model based design of efficient power take-off
DESCRIPTION
Model Based Design of Efficient Power Take-OffTRANSCRIPT
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MODEL BASED DESIGN OF EFFICIENT POWER TAKE-OFFSYSTEMS FOR WAVE ENERGY CONVERTERS
ABSTRACT
The Power Take-Off (PTO) is the core of a Wave Energy Converter (WECs), being thetechnology converting wave induced oscillations from mechanical energy to electricity.The induced oscillations are characterized by being slow with varying frequency andamplitude. Resultantly, fluid power is often an essential part of the PTO, being theonly technology having the required force densities. The focus of this paper is toshow the achievable efficiency of a PTO system based on a conventional hydro-statictransmission topology. The design is performed using a model based approach. Genericcomponent models are developed and combined into a PTO system, describing thedynamics and power losses from wave to grid. Using the model, components sizes andcontrol are optimised and the achievable performance of the PTO is identified.
KEYWORDS: PTO, Hydraulics, Fluid Power, Point absorber, WEC, Wave Energy
1. INTRODUCTION
Numerous types of Wave Energy Converters (WECs) are under development for har-vesting the energy of the ocean waves, where several have reached the proof-of-conceptstage, showing it is possible to produce power, see e.g. [1] and [2] for a survey. A largegroup of WECs bases on directly converting the waves into an oscillating mechanicalmotion, e.g. point absorbers and multiple point absorber systems, see Fig. 1. Convertingthe mechanical motion into electricity is performed by the Power Take-Off (PTO).
Today, PTO solutions for such systems are characterized by poor efficiencies andreliabilities. The reason is that the waves induce slow irregular oscillations, whichrequires processing of large alternating forces in order to extract power [3]. Resultantly,fluid power is often a crucial part in the PTO system, being the only technology havingthe required force densities. However, fluid power systems are often characterized bypoor efficiencies, especially at part load which is an inherit property of wave power.A ratio of ten between peak and mean absorbed wave power is common, [4].
The Twelfth Scandinavian International Conference on Fluid Power, May 18-20, 2011, Tampere, Finland
Rico H. Hansen, Torben O. Andersen, Henrik C. PedersenAalborg University
Department of Energy TechnologyPontoppidanstrde 101, 9220 Aalborg, DenmarkPhone: + 45 9940 9240, Fax: + 45 9815 1411
E-mail: [email protected], [email protected], [email protected]
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Reciprocatingmotion
(a) (b)
PTO
Pout
text
tPTO
P =in warmtPTO
warm
(c)
Pointabsorber Multiplepointabsorber WaveVtarWEC
Figure 1: Point absorber type WECs and the Wavestar 600kW WEC [10].
The PTO extracts energy from the waves by applying a damping torque PTO to thefloat, such that the float performs work on the PTO system. As a result, the powerPhav = PTO!arm is extracted from the waves. In order to maximise the amount ofharvested power Phav, PTO has to be controllable. How to generate the optimal PTOforce trajectory is referred to as Wave Power Extraction Algorithms (WPEA). It canbe shown, see e.g. [4] and [5], that the WPEA optimizing the amount of harvestedpower requires the PTO to periodically transfer power to the float, i.e. four-quadrantbehaviour. This type of WPEA is termed reactive control. The main reason for usingreactive control is that the floats natural frequency should match the wave frequency.As the wave frequency varies, the PTO is used to change the natural frequency, whichrequires reactive power. This will described more thoroughly in section 3.2.
The focus of this paper is to investigate a PTO system for a multiple point absorberWEC, based on using conventional hydraulic and electrical components. The PTOsystem should be able to perform reactive control. The evaluation is performed forthe Wavestar 600kW WEC [9] seen in Fig. 1c, consisting of 20 hemisphere shapedfloats, each 5m in diameter. The advantage of a multiple point absorber system is theincreased power smoothing, [5].
The investigated PTO system is seen in Fig. 2. The PTO torque is produced by asymmetrical cylinder, which is operated in closed circuit with a variable displacementswash-plate pump/motor. The motor can stroke both positive and negative. Thus, themotor converts the bi-directional cylinder flow into a uni-directional high speed rotationfor powering a generator. Pressure control is performed by the swash-plate motor inorder to control the torque PTO applied to the float. Accordingly, a bent-axis motor isnot utilized as its bandwidth is too low to perform pressure control. To avoid oversizingmotor and generator, an energy overflow system is added such that cylinder flowsexceeding the motor capacity are combined in a common line, powering an extragenerator. Similar PTO concepts to Fig. 2 are suggested in e.g. [6]. More simplifiedhydraulic system have been proposed in [7] and [8], however, these can only providea constant PTO torque.
Sym
metr
iccylin
der
G
Flu
shin
gvalv
e DCAC
ext
Energy overflow
pEO
Float module
Floatmodule
PTO System
Inverter
G
DC bus
Energy overflow
Floatmodule
Floatmodule
Floatmodule
Floatmodule
Floatmodule
Figure 2: Investigated PTO system.
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2. METHODS
The evaluation of the PTO system in Fig. 2 is based on performing time simulationof the WEC and PTO for different wave inputs. Hence, to evaluate and optimize thePTO system, a time-efficient system model, which reflects the WEC and describedPTO concept is developed. The components are modelled generically to accommodatefree and rapid change of component sizes and properties, and only the dominatingdynamics and power losses are included. The component models are combined into acomplete model from wave to grid. A suitable WPEA is identified for the system, andthree different overall PTO control strategies is developed and evaluated. To evaluatethe performance, the system is simulated for three representative sea states.
The system is divided into the sub-models seen in Fig. 3. The sub-models are arrangedin four main blocks, i.e. Wave Input, Wave and Float Interaction, Main PTO Systemand Energy Overflow. The Wave Input and Float Arm blocks are fixed, whereas theremaining blocks consist of components, where component sizes and control is to beoptimized to minimize losses and maximize power output of the WEC.
GpA
pB
Fc
QBcQAc
pB
pA
M
QA
QB
G
totext
PTOI,V,v
armxc
darm
Float/arm Kinematics Cylinder Hyd. motor Generator Inverter
Wave
H Ts, P
arm
arm
PTO
ext
xcvc
FcQBQA
pBpA
M
G
I
V
v
v
Manifold
QBQA
QEO
pB pA QA QB
pEO
Energy overflow conversion
G
Inverter
v
PEO
Pout
PEO
P1
Main PTO system
Energy overflow systemWave and floatinteraction
WPEAarmarm
ControlPTO,ref
ref Gn,ref
Gn,refref
Figure 3: System model for evaluating and optimising PTO performance.
Multiple levels of optimization is performed, see Fig. 4. The WPEA algorithm calcu-lates the time-varying torque ref to maximize the expected energy output of the WEC,taking into account the PTO efficiency. Hence, an initial efficiency guess is required.Next, the PTO control is tuned and the system is evaluated, and with a new efficiency,the WPEA algorithm is updated. With a converged solution of WPEA and control, thelosses of the components are identified. With this knowledge the component sizes andproperties are re-adjusted and the loop is performed again.
WPEAPTO
controlSystem Evaluate
PTO
OK?control
Eff.converg-
ed?
Sys.perform.conv.?
Initialsystem
Y Y Y
UpdatecontrolUpdateWPEA
Manualupdatesystem
N N NPTOevaluated
Figure 4: Strategy for optimising and evaluating the PTO system.
3. MODELLING
The system is modelled in the following according to the sub-systems in Fig. 3.
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3.1. Wave Model
Ocean waves are irregular waves, i.e. waves with varying frequency and amplitude.As a result, irregular waves are described by a wave amplitude spectrum, see Fig. 5.A sea state or spectrum is usually represented by two quantities, the significant waveheight Hs and the peak wave period Tp. The significant wave height is the average ofthe wave heights of the one-third highest waves, and Tp is the period where the wavesat average are highest. The Pierson-Moskowitz spectrum is utilized [11].
0.1 0.202
4
WaveFrequency[Hz]
[ms]
2
0.3
Df
0 20 40 60 80 100-101
Time[s]
[m]
Tp H =2mm0T =6sP
SpectraldensityexampleS (f)A
Waveheighth
0 0.1 0.2 0.30
4
S(f
)[m
s]
A
2
0.5WaveFrequency[Hz]
Spectraldensityforrepresentiveseastates
H =2.50mm0H =1.75mm0H =1.00mm0
T =6.44spT =5.57spT =4.62sp
State3:(Large)
State2:(Medium)
State1:(Small)
2
0.4
Figure 5: Wave spectra for sea states and an example of a corresponding wave.
From a spectrum, the individual wave components can be extracted as,
w,i(t) =p2SA(fi)f sin(2fit) [m ] (1)
and a time series of an irregular wave, can be generated as a sum of wave components,
w(t) =nXi=1
p2SA(fi)f sin(2fit+ 'rand,i) [m ] (2)
where 'rand,i is a random phase for each component. This is known as the random-phase method. However, a more random wave which represents sea waves better isobtained by filtering white noise using proper digital filters designed according to thespectra, see [11] for reference. This method is utilized instead to generate time-seriesof waves.
To evaluate the performance of the PTO, the three sea states shown in Fig. 5 are used,which represents the range of waves in which the WEC should be able to producepower. A wave time series has been generated for each sea state for evaluation of PTOperformance.
The following section describes how the wave interacts with the float.
3.2. Wave and Float Interaction
The equation of motion for a float is given as,
Jarm+floatarm(t) = wave(t) G(t) PTO(t) [Nm ] (3)where Jarm+float is the inertia of float and arm, wave is the torque due to wave-floatinteraction, G is the torque due to gravity and PTO is the torque applied by the PTOsystem to the float arm.
To describe the interaction between wave and float, wave(t), linear wave theory isoften applied, as it gives an adequate description in the conditions in which a WECis producing energy, [14]. In linear wave theory simplified fluid dynamics is assumed
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in order to apply linear potential theory. Resultantly, the wave-float interaction can bedescribed by superimposing three torques,
wave(t) = rad(t) + Arch(t) + ext(t) [Nm ] (4)
where ext(t) is the excitation torque an incoming regular wave applies to a float heldfixed, rad(t) is the radiation toque experienced from oscillating the float in otherwise
water, and Arch is the torque due to the Archimedes force, i.e. buoyancy.
The sum of the three torques gives,
wave(t) = J1 _!arm(t) hrad(t) !arm(t)| {z }rad
+Arch(t) + ext(t) [Nm ] (5)
where hrad is the impulse response function from float velocity to torque, describingthe hydrodynamic damping. The impulse response hrad can be viewed as a high orderdamping term. The inertia term J1 represents the added mass, which contains theeffect, that when oscillating a float, it will appear to have a greater mass due to thewater being displaced along with the float.
The coefficients of Eq.5 are identified by applying the numerical tool WAMIT tothe float. WAMIT is a computer program for computing wave loads and motions ofstructures in waves [12]. WAMIT also outputs a force filter, which can be applied tow(t) to find ext(t).
Inserting Eq.5 into Eq.3 gives the equation of motion for the float,
_!arm =1
Jarm+float + J1
kresarm(t) hrad(t) !arm(t)+ ext(t) PTO(t)
[ ms2] (6)
where the sum of gravity and Archimedes term has been linearised around the draft ofthe float, res(t) = Arch(t) G(t) arm(t)kres. Thus the input to float-arm subsystemare the torques ext and PTO, and the output is the angular position and velocity of thearm. To avoid the convolution term hrad(t) !arm(t), the impulse response has beenfitted with a fifth-order system using Pronys methods [15].
The power extracted or harvested from a wave Phav is the product of the PTO torquePTO and arm velocity !arm. Hence, PTO should be controlled such that harvested energyEhav is optimised:
Ehav =
Z 10
PTO(t)!arm(t)dt [ J ] (7)
In general, to maximise Eq.7 the float should be in phase with the exiting wave torqueext, i.e. the natural frequency of the float and arm should match the incoming wave.However, as the dominating wave frequency varies, the natural frequency will notmatch. Consequently, the PTO system is used to move the natural frequency to increasepower capture. This is depicted in Fig. 6a, where the reference of the PTO torque isgenerated by a damping term bPTO and a spring term kPTO:
PTO,ref = kPTOarm + bPTO!arm [Nm ] (8)
The effect of including the stiffness term is illustrated in Fig. 6c, where a regularwave is applied to the system. In the first case, linear damping is utilized, i.e. kPTOis zero, and in the second case kPTO is non-zero (Reactive control). When using thelinear damping, the power Phav is always positive. In the second case, the power is
calm
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periodically negative, but the average harvested power is twice compared to lineardamping. Hence, more power is extracted, but it requires a PTO with four-quadrantoperation as reactive power is involved.
The optimal control in regard to power output depends on the PTO efficiency PTO,as the loss associated with the power required to move the natural frequency beginsto outweigh the extra harvested power. To find the optimal parameters bPTO and kPTOas a function of PTO efficiency PTO, time-series simulation has been executed fordifferent efficiencies and sea states, and the values of bPTO and kPTO maximising theaverage power Pout,avg have been found. These were found by using a simplex-basedoptimisation algorithm. The simulation model is seen in Fig. 6a. Note that also asaturation limit has been added to the PTO torque of 1MNm, as it has been found tobe a reasonable limit in regard to harvested power versus requirements of the PTO.The limit have been found by multiple simulations,where the limit have graduallydecreased. The results for the optimal values of kPTO and bPTO for sea state 1 and seastate 2 is seen in Fig. 6b as a function of efficiency. Also the expected power outputsare shown.
bPTO
kPTO
textS
S
tPTO
+
-+
qarm
warm
+
text
tPTO
qarm
+
Phav
(c)
LinearDamping(k =0)PTO ReactiveControlWPEA
hPTO
hPTO
1
Pout
tPTO,max
1s Eout
(a)
bP
TO,-k
PT
O
1e6P
[kW
]out,a
vg
bP
TO,-k
PT
O
1e6
PTOefficiency [%]hPTO PTOefficiency [%]hPTO
Seastate1 Seastate2
Time[s] Time[s](b)
P[k
W]
out,a
vg
1tend Pout,avg
70 80 90 100 70 80 90 100
10
5
0
10
5
0
10
5
0
30
15
0
-kPTO-kPTObPTO
bPTO
Pout,avg
Pout,avg
Figure 6: Power extraction from waves, optimising the WPEA as a function of PTO.
3.3. Hydraulic System - Main PTO System
The hydraulic system consist of a closed circuit pump/motor and a cylinder. The outputof the hydraulic system is the torque M for driving the generator, and the cylinderforce Fc acting on the float and arm.
To simplify dynamics, hose losses are neglected, such that the pressure in cylinder andat motor are equal. Power loss associated due to hose loses will be discussed afterwardswhen evaluating efficiency.
Using the flow continuity equation the following expression is obtained for the sym-metric cylinder,
_pB =e,1
Acxc + V0,1(QB _vcAc) [ bars ] (9)
_pA =e,2
Ac(xc,max xc) + V0,2 (QA + _vcAc) [bars] (10)
where Ac is the cylinder area, xc,max is the maximum stroke of cylinder and the volumesV0,1 and V0,2 are volumes of hoses.
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The cylinder force is calculated as,
Fc=pAcFfric ; Ffric=8 0tanh(avc)jpAcj
1
c 1
; pAcvc 0
[N ] (11)
where p = pB pA. The cylinder friction Ffric is defined such that the cylinder has aconstant efficiency of c. The function tanh(avc) is used instead of sign(vc) to avoiddiscontinuity, where a adjust the steepness around zero velocity.
The hydraulic motor is a closed-circuit swash-plate pump. The model is based onmeasured efficiency plots for different pump sizes. A typical efficiency plot is seen inFig. 7a for 100% and 50% displacement respectively. Using Schlsser formula [13] forfriction and flow loss, the following expression are used for motor torque and flow:
QM,nom(!M;p) = D!!M pCQ1 [ m3s ] (12)M,nom(!M;p) = D!p
C1 + C2p+ C3!M + C4!
2M
[Nm ] (13)
The efficiency of the fitted model is seen in Fig. 7b. If the fitted pump is referred toas the nominal size, other motor size is obtained by scaling this model,
QM,new(!M;p) =D!,newD!,nom
!rated,new!rated,nom
QM,nom
!rated,nom!rated,new
!M;p
[ m
3
s] (14)
M,new(!M;p) =D!,newD!,nom
M,nom
!rated,nom!rated,new
!M;p
[Nm ] (15)
where D!,new and !rated,new is the displacement and rated speed of the new motorrespectively.
p [bar]
0.9
0.89
0.8750.
85
0.82
5
0.7
5
0
10
20
30
40
0.840
.8250.
800.750.7
0.7
70.8
40.
88
0.89
0.905
0.91
0.6
80.
750.
80
0.815
0.82
n [RPM]1000 2000 3000
n [RPM]
00
10
20
30
40
p [bar]
=1 =0.5
1000 2000 300001000 2000 30000 1000 2000 30000n [RPM] n [RPM]
(a) (b)
=1 =0.5
Figure 7: Efficiency plots for a typical swash-plate pump, measurements and model.
To replenish the fluid leaked by the motor and to give the necessary flushing for coolingand filtering, a charge/booster pump is installed. The charge pump is set to maintaina pressure of 17bar, which is a low but sufficient charge pressure. According to datasheets a rule-of-thumb is to size the charge pump to be 10% of the installed displace-ment. Consequently, to model the required power for flushing, a fixed displacementpump running together with the motor is used:
Pflush = D!,charge pcharge !M = 0:1 D!,M pcharge !M [W ] (16)
Regarding swash-plate dynamics, it is assumed that the swash-plate control is fastenough for controlling the pressure as the pressure reference is dictated by the wavefrequency, which is low. Hence swash-plate dynamics is omitted.
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3.4. Generator and Inverter - Main PTO System
The generator setup consists of an asynchronous generator and an inverter for gridconnection and to enable variable speed control. The input to the generator is thehydraulic motor torque and the output of the power system is the angular velocity ofthe generator !M and output power.
The electrical properties of the generator is modelled in steady state. This assumed tobe adequate, as the inverter handles the dynamics. An equivalent circuit for a phase ofa three-phase Delta-connected induction motor is seen in Fig. 8b, where denotes themotor slip. The slip is defined as,
= 1 npp!Gn!V
[ ] (17)where npp is the number of pole pairs and !V is the frequency of the supply voltage. Theresistor R2 1
represents the mechanical input to the generator, i.e. Gn!Gn = I2R2
1
,
for reference see e.g. [16].
As the current I2 IM, the generator torque is given as,Gn =
3nppR2
!V
V 2RMSR1 +R2 +
1
R2
2+ (!V(L1 + L2))
2[Nm ] (18)
where VRMS is the RMS-value of the line-to-line voltage.
The steady-state phase current IP of the generator is given as:
IP =VP
jHGn(j!V)j ; HGn(j!V ) =VpIP
=Z2(s)ZM(s)
Z2(s) + ZM(s)+ Z1(s)
s=j!V
(19)
where Z1 = R1 + L1s, Z2 = R2 + L2s and ZM =RFesLMRFe+sLM
.
The electrical output power of the generator is three times the power per phase:
PGn,out = 3VPIP cos(6 HGn(j!V)) =p3VLIL cos(6 HGn(j!V)) [W ] (20)
As hydraulics motors are typically operated in the range of 500-2500RPM, a 4-poledgenerator is used, as it operates at 1500RPM at a voltage frequency of 50Hz. Anominal model is based on the measurement of an asynchronous high-efficiency 4-pole55-kW generator, where the parameters of the equivalent circuit has been identified.The model result is seen in Fig. 8c, where the efficiency is plotted as a function of loadat 1500RPM. The torque characteristic as a function of slip produced by the modelseen in Fig. 9. Other generator sizes are obtained by scaling the nominal model similarto the methods applied to the hydraulic motor.
The angular velocity of the generator is given by,
_!Gn =1
JGn + JM(M Gn) [ 1s2 ] (21)
where JGn and JM is the inertia of the rotor of the generator and hydraulic motorrespectively.
The torque of the generator is controlled by an inverter. The inverter is modelledwith a constant efficiency inv of 95%. To control the torque of the generator, theexpressions for finding the appropriate voltage and voltage frequency for the generatoris implemented in the inverter, see Fig. 9. The modelled 55kW generator may beoperated at 150% load for two minutes, and may in shorter periods also be operatedat 200% load. Consequently, the inverter is limited to run the generator at 200% load.
-
R2
R2
L2L1R1
RFe LM
1-VP
IP I2+
-
IL1
IL2
IL3
V12
V23
V13
IP1 =
+
-
VP=VL
3
IL1
(b) (b)
Back e
mfIMZ1 Z2
ZM
0 40 80 120 160 2000.2
0.4
0.6
0.8
1
Load [%]
Effic
ein
cy [-]
(c)
Figure 8: Per phase equivalent circuit for an induction motor.
-0.04 -0.02 0 0.02 0.04
-800
-400
0
400
800
Slip [-]
[Nm
]
Gn,ref npp Gn1 - V=
V
VL 400V50Hz
Gn2piVL
V
VL
GGn
MI ,V ,L L vV
Gn
Inverter
PGn,outinvinv
1Pinv,out
Generator
M
Generator torque at1500RPM
Gn,ref
Figure 9: Torque characteristic of generator and torque control of generator.
3.5. Energy Overflow System
If a float cylinder produces more flow than the hydraulic motor can consume, thepressure builds up in the cylinder until opening the check-valve to the Energy Overflow(EO) system. Due to accumulators the EO system is assumed to be operating at asteady high pressure pEO. As simulating the behaviour of the EO system would requireto simulate all 20 floats, a fixed efficiency is assumed instead for the EO system.
A model of a check-valve to connect the cylinder to the EO system is included, whichdetermines the flow QEO entering the EO system. The remaining EO system consistof a long pipeline to connect overflow from all floats, a fixed displacement motor, agenerator and an inverter. The following efficiency EO is used for the EO system:
EO = pipe,avgM,avgGn,avginv,avg = 0:95 0:90 0:90 0:95 = 0:73 (22)Hence, if the power delivered to the EO system is PEO,in = pEOQEO, the power deliveredto the grid from the EO system is PEO,out = PEO,inEO.
3.6. Calculating Efficiencies and Power Losses
To optimize and evaluate the PTO system, power losses and efficiencies of the individ-ual components are calculated. If the instantaneous power in and out of a componentare Pin and Pout respectively, the efficiency and losses are calculated as:
Pin,avg =1
tend
Z tend0
Pin(t)dt ; Pout,avg =1
tend
Z tend0
Pout(t)dt (23)
=Pin,avgPout,avg
; Ploss,avg = Pin,avg Pout,avg (24)
As power transfer in both direction occur, the efficiency does not specify the componentefficiency but a resulting efficiency, e.g. a component with a fixed efficiency will showa lower efficiency when reactive power is involved.
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4. DESIGN OF PTO
The design of PTO is organized by first taking a brief view on the requirements,combined with an initial sizing of the PTO components. For evaluating the PTOperformance, three different control strategies for control of motor and generator aredeveloped and applied. Based on the control strategies and initial sizing, the PTOsystem is optimised.
4.1. Requirements and Initial Sizing of PTO
The requirements of the PTO system is to be able to produce power at sea statesranging from a significant wave height of about 1m to 3m. To design and evaluate thePTO system, the three representative sea states defined in Fig. 5 are utilized.
In order to quantify the requirements, simulation of cylinder forces Fc and powerinput have been made by applying the three different sea states to the float model, seeFig. 10, where a power extraction algorithm tuned for a PTO with a efficiency of 70%is applied.
Roshage float
ext
xc
Pharvested
Wave
FcQ
Q
Float Dynamic Model
vc
bPTO
kPTO ++
WPEA optmized for 70% efficient PTO
extFc
1Ac
p
Ac Q
Figure 10: Simulation for estimating requirements of PTO.
The flow and pressure requirements depends on the cylinder size. To minimize flowlosses, the pressure should be as high as possible, however, according to the typicalpump efficiency data displayed in Fig. 7, the efficiency drops above 300bar. As a result,the cylinder is designed such that the maximum required force is obtained at a deltapressure of 300bar. To give a torque of 1MNm, a cylinder force of 420kN is required,yielding Ac = 140 cm2. The pressure of the EO system is set to 325bar. The resultof applying the cylinder area to the simulation is seen in Fig. 11, where the requiredpressures and flows are seen.
According to Fig. 11 the peak power in sea state 3 is about 250kW, however havinge.g. a 250kW hydraulic motor and generator producing an average power of 29kWwill lead to very poor efficiencies. As sea state 2 is more frequently occurring, thefirst iteration of a PTO is based on this sea state. The peak flows are approximately250L/min. If the generator is set to run at a fixed speed of 1500RPM, a 160cc motoris required.
If the generator is assumed to be able run at 100% overload in shorter periods, thegenerator matching a hydraulic motor is found as,
M,max = D!pmax [Nm ] (25)
PGn,norm =1
2M,max !Gn,max [W ] (26)
where !Gn,max is the chosen maximum motor/generator speed and D! is the stroke
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28.93
0 5 10 15 20 0 10 20 30 0 10 20 30
-500
500
0
-300
300
0
-500
500
0
250
0
125
[kN
][b
ar]
[L/m
in]
[kW
]
Phav Phav PhavP = 4.1kWavg P = 15.6kWavg P = 28.9kWavg
Time [s] Time [s] Time [s]
QM QMQM
p p
Fc FcFc
p
Sea State 1 Sea State 2 Sea State 3
Figure 11: Power, flow and pressure at different sea states.
displacement of the hydraulics motor in m3/s. The pressure pmax is maximum allowedpressure, in this case 300bar.
The generator size matching a 160cc motor is then a 60kW unit. If the cylinderproduces more flow than the motor can consume, the pressure builds up until openingthe check-valve to the Energy Overflow (EO) system.
4.2. PTO Control Strategies
The objectives of the PTO control is to track the cylinder force reference producedby the WPEA algorithm while minimizing power losses. The control inputs are thedisplacement control of the hydraulic motor and the generator torque Gn.
Three control strategies are tested:
1) Fixed speed of generator according to sea state and force control using 2) Slowly varying generator speed according to average peak flow requirement.3) Generator speed is controlled to keep motor displacement at maximum.
A comparison of the three control strategies is shown in Fig. 12. In the first strategythe generator is running at 1500RPM, as a result, the motor is at part stroke most ofthe time. In strategy 2 the engine speed is varied according to the average requiredflow, which leads to the motor being closer to full stroke. In strategy 3 the generatorspeed is continues controlled to get the motor to 95% stroke, however this requires thegenerator speed to oscillate together with the wave. To avoid using to much electricalpower to accelerate the generator inertia, the generator is not allowed to operate inmotor mode above e.g. 1000RPM.
4.3. Evaluation and Optimization of PTO
The initial PTO design is evaluated for each sea state using the three described controlstrategies. The results seen in Tab. 1, Tab. 2 and Tab. 3, where PL and denotesaverage power loss [kW] and efficiency [%] respectively, and the columns Pin and Poutare the average harvested power and power output of the system in [kW]. The overallefficiency and power output is best for control method three. It overall gives a 2kWhigher output. Control strategy 1 and 2 giv approximately the same power output,
are
e
-
Control Strategy 1 Control Strategy 2 Control Strategy 3
Dis
pla
cem
ent
contr
ol
[-]
Genera
tor
speed
[RP
M]
G
n
Time [s] Time [s] Time [s]
Figure 12: Comparison of the three control strategies.
however, strategy 2 has a better efficiency, so the required cooling would be lower.From the tables it seen that generally, the hydraulic motor is dropping below 80%efficiency in sea state 1 and 2. Also, the generator efficiency is dropping low in seastate 1.
Table 1: Initial system with control strategy 1
SS
Cylinder Motor Flush Generator Inverter EO TotalPL PL Pflush PL PL PL Pin Pout
1 0.31 94.4 1.52 69.8 0.34 0.80 74.8 0.27 88.7 0.00 5.48 2.09 38.22 1.32 94.3 5.14 74.3 0.68 1.74 87.7 1.10 91.2 0.29 23.2 12.3 52.93 2.39 94.6 7.26 78.5 0.68 2.21 91.5 1.73 92.7 1.58 44.0 27.1 61.6
Table 2: Initial system with control strategy 2
SS
Cylinder Motor Flush Generator Inverter EO TotalPL PL Pflush PL PL PL Pin Pout
1 0.34 94.3 1.53 72.1 0.34 0.80 77.9 0.29 89.6 0.00 5.97 2.52 42.22 1.20 94.4 3.84 78.8 0.43 1.27 90.8 0.95 92.5 0.34 21.4 12.8 59.73 2.25 94.6 6.12 80.3 0.46 1.78 92.7 1.54 93.2 1.74 41.9 27.0 64.4
Table 3: Initial system with control strategy 3SS
Cylinder Motor Flush Generator Inverter EO TotalPL PL Pflush PL PL PL Pin Pout
1 0.37 94.2 1.42 75.8 0.30 0.75 82.0 0.27 92.1 0.00 6.39 3.13 49.02 1.31 94.3 3.75 81.3 0.39 1.24 92.2 0.96 93.4 0.27 23.2 14.6 63.13 2.35 94.6 5.89 82.8 0.42 1.79 93.6 1.60 93.9 1.44 43.8 29.3 66.9
By optimising on the simulation model, it has been found that to have good efficienciesat sea state 1 and 2, it is best to utilize a smaller hydraulic motor and instead increasethe speed in high power periods, e.g. up to 2500RPM. After optimising control andcomponents, the values in Tab. 4 have been identified.
Table 4: Optimized system parameters.Cylinder Area Motor size Generator size Maximum speed140cm2 80cm3 45kW 2500RPM
4.4. Optimized Solution
The results for the three control strategies applied to the optimised solution are seenin Tab. 5, Tab. 6 and Tab. 7. Compared to the previous solution, the harvested power
Resultantly, both the hydraulic motor and the generator are downsized.
-
have been reduced with 2-5kW, however the output power remains unchanged, whichgives a rise in efficiency. The average efficiency improvement is 5%. The reduction inharvested power is due to the main PTO system more often becoming saturated, e.g.the flow from the cylinder cannot be consumed by the motor, leading to the pressurerising to pEO. As a results, the system cannot track the optimal cylinder force trajectory.
Comparing the results of the three control strategies, strategy 1 and 2 outputs thesame amount of power, but less is harvested in strategy 2, giving it a better efficiencyscore. Strategy 2 harvest less power, as the generator speed is too low in periods. Toimprove the control, the controller must be improved in predicting when to increasethe generator speed. Control strategy 3 shows the best results, harvesting power ascontrol strategy 1 while reducing losses. Also this strategy is able to maintain a motorefficiency above 80% in all sea states.
One of the reasons for the relative good efficiency of strategy 3 is, that the generatorpower is mostly positive. This is seen in Fig. 13, where the generator power is comparedfor the three strategies. When the system requires reactive power this is actually takenfrom the kinetic energy saved in the inertia of motor and generator when the generatorspeed is reduced. In the two other strategies, the reactive power is drawn from theinverter,
Table 5: Optimised system with control strategy 1
SS
Cylinder Motor Flush Generator Inverter EO TotalPL PL Pflush PL PL PL Pin Pout
1 0.20 94.7 0.79 77.3 0.17 0.58 76.8 0.17 91.3 0.00 3.83 1.77 46.22 1.12 94.5 3.18 80.9 0.45 1.58 87.8 0.88 92.3 0.47 20.2 12.1 60.03 2.19 94.7 4.78 83.5 0.50 1.99 91.6 1.47 93.2 2.21 41.2 27.4 66.6
Table 6: Optimised system with control strategy 2
SS
Cylinder Motor Flush Generator Inverter EO TotalPL PL Pflush PL PL PL Pin Pout
1 0.30 94.4 1.18 76.5 0.28 0.86 75.9 0.25 90.6 0.00 5.45 2.45 44.92 1.04 94.5 2.57 83.4 0.35 1.22 90.3 0.77 93.2 0.47 18.9 12.1 64.03 2.05 94.7 3.92 85.0 0.37 1.52 93.0 1.27 93.8 2.32 38.8 26.7 68.9
Table 7: Optimised system with control strategy 3
SS
Cylinder Motor Flush Generator Inverter EO TotalPL PL Pflush PL PL PL Pin Pout
1 0.34 94.3 1.00 81.8 0.22 0.73 82.8 0.25 92.9 0.00 5.93 3.28 55.32 1.13 94.5 2.38 86.4 0.30 1.10 92.6 0.74 94.6 0.35 20.5 14.2 68.93 2.15 94.7 3.77 87.4 0.33 1.46 94.3 1.29 94.7 1.91 40.9 29.3 71.8
5 10 15 20 25 30 35-20
0
20
40
60
80
40Time[s]
Controlstrategy1
Controlstrategy2
Controlstrategy3
Pow
er
outp
ut
ofgen
era
tor
[kW
]
Figure 13: Power output of the generator for the three control strategies.
i.e. the power travels through both the generator and inverter.
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5. DISCUSSION
Based on the modelled system, the best efficiency achievable of the investigated PTOsystem is between 55% and 72% in the production range of the wave energy converter.These results are obtained using control strategy 3, see the summarized results in Tab.8.
However, control strategy 3 requires the motor and generator to speed up and downaccording to the float velocity, e.g. from low to high speed two times per wave period.Hence, lifetime of the components may be reduced by this scheme. Consequently, anevaluation of components lifetime should be evaluated before using this control scheme.Nevertheless, control strategy 3 is good for showing the best achievable efficiency withoff-the-shelf components.
Table 8: Optimised system performance summary.
SS
Control 1 Control 2 Control 3Pin Pout Pin Pout Pin Pout
1 3.83 1.77 46.2 5.45 2.45 44.9 5.93 3.28 55.32 20.2 12.1 60.0 18.9 12.1 64.0 20.5 14.2 68.93 41.2 27.4 66.6 38.8 26.7 68.9 40.9 29.3 71.8
The output power of control strategy 1 and 2 is in average 2kW lower, however thesesolutions would be easy implementable. As such, control strategy 2 is preferred, asthe speed of the motor and generator are reduced during low power periods, e.g. wearand tear is reduced. Regarding generator efficiency, when operating at low speeds asin sea state 1, the generator shows a poor efficiency. This might be raised to about90% by reducing the magnetizing current, which gives the losses. For same reason, apermanent magnet generator will show better result at sea state 1, but it will not givea significant improvement at sea state 2 and 3.
To assess the accuracy of the results, an overview of the model properties is shownin Tab. 9, along with future improvements. If the transient behaviour was includedfor the generator, features as reducing the magnetizing current could be evaluated.The remaining features to be added represents additional losses. Hence it would bereasonable to subtract 3-5% from the results.
Table 9: Optimised system with control strategy 1Cylinder Motor Generator Inverter EO
Included
Pressure dynam-ics, hose vol-umes, const. eff.
Friction, flowlosses, powerfor flushing.
Mechanicaldynamics,steady stateelectrical model.
Const.efficiency,electrical modelof generator ctrl.
Constantefficiency.
Add
Hose loses, cyl.friction model.
Power for strokecontrol.
Electricaldynamics.
Efficiency as afunction of load.
Model EO with20 floats
To improve efficiency in the future, the swash-plate motor could be replaced withupcoming components like digital displacement motors [17], [18], which are charac-terized by having excellent part load efficiency. Also, the current solution relies onbeing a multiple absorber system to provide power smoothing. To change the conceptto include more smoothing would be advantageous, also to reduce component sizes.
Finally, PTO systems characterized by having hydraulic motors for e.g. 2 or 4 floatson a common shaft to power a larger generator have also been investigated during thisresearch. This will increase the generator efficiency, but only control strategy 1 wouldbe applicable. Hence, the motor efficiency drops below 80%, ie. this system setup willnot improve the efficiency.
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6. CONCLUSION
By optimizing the proposed PTO system for a multiple point absorber system, the bestachievable efficiency with conventional components is in the range from 52% to 68%under the different wave conditions at which a wave energy converter is producingpower. This emphasizes the need for new component types like digital-displacementmotors, or entirely new PTO concepts in order to utilize wave energy from pointabsorbers. New PTO concepts are therefor currently under investigation.
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