Multi-objective Design of a Modular Power Converter ... - Science Direct

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ScienceDirect Energy Procedia 35 (2013) 265 – 273

DeepWind’2013, 24-25 January, Trondheim, Norway

Multi-objective Design of a Modular Power Converter Based on Medium Frequency AC-Link for Offshore DC Wind Park Rene Barrera-Cardenasa,∗, Marta Molinasa a Department

of Electric Power Engineering, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway

Abstract The design of a modular power converter based on medium frequency AC-Link for offshore wind turbines regarding efficiency, power density and power to mass ratio is described in this paper. The impact of four design parameters in the three objectives is studied. Such parameters are the AC-AC converter topology, the number of modules, and the number of phases and frequency of the AC-link. Six topologies are investigated and compared. The conventional back-to-back (B2B) converter, the B2B with three phase squared wave output, the B2B with single phase squared wave output, the direct matrix converter, the indirect matrix converter, and the reduced matrix converter are the selected topologies. The Pareto surface of the three objectives is obtained for a set of design parameters. It has been found that a wind energy conversion system based on a medium frequency AC-link will lead the best trade-off between efficiency, power density and power to mass ratio when the AC-AC converter topology is the direct matrix converter, the AC-link frequency is selected around 1 kHz and the power per module is in the range of 2.5 to 4 MW.

© 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license. © 2013 Published by Elsevier Ltd. Selection and peer-review under responsibility of SINTEF Energi AS. Selection and peer-review under responsibility of SINTEF Energi AS Keywords: Modular converter, efficiency, power density, power-to-mass ratio, offshore power conversion

1. Introduction The proposed wind energy conversion system (WECS) to be analyzed is shown in Fig.1a. Each unit consist of a turbine, a permanent magnet synchronous generator (PMSG) with N insulated stars or a split drive train feeding N PMSGs, and a modular power converter consisting of N AC/DC converter modules. Converter for high power applications are usually build with N independent parallel sub-converters, each one with the rated power per module reduced by a factor of 1/N [1]. The AC/DC converter module based on medium frequency link considered in this paper, depicted in Fig.1a, is composed of three main stages: an AC-AC converter, a medium/high frequency transformer used as a galvanic isolation, and a full-bridge diode rectifier to convert the high frequency voltage waveform in a DC one. In addition, it is considered that the AC-AC converter has input/output filter in order to limited the current and DC-voltage ripple. This paper investigates the incidence of the AC-Link frequency and the number (N) of AC/DC converter modules in the efficiency, power density and power to mass ratio of the WECS of Fig.1a, when a total rated power of 10 MW is required. This analysis is carried out for six different potentials solutions based ∗ Corresponding

author Email addresses:

(Rene Barrera-Cardenas),

1876-6102 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.

Selection and peer-review under responsibility of SINTEF Energi AS

doi:10.1016/j.egypro.2013.07.179

(Marta Molinas)

266

Rene Barrera-Cardenas and Marta Molinas / Energy Procedia 35 (2013) 265 – 273

AC/DC

Module

AC/DC

Module

VSI

VSI

AC/DC

Module

B2B

Modular Power Converter

C

B2B

Nacelle

AC/DC Module AC Link

Input Vin, Pmod I, PFin

AC/AC

HFT

Converter

Output Vdc, Pmod Vdc

sw1

sw2

FBD

(a) Power conversion scheme for offshore wind turbine

(b) Conventional Back-to-Back converter

Figure 1: Wind Energy Conversion System to be optimized

on different AC-AC converter topologies. The conventional back-to-back (B2B) converter with sinusoidal waveform (B2B3p), the B2B with three phase squared wave output (B2B3pSq), the B2B with single phase squared wave output (B2B1p), the direct matrix converter (DMC), the indirect matrix converter (IMC), and the reduced matrix converter (RMC) are the six selected topologies to be investigated. The goal of the analysis is to show convenient converter solutions for each objective and detect the solutions with the better trade-off between the three objectives. 2. AC-AC Converter 2.1. Back-to-Back Topologies In this paper the conventional Back-to-Back converter (B2B) is the reference topology which is a wellestablished technology, see Fig.1b. It features a DC-link capacitor separating the two Voltage Source Inverters (VSI) and smoothing inductors. The space vector modulation is used for each VSI in the B2B. From the variation of the number of phases and waveform in the output, three converter topologies have been taken into account for this study: the conventional B2B with three-phase sinusoidal wave output (B2B3p), the B2B with three-phase squared wave output (B2B3pSq) and the B2B with single-phase square wave output (B2B1p). The characteristic of these topologies are briefly discussed below. The generator side VSI and the input filter are common in these three topologies (left side converter in Fig.1b). Since DC-Link capacitor provides decoupling in switching operation, the generator side converter can be operated at a different switching frequency than the transformer side converter. The values of inductance and DC-Link capacitance are designed according to recommendations presented in [1]: C B2B =

Iin,rms √ 4 2·VDC ·VDC · f sw1

LB2B =

VDC √ 12 2Iin ·Iin,rms · f sw1

(1)

where VDC is the relative peak to peak DC-link ripple (limited to 1%), VDC is the DC-Link voltage, Iin is the current ripple, Iin,rms is the rms value of the current input converter, and f sw1 is the switching frequency at generator √ side. The DC voltage itself is designed taking a 10% safety margin on the rated voltage (VDC = 1.1 2VLL ). The current input converter is defined in function of the power per module (Pmod = Ptotal/N ), line to line voltage (VLL ) and input power factor (PFin ) by: Iin,rms = √3VPmodPF LL in The B2B3p topology is shown in Fig.2a and this is the converter that is traditionally used for AC-AC conversion. An output LC filter is considered in order to obtain a smoothing waveform in the transformer input. Also, the switching frequency in the DC/AC converter (transformer side, f sw2 ) is setting it to be 6 times higher than the AC-Link frequency. The inductance and capacitance of LC-filter are designed with:

267


LC filter

(a) B2B-3p with sinusoidal output

(b) B2B-3p with square wave output

(c) B2B-1p with square wave output

Figure 2: Transformer side VSI of the three different B2B topologies

CSR LMC

VSI

LC filter

MC

LC filter

MC

CMC

CMC

CMC

(a) Direct Matrix Converter (DMC)

(b) Indirect Matrix Converter (IMC)

(c) Reduced Matrix Converter (RMC)

Figure 3: The matricial topologies

LOut f iler =

2 VLL 4·π· fcut ·Pmod

COut f ilter =

Pmod 2 π· fcut VLL

(2)

where fcut is the cut-off frequency, setting it to be 3 times lower than the switching frequency. Fig.2b shows the topology of the B2B3pSq. In this case, output filter is not required since the square wave output voltage is applied to the transformer winding. Also, in this topology the switching frequency in the transformer side converter ( f sw2 ) is equal to the AC-Link frequency. The converter topology analyzed for B2B1p is shown in Fig.2c. The main difference with the topology of the Fig.2a is that in this topology the output is square wave form, hence the output filter is not required. Also, a reduction in the number of switches is achieved and the switching frequency in the DC/AC converter (transformer side) is equal to the AC-Link frequency. The switching frequency in the AC/DC converter (generator side) is setting like in the three-phase case. 2.2. Matrix converter Topologies The DMC, in Fig.3a is a direct AC-AC converter which unlike the B2B does not feature a DC link capacitor saving volume and possibly increasing the lifetime. The IMC, in Fig.3b, possesses a DC link stage, however no capacitor. Both matrix converter topologies require a clamp circuit as they do not have a natural freewheeling path like the B2B converter in case of converter shutdown [2]. In this paper, the clamp circuit is not taken into account. The modulation scheme used for both matrix converters is the indirect space vector modulation explained in [3, 4]. Bidirectional switches are required in the DMC and in the Current Source Rectifier part of the IMC. The switching frequency is 6 times the frequency of the AC Link (transformer frequency). Input and Output LC filters are also needed to filter out switching frequency harmonics. The inductance and capacitance of LC-filter are designed with equation 2, for the input LC-filter the cut-off frequency is limiting to 20 times the supply frequency and the line-to-line voltage is reduced by a factor of 0.866 (nominal modulation value).

268

Rene Barrera-Cardenas and Marta Molinas / Energy Procedia 35 (2013) 265 – 273 Table 1: Parameters of passive component models (a) Parameters of inductor model based on inductors Siemens series

Parameter KV L1 KV L0 KρW Kρcore

AC-inductor 1.7 3.8 7.8 6.8

DC-inductor 1.6 0.2 9.4 0.57

Units dm3 dm3 kW/m3 kW/m3

(b) DC-Link and AC capacitor model parameters

Parameter

Units

KVC1 KVC0

m3 /F m3

DC-Link 1100 V 33 KV 1.944 1749 8.021e-5 7.22e-2

AC 780 V 17.13 2.627e-4

The RMC is a direct AC-AC converter with three-phase sinusoidal wave as input and single-phase high frequency square wave as output. This topology is widely studied in [5, 6, 7] and its basic scheme is shown in Fig.3c. Unlike the converter topology with DC-Link, the RMC needs to be protected against the over voltages that might be destructive for its semiconductor devices. The protection scheme (clamp circuit) presented in [5] is not considered in this study. The modulation schemes for RMC are presented and analyzed by [8]. The space vector modulation is considered in this comparison and its characteristics and parameters are taken from the authors report. The inductance and capacitance of input LC-filter are designed with equation 2. 2.3. Passive components models In this section the models for evaluation of power losses, volume and mass of the passive components i.e. the AC-inductor, AC-capacitance and DC-capacitance are shown. The inductor volume (VolL ) and mass (mL ) can be expressed in dependence of the stored energy (E L = 0.5 · L · I 2 ) [1] and is given by: 3/4 L · I2 + KV L0 mL = mρL · VolL (3) VolL = KV L1 2 where KV L1 ,KV L0 and mρL are proportionality constants regression found by taking data from references inductors and their values are shown in Table 1a. The inductors Siemens series Ref. 4EUXX are used to estimate these parameters for the AC-input filter [9]. The inductor power losses are divided in winding and core losses. In order to estimate winding and core losses in the inductor, the model presented in [10] is considered:

PW,L

⎤ ⎡ α L

1 f sw 2 ⎥⎥⎥ ⎢⎢⎢ 1 + 3 f1 ⎢ 2⎥ βL ⎥⎥⎥ · KρW · VolL ; and Pcore,L = 1 + f sw = ⎢⎢⎢⎢1 + · I I · Kρcore · VolL ⎥⎦ 4/3 ⎣ f1

(4)

where f sw is the switching frequency, f1 the fundamental frequency, ΔI is the current ripple in the inductor, αL , βL are the Steinmetz coefficients and KρW , Kρcore are power loss density in the winding and core, respectively. The volume of the capacitor is proportional to the stored energy. Then, the volume (VolC ) and the mass (mC ) scales for a given rated voltage linearly with the capacitance: VolC = KVC1 · C + KVC0

mC = mρC · VolC

(5)

where KVC1 , KVC0 and mρC are dependent of the rated voltage and the capacitor type (DC-Link or AC capacitors). The losses in the DC-capacitor are neglected due to the low equivalent series resistance of the used polyethylene capacitors. DC-Link capacitors are used in the B2B topologies at 1.1 kV and in the DC output filter of the power module at 33 kV. EPCOS is the reference manufacturer selected [11]. The capacitor of reference MKP DC B256xx-series are used to estimate the parameters of the equation 5. AC capacitors are used in the matrix topologies at rated voltage of 690 V. The 780 V capacitors of EPCOS reference MKP AC B2536-series are used to estimate the parameters and these are shown in Table 1b.

269


2.4. Power Semiconductors Losses The power semiconductor losses model presented in [12] is considered in order to evaluate the losses in the Insulated-gate bipolar transistors (IGBTs) and power diodes. 2.5. Volume and Mass of the power switch: Heat Sink and Thermal model The volume of a power switch is given by the IGBT/DIODE module itself and by the heat sink. The IGBT/Diode module volume (Volmod ) can be found in the datasheet of the power module, the heat sink volume (VolHS ) given by the aluminum structure volume (VolHS al ) and the fan volume (VolFAN ). The air forced heat sink is designed based on a fix fan velocity of 5 m/s and the fan volume is proportional to the aluminum structure volume. The aluminum structure volume (VolHS al ) is inversely proportional to the thermal resistance of the heat sink for a given fan velocity, and combining this model with the definition of thermal resistance (Rth = T/Ploss ) is obtained: KHS 1 KHS 1 + KHS 0 = Ploss,mod + KHS 0 (6) Rth T HS max where T HS max is the maximum allowable Heat Sink-to-ambient temperature, Ploss,mod is the total power losses of the power module (IGBT/Diode) and KHS 1 , KHS 0 and KHS f an are proportionality constants regression found by taking data from reference heat sink DAU series BF-XX and the axial fans SEMIKRON series SKF-3XX. In this paper KHS 1 = 0.215 K · dm3 /W, KHS 0 = 0.3 dm3 , KHS f an = 0.61 and T HS max is calculated based on thermal analysis of IGBT module with the model: (7) T HS max + T amb = 0.9 · T jmax + max Rth,igbt · Pigbt ; Rth,diode · Pdiode VolFAN = KHS f an VolHS al ; and VolHS al =

where T jmax is the maximum junction temperature of the semiconductor module, Rth,igbt , Rth,diode are the thermal resistance of the IGBT and diode respectively, and these values can be found in the datasheet of the device. In this paper, an ambient temperature T amb of 40 ºC is considered. The mass of the switch can be expressed by the density and volume of the each element (IGBT module, heat sink and fan): m ps = mρmod · Volmod + mρHS al VolHS al + mρFAN VolFAN

(8)

where the density values are calculated from the reference data sheet for each element. In this paper mρmod = 1187.2 Kg/m3 , mρHS al = 1366 Kg/m3 and mρFAN = 769.23 Kg/m3 . 2.6. Semiconductor Parameters In this study the IGBT devices selected to implement the power switches are the 1.7 kV IGBTs due to the generator output voltage considered is 690 V and the large availability of the components on the market [1]. The parameters of the Infineon IGBT modules IGBT4 technology FZXXR17HP4 have been used in this research. Since these parameters depend of the power rating of the IGBT module and use of a high power semiconductor module in low power applications is not cost-effective, then it is proposed to use a model of these parameters depending on the power rating. From the analysis of the parameters of Infineon 1.7 kV IGBTs, it is possible to determinate that the thermal and electrical resistances Rth,igbt/diode and Kcond2,(igbt/diode) are inversely proportional to the nominal current of the semiconductor, and the IGBT/Diode module volume (Volmod ) is directly proportional to the nominal current. The other parameters are constant for this type of technology. Then the follow models are proposed: Kcond21 KRth1 + Kcond20 ; Rth = + KRth0 ; Volmod = Kvolmod1 In + Kvolmod0 (9) In In Where In is the nominal current of the module and the constants are given in Table 2. On the other hand, the full bridge diode rectifier is implemented with power diodes for 3.3 kV applications. The parameters of the Infineon power diode modules IGBT3 technology DDXXS33HE3 have been considered. The same analysis have been done for these devices and the parameters are shown in Table 2. Kcond2 =

270

Rene Barrera-Cardenas and Marta Molinas / Energy Procedia 35 (2013) 265 – 273 Table 2: Parameters of the semiconductor modules

Parameters MOD. IGBT 1.7 kV Diode Power Diode

Kcond1 1.08 0.98 1.44

B2B1p

Kcond21 1.47 0.97 1.12

B2B3p

B2B3pSq

Kcond20 -5.4e-5 -1.7e-4 0

Matrix

Rth1 28.3 40.8 11

Rth0 0.009 0.008 0.008

RMC

KEon 3.1e-7 0 0

B2B1p

B2B3p

KEo f f /rr 4.7e-7 4.08e-7 7.22e-7

B2B3pSq

Matrix

Kvolmod1

Kvolmod0

2.69e-7

2.53e-4

3.4e-7

0.4e-3

RMC

4.4

Power Density [MW/m3]


4.5

4.2 4 3.8 3.6 3.4 3.2

1

10

4

3.5

3 1

Frequency [kHz]

10 Power [MW]

(a) Power Density versus frequency, at a power of 1(b) Power density versus power, at a frequency of 5 kHz MVA Figure 4: Example of the transformer power density for different topologies

3. Medium frequency transformer The losses, volume and mass of the transformer are evaluated based on the model presented in [12, 10]. An example of transformer power density with the design criterion for the six different converters and rated power of 1 MVA is presented in Fig.4a. Power density dependence to the input power is presented in Fig.4b for a frequency of 5 kHz. 4. Full Bridge Diode Rectifier The Full Bridge Diode Rectifier (FBD) is implemented by discrete diodes, and series connected diodes have been considered in order to fulfill the output voltage. A output filter (LC) to limit the DC-voltage and DC-current ripple is also considered. The parameters of the Infineon Diode modules are shown in Table 2 and they have been used in this research to estimate the power losses and volume with the models presented in section 2.4 and 2.5. The volume and mass of the DC capacitor and Inductor are calculated by methodology of section 2.3. 5. RESULTS The efficiency, power density and ratio of power to mass are evaluated for the complete modular power converter of 10 MW with different power per module (number of modules). The WECS shown in Fig.1a Table 3: Parameters and design constraints

Parameter Total Power Input voltage line-line AC-Link Freq. (ftr) Power per module (Pin) Input Power factor

Value 10 MW 690 V 500 Hz...10 kHz (0.2,...,10) MW 0.9

Parameter Max. current ripple (ΔI ) Max. DC-voltage ripple (ΔVdc) Temperature ambient Temperature Rise Magnetic Material

Value 20% 1% 40 ºC 70 K Metglas alloy 2605SA1

271


100

99

Efficiency [%]

Efficiency [%]

98 95

90

97 96 95

B2B3p

85

B2B3pSq

B2B1p

RMC

IMC

3

DMC

B2B3p

94 0

4

10

10

B2B3pSq

2

AC link freq. [Hz]

(a) Maximum Efficiency Vs. AC-Link frequency

B2B1p

RMC

4 6 Power per module [MW]

IMC

DMC

8

10

(b) Maximum Efficiency Vs. Power per module

P. density [MW/m3]

3

P. Density [MW/m ]

2.2 2

1.5

1

0.5

B2B3p

B2B3pSq

B2B1p

RMC

IMC

3

1.6 1.4

DMC

B2B3p

1.2 0

4

10

2 1.8

10

B2B3pSq

2

AC link freq. [Hz]

0.45

0.4

0.35

0.3 B2B3p

0.25

B2B3pSq

B2B1p

3

RMC

IMC

DMC 4

10

10 AC link freq. [Hz]

(e) Maximum Power to mass ratio Vs. AC-Link frequency

RMC

IMC

8

DMC

10

(d) Maximum Power density Vs. Power per module

Power to mass ratio [KW/Kg]


(c) Maximum Power density Vs. AC-Link frequency

B2B1p


0.4

0.35

B2B3p

0.3 0

B2B3pSq

2

B2B1p

RMC


IMC

8

DMC

10

(f) Maximum Power to mass ratio Vs. Power per module

Figure 5: Results of the optimization process regarding the three objectives

and the topologies for the AC-AC converter shown in Fig.1b, 2 and 3 are compared. The Parameters used in the comparison are indicated in Table 3. Configurations which do not correspond to the requirements in thermal and magnetic design are not shown. First, an optimization has been done in order to find the solutions with maximum efficiency in function of the AC-Link frequency and the power per module. Fig.5a and 5b show the solutions with maximum efficiency for each converter topology analyzed. From Fig.5a, it can be noted that the efficiency decreases exponentially with the AC-link frequency, then the AC-Link frequency for the solutions in this power range is expected to be fairly small since the switching losses are becoming dominant for higher values. The dependence of the efficiency with the power per module (or number of modules) is shown in Fig.5b. In general, it can be observed that matricial topologies are more efficient than topologies based on B2B technology. The solutions based on RMC are the most efficient for any power per module selected and any AC-link frequency. Fig.5c and 5d show the optimization results of the power density of the WECS for a range of AC-link frequencies and power per module, respectively. From Fig.5c, it can be observed that the more compact solutions are achieved with RMC topology and AC-link frequencies in the range of 2.5 kHz to 3.5 kHz, however with DMC topology very close power density results are obtained when the AC-Link frequency is in the range of 700 Hz to 900 Hz. Also, from Fig.5d, it can be noted that solutions with RMC and DMC present the more compact solution. The highest power density (2.185 MW/m3 ) is obtained for RMC

272


99

99 B2B3p B2B3pSq B2B1p RMC IMC DMC

98

B2B3p B2B3pSq B2B1p RMC IMC DMC

98.5 Efficiency [%]

Efficiency [%]

98.5

97.5 97

98 97.5 97 96.5

96.5 96

1.4

1.6 1.8 Power Density [MW/m3]

2

96 0.32

2.2

(a) Pareto Front: Efficiency Vs. Power Density

0.34

B2B1p

RMC

IMC

DMC

98.5 Efficiency [%]


B2B3pSq

99

B2B3p B2B3pSq B2B1p RMC IMC DMC

0.4

0.44

(b) Pareto Front: Efficiency Vs. Power to mass ratio

B2B3p

0.42

0.36 0.38 0.4 0.42 Power to mass ratio [KW/Kg]

0.38

98 97.5 97 96.5

0.36

0.6

96 1.4

0.34

1.6

1.7

1.8 1.9 2 3 Power Density [MW/m ]

2.1

2.2

(c) Pareto Front: Power density Vs. Power to mass ratio

0.5 1.6

1.8


0.4 2

2.2


(d) Pareto Surface for the three objectives

Figure 6: Decision Maps: Pareto Frontier Efficiency, Power Density and Power to mass ratio

topology with power per module of 4.2 MW and AC-Link frequency of 3 kHz. On the other hand, DMC topology based solutions present their maximum power density (2.144 MW/m3 ) when a power per module of 5.1 MW and AC-link frequency of 800 Hz are selected. The results of the optimization to maximize the power to mass ratio are shown in Fig.5e and 5f. From Fig.5e, it can be noted that the highest values of power to mass ratio are obtained for DMC topology and frequencies below 4 kHz. Also, IMC based solution presents good ratio of power to mass when the AClink frequency is limited to 1.6 kHz. For frequencies above 4 kHz, RMC based solutions are the dominant solutions. When a variation in the power per module is considered, DMC solutions are the dominant solution as it is observed from Fig.5f. The highest power to mass ratio (0.4213 KW/Kg) is obtained for DMC topology with AC-Link frequency of 1.2 kHz and power per module of 2.5 MW. The decision maps and Pareto frontier of efficiency, power density and power to mass ratio for the six topologies are shown in Fig.6. From the Pareto front of efficiency and power density (see Fig.6a), it can be noted that RMC topology presents the best trade-off when the power to mass ratio is not taken into account, however DMC topology presents results very closed to RMC topology in this subspace of design. On the other hand, it can be observed that in the subspace of efficiency and power to mass ratio (see Fig.6b), the DMC topology presents the best trade-off and there is a notable difference relative to the solutions based on RMC topology in terms of power to mass ratio. This difference can also be observed from Fig.6c when the subspace of power density and power to mass ratio is plotted. Finally, the Pareto surface for the three


objectives is shown in Fig.6d. From Fig.6d, it can be remarked that the dominant solutions are based on RMC and DMC topologies, however the best trade-off between the three objectives is obtained with solution based on DMC topology. 6. Conclusion In this paper, the design of modular power converters with medium frequency AC-Link for offshore wind turbines regarding efficiency, power density and power to mass ratio have been analyzed. The incidence of four design parameters (the AC-AC converter topology, the number of modules, the number of phases and frequency of the AC-link) in the three objectives have been studied. It has been found that WECS with the scheme of Fig.1a and based on DMC topology will lead the best trade-off between efficiency, power density and power to mass ratio when the AC-link frequency is selected around 1 kHz and the power per module is in the range of 2.5 to 4 MW (two or three modules). Acknowledgments Authors greatly appreciate support of the Norwegian Research Center for Offshore Wind Technology (NOWITECH) which is the source of funding for this research. This paper is part of a PhD project in Work Package 4. References [1] M. Preindl, S. Bolognani, Optimized design of two and three level full-scale voltage source converters for multi-MW wind power plants at different voltage levels, in: IECON 2011 - 37th Annual Conference on IEEE Industrial Electronics Society, IEEE, 2011, pp. 3634–3639. doi:10.1109/IECON.2011.6119899. [2] P. W. Wheeler, J. Rodriguez, J. C. Clare, L. Empringham, A. Weinstein, Matrix converters: a technology review, IEEE Transactions on Industrial Electronics 49 (2) (2002) 276–288. doi:10.1109/41.993260. [3] N. Holtsmark, M. Molinas, Reactive power compensation using an indirectly space vector-modulated matrix converter, in: 2010 IEEE International Symposium on Industrial Electronics (ISIE), IEEE, 2010, pp. 2455–2460. doi:10.1109/ISIE.2010.5637727. [4] N. Holtsmark, M. Molinas, Matrix converter efficiency in a high frequency link offshore WECS, in: IECON 2011 - 37th Annual Conference on IEEE Industrial Electronics Society, IEEE, 2011, pp. 1420–1425. doi:10.1109/IECON.2011.6119516. [5] A. Garces, M. Molinas, A study of efficiency in a reduced matrix converter for offshore wind farms, IEEE Transactions on Industrial Electronics 59 (1) (2012) 184–193. doi:10.1109/TIE.2011.2130502. [6] A. Garces, M. Molinas, Reduced matrix converter operated as current source for off-shore wind farms, in: Power Electronics and Motion Control Conference (EPE/PEMC), 2010 14th International, IEEE, 2010, pp. T12–149–T12–154. doi:10.1109/EPEPEMC.2010.5606549. [7] A. Garces, M. Molinas, Impact of operation principle on the losses of a reduced matrix converter for offshore wind parks, in: 2010 IEEE International Symposium on Industrial Electronics (ISIE), IEEE, 2010, pp. 2412–2419. doi:10.1109/ISIE.2010.5637529. [8] A. Garces, M. Molinas, Comparative investigation of losses in a reduced matrix converter for off-shore wind turbines, in: 5th IET International Conference on Power Electronics, Machines and Drives (PEMD 2010), IET, 2010, pp. 1–6. doi:10.1049/cp.2010.0096. [9] Siemens, Reactors and filters - catalog LV 60 (2010). URL [10] R. Barrera-Cardenas, M. Molinas, Comparison of wind energy conversion systems based on high frequency AC-Link: threephase vs. single-phase, in: Power Electronics and Motion Control Conference (EPE/PEMC), 2012 15th International, 2012, pp. LS2c.4–1 –LS2c.4–8. doi:10.1109/EPEPEMC.2012.6397416. [11] TDK, EPCOS product profile 2012, power capacitors for industrial applications and renewable energy (2012). URL [12] R. Barrera-Cardenas, M. Molinas, A simple procedure to evaluate the efficiency and power density of power conversion topologies for offshore wind turbines, Energy Procedia 24 (0) (2012) 202–211. doi:10.1016/j.egypro.2012.06.102. URL

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