Modeling and Validation of an Electrohydraulic Power Take-Off

energies

Article Modeling and Validation of an Electrohydraulic Power Take-Oﬀ System for a Portable Wave Energy Convertor with Compressed Energy Storage

Hao Tian 1,2,* , Zijian Zhou 1 and Yu Sui 1

1 Mechanical Engineering Department, Dalian Maritime University, Dalian 116026, China 2 Liaoning Key Laboratory on Rescue and Salvage Engineering, Dalian Maritime University, Dalian 116026, China * Correspondence: [email protected]

Received: 9 May 2019; Accepted: 29 August 2019; Published: 2 September 2019

Abstract: Small-scale, portable generation of electricity from ocean waves provides a versatile solution to power the ocean sensors network, in addition to the traditional large-scale wave energy conversion facilities. However, one issue of small-scale wave energy convertor (WEC) is the low capturable power density, challenging the design of the efficient power take-off (PTO) system. To tackle this challenge, in this paper, an electrohydraulic PTO system with compressed energy storage was proposed to boost output power of a portable WEC. Lumped-parameter kinematics and dynamics of the four-bar mechanism, the fluid dynamics of the digital fluid power circuit, and the mechanical and volumetric power losses were modeled and experimentally validated. Initial test results of the 0.64 m2 footprint prototype showed that the inclusion of storage improved the averaged electric power output over 40 times compared to the traditional architecture, and the proposed device can deliver up to 122 W at peaks.

Keywords: wave energy convertor; electrohydraulic power take-oﬀ; compressed energy storage; lumped dynamic models

1. Introduction Oceans on earth are enormous bodies with rich renewable resources. As interests in ocean sensing continue to grow, e.g., building an ocean sensing array composed of smart surface or subsea beacons, etc., provisions of electrical power for the distributed sensors’ network becomes a necessity. Adjacent to several oceans, China has a long coastline and is abundant in wave energy reserves, whose mean power is estimated to be over 12 gigawatts; even in the less wave energy dense regions, such as Liaoning Province in the far north, the annual mean wave height is still around 0.4 m [1]. Electricity generation from the heaving motion of the waves is clean and sustainable, and a viable solution to long-term maritime operations [2]. One kind of device that achieves the function is a wave energy convertor (WEC). A typical WEC includes a buoy that draws in the power from the motion of the oscillating wave, and a power take-off (PTO) system that converts it into electrical power [2,3]. Thus, the performance depends on both the buoy hydrodynamics and the energy conversion processes. As a result, in the design of efficient WECs, the two major approaches are either through the optimization of the fluid-structure interaction between the wave and the buoy, or through the PTO design. The former often employs tools such as computational fluid dynamics (CFD) or experiments, and the goals are to improve the efficiency of the buoy responding to the wave motion [4–7]. The latter usually focuses on improving the PTO’s architectural features, such as the traditional single or multiple-step conversion types [8–18]. Single step conversion usually requires a linear electric generator, the advantage of which,

Energies 2019, 12, 3378; doi:10.3390/en12173378 www.mdpi.com/journal/energies Energies 2019, 12, 3378 2 of 15 Energies 2019, 12, x FOR PEER REVIEW 2 of 16 ofis a that multiple the direct-step conversionconversion eliminatessystem [8]. the However, inter-step due losses to the of uncertainty a multiple-step of wave conversion condition systems during [8]. aHowever, short period due in to a theregion, uncertainty contrasting of wave with conditionsthe stable year during-round a short mean period wave inpower, a region, it is contrastingdifficult to maintainwith the consistent stable year-round performance mean. To wave generate power, electric it isity di morefficult stably to maintain, multiple consistent-step conversion performance. WECs areTo generate developed. electricity In such more systems, stably, m multiple-stepost PTOs would conversion employ WECs a rotary are developed. electric generator, In such systems, driven mechanicallymost PTOs would [9–11] employ, pneumatically a rotary electric[12], or hydraulically generator, driven [13,14] mechanically. Though the [9 –overall11], pneumatically efficiency could [12], beor offset hydraulically by the increased [13,14]. Thoughnumber theof energy overall conversion efficiency could steps, be the o ffarchitectureset by the increased could utilize number more of complicatedenergy conversion energy steps,conversion the architecture schemes, such could as utilizemultiple more connected complicated bodies energy to resonate conversion to a particular schemes, bandsuch of as multiplewave frequencies connected [11,15] bodies, or to resonatethe accumulators to a particular in hydraulic band of waveor pneumatic frequencies PTOs [11 ,to15 ],absorb or the excessiveaccumulators pressure in hydraulic fluctuations or pneumaticfor more consistent PTOs to absorbpower excessiveoutput [13] pressure. For this fluctuations reason, traditional for more largeconsistent-scale powerwave energy output conversion [13]. For this facilities reason, are traditional often of large-scalemultistage wavedesign energy [16–18] conversion. However, facilities since centralizedare often of wave multistage energy design conversion [16–18 facilities]. However, are usually since centralized permanently wave deployed energy near conversion shore [16 facilities,17] or requireare usually certain permanently mooring equip deployedmentnear [18] shore, the [traditional16,17] or require large-scale certain WE mooringCs lack equipment the ability [18 of], redeploymentthe traditional. Additionally, large-scale WECs mitigati lackng the line ability losses of redeployment. could be a challenging Additionally, engineering mitigating task line for losses the longcould transmission be a challenging distances engineering (in the magnitude task for the of longseveral transmission hundred kilometers) distances (inbetween the magnitude the sensors of andseveral power hundred hub. In kilometers) contrast, distributed between the power sensors generation and power by small hub.- Inscale contrast, WECs distributedcould offer powermore flexibilitygeneration through by small-scale onsite power WECs generation could offer with more tunable flexibility transmission through onsite losses power [19]. generation Nonetheless, with a majortunable drawback transmission of small losses-scale [ 19WECs]. Nonetheless, is the low power a major output drawback (only a few of small-scale Watts), which WECs is an is intrinsic the low limitationpower output, since (only the capacity a few Watts), of the which wave is power an intrinsic absorbable limitation, by the since WEC the is capacity directly of governed the wave by power the projectedabsorbable area by of the the WEC buoy is directlyon the ocean governed surface by the[20] projected. area of the buoy on the ocean surface [20]. ToTo improve improve the the limited limited out outputput power power of of a a small small-scale-scale WEC, WEC, this this paper paper explores explores the the feasibility feasibility of of aa new electrohydraulicelectrohydraulic PTO PTO design design with with energy energy storage storage to achieve to achieve greater powergreater output. power An output illustration. An illustrationof the proposed of the proposed WEC is shown WEC is in shown Figure in1. TheFigure first 1. stageThe first features stage features a hinged a twin-boardhinged twin design:-board designAn inverted: An inverted four-bar four double-bar slider double mechanism slider mechanism connects theconnects two hinged the two boards, hinged which boards, captures which the captureheavings motionthe heaving of the motionwave to of drive the a wave single to cylinder drive hydraulica single cylinder piston pump. hydraulic The secondpiston stagepump utilizes. The seconddigital stage fluid powerutilizes control. digital First,fluid thepower taken-o control.ff wave First, kinetic the taken energy-off is wave converted kinetic into energy stored is compressed converted intoenergy stored in acompressed bladder-type energy accumulator; in a bladder then-type a digital accumulator on-off valve; then a controls digital on the-off release valve of controls the energy the releasestorage of of the the energy accumulator storage to generateof the accumulator electricity through to generate a hydraulic electricity motor through coupled a tohydraulic a rotary electricmotor coupledgenerator. to a The rotary choice electric of the generator. proposed The electrohydraulic choice of the proposed PTO system electrohydraulic with energy PTO storage system capability with energyenables, storage in particular, capability a more enables compact, in particular, system [ 21a more]. compact system [21].

FigureFigure 1. 1. AnAn overview overview of of the the proposed proposed wave wave energy energy converter converter (WEC (WEC)) with with an an electrohydraulic electrohydraulic power power taketake-o-offﬀ ((PTO)PTO) system.system. 1:1: PistonPiston rod;rod; 2:2: Hydraulic Hydraulic piston piston pump; pump; 3: 3 Electric: Electric circuit circuit (battery, (battery control,, control, etc.); etc.)4: Electric; 4: Electric generator; generator; 5: Hydraulic 5: Hydraulic motor; motor; 6: Digital 6: Digital on-o onﬀ valve;-off valve; and 7:and Hydraulic 7: Hydraulic accumulator. accumulator. Note Notethe wave the wave length length of the of surface the surface wave iswave much is longer much than longer that than of the that buoy, of the and buoy, the buoy and is the assumed buoy is to assumedfollow the to heavingfollow the motion heaving of the motion wave. of the wave.

TheThe goal goal of of this this paper paper is to is model to mandodel validate and the validate key dynamics the key of dynamics the proposed of electrohydraulic the proposed electrohydraulicPTO system, and PTO study system, the effects and of study accumulator the effect pre-chargeds of accumulator pressure pre on system-charged performance. pressure on The system paper performanceis organized. as Th follows.e paper In is Sectionorganized2, the as design follows. of the In proposedSection 2 WEC, the design is demonstrated, of the proposed and the WEC lumped is demonstrated,dynamic models and of the mechanism,lumped dynamic the fluid models power of system, the mechanism, and the mechanical the fluid andpower volumetric system, lossesand the are mechanical and volumetric losses are established. In Section 3, a numerical solution to the dynamics

Energies 2019, 12, 3378 3 of 15 Energies 2019, 12, x FOR PEER REVIEW 3 of 16 established.of the digital In hydraulic Section3, acircuit numerical is proposed. solution In to theSection dynamics 4, an experimental of the digital hydraulic testbed and circuit test is procedures proposed. Inof Sectionthe proposed4, an experimental WEC are demonstrated. testbed and In test Sections procedures 5 and of6, thethe proposedderived PTO WEC models are demonstrated. are validated, Inand Section effects5, of the key derived design PTO parameters models are are validated, discussed. and effects of key design parameters are discussed.

2.2. Mathematical ModelsModels

2.1.2.1. DynamicsDynamics ofof thethe LinkageLinkage WaveWave FollowerFollower TheThe proposedproposed hingedhinged twin-boardtwin-board WEC is assumedassumed to reactreact toto thethe heavingheaving motion of thethe wave,wave, resultingresulting inin anan oscillatingoscillating angleangle betweenbetween thethe twotwo boardsboards aboutabout thethe hinge.hinge. AA four-barfour-bar double-sliderdouble-slider mechanismmechanism isis usedused toto convertconvert thethe wavewave activatedactivated rockingrocking motionmotion ofof thethe inputinput linklink (i.e.,(i.e., torquetorque andand angularangular velocity)velocity) intointo thethe motionmotion ofof thethe pistonpiston pumppump (i.e.,(i.e., forceforce andand linearlinear velocity),velocity), visualizedvisualized inin FigureFigure2 2..

Figure 2. Mechanism kinematics of the proposed WEC. Figure 2. Mechanism kinematics of the proposed WEC.

AssumingAssuming allall mechanicalmechanical componentscomponents are rigidrigid bodies,bodies, thethe motionmotion ofof thethe pistonpiston cancan bebe simplysimply derivedderived fromfrom thethe vectorvector equalityequality inin aa complexcomplex coordinatecoordinate systemsystem asas follows:follows: 푟⃑⃑⃑ = ℎ⃑ − 푟⃑⃑⃑ (1) *3 * *2 r3 = h r2 (1) 푖휃3 ⃑ where 푟⃑⃑⃑3 = 푟3푒 is the vector defining piston displacement,− ℎ is the constant horizontal vector * 푖휃2 pointing* fromi θthe revolute joint to the piston axis, and ⃑푟⃑⃑2 = 푟2푒 is the rocker link vector, rotated where r3 = r3e 3 is the vector deﬁning piston displacement, h is the constant horizontal vector pointing and retracted from 푟⃑⃑⃑20⃑⃑ , the vector denoting the* maximumiθ liftable position of the rocker link. from the revolute joint to the piston axis, and r2 = r2e 2 is the rocker link vector, rotated and retracted The* velocity and acceleration characteristics of the wave absorber linkage can be found through from r , the vector denoting the maximum liftable position of the rocker link. temporal20 derivation of the vector loop equation. Since the distance and orientation of the relative The velocity and acceleration characteristics of the wave absorber linkage can be found through position between the rocker pivot and piston axis are constant; i.e., 푑ℎ⃑ /푑푡 = 0. Thus, the velocity temporal derivation of the vector loop equation. Since the distance and orientation of the relative vector loop is found by * position between the rocker pivot and piston axis are constant; i.e., d h /dt = 0. Thus, the velocity ̇ ̇ 푖휃2 푖휃2 vector loop is found by ⃑푟⃑⃑3 = −푟⃑⃑⃑2 = −푟2̇ 푒 − 푟2휔2푒 𝑖 (2) . . * * . By performing one more derivationr = withr = respectr eiθ2 to time,r ω e theiθ2 i acceleration relationship is obtained(2) 3 − 2 − 2 − 2 2 ̈ 푖휃2 푖휃2 푖휃2 2 푖휃2 By performing one more푟⃑⃑⃑3 = derivation−푟2̈ 푒 − with2푟2̇ 휔 respect2푒 𝑖 + to푟 time,2훼2푒 the𝑖 + acceleration푟2휔2푒 relationship is obtained(3)

The buoy (Link 2) of the.. mechanism is activated by the heaving motion of the wave, resulting in ̇ * .. iθ . iθ iθ 2 iθ relative revolute motion (휃2r) about= r thee 2 pivot2r ω jointe 2 i표+: r α e 2 i + r ω e 2 (3) 3 − 2 − 2 2 2 2 2 2 ̇ ⃑⃑̇⃑ ′ (4) The buoy (Link 2) of the mechanism is activated휃2 = ∠ by푟2 the heaving motion of the wave, resulting in . relative revolute motion (θ ) about the⃑⃑⃑ ′ pivot joint′ o: ′ where the definition of the2 angle is ∠푟2 = im(푟2)/re(푟2). ̈ ⃑⃑̈⃑ ′ Similarly, the angular acceleration of the buoy is 휃2 = ∠푟2 . The dynamics of the mechanism is solved by constructing the free body diagrams and analyzing all the forces and moments in every link, as in Figure 3. Applying d’Alembert’s principle [22] and

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. . * θ2 = ∠r20 (4) * = where the deﬁnition of the angle is ∠r20 im r20 /re r20 . .. .. * = Similarly, the angular acceleration of the buoy is θ2 ∠r20 . The dynamics of the mechanism is solved by constructing the free body diagrams and analyzing Energiesall the 2019 forces, 12, andx FOR moments PEER REVIEW in every link, as in Figure3. Applying d’Alembert’s principle [ 224] of and 16 balancing forces on the horizontal and vertical axes and torques on links 2 and 3, the matrix deﬁning balancingthe dynamics forces of on the the mechanism horizontal can and be vertical obtained axes as: and torques on links 2 and 3, the matrix defining the dynamics of the mechanism can be obtained as:      m a 1 0 1 0 0 0 F  2 2x 푚 푎   퐹 12x   2 2푥  −−1 0 1 0 0 0  12푥   m 2a2y푚 푎   0 1 0 1 0 0   F12y   2 2푦   0 −−1 0 1 0 0 퐹12푦         I3α3 퐼3훼3   000 0 −푙l2 00 −푙l1 0 퐹 F23x    ==  − − 1   23푥  (5(5))  m3a3x 푚3푎3푥   000 0 −110 0 −1 0 퐹 F23y     − −   23푦   푚+3푎3푦 + 퐹13푦  0 0 0 −1 0 0    m3a3y F13y   0 0 0 1 0 0  퐹13푥 F13x   [퐼 훼 + 푚 푎 푟] [ 0 0 푙3 sin 휃2 푙3 cos− 휃2 0 −1]  I α +2m 2a r 2 2 4 0 0 l sin θ l cos θ 0 1 [ 푇푤 ] Tw 2 2 2 2 4 3 2 3 2 − where 퐹13푦 is an input, calculated from the piston cylinder pressure (which will be discussed in where F13y is an input, calculated from the piston cylinder pressure (which will be discussed in Section3) 퐼 Secmultipliedtion 3) multiplied by the piston by area,the pistonIs are thearea, rotary s are moments the rotary of inertia, moment fors whichof inertia, subscript for which denotes subscript the link denotes the link number, and 푙s are the normal distances of force about the revolution center. By number, and ls are the normal distances of force about the revolution center. By applying matrix−1 inversion h i 1 [퐹 퐹 퐹 퐹 퐹 푇 ] applying matrix inversion to Equation (5), the reaction forces−, 12푥 12푦 23푥 23푦 13푥 푤 , can be to Equation (5), the reaction forces, F12x F12y F23x F23y F13x Tw , can be resolved. The properties of the resolved. The properties of the mechanism can be found in Table 1. mechanism can be found in Table1.

FigureFigure 3. FreeFree body body diagrams diagrams for forthe piston the piston and rocker and rockerlink of the link proposed of the proposedwave absorption wave mechanism. absorption mechanism. Table 1. Mechanism parameters.

Symbol TableParameter 1. Mechanism Deﬁnition parameters.Value Unit

Symbolm2 massParameter of link 2 Definition Value 33.6 Unit kg m3 mass of link 3 0.2 kg 푚2 mass of link 2 33.6 kg 2 I2 moment of inertia of link 2 0.14 kgm 푚I 3 momentmass of oflink inertia 3 of link 3 0.100.2 kgmkg 2 3 *퐼 moment of inertia of link 2 0.14 kgm2 h2 length of ground link 23 mm 퐼 moment of inertia of link 3 0.10 kgm2 *3 r|20ℎ⃑ | maximumlength of lengthground of link link 2 3423 mm mm

|⃑푟⃑⃑20⃑⃑ | maximum length of link 2 34 mm 2.2. Dynamics of the Electrohydraulic PTO System 2.2. Dynamics of the Electrohydraulic PTO System The pressure dynamics of the fluid power circuit are modeled based on the definition of the fluid bulkThe modulus pressure (βe ),dynamics the orifice of flowthe fluid equation power ( qcircuiti,o), the are leakage modeled due based to valve on the clearance definition (ql), of and the checkfluid bulkvalue modulus dynamics (훽푒 (q),c ),the shown orifice below: flow equation (푞푖,표), the leakage due to valve clearance (푞푙), and check value dynamics (푞푐), shown below:

훽푒 푝̇ = − (푉̇ + 푞 + 푞 + 푞 ) (6) 푉 푖,표 푙 푐 where 푉 is the volume of the fluid within a given control surface; i.e., the total volume of oil in the accumulator plus the volume in the manifold and hoses; the latter two are neglected as the accumulator volume dominates, and the effective bulk modulus (훽푒) of oil with entrained air can be modeled using the two-phase (air-oil) polytropic model [23,24]. The constitutive relationships between pressure and flow can be modeled traditionally using lumped parameter models, e.g., the discharge flow equation, so that the rate of volumetric flow is modeled to be proportional to the square root of pressure differential across the valve orifice, the

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. βe . p = V + q + q + qc (6) − V i,o l where V is the volume of the fluid within a given control surface; i.e., the total volume of oil in the accumulator plus the volume in the manifold and hoses; the latter two are neglected as the accumulator volume dominates, and the effective bulk modulus (βe) of oil with entrained air can be modeled using the two-phase (air-oil) polytropic model [23,24]. The constitutive relationships between pressure and flow can be modeled traditionally using lumped parameter models, e.g., the discharge flow equation, so that the rate of volumetric flow Energies 2019, 12, x FOR PEER REVIEW 5 of 16 is modeled to be proportional to the square root of pressure differential across the valve orifice, the valve open area, the density of fluid, and the parallel plates’ leakage, etc. [24,25]. Alternatively, valve open area, the. density of fluid, and the parallel plates’ leakage, etc. [24,25]. Alternatively, the theaforementioned aforementioned 푉̇ , V푞,푖,q표i,o ,푞q푙l,, andand q푞c 푐models models can can be constructedbe constructed in a Simulinkin a Simulink block diagram,block diagram as shown, as inshown Figure in4 Figure. Then, 4. the Then, dynamic the dynamic pressure pressure in Equation in Equation (6) can be (6) solved. can be solved.

Figure 4.4. Simulink block diagram for dynamic simulation of thethe electrohydraulicelectrohydraulic circuit.circuit. Note the electrical generator is emulated by a user-deﬁneduser-defined “generator module,”module,” whichwhich containscontains aa rotaryrotary inertia,inertia, a rotational damper,damper, andand friction.friction. The motor shaft motion works as the input.input. The resultantresultant angular velocity and the torque are thethe outputs.outputs.

In the simulation,simulation, a double acting hydraulic cylinder block with only one port used acts as the hydraulic cylinder, whilewhile the piston displacement information either comes from user-defineduser-defined input or the measured data (details on setting up the experimental work work are shown in the next section section).). TwoTwo ball-typeball-type check check valve valve blocks block ares are used used to ensureto ensure the flowthe flow direction direction of the of single the single cylinder cylinder piston piston pump ispump checked. is checked A rotary. A inertia-damper-friction rotary inertia-damper combination-friction combination is used to mimic is used the to dynamic mimic the performance dynamic ofperformance the electrical of generator. the electric Aaltwo-position-two-way generator. A two-position (2/2-way)-two-way digital (2/2 on-o-wayff)valve digital is usedon-off to valve control is theused release to control of the the compressed release of the energy compresse from thed energy accumulator, from the following accumulator, the external following valve the command external signalvalve command (uv): signal (푢푣):

1 𝑖푓 푝푎 ≥ 푝푠푒푡 표푛 푢푣 = { (7) 0 𝑖푓 푝푎 ≤ 푝푠푒푡 표푓푓 where 푝푠푒푡 표푛 and 푝푠푒푡 표푓푓 are the two set pressure values to command the on-off valve to whether isolate or release the accumulator to the hydraulic motor. The simulation parameters can be found in Table 2.

Table 2. Simulation parameters for the block diagram.

Simulation Parameters Value Unit Simulation duration 100 s Solver ODE15s −

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 1 i f pa pset on u =  ≥ (7) v  0 i f pa p ≤ set o f f where pset on and pset o f f are the two set pressure values to command the on-oﬀ valve to whether isolate or release the accumulator to the hydraulic motor. The simulation parameters can be found in Table2.

Table 2. Simulation parameters for the block diagram.

Simulation Parameters Value Unit Simulation duration 100 s Solver ODE15s − Piston area 1 10 4 m2 × − Piston stroke (nominal) 0.025 m Bulk modulus 1.4 GPa Entrained air vol. fraction 0.02 − Moment of inertia of motor 0.05 kgm2 Rotary damping coeﬃcient 0.5 Nm/rad/s Crack pressure (check valve) 7 kPa Accumulator volume 0.5 L

2.3. Energy Storage and Power Output Based on the proposed two-stage design, the output electric power of the PTO system can be expressed as . . . . WE = η (ωrotor) WP(ωwave) WF(ωwave) WH(p) (8) G − − where ηG is the generator efficiency, which is an intrinsic property of the generator, determined by the rotor rotational frequency; and ωwave is the frequency of the wave. In this work, it is the frequency of . . the piston cylinder input. WP and WF represent the piston input and the mechanism friction power . respectively; each is a function of the wave frequency. WH is the leakage loss at a given hydraulic . circuit pressure. Obviously, for a higher electrical power output, one can increase WP, while keeping . . WF and WH low. The friction work in the mechanism includes the translational and rotational pin friction in the joints: . * * . WF(ωwave) = µF32r3 + T f 12θ2 (9) * * where µ is the friction coefficient, F is the force acting on the pin; T = µ F r is the friction 32 f 12 12 pin . * . torque on a pin with radius of rpin; r3 and θ2 are solved from the kinematic relationships in Equations (2) * * and (4); and both F12 and F32 are the reaction forces solved from Equation (5). The power of leakage loss is modelled as a simple parallel plate flow with hydrodynamic clearance:

. 2 WH(p) = C1p , (10)

Bc3 where C1 = 12µL is the lumped leakage coeﬃcient. Derivation details can be found in AppendixA. The piston input power is directly coupled to the wave frequency, and the average input power is governed by the pressure–volume (P–V) trajectory:

. . Z WP(ωwave) = pdv (11)

* where dv = dr3Ap, and Ap is the area of the piston. A special case is that when the accumulator is storing compressible energy; i.e., when the 2/2-way digital valve is deenergized, allowing the Energies 2019, 12, 3378 7 of 15 compressed ﬂuid to ﬁrst be accumulated before being released at a later time. In this case, the input work can be simply calculated by integrating the P–V trajectory under adiabatic heat capacitance ratio of γ (γ = 1.4), assuming the gas side of the accumulator follows the ideal gas law:

. Z V1 γ . V0 1 WP = p0 dν = (p1V1 p0V0) (12) ν (1 γ)∆t − V0 − . Equation (12) shows that WP monotonically increases with the final pressure, p1. It is, therefore, obvious to increase the final pressure for a higher amount of stored energy. That way, during the electrical generation process, releasing the compressible potential energy from the accumulator through the activation of the on-off valve at a higher pressure than in normal operating conditions can increase the overall power output, which will be validated in the experiments displayed in Section4. Though it Energies 2019, 12, x FOR PEER REVIEW . 7 of 16 is a linear relationship of final pressure with respect to WP, it is worth mentioning that in the design ofthat economical in the design fluid of power economical components, fluid the power magnitude components, of pressure the magnitude should be limited of pressure within should 30 MPa, be reconcilinglimited within the 30 material MPa, reconciling strength, weight, the material and cost. strength, weight, and cost.

3.3. Experimental System

3.1.3.1. Testbed TheThe proposedproposed electrohydraulicelectrohydraulic PTO systemsystem waswas designeddesigned andand fabricatedfabricated inhouseinhouse withwith aa smallsmall footprintfootprint ofof 0.80.8 mm byby 0.80.8 m.m. The schematic and a photo of the testbed are shown in Figures 55 andand6 6. . TheThe core core components components of the of PTO the are PTO the invertedare the four-bar inverted double four slider-bar double mechanism, slider the mechanism, electrohydraulic the circuit,electrohydraulic and the electronics circuit, and that thecoverts electronics the rotarythat coverts motion the of rotary the hydraulic motion of motor the hydraulic into direct motor current into electricdirect current power electric through power a generator. through The a generator. heaving motion The heaving of the buoymotion was of simulatedthe buoy was with simulated an input handlewith an pushinginput handle and pullingpushing the and piston pulling of the piston hydraulic of the cylinder. hydraulic The cylinder goals of. The the goals testbed of the are test to measurebed are to the measure displacement the displacement input of the input rocker, of thethe pressurerocker, the of thepressure accumulator, of the accumulator, the torque and the angular torque velocityand angular of the velocity hydraulic of the motor, hydraulic and the motor, electric and output the electric power output of the system.power of the system.

FigureFigure 5.5. CircuitCircuit diagramdiagram of of the the experimental experimental system. system. Note: Note: T representsT represents the the torque torque transducer; transducer; G is G the is electricthe electric generator; generator; E is the E is rotary the rotary encoder; encoder and U,; and V, and U, WV, areand the W three are the winding three coilswinding of the coils generator. of the generator. As shown in Figure6, a manual pump is used to mimic the relative motion of the buoy to the frame of the WEC when reacting to surface wave. The displacement of the plunger is directly measured using a laser triangulation sensor (LTS). The pumped fluid travels through the valve block into the accumulator pre-charged with nitrogen gas, and the storage pressure is regulated through a 2/2-way on-off valve. A pressure transducer senses the pressure in the accumulator. When the valve energizes, the released high-pressure flow drives a gerotor hydraulic motor and a 3-phase electric generator. The generated three-phase alternating current is rectified by a full diode bridge, and the load is simulated by two load resistors, R1 and R1, of whose resistance values are 0.1 Ω and 0.3 Ω,

Figure 6. A photo of the WEC core components testbed. A: Laser displacement sensor; B: Manual single cylinder piston pump; C: Compressed nitrogen gas accumulator; D: Torque transducer; E: Gerotor motor; F: Rotary encoder; G: Three-phase 12 V electric generator; H: Three-phase full-wave bridge rectifier; I: Load resistors; J: Solenoid on-off valve; K: Oil reservoir.

As shown in Figure 6, a manual pump is used to mimic the relative motion of the buoy to the frame of the WEC when reacting to surface wave. The displacement of the plunger is directly measured using a laser triangulation sensor (LTS). The pumped fluid travels through the valve block into the accumulator pre-charged with nitrogen gas, and the storage pressure is regulated through a 2/2-way on-off valve. A pressure transducer senses the pressure in the accumulator. When the valve

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that in the design of economical fluid power components, the magnitude of pressure should be limited within 30 MPa, reconciling the material strength, weight, and cost.

3. Experimental System

3.1. Testbed The proposed electrohydraulic PTO system was designed and fabricated inhouse with a small footprint of 0.8 m by 0.8 m. The schematic and a photo of the testbed are shown in Figures 5 and 6. The core components of the PTO are the inverted four-bar double slider mechanism, the electrohydraulic circuit, and the electronics that coverts the rotary motion of the hydraulic motor into direct current electric power through a generator. The heaving motion of the buoy was simulated with an input handle pushing and pulling the piston of the hydraulic cylinder. The goals of the test bed are to measure the displacement input of the rocker, the pressure of the accumulator, the torque and angular velocity of the hydraulic motor, and the electric output power of the system.

Energies 2019, 12, 3378 8 of 15

respectively. The accumulator pressure, the piston displacement, the angular velocity, the torque on the generatorFigure shaft, 5. andCircuit the diagram output of the voltage experimental on system. the load Note: resistors T represents are the sampledtorque transducer; by a G data is acquisition system (Nationalthe e Instrumentslectric generator; USB6009).E is the rotary encoder; and U, V, and W are the three winding coils of the generator.

Energies 2019, 12, x FOR PEER REVIEW 8 of 16

energizes, the released high-pressure flow drives a gerotor hydraulic motor and a 3-phase electric generator. The generated three-phase alternating current is rectified by a full diode bridge, and the load is simulated by two load resistors, 푅 and 푅 , of whose resistance values are 0.1 Ω and 0.3 Ω, Figure 6. A photo of the WEC core components1 testbed.1 A: Laser displacement sensor; B: Manual Figure 6. A photo of the WEC core components testbed. A: Laser displacement sensor; B: Manual single respectively.single The cylinder accumulator piston pump; pressure, C: Compressed the piston nitrogen displacement, gas accumulator; the D: angular Torque transducer;velocity, the E: torque on cylinderthe generator pistonGerotor shaft, pump; motor; and F: C: R otary Compressedthe outputencoder; voltageG: nitrogen Three- phaseon gasthe 12 accumulator;loadV electric resistors generator; D:are H: Torque sampled Three-phase transducer; by full a -datawaveE: acquisition Gerotor motor;system F: (National Rotarybridge rectifier; encoder; Instruments I: Load G: resistors; Three-phase USB6009). J: Solenoid 12 on V- electricoff valve; generator;K: Oil reservoir. H: Three-phase full-wave bridge rectiﬁer; I: Load resistors; J: Solenoid on-oﬀ valve; K: Oil reservoir. 3.2. Test AsProcedures shown in Figure 6, a manual pump is used to mimic the relative motion of the buoy to the 3.2. Test Proceduresframe of the WEC when reacting to surface wave. The displacement of the plunger is directly measuredDuring the using dynamic a laser triangula test, an tionoperator sensor would (LTS). The manually pumped pump fluid travel at nearlys through constant the valve frequencies block (~1 DuringHz) intofor the the a dynamic accumulator given number test, pre an-charged of operator reciprocati with wouldnitrogenng manuallycycles gas, and. Synchronous the pump storage at pressure nearly real- timeis constant regulated acquisition frequencies through of a spool (~1 Hz) for a givendisplacement,2/2 number-way on -coiloff of valve. reciprocating, and Adrive pressure current cycles. transducer was Synchronous performed. senses the pressure The real-time acquisition in the acquisitionaccumulator started. afterWhen of spool thethe valvesystem displacement, was coil, andwarmed drive up current; i.e., the was solenoid, performed. electric The circuit, acquisition and sensors started were after on for the 10 system min to wasavoid warmed temperature up; i.e., the solenoid,drift. In electric a multiple circuit,-cycle and test, sensors the acquisition were on fortime 10 was min 100 to s avoid and the temperature sampling frequency drift. In awas multiple-cycle 10 kHz. test, theThe acquisition equations set time to calculate was 100 the s and experimental the sampling heaving frequency input, the was hydraulic 10 kHz. motor The output, equations and the set to electric output power, are summarized in Table 3. Additionally, a measured input piston motion (i.e., calculate the experimental heaving input, the hydraulic motor output, and the electric output power, 50 pumping cycles) is shown in Figure 7. It is worth noting that the experimental input was done by are summarizedmanual pumping in Table; no3 advanced. Additionally, trajectory a measured control wa inputs implemented piston motion beyond (i.e., the operator’s 50 pumping perception. cycles) is shownFor in Figure PTO performance7. It is worth under noting realistic that the wave experimental conditions, input a simulation was done using by manual the experimentally pumping; no advancedvalidated trajectory models control and wave was implementeddata from ocean beyond sensors the can operator’s be found in perception. Section 4.2. For PTO performance under realistic wave conditions, a simulation using the experimentally validated models and wave data from ocean sensors can beTable found 3. Equation in Sections set to 4.2 calculate. the experimental averaged power. Description Equation Unit Table 3. Equations set to calculate the experimental1 averaged power. Heaving input ∫ 푝퐴 푟̇ d푡 W ∆푡 푝 3 Description Equation1 Unit R . HydraulicHeaving motor input output 1 ∫pA푇푚r 휔d푚t d푡 WW ∆t∆R푡 p 3 Hydraulic motor output 1 1 T ω dt W ∆tR m 2m Electric output 1 2∫P𝑖퐿 ∑푅퐿d푡 W Electric output ∆t ∆푡iL RLdt W

Note: TNote:m and 푇ω푚m areand the 휔푚 measured are the measured torque and torque angular and velocity angular at velocity the hydraulic at the hydraulic motor shaft, motor and shaft,iL and andRL are 𝑖퐿 the load currentand 푅 and퐿 are resistance, the load respectively.current and resistance, Since the heaving respectively. input Since is simulated the heaving through input the is operation simulated of through the manual pump, the equation in the ﬁrst line is equivalent to Equation (11). the operation of the manual pump, the equation in the first line is equivalent to Equation (11).

0.03

0.025

0.02

0.015

0.01

0.005

Input piston displacement (m)Input piston displacement 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (s)

FigureFigure 7. Piston 7. Piston pump pump input input trajectory. trajectory. Note Note that that there there areare 50 pump pumpinging cycles cycles in intotal. total.

4. Results and Discussion

4.1. Model Validation The performance of the proposed PTO system depends upon that of the electrohydraulic circuit. Therefore, the fluid power models developed in Section 2.2 were validated first. A comparison between the measured and the simulated accumulator pressure based on Equation (6) was made when the accumulator was pre-charged to 3 MPa, 6.6 MPa, or 15 MPa, as shown in Figure 8. The simulation results match the measurement in three experimental settings. For the same number of

Energies 2019, 12, 3378 9 of 15

4. Results and Discussion

4.1. Model Validation The performance of the proposed PTO system depends upon that of the electrohydraulic circuit. Therefore, the fluid power models developed in Section 2.2 were validated first. A comparison between the measured and the simulated accumulator pressure based on Equation (6) was made when the Energies 2019, 12, x FOR PEER REVIEW 9 of 16 accumulator was pre-charged to 3 MPa, 6.6 MPa, or 15 MPa, as shown in Figure8. The simulation results match the measurement in three experimental settings. For the same number of input pump input pump strokes as in Figure 7, the accumulator pressure reached a higher magnitude, as the pre- strokes as in Figure7, the accumulator pressure reached a higher magnitude, as the pre-charged charged pressure increased. The pressure history between 5 s and 45 s shows a trend that almost pressure increased. The pressure history between 5 s and 45 s shows a trend that almost linearly linearly increases with time, which is due to the charging of the pressurized fluid into the increases with time, which is due to the charging of the pressurized fluid into the accumulator by the accumulator by the hydraulic piston pump. The sharp corners at 52 s for the 15 MPa case, 65 s for the hydraulic piston pump. The sharp corners at 52 s for the 15 MPa case, 65 s for the 6.6 MPa case, or 47 s 6.6 MPa case, or 47 s for the 3 MPa case, indicate rapid loss of pressurized fluid in the accumulator for the 3 MPa case, indicate rapid loss of pressurized fluid in the accumulator chamber, which was chamber, which was due to the energizing of the digital on-off valve at those designated times to due to the energizing of the digital on-off valve at those designated times to discharge. It is also noticed discharge. It is also noticed that the duration of the accumulator discharge decreased with the pre- that the duration of the accumulator discharge decreased with the pre-charged pressure. This was also charged pressure. This was also expected, as most hydraulic motors output higher shaft speeds under expected, as most hydraulic motors output higher shaft speeds under elevated pressure. elevated pressure.

7 x 10 2.5 Simulation w/ p =3 MPa 2.25 ac Measurement w/ p =3 MPa ac 2 Simulation w/ p =6.6 MPa ac 1.75 Measurement w/ p =6.6 MPa ac Simulation w/ p =15 MPa 1.5 ac Measurement w/ p =15 MPa 1.25 ac 1 0.75 0.5

Accumulator pressure (Pa) pressure Accumulator 0.25 0 0 10 20 30 40 50 60 70 80 90 100 Time (s)

FigureFigure 8. 8. AA comparison comparison between between the the dynamic dynamic pressure pressure simulation simulation and and the the experiment experiment results results when when thethe accumulator accumulator is is pre pre-charged-charged to to 3 3 MPa, MPa, 6.6 6.6 MPa, MPa, and and 15 15 MPa. MPa. Note Note the the simulation simulation takes takes piston piston displacementdisplacement as as input input and and output output is is the the accumulator accumulator pre pressure.ssure.

TheThe output output power power from from the the hydraulic hydraulic motor motor shaft shaft drives drives the the electrical electrical generation generation system, system, higher higher outputoutput power power indicates indicates greater greater potential potential for for electricity electricity generation generation.. T Thehe simulated simulated hydraulic hydraulic motor motor outputoutput power power of of 3 3 MPa, MPa, 6.6 6.6 MPa, MPa, or or 15 15 MPa MPa accumulator accumulator pre pre-charged-charged pressure pressuress we werere validated validated by by beingbeing compared compared to to the the experimental experimental results, results, as as shown shown in in Figure Figure 99a–c.a–c.

360As shown in Figure9a,b the simulated results estimate200 the output power with good precision Simulation w/ p =6.6 MPa Simulation w/ p =15 MPa ac compared to the measurements. However,ac in the case of Figure180 9c, the deviation is over 50%. The significant 320 Measurement w/ p =6.6 MPa Measurement w/ p =15 MPa ac ac deviation280 is due to the unmodeled nonlinearities in the160 combined hydraulic motor-electric generator simulation;240 in Figure9a–c, all use the same damping coefficient140 0.50 Nm /(rad/s), as in Table2. By reducing 120 the damping200 coefficient for Figure9c to 0.20 Nm /(rad/s), the updated simulated results show a better 100 match160 with experiments, as demonstrated in Figure9d, which supports the assumption that the damping 80 effect120 in the combined motor-generator is nonlinear with respect to the shaft rotational speed. In addition, 60 the case80 where the digital on-off valve is kept energized during the entire experiment, i.e., the accumulator Motor outputMotor power (W) outputMotor power (W) 40 only acts40 as a pressure damper, as in [12], was also tested20 and validated, as in Figure 10. Compared to the case0 of Figure9d, without the storage and release of0 compressible energy from the accumulator, 52.6 52.7 52.8 52.9 53 53.1 53.2 53.3 53.4 53.5 53.6 65 65.2 65.4 65.6 65.8 66 66.2 66.4 66.6 66.8 the output shaft power fromTime (s) the hydraulic motor is strained under 60 WattsTime (W), (s) where for the same input motion, the peak(a output) power in Figure9d can reach as high as 122(b) W; or by increasing the

Energies 2019, 12, x FOR PEER REVIEW 9 of 16 input pump strokes as in Figure 7, the accumulator pressure reached a higher magnitude, as the pre- charged pressure increased. The pressure history between 5 s and 45 s shows a trend that almost linearly increases with time, which is due to the charging of the pressurized fluid into the accumulator by the hydraulic piston pump. The sharp corners at 52 s for the 15 MPa case, 65 s for the 6.6 MPa case, or 47 s for the 3 MPa case, indicate rapid loss of pressurized fluid in the accumulator chamber, which was due to the energizing of the digital on-off valve at those designated times to discharge. It is also noticed that the duration of the accumulator discharge decreased with the pre- charged pressure. This was also expected, as most hydraulic motors output higher shaft speeds under elevated pressure.

Accumulator pressure (Pa) pressure Accumulator 0.25 0 0 10 20 30 40 50 60 70 80 90 100 Time (s) Figure 8. A comparison between the dynamic pressure simulation and the experiment results when the accumulator is pre-charged to 3 MPa, 6.6 MPa, and 15 MPa. Note the simulation takes piston

Energiesdisplacement 2019, 12, x FOR as input PEER andREVIEW output is the accumulator pressure. 10 of 16 Energies 2019, 12, 3378 10 of 15 The output power from the hydraulic motor shaft drives the electrical generation system, higher 160 160 output power indicates greaterSimulation potential w/ p =3 for MPa electricity generation. The simulatedSimulation hydraulic w/ p =3 MPa motor pre-charge pressure of the accumulator,ac the peak is found140 over 220 W in Figure9a. The instantaneousac 140 Measurement w/ p =3 MPa output power of 3 MPa, 6.6 MPa, or 15 MPaac accumulator pre-charged pressures Measurementwere validated w/ p =3 MPa by output power gain from the proposed PTO system with a higher storage pressure is significant.ac being 120compared to the experimental results, as shown in120 Figure 9a–c. 100 100 360 200 Simulation w/ p =6.6 MPa 80 Simulation w/ p =15 MPa 80 ac ac 180 320 Measurement w/ p =6.6 MPa Measurement w/ p =15 MPa ac ac 28060 16060 24040 14040

Motor outputMotor power (W) 120 outputMotor power (W) 20020 20 100 1600 0 48.6 49 49.4 49.8 50.2 50.6 51 51.4 51.8 8048.6 49 49.4 49.8 50.2 50.6 51 51.4 51.8 120 Time (s) Time (s) 60 80 (c) (d) Motor outputMotor power (W) outputMotor power (W) 40 40 Figure 9. Simulated and experimental results on the hydraulic20 output power: (a) Accumulator pre- 0 0 charged52.6 52.7 to52.8 15 MPa52.9 53and53.1 released53.2 53.3 at 2153.4 MPa;53.5 (b53.6) accumulator65 pre65.2-charged65.4 65.6 to 65.86.6 MPa66 and66.2 released66.4 66.6 at 66.8 Energies 2019, 12, x FOR PEER REVIEWTime (s) Time (s) 10 of 16 10 MPa; (c) accumulator pre-charged to 3 MPa and released at 4 MPa; and (d) accumulator pre- (a) (b) charged to 3 MPa and released at 4 MPa, but with an adjusted rotational damping coefficient from 1600.50 Nm/(rad/s) to 0.20 Nm/(rad/s). 160 Simulation w/ p =3 MPa Simulation w/ p =3 MPa ac ac 140 140 Measurement w/ p =3 MPa Measurement w/ p =3 MPa ac ac 120As shown in Figure 9a,b the simulated results estimate120 the output power with good precision compared100 to the measurements. However, in the case100 of Figure 9c, the deviation is over 50%. The significant80 deviation is due to the unmodeled nonlinearities80 in the combined hydraulic motor-electric generator simulation; in Figure 9a–c, all use the same damping coefficient 0.50 Nm/(rad/s), as in Table 60 60 2. By reducing the damping coefficient for Figure 9c to 0.20 Nm/(rad/s), the updated simulated results 40 40

Motor outputMotor power (W) show a better match with experiments, as demonstrated outputMotor power (W) in Figure 9d, which supports the assumption 20 20 that the damping effect in the combined motor-generator is nonlinear with respect to the shaft 0 0 rotational48.6 speed.49 49.4 In 49.8addition,50.2 50.6the case51 where51.4 51.8 the digital48.6 on-off49 valve49.4 49.8is kept50.2 energized50.6 51 during51.4 51.8 the Time (s) Time (s) entire experiment, i.e., the accumulator only acts as a pressure damper, as in [12], was also tested and (c) (d) validated, as in Figure 10. Compared to the case of Figure 9d, without the storage and release of compressibleFigureFigure 9. 9. Simulated energySimulated fromand and experimental the experimental accumulator results results, on the the on output hydraulic the hydraulic shaft output power output power: from power: ( a the) Accumulator ( hydraulica) Accumulator pre motor- is strainedchargedpre-charged under to 15 6 to0MPa 15Watts MPaand (W), andreleased releasedwhere at 21 for at MPa; 21 the MPa; (sameb) (abccumulator) input accumulator motion, pre pre-charged-charged the peak to to6.6 output 6.6 MPa MPa andpower and released released in Figure at at 9d can 10reach10 MPa; MPa; as ( highc)) accumulatoraccumulator as 122 W pre-charged;pre or -bycharged increasing to to 3 MPa 3 MPa the and andpre released- charge released at 4pressure at MPa; 4 MPa; and of ( andd the) accumulator (accumulator,d) accumulator pre-charged the pre peak- is foundchargedto over 3 MPa 220to and 3 WMPa released in andFigure atreleased 4 MPa,9a. The butat 4instantaneous with MPa, an but adjusted with output an rotational adjusted power damping rotational gain coe from ﬃdampingcient the fromproposed coefficient 0.50 Nm PTO/ (radfrom system/s) with0.50 toa higher 0.20 Nm/(rad/s) Nm storage/(rad to/s). 0.20 pressure Nm/(rad/s) is significant..

As 80shown in Figure 9a,b the simulated results estimate the output60 power with good precision Simulation w/ p =3 MPa compared70 to the measurements. However, in athec case of Figure 9c, the deviation is over 50%. The Measurement w/ p =3 MPa 50 significant60 deviation is due to the unmodeled nonlinearitiesac in the combined hydraulic motor-electric generator simulation; in Figure 9a–c, all use the same damping coefficient40 0.50 Nm/(rad/s), as in Table 50 2. By reducing the damping coefficient for Figure 9c to 0.20 Nm/(rad/s), the updated simulated results show a better40 match with experiments, as demonstrated in Figure 9d, 30which supports the assumption that the30 damping effect in the combined motor-generator is nonlinear with respect to the shaft 20 rotational20 speed. In addition, the case where the digital on-off valve is kept energized during the

Motor outputMotor power (W) entire experiment outputMotor power (W) , i.e., the accumulator only acts as a pressure damper10, as in [12], was also tested and validated10, as in Figure 10. Compared to the case of Figure 9d, without the storage and release of compressible0 energy from the accumulator, the output shaft power0 from the hydraulic motor is 0 5 10 15 20 25 30 35 40 45 50 55 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Time (s) strained under 60 Watts (W), whereTime (s) for the same input motion, the peak output power in Figure 9d can reach as high as 122 W; or by(a) increasing the pre-charge pressure of the accumulator,(b) the peak is found over 220 W in Figure 9a. The instantaneous output power gain from the proposed PTO system Figure 10. Simulated and experimental results on the hydraulic output power when the accumulator with aFigure higher 10. storageSimulated pressure and experimental is significant. results on the hydraulic output power when the accumulator isis pre pre-charged-charged to 3 MPa and is always connected to the motor (i.e., the digital on on-o-offﬀ valve is kept energized80 the the entire entire time time during during the the experiment) experiment):: (a ()a Full) Full 50 50-cycle-cycle comparison comparison,60 , and and (b) ( bz)oomed zoomed-in-in 4- Simulation w/ p =3 MPa cycle4-cycle70 result result timed timed from from 2 s 2 to s to7 s 7 for s for clarity. clarity. ac Measurement w/ p =3 MPa 50 60 ac 40 50 40 30 30 20 20

Motor outputMotor power (W) Motor outputMotor power (W) 10 10

0 0 0 5 10 15 20 25 30 35 40 45 50 55 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Time (s) Time (s) (a) (b)

Figure 10. Simulated and experimental results on the hydraulic output power when the accumulator is pre-charged to 3 MPa and is always connected to the motor (i.e., the digital on-off valve is kept energized the entire time during the experiment): (a) Full 50-cycle comparison, and (b) zoomed-in 4- cycle result timed from 2 s to 7 s for clarity.

Energies 2019, 12, x FOR PEER REVIEW 11 of 16 EnergiesEnergies 20192019, 12, 12, x, 3378FOR PEER REVIEW 1111 of of 16 15

4.2.4.2. Power Power Output Output and and Losses Losses 4.2. Power Output and Losses TheThe performance performance of theof the PTO PTO balances balances be tweenbetween the the power power output output and and losses. losses. To Tocalculate calculate the the inputinput Thepiston piston performance work, work, and and the of the mechanical mechanical PTO balances and and volumetric between volumetric the losses powerlosses in thein output the proposed proposed andlosses. PTO PTO using To using calculate Equations Equations the (9)input (9) through through piston (12), work, (12), the and the link thelink velocit mechanical velocity, they, the andpin pin volumetric reaction reaction force losses forces, ands in, and the the proposed the leakage leakage PTO coefficient coefficient using Equations need need to beto (9) be ̇ throughdetermined (12), the. In linkFigure velocity, 11, the the translational pin reaction velocity forces, and of Link the leakage 푟⃑2,⃑⃑ ̇ 푟⃑⃑⃑2 , is coe obtainedﬃcient by need calculating to be determined. Equation determined. In Figure 11, the translational velocity. of Link 2, 2, is obtained by calculating Equation (2) using the trajectory in Figure 7, and the rotational* angular velocity from Equation (4). With the (2)In using Figure the 11 ,trajectory the translational in Figure velocity 7, and ofthe Link rotational 2, r , is angular obtained velocity by calculating from Equation Equation (4). (2) With using the the knowledge of those parameters, and 퐹 using2 measured piston pressure, the reaction forces on the knowledgetrajectory inof Figurethose parameters,7, and the rotational and 퐹13푦 13 angularusi푦 ng measured velocity frompiston Equation pressure, (4). the With reaction the knowledgeforces on the of rightright-hand-hand side side of theof the Equation Equation (5) (5)were were calculated. calculated. Then Then all allthe the unknowns unknowns in Equationin Equation (9) (9)we rewe re those parameters, and F13y using measured piston pressure, the reaction forces on the right-hand side obtained. obtained.of the Equation (5) were calculated. Then all the unknowns in Equation (9) were obtained.

5 5 0.2 0.2

2.5 2.5

0 0 0 0

-2.5-2.5

Angularvelocity (rad/s)

Translationalvelocity (m/s) -5 -5 -0.2-0.2Translationalvelocity (m/s) 0 0 2.5 2.5 5 5 7.5 7.5 10 1012.512.515 1517.517.520 2022.522.525 25 TimeTime (s) (s)

FigureFigureFigure 11. 11. 11.CalculatedCalculated Calculated rotational rotational rotational angular angular angular velocity velocity velocity (dotted (dotted (dotted line) line) line) and and and translational translational translational velocity velocity velocity (solid (solid (solid line) line) line) of of of LinkLinkLink 2. 2. Note 2. Note Note the the thetranslational translational translational velocity velocity velocity has has has been been been smooth smoothed smoothed byed by aby amoving movinga moving window window window with with with a awidth widtha width of of 2001 of 2001 2001 datadatadata points. points. points.

ByBy By substituting substituting substituting the the the measured measured measured piston piston piston displacement displacement displacement and and and accumulator accumulator accumulator chamber chamber chamber pressure pressure pressure into into into EquationEquationsEquations ( (9)–(12),9s )–(9(1)–2(1), 2 the), the hydraulic hydraulic hydraulic motor motor motor output, output, output, the the electrical the electrical electrical generator generator generator output, output, theoutput, mechanical the the mechanical mechanical friction frictionlossfriction due loss to loss due the due relativeto theto the relative motion relative motion between motion between the between pin the and the pin slot, pin and and and slot the slot, and leakage, and the the leakage loss leakage power loss loss can power bepower obtained, can can be be obtainedasobtained in Figure, as, inas 12 Figurein. Figure 12. 12.

3 3 10 10

2 2 10 10

1 1 10 10

0 0 10 10

-1 -1 10 10

Averagedpower(W)

Averagedpower(W) HydraulicHydraulic motor motor output output -2 -2 GeneratorGenerator output output 10 10 MechanicalMechanical friction friction LeakageLeakage -3 -310 10 1 2 3 4 3 MPa13 MPa 3 MPa23 MPa 6.63 6.6MPa MPa 154 MPa15 MPa w/ow/o active active w/ activew/ active w/ activew/ active w/ activew/ active storagestorage storagestorage storagestorage storagestorage

FigureFigureFigure 12. 12. 12.CalculatedCalculated Calculated average averaged averaged powerd power power of of theof the theproposed proposed proposed PTO PTO PTO using using using experimental experimental experimental data data. data. Note Note. Note the the the magnitudesmagnitudesmagnitudes of of theof the theaveraged averaged averaged power power power are are areshown shown shown in in ain asemi semi-logarithmica semi-logarithmic-logarithmic plot plot plot for for forclarity. clarity. clarity. The The The averaged averaged averaged outputoutputsoutputs of ofs electrical of electrical electrical power power power for for forthe the thefour four four cases cases cases are are are1.3 1.3 1.3W, W, W,5.0 5.0 5.0W, W, W,20.6 20.6 20.6 W W,, Wand and, and 60.2 60.2 60.2 W. W. W.

Energies 2019, 12, x FOR PEER REVIEW 12 of 16 Energies 2019, 12, 3378 12 of 15 From Figure 12, the performance of the proposed PTO shows that for the same input number of waves,From higher Figure accumulator 12, the performance pressure ofresults the proposed in greater PTO generated shows thatelectric for thepower. same In input the 3 numberMPa case of, waves,without higher active accumulator energy storage, pressure the generator results in output greater power generated is only electric a few Watts power., comparable In the 3 MPa to other case, withoutWEC design actives energy under storage,a similar the footprint generator [12] output. However, power once is onlythe pressurized a few Watts, flow comparable from the pump to other is WECactively designs stored under as in a similarthe other footprint three cases [12]., the However, output oncepower the increases pressurized significantly flow from, especially the pump at isa activelyhigher stored pre-charged as in the pressure other three. When cases, the the accumulator output power is discharged increasessignificantly, at 21 MPa inespecially the 15 MPa at case a higher, the pre-chargedaverage electric pressure. power When reaches the accumulator60.2 W (with peak is discharged power over at 2112 MPa2 W), inwhich the 15 is MPaat least case, 46 times the average higher electricthan powerin those reaches without 60.2 Wenergy (with storage. peak power And over this 122 supports W), which the isauthors at least’ 46argument times higher that than the implementation of energy storage devices on portable WECs significantly boosts the output electric in those without energy storage. And this supports the authors’ argument that the implementation power. Another observation is that the leakage loss increases with pre-charged pressure, but the of energy storage devices on portable WECs significantly boosts the output electric power. Another magnitude is much smaller compared to the mechanical friction; e.g., leakage power is only 0.4 W in observation is that the leakage loss increases with pre-charged pressure, but the magnitude is much the 15 MPa case according to Equation (10), whereas the mechanical friction is over 4.2 W by Equation smaller compared to the mechanical friction; e.g., leakage power is only 0.4 W in the 15 MPa case (9). Additionally, the mechanical friction loss could offset the electrical output at a higher pressure or according to Equation (10), whereas the mechanical friction is over 4.2 W by Equation (9). Additionally, faster pin rotational frequency, according to Equation (9). Nonetheless, results show that under 15 the mechanical friction loss could offset the electrical output at a higher pressure or faster pin rotational MPa pressure, and 1 Hz, the combined leakage and mechanical friction losses constitute only 7.6% of frequency, according to Equation (9). Nonetheless, results show that under 15 MPa pressure, and 1 Hz, the electrical output power. the combined leakage and mechanical friction losses constitute only 7.6% of the electrical output power. To estimate the performance of the PTO under real ocean environment, the validated models To estimate the performance of the PTO under real ocean environment, the validated models were were simulated using recorded ocean wave input from published surface elevation data in [26]. The simulated using recorded ocean wave input from published surface elevation data in [26]. The four four configurations for the power take-off were tested, the same way as for Figure 12, and the results configurations for the power take-off were tested, the same way as for Figure 12, and the results are are shown in Figure 13. The averaged electrical outputs are 0.5 W, 7.3 W, 20.2 W, and 69.1 W. The shownoverall in trend Figure and 13 .magnitude The averaged of the electrical simulation outputs results are match 0.5 W, th 7.3ose W, in 20.2Figure W, 12 and. It 69.1was expected W. The overall, since trendthe and selected magnitude wave data of the also simulation contained results 50 input match cycles those, the in result Figure would 12. It was be similar expected, accumulated since the selectedpressure wave. However data also, the contained mechanical 50 input friction cycles, reduces the result about would 20% be from similar the accumulated experiment, pressure. due to However,significant thely mechanical slower wave friction frequency reduces of the about real 20% wave from at 0.05 the experiment,Hz, compared due to to the significantly manual pumping slower waveexperiment frequency at 1 of Hz. the The real leakage wave atstay 0.05s relatively Hz, compared constant to, theas it manual is a function pumping of pressure experiment. Although at 1 Hz.the Thesimulated leakage staysoutput relatively power isconstant, consistent as with it is athe function experiment, of pressure. the simulation Although took the about simulated 6 to 10 output times powerlonger is consistentto charge the with accumulator the experiment, than thethat simulation in the experiment took about, as 6 t tohe 10recorded times longer wave tofrequency charge the is accumulatorsignificantly than slower. that in the experiment, as the recorded wave frequency is significantly slower.

3 10

2 10

1 10

0 10

-1 10

-2 10

Averaged power (W)

-3 10 Hydraulic motor output Generator output -4 10 Mechanical friction Leakage

-5 10 3 MPa1 3 MPa2 6.6 3MPa 15 MPa4 w/o active w/ active w active w active storage storage storage storage

FigureFigure 13. 13.Simulated Simulated averaged averaged power power under under realistic realistic wave wave input. input. Note Note thethe time time series series of of surface surface elevationselevations data data was was recorded recorded by a by wave a wave buoy atbuoy the Southat the West South UK, West on 18 UK, March on 18 2010, Mar 15:00,ch 2010 published, 15:00, inpublished [26]. The peakin [26 frequency]. The peak of frequency the wave of is 0.05the wave Hz and is 0.05 the maximumHz and the amplitude maximum isamplitude 5 m. A saturation is 5 m. A operationsaturation was operation applied towas the applied wave trajectoryto the wave to trajectory limit input to tolimit piston input displacement to piston displacement between 0 mmbetween and 250 mm. mm Additionally,and 25 mm. A additionally, total duration a total of 430 duration s of data of 43 was0 s used of data so thatwas 50used completed so that 50 piston complete inputd cyclespiston wereinput achieved cycles were to match achieved that of to Figure match 12 that. The of Figure averaged 12. outputThe averaged electrical output power electrical of the four power cases of arethe 0.5four W, 7.3cases W, are 20.2 0.5 W, W, and 7.3 69.1 W, 20.2 W. W, and 69.1 W.

Energies 2019, 12, 3378 13 of 15

In terms of application of the proposed energy storage-and-release concept for PTOs, it can be applied to industrial or commercial electrohydraulic PTO systems for boosted output power. If the original PTO system is already based on fluid power transmission, the proposed method can be readily applied, and the benefits of an increased output power are expected by adding an on/off valve to control the release of the accumulator storage energy, as the schematic shows in Figure5. Conveniently, the target system still operates at the original pressure rating in this case, without the need for replacing the existing components. As for the improvement, according to the results in Figures 12 and 13, if the target system has a similar footprint as the one in this paper, a two to four times increase of output power is expected. To further increase the output power, one needs to dial up the magnitude of pre-charged pressure of the accumulator. Although, according to Equations (11) and (12), for the same input heaving motion, the input power grows proportionally with both the accumulator’s pre-charge pressure and the volume; neither can be set infinitely high. This is because the power of leakage loss is directly proportional to the square of the accumulator pressure, as in Equation (10), which grows much faster than the output power does. Also, practical constraints, such as the fluid pressure rating of the original system (e.g., economically, commercial fluid power systems are usually rated below 30 MPa), and the difficulty in manufacturing large fluid power components, could set additional obstacles, which all need to be removed before the proposed method can be applied at significantly elevated pressure settings. In all, the proposed method is tested to boost the output power of a WEC over 40 times compared to a traditional electrohydraulic PTO system without storage, when the pre-charged pressure of the accumulator is set over 15 MPa; even if the original system is operating on low pressure settings (i.e., below 3 MPa), the improvement of the system output is still significant. Yet, there is still room for future improvements on the understanding of the combined effects of the motor/generator rotation speed, accumulator volume, and storage pressure, with further optimization and experimental study.

5. Conclusions The electrical output capability of a traditional small-scale WEC is limited by its physical dimensions. To increase the electricity output of small-scale, portable WECs, a hinged twin-board designed WEC, utilizing an electrohydraulic PTO system with compressed energy storage is proposed, modeled, and experimentally validated. Initial test results showed that the derived models well predict the performance of the system, and the proposed PTO system with high pre-charge accumulator pressure can improve the peak electric output by up to 122 W. The two major conclusions derived from this combined simulation and experimental study are: (1) Energy storage concept was proposed for the fluid-power-based PTO systems in a portable WEC. Simulation and experimental measurements demonstrated output power improvements of two to over 40 times, depending on the accumulator’s pre-charged pressure. (2) A combined kinematic-fluid power model was derived, simulated, and experimentally validated for the proposed electrohydraulic PTO system, laying the ground work for future parametric studies. Apart from the benefits of the proposed approach, the pressure rating of the original system and regulating of high flow rate are the two major challenges. In future work, through further optimization and experimental study, the combined effects of the rotation speed, accumulator volume, storage pressure, and the constraints of manufacturability, can be better evaluated to improve the output power of the PTO.

Author Contributions: Formal analysis, H.T. and Z.Z.; methodology, H.T.; validation, Z.Z. and Y.S.; writing, H.T. Funding: This research was funded by National Natural Science Foundation of China, grant number 51705061, Key Laboratory for Precision and Non-traditional Machining of Ministry of Education, Dalian University of Technology, grant number JMTZ201703, and Fundamental Research Funds for the Central Universities, grant number 3132019121. Energies 2019, 12, x FOR PEER REVIEW 14 of 16

Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the Energies 2019, 12, 3378 14 of 15 study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study;Appendix in the collection,A Derivation analyses, of the or interpretationPower Loss on of data;Leakage in the writing of the manuscript, or in the decision to publish the results. Since the volumetric flow rate of the leakage cannot be directly measured, and usually only the Appendixsystem pressure A Derivation can be obtained of the Power in an Loss experimental on Leakage system, the power loss on leakage based purely on theSince system the volumetric pressure is flow derived rate ofas the follows. leakage Based cannot on bethe directly lumped measured, pressure dynamics and usually in onlyEquation the ∆푝퐵푐3 system(6), if we pressure only consider can be obtained leakage inin anthe experimental form of parallel system, plate the flow power (푞 = loss on) leakage[24,25], then based the purely leakage on– 푙 12휇퐿 the system pressure is derived as follows. Based on the lumped pressure dynamics in Equation (6), if we pressure relationship is: ∆pBc3 only consider leakage in the form of parallel plate flow3 (ql = 12µL )[24,25], then the leakage–pressure 훽푒 ∆푝퐵푐 relationship is: 푝̇ = − = −퐶0푝 (A1) 푉 123휇퐿 . βe ∆pBc p = = C p (A1) where 휇 is the viscosity of the fluid, 퐿 and− V 퐵 12areµL the length− 0 and width of the leakage path, 푐 is the ∆푝 ∆푝 = wherehydrodynamicµ is the viscosity clearance of height, the fluid, andL and isB theare pressure the length differential and width across of the the leakage leakage path, regionc is the 푝 퐶 hydrodynamic, if gauge pressure clearance is used. height, Then and one∆ pcanis thelump pressure all the diparametersfferential acrossexcept thethe leakagegauge pressure region ∆ intop = p,0, arriving at a linear function of the rate of pressure change, 푝̇ about 푝. Then the magnitude of 퐶0 can if gauge pressure is used. Then one can lump all the parameters except the gauge pressure into C0, be obtained from the slope of the pressure drop in Figure. 12. arriving at a linear function of the rate of pressure change, p about p. Then the magnitude of C0 can be obtainedFinally from, the slope power of loss the pressure due to leakage drop in Figure is the multiplication12. of the gauge pressure and the volumetricFinally, therate power flow: loss due to leakage is the multiplication of the gauge pressure and the volumetric rate flow: ̇ 2 .푊퐻 = 퐶1푝 (A2) 2 푉 WH = C1p (A2) where 퐶1 = 퐶0. V훽푒 where C = C0. Based1 βone the experimentally obtained pressure drop rate as a function of pressure, as in Figure Based on the experimentally obtained pressure drop rate as a function of pressure, as in Figure A1, A2, a rather linear relationship was found, confirming that the leakage is dominated by a rather linear relationship was found, confirming that the leakage is dominated by hydrodynamic hydrodynamic clearance flow. clearance flow.

0 Experimental data -0.01 Linear least square fit

-0.02

-0.03

-0.04

Pressure Pressure drop (MPa/s) rate R2=0.966 -0.05 4 5 6 7 8 9 10 11 12 13 14 15 16 Pressure (MPa) FigureFigure A1. AExperimental1. Experimental leakage leakage measurement. measurement. Note that Note the that linear the least linear square least ﬁt of square the experimental fit of the

dataexperimental showed the data coeﬃ showedcient (C 1 the) of the coefficient pressure ( dropC1) of rate the with pressure respect drop to the rate accumulator with respect pressure to isthe 0.0036accumulator MPa/s per pressure 1 MPa. is Note, 0.0036 the MPa/s regression per 1 MPa. performance Note, the value, regression R2, is performance 0.966. value, R2, is 0.966.

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