Abstract—Direct Drive Wind Generators with full-scale con-verters are used increasingly due to the high reliability andefficiency. These systems can also be easily adapted to changinggrid quality requirements. Volume and power losses of full scaleconverters become large increasing the rated power and for thisreason an increase of power density and efficiency is desired.For this reason, an optimization is proposed in this paper inorder to find convenient converter solutions dependent on theturbine power, number of modules, and switching frequency.Analytical, volume and power loss models are derived for themain converter components. Design and scaling laws are shown,which are used to evaluate the convenience of a convertersolution. The optimization shows that semiconductors with lowerblocking voltages lead to benefits in terms of both, power densityand efficiency. A convenient increase of the rated voltage of theconverter can be obtained using multilevel converters.
I. INTRODUCTION
Full-scale power converters combined with permanent mag-net synchronous generators (PMSG) are used increasingly inwind-power plants and comes along with several benefits. Agearbox is no longer necessary increasing efficiency, reliabil-ity, and reduces maintenance [1], which makes the solutionpromising, above all for offshore wind-parks.
Grid standards and transmission system operator (TSO)requirements are becoming more and more demanding forwind-power systems. Wind turbines using full-scale convertersare most suitable to be adapted to increasing grid requirements.Moreover, the reactive power can be controlled directly andadditional reactive power compensation equipment is avoided.
Major concerns in the converter design are the efficiencyη and the power density ρp. Both quantities are influencedby multiple parameters such as the rated power, the switchingfrequency, the number of sub-converters, the voltage level, thetopology, etc. A comprehensive optimization is necessary inorder to find convenient solutions. In order to compare differ-ent solutions, the converters are designed with components ofthe same type. Volume and power-loss models are necessaryto evaluate the component scaling dependent on parametervariation.
The standard full-scale converter solution for wind-turbinesis the two level voltage source inverter (2L-VSI) with lowvoltages up to 700V . However, an increase of voltage isdesired in order to reduce power losses and copper costs [2]
[3] and medium voltage solutions can be convenient dependenton the rated power.
An increase of the voltage level can be obtained changingthe converter topology using the same IGBTs. Beside the 2L-VSI, the three level neutral point clamped VSI (3L-NPC) iswidely used in drive systems [4] and it has successfully appliedto wind-power plants [5]. On the other hand, IGBTs withhigher blocking voltages can be used. In this research, 1.7kVand 3.3kV IGBTs have been used due to the large availabilityof high power components with these characteristics. Com-bining the chosen topologies and switches, four solutions arepossible: 700V 2L-VSI, 1.4kV 2L-VSI, 1.4kV 3L-NPC, and2.8kV 3L-NPC.
The design criteria and design laws for the passive compo-nents are derived in Section II. The used volume and powerloss models are shown in Section III. The results of theoptimization and a direct comparison of the most convenientsolutions is shown in Section IV.
II. DESIGN
The goal of the optimization is to show convenient convertersolutions dependent on the rated power PN which can varyfrom 1MW to 10MW and the rated voltage can be 700V ,1.4kV and 2.8kV , according to the possible combinations oftopologies and semiconductors. The converter solutions, whichare proposed by the optimizing algorithm, must fulfill thedesign criteria that are shown in this section.
TABLE IDESIGN CONSTRAINTS
Parameter ValueRated Power PN 1MW .. 10MW
Number Modules N 1 .. 20
Rated Voltage UN 700V ;1.4kV ;2.8kVGrid Side Power Factor PF1 0.9
Fig. 1. Schematic of the drive system: transformer for grid connection,power converter with N modules, and permanent synchronous generator withN galvanic insulated stars.
A. Design Constraints
Converters for high power applications are usually buildwith N independent parallel sub-converters i.e. modules(Fig.1) with the rated power per module PM = PN/N . Moremodules in parallel can be necessary in order to achieve therequired rated power or advantageous to maximize the powerdensity of the converter. However, the number of parallelmodules should not be too high and the accepted maximumnumber is set to 20 in optimization. Moreover, the converterefficiency at rated power should be at least 95%.
The drive system and the grid should be properly decoupledin order to avoid harmonic propagation. Thus the peak to peakDC-link ripple is limited to 1% of the DC-link voltage. TheDC voltage itself is designed with
UDC =√
2UN1.1 (1)
taking a 10% saefty margin on the rated voltage.The peak to peak current ripple at the grid side is limited
to 20% of the nominal peak current [6] in order to havecomparable performance. If more modules are connected inparallel, the current ripple can be partially cancelled usingan interleaving strategy [6] and the grid side inductance canbe reduced. However, the current ripple per module shouldnot be larger than the globally permitted one, due to practicalconcerns, e.g. if the plant is operated with less modules atpartial power. Thus, the ripple is designed that each modulewill achieve the peak ripple requirements in stand alone andthe maximum relative current ripple per module at grid sideis ∆I1%M = N∆I1%
The current ripple at generator side depend mostly on thegenerator inductance. However, an additional inductor is usu-ally installed in order to prevent undesired cable, dv/dt, etc.effects. Reasonable generator side inductances are obtainedlimiting the current ripple to 100% of the nominal peakcurrent without taking into account the PMSG inductance.On generator side, no parallel connection is introduced sinceparallelization would lead to circulating currents. Thus, themaximum relative current ripple per module at generator sideis ∆I2%M = ∆I2%.
Fig. 2. Topologies: (A) 2L-VSI, (B) 3L-NPC
The currents at motor and generator side can be calculatedwith the plant power, voltage and the required power factorPF . The currents per module are given by
IMj =PM√
3UNPFj(2)
where the indice j indicates the grid or generator side. Therequired PF of a PMSG can be much lower than 1 and atgrid side, reactive power generation is demanded by manygrid operators and reactive power of grid filters must becompensated. For this reason, the maximum PF is set to 0.7and 0.9 at generator and grid side, respectively.
The maximum power loss per IGBT is also limited inorder to limit the temperature difference between junction andcase to 45C. If the maximum junction temperature is set to125C, the case temperature must remain below 80C. Thecorresponding maximal power loss is approximately 3kW forthe IGBTs shown in Table II.
An overview of the design constraints is shown in Table I.
B. Topology
The topologies under investigation are the two level voltagesource inverter (2L-VSI) and the three level neutral pointclamped VSI (3L-NPC), which are shown in Fig.2. The 2L-VSI topology is widely used in multi-megawatt wind-powerplants and it can be seen as the standard solution in thisapplication. The 3L-NPC is widely used e.g. for high powerdrive systems and has been recently applied wind-powerplants.
The main advantage [7] of the 3L-NPC compared to the2L-VSI is the increase of the rated voltage using IGBTs witha given blocking voltage. Moreover, the relative dv/dt andthe common mode impact is reduced. Many authors showalso a higher efficiency of the topology in partial power [8],[9], where wind power plants are operated most of the time.On the other hand the 3L-NPC requires a higher number ofsemiconductors and the voltage must be balanced on the DC-Link capacitors.
C. Semiconductors
The switches, which have been chosen for the comparison,are the 1.7kV IGBT and the 3.3kV due to the large avail-ability of the components on the market e.g. ABB 5SNA orMitsubishi Electric CM series. The parameters of the ABB2400E170100 and 1200E330100 components have been usedin this research for comparison and they are shown in TableII, where the switching parameters are obtained for the testing
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voltages 900V and 1800V for the 1.7kV and 3.3kV IGBT,respectively.
D. Passive Components
The passive components are designed in order to fulfillthe ripple requirements. Both the DC-link capacitor and AC-inductor depend on the used modulation scheme and thus onthe topology. The capacitor is designed in order to limit theDC voltage ripple and the inductor to limit the AC currentripple.
1) AC-Inductor: The AC inductor smooths the output cur-rent of the converter and its value influences proportionally thecurrent ripple limiting the di/dt. The maximum peak to peakripple depends on the line inductance, the modulation scheme,the switching frequency, etc. [10]. However, the peak topeak ripple can be approximated with worst case assumptionsby ∆IAC = U∗
DC/(6Lfs) [6], where fs is the switchingfrequency. U∗
DC is the capacitor voltage, which U∗DC = UDC
for the 2L-VSI and U∗DC = UDC/2 for the 3L-NPC.
Thus, the inductance is desined with
L =U∗DC
6∆Ij%Ijppfs=
U∗DC
12√
2∆Ij%Ijfs(3)
where the indice j is j = 1 for the grid side and j = 2 forthe generator side. The relative current ripple is evaluated onthe peak to peak current Ikpp.
2) DC-Capacitor: The DC-voltage ripple depends on sev-eral converter parameters [11] and there exists several ap-proaches to calculate it. A simplified approach to calculatethe peak to peak ripple with worst case assumptions is shownin ∆UDC = I2/(4
√2C∗fs) [6], where C∗ is the capacitance
between two voltage levels of the converter. The total capac-itance is C = C∗ for the 2L-VSI and C = C∗/2 for the3L-NPC.
The generator side is chosen to design the capacitance dueto the higher peak current and it is designed with the equation
C∗ =I2
4√
2∆UDC%UDCfs(4)
III. MODEL
The volume and power loss models, which are used foroptimization, are derived in this section.
TABLE IIIGBT PARAMETERS
Parameter 1.7kV 3.3kVBlocking Voltage UCE 1.7kV 3.3kV
1) Power Losses: The power losses in the semiconductorscan be divided into conduction and switching losses. Thecurrent average IAVG and RMS IRMS value is necessaryfor power loss calculation and must be calculated for eachcomponent.
IAVG =1
Tn
∫ Tn
0
i(t)dt (5)
IRMS =
√1
Tn
∫ Tn
0
i2(t)dt (6)
The values depend on the topology, component (IGBT ordiode), current amplitude and cosφ and are shown in [12],[13].
The conduction losses Pcond are given by the equation
Pcond = UCEonIAVG +RCEonI2RMS (7)
UCEon is the constant forward voltage drop and RCEon isthe resistance during conduction. Both parameters can becalculated from the component data sheets.
The switching power loss Pswitch can be calculated withthe average energy loss per switching cycle Eswitch and theaverage switching frequency fs.
Pswitch = fsEswitch (8)
The energy loss depend on the current and is approximatedby the quadratic function
Eswitch = k2I2RMS + k1IAVG + k0 (9)
The switching energy loss coefficients k2, k1, and k0 are givenfor a test DC-voltage Utest in the ABB data-sheets. Linearinterpolation has been used in order to apply the coefficientsto the designed converters with different (about 10%) DC-linkvoltages UDC , i.e. k0..2 = k0..2testU
∗DC/Utest.
2) Volume: The volume of the switches Vs is given by theIGBT itself and by the heat sink. For high power converters,water cooling is the most used cooling solution. In this case,the heat sink volume can be approximated with 200% of theIGBT volume. Thus the volume of one switch is vs = 3.03land total IGBT volume per converter module is
Vs = kvs (10)
TABLE IIIPARAMETERS OF THE REFERENCE CAPACITOR AND INDUCTOR
CapacitorCapacitance C 600µF
Volume V ∗c 2.55l
Energy E∗c = 1/2CU2 363J
InductorInductance L 48.4µH
Core Power Loss Pi 350W
Winding Power Loss Pw 500W
Volume V ∗l 57.4l
Energy E∗l = 3/2LI2 72.6J
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where k is the number of switches. k = 12 for the 2L-VSIand k = 30 for the 3L-NPC, approximating the clamping diodevolume with the half of IGBT volume.
B. Passive Components
In this section the models of the passive components i.e.the AC-inductor and DC-capacitance are shown.
1) Volume: The capacitance of a plate capacitor is givenby the equation C = εA/d. where ε is the permittivity, A theplate area and d the distance between the plates. Increasingthe voltage, the distance between the plates must be increasedin order to limit the electric field E, which must be belowthe electric strength EBD of the dielectric material. Assuminglinear dependences in the plate capacitor, the condition isU/l < EBD.
The volume V of a capacitor is proportional to Vc ∝ Adand combining the equations the volume is
Vc ∝CU2
εE2BD
∝ Ec =1
2CU2 (11)
where Ec is the energy stored in the capacitor. Thus thevolume of a capacitor can be extrapolated with the equation
Vc = V ∗c
EcE∗c
(12)
where V ∗c and E∗
c is the volume and the stored energy of areference capacitor, respectively.
The inductor design depends on the area product [14]
AwAi =LIpIRMS
kwJRMSBs∝ V
4/3l (13)
where Aw and Ai is the winding and iron area, respectively. Lis the inductance, Ip, IRMS , and JRMS is the peak current, theRMS current and the current density, respectively. Bs is thesaturation induction and Vl the inductor volume. The inductorvolume is
Vl ∝ (AwAi)3/4 ∝ E
3/4l =
(1
2LI2
)3/4
(14)
where El is the stored energy in the inductor. Thus the volumeof an inductor can be extrapolated with the equation
Vl = V ∗l
(ElE∗l
)3/4
(15)
where V ∗l and E∗
l is the volume and the stored energy of areference inductor, respectively.
2) Power Losses: The losses in the DC-capacitor are ne-glected due to the low equivalent series resistance (ESR) ofthe used polyethylene capacitors. Power losses are expectedto be decades below the semiconductor and inductor losses.
The energy loss in inductors can be calculated with the losspower density of an element with volume dV = dAdl in thewinding and core. The winding power loss density pw is
pw =dPwdVw
= ρJ2RMS (16)
Fig. 3. Efficiency η and power density ρ depending on the number of modulesN at constant switching frequency fs = 1.5kHz and evaluated for differentrated powers PN = 2; 4; 6; 8; 10MW . The solid blue and the dashed redcurves are obtained using the 1.7kV and 3.3kV IGBT, respectively. Thecircles indicate the characteristics of a realized power converters.
neglecting high frequency effects. JRMS is the current densityand ρ is the resistivity of the material.
The core power loss density pi is given by the empiricalSteinmetz equation
pi =dPidVi
= kfαBβ (17)
where k, α = 1.2..2, and β = 2.3..3 are usual Steinmetz coef-ficients. f , fn is the applied and rated frequency, respectively.
Thus the total inductor power losses Pl is calculated with thewinding Vw and core Vi volume, assuming constant inductionB and constant current density JRMS
Pl = pwVw + pi
(f
fn
)αVi (18)
Assuming the dependences Vw ∝ Vl and Vi ∝ Vl theequation can be simplified to
Pl =
[Pw + Pi
(f
fn
)α](VlV ∗l
)(19)
3) Reference Components: The capacitor ”ICAR LNK-8PX-600-110” and inductor ”Siemens 4EU45 21-1AA00” areused as reference components and their main parameters areshown in Table III.
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Fig. 4. Efficiency η and power density ρ depending on the rated power PN
at constant switching frequency fs = 1.5kHz and evaluated for differentnumbers of modules N = 4; 8; 12; 16; 20. The solid blue and the dashedred curves are obtained using the 1.7kV and 3.3kV IGBT, respectively. Thecircles indicate the characteristics of a realized power converters.
C. Evaluation
The power density and efficiency can be calculated with thederived models. Both, entities depend on the total converterpower, the number of modules, the switching frequency, thetopology, and the rated voltage. Thus, the functions
ρp = fρ (PN , N, fs, T opology, UN ) (20)
ηp = fη (PN , N, fs, T opology, UN ) (21)
can be defined and the results can be plotted dependent on theinputs.
IV. RESULTS
A. Optimization
The optimization has been done in order to find convenientconverter solutions in terms of efficiency and power density forwind-turbines with different rated powers. The analysis havebeen done for the rated power range Pn = 1MW..10MW ,N = 1..20 modules and the switching frequency rangefs = 500Hz..5kHz. Due to the large amount of dependences,the results have been plotted in various figures keeping param-eters constant. Configuration which do not correspond to therequirements in Table I are not shown.
The dependences of the number of modules is shown inFig.3. The Efficiency η and the power density ρ is showndepending on the number of modules N at constant switching
Fig. 5. Efficiency η and power density ρ depending on the switchingfrequency fs at constant power P = 3MW and evaluated for differentnumbers of modules N = 4; 8; 12; 16; 20. The solid blue and the dashedred curves are obtained using the 1.7kV and 3.3kV IGBT, respectively. Thecircles indicate the characteristics of a realized power converters.
frequency fs = 1.5kHz and it is evaluated for different ratedpowers PN . Relatively flat optima are found for the 2L-VSIwhile optimal module number is more evident for the 3L-NPC.
The dependences of the rated power is shown in Fig.4. Theefficiency η and the power density ρ is shown depending on therated power PN at constant switching frequency fs = 1.5kHzand evaluated for different numbers of modules N . It can beobserved corresponding to Fig.3, that a design with a highnumber of modules will lead to a reduction of both, efficiencyand power density. Optima are observed to be at a low numberof modules and optima are fairly flat close to one module.Thus, a solution with a low number of modules is generallypreferable.
The dependences of the switching frequency is shown inFig.5. The efficiency η and the power density ρ is showndepending on the switching frequency fs at constant powerP = 3MW and evaluated for different numbers of modulesN . The switching frequency for power converters in this powerrange is expected to be fairly small since the switching lossesare becoming dominant for higher values. On the other hand,a low switching frequency requires large passive componentswhich means the power density is small. These dependencesare confirmed by Fig.5 and the converter switching frequencyis a result trading efficiency off against power density.
Moreover, an efficiency decrease is observed using convert-ers based on the 3.3kV IGBT with double the rated voltage
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compared to 1.7kV one while the power density remainsconstant. On the other hand, the switching frequency could bedecreased in order to obtain the same efficiency. In this case,the converter based on the 3.3kV IGBT will have a lowerpower density compared to the 1.7kV one. For this reason,IGBTs with lower voltage ratings e.g. the 1.7kV IGBT shouldbe the preferred solution for power converters in question.
If, an increase of the voltage level is desired [2], the 1.4kV3L-NPC is a promising solution for future multi-megawattplants. More generally, the optimization shows a tendencyto increase the rated voltage of converters using multileveltopologies instead of high voltage components.
B. Reference Design
Both promising converter solutions, the 1.4kV 3L-NPCand 700V 2L-VSI are compared for the rated power 5MW(Table IV). The 3L-NPC leads to a higher power densityand efficiency. Moreover, some components, which are notmodeled in this optimization e.g. control boards, etc. must beinstalled per module. Thus, the gap of the power density caneven augment. It is also observed, that both solutions have asimilar number of semiconductors.
However, the 1.4kV 3L-NPC leads to an increase of thevoltage level and copper costs and power losses of the wind-power plant can be reduced. On the other hand, the 3L-NPC is barely a medium voltage solution and thus regulationschanges. For this reason, it must be evaluated if the voltagelevel leads to a noticeable increase of the cost of electricalcomponents in the wind turbine.
TABLE IVREFERENCE DESIGN
Overall Characteristics 2L-VSI 3L-NPCRated Power PN 5.0MW
Switching Frequency fs 1.5kHz
Rated Voltage UN 700V 1.4kV
Number of Modules N 4 2
Power Density ρd 4.9kW/dm3 7.3kW/dm3
Efficiency η 97.9% 98.3%
Characteristics per Module 2L-VSI 3L-NPCDC Voltage VDC 1089V 2178V
DC Capacitance C 15.9mF 4.0mF
Capacitor Volume VC 66.4dm3 66.4dm3
Grid Current I1M 1146A 1146A
Generator Current I2M 1473A 1473A
Inductance L1 46.7µH 93.4µH
Inductance L2 29.0µH 29.0µH
Inductor Volume VL 138.4dm3 185.1dm3
Inductor Power Loss PL 2.1kW 2.7kW
IGBT Volume VS 36.4dm3 90.9dm3
Conduction Losses Pcond 13.6kW 26.7kW
Switching Losses Pswitch 11.3kW 14.2kW
Volume VM 241.2dm3 342.4dm3
Power Loss PM 26.9kW 43.6kW
V. CONCLUSION
In this work, different converter solutions have been com-pared and their convenience for multi-megawatt wind-powerplants is evaluated. Combining the two (2L-VSI) and three(3L-NPC) level voltage source inverter with IGBTs with twoblocking voltages (1.7kV , 3.3kV ), three rated voltage levels(700V , 1.4kV , 2.8kV ) can be obtained.
It has been found that converters based on the 1.7kV IGBTwill lead whether to a higher efficiency obtaining the samepower density or to the same efficiency with a higher powerdensity, i.e. this component is generally preferable. Combiningthe 1.7kV IGBT with the three level NPC topology, a furtherincrease of the power density and efficiency can be obtained.This converter has the best characteristics between the com-pared ones, i.e. it appears to be the most convenient solutionfor MW wind power plants, with respect to the optimizationmodel.
In further work, the costs of the medium voltage solution(1.4kV 3L-NPC) should be evaluated and compared to thecosts of the low voltage one (700V 2L-VSI). Moreover, theoptimization shows advantages of multilevel topologies andconverters with even more voltage levels than three should becompared.
REFERENCES
[1] R.K.Behera, W.Gao, and O.Ojo, “Simulation study of permanent magnetsynchronous machine direct drive wind power generator using three levelnpc converter system,” in PEMWA, 2009.
[2] J.Bordonau, “Generators and converters in low and medium voltage windenergy conversion systems,” in EWEC, 2007.
[3] B. Backlund, M. Rahimo, S. Klaka, and J. Siefken, “Topologies, voltageratings and state of the art high power semiconductor devices for mediumvoltage wind energy conversion,” in IEEE PEMWA, 2009.
[4] L. Tolbert, F. Peng, and T.Habetler, “Multilevel converters for largeelectric drives,” IEEE Trans. Ind. Appl., vol. 35, pp. 36–44, 1999.
[5] P.Maibach, A.Faulstich, M.Eichler, and S.Dewar. (2010) Full-scalemedium-voltage converters for wind power generators up to 7mva.ABB. [Online]. Available: www.abb.com
[6] L. Asiminoaei, E. Aeloiza, J. H. Kim, P. Enjeti, F. Blaabjerg, L. T.Moran, and S. K. Sul, “Parallel interleaved inverters for reactive powerand harmonic compensation,” in IEEE PESC, 2006, pp. 1–7.
[7] B.Sahan, S.V.Araujo, A.Engler, and F.L.M.Antunes, “Design and bench-mark of a multilevel converter for large-scale wind power systems,” inEWEC, 2007.
[8] O. Al-Naseem, R.W.Erickson, and P.Carlin, “Prediction of switchingloss variations by average switch modeling,” in IEEE APEC, 2000.
[9] R.Erickson, S.Angkititrakul, and K.Almazeedi, “A new family of mul-tilevel matrix converters for wind power applications: Final report,”National Renewable Energy Laboratory, Tech. Rep., 2006.
[10] J. W. Kolar, H. Ertl, and F. C. Zach, “Influence of the modulation methodon the conduction and switching losses of a pwm converter system,”IEEE Trans. Ind. Appl., vol. 27, no. 6, pp. 1063–1075, 1991.
[11] M. H. Bierhoff and F. W. Fuchs, “Dc-link harmonics of three-phasevoltage-source converters influenced by the pulsewidth-modulationstrategy—an analysis,” IEEE Trans. Ind. Electron., vol. 55, no. 5, pp.2085–2092, 2008.
[12] G.Tomta and R.Nielsen, “Analytical equations for three level npc con-verters,” in EPE, 2001.
[13] F.Blaabjerg, U.Jaeger, and S.Munk-Nielsen, “Power losses in pwm-vsiusing npt or pt igbt devices,” IEEE Trans. Power Electron., vol. 10,no. 3, pp. 358–367, 1995.
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