MODEL BASED DESIGN OF EFFICIENT POWER TAKE-OFF SYSTEMS FOR WAVE ENERGY CONVERTERS

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1 The Twelfth Scandinavian International Conference on Fluid Power, May 18-2, 211, Tampere, Finland MODEL BASED DESIGN OF EFFICIENT POWER TAKE-OFF SYSTEMS FOR WAVE ENERGY CONVERTERS Rico H. Hansen, Torben O. Andersen, Henrik C. Pedersen Aalborg University Department of Energy Technology Pontoppidanstræde 11, 922 Aalborg, Denmark Phone: , Fax: rhh@et.aau.dk, toa@et.aau.dk, hcp@et.aau.dk ABSTRACT The Power Take-Off (PTO) is the core of a Wave Energy Converter (WECs), being the technology converting wave induced oscillations from mechanical energy to electricity. The induced oscillations are characterized by being slow with varying frequency and amplitude. Resultantly, fluid power is often an essential part of the PTO, being the only technology having the required force densities. The focus of this paper is to show the achievable efficiency of a PTO system based on a conventional hydro-static transmission topology. The design is performed using a model based approach. Generic component models are developed and combined into a PTO system, describing the dynamics and power losses from wave to grid. Using the model, components sizes and control 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 harvesting the energy of the ocean waves, where several have reached the proof-of-concept stage, showing it is possible to produce power, see e.g. [1] and [2] for a survey. A large group of WECs bases on directly converting the waves into an oscillating mechanical motion, e.g. point absorbers and multiple point absorber systems, see Fig. 1. Converting the mechanical motion into electricity is performed by the Power Take-Off (PTO). Today, PTO solutions for such systems are characterized by poor efficiencies and reliabilities. The reason is that the waves induce slow irregular oscillations, which requires 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 having the required force densities. However, fluid power systems are often characterized by poor 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].

2 P = in PTO arm PTO P out Reciprocating motion ext arm PTO Point absorber Multiple point absorber Wave tar WEC (a) (b) (c) Figure 1: Point absorber type WECs and the Wavestar 6kW WEC [1]. The PTO extracts energy from the waves by applying a damping torque τ PTO to the float, such that the float performs work on the PTO system. As a result, the power P hav = τ PTO ω arm is extracted from the waves. In order to maximise the amount of harvested power P hav, τ PTO has to be controllable. How to generate the optimal PTO force trajectory is referred to as Wave Power Extraction Algorithms (WPEA). It can be shown, see e.g. [4] and [5], that the WPEA optimizing the amount of harvested power requires the PTO to periodically transfer power to the float, i.e. four-quadrant behaviour. This type of WPEA is termed reactive control. The main reason for using reactive control is that the float s natural frequency should match the wave frequency. As the wave frequency varies, the PTO is used to change the natural frequency, which requires 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 absorber WEC, based on using conventional hydraulic and electrical components. The PTO system should be able to perform reactive control. The evaluation is performed for the Wavestar 6kW WEC [9] seen in Fig. 1c, consisting of 2 hemisphere shaped floats, each 5m in diameter. The advantage of a multiple point absorber system is the increased power smoothing, [5]. The investigated PTO system is seen in Fig. 2. The PTO torque is produced by a symmetrical cylinder, which is operated in closed circuit with a variable displacement swash-plate pump/motor. The motor can stroke both positive and negative. Thus, the motor converts the bi-directional cylinder flow into a uni-directional high speed rotation for powering a generator. Pressure control is performed by the swash-plate motor in order to control the torque τ PTO applied to the float. Accordingly, a bent-axis motor is not utilized as its bandwidth is too low to perform pressure control. To avoid oversizing motor and generator, an energy overflow system is added such that cylinder flows exceeding the motor capacity are combined in a common line, powering an extra generator. Similar PTO concepts to Fig. 2 are suggested in e.g. [6]. More simplified hydraulic system have been proposed in [7] and [8], however, these can only provide a constant PTO torque. Symmetric cylinder τ ext Flushing valve Float module p EO G AC DC Inverter Energy overflow Float module Energy overflow Float module Float module Float module Figure 2: Investigated PTO system. Float module DC bus Float module PTO System G

3 2. METHODS The evaluation of the PTO system in Fig. 2 is based on performing time simulation of the WEC and PTO for different wave inputs. Hence, to evaluate and optimize the PTO system, a time-efficient system model, which reflects the WEC and described PTO concept is developed. The components are modelled generically to accommodate free and rapid change of component sizes and properties, and only the dominating dynamics and power losses are included. The component models are combined into a complete model from wave to grid. A suitable WPEA is identified for the system, and three different overall PTO control strategies is developed and evaluated. To evaluate the 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 arranged in four main blocks, i.e. Wave Input, Wave and Float Interaction, Main PTO System and Energy Overflow. The Wave Input and Float Arm blocks are fixed, whereas the remaining blocks consist of components, where component sizes and control is to be optimized to minimize losses and maximize power output of the WEC. θ arm ω arm WPEA τ PTO,ref Control τ Gn,ref α ref Main PTO system α ref τ Gn,ref τ PTO τext θ arm ω arm x c θ arm τ PTO d arm x c v c F c p A F c p B Q Ac Q Bc p B p A Q B Q A Q B Q A p B p A α τ M τ tot ω G G I,V,ω v Float/arm Kinematics Cylinder Hyd. motor Generator Inverter τ M ω G I V ω v ω v P 1 ω v Inverter P out τ ext p B p A Q A Q B H s, T P Q A Q B P EO G p EO P EO Wave Wave and float interaction Q EO Manifold Energy overflow system Energy overflow conversion Figure 3: System model for evaluating and optimising PTO performance. Multiple levels of optimization is performed, see Fig. 4. The WPEA algorithm calculates the time-varying torque τ 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, the losses of the components are identified. With this knowledge the component sizes and properties are re-adjusted and the loop is performed again. Initial system Manual update system System WPEA Update WPEA PTO control Update control Evaluate N N N PTO PTO Eff. Sys. control converged? Y conv.? perform. evaluated OK? Y Y 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.

4 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 wave height H s and the peak wave period T p. The significant wave height is the average of the wave heights of the one-third highest waves, and T p is the period where the waves at average are highest. The Pierson-Moskowitz spectrum is utilized [11]. 2 [m s] [m] 4 2 Spectral density example S A(f) T p.1.2 Wave Frequency [Hz] Wave height h f H m= 2 m T P= 6 s Time [s] 2 S A (f) [m s] Spectral density for representive sea states 4 H m=2.5mt p=6.44s 2 State 3: (Large) State 2: (Medium) State 1: (Small) H m=1.75m H m=1.m T p=5.57s T p=4.62s Wave Frequency [Hz] 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, η w,i (t) = 2S A (f i ) f sin(2πf i t) [ m ] (1) and a time series of an irregular wave, can be generated as a sum of wave components, n η w (t) = 2SA (f i ) f sin(2πf i t + φ rand,i ) [ m ] (2) i=1 where φ rand,i is a random phase for each component. This is known as the randomphase method. However, a more random wave which represents sea waves better is obtained by filtering white noise using proper digital filters designed according to the spectra, see [11] for reference. This method is utilized instead to generate time-series of 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 produce power. A wave time series has been generated for each sea state for evaluation of PTO performance. The following section describes how the wave interacts with the float Wave and Float Interaction The equation of motion for a float is given as, J arm+float θarm (t) = τ wave (t) τ G (t) τ PTO (t) [ Nm ] (3) where J arm+float is the inertia of float and arm, τ wave is the torque due to wave-float interaction, τ G is the torque due to gravity and τ PTO is the torque applied by the PTO system to the float arm. To describe the interaction between wave and float, τ wave (t), linear wave theory is often applied, as it gives an adequate description in the conditions in which a WEC is producing energy, [14]. In linear wave theory simplified fluid dynamics is assumed.5

5 in order to apply linear potential theory. Resultantly, the wave-float interaction can be described by superimposing three torques, τ wave (t) = τ rad (t) + τ Arch (t) + τ ext (t) [ Nm ] (4) where τ ext (t) is the excitation torque an incoming regular wave applies to a float held fixed, τ rad (t) is the radiation toque experienced from oscillating the float in otherwise calm water, and τ Arch is the torque due to the Archimedes force, i.e. buoyancy. The sum of the three torques gives, τ wave (t) = J ω arm (t) h rad (t) ω arm (t) } {{ } +τ Arch (t) + τ ext (t) [ Nm ] (5) τ rad where h rad is the impulse response function from float velocity to torque, describing the hydrodynamic damping. The impulse response h rad can be viewed as a high order damping term. The inertia term J represents the added mass, which contains the effect, that when oscillating a float, it will appear to have a greater mass due to the water being displaced along with the float. The coefficients of Eq.5 are identified by applying the numerical tool WAMIT to the float. WAMIT is a computer program for computing wave loads and motions of structures in waves [12]. WAMIT also outputs a force filter, which can be applied to η w (t) to find τ ext (t). Inserting Eq.5 into Eq.3 gives the equation of motion for the float, 1 ( ) ω arm = k res θ arm (t) h rad (t) ω arm (t)+ τ ext (t) τ PTO (t) J arm+float + J [ m s 2 ] (6) where the sum of gravity and Archimedes term has been linearised around the draft of the float, τ res (t) = τ Arch (t) τ G (t) θ arm (t)k res. Thus the input to float-arm subsystem are the torques τ ext and τ PTO, and the output is the angular position and velocity of the arm. To avoid the convolution term h rad (t) ω arm (t), the impulse response has been fitted with a fifth-order system using Prony s methods [15]. The power extracted or harvested from a wave P hav is the product of the PTO torque τ PTO and arm velocity ω arm. Hence, τ PTO should be controlled such that harvested energy Ehav is optimised: E hav = τ PTO (t)ω arm (t)dt [ J ] (7) In general, to maximise Eq.7 the float should be in phase with the exiting wave torque τ ext, 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 not match. Consequently, the PTO system is used to move the natural frequency to increase power capture. This is depicted in Fig. 6a, where the reference of the PTO torque is generated by a damping term b PTO and a spring term k PTO : τ PTO,ref = k PTO θ arm + b PTO ω arm [ Nm ] (8) The effect of including the stiffness term is illustrated in Fig. 6c, where a regular wave is applied to the system. In the first case, linear damping is utilized, i.e. k PTO is zero, and in the second case k PTO is non-zero (Reactive control). When using the linear damping, the power P hav is always positive. In the second case, the power is

6 periodically negative, but the average harvested power is twice compared to linear damping. Hence, more power is extracted, but it requires a PTO with four-quadrant operation as reactive power is involved. The optimal control in regard to power output depends on the PTO efficiency η PTO, as the loss associated with the power required to move the natural frequency begins to outweigh the extra harvested power. To find the optimal parameters b PTO and k PTO as a function of PTO efficiency η PTO, time-series simulation has been executed for different efficiencies and sea states, and the values of b PTO and k PTO maximising the average power P out,avg have been found. These were found by using a simplex-based optimisation algorithm. The simulation model is seen in Fig. 6a. Note that also a saturation limit has been added to the PTO torque of 1MNm, as it has been found to be 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 gradually decreased. The results for the optimal values of k PTO and b PTO for sea state 1 and sea state 2 is seen in Fig. 6b as a function of efficiency. Also the expected power outputs are shown. WPEA + + b PTO k PTO arm arm Linear Damping (k PTO = ) Reactive Control PTO,max PTO ext + - PTO ext + arm P hav PTO P out 1 PTO 1 1 s Eout tend P out,avg (a) b PTO, -k PTO 1e k PTO Sea state 1 1e6 Sea state P out,avg b PTO 5 P out,avg [kw] b PTO, -k PTO PTO efficiency PTO [%] PTO efficiency PTO [%] (b) 5 -k PTO P out,avg b PTO 3 15 P out,avg [kw] Time [s] (c) Time [s] Figure 6: Power extraction from waves, optimising the WPEA as a function of η PTO Hydraulic System - Main PTO System The hydraulic system consist of a closed circuit pump/motor and a cylinder. The output of the hydraulic system is the torque τ M for driving the generator, and the cylinder force F c acting on the float and arm. To simplify dynamics, hose losses are neglected, such that the pressure in cylinder and at motor are equal. Power loss associated due to hose loses will be discussed afterwards when evaluating efficiency. Using the flow continuity equation the following expression is obtained for the symmetric cylinder, β e,1 ṗ B = ( Q B v c A c ) [ bar ] (9) s A c x c + V,1 β e,2 ṗ A = (Q A + v c A c ) [ bar ] (1) s A c (x c,max x c ) + V,2 where A c is the cylinder area, x c,max is the maximum stroke of cylinder and the volumes V,1 and V,2 are volumes of hoses.

7 The cylinder force is calculated as, tanh(av c ) pa c (1 η c ) ; pa c v c > ( ) F c = pa c F fric ; F fric = 1 tanh(av c ) pa c 1 ; pa c v c η c [ N ] (11) where p = p B p A. The cylinder friction F fric is defined such that the cylinder has a constant efficiency of η c. The function tanh(av c ) is used instead of sign(v c ) to avoid discontinuity, where a adjust the steepness around zero velocity. The hydraulic motor is a closed-circuit swash-plate pump. The model is based on measured efficiency plots for different pump sizes. A typical efficiency plot is seen in Fig. 7a for 1% and 5% displacement respectively. Using Schlösser formula [13] for friction and flow loss, the following expression are used for motor torque and flow: Q M,nom (ω M, p) = αd ω ω M pc Q1 τ M,nom (ω M, p) = αd ω p ( C τ1 + C τ2 p + C τ3 ω M + C τ4 ω 2 M ) [ m3 ] s (12) [ Nm ] (13) The efficiency of the fitted model is seen in Fig. 7b. If the fitted pump is referred to as the nominal size, other motor size is obtained by scaling this model, Q M,new (ω M, p) = D ( ) ω,new ω rated,new ωrated,nom Q M,nom ω M, p [ m3 ] (14) s D ω,nom ω rated,nom ω rated,new τ M,new (ω M, p) = D ( ) ω,new ωrated,nom τ M,nom ω M, p [ Nm ] (15) D ω,nom ω rated,new where D ω,new and ω rated,new is the displacement and rated speed of the new motor respectively. p [bar] α=1 α= n [RPM] n [RPM] (a).7 p [bar] α=1 α= n [RPM] (b) n [RPM] 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 cooling and filtering, a charge/booster pump is installed. The charge pump is set to maintain a pressure of 17bar, which is a low but sufficient charge pressure. According to data sheets a rule-of-thumb is to size the charge pump to be 1% of the installed displacement. Consequently, to model the required power for flushing, a fixed displacement pump running together with the motor is used: P flush = D ω,charge p charge ω M =.1 D ω,m p charge ω M [ W ] (16) Regarding swash-plate dynamics, it is assumed that the swash-plate control is fast enough for controlling the pressure as the pressure reference is dictated by the wave frequency, which is low. Hence swash-plate dynamics is omitted.

8 3.4. Generator and Inverter - Main PTO System The generator setup consists of an asynchronous generator and an inverter for grid connection and to enable variable speed control. The input to the generator is the hydraulic motor torque and the output of the power system is the angular velocity of the generator ω M and output power. The electrical properties of the generator is modelled in steady state. This assumed to be adequate, as the inverter handles the dynamics. An equivalent circuit for a phase of a three-phase Delta-connected induction motor is seen in Fig. 8b, where γ denotes the motor slip. The slip is defined as, γ = 1 n ppω Gn [ ] (17) ω V where n pp is the number of pole pairs and ω V is the frequency of the supply voltage. The 1 γ 1 γ resistor R 2 represents the mechanical input to the generator, i.e. τ γ Gn ω Gn = I 2 R 2, γ for reference see e.g. [16]. As the current I 2 I M, the generator torque is given as, τ Gn = 3n ppr 2 γω V V 2 RMS ( ) 2 [ Nm ] (18) R 1 + R γ R γ 2 + (ωv (L 1 + L 2 )) 2 where V RMS is the RMS-value of the line-to-line voltage. The steady-state phase current I P of the generator is given as: V P I P = H Gn (jω V ), H Gn(jω V ) = V p = Z 2(s)Z M (s) I P Z 2 (s) + Z M (s) + Z 1(s) (19) s=jωv where Z 1 = R 1 + L 1 s, Z 2 = R 2 γ + L 2 s and Z M = R FesL M R Fe +sl M. The electrical output power of the generator is three times the power per phase: P Gn,out = 3V P I P cos( H Gn (jω V )) = 3V L I L cos( H Gn (jω V )) [ W ] (2) As hydraulics motors are typically operated in the range of 5-25 RPM, a 4-poled generator is used, as it operates at 15RPM at a voltage frequency of 5Hz. A nominal model is based on the measurement of an asynchronous high-efficiency 4-pole 55-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 load at 15RPM. The torque characteristic as a function of slip produced by the model seen in Fig. 9. Other generator sizes are obtained by scaling the nominal model similar to the methods applied to the hydraulic motor. The angular velocity of the generator is given by, 1 ω Gn = (τ M τ Gn ) J Gn + J M [ 1 ] s 2 (21) where J Gn and J M is the inertia of the rotor of the generator and hydraulic motor respectively. The torque of the generator is controlled by an inverter. The inverter is modelled with a constant efficiency η inv of 95%. To control the torque of the generator, the expressions for finding the appropriate voltage and voltage frequency for the generator is implemented in the inverter, see Fig. 9. The modelled 55kW generator may be operated at 15% load for two minutes, and may in shorter periods also be operated at 2% load. Consequently, the inverter is limited to run the generator at 2% load.

9 I L1 V 12 I L3 I L2 V 13 I P1 = + V 23 (b) I L1 3 V P =V L - I P R 1 L 1 I 2 + V P - I M Z 1 Z 2 L 2 R 2 Z M R 2 1-γ γ R Fe L M (b) Figure 8: Per phase equivalent circuit for an induction motor. Back emf Efficeincy [-] Load [%] (c) [Nm] Generator torque at 15RPM Inverter γ τ Gn,ref γ n pp ω Gn τ ω V = Gn,ref 1 - γ ω V V L ω Gn 2π V L 4V 5Hz ωv V L ω V ω Gn Generator I L,V L, ωv τ M ω Gn G Slip [-] P inv,out η inv η inv 1 P Gn,out τ M Figure 9: Torque characteristic of generator and torque control of generator Energy Overflow System If a float cylinder produces more flow than the hydraulic motor can consume, the pressure 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 a steady high pressure p EO. As simulating the behaviour of the EO system would require to simulate all 2 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, which determines the flow Q EO entering the EO system. The remaining EO system consist of a long pipeline to connect overflow from all floats, a fixed displacement motor, a generator and an inverter. The following efficiency η EO is used for the EO system: η EO = η pipe,avg η M,avg η Gn,avg η inv,avg = =.73 (22) Hence, if the power delivered to the EO system is P EO,in = p EO Q EO, the power delivered to the grid from the EO system is P EO,out = P EO,in η EO Calculating Efficiencies and Power Losses To optimize and evaluate the PTO system, power losses and efficiencies of the individual components are calculated. If the instantaneous power in and out of a component are P in and P out respectively, the efficiency and losses are calculated as: P in,avg = 1 t end tend P in (t)dt, P out,avg = 1 t end tend P out (t)dt (23) η = P in,avg P out,avg, P loss,avg = P in,avg P out,avg (24) As power transfer in both direction occur, the efficiency does not specify the component efficiency but a resulting efficiency, e.g. a component with a fixed efficiency will show a lower efficiency when reactive power is involved.

10 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 PTO performance, three different control strategies for control of motor and generator are developed and applied. Based on the control strategies and initial sizing, the PTO system is optimised Requirements and Initial Sizing of PTO The requirements of the PTO system is to be able to produce power at sea states ranging from a significant wave height of about 1m to 3m. To design and evaluate the PTO system, the three representative sea states defined in Fig. 5 are utilized. In order to quantify the requirements, simulation of cylinder forces F c and power input have been made by applying the three different sea states to the float model, see Fig. 1, where a power extraction algorithm tuned for a PTO with a efficiency of 7% is applied. WPEA optmized for 7% efficient PTO Wave p 1 A c F c τ ext + Σ + Float Dynamic Model Q F c τ ext b PTO k PTO Q x c v c A c P harvested Q Roshage float Figure 1: Simulation for estimating requirements of PTO. The flow and pressure requirements depends on the cylinder size. To minimize flow losses, the pressure should be as high as possible, however, according to the typical pump efficiency data displayed in Fig. 7, the efficiency drops above 3bar. As a result, the cylinder is designed such that the maximum required force is obtained at a delta pressure of 3bar. To give a torque of 1MNm, a cylinder force of 42kN is required, yielding A c = 14 cm 2. The pressure of the EO system is set to 325bar. The result of applying the cylinder area to the simulation is seen in Fig. 11, where the required pressures and flows are seen. According to Fig. 11 the peak power in sea state 3 is about 25kW, however having e.g. a 25kW hydraulic motor and generator producing an average power of 29kW will lead to very poor efficiencies. As sea state 2 is more frequently occurring, the first iteration of a PTO is based on this sea state. The peak flows are approximately 25L/min. If the generator is set to run at a fixed speed of 15RPM, a 16cc motor is required. If the generator is assumed to be able run at 1% overload in shorter periods, the generator matching a hydraulic motor is found as, τ M,max = D ω p max [ Nm ] (25) P Gn,norm = 1 2 τ M,max ω Gn,max [ W ] (26) where ω Gn,max is the chosen maximum motor/generator speed and D ω is the stroke

11 [kn] [bar] [L/min] [kw] F c p Q M Sea State 1 Sea State 2 Sea State 3 F c p Q M P hav P avg = 4.1kW P hav P avg = 15.6kW P hav P avg = 28.9kW Time [s] Time [s] Time [s] Figure 11: Power, flow and pressure at different sea states. displacement of the hydraulics motor in m 3 /s. The pressure p max is maximum allowed pressure, in this case 3 bar. The generator size matching a 16cc motor is then a 6kW unit. If the cylinder produces more flow than the motor can consume, the pressure builds up until opening the check-valve to the Energy Overflow (EO) system PTO Control Strategies The objectives of the PTO control is to track the cylinder force reference produced by the WPEA algorithm while minimizing power losses. The control inputs are the displacement control α of the hydraulic motor and the generator torque τ Gn. Three control strategies are tested: 1) Fixed speed of generator according to sea state and force control using α 2) Slowly varying generator speed according to average peak flow requirement. 3) Generator speed is controlled to keep motor displacement α at maximum. A comparison of the three control strategies is shown in Fig. 12. In the first strategy the generator is running at 15RPM, as a result, the motor is at part stroke most of the time. In strategy 2 the engine speed is varied according to the average required flow, which leads to the motor being closer to full stroke. In strategy 3 the generator speed is continues controlled to get the motor to 95% stroke, however this requires the generator speed to oscillate together with the wave. To avoid using to much electrical power to accelerate the generator inertia, the generator is not allowed to operate in motor mode above e.g. 1 RPM Evaluation and Optimization of PTO The initial PTO design is evaluated for each sea state using the three described control strategies. The results are seen in Tab. 1, Tab. 2 and Tab. 3, where P L and η denotes average power loss [kw] and efficiency [%] respectively, and the columns P in and P out are the average harvested power and power output of the system in [kw]. The overall efficiency and power output is best for control method three. It overall gives a 2kW higher output. Control strategy 1 and 2 give approximately the same power output, F c p Q M

12 Displacement control α [-] Control Strategy 1 Control Strategy 2 Control Strategy 3 Generator speed ω Gn [RPM] 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 8% efficiency in sea state 1 and 2. Also, the generator efficiency is dropping low in sea state 1. Resultantly, both the hydraulic motor and the generator are downsized. Table 1: Initial system with control strategy 1 Cylinder Motor Flush Generator Inverter EO Total P L η P L η P flush P L η P L η P L P in P out η SS Table 2: Initial system with control strategy 2 Cylinder Motor Flush Generator Inverter EO Total P L η P L η P flush P L η P L η P L P in P out η SS Table 3: Initial system with control strategy 3 Cylinder Motor Flush Generator Inverter EO Total P L η P L η P flush P L η P L η P L P in P out η SS By optimising on the simulation model, it has been found that to have good efficiencies at sea state 1 and 2, it is best to utilize a smaller hydraulic motor and instead increase the speed in high power periods, e.g. up to 25RPM. After optimising control and components, the values in Tab. 4 have been identified. Table 4: Optimized system parameters. Cylinder Area Motor size Generator size Maximum speed 14cm 2 8cm 3 45kW 25RPM 4.4. Optimized Solution The results for the three control strategies applied to the optimised solution are seen in Tab. 5, Tab. 6 and Tab. 7. Compared to the previous solution, the harvested power

13 have been reduced with 2-5 kw, however the output power remains unchanged, which gives a rise in efficiency. The average efficiency improvement is 5%. The reduction in harvested 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 pressure rising to p EO. 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 the same amount of power, but less is harvested in strategy 2, giving it a better efficiency score. Strategy 2 harvest less power, as the generator speed is too low in periods. To improve the control, the controller must be improved in predicting when to increase the generator speed. Control strategy 3 shows the best results, harvesting power as control strategy 1 while reducing losses. Also this strategy is able to maintain a motor efficiency above 8% in all sea states. One of the reasons for the relative good efficiency of strategy 3 is, that the generator power is mostly positive. This is seen in Fig. 13, where the generator power is compared for the three strategies. When the system requires reactive power this is actually taken from the kinetic energy saved in the inertia of motor and generator when the generator speed is reduced. In the two other strategies, the reactive power is drawn from the inverter, i.e. the power travels through both the generator and inverter. Table 5: Optimised system with control strategy 1 Cylinder Motor Flush Generator Inverter EO Total P L η P L η P flush P L η P L η P L P in P out η SS Table 6: Optimised system with control strategy 2 Cylinder Motor Flush Generator Inverter EO Total P L η P L η P flush P L η P L η P L P in P out η SS Table 7: Optimised system with control strategy 3 Cylinder Motor Flush Generator Inverter EO Total P L η P L η P flush P L η P L η P L P in P out η SS Power output of generator [kw] Control strategy 1 Control strategy 2 Control strategy Time [s] Figure 13: Power output of the generator for the three control strategies.

14 5. DISCUSSION Based on the modelled system, the best efficiency achievable of the investigated PTO system 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 down according 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, an evaluation of components lifetime should be evaluated before using this control scheme. Nevertheless, control strategy 3 is good for showing the best achievable efficiency with off-the-shelf components. Table 8: Optimised system performance summary. Control 1 Control 2 Control 3 P in P out η P in P out η P in P out η SS The output power of control strategy 1 and 2 is in average 2kW lower, however these solutions would be easy implementable. As such, control strategy 2 is preferred, as the speed of the motor and generator are reduced during low power periods, e.g. wear and tear is reduced. Regarding generator efficiency, when operating at low speeds as in sea state 1, the generator shows a poor efficiency. This might be raised to about 9% by reducing the magnetizing current, which gives the losses. For same reason, a permanent magnet generator will show better result at sea state 1, but it will not give a significant improvement at sea state 2 and 3. To assess the accuracy of the results, an overview of the model properties is shown in Tab. 9, along with future improvements. If the transient behaviour was included for the generator, features as reducing the magnetizing current could be evaluated. The remaining features to be added represents additional losses. Hence it would be reasonable to subtract 3-5% from the results. Table 9: Optimised system with control strategy 1 Included Add Cylinder Motor Generator Inverter EO Pressure dynamics, Friction, flow Mechanical Const. hose vol- losses, power dynamics, efficiency, umes, const. eff. for flushing. steady state electrical model electrical model. of generator ctrl. Hose loses, cyl. Power for stroke Electrical Efficiency as a friction model. control. dynamics. function of load. Constant efficiency. Model EO with 2 floats To improve efficiency in the future, the swash-plate motor could be replaced with upcoming components like digital displacement motors [17], [18], which are characterized by having excellent part load efficiency. Also, the current solution relies on being a multiple absorber system to provide power smoothing. To change the concept to 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 floats on a common shaft to power a larger generator have also been investigated during this research. This will increase the generator efficiency, but only control strategy 1 would be applicable. Hence, the motor efficiency drops below 8%, ie. this system setup will not improve the efficiency.

15 6. CONCLUSION By optimizing the proposed PTO system for a multiple point absorber system, the best achievable efficiency with conventional components is in the range from 52% to 68% under the different wave conditions at which a wave energy converter is producing power. This emphasizes the need for new component types like digital-displacement motors, or entirely new PTO concepts in order to utilize wave energy from point absorbers. New PTO concepts are therefor currently under investigation. REFERENCES [1] A. Muetze and J.G. Vining. Ocean wave energy conversion - a survey. In Industry Applications Conference, 26. [2] B. Drew, A. Plummer and M.N. Sahinkaya. A review of wave energy converter technology. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 223 (8), 29. [3] J Cruz. Ocean Wave Energy: Current Status and Future Perspectives, 28, Green Energy and Technology Series, ISBN: [4] S.H. Salter, J.R.M. Taylor and N.J. Caldwell. Power Conversion Mechanisms for Wave Energy. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 22. [5] J. Falnes. Optimum Control of Oscillation of Wave-Energy Converters. International Journal of Offshore and Polar Engineering, vol [6] E. Wood. Power generation systems in buoyant structures. US-patent: US415878, [7] A.F. de O. Falcao. Modelling and control of oscillating-body wave energy converters with hydraulic power take-off. Ocean Engineering, vol. 35, 28. [8] A. Babarit,M. Guglielmi and A.H. Clement. Declutching control of a wave energy converter. Journal of Ocean Engineering, vol. 36, 29. [9] L. Marquis, M. Kramer and P. Frigaard. First Power Production figures from the Wave Star Roshage Wave Energy Converter. 3rd International Conference and Exhibition on Ocean Energy, 21. [1] Wave Star A/S. [11] M.J. Ketabdari and A. Ranginkaman. Simulation of Random Irregular Sea Waves for Numerical and Physical Models Using Digital Filters. Transaction B: Mechanical Engineering Vol. 16, No. 3, 29. [12] [13] K. Huhtala, J. Vilenius, A. Raneda and T. Virvalo. Energy losses of a tele-operated skid steering mobile machine. Power transmission and motion control, 22. [14] J.Falness. Ocean Waves and Oscillating Systems. ISBN: [15] G. De Backer. Hydrodynamic Design Optimization of Wave Energy Converters Consisting of Heaving Point Absorbers. Ph.D. thesis, 29. [16] A. Hughes. Electrical motor and drives. Third Edition, 26, ISBN: [17] G.S. Payne,U.B.P. Stein, M. Ehsan, N.J. Caldwell and W H.S. Rampen. Potential of Digital Displacement Hydraulics for Wave Energy Conversion. In proc. of the 6th European Wave and Tidal Energy Conference, Glasgow, UK, 25. [18] M. Ehsan, W.H.S. Rampen and J.R.M Taylor. Simulation and Dynamic Response of Computer Controlled Digital Hydraulic Pump/Motor System Used in Wave Energy Power Conversion. In proc. 2nd European Wave Power Conference, Lisbon, 1995.