Research Article Grid Connection of Wave Power Farm Using...

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2013 Article ID 562548 9 pageshttpdxdoiorg1011552013562548

Research ArticleGrid Connection of Wave Power Farm Using an N-LevelCascaded H-Bridge Multilevel Inverter

Rickard Ekstroumlm and Mats Leijon

Division of Electricity Department of Engineering Sciences Swedish Centre for Renewable Electric Energy ConversionUppsala University PO Box 534 751 21 Uppsala Sweden

Correspondence should be addressed to Rickard Ekstrom rickardekstromangstromuuse

Received 28 February 2013 Revised 21 May 2013 Accepted 22 May 2013

Academic Editor Chuanwen Jiang

Copyright copy 2013 R Ekstrom and M Leijon This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

An N-level cascaded H-bridge multilevel inverter is proposed for grid connection of large wave power farms The point-absorberwave energy converters are individually rectified and used as isolated DC-sources The variable power characteristics of the waveenergy converters are discussed and amethod of mitigating this issue is demonstratedThe complete power control system is givenin detail and has been experimentally verified for a single-phase setup of the 9-level inverter Theoretical expressions of the powersharing between multilevel cells are derived and show good correspondence with the experimental results

1 Introduction

In the last decade a wave energy converter (WEC) con-cept has been developed and experimentally verified at theCentre for Renewable Electric Energy Conversion UppsalaUniversity [1ndash3] The point-absorber type WEC shown inFigure 1(a) consists of a linear generator placed on the seabedconnected with a line to the buoy The generator is of thedirect-driven permanent magnet type with only electricaldamping used The mechanical design is simple and robustto withstand the violent sea states Since the point-absorberWEC has a natural upper limit in power absorption the ideais to deploy multiple units operating as a farm To reduce thenumber of sea cables from the offshore farm to the coastlineand also to improve the transmission efficiency an offshoremarine substation is proposed The substation gathers all theWEC outputs and transfers the power to the electric gridonshore via a single power cable As a part of the UppsalaUniversity project amarine substation is under constructionas shown in Figure 1(b) The substation will connect theresearch wave power farm of multiple WECs to the local gridat 1 kV

To optimize the absorbed wave power both mechanicaland electrical damping control strategies have been proposed[4ndash7] Even though the power absorption may increase

so will the complexity and investment cost of the externalcircuits Considering the small-scale nature of the WECsa simpler strategy may be advantageous In [8] passiverectification onto a constant DC-bus is evaluated where theoptimal DC-voltage is a function of the sea state

The selection of transmission technology to shoredepends on the power and voltage ratings of the farm andis discussed in [9] For very remote ocean resources as forexample offshore wind farms the capacitive nature of thesea cable urges for the use of a high-voltage direct current(HVDC) link Only if the plant is within a few km from shorethe medium voltage AC transmission link would be a morecost-efficient alternative

As the technical evolution of semiconductor devices likethe insulated gate bipolar transistor (IGBT) continuouslyreach higher voltage and current ratings the IGBT-basedvoltage-source inverter (VSI) has become a popular choice forgrid connection of renewable energy sources To reduce thegrid current ripple a passive harmonic filter is put in serieswith the VSI This is typically an L or LCL-filter followedby a stepup transformer This set-up does not only reducethe system efficiency but also tends to get bulky if put in amarine substation As an alternative this paper proposes thecascaded H-bridge multilevel inverter (CHB-MLI) for gridconnection of the wave power farm This topology assumes

2 Journal of Electrical and Computer Engineering

Foundation

Generator

Line

Buoy

(a) (b)

Figure 1 (a) Schematic view of the wave energy converter The linear generator is put on the seabed and is connected with the buoy throughthe line (b) Offshore marine substation for connection of multiple WECs to the onshore electric grid

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

Va VcVb

Figure 2 Proposed grid connection topology for a small-scale wave power farm using the Y-connected 9-level CHB-MLI

the DC-sources to be electrically isolated as is the case forthe farm The electrical overview of the proposed scheme isshown in Figure 2 for the three-phase 9-level CHB-MLI instar connection Few advantages of this topology comparedto the two-level VSI include

(i) reduced filter size and losses(ii) no step-up transformer

(iii) reduced voltage stresses in the system

(iv) improved electromagnetic compatibility

(v) reduced switching losses

(vi) IGBTs can be rated for lower voltages

(vii) the individual DC-levels may be optimized for thedifferent WECs

Journal of Electrical and Computer Engineering 3

S1

S2

S3

S4

VDC Vcell

(a)

0

01

10

0S1

S3

minusVDCVcell

+VDC

(b)

Figure 3 (a) The H-bridge cell unit consisting of four active devi-ces (b) The four possible switching states 119878

2is complementary to

1198781 and 119878

4is complementary to 119878

3

while the main drawbacks are

(i) more active devices(ii) more complex control system(iii) increased conduction losses

In this paper the CHB-MLI is proposed for grid connectionof a wave power farmThepower flow control from theWECsinto the grid is discussed A simple method of DC-voltagebalancing is evaluated Experimental results on a single-phase9-level CHB-MLI connected to the grid are presented alongwith the control system strategy

2 The Cascaded H-Bridge Multilevel

The CHB-MLI is the most device-efficient of the establishedmultilevel topologies with respect to the number of outputvoltage levels The basic building block cells consist of an H-bridge with four active devices as is depicted in Figure 3(a)Switches 119878

1and 119878

2are complementary as well as the switch

pair 1198783and 1198784 There are four possible switching states for the

H-bridge resulting in output voltages of +119881DC 0 or minus119881DC asshown in Figure 3(b) By alternating between the two statesof zero all active devices get exposed to the same amount ofcurrent

As long as the DC-sources of all cells are isolatedthe cells may be connected in series as was depicted inFigure 2 This requirement makes the topology suitable for

minus4VDC

V4

V3

V2

V1

minusVDC

+VDC

VLN

+4VDC

Figure 4 Superposition of the cell voltages for one phase-leg of the9-level CHB-MLI

for example fuel cells and photovoltaic cells Its usage hasalso been suggested for power line conditioning [10] VARcompensation [11] and for motor drives [12] The outputphase voltage is the sum of all cell voltages that is 119881LN =

V1+ V2+ V3+ V4 Operating in the linear range that is the

amplitude modulation119898119886isin [0 1] the total number of levels

119898 for the phase voltage is a function of the number of cells119904 according to

119898 = 2 lceil119898119886119904rceil + 1 (1)

where lceilrceil is the ceiling function The number of levels in theline current 119897 for the three-phase setup becomes

119897 = 2119898 minus 1 (2)

In Figure 4 the superposition principle of the cell voltagesis demonstrated Here fundamental switching is applied toeach cell meaning that each cell will generate a quasi-squarewave

3 System Voltage Buildup

A major benefit of the CHB-MLI as stated above is that allactive devices only have to be rated to a fraction of the phasevoltage However stating that the WECs are isolated fromeach other is only partially true In Figure 5(a) the statorwindings of a linear generator are shown as mounted in thehull The hull has direct contact with the sea water resultingin that the different generators are isolated from each otheronly by their cable insulation

In Figure 5(b) two of the generator circuits are displayedThe grounding impedance of each generator119885

119892 is a function

of the cable characteristics All generators in between whenturned on will add a potential drop of 119881DC between thegenerators The path of a possible voltage buildup in thecircuit is illustrated by the red line in Figure 5(b) Assumingthat 119885

1198921= 1198851198922 the highest potential drop will occur across


(a)

Va

Vb

mVDC

Vg1

Zg1

Vg2

Zg2

VLN1

VLN2

(b)

Figure 5 (a) Bottom view of the linear generator where it can beseen how the stator windings aremounted against the hullThe hullsof the generators in the farm provide a low-impedance path to eachother via the sea water (b) The common ground path through thesea water via their grounding impedances119885

119892 which are dominated

by the cable insulation impedance of the stator windings The redline illustrates one possible path for 119881

1198921and 119881

1198922to build up The

cable insulation must be rated above this to withstand an electricalbreakdown

the main voltage at119898119886= 1 The voltage drop across the cable

insulation 1198811198921 can then be expressed as

1198811198921

=

lfloorradic3 (119904 minus 1)rfloor119881DC + 119881LN1 + 119881LN2 minus 2119881119889

2 (3)

where lfloorrfloor is the floor function and 119881119889is the diode voltage

drop 1198811198921

may be several magnitudes higher than the WECvoltage rating andmust be accounted for when selecting cableinsulation This challenge may be solved by putting externalinsulation covers between the windings and the hull

4 Switching Control Strategies

There are various suggested modulation strategies of multi-level inverters where the main three categories are [13 14]

(i) selective harmonic elimination (SHE)

(ii) space vector modulation (SVM)(iii) sinusoidal pulse-width modulation (SPWM)

In SHE the firing angles of each H-bridge are set to eithercancel a specific number of harmonics or keep the totalharmonic distortion (THD) atminimum [15 16] In SVM theoptimal switching state is selected based on feedback controlof the current state [17] It is seldom used for more than threelevels due to increased complexity SPWM is a very popularalternative not least due to its simple implementation Acarrier wave is compared with a sinusoidal reference waveto turn the switches on or off Much research has beenconducted in optimizing the harmonic output performanceby using different types of carrier waves and phase shifting[18 19] In Figure 6(a) the phase dissipation (PD) strategyis depicted in Figure 6(b) the phase opposition dissipation(POD) in Figure 6(c) the alternative phase opposition dis-sipation (APOD) and in Figure 6(d) the phase shifted (PS)control technique

5 Power Flow

The purpose of the power control system is to safely transferthe generated WEC powers into the grid at unity powerfactor It should also keep the DC-voltage within a range[119881DClow 119881DCup] depending on sea state to optimize theWEC damping as discussed in Paper [8] The DC-voltageprovides an excellent measure of the system power balanceand by using a DC buffer capacitor the required systemdynamics are reducedThenecessary capacitor size119862 for eachcell of the CHB-MLI depends on the allowed DC-voltagerange according to

1

2119862 (1198812

DCup minus 1198812

DClow) = int

1199052

1199051

(119875WEC (119905) minus 119896119875grid (119905)) 119889119905

(4)

where119875WEC is theWECpower input and119875grid the total powerinjected in the grid The variable 119896 gives the relative cellpower in proportion to the total power as will be discussedin Section 53

51 WEC Output Power In deep water the average power ofthe waves can be derived using potential wave theory as

119869 =1205881198922

62120587119879119864119867119904

2[Wm] (5)

where 120588 is the water density and 119892 is the gravity constantThesignificant wave height119867

119904and the wave energy period 119879

119864are

calculated by

119867119904= 4radic119898

0 119879

119864=119898minus1

1198980

(6)

where the 119899th moment of the spectral density 119878(119891) is definedby

119898119899= int

infin

0

119891119899119878 (119891) 119889119891 (7)


t

ma Vc

(a) PD

t

ma Vc

(b) POD

t

ma Vc

(c) APOD

t

ma Vc

(d) PS

Figure 6 Multicarrier SPWM control strategies The sinusoidal control reference 119881119888is compared with different types of carrier waveforms

to generate the switching logic for the H-bridges

10

8

6

4

2

00 10 20 30 40 50

Time (s)

Elec

tric

al p

ower

(kW

)

PWEC1

PWEC2

PTOT

Figure 7 The power output from two WECs in real sea trials aredisplayed [21] By connecting several units in parallel the totaloutput power variance can be reduced

The power absorbed by the WEC varies vastly from 5ndash40 depending on the sea state [20] as well as the WECdesign The direct-driven WEC without any intermediateenergy storage will pulsate power twice per wave periodA typical wave energy period of 119879

119864= 5 s corresponds to

power peaks around 04Hz In Figure 7 [21] the typicaloutput power of two three-phase WECs under real sea trialsis presentedThe peak power may be in the order of ten timesthe average power By connecting multiple WECs in paralleland distributing their position along the wave direction theoutput power variance is much reduced [22]

52 Grid Connection Control Assuming a stiff grid thesingle-phase active power 119875 and reactive power 119876 for a grid-connected CHB-MLI are governed by

119875 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883sin (120575) 119876 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883cos (120575) minus

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

2

119883

(8)

where 119881119892is the grid voltage 119881

119894the inverter output voltage 120575

the load angle and 119883 the equivalent reactance between theinverter and the grid

To simplify the current control feedback loop all phasecurrents are transformed into the dq0-frame by

119868dq0 = 119879 lowast 119868abc (9)

where 119879 is the ClarkePark transformation matrix [23]

119879 = radic2

3

((

(

cos (120579) cos(120579 minus 2120587

3) cos(120579 + 2120587

3)

sin (120579) sin(120579 minus 2120587

3) sin(120579 + 2120587

3)

1

radic2

1

radic2

1

radic2

))

)

(10)

The sinusoidal reference signal 119881119888 shown in Figure 6 is

generated by

119881119888= 119881lowast

cd sdot sin (120596119905) + 119881lowast

cq sdot cos (120596119905)

= 119898119886sin (120596119905 + 120575)

(11)


where 119881lowast

cd and 119881lowast

cq are current control feedback variablesused to control the active and reactive power flows Theamplitude modulation index is 119898

119886= radic(119881

lowast

cd)2+ (119881lowastcq)

2 andthe load angle is 120575 = tanminus1(119881lowastcq119881

lowast

cd) If 119898119886 lt 1 the inverterfundamental output rms phase voltage 119881out is derived as

119881out = 119898119886

119904119881DCradic2

(12)

where 119904 is the number of cells per phase

53 Power from the Cells At unity power factor if the loadangle is assumed small and neglecting the internal H-bridgelosses the power drawn from each cell can be calculated as

119901cell (119905) = 119881DC (119905) 119868DC (119905) = 119881cell (119905) 119868119892 (119905) (13)

where 119868119892(119905) is the grid current and 119881cell(119905) the cell output

voltageAt fundamental switching assuming the DC-voltage

constant and using the quarter symmetry of the waveformsthe average cell power can be expressed as

119875cell =4119881DC119879

int

(1205872)

120579119899

119868119892(119905) 119889119905 (14)

where 119879 is the fundamental period of the grid voltage and120579119899the angle when the 119899th cell is triggered Setting 119868

119892(119905) =

119868 sin(120596119905) this simplifies to

119875cell =2119881DC119868119892

120587cos (120579

119899) (15)

If an SPWM-control strategy is used like in Figure 6 theoutput voltage can be in three different modes dependingon whether the reference signal is above below or inside thecarrier wave band In the last case the cell SPWM-voltage hasthe same average curvature as the control signal 119881

119888 allowing

the following approximation

119881cell =

0 if 0 le 120579 lt 1205791119899

119881DC [119898119886 sin (120596119905) minus119904119899minus 1

119904] if 120579

1119899le 120579 lt 120579

2119899

119881DC if 1205792119899

le 120579 le120587

2

(16)

where 119904119899is the order of the cell 120579

1119899and 1205792119899are the lower and

upper boundaries of the 119899th carrier wave band It is obvioushow the relative cell power depends on 119898

119886for SPWM-

control Repeating the derivation of (15) with the cell voltagesin (16) the cell power may be derived In Figure 8 119898

119886is

swept in its linear region and the relative power distributionbetween the cells is displayed Knowing the grid power and119898119886 the power from each cell can be calculated At119898

119886= 095

the power distribution between cells is 382 340 245and 33

0 02 04 06 08 10

20

40

60

80

100

Cell 1Cell 2

Cell 3Cell 4

Amplitude modulation ma

Pow

er sh

are (

)

Figure 8 Relative power distribution between the four cells fordifferent119898

119886 using the PD control strategy

54 Power Control System Layout The main challenge ofthe power control loop is to handle the power fluctuationsfrom the WECs The issue is mitigated but not resolvedby increasing the size of the buffer capacitors or connectingmultiple units to the same capacitor One solution is to sharepower between capacitors where a stronger DC-source is setto temporary charge a weaker DC-source as discussed in[24]

The benefit of having isolated DC-sources allows forselecting the order of triggering andmay be done at any timeduring the cycle In [25] the order of the cells is rotated toget equal discharge of the batteries in an electric vehiclesSimilarly if feedback control is applied on all DC-voltagesthe order of rotation may be selected to always start with thehighest DC-voltage first This gives some degree of freedomlimited by the curves of Figure 8 To get further redundancyin the sorting process more DC-sources may be connectedto the CHB-MLI while keeping the number of carrier wavesfixed Such a setup allows for bypassing of cells when theirWEC power is low

In Figure 9 the general power control system blockdiagram is depictedThe grid connection consists of two feed-back loops an inner current control loop to keep unity powerfactor and an outer 119881DC-loop to balance the total DC-levelThe system reference frame is obtained by tracking the gridvoltage using a phase-locked loop (PLL) All four DC-levelsare measured and compared and the cell with highest DC-voltage is set to trigger first in the SPWM-control The orderis set once per fundamental cycle but could be updated at anytime for improved system dynamics

6 Experimental Setup

A phase leg of the proposed circuit in Figure 2 has beenexperimentally implemented Each H-bridge consists of twodualpackage 400GB126D IGBT modules with inbuilt free-wheeling diodes that are shown in Figure 10 The driverboards are mounted in shielded boxes on top of the H-bridges


Vgrid

sumVDC

sum

PLL

SPWM

cos(120579)

sin(120579)Vlowast

abc

Vg

ilowastd = 0

X

ilowastq

iq

id

minus+

minus+

minus+

Iabc

PI

PI

PI

VDC4

VDC3

VDC2

VDC1

VlowastDC

Setorder

Gate signals

9-levelCHB-MLI

abc

abc

120572120573

120572120573

120572120573

120572120573

dqdq

Figure 9 Layout of the control system The total DC-voltage of each phase leg is controlled by varying 119894119902and thus the load angle to the grid

voltage The individual DC-voltages may be partially controlled by setting the order of conduction of the cascaded H-bridges

Figure 10 Two of the four H-bridge cells with associated drivercircuits mounted in the shielded boxes above the IGBTs

The control system in Figure 9 is implemented in a field-programmable gate array (FPGA) chip using the PD-SPWMcontrol strategy The switching frequency of the carrierwaveforms was set to 6 kHz and blanking time betweenswitching states was 25 120583s

Four isolated DC-sources at 105V each were used byrectifying the outputs of a multi-winding transformer TheCHB-MLI was connected to the local grid at 400V 50Hzthrough a filter inductor of 3mH The grid voltage andDC-voltages were measured with high-frequency differentialvoltage probes SI-9002 having an accuracy of plusmn1 The gridcurrent andDC-currents weremeasured with current clampsFluke i310s having an accuracy of plusmn2

7 Results and Discussion

In Figure 11 the individual cell voltages of the single-phaseCHB-MLI have been measured at noload The amplitudemodulation is 09 and the output phase voltage has nine

0 5 10 15 20

minus400minus300minus200minus100

0100200300400

Cell 1 voltageCell 2 voltageCell 3 voltage

Cell 4 voltageTotal output voltage

Time (ms)

Volta

ge (V

)

Figure 11 Cell voltages and the total output voltage of the 9-levelCHB-MLI

levels In Figure 12 the four cells rotate in order once perfundamental cycle to vary the power extracted from eachDC-source It is clear that the total output voltage is notaffected by the order of the cells as long as all DC-voltagesare similar

In Figure 13 the 9-level CHB-MLI is connected to theelectric grid via a 3mH inductor injecting 2 kW at unitypower factor The switching frequency is very attenuated inthe current compared to the two-level inverter counterpartThe grid current contains lower order harmonic frequenciesdue to distortions in the grid voltage

In Figure 14 the power from each cell has beenmeasuredAssuming a constantDC-voltage theDC-current are propor-tional to the powerThe relative power from the different cells


10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)

Figure 12 The order of the cell voltages is rotated once per cyclewith the output voltage unaffected

minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15

Inverter voltageGrid voltageGrid current

Volta

ge (V

)

Time (ms)

Curr

ent (

A)

Figure 13 Grid connection of a single-phase 9-level inverter

120 125 130 135 1400

05

1

15

Power cell 1Power cell 2


Time (ms)

Pow

er (k

W)

Figure 14 Power output from each cell during one fundamentalcycle of grid connectionThe power is divided between the cells into43 336 255 and 366 respectively

120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)

Figure 15 Rotating the cell order to vary the power output fromeach cell The average power for four cycles is evenly distributedamong the cells

are 43 336 255 and 366 respectively and 119898119886for

this case was 09 This shows very good resemblance with thetheoretically derived values in Section 53

In Figure 15 the order of the cells is rotated duringgrid connection The average power extracted from each cellduring four cycles is very similar for all cells

8 Conclusion

An N-level cascaded H-bridge multilevel inverter is pro-posed for grid connection of a large wave power farm Thevariable power outputs from the wave energy convertersare considered and the complete power control system forgrid connection is demonstrated By rotating the conductionorder of the cells more powermay be extracted from the cellswith more energetic WECs connected A single-phase setupof the 9-level CHB-MLI has been connected to the grid andthe power has successfully been varied according to theory

Acknowledgments

The Lysekil Project is supported by Statkraft AS KICInnoEnergy-CIPOWER Fortum oy the Swedish EnergyAgency Draka Cable AB the Gothenburg Energy ResearchFoundation Falkenberg Energy AB the Wallenius Founda-tion Helukabel ProEnviro Seabased AB the Olle EngkvistFoundation the J Gust Richert Foundation Angpannefore-ningenrsquos Foundation for Research and Development CFEnvironmental Fund the Goran Gustavsson Research Foun-dation Vargons Research Foundation And This support isgratefully acknowledged

References

[1] M Eriksson R Waters O Svensson J Isberg and M LeijonldquoWave power absorption experiments in open sea and simula-tionrdquo Journal of Applied Physics vol 102 Article ID 084910 5pages 2007


[2] O Danielsson M Leijon K Thorburn M Eriksson and HBernhoff ldquoA direct drive wave energy convertermdashsimulationsand experimentsrdquo in Proceedings of the 24th International Con-ference on Offshore Mechanics and Arctic Engineering (OMAErsquo05) pp 797ndash801 June 2005

[3] M Leijon H Bernhoff O Agren et al ldquoMultiphysics simula-tion of wave energy to electric energy conversion by permanentmagnet linear generatorrdquo IEEE Transactions on Energy Conver-sion vol 20 no 1 pp 219ndash224 2005

[4] H Luan O C Onar and A Khaligh ldquoDynamic modelingand optimum load control of a PM linear generator for oceanwave energy harvesting applicationrdquo in Proceedings of the24th Annual IEEE Applied Power Electronics Conference andExposition (APEC rsquo09) pp 739ndash743 February 2009

[5] J K H Shek D E Macpherson and M A Mueller ldquoExper-imental verification of linear generator control for direct drivewave energy conversionrdquo IET Renewable Power Generation vol4 no 5 pp 395ndash403 2010

[6] P Ricci J Lopez M Santos et al ldquoControl strategies for a waveenergy converter connected to a hydraulic power take-offrdquo IETRenewable Power Generation vol 5 no 3 pp 234ndash244 2011

[7] D Valerio P Beirao and J Sa da Costa ldquoOptimisation ofwave energy extractionwith the archimedeswave swingrdquoOceanEngineering vol 34 no 17-18 pp 2330ndash2344 2007

[8] R Ekstrom V Kurupath C Bostrom O Svensson R Watersand M Leijon ldquoEvaluating constant DC-link operation of awave-energy converterrdquo in Proceedings of the ASME 31st Inter-national Conference on Ocean Offshore and Arctic Engineering2012

[9] K Thorburn H Bernhoff and M Leijon ldquoWave energy trans-mission system concepts for linear generator arraysrdquo OceanEngineering vol 31 no 11-12 pp 1339ndash1349 2004

[10] F Z Peng J W McKeever and D J Adams ldquoPower lineconditioner using cascade multilevel inverters for distributionsystemsrdquo in Proceedings of the IEEE 32nd IASAnnualMeeting onIndustry Applications Conference pp 1316ndash1321 New OrleansLa USA October 1997

[11] Y Liang and C O Nwankpa ldquoA new type of STATCOMbased on cascading voltage-source inverters with phase-shiftedunipolar SPWMrdquo IEEE Transactions on Industry Applicationsvol 35 no 5 pp 1118ndash1123 1999

[12] P W Hammond ldquoA new approach to enhance power qualityfor medium voltage AC drivesrdquo IEEE Transactions on IndustryApplications vol 33 no 1 pp 202ndash208 1997

[13] J Rodrıguez J Lai and F Z Peng ldquoMultilevel inverters a surveyof topologies controls and applicationsrdquo IEEE Transactions onIndustrial Electronics vol 49 no 4 pp 724ndash738 2002

[14] I Colak E Kabalci and R Bayindir ldquoReview of multilevelvoltage source inverter topologies and control schemesrdquo EnergyConversion and Management vol 52 no 2 pp 1114ndash1128 2011

[15] S Sirisukprasert J Lai and T Liu ldquoOptimum harmonic reduc-tion with a wide range of modulation indexes for multilevelconvertersrdquo in Proceedings of the 35th IAS Annual Meeting andWorld Conference on Industrial Applications of Electrical Energy(IEEE-IAS rsquo00) pp 2094ndash2099 October 2000

[16] L Li D Czarkowski Y Liu and P Pillay ldquoMultilevel selectiveharmonic elimination PWM technique in series-connectedvoltage invertersrdquo in Proceedings of the IEEE Industry Applica-tions Conference pp 1454ndash1461 October 1998

[17] A K Gupta and A M Khambadkone ldquoA space vector PWMscheme for multilevel inverters based on two-level space vector

PWMrdquo IEEE Transactions on Industrial Electronics vol 53 no5 pp 1631ndash1639 2006

[18] L M Tolbert and T G Habetier ldquoNovel multilevel invertercarrier-based PWM methodrdquo IEEE Transactions on IndustryApplications vol 35 no 5 pp 1098ndash1107 1999

[19] V G Agelidis and M Calais ldquoApplication specific harmonicperformance evaluation of multicarrier PWM techniquesrdquo inProceedings of Power Electronics Specialist Conference pp 172ndash178 Fukuoka Japan May 1998

[20] S Tyrberg R Waters and M Leijon ldquoWave power absorptionas a function of water level and wave height theory andexperimentrdquo IEEE Journal of Oceanic Engineering vol 35 no3 pp 558ndash564 2010

[21] M Rahm C Bostrom O Svensson M Grabbe F Bulow andM Leijon ldquoLaboratory experimental verification of a marinesubstationrdquo in Proceedings of the 8th European Wave and TidalEnergy Conference (EWTEC rsquo09) pp 51ndash58 Uppsala Sweden2009

[22] M Rahm O Svensson C Bostrom R Waters and M LeijonldquoExperimental results from the operation of aggregated waveenergy convertersrdquo IET Renewable Power Generation vol 6 no3 pp 149ndash160 2012

[23] R Park ldquoTwo reaction theory of synchronous machinesrdquo AIEETransactions vol 48 no 4 pp 716ndash730 1929

[24] Z Du L M Tolbert B Ozpineci and J N Chiasson ldquoFunda-mental frequency switching strategies of a seven-level hybridcascaded H-bridge multilevel inverterrdquo IEEE Transactions onPower Electronics vol 24 no 1 pp 25ndash33 2009

[25] L M Tolbert F Z Peng T Cunnyngham and J N Chias-son ldquoCharge balance control schemes for cascade multilevelconverter in hybrid electric vehiclesrdquo IEEE Transactions onIndustrial Electronics vol 49 no 5 pp 1058ndash1064 2002

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VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Foundation

Generator

Line

Buoy

(a) (b)

Figure 1 (a) Schematic view of the wave energy converter The linear generator is put on the seabed and is connected with the buoy throughthe line (b) Offshore marine substation for connection of multiple WECs to the onshore electric grid

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

WEC

Va VcVb

Figure 2 Proposed grid connection topology for a small-scale wave power farm using the Y-connected 9-level CHB-MLI

the DC-sources to be electrically isolated as is the case forthe farm The electrical overview of the proposed scheme isshown in Figure 2 for the three-phase 9-level CHB-MLI instar connection Few advantages of this topology comparedto the two-level VSI include

(i) reduced filter size and losses(ii) no step-up transformer

(iii) reduced voltage stresses in the system

(iv) improved electromagnetic compatibility

(v) reduced switching losses

(vi) IGBTs can be rated for lower voltages

(vii) the individual DC-levels may be optimized for thedifferent WECs


S1

S2

S3

S4

VDC Vcell

(a)

0

01

10

0S1

S3

minusVDCVcell

+VDC

(b)



1198781 and 119878


3






1and 119878





minus4VDC

V4

V3

V2

V1

minusVDC

+VDC

VLN

+4VDC






119898 = 2 lceil119898119886119904rceil + 1 (1)


119897 = 2119898 minus 1 (2)









(a)

Va

Vb

mVDC

Vg1

Zg1

Vg2

Zg2

VLN1

VLN2

(b)




1198921and 119881





1198811198921

=


2 (3)


drop 1198811198921







5 Power Flow


1

2119862 (1198812

DCup minus 1198812

DClow) = int

1199052

1199051

(119875WEC (119905) minus 119896119875grid (119905)) 119889119905

(4)



119869 =1205881198922

62120587119879119864119867119904

2[Wm] (5)



119864are

calculated by

119867119904= 4radic119898

0 119879

119864=119898minus1

1198980

(6)


119898119899= int

infin

0

119891119899119878 (119891) 119889119891 (7)


t

ma Vc

(a) PD

t

ma Vc

(b) POD

t

ma Vc

(c) APOD

t

ma Vc

(d) PS



10

8

6

4

2

00 10 20 30 40 50

Time (s)

Elec

tric

al p

ower

(kW

)

PWEC1

PWEC2

PTOT






119875 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883sin (120575) 119876 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883cos (120575) minus

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

2

119883

(8)





119868dq0 = 119879 lowast 119868abc (9)


119879 = radic2

3

((

(

cos (120579) cos(120579 minus 2120587

3) cos(120579 + 2120587

3)

sin (120579) sin(120579 minus 2120587

3) sin(120579 + 2120587

3)

1

radic2

1

radic2

1

radic2

))

)

(10)


generated by

119881119888= 119881lowast


cq sdot cos (120596119905)

= 119898119886sin (120596119905 + 120575)

(11)


where 119881lowast

cd and 119881lowast


119886= radic(119881

lowast



lowast


119881out = 119898119886

119904119881DCradic2

(12)



119901cell (119905) = 119881DC (119905) 119868DC (119905) = 119881cell (119905) 119868119892 (119905) (13)




119875cell =4119881DC119879

int

(1205872)

120579119899

119868119892(119905) 119889119905 (14)


119892(119905) =


119875cell =2119881DC119868119892

120587cos (120579

119899) (15)


119888 allowing


119881cell =

0 if 0 le 120579 lt 1205791119899


119904] if 120579

1119899le 120579 lt 120579

2119899

119881DC if 1205792119899

le 120579 le120587

2

(16)




119886for SPWM-


119886is


119886= 095


0 02 04 06 08 10

20

40

60

80

100

Cell 1Cell 2

Cell 3Cell 4


Pow

er sh

are (

)









Vgrid

sumVDC

sum

PLL

SPWM

cos(120579)

sin(120579)Vlowast

abc

Vg

ilowastd = 0

X

ilowastq

iq

id

minus+

minus+

minus+

Iabc

PI

PI

PI

VDC4

VDC3

VDC2

VDC1

VlowastDC

Setorder

Gate signals

9-levelCHB-MLI

abc

abc

120572120573

120572120573

120572120573

120572120573

dqdq








0 5 10 15 20


0100200300400



Time (ms)

Volta

ge (V

)






10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)


minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15


Volta

ge (V

)

Time (ms)

Curr

ent (

A)


120 125 130 135 1400

05

1

15



Time (ms)

Pow

er (k

W)


120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)





8 Conclusion


Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










S1

S2

S3

S4

VDC Vcell

(a)

0

01

10

0S1

S3

minusVDCVcell

+VDC

(b)



1198781 and 119878


3






1and 119878





minus4VDC

V4

V3

V2

V1

minusVDC

+VDC

VLN

+4VDC






119898 = 2 lceil119898119886119904rceil + 1 (1)


119897 = 2119898 minus 1 (2)









(a)

Va

Vb

mVDC

Vg1

Zg1

Vg2

Zg2

VLN1

VLN2

(b)




1198921and 119881





1198811198921

=


2 (3)


drop 1198811198921







5 Power Flow


1

2119862 (1198812

DCup minus 1198812

DClow) = int

1199052

1199051

(119875WEC (119905) minus 119896119875grid (119905)) 119889119905

(4)



119869 =1205881198922

62120587119879119864119867119904

2[Wm] (5)



119864are

calculated by

119867119904= 4radic119898

0 119879

119864=119898minus1

1198980

(6)


119898119899= int

infin

0

119891119899119878 (119891) 119889119891 (7)


t

ma Vc

(a) PD

t

ma Vc

(b) POD

t

ma Vc

(c) APOD

t

ma Vc

(d) PS



10

8

6

4

2

00 10 20 30 40 50

Time (s)

Elec

tric

al p

ower

(kW

)

PWEC1

PWEC2

PTOT






119875 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883sin (120575) 119876 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883cos (120575) minus

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

2

119883

(8)





119868dq0 = 119879 lowast 119868abc (9)


119879 = radic2

3

((

(

cos (120579) cos(120579 minus 2120587

3) cos(120579 + 2120587

3)

sin (120579) sin(120579 minus 2120587

3) sin(120579 + 2120587

3)

1

radic2

1

radic2

1

radic2

))

)

(10)


generated by

119881119888= 119881lowast


cq sdot cos (120596119905)

= 119898119886sin (120596119905 + 120575)

(11)


where 119881lowast

cd and 119881lowast


119886= radic(119881

lowast



lowast


119881out = 119898119886

119904119881DCradic2

(12)



119901cell (119905) = 119881DC (119905) 119868DC (119905) = 119881cell (119905) 119868119892 (119905) (13)




119875cell =4119881DC119879

int

(1205872)

120579119899

119868119892(119905) 119889119905 (14)


119892(119905) =


119875cell =2119881DC119868119892

120587cos (120579

119899) (15)


119888 allowing


119881cell =

0 if 0 le 120579 lt 1205791119899


119904] if 120579

1119899le 120579 lt 120579

2119899

119881DC if 1205792119899

le 120579 le120587

2

(16)




119886for SPWM-


119886is


119886= 095


0 02 04 06 08 10

20

40

60

80

100

Cell 1Cell 2

Cell 3Cell 4


Pow

er sh

are (

)









Vgrid

sumVDC

sum

PLL

SPWM

cos(120579)

sin(120579)Vlowast

abc

Vg

ilowastd = 0

X

ilowastq

iq

id

minus+

minus+

minus+

Iabc

PI

PI

PI

VDC4

VDC3

VDC2

VDC1

VlowastDC

Setorder

Gate signals

9-levelCHB-MLI

abc

abc

120572120573

120572120573

120572120573

120572120573

dqdq








0 5 10 15 20


0100200300400



Time (ms)

Volta

ge (V

)






10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)


minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15


Volta

ge (V

)

Time (ms)

Curr

ent (

A)


120 125 130 135 1400

05

1

15



Time (ms)

Pow

er (k

W)


120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)





8 Conclusion


Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

Va

Vb

mVDC

Vg1

Zg1

Vg2

Zg2

VLN1

VLN2

(b)




1198921and 119881





1198811198921

=


2 (3)


drop 1198811198921







5 Power Flow


1

2119862 (1198812

DCup minus 1198812

DClow) = int

1199052

1199051

(119875WEC (119905) minus 119896119875grid (119905)) 119889119905

(4)



119869 =1205881198922

62120587119879119864119867119904

2[Wm] (5)



119864are

calculated by

119867119904= 4radic119898

0 119879

119864=119898minus1

1198980

(6)


119898119899= int

infin

0

119891119899119878 (119891) 119889119891 (7)


t

ma Vc

(a) PD

t

ma Vc

(b) POD

t

ma Vc

(c) APOD

t

ma Vc

(d) PS



10

8

6

4

2

00 10 20 30 40 50

Time (s)

Elec

tric

al p

ower

(kW

)

PWEC1

PWEC2

PTOT






119875 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883sin (120575) 119876 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883cos (120575) minus

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

2

119883

(8)





119868dq0 = 119879 lowast 119868abc (9)


119879 = radic2

3

((

(

cos (120579) cos(120579 minus 2120587

3) cos(120579 + 2120587

3)

sin (120579) sin(120579 minus 2120587

3) sin(120579 + 2120587

3)

1

radic2

1

radic2

1

radic2

))

)

(10)


generated by

119881119888= 119881lowast


cq sdot cos (120596119905)

= 119898119886sin (120596119905 + 120575)

(11)


where 119881lowast

cd and 119881lowast


119886= radic(119881

lowast



lowast


119881out = 119898119886

119904119881DCradic2

(12)



119901cell (119905) = 119881DC (119905) 119868DC (119905) = 119881cell (119905) 119868119892 (119905) (13)




119875cell =4119881DC119879

int

(1205872)

120579119899

119868119892(119905) 119889119905 (14)


119892(119905) =


119875cell =2119881DC119868119892

120587cos (120579

119899) (15)


119888 allowing


119881cell =

0 if 0 le 120579 lt 1205791119899


119904] if 120579

1119899le 120579 lt 120579

2119899

119881DC if 1205792119899

le 120579 le120587

2

(16)




119886for SPWM-


119886is


119886= 095


0 02 04 06 08 10

20

40

60

80

100

Cell 1Cell 2

Cell 3Cell 4


Pow

er sh

are (

)









Vgrid

sumVDC

sum

PLL

SPWM

cos(120579)

sin(120579)Vlowast

abc

Vg

ilowastd = 0

X

ilowastq

iq

id

minus+

minus+

minus+

Iabc

PI

PI

PI

VDC4

VDC3

VDC2

VDC1

VlowastDC

Setorder

Gate signals

9-levelCHB-MLI

abc

abc

120572120573

120572120573

120572120573

120572120573

dqdq








0 5 10 15 20


0100200300400



Time (ms)

Volta

ge (V

)






10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)


minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15


Volta

ge (V

)

Time (ms)

Curr

ent (

A)


120 125 130 135 1400

05

1

15



Time (ms)

Pow

er (k

W)


120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)





8 Conclusion


Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










t

ma Vc

(a) PD

t

ma Vc

(b) POD

t

ma Vc

(c) APOD

t

ma Vc

(d) PS



10

8

6

4

2

00 10 20 30 40 50

Time (s)

Elec

tric

al p

ower

(kW

)

PWEC1

PWEC2

PTOT






119875 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883sin (120575) 119876 =

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

10038161003816100381610038161198811198941003816100381610038161003816

119883cos (120575) minus

10038161003816100381610038161003816119881119892

10038161003816100381610038161003816

2

119883

(8)





119868dq0 = 119879 lowast 119868abc (9)


119879 = radic2

3

((

(

cos (120579) cos(120579 minus 2120587

3) cos(120579 + 2120587

3)

sin (120579) sin(120579 minus 2120587

3) sin(120579 + 2120587

3)

1

radic2

1

radic2

1

radic2

))

)

(10)


generated by

119881119888= 119881lowast


cq sdot cos (120596119905)

= 119898119886sin (120596119905 + 120575)

(11)


where 119881lowast

cd and 119881lowast


119886= radic(119881

lowast



lowast


119881out = 119898119886

119904119881DCradic2

(12)



119901cell (119905) = 119881DC (119905) 119868DC (119905) = 119881cell (119905) 119868119892 (119905) (13)




119875cell =4119881DC119879

int

(1205872)

120579119899

119868119892(119905) 119889119905 (14)


119892(119905) =


119875cell =2119881DC119868119892

120587cos (120579

119899) (15)


119888 allowing


119881cell =

0 if 0 le 120579 lt 1205791119899


119904] if 120579

1119899le 120579 lt 120579

2119899

119881DC if 1205792119899

le 120579 le120587

2

(16)




119886for SPWM-


119886is


119886= 095


0 02 04 06 08 10

20

40

60

80

100

Cell 1Cell 2

Cell 3Cell 4


Pow

er sh

are (

)









Vgrid

sumVDC

sum

PLL

SPWM

cos(120579)

sin(120579)Vlowast

abc

Vg

ilowastd = 0

X

ilowastq

iq

id

minus+

minus+

minus+

Iabc

PI

PI

PI

VDC4

VDC3

VDC2

VDC1

VlowastDC

Setorder

Gate signals

9-levelCHB-MLI

abc

abc

120572120573

120572120573

120572120573

120572120573

dqdq








0 5 10 15 20


0100200300400



Time (ms)

Volta

ge (V

)






10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)


minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15


Volta

ge (V

)

Time (ms)

Curr

ent (

A)


120 125 130 135 1400

05

1

15



Time (ms)

Pow

er (k

W)


120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)





8 Conclusion


Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










where 119881lowast

cd and 119881lowast


119886= radic(119881

lowast



lowast


119881out = 119898119886

119904119881DCradic2

(12)



119901cell (119905) = 119881DC (119905) 119868DC (119905) = 119881cell (119905) 119868119892 (119905) (13)




119875cell =4119881DC119879

int

(1205872)

120579119899

119868119892(119905) 119889119905 (14)


119892(119905) =


119875cell =2119881DC119868119892

120587cos (120579

119899) (15)


119888 allowing


119881cell =

0 if 0 le 120579 lt 1205791119899


119904] if 120579

1119899le 120579 lt 120579

2119899

119881DC if 1205792119899

le 120579 le120587

2

(16)




119886for SPWM-


119886is


119886= 095


0 02 04 06 08 10

20

40

60

80

100

Cell 1Cell 2

Cell 3Cell 4


Pow

er sh

are (

)









Vgrid

sumVDC

sum

PLL

SPWM

cos(120579)

sin(120579)Vlowast

abc

Vg

ilowastd = 0

X

ilowastq

iq

id

minus+

minus+

minus+

Iabc

PI

PI

PI

VDC4

VDC3

VDC2

VDC1

VlowastDC

Setorder

Gate signals

9-levelCHB-MLI

abc

abc

120572120573

120572120573

120572120573

120572120573

dqdq








0 5 10 15 20


0100200300400



Time (ms)

Volta

ge (V

)






10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)


minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15


Volta

ge (V

)

Time (ms)

Curr

ent (

A)


120 125 130 135 1400

05

1

15



Time (ms)

Pow

er (k

W)


120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)





8 Conclusion


Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Vgrid

sumVDC

sum

PLL

SPWM

cos(120579)

sin(120579)Vlowast

abc

Vg

ilowastd = 0

X

ilowastq

iq

id

minus+

minus+

minus+

Iabc

PI

PI

PI

VDC4

VDC3

VDC2

VDC1

VlowastDC

Setorder

Gate signals

9-levelCHB-MLI

abc

abc

120572120573

120572120573

120572120573

120572120573

dqdq








0 5 10 15 20


0100200300400



Time (ms)

Volta

ge (V

)






10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)


minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15


Volta

ge (V

)

Time (ms)

Curr

ent (

A)


120 125 130 135 1400

05

1

15



Time (ms)

Pow

er (k

W)


120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)





8 Conclusion


Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10 20 30 40 50 60 70 80


0100200300400



Time (ms)

Volta

ge (V

)


minus400

minus200

0

200

400

0 5 10 15 20 25 30 35 40minus15

minus10

minus5

0

5

10

15


Volta

ge (V

)

Time (ms)

Curr

ent (

A)


120 125 130 135 1400

05

1

15



Time (ms)

Pow

er (k

W)


120 130 140 150 160 170 180 190 2000

05

1

15



Time (ms)

Pow

er (k

W)





8 Conclusion


Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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