Development of a wave energy converter using a two chamber oscillating water column

482 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 3, JULY 2012

Development of a Wave Energy Converter Using aTwo Chamber Oscillating Water Column

Min-Fu Hsieh, Senior Member, IEEE, I.-Hsien Lin, Student Member, IEEE, David G. Dorrell, Senior Member, IEEE,Ming-June Hsieh, and Chi-Chien Lin

Abstract—This paper presents the development and system anal-ysis of segmented oscillating water columns (OWC) for wave en-ergy conversion based on the wave conditions around Taiwan. TheOWC chambers are designed for a target site and the power con-verted by each component (i.e., the chambers, turbine and gen-erator) in the power chain is analyzed so that the overall poweroutput and efficiency can be calculated. The characteristic matchbetween the turbine and the generator is also discussed. The de-veloped OWC is side-mounted and this allows the waves to pen-etrate and continue propagating after transferring power to thechambers. The OWC consists of two adjacent chambers which arealigned in the direction of the wave propagation. Each chamber hasone Savonius turbine on top to convert the chamber power intomechanical shaft power. The two turbines are connected in-lineand the individual chambers transfer power to the turbines witha phase difference, so that the power output can be smoothed. Abrushless permanent-magnet generator is used to convert the tur-bine output power into electricity. Experiments are conducted ona scaled-down model in a wave tank to evaluate the performanceand the results verify the design. It is also found that the successivechamber should have a different design to the first one as it suffersslight wave attenuation.

Index Terms—Marine energy, oscillating water column, savo-nius rotor, wave energy.

NOMENCLATURE

Wave attenuation rate.

Area of water surface in single chamber.

Turbine inlet area.

Sweep area of turbine blades.

Turbine power coefficient.

CR Turbine power conversion rate.

Water depth.

Water depth in test environment.

Water depth in real site.

Manuscript received April 18, 2011; revised February 27, 2012; acceptedMarch 07, 2012. Date of publication May 30, 2012; date of current versionJune 15, 2012. This work was supported in part by the Taiwan National Sci-ence Council and in part by Bureau of Energy, Ministry of Economic Affairsunder GrantNSC 99-ET-E-006-007-ET.M.F. Hsieh, I-H. Lin, M.-J. Hsieh and C.-C. Lin are with the Systems and

Naval Mechatronics Engineering, National Chen Kung University, Tainan 701,Taiwan (e-mail: [email protected]).D. G. Dorrell is with University of Technology Sydney, Sydney, NSW 2007,

Australia (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSTE.2012.2190769

Generator efficiency.

Wave frequency.

Froude number.

Gravitational acceleration.

Gravitational acceleration in test environment.

Gravitational acceleration in real site.

Wave surface elevation.

Wave surface elevation in test environment.

Wave surface elevation in real site.

Loading current.

Phase armature reactance.

Line-to-line back-EMF constant.

Generator with a smaller back-EMF constant.

Generator back-EMF constant for peak power.

Actual wavelength.

Single chamber length in wave propagationdirection.Theoretical wavelength for deep water.

Phase inductance.

Atmosphere pressure.

Inner chamber pressure.

Inner pressure near turbine.

Power acting on turbine due to airflow.

Available chamber power.

Generator output power.

Turbine mechanical output power.

Power due to pressure difference across theturbine.Electrical output power.

Wave power.

Volumetric airflow rate.

Generator referred winding resistance.

Load resistance.

Load resistance for operation at peakconversion rate.Load resistance for operation at lower wavepower.Generator equivalent resistance.

Generator phase resistance.

Total effective resistance.

1949-3029/$31.00 © 2012 IEEE

HSIEH et al.: DEVELOPMENT OF A WAVE ENERGY CONVERTER 483

Scaling factor.

Wave period.

Wave period in test environment.

Turbine shaft torque.

Wave period in real site.

Rated torque.

TSR Tip speed ratio.

Characteristic velocity.

Voltage on load resistance.

Airflow velocity at chamber inner watersurface.Complex term of airflow velocity near Chamber1/2 water surface.Turbine inlet airflow velocity for singlechamber.Mean inlet airflow velocity of two chambers.

Diode voltage drop.

Characteristic velocity in test environment.

Generator phase back-EMF.

Generator referred equivalent output voltage.

Inlet airflow velocity through the turbine.

Characteristic velocity in real site.

Pressure drop across the turbine.

Incident outer wave surface elevation.

Magnitude of time-domain incident wavessurface elevation.Complex term of incident waves surfaceelevation.Mean wave surface elevation across chamberside faces.Chamber 1/2 inner wave surface elevation.

Magnitude of time-domain water surfaceelevation inside Chamber 1/2.Complex term of Chamber 1/2 water surfaceelevation.Chamber 2/2 inner wave surface elevation.

Angular chamber length.

Phase lag angle of internal water height.

Air density.

Water density.

Potential flow.

Wave oscillating angular velocity.

Electrical angular velocity.

Mechanical angular velocity.

Rated speed.

I. INTRODUCTION

R ENEWABLE energy, such as wind and marine energy,provides a solution to the issue of carbon dioxide emis-

sion reduction and energy shortage [1]. As an island surrounded

Fig. 1. Oscillating water column arrangement with incident waves.

by sea, marine energy (e.g., wave energy) is considered to be anexcellent renewable energy source for Taiwan.Many forms of wave energy converters have been proposed

and investigated; several are under development or being as-sessed for feasibility [2]–[4]. A review on the maturity of waveenergy conversion technologies shows that only 7% of the de-veloping systems are pre-commercial and none have been fullycommercialized [5]. A current design (the Pelamis) is close tofull commercialization [6]. At this current time the wave energycommunity is still debating about the best design for producingelectrical power from sea waves. A recent count numbered overa thousand patented ideas for wave energy conversion [7]. Thesesystems can be broken down into five technology categories: os-cillating water columns (e.g., the Land Installed Marine PowerEnergy Transmitter, LIMPET [8]), overtopping devices, pointabsorbers, surging devices, and mechanical extraction.According to the survey data in [9], Taiwan’s eastern coast is

considered as a potential area for development of wave energy.However, it is at the edge of a one thousand meter deep oceantrench and hence offshore devices may not be a good choice interms of cabling and installation. Instead, onshore or near-shorestructures may be good candidates. Taiwan is subjected tofrequent typhoons; hence, even shore-line devices should besufficiently robust to withstand high-level storms. This paperdevelops a wave energy converter using a shore-line oscillatingwater column (OWC). This appears to be appropriate for siteswhere the tide range is small, as in Taiwan, where an averagetide range of 2.5 m has been recorded by the Central WeatherBureau [10]. This should not significantly affect the perfor-mance of a full-scale OWC. The shore-line OWC is simpleand robust, and should be able to survive in a harsh oceanenvironment.OWC devices have been tested by several research groups

and countries (e.g., UK, Japan, Portugal, Norway, and severalothers). A simple OWC is illustrated in Fig. 1; the OWC con-sists of two basic components: the chamber and the turbine.Waves propagate into or across the front of the chamber so thatthe water level inside oscillates with height and phase whichare different with respect to the wave fronts. This pressurizesand depressurizes the column so that air moves into and out ofthe chamber via a bidirectional turbine (e.g., a Wells turbinein large columns or Savonius turbines in small columns [11],[12]). However, since the device is shore-based, the incidentwave-field is likely to be, at best, weakly nonlinear [13].This paper focuses on the design of an OWC wave en-

ergy converter (wall mounted with passing waves rather than


shore-mounted with full-frontal incident waves) which is aimedfor the wave conditions around Taiwan. The key to successfulOWC design is considered to be system analysis, rather thanemphasis on performance of individual components. Nev-ertheless, the characteristics of individual components needto be identified. In this study, a system analysis approach istaken together with individual component study. This allowsassessment of the system and identification of the effectivenessof different components. This also allows system improvement;for instance, for the experimental work here, a Savonius rotoris used because it gives reasonable energy conversion (15 to20% even for small rotors). If a large system is developed thenthese can be changed for Wells turbines which will give higherconversion rates (about 50%); when they are large in size theyhave good conversion rates whereas when they are small theyhave much poorer conversion rates [14].The first component is the multiple chamber arrangement that

converts the wave power into air flows; these drive the turbines.The ratio of the internal chamber water surface area to the tur-bine inlet area is a key factor that affects the chamber powerconversion. This will be discussed. Second, normal OWC ar-rangements utilize bidirectional air turbines, as shown in Fig. 1.These can take the form of a Wells turbine as extensively re-viewed in [15]. They have high tip speed ratios making themcompact. However, as previously mentioned, they do not workwell in small units (e.g., the test model in this paper). There-fore, the Savonius rotor is a compromise option at this stage.Third, power smoothing is also considered here because thechamber power (thus the turbine input power) oscillates withthe waves. A two-chamber design with in-line Savonius rotorsis used in this study, as illustrated in Fig. 2. The oscillating airflows through the corresponding turbines of the two chamberswill have a phase shift. The resultant effect is to smooth the com-bined mechanical power output from the two Savonius turbines.This has been preliminarily investigated in [11], [12], where thefeasibility was demonstrated and it was able to generate elec-tricity. Finally, the generator should be able to match the speed,torque and power characteristics of the turbine output; a briefanalysis of the system necessary for conversion of turbine ki-netic power into electrical power is given below.In this paper, an analysis, with performance assessment of in-

dividual components, is conducted and experimentally verified.An assessment of the wave resource around Taiwan is also putforward. The paper provides data and information for furtherOWC design in a variety of locations.

II. THE OSCILLATING WATER COLUMN

A. Two-Chamber OWC

The two-chamber OWC can smooth the power output and in-crease overall generation [12]. In a shore-line installation, suchas found on the Isle of Islay, UK [8], the incoming waves areorthogonal to the column so that the front face has to be in-clined and act as a beach to prevent damage, as shown in Fig. 1.This does have the advantage of increasing the surface area ofthe internal water column which increases the effective sizeof the column. However, the side-mounted segmented OWC

Fig. 2. OWC. (a) Schematic of two-segmented OWC, turbine and direction ofincoming wave. (b) Construction of the developed OWC.

(Fig. 2) allows the waves to travel across the side face of thecolumn rather than front on. This means that it is suitable foruse on harbor walls, breakwaters, barrages and piers. It can beused off-shore on floating platforms (such as the Mighty Whale[16]) and also there is the possibility of use on ships for auxil-iary power units. The design and installation of OWC chambersshould carefully consider the tidal range of the target location sothat the performance is not significantly affected. Generally thecolumn should be vertical with ducting which guides air throughthe turbine. When the water around the column oscillates dueto the passing waves, the air inside the chamber is pressurizedand depressurized with the internal oscillating water level. Al-ternating airflow through the turbine leads to the generation ofelectrical energy.As shown in Fig. 2, the proposed OWC consists of two cham-

bers [denoted Chamber 1/2 and Chamber 2/2 in Fig. 2(b)]. Onthe top of each column is a Savonius turbine which convertsthe airflow power into rotary mechanical power. The two tur-bines are connected in line with a three-phase brushless per-manent-magnet generator. This means that individual chamberswill separately deliver power to the corresponding turbine witha phase difference. The torque acting on the turbines will then beconverted into electric power via the generator; the power con-version pulsates with the alternating airflow but it is smoothedby the fact that the two columns work out of phase.The individual components in the power train, i.e., chamber

to turbine, turbine to generator and generator to load, need tobe analyzed to improve the overall system efficiency. To allowthis component-level study, an OWC wave conversion systemwas constructed and measurements were performed on param-eters such as wave surface elevations inside and outside thechambers, the inlet airflow velocity through the turbines, the tur-bine/generator speed (torque is also retrievable for calculation


Fig. 3. Location of target site (Chenggong) (modified from [17]).

of mechanical power) and the generator output power. The mea-sured data are used to verify the designed OWC and the overallenergy conversion system. The power electronic design is notconsidered at this stage but will be in a future study. This willbe fulfilled when an OWC prototype is constructed at the targetsite.

B. Site Selection

As previously mentioned, the east coast of Taiwan is a poten-tial site for a wave energy generator, and Chenggong (shown inFig. 3) is one of the most suitable locations [9]. The local wavecondition is illustrated in Fig. 4(a) ([10], statistics by CentralWeather Bureau of Taiwan, 2010), where the mean significantwave height in winter (close to 2 m) is higher than in summer.The extremely high maximum significant wave height was pri-marily due to several typhoons striking Taiwan or nearby areas.Generally, this location has a weaker wave energy resource thansome high energy areas such as off the north-east coast of theUK; however, the wave energy is still considered harvestable[9].Fig. 4(b) shows the significant wave heights, wave energy

periods and their percent frequencies at the Chenggong coastfrom the joint probability spread of the waves. These were pub-lished in 2006 based on statistics of the data recorded for oneyear (2005), which measured wave periods ranging from 2 to16 seconds, at a sampling time of 1 second, and wave heightsbetween 0.5 m and 10 m at a sampling rate of 0.5 s [9]. It wasfound that in the 7 to 8 s wave period range, wave surface ele-vations of 1 to 3.5 m occur most frequently. This condition willbe used for the design of the OWC in this paper.

C. Wave Condition for OWC Chamber Design

The OWC should ideally be designed using the the target site(Chenggong) data with a full-size prtototype; however, this canbe a huge financial and environmental risk before being vali-dated as feasible. Therefore, the developed OWC system shouldbe tested in a laboratory wave tank prior to the future imple-mentation of a full size system. However, the test results of thislaboratory model should realistically represent that of the de-sign in the real site so that the laboratory model can be easilyand readily scaled up to full size for the target site. This meansthat the generated wave tank waves need to be equivalent to thereal situation. To achieve this, a suitable scaling factor shouldbe applied. In fluid mechanics, the Froude number is often usedfor this which permits the comparison of systems and devicesof different sizes. The Froude number is defined by [18]

Fig. 4. Wave conditions at Chenggong. (a) Wave height distribution over oneyear in 2010 (modified from [10]). (b) Joint probability of waves of Chenggong[9]. Note that these two diagrams were produced by different organizations andthere are no data in the same year.

(1)

where is the characteristic velocity, is gravitational acceler-ation, is the water depth and is the water density. It can bereasonably assumed that the viscous effects are negligible [18],[19]. For the similarity of the two conditions the following re-lationship should be satisfied

(2)

where the suffix is the test environment for the laboratorymodel and the suffix represents the target site. These are usedthrough the analysis below. It is assumed that the gravitationalacceleration is the same in the test environment and real siteconditions [19], therefore

(3)

For OWC, the combination of hydrodynamics and aerody-namics makes the scaling consideration more complex than thestandard Froude scaling. The hydrodynamics interaction be-tween waves and the OWC body are dominated by inertia andgravitational forces, which are the two factors in (1), while theaerodynamics in the OWC are dominated by the compressionforce. Therefore, for an OWC, to maintain consistency between


Fig. 5. OWC mounted on the side wall of the tank, which is 180 m long, 8 mwide and maximum 4 m deep. (a) Wave setting panel. (b) Top of OWC withturbine spinning.

TABLE IPARAMETERS SCALED DOWN BY FROUDE NUMBER

the tank and real sites, it should be assumed that the ratio ofinertia force to compression force is kept constant [19].The average flow velocity in the cross section of the full scale

OWC should be used for calculation of the Froude number [20].Thus, the geometric scaling factor is defined as [19]

(4)

where is the peak-to-peak wave surface elevation. Thus, thescaling factor for the wave surface elevations is also defined.From (3) and (4), and from [19]

(5)

where is the wave period. The experimental wave tank used(Fig. 5) has a water depth of 3.35 m; for water depth of thetarget site (Chenggong) is 38.9 m [9]. Hence, the basic scalingfactor . Deep water is assumed here as (9)–(11) inSection II.D show that the test environment is close to deepwater with a wave length of 6.75 m. This is slightly shorter thanit would be for deep water (7.75 m). However, the wavelengthin the intermediate water depth of the present case is used forall the following calculations.From the survey data shown in Fig. 4, the average wave pe-

riod for the OWC design is taken to be 7.5 s and a reasonablewave surface elevation range is 1 to 3.5 m. The scaled waveperiod and wave surface elevation are given by (4) and(5); hence, is around 2.2 s and ranges from about 0.1 mto 0.3 m. These parameters, as summarized in Table I, are themost significant parameters when sizing the OWC.In the following analysis, and are simply used to repre-

sent the wave period and peak-to-peak wave surface elevationfor the wave conditions in the laboratory wave tank.

Fig. 6. Chamber arrangement and parameters.

D. Chamber Parameter Definition and Chamber Power

It should be noted that this paper focuses on system analysisand therefore, the modeling for individual components, such asthe OWC chambers, is simplified. Detailed and complete hydro-dynamics modeling for OWC can be found in [21], [22], where amore accurate model is developed. This will help engineers whowould like to apply the proposed methodology in this paper toconstruct the system, but want a more precise hydrodynamicsmodel.The parameters related to the proposed OWC are illustrated

in Fig. 6. The oscillating wave surface elevation inside theOWC chamber is the major factor that directly affects theavailable chamber power fed to the turbines since it is relatedto the outer wave surface elevation, water depth, chamberdimensions, chamber air pressure, and the turbine inlet airpressure, etc. It is first assumed that the incident outer wave(regular wave) surface elevation can be expressed as [23]

(6)

where is wave oscillating angular velocity.The mean wave surface elevation across the side faces of the

OWC can be given by [11]

(7)

The angular chamber length (rad) is defined as

(8)

where is the single chamber length in the wave propagationdirection, and is the actual wavelength, which should be firstdetermined for the wave tank ( s and m). Thetheoretical wavelength for deep water is [18]

(9)

where is the theoretical wave length for deep water and isthe wave frequency. However, the experimental condition in thewave tank is just marginally into the intermediate water depth


conditions since the deep water condition is not quite met [18]where, for m

(10)

If and are given in Table I, and is calculated using (9),then we need to adjust the wavelength for intermediate depths.Hence, an equation can be formulated for calculating the wavelength in the laboratory wave tank [18]

(11)

where m.The equation of motion for the water inside the OWC is de-

rived from Newton’s Law when considering thepressure drop between the inner chamber and the ambient air[24] (i.e., across the turbine). This becomes

(12)

where is the pressure drop across the turbine, is the innerwave surface elevation and is the area of the water surfacein a single chamber; the definitions for the remaining variablesin (12) are given in Fig. 6. This can be rearranged to be

(13)

The function can be written as

(14)

Assuming the air is uncompressible, the inlet airflow velocityof the chamber can be simply defined

(15)

From the Bernoulli’s equation, the inner chamber pressure ,as illustrated in Fig. 6, is

(16)

where is the airflow velocity immediately above the chamberinternal water surface, is the air density, is turbine inletarea, is the single chamber turbine inlet airflow velocity andis the inner pressure near the turbine. To solve (13) and (15),

an expression for against needs be determined. This isobtained using the computational fluid dynamic (CFD) packageCFX. A turbine model was built in CFD, as shown in Fig. 7(a),where the dimensions of all the components (e.g., the Savoniusturbine) were preliminarily designed. From the CFX simulation

Fig. 7. Turbine simulation: (a) CFX model for Savonius turbine; (b)curve of Savonius turbine.

results, the characteristic is plotted in Fig. 7(b) and acurve fitted. This is given by

(17)

Assuming regular wave operation and neglecting higher differ-ential terms as discussed in [11], (13) can be approximated to be

(18)

Substituting (17) into (18), can then be obtained

(19)

(20)

(21)


The first and third terms in (21) are squared terms and the systemis assumed to be sinusoidal. These squared terms will lead tosecond harmonics. Experimental observation suggests there issome second harmonic content in the internal water surface el-evation but the fundamental component dominates. This is val-idated by the Runge-Kutta-Nystrom simulations in [12] wherethere is some second harmonic content in simulations; how-ever, this is much less in terms of the water surface elevationsince is the derivative. Therefore, if the sea wave height istaken as the wholly real reference and the second-order termsare neglected then

(22)

As stated above, assuming that the system is sinusoidal, it canbe represented in complex phasor terms for and so that

(23)

(24)

(25)

where and are the time domain magnitudes of the watersurface elevations of the incident wave and inside Chamber 1/2,respectively, and are the complex terms of these water sur-face elevations, and is the complex term of airflow velocityabove water surface in Chamber 1/2. If the surface elevations inthe time and frequency domains have the same magnitude, i.e.,

, the water surface elevation becomes

(26)

(27)

(28)

where is the attenuation rate for the incident wave propagatinginto Chamber 1/2. It is assumed that the wave traveling fromChamber 1/2 to Chamber 2/2 is subject to the same attenuationrate . Thus, the surface elevation in Chamber 2/2 becomes

. It should be noted that the phase differencesbetween these wave surface elevations ( and can bedetermined by (8).Having determined , the airflow velocity above the

chamber internal water surface is obtained from

(29)

The power acting on the turbine due to the airflow is

(30)

This is only part of the total chamber power available to the tur-bines; the other chamber power component is due to the pressuredifference inside and outside the chambers. From Bernoulli’sequation, the pressure difference is given by

(31)

where ; this is the potential flow, and is the vol-umetric airflow rate. This is a simple analytic equation. Thesystem is low pressure so energy is stored in kinetic energy aswell as the pressure term. In this paper we are aiming to producean overall design and analysis procedure for the system ratherthan focusing on individual components. For further fine tuningand precise calculation CFD analysis can be used as illustratedin [36]; we used CFD for obtain the curve in Fig. 7 and hencethe coefficients in (28). Hence, the power due to the pressuredifference across the turbine becomes

(32)

Hence, the total chamber power available at the turbine is

(33)

III. OWC CHAMBER DESIGN

Tomaximize the available chamber power under the waveconditions described in Section 2.3 and Table I, the OWC testmodel should be correctly designed. From (30) and (32), it wasfound that under the assumption of steady-state sinusoidal waveconditions, increasing increases the overall chamber power;this is the key index for the chambers in this paper.

A. Effect of Area Ratio

The ratio of the water surface area in the chamber to the tur-bine inlet area is a factor that significantly affects and theavailable chamber power. In this paper, the water surface areain the chamber and turbine inlet area were determined byconsideration of factors such as the power output scale, spaceavailability and wave conditions. The available chamber poweris plotted against the area ratio is shown in Fig. 8 underthe wave conditions in Table I. For each curve, is constantwhile varies (the single chamber width-to-length ratio main-tained at 1/2). As can be seen, each curve has a peak power atcertain area ratio. For instance, there is a theoretical peak poweravailability of 316 W at for m .Also, as decreases, the power increases. However, it is notnecessary to select this area ratio or small as there are somefactors that should be simultaneously considered, as discussedbelow.1) This is a small-scale model, hence, for a certain , if thearea ratio is large, such that the turbine inlet opening (andthus the turbine) is small, the turbine will operate at highspeed under the same chamber conditions. This will gen-erate high windage and friction losses in a Savonius turbinewhich will decrease the output power (discussed in detaillater). The Savonius rotor operates at a low tip speed ratio(about 1) for peak conversion factor, so is relatively a largeturbine. Therefore, should not be too small. The casessuch as m or 0.012 m will result in smallturbine operating at very high air flow velocity. This willcause significant windage loss. However, for a full-scaleOWC, this may not be a problem if a Wells turbine is used(as used in many OWC).


Fig. 8. Available chamber power versus area ratio with m, s.For each curve is fixed with varying.

2) Larger area ratios may cause air compressibility effects tobe noticeable (it is assumed in the analysis here that the airis incompressible).

3) If a small area ratio is chosen, the available chamber powerwill be small. This would not be an economic option.

For a good power output, a larger area ratio is required; how-ever, for less windage and friction loss, a small area ratio isrequired. In this study, a compromise design is chosen where

m and m so that . Thisprovides a reasonable power output. Based on the wave condi-tion ( s and m), an average available chamberpower of 301.6 W can be obtained.

B. Effect of Single Chamber Length

Thewave length is determined using (11) for a knownwaveperiod and water depth. The chamber length should be designedusing a specific wave length, or wavelength range, for a betterpower conversion rate. From (7) and (8), the relationship be-tween the chamber length, wavelength and wave surface eleva-tion is specified. It should be borne in mind that is directlyrelated to , which in turn dictates and hence the chamberpower. Fig. 9 shows the variation of (mean value of the inletairflow velocity of Chambers 1/2 and 2/2, as will be explained inSection III.C and illustrated in Fig. 10) with the single chamberlength with the other factors maintained at constant values.The result shows that a shorter chamber length (in the direc-tion of wave propagation) gives higher . However, when con-sidering the chamber area ratio and water surface area in thechamber together in order to maintain a power output level, ashorter chamber (in the wave travelling direction) will increasethe width of chamber. This may cause mounting difficulty andstructural weakness. To overcome this more chambers can beused. Since the area of the water surface in the chamber wasdetermined to be 2 m in Section III.A, for practical reasons,

is chosen to be 2 m, and thus the chamber width is 1 m.This consequently gives a of 15.6 m/s, as shown in Fig. 9.

Fig. 9. versus single chamber length with m, s at.

Fig. 10. Resultant airflow velocity of two chambers (with m,. s, m).

C. Effect of Two Chambers

The OWC consists of two chambers, as shown in Fig. 2. Forany chamber length, the waves in the two chamber segmentsare out of phase, and this means that the pulsating power avail-able at the individual chambers turbines will also have phasedifferences. It is assumed that the wave power delivered to thetwo in-line chambers is the same, and the airflow through theturbines due to wave oscillation is also the same in terms ofmagnitude. The Savonius turbines are bidirectional, and thereis positive power flow into the turbine generator regardless ofthe airflow direction, hence only velocity magnitude is required.Fig. 10 shows the resultant airflow velocity acting on the twocascaded turbines and it is much smoother in comparison withthe original individual oscillating airflows. This is indicative ofthe turbine power. In Fig. 10, the mean airflow velocity mag-nitude ( m/s, the mean value of the inlet airflow ve-locity of Chambers 1/2 and 2/2) is used for further calculationof the average chamber power available at the turbine. As canbe seen in Fig. 10, the two chambers work out of phase and the“ combined velocity” averages the two chamber velocities.This clearly shows that the “ combined velocity” has a sig-nificantly smaller oscillation than that in any individual chamber


Fig. 11. Chamber power operated at rated condition (with m,. s, m).

TABLE IIMAJOR CHAMBER DIMENSIONS WITH OPERATING CONDITIONS

and this will smooth the power output. Finally, takes themean value.

D. Overall Chamber Characteristics

Having completed the above analysis, the chamber dimen-sions need to be determined; these as given in Table II. Eachof the two chambers has a water surface area of 2 m anda turbine inlet area of 0.02422 m . The single chamberlength is 2 m and this makes the entire chamber 4 m longin the direction of wave propagation. Using the compound air-flow velocity shown in Fig. 10, and also using (30), (32) and(33), the available turbine power for s and mcan be calculated, as shown in Fig. 11. The average availablepower was found to be 301.6 W. This will be compared to theexperimental results.To briefly verify the design, the inlet airflow velocity was

calculated with different wave periods. As shown in Fig. 12,the wave period s gives the best performance for allthe three different wave surface elevations, where at mthe velocity of the mean inlet airflow reaches the expected15.6 m/s. This will also be validated experimentally.The estimated overall performance for the OWC is tabulated

in Table III. The chamber input power delivered fromwavesis calculated from [17], [24]

(34)

Fig. 12. Inlet airflow velocity versus wave period under different wave surfaceelevation (two chambers).

TABLE IIIESTIMATED PERFORMANCE OF DESIGNED CHAMBER

where is the width of the incomingwave (here it is the chamberwidth), and is the group (wave) velocity defined by

(35)

where the wavelength is as defined in (11) and is the waveperiod.From (34) and considering the proposed chamber, the avail-

able wave power was calculated to be 338.1W and the availablechamber power for the turbine was calculated to be 301.6W.This simple calculation indicates that the maximum theoreticalefficiency of the OWC chambers is 89.2% (with turbines andgenerators excluded). This high chamber efficiency might indi-cate a possible overestimation for the available chamber power.

IV. TURBINES AND GENERATOR

A. Turbine Specification

Once the chamber power and the inlet airflow velocity aredetermined, the turbine can be operated at an appropriate speedto maximize the power conversion. Conventionally, for air


Fig. 13. Dimensions of Savonius turbine.

turbines in free space, the turbines are characterized using thepower coefficient , which is defined by

(36)

where is the shaft torque of the turbine, is the turbinerotational speed, is the sweep area of the turbine blades and

is the inlet airflow velocity through the turbine. The powerinput to the turbines from the chamber consists of two compo-nents (airflow and pressure difference). Hence, the conversionrate CR is

(37)

where is the total chamber power as calculated using (33).To maximize CR, the turbines should operate at an appro-

priate speed with respect to the inlet airflow velocity. This canbe determined from the CR against Tip Speed Ratio (TSR) char-acteristic, where the TSR is defined by

(38)

where is radius of the turbine blades. The major dimensionsof the Savonius rotors are shown in Fig. 13. The TSR for aSavonius rotor should be about 1 (or slightly less) at peakconversion [11]. The radius of the turbines used in the studywas not precisely calculated so that it was expected that theconversion rate would not be as high as theoretically possible.As shown in Fig. 14, the performance of the turbines wasexperimentally evaluated. To plot the curve, the mechanicalpower (turbine shaft torque speed) needs to be measured.For the experimental setup, it was difficult to install a torquetransducer. To solve this problem, the motor parameters wererecorded, including the generator output voltages (before andafter the rectifier), dc current fed to the load resistance, andgenerator speed, when the OWC was operated at various wavesurface elevations and periods. The experimental arrangementis shown in Fig. 2(a). The shaft torque was not measured insitu but was measured afterwards using a dynamometer, wherethe operating conditions (currents, voltages, loads, generatorspeed, etc.) matched the OWC experimental conditions. Theexperimental results were curve-fitted and found to have a

Fig. 14. Experimental and simulation CR versus TSR curves (Savonius turbinem).

of about 0.19 (where ). This is a reason-able conversion rate for a turbine of this type.As previously mentioned, for m and s, the

estimated m/s and W. Using the turbineCR in Fig. 14, the average turbine output shaft power can becalculated from

(39)

where is the turbine shaft power. From the output of theturbines ( W with a turbine speed of 1842 rpm), atorque of 0.297 N-m should be developed to turn the directly-coupled generator at that operating point.

B. Brushless Permanent-Magnet Generator

The three-phase ac power output from the brushless perma-nent magnet (PM) generator is converted from ac to dc usinga full-bridge rectifier and the dc power dissipated in a resis-tive load. This is shown in Fig. 15(a) [26]. is the phaseback-EMF of the generator, is the phase resistance,is the phase armature reactance, is the load resistance andis the rectifier output voltage. Fig. 15(b) shows a simplified

dc equivalent circuit, where is again the phase inductancewhich is referred to the dc equivalent circuit via the equivalentresistive component . In addition, is the generator re-ferred equivalent output voltage, is the referred windingresistance and is the line-to-line back-EMF constant. iselectrical angular velocity in radians per second while ismechanical speed in radians per second. A dc electronic loadis used for the test and hence a dc equivalent circuit would bemore convenient for analysis.The total power from the generator back-EMF sources is

(40)

where the total effective resistance is. From Fig. 15(b), the terminal output power is given by

(41)


Fig. 15. Equivalent circuits and efficiency of generator: (a) generator modelwith a full-bridge rectifier and resistive output, (b) equivalent dc circuit loop forgenerator efficiency calculation and (c) output characteristics.

The generator and load need to be matched to the turbineand the particular operating point to ensure that the system op-erates at the correct speed for peak TSR and hence maximumconversion. To explain this, an experimental power curves forthe Savonius turbine, which can be extracted from the CR-TSRcurve in Fig. 14, are shown in Figs. 16(a) and (b). The horizontalaxis is turbine speed while the vertical is the calculated turbineoutput power at different turbine inlet speed due to dif-ferent wave power.In Fig. 16(a), two curves for different generator back-EMF

constants with constant load resistance are shown, while inFig. 16(b) the back-EMF constant is maintained and two curvesfor different load resistances are illustrated. In both graphsthere is a curve for peak power conversion. As the turbine inletairflow velocity increases, the peak power point increases.These peaks will represent the peak TSR which should beconstant. In Fig. 16(a) the generator has a back-EMF constant

which is capable of satisfying the requirements ofthe turbine operation at a peak mechanical power of 57.3 W at

m/s mean airflow velocity, and this is indicated by

Fig. 16. Parameter variation effects on turbine mechanical output power andgenerator electric output power: (a) effect of generator and (b) effect ofload resistance .

the generator curve. However, at lower inlet veloci-ties ( and 13.6 m/s, i.e., smaller waves) thecurve does not cross the two power characteristics so that therewould be issues with generating with this arrangement—theload resistor would have to be changed under these operatingconditions. For the same , a generator with a smaller(i.e., will produce a different operating profile. Thecurve shows that this machine would operate at much lowerpower conversion rate.In Fig. 16(b) the back-EMF constant is maintained as

, and the load resistance is varied. Withthe system operates well at the peak conversion

rate ( m/s) as highlighted in (a). However, toallow operation at lower wave heights the load resistance isreduced to . This now gives almost the correct loading at

m/s.From the above discussion, the back-EMF constant and

the winding impedance of a generator have to be well designedto satisfy the turbine operation. To connect the developed OWCPM generator output to the grid, a power electronic inverter isneeded on the output of the dc link. However, this is not thefocus of this paper, where the system design is presented, and arectifier and a dc load is used to regulate the generator; this keepsthe power delivery simple to control. However, it is appreciatedthat in a wave energy system, the power does pulsate and largedc link capacitors are needed to smooth power delivery [27].The use of multiple chambers and mechanical coupling of the


TABLE IVRESULTS OF GENERATOR DESIGN

Fig. 17. Installation of the two-chamber OWC test model.

chamber turbines will reduce the power pulsations and hence thedc link energy storage requirement, if power pulsation onto thegrid is required to be limited. From the electric machine designprocess given in [28], the generator can be designed from thespecification determined from the turbine output characteristics;the design results are formulated and are given in Table IV. Thegenerator output characteristics are plotted in Fig. 15(c) basedon the equivalent model from Figs. 15(a) and (b), (40) and (41),and the parameters in Table IV. Therefore, , and theefficiency can be plotted with a load resistancefor the rotation speed from 0 to 2000 rpm. is simply theoutput power from the turbine since it is directly attached tothe generator. While a machine with this specification could befabricated, this is expensive, and a very similar machine wasfound to be commercially available.

V. EXPERIMENTAL STUDIES

A. Setup of Test Model

The experimental arrangement is presented in Figs. 17 to 19.Fig. 17 shows the OWC side-mounted on the wall of the wavetank. On the top are the two in-line turbines. Waves are gener-ated by servo-driven paddles at one end of the tank. In the figurethe waves will propagate from bottom left to top right across theface of the OWC. The wave generating paddles were accuratelycalibrated and could generate waves with the required periodsand heights.A dc electronic load was used as the regulated resistive load

applied to the generator. This allowed a variable and control-

Fig. 18. Measurement equipment.

Fig. 19. Hot-wire anemometer to measure the inlet airflow velocity.

lable loading point; this is illustrated in Fig. 18. The brushlessgenerator was directly coupled to the two in-line turbines. Threewave probes were installed for wave surface elevation measure-ment and their amplifier is shown in Fig. 18. A digital storageoscilloscope was used to record the generator speed and electricoutputs. To measure the inlet airflow velocity to the turbines, ahot-wire anemometer was installed exactly underneath the tur-bines to measure the airflow velocity required. This is illustratedin Fig. 19.

B. Wave and Chamber Water Surface Elevation Measurement

In this section the measurements of the wave and chamberwater surface elevations are investigated. The external wavesurface elevation and internal chamber water surface elevationwere measured using the three wave height probes (previouslycalibrated) as illustrated in Fig. 20(a). Probes 1 and 2 mea-sured the internal chamber water surface elevation while Probe3 measured the incident waves before reaching the OWC. UsingTable III and (28), the calculated surface elevations are plottedin Fig. 20(b); the wave probe locations are given in Fig. 20(a).The nominal waves were set to a period of s and

a height of 0.3 m which should give an available turbine inletpower of 301.6 W. The turbine/generator unit was loaded at therated power condition and the results for the wave and chambersurface elevations are presented in Fig. 20(b). Probe 3 showsgood correlation to the expected surface elevation. Probe 1 inChamber 1/2 has a surface elevation of 0.23 m, which givesa 0.78% drop based on the calculation [0.232 m, as shown inFig. 20(b)]. From probe 2, the surface elevation in Chamber 2/2is attenuated to around 0.19 m, which is a 5.6% increase com-pared to the calculation [0.18 m, as shown in Fig. 20(b)]. There-fore, the excellent correlation between the experiments and sim-ulations validate the developed model.


Fig. 20. Wave probe location and phasing. (a) Arrangement and location ofwave height probes. (b) Surface elevation calculation ( sec). (c) Surfaceelevation measurements ( sec).

Re-Calculation: The error due to the attenuation of wave en-ergy that Chamber 2/2 experiences, as highlighted in Fig. 20(b),needs to be examined. Using the attenuated measured water sur-face elevation in Chamber 2/2, as well as the measured heightin Chamber 1/2, the turbine inlet mean airflow velocity can bere-calculated to be 17.97 m/s for Chamber 1/2 and 15.02 m/sfor Chamber 2/2, with a mean velocity m/s. There-calculated total chamber power available to the two turbinesis now 308.8 W. This is an error of only 2.38% compared to thecalculated chamber power , which is excellent for the simpleanalytical algorithm developed in the paper.

C. Air Flow Measurement

In addition to the wave and chamber water surface elevationmeasurement, the turbine inlet velocity was also measured. Themeasured inlet airflow velocity at s and m

Fig. 21. Turbine output power versus speed (Savonius turbine m).

was found to be 16.76 m/s for Chamber 1/2 and 14.3 m/s forChamber 2/2. Thus, the mean velocity combining the two cham-bers m/s. These measurements can be comparedto both the overall prediction and also the prediction from thewater surface elevation measurement in the previous section,which is a reduction of 0.45% compared to the calculated valueof 15.6 m/s. The airflow velocity ( m/s) also has anerror of 0.96% which shows excellent correlation.When comparing the turbine inlet velocity predictions from

the water surface elevation measurements to the actual velocitymeasurements the correlation is excellent. This shows the mea-surements to be good (within a few percent variation) and alsothat the assumption that the air is not compressed is a goodapproximation.Re-Calculation: From the measured velocity values, the re-

calculated turbine inlet power is 312.8 W, which is 3.7% errorfrom the overall system prediction and very similar to the calcu-lation from the chamber water surface elevation calculations inthe previous section. As already stated, this verifies the analyt-ical model and design of the OWC chambers. These errors maybe due to the power loss in the air flow through the chamber.The uncompressible air assumption may also lead to overesti-mation of the design value.

D. Overall System Tests

The turbine output shaft power at various wave periods isshown in Fig. 21 for a constant wave surface elevation of 0.3 m.At a wave period of s, the turbine output is 57.1 W,which is slightly lower than the theoretical 57.3 W. This is a0.36% drop in power. The operating speed of the turbine hasbeen shifted to 1742 rpm to obtain peak TSR, and hence thepeak power, since the inlet turbine velocity is reduced. Fig. 21verifies that the s period produces the best power outputamong the three wave periods when the wave surface elevationis maintained.Fig. 21 shows the power at the shaft of the two turbines con-

nected together. However there will be losses in the generator.Fig. 22 presents the output electric power at the generator ter-minals against the generator/turbine speed. The points in thisfigure correspond to those in Fig. 21. The peak output power


Fig. 22. Generator output power.

TABLE VCOMPARISON OF DESIGN AND EXPERIMENTAL RESULTS (* MEASURED)

for the 2.2 s period is 45.6 W at 1742 rpm, which gives a gener-ator efficiency of 79.9%. The 2.2 s wave period produces peakelectric power, as expected.

E. Discussion

It has been shown that the OWC system generates peak powerat s. To fully verify the individual components and theoverall OWC system, the following cases are compared.

Case 1: Calculation—purely analytical designCase 2: Experiment—purely experimental results withoverall performance onlyCase 3: Re-calculation using measured airflow

The comparison is given in Table V. For the comparison be-tween the purely analytical design (Case 1) and purely experi-mental cases (Case 2), the output electric power has an error of2.4% based on the analysis. For the comparison between Case 1and Case 3, the output electric power has an error of 3.7%. Thisis considered to be acceptable for the analytical model devel-oped. The turbine shaft power is approximately proportional tothe cube of the inlet airflow velocity, and a small error in the air-flow velocity can cause significant difference in output power.The overall experimental system energy conversion rate (fromthe initial wave power to final electric power) was found to be13.9% in the experiments. Compare to the similar OWC system“Mighty Whale”, the maximum total energy efficiency is about15% [16], the efficiency of the proposed system is reasonable.There is only a small drop (7.63%) from the design efficiency.It should be noted that Savonius turbines (low conversion rate)

TABLE VIDIMENSION OF TEST MODEL AND SCALED-UP MODEL

Fig. 23. Turbine windage loss versus turbine speed.

are used in this paper, and an overall conversion rate can be fur-ther enhanced if higher performance turbines were used (suchas a Darrieus turbine that can reach conversion rates of 0.3 to0.35).In terms of an overall system context, there are many loca-

tions where wave energy systems are being assessed and con-sidered [29]–[34]. It may also be possible to combine with short-term wave forecasting systems as described in [35] for furtherpower control.We can now conduct a scaling exercise using the equations

set out in [19] for the future plan to construct a full-scale model.As previously calculated, the geometric scaling .Table VI lists the dimension comparisons of the test modeland the scaled-up chamber, i.e., the original design based onwave conditions of Chenggong. From the developed analyticalmodels, the scaled-up chamber is capable of providing electricpower output of 402.27 kW (calculated from (33), (39) andthe designed generator efficiency of 88.6%). In [19] the poweris scaled by , from the experimental electric power of thetest model, this gives the scaled-up power to be 271.54 kW.Compared to the analytical electric power output 402.27 kW,this gives a 32.5% error, which could be partly due to thewindage/friction in the test model and partly due to the over-estimation of the analytical model. It should be noted that asmentioned in [19], the scale of requires the assumptionof negligible windage/friction or being a linear system inthe power take-offs. Thus, this makes the power scaling anunderestimate. This is further detailed below.A simple test for windage/friction loss of the Savonius turbine

used in this paper is shown in Fig. 23. The turbine was driven by


a servomotor. The torque and speed, as well as the power (calledthe “turbine motor” power loss or total power loss) were mea-sured by a dynamometer. The sole power loss of the servomotorhas also been measured so that the turbine windage/friction losswas easily obtained by subtracting the servomotor power lossfrom the total power loss. As can be seen, the power loss in-creases as speed squared and at around 1800 rpm, the windageloss reaches 33.9 W, which is over half of the turbine mechan-ical output power. This accounts for the low conversion rate ofthe Savonius turbine at high speed operation. This also explainswhy small was not preferred in this small-scale model. Sincethe power scaling mentioned above, this would underesti-mate the electric output power of the full-scale model. There-fore, the turbine rotational speed should be limited to avoid sig-nificant windage loss. From the above discussion, the strongnonlinear behavior in the power take-off affects the accuracy ofpower scaling. By consideration of the windage and friction, theaccuracy of the power scaling can be improved and the poweroutput for the full-scale prototype can be predicted.

VI. CONCLUSION

This paper has successfully designed and analyzed a two-chamber oscillating water column wave energy converter for aspecific site on the eastern coast of Taiwan. A test model hasbeen constructed and tested under the laboratory wave condi-tions. These are capable of representing the target site condi-tions according to the scaling from the Froude number. From theexperiments, the analytical models for individual componentshave been verified as being valid. The power transferred fromthe waves to the electrical load through the entire system hasbeen measured and calculated. The results show that the anal-ysis simulations agree well with the experiments. It was foundthat the two chamber design can increase the overall poweroutput and smooth the energy delivery. Successive chambersrequire careful design by taking the down-wave power dropinto account if the device experiences a prevailing wave direc-tion. An overall efficiency of 13.9% is recorded but this canbe significantly increased by using higher conversion rate tur-bines and possibly by increasing the size of the device from thesmall-scale system developed here.This sort of segmented oscillating water column device

presents a realistic option for full scale deployment. A systemthat also uses multiple chambers was reported in [37]. Inthis paper a full technical report on analyzing, designing andscaling multi-chamber OWCs is put forward and several ap-proximations are used. This is still a developing subject; studiesdetailing behavioral analyses for wave devices, such as that in[38] for a buoy type arrangement, are now being put forward.While the penetration of wave energy is still negligible, re-

searchers are also starting to include wave energy in resourcestudies; in [39], it is assumed that there will be 2.5 to 5% waveenergy resource penetration in some of the scenarios.

ACKNOWLEDGMENT

The authors would like to thank Prof. W.-T. Wu, the formerDean of College of Engineering, National Cheng Kung Univer-sity, Taiwan, for support of this work.

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Min-Fu Hsieh (M’02–SM’11) was born in Tainan,Taiwan. He received the B.Eng. degree in mechan-ical engineering from National Cheng Kung Univer-sity (NCKU), Tainan, Taiwan in 1991. He then re-ceived the M.Sc. and Ph.D. degrees in mechanicalengineering from the University of Liverpool, U.K.,in 1996 and 2000, respectively.From 2000 to 2003, he served as a Researcher

in the Electric Motor Technology Research Center,NCKU. In 2003, he joined the Department of Sys-tems and Naval Mechatronic Engineering, NCKU

as an Assistant Professor. His area of interests includes renewable energygeneration (wave, tidal current and wind), electric machine design and servocontrol. In 2007, he was promoted to associate professor.

Dr. Hsieh is a member of the IEEE Industry Applications, Magnetics, andIndustrial Electronics Societies.

I.-Hsien Lin (S’08) received the B.Eng. and M.Eng.degrees in 2005 and 2007, respectively, from theDepartment of Systems and Naval MechatronicEngineering, National Cheng Kung University,Tainan, Taiwan, where he is currently pursuing thePh.D. degree.His research interests include embedded system

applications, OWC type wave energy generationsystems and electric machines.

David G. Dorrell (M’95–SM’08) is a native of St.Helens, U.K. He received the B.Eng. (Hons) degreein electrical and electronic engineering from the Uni-versity of Leeds, Leeds, U.K., in 1988, the M.Sc. de-gree in power electronics engineering from the Uni-versity of Bradford, Bradford, U.K., in 1989, and thePh.D. degree in engineering from the University ofCambridge, Cambridge, U.K., in 1993He has held lecturing positions with The Robert

Gordon University and The University of Reading.He was a Senior Lecturer with The University of

Glasgow, U.K., for several years. In 2008 he took up a post with The Universityof Technology Sydney, Australia, and he was promoted to Associate Professorin 2009. He is also an Adjunct Associate Professor with The National ChengKung University, Taiwan. His research interests cover the design and analysisof various electrical machines and also renewable energy systems with over150 technical publications to his name.Dr. Dorrell is a Chartered Engineer in the UK and a Fellow of the Institution

of Engineering and Technology.

Ming-June Hsieh was born in Yunlin, Taiwan. Hereceived the Ph.D. degree from the Department ofAeronautics and Astronautics, National Cheng KungUniversity, Tainan, Taiwan.After finishing the military service, he joined Dr.

Min-Fu Hsieh’s research group as a postdoctoralResearcher in the Department of Systems and NavalMechatronic Engineering, NCKU. His major is turbomachinery, heat transfer and CFD (computationalfluid dynamics) analysis.

Chi-Chien Lin received the B.Eng. degree from theDepartment of Automatic Control Engineering, FengChia University, Taichung, Taiwan, in 2007. He iscurrently working toward the M.S. degree in the De-partment of Systems and Naval Mechatronic Engi-neering, NCKU.His major research interests include wave energy

systems and permanent magnet generator/motordesign.

Development of a wave energy converter using a two chamber oscillating water column

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