energies Article
Perturb and Observe Control for an Embedded Point Pivoted Absorber Gianluca Brando 1, *, Domenico Pietro Coiro 2 , Marino Coppola 1 , Adolfo Dannier 1 , Andrea Del Pizzo 1 and Ivan Spina 1 1
2
*
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy;
[email protected] (M.C.);
[email protected] (A.D.);
[email protected] (A.D.P.);
[email protected] (I.S.) Department of Industrial Engineering, University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy;
[email protected] Correspondence:
[email protected]; Tel.: +39-081-7683233
Academic Editor: Stephen Nash Received: 1 August 2016; Accepted: 8 November 2016; Published: 10 November 2016
Abstract: Marine energy sources represent an attractive and inexhaustible reservoir able to contribute to the fulfillment of the world energy demand in accordance with climate/energy regulatory frameworks. Wave energy converter (WEC) integration into the main grid requires both the maximization of the harvested energy and the proper management of the generation variability. The present paper focuses on both these mentioned issues. More specifically, it presents an embedded point pivoted absorber (PPA) and its related control strategy aimed at maximizing the harvested energy. Experimental and numerical investigations have been carried out in a wave/towing tank facility in order to derive the design characteristics of the full-scale model and demonstrate the validity and effectiveness of the proposed control strategy. Keywords: wave energy converter (WEC); scale model; marine; perturb and observe (P&Q); maximum power point tracking (MPPT)
1. Introduction Nowadays, national energy policies are driven by several needs such as promoting the use of endogenous sources in order to limit the energy dependence from foreign countries and enhance the security of the energy supply, respecting the energy/environmental targets established in the international frameworks, and stimulating the global cost competitiveness [1]. Renewable energy sources (RES) are playing a primary role in worldwide energy demand fulfillment due both to the rapid exhaustion of the oil resources [2,3] and due to their “friendly” environmental impact. In particular, with reference to a highly distributed renewable energy generation system, a proper forecasting of the available RES power behavior can lead to a more efficient electrical transmission versus high power centralized systems [4–6]. Among the multitude of RES energy options, the ocean is considered one of the most energy-dense: it has been estimated that 0.1% of the energy in ocean waves is five times more than the whole world’s energy requirements [7]. Nevertheless, today its exploitation is very limited, whilst several conversion technologies are available for exploiting diversified energy forms such as tidal and marine energy, wave energy, and salinity energy [8]. Wave energy converters (WECs) can be classified according to different criteria such as the working principle (energy extraction principle), the water depth, the location (shoreline, near-shore, offshore), the size, and so on [9–13]. With respect to a working-principle based classification, three main WECs categories can be identified: oscillating water column, overtopping converters, and oscillating bodies. The electric energy generation in oscillating water column systems and overtopping converters
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is ensured by an electric generator. In oscillating water column systems the electric generator is moved by a turbine, which is driven in turn by the airflow ducted in a column by the incident waves. In overtopping converters, the electric generator is instead driven by a hydraulic turbine which converts the potential energy obtained by capturing the incident sea waves in a reservoir above the surrounding water surface. Finally, in the oscillating bodies systems, the linear/tubular electric generators, or rotating generators with mechanical actuators (for example, ball screw actuators), convert the kinetic energy transmitted by the sea waves to oscillating floating or submerged bodies. Recently, different offshore wave generation devices have reached the full-scale demonstration stage and they are generally constituted by means of oscillating bodies, either floating or fully submerged. Practical examples are heaving mode point absorbers, which received great attention through many analytical studies as well as numerical and experimental investigations aimed at optimizing their shape and performances [14,15]. Pivoted type energy converters exploit both horizontal and vertical translations of the floating body [16–18]. In this regard, Wavestar and Seapower platform are examples of full-scale devices characterized by a hydraulic power take-off system using oil as the working fluid and requiring a complex control mechanism [19]. Two key issues have to be addressed for WEC integration into the main grid. The first issue is the maximization of the available energy, which can be pursued by deploying adequate control strategies for the electric generator. The second is the grid integration of the system, an aspect complicated by the oscillating mechanical power transferred to the electric generator. A promising solution for mitigating this effect and in doing so promote the WECs’ network integration is represented by energy storage systems (ESSs), able to compensate for the power fluctuations in highly variable RES [11,20–22]. Armed with such a vision, this paper is focused on the design/implementation of an embedded pivoted point absorber and its related maximum power point tracking (MPPT) control strategy. In particular, the paper proposes an innovative perturb and observe (P&O) algorithm [23], designed to maximize the harvested energy in a wide range of operating conditions. The effectiveness of the proposed system is strengthened by the envisioned pivoted point absorber, which guarantees a higher energy extraction rate when compared to the traditional heaving mode system. The electric energy conversion is performed by an AC brushless rotating generator, coupled with an electromechanical actuator based on a ball screwing system, characterized by a high-speed ratio in order to maximize the power density of the generator. Finally, the mitigation of the WEC power fluctuations, needed to ensure a quasi-constant grid injected power, can be performed by means of the supercapacitor based ESS presented in [24] by some of the authors of this work. Starting from several experimental results obtained for a reduced scale prototype operating in a wave/towing tank facility (Section 3), some numerical investigations (Section 6) have been performed in order to validate the proposed P&O algorithm (Section 5). Finally, Section 7 provides conclusions and final remarks. The obtained outcomes will permit the deployment of a 1:1 scale model in the near future. 2. The Proposed Wave Energy Converter In this Section, each of the facilities upon which the proposed system is built are described. 2.1. The Power Buoy The primary system configuration is shown in Figure 1: it deals with a floating body anchored to a fixed frame; two hinges allow rotation of the body with respect to the frame and to the power take off (PTO) device. The PTO is represented by a device able to convert the rotational oscillation of the buoy into electrical energy; a rotational generator with a ball-screw is chosen for this purpose. The action of the waves yields a rotational movement of the buoy around the submerged hinge, which the floating body is anchored to, by means of the support arms.
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Figure 1. Schematic representation of the system. PTO: power take off.
Figure 1. Schematic representation of the system. PTO: power take off.
The main dimensions of the WEC scale model are reported in Table 1.
The main dimensions of1.the WEC representation scale modelofare inpower Tabletake 1. off. Figure Schematic the reported system. PTO: Table 1. Reduced scale prototype parameters. WEC: wave energy converter. The main ofscale the WEC scale model are reported Tableenergy 1. Tabledimensions 1. Reduced prototype parameters. WEC:inwave converter. Main Dimensions of the WEC Dimension Unit Body height 0.6 m Table 1.Main Reduced scale prototype parameters. WEC: wave energy converter. Dimensions of the WEC Dimension Unit Body width 1.0 m Main weight Dimensions of+the WEC Dimension Unitkg Body(body height 0.632.5 m Body arms) height 0.6 m Body width 1.0 m Hinge moment of inertia (body + arms) 21.65 kg·m2 Body weight 32.5 kgm Body (body width + arms) 1.0 Draft 0.2 m Hinge moment of inertia 21.65 kg·m Body weight (body (body + arms)+ arms) 32.5 kg2 2 Body section at water level 0.21 m 0.2 m 2 Hinge moment ofDraft inertia (body + arms) 21.65 kg·m 3 Immersed volume 0.0325 Body section at water level 0.21 m2 m
For sake of clarity, a
Draft Immersed Body section atvolume water level pictorial representation of Immersed volume
0.2
0.0325 0.21
m
32 mm
the latter has also been reported in Figure 2. 0.0325 m3
For sake of clarity, a pictorial representation of the latter has also been reported in Figure 2. For sake of clarity, a pictorial representation of the latter has also been reported in Figure 2.
Figure 2. Reduced scale prototype main dimensions. Figure 2. Reduced scale prototype main dimensions.
2.2. The Power Take Off
Figure 2. Reduced scale prototype main dimensions.
2.2. The Power Take Off
As hinted 2.2. The Power Takeabove, Off the PTO considered in this paper is a ball screw-based generator. This design As hinted above, the PTO considered in this paper is a ball screw-based generator. This design
assumption is driven bybythe fact that this technological solution,with withrespect respect to direct drive linear is driven theconsidered fact that thisin technological solution, to direct drive linear Asassumption hinted is above, the PTO this paper isand, a ball screw-based generator. This design generators, able to ensure a relative higher speed ratio hence, higher power density generators, is able to ensure a relative higher speed ratio and, hence, higher power density [25].[25]. In In assumption is driven by the fact that this technological solution, with respect to direct drive linear thisthis manner, a significant sizecan canbebeachieved, achieved, minimizing space manner, a significantreduction reductionof of the the generator generator size minimizing the the space generators, is able to ensure a relative higher speed ratio and, hence, higher power density [25]. In employed on on thethe floating structure. generatorincluded included WEC scale model this employed floating structure.The Theball ball screw-based screw-based generator in in thethe WEC scale model manner, a significant reduction of the generator size can be achieved, minimizing the space employed has has been preliminary designed via finite method (FEM)simulations. simulations. main electrobeen preliminary designed via finite element element method (FEM) TheThe main electromechanical parameters are reported Table 2. 2.generator included in the WEC scale model has been on the floating structure. The ball screw-based mechanical parameters are reported ininTable
preliminary designed via finite element method (FEM) simulations. The main electro-mechanical parameters are reported in Table 2.
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Table 2. Ball screw brushless generator electro-mechanical characteristics. AC Brushless with Ball-Screw
Value
Unit
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Power 20 kVA Maximum Speed 1200 rpm Table 2. Ball screw brushless generator electro-mechanical characteristics. Maximum Frequency 60 Hz Voltage 460 V Unit AC Brushless Rated with Ball-Screw Value Rated Current A kVA Power 20 30 Efficiency 0.93 Maximum Speed 1200 rpm Pole pairs 3 Maximum Frequency 60 Hz External Diameter 0.28 m Rated Voltage 460 V Magnetic stack length 0.15 m Rated Current 30 A Efficiency 0.93 3 The Measurement Apparatus Pole pairs External Diameter 0.28 m The system under test Magnetic is equipped with a sensor network able to monitor the stack length 0.15 m
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produced electric power, the wave elevation, and the buoy displacement. While the electric power measurements have 2.3. The Measurement Apparatus been implemented by using Hall effect current/voltage transducers, the wave elevation measurement is system test isprobes. equipped with a the sensor network abledisplacement to monitor the around produced obtained byThe means of under ultrasonic Finally, buoyant body itselectric equilibrium power, the wave elevation, and the buoy displacement. While the electric power measurements position is derived by a linear variable differential transformer (LVDT), which transduceshave the linear been position of implemented the system. by using Hall effect current/voltage transducers, the wave elevation measurement is obtained by means of ultrasonic probes. Finally, the buoyant body displacement around its The collected data have been used to compare the experimental results with the ones derived by equilibrium position is derived by a linear variable differential transformer (LVDT), which an accurate numerical model [26]. transduces the linear position of the system. The collected data have been used to compare the experimental results with the ones derived by
3. Experimental Test Bench an accurate numerical model [26]. In the following Subsections, the experimental test bench and several prototype results based on 3. Experimental Test Bench a 1:2000 scale-model are shown. In the following Subsections, the experimental test bench and several prototype results based on a 1:2000 scale-model are shown. 3.1. Towing Tank
The 3.1.experimental Towing Tank results reported in this section have been obtained in the towing tank of the Department of Industrial Engineering (Naval section) at the University of Naples Federico II. A picture The experimental results reported in this section have been obtained in the towing tank of the of the towing tankofis Industrial shown in Engineering Figure 3. The related overall dimensions basinFederico are 120 II. mA (length), Department (Naval section) at the Universityofofthe Naples 9 m (width), 4.5 m (depth). picture and of the towing tank is shown in Figure 3. The related overall dimensions of the basin are 120 Am wave generator produces with the required amplitude and frequency, thus emulating (length), 9 m (width), and 4.5waves m (depth). A wave generator produces the required amplitude and frequency, thus emulating different sea conditions. The towingwaves tank with is equipped with a towing carriage, which is able to move different sea conditions. The towing tank is equipped with a towing carriage, which is able move while along its length (Figure 3). The small-scale WEC prototype is rigidly anchored to the to bridge, along its length (Figure 3). The small-scale WEC prototype is rigidly anchored to the bridge, while a a moving wall wave generator, installed at one end of the basin, is able to work in the operating moving wall wave generator, installed at one end of the basin, is able to work in the operating frequency interval (0.35–1.2 Hz) with a maximum wave height value of 0.6 m. frequency interval (0.35–1.2 Hz) with a maximum wave height value of 0.6 m.
Figure 3. Towing tank and towing carriage.
Figure 3. Towing tank and towing carriage.
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The main aim of the towing tank tests was to analyse the response of the system prime mover different operating conditions. In order to achieve such a task, a load cell and 3.2.under Experimental Results Energies 2016, 9, 939 5 of 14 a potentiometer were on the PTO obtained byofdisplacement differentiation The main aimmounted of the towing tank testspiston. was to Speed analyseisthe response the system prime mover 3.2. Experimental Resultsconditions. of theunder potentiometer measurement signal. different operating In order to achieve such a task, a load cell and a potentiometer In order to the behaviour, a suitable control law hasofto chosen. were mounted onaim theofPTO PTO piston. is toobtained byresponse displacement differentiation the tests, Thedefine main the towing tankSpeed tests was analyse the thebe system primeDuring moverof the under different operating conditions. In order to achieve such a task, a load cell and a potentiometer a purely active control law hassignal. been assumed, defining a linear relation between piston force and potentiometer measurement were mounted the PTO PTO equation: piston. Speed is obtained by law displacement of the the tests, In order to define the behaviour, a suitable control has to bedifferentiation chosen. During speed, according the on following potentiometer measurement signal. a purely active control law has been assumed, defining a linear relation between piston force and In order to define the PTO behaviour, a suitable control law has to be chosen. During the tests, speed, according to the following equation: Fg = −k PPA v PPA a purely active control law has been assumed, defining a linear relation between piston force and speed, according to the following equation: F g = − k PP A v P PA (1)
(1)
Where Fg is the force acting on the PTO piston, v v is the piston deformation speed, and k PPA is F = − kPPA v k(1) g is the force acting on the PTO piston, is the piston deformation speed, is an Where F an adjustable gain; the negative sign is related to the direction of force and and speed. The system PPA opposite PPA g is the force acting on the PTO piston, vPPA is the piston deformation speed, and kPPA is an Where F adjustable gain; the negative sign related to theinfluenced opposite direction of force The system gain. response and power performance areissignificantly by the value ofand the speed. PTO force-speed adjustable gain; the negative signare is related to the opposite direction of force and The response power performance significantly influenced by actuator the value ofspeed. the PTO force-speed To impose theand required force control law, a controlled pneumatic acting as a system damper is used. response andthe power performance are significantly influencedpneumatic by the valueactuator of the PTO force-speed gain. To impose required force control law, a controlled acting as a damper Force and gain. speed signals are also used by the control system to determine the required force response. To impose the required force control law, a controlled pneumatic actuator acting as a damper is used. Force and speed signals are also used by the control system to determine the required force Power output has been from theused piston force and speed; such anthe estimation method has is used. Force andestimated speed signals are also by the control system to determine required force response. Power output has been estimated from the piston force and speed; such an estimation response. Power output has been estimated from the piston force and speed; such an estimation been used in consideration of the relatively low level of expected output power. method has been used in consideration lowlevel level expected output power. method has been used considerationofofthe the relatively relatively low of of expected output The The system installed ininin the Naples towing tank is depicted depicted in Figure 4power. for one of tested the tested system installed the Naples towing tank is in Figure 4 for one oftested the The system installed in the Naples towing tank is depicted in Figure 4 for one of the configurations (see(see [26] for[26] a more detailed description ofthe the test configurations). configurations [26] for a more detailed of the test configurations). configurations (see for a more detaileddescription description of test configurations). g
PP A
P PA
Figure 4. Scale model installed in the towing tank.
Figure 4. Scale model installed in the towing tank. Figure Scale model installed the towing tank. During a test run, the time 4. histories of piston force,in displacement, and speed were recorded. A typical set of test results is reported in Figure 5.
During a test run, the time histories of piston force, displacement, and speed were recorded. During a test run, the time histories of piston force, displacement, and speed were recorded. A A typical set ofoftest isis reported inFigure Figure5.5. piston displacement (mm) 40 typical set testresults results reported in piston velocity (cm/s) piston force (kgf)
30
piston displacement (mm) piston velocity (cm/s) piston force (kgf)
40 20
30
10
20
0
10
-10
0
-20
-10
-30 -40
-20 0
2
4
6
8
10 T (s)
12
14
16
18
20
-30
Figure 5. Test measured results for a wave frequency of 0.8 Hz and a wave amplitude of 5 cm. -40 0
2
4
6
8
10 T (s)
12
14
16
18
20
Figure 5. Test measured results for a wave frequency of 0.8 Hz and a wave amplitude of 5 cm.
Figure 5. Test measured results for a wave frequency of 0.8 Hz and a wave amplitude of 5 cm.
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Several tests have been performed under different operating conditions with different wave Several tests have been performed under different operating conditions with different wave frequencies and amplitudes and for different values of the force-speed gain. A brief summary of the frequencies and amplitudes and for different values of the force-speed gain. A brief summary of the test output power output outputfor fordifferent differentfrequency frequencyand and gain test outputisisreported reportedininFigure Figure66in interms terms of of average average power gain values and for a 5 cm wave amplitude. values and for a 5 cm wave amplitude.
Figure 6. Extracted average power P vs. energy extraction strength kEES for different wave Figure 6. Extracted average power P g vs. genergy extraction strength kEES for different wave frequency frequency values andwave for aamplitude. 5 cm wave amplitude. values and for a 5 cm
A peak in power output is observed in proximity of the system natural frequency (0.83 Hz), and A peak in powerofoutput is observed proximity of thevalue system frequency (0.83 Hz), and in in correspondence an optimal pistoninforce-speed gain ofnatural ~540 Ns/m; the observed power correspondence of an optimal force-speed gain value ~540 Ns/m; the observed power peak peak value is around 8 W for piston an incident wave amplitude ofof 5 cm. value isInaround 8 W for an incident wave amplitude of 5 cm. order to obtain an adequate characterization of the wave energy source and simultaneously In order obtain anextractable adequatepower, characterization of the wavethe energy source and simultaneously evaluate theto maximum it is necessary to know energy spectrum in the real-sea evaluate the of maximum is necessary know the energy spectrum the real-sea “mixture” waves. Inextractable particular,power, for realitsea waves, thetoaverage stored energy per unitinarea of sea “mixture” of waves. In particular, for real sea waves, the average stored energy per unit area of sea surface is: surface is: Z ∞ h i ∞ ρg ρg ρg SS( (f f))dfd f= = H s2Hs2 J J/m / m2 2 (2) (2) Et E=t =ρg 16 16 00 where = 1030kg/m kg/misisthe themass massdensity density of of sea sea water, g = 9.81 ofof gravity, and where ρ =ρ 1030 9.81 m/s m/s2 2isisthe theacceleration acceleration gravity, and thesignificant significantwave waveheight heightfor forthe the current current sea state, average HsHiss is the state, which whichisistraditionally traditionallydefined definedasasthe the average trough-to-crestheight heightofofthe theone onethird thirdof of the the recorded recorded waves waves with t is equally trough-to-crest with the the highest highestheights. heights.EE equally t is subdividedbetween betweenkinetic kineticenergy, energy, as as the the result result of the subdivided the water water motion, motion,and andpotential potentialenergy, energy,asasthe the result of its position. The energy spectrum can be derived either by a classical Fourier analysis or, in result of its position. The energy spectrum can be derived either by a classical Fourier analysis or, in the the case case of of “fully “fully developed developedwind windsea”, sea”,by byusing usingthe thesemi-empirical semi-empiricalPierson–Moskowitz Pierson–Moskowitzspectrum spectrum approximation [8]. Once the wave energy has been characterized, Newton’s can approximation [8]. Once the wave energy has been characterized, Newton’slaw lawon onfloating floatingbuoy buoy can be formulated by considering the contribution of all of the forces acting on the WEC. be formulated by considering the contribution of all of the forces acting on the WEC. Overall,it itisiswidely widelyknown knownthat thatthe the maximum maximum power Overall, power extraction extractionoccurs occurswhen whenthe thebuoy buoyoscillates oscillates synchronously and in quadrature with the wave at the installation site, with a displacement synchronously and in quadrature with the wave at the installation site, with a displacement proportional to the wave amplitude according to its wavelength. These optimal conditions can be proportional to the wave amplitude according to its wavelength. These optimal conditions can followed either by a proper control strategy (i.e., latching control) or by specifically sizing the be followed either by a proper control strategy (i.e., latching control) or by specifically sizing the oscillating system in order to match its natural frequency and the expected wave frequency in the oscillating system in order to match its natural frequency and the expected wave frequency in the installation site. This last approach has been used for the considered system, i.e., no latching control installation site. This last approach has been used for the considered system, i.e., no latching control is is used while the proposed control strategy refers to an active control law for which the extraction used while the proposed control strategy refers to an active control law for which the extraction gain is gain is dynamically adjusted. dynamically adjusted.
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Moreover, it has to be highlighted that for a heaving point absorber only half of the stored energy it hasIntothis be case, highlighted that a heaving point absorber only half thewave storednot energy waveMoreover, can be taken. instead, thefor proposed WEC is able to extract fromofthe only wave can be taken. In this case, instead, the proposed WEC is able to extract from the wave not only the energy due to the vertical motion, but also an additional contribution, to be assessed, relative to the energy due thrust. to the vertical butinalso an additional contribution, to be assessed, the horizontal Indeed,motion, as shown Figure 6, for a fixed amplitude/frequency of arelative wave, to equal horizontal thrust. Indeed, as shown in Figure 6, for a fixed amplitude/frequency of a wave, equal to to 5 cm and 0.8 Hz, respectively, the maximum power extractable by the proposed WEC is higher 5than cm the andideal 0.8 Hz, respectively, the maximum power extractable by the proposed WEC is higher than amount a heaving mode WEC (50%) would extract from the incoming wave. Indeed, the ideal amount ascale heaving mode WEC (50%) rate would extract from the incoming forrate, the for the considered prototype, the power extraction has reached almostwave. 65% ofIndeed, the ideal considered scale prototype, the power rate extraction has reached almost 65% of the ideal rate, equal equal to a 30% increment with respect to a heaving mode WEC. This result can be confirmed starting to a 30% with to a heaving from the increment mean power of respect a sinusoidal wave: mode WEC. This result can be confirmed starting from the mean power of a sinusoidal wave: 11 gA22v (3) ρgA vg g (3) PbPb== 8 ρ 8 where A is is the the wave wave amplitude amplitude and and vvgg is the wave group speed. In particular, at 0.8 Hz, with a wave amplitude amplitude of of 0.05 0.05 m, m, the the expected expectedwave wavepower powerdensity densityisis12 12W/m W/m versus versus about about 7.8 7.8 W/m W/m extracted by the proposed WEC. 3.3. Buoy Oscillation Oscillation Response 3.3. Buoy Response Numerical Numerical Model Model A also been developed for the of the wave-body interaction problem A numerical numericalmodel modelhas has also been developed forsolution the solution of the wave-body interaction and the analysis the system Theresponse. model’s purpose is to give a better of problem and theof analysis of response. the system The model’s purpose is understanding to give a better the floating body behavior and to compare different buoy shapes and solutions at a design stage. understanding of the floating body behavior and to compare different buoy shapes and solutions at The modelstage. is based on model a potential flow solver After flow an analysis the hydrodynamic parameters a design The is based on a [26]. potential solverof[26]. After an analysis of the in the frequencyparameters domain, theinmodel provides domain, a time domain solution of theafloating body motion and hydrodynamic the frequency the model provides time domain solution of allows for an estimation of the system mechanical output. The model also accounts for the chosen the floating body motion and allows for an estimation of the system mechanical output. The model PTO force control lawchosen (proportional relation between piston force relation and speed) and for the geometric also accounts for the PTO force control law (proportional between piston force and non-linearity in body motion. speed) and for the geometric non-linearity in body motion. A A comparison comparison of of the the numerical numerical and and experimental experimental results results is is reported reported in in Figures Figures 77 and and 8, 8, in in terms terms of speed and and mechanical mechanical power power output, output,with withreference referencetotoaawave waveamplitude amplitudeofof5 5cm cmand anda of piston piston speed afrequency frequencyvalue valueofof0.8 0.8Hz. Hz. As seen, even even if if the the power power output output is is largely largely overestimated, overestimated, the the qualitative qualitative response As can can be be seen, response of of the the system system seems seems to to be be well well represented, represented, at at least least for for the the examined examined operating operating conditions. conditions. The The difference difference between between the the simulated simulated and and experimental experimental results results may may partially partially be be explained explained as as aa consequence consequence of of the the model model assumption assumption of of potential potential flow, flow, which which completely completelyneglects neglectsviscosity viscosityeffects. effects. Although Although aa discrepancy discrepancy is is observed observed between between the the numerical numerical and and experimental experimental results, results, with with the the proper attention and the eventual use of suitable correction factors, the model may be considered proper attention and the eventual use of suitable correction factors, the model may be considered acceptable acceptable in in aa design design stage stage for for comparing comparing different different system system configurations configurations and and for for parameter parameter sizing. sizing.
Figure 7. simulation model—piston speed. Figure 7. Numerical-experimental Numerical-experimentalcomparison comparisonfor forthe thehydrodynamic hydrodynamic simulation model—piston speed.
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Figure 8. 8. Numerical-experimental Figure Numerical-experimental comparison comparison for for the the hydrodynamic hydrodynamic simulation simulation model—mechanical model—mechanical power output. power output.
4. Control Strategies for Maximization of the Energy Harvesting from Wave Energy Converter 4. Control Strategies for Maximization of the Energy Harvesting from Wave Energy Converter As highlighted in the previous sections, the energy from marine waves offers great potential in As highlighted in the previous sections, the energy from marine waves offers great potential in the field of energy production from renewable sources. Different types of WECs are classified by their the field of energy production from renewable sources. Different types of WECs are classified by their mechanical structure and by the function of the working principles. In this section, a brief overview mechanical structure and by the function of the working principles. In this section, a brief overview of of strategies for the electrical control of the WECs is presented. In particular, these strategies are used strategies for the electrical control of the WECs is presented. In particular, these strategies are used in in order to obtain higher harvested energy from the employed WEC. Obviously, the control strategies order to obtain higher harvested energy from the employed WEC. Obviously, the control strategies are dependent on the type of implemented wave energy absorber (point pivoted absorber (PPA) or are dependent on the type of implemented wave energy absorber (point pivoted absorber (PPA) or heaving point absorber), on the electric generator, on the topology of power converters and, heaving point absorber), on the electric generator, on the topology of power converters and, eventually, eventually, on the ESS. Based on several different combinations, it is clear that a large variety of on the ESS. Based on several different combinations, it is clear that a large variety of strategies can strategies can be employed. be employed. Each of these strategies, although aiming to maximize the energy harvesting from the marine Each of these strategies, although aiming to maximize the energy harvesting from the marine waves, have other additional features that are of interest in identifying the correct strategy regarding waves, have other additional features that are of interest in identifying the correct strategy regarding the proposed application. In particular, the WEC control strategy can be twofold: it is possible to the proposed application. In particular, the WEC control strategy can be twofold: it is possible to make make a “hydraulic” control and/or use “full electric control strategies”. In the latter case, the whole a “hydraulic” control and/or use “full electric control strategies”. In the latter case, the whole system system control strategy can be arranged in different hierarchical layers. Indeed, the WEC control control strategy can be arranged in different hierarchical layers. Indeed, the WEC control strategy strategy computes the references for the electric generator control strategy, which in turns drives the computes the references for the electric generator control strategy, which in turns drives the power power converter modulation. converter modulation. Moreover, with reference to the power grid connected converter, a proper grid control strategy Moreover, with reference to the power grid connected converter, a proper grid control strategy has has to be formulated in order to minimize the power fluctuation. Different solutions have been to be formulated in order to minimize the power fluctuation. Different solutions have been previously previously proposed [27–29]. Some of the authors have proposed as a viable solution a grid control proposed [27–29]. Some of the authors have proposed as a viable solution a grid control strategy with strategy with a supercapacitor-based ESS in [24]. Typically, the electric generator torque reference is a supercapacitor-based ESS in [24]. Typically, the electric generator torque reference is processed by processed by a direct torque control with space vector modulation (DTC-SVM), while the a direct torque control with space vector modulation (DTC-SVM), while the instantaneous grid active instantaneous grid active power is imposed by means of a direct power control with space vector power is imposed by means of a direct power control with space vector modulation (DPC-SVM). modulation (DPC-SVM). This paper proposes a P&O full electric control strategy for an embedded PPA. This paper proposes a P&O full electric control strategy for an embedded PPA. 5. Proposed Control Strategy: Perturb and Observe 5. Proposed Control Strategy: Perturb and Observe The full electric control strategy has the aim of extracting the maximum power from WEC The full strategy thevariability. aim of extracting the starting maximum power from WEC regardless of electric the typecontrol of wave and itshas time However, from a WEC already regardless of the type of wave and its time variability. However, starting from a WEC already optimized for a wide frequency spectrum, no latching control is needed in the proposed application. optimized only for a one widedegree frequency spectrum, no latching is needed thethe proposed application. Therefore, of freedom remains once ancontrol active control lawinfor PTO is formulated: Therefore, only one degree of freedom remains once an active control law for the PTO is formulated: Fg = −k EES (t) · v PPA
Fg = −kEES ( t ) ⋅ vPPA
where k EES (t) is defined as wave energy extraction strength. where kEES ( t ) is defined as wave energy extraction strength.
(4) (4)
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While v PPA can be estimated by the buoy position measurement, k EES should be chosen in order to maximize the average power extracted by the WEC over a fixed time interval. The tracking of the optimal k EES value can be implemented by a P&O strategy. The P&O strategy aims to evaluate the wave energy extraction strength k EES , kept constant in the “control strategy update time interval Tc ”. This time interval is linked to the wave period Tw , evaluated by means of a dq phase locked loop (PLL), the input of which is the estimated speed v PPA . In particular, Tc is chosen as: Tc = kWP TW
(5)
where kWP is an integer >1. kWP should be chosen in order to minimize the energy oscillations induced by frequency oscillations in the wave motion over the time interval Tc . Greater values of Tc optimize the behavior of the measured energy with respect to small perturbations while negatively affecting the control time response. Therefore, a trade-off value should be chosen. The proposed control strategy evaluates in each control instant tc ,k the energy extracted by the electric generator Ec ,k over a moving window with width Tc :
Ec,k =
Ztc,k
k EES,k−1 · v PPA (t) dt
(6)
tc,k−1
and computes the new value of the energy extraction strength k EES,k to be applied in the interval (tc,k , tc,k+1 ) based on Table 3. Table 3. Update logic at each sampling interval for the wave energy extractor extraction strength. kEES Comparison kEES,k −1 kEES,k −1 kEES,k −1 kEES,k −1
> kEES,k −2 > kEES,k −2 < kEES,k −2 < kEES,k −2
Energy Comparison Ec,k Ec,k Ec,k Ec,k
> Ec,k −1 < Ec,k −1 > Ec,k −1 < Ec,k −1
kEES Update Strategy kEES,k = kEES,k −1 + ∆kEES kEES,k = kEES,k −1 − ∆kEES kEES,k = kEES,k −1 − ∆kEES kEES,k = kEES,k −1 + ∆kEES
The wave energy extraction strength evaluation is then processed according to the following steps: (1) (2)
An initial value of k EES is properly set based on the system size/power; Afterwards, k EES is updated in each control instant based on the proposed MPPT algorithm (see Table 3).
The strategy is then able to track the maximum power point by varying the energy extraction strength with step ∆k EES . While large values of ∆k EES would lead to a faster system response, they could also negatively perturb the energy measurement and thus affect the effectiveness of the P&O. Therefore, a compromise is needed in order to ensure an optimal overall performance and robustness. 6. Numerical Results In order to verify the effectiveness of the proposed P&O, some numerical analysis were carried out in the Matlab Simulink™ (MathWorks, Natick, MA, USA) environment. In particular, the P&O control strategy was tested for three values of the wave frequency: 0.7 Hz, 0.8 Hz, and 0.9 Hz. The wave amplitude was set to 5 cm, i.e., the test conditions reproduce the conditions reported in Section 3. The implemented control is shown in Figure 9, in which a block diagram synthetizes the P&O algorithm discussed in the previous section. It should be noted that the control law depends only on the measured WEC position.
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Figure 9. Maximum power point tracking (MPPT) control diagram. LVDT: linear variable differential Figure 9. Maximum power point tracking (MPPT) control diagram. LVDT: linear variable differential transformer; PLL: phase locked loop; and P&O: perturb and observe. Figure 9.PLL: Maximum point tracking (MPPT) controland diagram. LVDT: linear variable differential transformer; phasepower locked loop; and P&O: perturb observe. Figure 9. Maximum power pointloop; tracking (MPPT) control diagram. LVDT: linear variable differential transformer; PLL: phase locked and P&O: perturb and observe.
transformer; PLL: phase locked loop; of andthe P&O: perturb and observe.power P and of the wave energy Figures 10–12 show the behaviors extracted average Figures 10–12 show the behaviors of the extracted average power Pgg and of the wave energy Pg13–15 Figures 10–12 show the behaviors of the extracted average power and of the wave thethe whole simulation interval, while Figures depict the energy steady state extraction strength strength kkESS whole simulation interval, while Figures 13–15 depict the steady ESSinin
Figures 10–12 show the behaviors of the extracted average power
Pg and of the wave energy
extraction strength kESS to in the whole simulation interval, while Figures depict thespeed steady vvPPA evolution corresponding the maximum power point (MPP) of13–15 thethe piston state evolution corresponding to the maximum power point (MPP) of piston speedstate PPA and extraction strength k ESS in the whole simulation interval, while Figures 13–15 depict the steady state v and evolution corresponding to the maximum power point (MPP) of the piston speed PPA instantaneous generator power Pg. It can be noted that the maximum value of P g and the corresponding P and instantaneous power Pg.maximum It can be noted that the of maximum and the evolution generator corresponding to the power point (MPP) the pistonvalue speedofvPPA Pg andgMoreover, Pg. It can be noted thatofthe value of values. the value instantaneous of kESS agreesgenerator with thepower experimental results for all themaximum tested frequency corresponding of kESS agrees with experimental results for all of the tested values. Pg and instantaneous generator power Pg. the It can be noted that theaverage maximum value of frequency the in steady state,value while the variation are evident, the power is practically corresponding value ofkESS kESS agrees withsteps the experimental results for all of the testedextracted frequency values. Moreover, in steady state, while the k ESS variation steps are evident, the average power extracted is corresponding value state, ofpower kESSwhile agrees with the experimental results allthe of the tested frequency values. constant, i.e., theininduced ripple the proposed isfor very small. In the worst-case scenario, Moreover, steady the kby ESS variation steps P&O are evident, average power extracted is practically constant, i.e., the induced power ripple by the proposed P&O is very small. In the worstMoreover, in steady i.e., state, the kpower ESSisvariation steps are evident, the power extracted is could constant, thewhile induced ripple by thethe proposed isthan very20 small. the worstwith apractically fixed perturbation step, the control able to track MPP inP&O lessaverage min.InThis result practically constant, i.e., the induced power ripple by the proposed P&O is very small. In the worstcase scenario, with a fixed perturbation step, the control is able to track the MPP in less than min. case scenario, with a fixed perturbation step, the control is able to track the MPP in less than 20 min. be improved by adopting an adaptive perturbation step approach that could maintain excellent20 steady case scenario, with a fixed perturbation step, the is able to track thestep MPP in approach less than min. could This result could be improved byadopting adopting ancontrol adaptive perturbation approach that20could This result could be improved by an adaptive perturbation step that state performance while improving the transient response. Finally, the steady state results confirm the Thisexcellent result could be improved by adoptingwhile an adaptive perturbation step response. approach that Finally, could maintain excellent steady state performance while improving the transient Finally, the the maintain steady state performance improving transient response. power ripple atexcellent twice the wave frequency. As expected, the powerthe oscillations are asymmetrical maintain performance while improving transient thein one steady state results steady confirmstate the power ripple at twice the wave the frequency. Asresponse. expected,Finally, the power steady state results confirm the power ripple at twice the wave frequency. As expected, the power periodoscillations of thestate wave frequency. behavior is by the frequency. waveform ofexpected, the piston steady results confirmThis the power ripple at twice wave As thespeed, power are asymmetrical in one period of confirmed the wave the frequency. This behavior is confirmed by thewhich oscillations are asymmetrical in one period of the wave frequency. This behavior is confirmed by the is not waveform purely alternative. oscillations one period the wave frequency. This behavior is confirmed by the ofare theasymmetrical piston speed,inwhich is not of purely alternative. waveform of theofpiston speed, which alternative. waveform the piston speed, whichisisnot notpurely purely alternative. 1000
10
10
10 a) 8 a) a) 8 6
f=0,7 f=0,7 HzHz
6 4
4
4 2
2
2 0 0 0 0
1000 b) 1000 800 b)b) 800 800
k[N/(m/s)] [N/(m/s)] kEES kEES [N/(m/s)] EES
6
Pg [W] Pg [W]
Pg [W]
8
f=0,7 Hz
500 500
1000 t [s] 1000 t [s]
1500
f=0,7 Hz f=0,7 f=0,7 Hz Hz
600
600
600
400
400 400 200 200 0 200 0
500
0 0
1500
500
1000 t [s] 1000 t [s]
1500 1500
0 for f = 0.7 Hz of: (a) average extracted 0 Figure 10. Behavior whole simulation time window 500 in the1000 1500 0 1000 1500 Figure 10.0 Behavior in the twhole simulation time window for f = 500 0.7 Hz of: (a) average extracted [s] t [s]average Figure 10. Behavior in the whole simulation time window for f = 0.7 Hz of: (a) extracted power; and (b) wave energy extraction strength. power;power; and (b) energy extraction strength. andwave (b) wave energy extraction strength.
Figure 10. Behavior in the whole simulation time window for f = 0.7 Hz of: (a) average extracted 10 1000 power; and10(b)a)wave energy extraction strength. 1000 b) f=0,8 Hz f=0,8 Hz
Pg [W]
6
Pg [W] Pg [W]
a)
8
a)
6
f=0,8 Hz
6 4 4 2 2
4
0 0 0 0
800
f=0,8 Hz
8
500 500
1000 t [s] 1000 t [s]
1500 1500
[N/(m/s)] kEESk[N/(m/s)] kEES [N/(m/s)] EES
8
10
800 1000 600 600 800 400
b)
f=0,8 Hz
b)
f=0,8 Hz
400 600 200 200 400 0 0 0 0
500 500
1000 t [s] 1000 t [s]
1500 1500
2 200 Figure 11. Behavior in the whole simulation time window for f = 0.8 Hz of: (a) average extracted Figure 11. the whole simulation time window for f = 0.8 Hz of: (a) average extracted power; andBehavior (b) wave in energy extraction strength. Figure 011. Behavior in the whole simulation time window0for f = 0.8 Hz of: (a) average extracted power; and (b) strength. 0 500wave energy 1000 extraction 1500 0 500 1000 1500 power; and (b) wave energy t [s]extraction strength. t [s]
Figure 11. Behavior in the whole simulation time window for f = 0.8 Hz of: (a) average extracted power; and (b) wave energy extraction strength.
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f=0,9 Hz
108 a) 108 a) 86 a) 86 64
f=0,9 Hz f=0,9 Hz
64 42 42 200 500 1000 1500 t [s] 20 0 500 1000 1500 t [s] 0 1000 simulation 1500 time Figure 12. 0Behavior500 in the whole 0 t [s] Figure 12. Behavior in the whole 1000simulation 1500 time power; (b) wave500 energy extraction strength. Figure and 12. 0Behavior in the whole simulation time t [s] power; and (b) wave energy extraction strength.
EES EES
f=0,9 Hz
kEESkEES [N/(m/s)] k[N/(m/s)] [N/(m/s)] k[N/(m/s)]
g
g
Pg [W] Pg [W] P [W] P [W]
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1000 b) 800 1000 b) 800 b) 1000 600 800 b) 600 800 400 600
400 600 f=0,9 Hz 200 400 f=0,9 Hz 200 400 0 f=0,9 Hz 2000 500 1000 1500 f=0,9 Hz t [s] 2000 0 500 1000 1500 t [s] 0 0 for f =500 1000 1500 extracted window 0.9 Hz of: (a) average 0 window for f 500 = 0.9 Hz of: (a) average extracted t [s] 0 for 1000 1500 extracted window f = 0.9 Hzt of: (a) average [s]
g
g
a) 20 10 20 a) 10 a) 100 10 0
Pg [W] Pg [W] P [W] P [W]
PPA PPA
vPPAvPPA [cm/s] v[cm/s] [cm/s] v[cm/s]
Figure the whole simulation time window for f = 0.9 Hz of: (a) average extracted power; 12. andBehavior (b) wavein energy extraction strength. 20 Behavior in the whole simulation time window 20 Figure 12. for f = 0.9 Hz of: (a) average extracted power; and (b) wave energy extraction strength. a) 20 (b) wave energy extraction strength. 20 b) power; and f=0,7 Hz
0 -10 0 -10
f=0,7 Hz
-10 -20 -10 -20
20 15 b) 20 b) 15 b) 15 10 15 10
f=0,7 Hz f=0,7 Hz f=0,7 Hz
105 10 5
5 Hz 1798 f=0,7 1799 1800 1796 1797 1798 1799 1800 5 t [s] f=0,7 Hz 1796 1797 1798 1799 1800 1796 1797 1798 1799 1800 f=0,7 Hz t [s] t [s] -20 1796 in 1797 1798 conditions 1799 1800 1796 1800 Figure 13. Behavior steady state for f = 0.7 Hz of: (a) piston1797 speed;1798 and (b)1799 instantaneous -20 t [s] 1798 t [s] 1798 1796 in 1797 1799 1800 1796 1800 extracted Figure 13.power. Behavior steady state conditions for f = 0.7 Hz of: (a) piston1797 speed; and (b)1799 instantaneous [s] [s] Figure 13. Behavior in steadyt state conditions for f = 0.7 Hz of: (a) piston tspeed; and (b) instantaneous
1796
1797
t [s]
Figure 13. power. Behavior in steady state conditions for f = 0.7 Hz of: (a) piston speed; and (b) instantaneous extracted
extracted power. 20 Behavior in steady state conditions for f = 0.7 Hz 20 of: (a) piston speed; and (b) instantaneous Figure 13. extracted power. a)
20 b)
a) 20 10 20 a) 10 a) 100 10 0
g
g
Pg [W] Pg [W] P [W] P [W]
vPPAvPPA [cm/s] v[cm/s] [cm/s] v[cm/s] PPA PPA
extracted20power.
0 -10 0 -10
20 15 b) 20 b) 15 b) 15 10 15 10
f=0,8 Hz
f=0,8 Hz f=0,8 Hz f=0,8 Hz
105 10 5
f=0,8 Hz 5 Hz 1798 f=0,8 1799 1800 1796 1797 1798 1799 1800 5 t [s] t [s] f=0,8 Hz 1796 1797 1798 1799 1800 1796 1797 1798 1799 1800 f=0,8 Hz t [s] t [s] -20 1796 in steady 1797 state 1798 conditions 1799 1800 1796 1799 1800 Figure 14. Behavior for f = 0.8 Hz of: (a) piston1797 speed;1798 and (b) instantaneous -20 t [s] 1798 1796 in steady 1797 t [s]state 1798 conditions 1799 1800 1796 1797 1799 1800 extracted Figure 14.power. Behavior for f = 0.8 Hz of: (a) piston speed; and (b) instantaneous t [s] t [s]
-10 -20 -10 -20
1796
1797
Figure 14. power. Behavior in steady state conditions for f = 0.8 Hz of: (a) piston speed; and (b) instantaneous extracted
g
g
a) 20 10 a) 20 10 a) 100 10 0
0 -10 0 -10 -10 -20 -10 -20
Pg [W] Pg [W] P [W] P [W]
vPPAvPPA [cm/s] v[cm/s] [cm/s] v[cm/s] PPA PPA
Figure 14. Behavior in steady state conditions for f = 0.8 20 Hzof: of:(a)(a) piston speed; and (b) instantaneous 20power. Figure 14. Behavior in steady state conditions for f = 0.8 Hz piston speed; and (b) instantaneous extracted a) f=0,9 Hz extracted power. 20power. 20 b) extracted
f=0,9 Hz
20 15 b) 20 b) 15 b) 15 10 15 10
f=0,9 Hz
f=0,9 Hz f=0,9 Hz
105 10 5
5 Hz 1798 f=0,9 1799 1800 1796 1797 1798 1799 1800 5 t [s] t [s] f=0,9 Hz 1796 1797 1798 1799 1800 1796 1797 1798 1799 1800 f=0,9 Hz t [s] t [s] -20 1796 in 1797 1798 conditions 1799 1800 1796 1800 Figure 15. Behavior steady state for f = 0.9 Hz of: (a) piston1797 speed;1798 and (b)1799 instantaneous -20 t [s] 1798 t [s] 1798 1796 in 1797 1799 1800 1796 1800 extracted Figure 15.power. Behavior steady state conditions for f = 0.9 Hz of: (a) piston1797 speed; and (b)1799 instantaneous t [s] t [s] 1796
1797
Figure 15. power. Behavior in steady state conditions for f = 0.9 Hz of: (a) piston speed; and (b) instantaneous extracted Figure 15.power. Behavior in steady state conditions for f = 0.9 Hz of: (a) piston speed; and (b) instantaneous extracted Figure 15. Behavior in steady state conditions for f = 0.9 Hz of: (a) piston speed; and (b) instantaneous extracted power.
extracted power.
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7. Conclusions In this work, an embedded PPA prototype has been tested in order to evaluate the increment of extracted power over a traditional heaving mode absorber. A FEM-based numerical model has been implemented in order to preliminarily evaluate the effectiveness of the proposed solution. A discordance between the numerical and experimental results has been found with respect to the extracted power. This difference is partially linked to the wave motion viscosity effect, which has been neglected in numerical analysis. Nevertheless, the experimental results, obtained at different wave frequency values, confirm the expected performance of the system, with an extracted power increase of about 30% with respect to the ideal heaving mode operation. Finally, a P&O strategy has been proposed to be coupled with the PPA, that aims to track the maximum power extractable from the WEC during either transient or steady state conditions. The proposed technique is easy to be implemented, requires only one system status measurement (the WEC position), and is able to operate with good performance in a large range of operating conditions. An evolution of this work could integrate an electrical storage system in order to filter out the WEC power oscillations, guaranteeing almost constant power flow to the grid. On the other hand, the P&O strategy could be updated by embedding a dynamic phase latch technique, to be implemented directly in a generalized control law. Author Contributions: Andrea Del Pizzo and Marino Coppola studied the state of art and gave the main directions of abstract, introduction and conclusions. Gianluca Brando and Ivan Spina conceived the P&O algorithm and the relative numerical analysis. Adolfo Dannier and Domenico Pietro Coiro sized the experimental prototype and performed the tests in the towing tank. All the authors participated together to the writing phase of the article. Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations A Ec,k Et f Fg g Hs k EES k PPA kWP Pb Pg S(f) tc,k Tc TW vg v PPA ∆k EES ρ
Wave amplitude Energy extracted by the electric generator in the time interval tc,k−1 , tc,k Average stored energy per unit area of sea surface Wave frequency The force acting on PTO piston Acceleration of gravity (9.81 m/s2 ) Significant wave height Wave energy extraction strength Adjustable gain of the PTO The number of wave periods on which the time control interval is based Mean power of the incident wave Extracted average power from PTO Wave energy spectrum Generic control instant Control strategy time interval Wave period Wave group speed Piston speed Energy extraction strength step variation Mass density of sea water (1030 kg/m)
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