
vsr.r=P
^∗
vsr,k+DP1,k+DP2,r(31)
where ΔP
1,k
, updated at 1/T
w
rate, takes into account the estimated
power variation of the WEC by means of the time derivative of
the WEC power, computed with respect to the two last
observations time intervals
DP1,k=
Pwec,k−
Pwec,k−1(32)
On the other hand, ΔP
2,r
, updated at 1/T
s
rate, takes into account the
distance of the supercapacitors actual SOC value with respect to the
reference value, fixed at 0.5
DP2,r=DPs(SOC −0.5)3(33)
This contribution is similar to a modified spring action that tries to
keep the SOC around 0.5. The constant ΔP
s
can be evaluated by
imposing that ΔP
2,r
is equal to the VSR power limit when SOC
assumes minimum and maximum values. Obviously ΔP
2,r
incidence for SOC values near 0.5 is negligible, as it should be, as
a consequence of the chosen cubic dependence. Obviously, P∗
vsr.r
is inherently limited to the maximum allowable value by the VSR
before driving the converter low level control. Field programmable
gate array could be a promising solution for the hardware
deployment of the described control strategy.
4 Numerical simulations
To confirm the validity and the effectiveness of the proposed control
strategy some numerical simulations are reported in this section. As
far as the simulation of the wave resource is concerned, the approach
described in the previous Sections has been applied. The equivalent
train of sinusoidal waves is characterised by a limit on the ratio
between the maximum and minimum wave heights A
max
/A
min
,
exactly equal to 5
√. More specifically, the significant wave height
considered in the simulations, summarised in Table 3, are the most
representative of a very wide observation period (almost 8 years).
Numerical simulations are performed in Simulink/Matlab
®
environment. The additional simulation parameters are synthesised
in Table 4. Components power ratings have been optimised for
Case B of Table 3. In fact Cases C and D numerical results have
been added in order to further validate the control strategy in the
presence of heavy sea waves conditions.
Figs. 6–9 show the behaviour of the main electrical quantities,
obtained in the four cases considered in Table 2. As it can be
easily deduced from Figs. 6a,band 7a,b(H
s
=0.5m and H
s
=1m),
the designed control strategy is able to keep the VSR power and
the residual RMS supercapacitor power near to the average and the
residual RMS WEC power, respectively, in the whole simulation
time interval (i.e. 30 min). Therefore, the average supercapacitors
power is negligible, as it can be deduced by the lower curves in
Figs. 6aand 7a. The SOC is kept around 0.5 in both the
considered cases, with relative oscillations that become higher with
H
s
= 1 m, as a consequence of the increased values of the residual
RMS supercapacitor power, which, as expected, increases by a
Table 3 Wave parameters adopted in the numerical simulations
Case A
min
H
s
A
max
T
p
A 0.12 0.5 0.26 4
B 0.23 1 0.52 4.5
C 0.46 2 1.03 6
D 0.94 4 2.1 7.5
Table 4 Additional parameters adopted in the numerical simulations
grid voltage 400 V
grid frequency 50 Hz
generator power 20 kVA
VSR power 40 kVA
ESS power 80 kW
ESS energy 84 Wh
sampling time 100 μs
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Fig. 7 Main electrical quantities recorded during the dynamic simulation –Case B
Fig. 6 Main electrical quantities recorded during the dynamic simulation –Case A
aAverage powers of the VSR, WEC generator and ESS with respect to the observation interval TW
bRMS of the residual powers of the WEC generator and ESS with respect to the observation interval TW
cESS state of charge
dInstantaneous value of the DC-Link voltage
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8&The Institution of Engineering and Technology 2015
factor equal to 4. Although not easily appreciable, P
VSR
has a
piecewise constant behaviour so it is constant on T
w
(i.e. 30 s).
Some non-idealities characterise the last two cases (H
s
= 2 m and
H
s
= 4 m), for which there is a major, although acceptable, the
difference between the VSR power and the average WEC power.
These results are justified by the discontinuities introduced in the
WEC power due to the active saturation of the generator power:
the strong variations of P
WEC
result in considerable differences
between the VSR reference power and the mean WEC power so
activating the conceptualised ‘spring equivalent action’of the
control strategy described above. This can be deduced from
Figs. 8cand 9c. The DC-link oscillations can be considered
Fig. 8 Main electrical quantities recorded during the dynamic simulation –Case C
Fig. 9 Main electrical quantities recorded during the dynamic simulation –Case D
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acceptable in all the considered cases, changing from the 0.8% (H
s
= 0.5 m) to 8% (H
s
= 4 m). It has to be noted that the ESS residual
RMS power is very close to the WEC RMS residual power in all
cases, while the ESS mean power (which should be ideally zero) is
kept at very reasonable levels, compatible with the sizing
procedure.
Finally, Fig. 10 shows the total (E
t
) and the average energy (E
m
)
exchanged by the ESS in Case A. As expected, E
m
reaches values
comparable with the ESS rated energy only at the beginning of the
simulation, when no one information is available about the WEC
power behaviour. Actually, after the control has stabilised, E
m
is
kept under 5% of the rated energy in the whole simulation. These
results confirm, therefore, the validity of both the control strategy
and the sizing procedure adopted.
5 Conclusive remarks
This paper presented an efficient control strategy for embedded
WECs with supercapacitor storage technology. Its objective is to
mitigate the inherent natural fluctuations of the wave resource
directly transferred to the electrical power produced.
Supercapacitor is demonstrated to be one of the best candidate
technology able provide good performance while ensuring at the
same time the technical/economic feasibility of the overall system.
The effectiveness of the designed control strategy has been tested
on a grid connected DC microgrid formed by a DC bus at which a
floating buoy generation system, interfaced with ESS
supercapacitors-based, is connected.
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