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Output Voltage Stability of Series Connected Transformers for Isolated Auxiliary Supplies in Modular Medium Voltage Converter Systems

S. Fuchs, J. Biela

Power Electronic Systems Laboratory, ETH Zürich Physikstrasse 3, 8092 Zürich, Switzerland

mailto:[email protected]

Output Voltage Stability of Series Connected Transformers for IsolatedAuxiliary Supplies in Modular Medium Voltage Converter Systems

Simon Fuchs, Jurgen BielaLaboratory for High Power Electronic Systems (HPE)

Email: [email protected]

ETH Zurich, Switzerland

AcknowledgementsThis research is part of the activities of the Swiss Centre for Competence in Energy Research on the FutureSwiss Electrical Infrastructure (SCCER-FURIES), which is financially supported by the Swiss Innovation Agency(Innosuisse - SCCER program).

Keywords�LLC Resonant�,�Gate Driver�,�DC/DC Converter�,�Contactless Power Supply�

Abstract

MMC modules

Vo,1 M1

Vo,2 M2

Vo,N MN

Transformers

Diode recifiers

Cr

Rectangularvoltage source(e.g. full bridgeconverter)

Lm

Ls,s

Ls,c

Ls,c

Ls,p

Detailed view ofone transformer

VM,N

VM,2

VM,1

VM,1 ... N = 0 ... VM,max

Primarywinding

SecondarywindingCouplingwinding

Couplingwinding

Fig. 1: Simplified circuit diagramm of the auxiliary supply pro-posed in [1, 2, 3] applied on a (single phase) MMC. The greyparts (the coupling windings) are introduced in this paper. Note,that the stray and magnetizing inductances of the transformersare only shown in the detailed view below the circuit. Here,as the MMC modules are on floating potential, the insulationrequirement for the transformers is N ·VM,max.

A common way of implementing MV insulated gateand/or auxiliary power supplies for modular convert-ers is using series connected transformers in an LLCresonant converter topology. The LLC converter canresult in output voltage instabilities for differing con-stant power loads at the outputs when operated at reso-nance frequency. To balance the output voltages, a newbalancing concept based on a coupling between the in-dividual transformers is proposed, which guaranteesconstant output voltages even for highly unbalancedpower consumptions at the outputs. Based on the cou-pling, a concept for a modular MV isolated auxiliarysupply for modular multilevel converters (MMCs) ispresented. Simulation and measurement results for thepresented concept, as well as a comparison with alter-native output voltage balancing solutions are provided.

1 IntroductionIsolated power supplies for gate drives of MV convert-ers becomes more and more challenging due to the in-creasing blocking capabilities of modern power semi-conductor devices. Moreover, in multilevel topologies,multiple gate drives on different potentials on mediumvoltage level have to be supplied. In Modular Con-verters (for example the MMC) additional power isneeded on each module for the communication inter-face, voltage measurements, cooling fans, etc. There-fore, a modular structure of the auxiliary power supplysystem is desirable to allow the simple scaling of thewhole converter.For the MMC, there are basically two possibilities pre-sented in literature:

Output Voltage Stability of Series Connected Transformers for Isolated AuxiliarySupplies in Modular Medium Voltage Converter Systems

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EPE'18 ECCE Europe ISBN: 978 - 9 - 0758 - 1528 - 3 - IEEE catalog number: CFP18850-ART P.1Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE)

RACLm

OutputInput

Cr

Ls

Vprim Vsec

a) b) fsw / f0

Vsec / Vprim

0.6 0.8 1 1.2 1.4

0.6

0.8

1

1.2Pout

Unstableoperation points

Fig. 2: (a) Circuit of the LLC resonant converter without the power electronic input and output stage. (b) Transfer function ofthe output voltage of an LLC resonant converter around the series resonance frequency f0 with constant power load.

1. A DC/DC buck converter on every module with a very high input to output voltage ratio, supplied from themodule capacitor (cf. [4, 5]).

2. A dedicated insulated supply via medium frequency (MF) transformers [1, 2, 3] or via coupled air coils [6].

During the passive precharging of the MMC, the well known capacitor voltage balancing methods can not beapplied. Thus, when using option 1, the module capacitor voltage can diverge quite strongly during the start-up ofthe MMC, because of variances of the power consumption of the individual module control circuits and variancesof the module capacitances [7]. If the MMC start-up procedure needs to be fully controlled e.g. for safety reasons,variant 2 is the only feasible option.For other modular converter systems that do not contain a capacitor charged to a specific voltage range in eachmodule, as well as for gate drives or isolated measurement circuits, a dedicated auxiliary supply is the only feasiblesolution.Due to the high insulation requirements in MV applications, the stray inductance of MF-auxiliary-transformersbecomes rather high. Therefore, a compensation of the reactive power/the inductive voltage drop with a seriescapacitance usually applied, what results in an LLC resonant converter (cf. Fig. 1).In [2] the topology shown in Fig. 1 without the coupling windings (in grey) is presented as an auxiliary powersupply for MMCs. It consists of a series connection of MF-transformers (one per output/module) and a resonancecapacitor supplied with a rectangular voltage by a full bridge converter. The resulting LLC resonant converter is notoperated at resonance frequency and thus has problems regarding the output voltage variation given different loadsituations for the totally consumed power. Also variances in the magnetizing inductance Lm cause output voltagevariations between the individual outputs. Apart from that, instability problems for differing power consumptions(P1,...,N) of the individual secondary sides arise, as will be shown in this paper.In [3], a modification of this topology is presented. It employs a frequency controlled current on the primaryside to overcome the output voltage being dependent on the total output power of the setup. A buck converter(hysteresis voltage controller) on each secondary side is used to keep the individual output voltages within acertain range. Here, the hysteresis control may result in a high switching frequency causing relatively high lossesif the hysteresis band is too narrow. This output voltage controller can keep the output voltages equal if differentmagnetizing inductances are the reason for the output voltage differences. The mentioned problem of the outputvoltage instability for an unbalanced power consumption of the individual outputs is not solved by using outputvoltage converters.A solution to overcome the output voltage instability problem is to not connect the primary transformer windingsin series, but in parallel. With this configuration, each transformer must have its dedicated resonance capacitor tocompensate for the individual stray inductances resulting in the same resonance frequency for all parallel connectedtransformers. Feeding the resulting circuit with a rectangular voltage at resonance frequency will result in an outputvoltage of the individual secondary sides, which is independent of the output power. However, the mechanicalconstruction of such parallel connected transformers in a stacked modular converter setup is challenging and mostlikely results in a large volume, as will be shown in this paper.Alternatively, saturable transformers can also be used to keep the output voltages close together for unbalancedsecondary loads. However, as explained later, this solution results in comparably high core losses.Therefore, in this paper, the concept presented in [2] is modified by adding coupling windings to the neighbouring

transformers/outputs to each of the series connected transformers (cf. [8]) as shown in grey in Fig. 1. This causes amagnetic coupling of the transformer cores and keeps the flux in the cores within tight bands. The output voltagesare practically constant over a large operating range and for highly differing power consumptions at the individualoutputs without requiring any (closed loop) control or additional output converter system.The paper is organized as follows: In section 2, the properties of the LLC resonant converter relevant for this paperare shortly recapitulated and the general stability of the LLC resonant converter is analysed for constant powerloads. Hereafter, an explanation for the output voltage instability problem for the series connected transformerspresented in [1, 2, 3] is given and simulation results are shown. In section 3, additional windings that couple the


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series connected transformers are introducedand the stabilizing effect of the coupling windings is explained. Insection 4, simulation results for the system shown in Fig. 1 with the new coupling windings are presented. Anexemplary mechanical design for the proposed transformer setup applied as an MMC auxiliary supply is given insection 5. The required insulation properties are validated using FEM simulations. The results are shown in section6. Experimental results proving the output voltage balancing with the proposed coupling windings are presentedin section 7. In section 8, the mentioned alternative concepts (saturable transformers, parallel connection of theprimary) are shortly analysed and evaluated.

2 LLC resonant converterThe LLC resonant converter (circuit shown in Fig. 2(a)) is a good choice for realizing a DC/DC converter with afixed input and output voltage and a large output power range [9]. Fig. 2(b) shows the transfer function of such anLLC resonant converter around the series resonance frequency for different output power levels. A constant out-put/secondary voltage for all output power levels is only given at the series resonance frequency f0 = 1/(2π

√LsCr),

where the resonance capacitance Cr and the series inductance Ls have a total impedance of zero. If this impedanceis not zero, only a limited load range is possible. Too high output power levels result in an unstable operation pointbecause the reactive power needed for the transmission via the transformers is higher than the transferred activepower. The same behaviour is well known from transmission lines (cf. e.g. [10]).With a series connection of transformers resulting in multiple outputs as presented in [2, 3], a simultaneous loadpower change of all outputs does not change the output voltages. The simulation results in Fig. 3(a) verify the loadindependence of the output voltage(s) of the LLC resonant converter at resonance frequency, as the load step of alloutputs at t = 2ms does not have a relevant influence on the three output voltages.Nevertheless, as soon as less power is consumed by one of the outputs than the others, its output voltage begins toincrease and the output voltages of the other modules decrease. This can be seen in the simulation results in Fig.3(a) with the slight decrease (5W) of the output power level of output 3 at t = 3ms. The sum of all output voltagesis constant all the time, but the individual output voltages show an unstable behaviour.Fig. 3(b) illustrates the reason for this. With an operation at the resonance frequency, the individual modulesbehave like a voltage divider for the input voltage. The AC output voltages can be calculated as

Vo,AC,x =RAC,x ‖ jωLm

∑Nk=1 (RAC,k ‖ jωLm)

·Vin (1)

for each output x. The higher the output power Po,x for an individual output x with an output voltage Vo,x, the loweris the equivalent AC resistance RAC,x = V 2

o,AC,x/Po,x. The resulting lower output voltage leads to an even furtherdecreasing RAC,x, which results in a lower output voltage - an obviously unstable behaviour.This paper presents a concept avoiding the instability arising from the different load power levels for the individualoutputs.

RAC,1

RAC,2

RAC,N

Lm

Lm

Lm

Input N Outputs

Vo,AC,1

Vo,AC,2

Vo,AC,N

Vin

a) b)

Ip

Primary Current [A]

Output voltage of module 1 [V]



Output power levels [W]

t [ms]

Po,1 and Po,2Po,3

Vi,1

Vi,2

Vi,N

Fig. 3: (a) Simulation results for a setup with three transformers/outputs and the parameters given in Table I. (b) Equivalentcircuit for the operation at resonance frequency of the AC part of the circuit without the coupling windings shown in Fig. 1.


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a) b)

n=2

n=3n=1

n=1

Rm,c

Rm,s,p

Rm,s,sRm,s,s

Rm,s,s

n=2

n=3n=1

n=1

Rm,c

Rm,s,p

Rm,s,sRm,s,s

Rm,s,s

n=2

n=3n=1

n=1

Rm,c

Rm,s,p

Rm,s,sRm,s,s

Rm,s,s

Cr

Vo,1

Vo,2

Vo,3

1

2

3

Ip

Is,1

Is,2

Is,3

Ic,12

Ic,23

Primary winding

Secondary winding

Coupling windings

Primary current [A]

Coupling current (module 1 and 2) [A]

Coupling current (module 2 and 3) [A]

Ouput voltage of module 1 [V]



Output power [W]

t [ms]

Po,1Po,2

Po,3

Fig. 4: (a) Simplified schematic of the proposed auxiliary power supply for three modules including the magnetic model(blue). Rm,c is the magnetic reluctance of the core material, Rm,s,X is the magnetic reluctance for the stray path of the indi-vidual windings. The full bridge converter at the input is represented by a voltage source. (b) Simulation results for a threeoutput/transformer setup with coupling windings and with the parameters given in Table I.

3 Magnetic CouplingTo overcome the problems described in section 2, coupling windings are added to the topology (cf. Fig. 1). Theadditional windings couple each transformer with the one(s) next to it. Looking at Fig. 1, coupling neighbouredtransformers only results in a much lower insulation requirement for the coupling winding as coupling for examplethe transformer of module 1 with the one of module N, as the maximum potential difference between two neigh-boured modules is always lower than the maximum module voltage. When applying the coupled transformers toother medium voltage converter topologies, similar considerations have to be performed.Fig. 4(a) shows the resulting equivalent circuit for a system with three transformers/outputs. The cores are repre-sented by their magnetic equivalent circuit. It consists of

1. the magnetic reluctance of the core material Rm,c,2. the primary winding and its stray path represented by a magnetic reluctance Rm,s,p in parallel to the winding,3. the secondary winding and its stray path represented by Rm,s,s and4. the two coupling windings and their stray paths represented by Rm,s,c.

In case the stray paths are neglected, the principle of the voltage stabilization can be explained very simply withthe Faraday’s law. As the coupling windings are in parallel, the voltage vc,x−1,x across each coupling pair is thesame (cf. Fig. 4(a)). Given that this voltage is vc,x−1,x =−nc · dΦx−1/x/dt, the fluxes Φx−1/x in both cores have to beequal. Thus, the output voltage of each transformer vo,AC,x =−ns · dΦx/dt is also equal for all transformers.The influence of the stray paths on the output voltage can be mitigated with an appropriate resonance capacitancein series to the individual windings to compensate the stray inductance’s voltage drop. As pointed out in [2],the distance between the primary winding and the cores is most likely much bigger than the distance between thesecondary windings and the cores due to the high insulation requirements. The resulting primary stray path parallelto the primary winding has a much lower reluctance and thereby results in a comparably large stray inductance.The stray inductances for the secondary and coupling windings are a lot smaller because of the good couplingof the secondary and the coupling winding. Thus, they do not have to compensated without having a relevantinfluence on the output voltage stability. Nevertheless, if the stray inductances of the secondary and the couplingwindings are large, they would have to be compensated by a series resonance capacitance that results in the same


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Connectors ofcoupling windings to the next transformer

Ring cores

Plastic housing for ring cores

Aluminium tubesfor field shapinga) b)

Couplingwinding

Secondarywinding

Secondarywindingoutputs

Couplingwinding

Secondarywinding

2 ring cores KaschkeR 102/65,8/15 [11, 12]

Capacitor bank

Module mainboard

Primary winding

Fig. 6: Auxiliary supply for MMCs: (a) Exemplary setup with three modules. The current path of the primary winding isinserted as a dashed line with arrows showing the direction of the current. (b) One of the plastic housings with the cores andthe windings mounted. Note, that there are two secondary windings that are connected in parallel. The housing is filled withepoxy, which is not shown, such that the windings can be seen.

resonance frequency as the one formed by the stray inductance and the resonance capacitance on the primary side.

4 Simulation ResultsIn this section, simulation results for the proposed setup (cf. Table I) including coupling windings with threetransformers are presented. The simulations have been performed with PLECS employing basically the samecircuit as shown in Fig. 4(a). Fig. 4(b) shows the results. As already shown in the simulation without the couplingwindings, simultaneous load steps of all outputs at a time do not further influence the output voltages (power stepat t = 2ms). The change of about 700mV is because of the increased voltage drop across the diode rectifier ofthe individual modules. At t = 3ms, the output power level of output 3 steps to 10W again. The resulting outputvoltage change of the individual modules is less than 700mV and coupling currents start to flow. At t = 4ms, theoutput power of output 2 also steps down. Here, the output voltage change also stays within the 700mV range thatis to be expected due to the diode rectifier voltage drop.

5 Mechanical Setup

Maximumfield strengthin epoxy/wireinsulation3.6 MV/m

Maximumfield strengthin air:1.8 MV/m

Primary winding

Secondary windings

Couple windings

Fieldshapingtube

Fig. 5: Top view on the transformer with the highest secondarywinding potential (ϕs = 22.5kV) showing the field strength am-plitude resulting from a FEM simulation. Both the epoxy andthe wire insulation are assumed to have an εr = 4.5.

A general mechanical setup for an auxiliary supply forMMC converters has been introduced in [2]. In this pa-per, the coupling windings are inserted into this design.A three module MMC stack with the proposed auxil-iary supply can be seen in Fig. 6(a). The placementof the cores and the primary winding is shown againin Fig. 10(a). The setup ensures an insulation capa-bility of more than 22.5kV without partial discharges.For placing the coupling windings, some modificationsto the plastic core housing have been done, as addi-tional notches are needed. The plastic housings withthe cores and the windings are shown in Fig. 6(b).

6 Insulation DesignAs only two neighbouring transformers are coupledwith one couple winding, the insulation requirementfor the coupling wire is rather low. To verify the insu-lation design, FEM simulations have been performed.The field shielding tubes are on earth potential (ϕ = 0V). Looking at Fig. 1 the most critical transformer in an


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Table I: CONSIDERED PARAMETERS

Symbol Parameter Value Symbol Parameter Valuenp Primary winding, No. of turns 2 Po Power consumed per output 10 . . .30W

ns Secondary winding, No. of turns 3 N No. of transformers/outputs 3

nc Coupling winding, No. of turns 1 Vo Amplitude of DC output voltages 22 . . .23V

Rm,s,p Magn. reluctance of primary stray path 3 ·106A/Wb Vin Amplitude rectangular input voltage 45V

Rm,s,s Magn. reluctance of secondary stray path 3 ·108A/Wb Ls Stray inductance per transformer 1.32µH

Rm,s,c Magn. reluctance of coupling stray path 3 ·108A/Wb fsw Switching frequency 100kHz

Rm,c Magn. reluctance of cores [11, 12] 132kA/Wb Cr Series compensation capacitor 650nF

Vo,1

Vo,2

Vo,3

Cr

44 V100 kHz

Ic,12

Ic,23

12 V

V-R

eg

12 V

V-R

eg

t = 012 V

V-R

eg

14 Ω

14 Ω

7 Ω 7 Ω

Fig. 7: Simplified schematic of the experimental setup. The constant power sinks have been realized with switched voltageregulators feeding resistive loads with a constant voltage of 12V.

MMC application of the auxiliary supply is the one being on the highest potential referring to the potential of theshielding tubes. The highest potential of the secondary winding is below ϕs,max = 22.5kV. The coupling windingsare not connected to a specific potential. Their potential is somewhere between the potentials of the secondarywindings of the transformers they couple. Here, the maximum potential difference of two neighbouring secondarywindings is ϕs,x−ϕs,x−1 = 2.2kV, which is the maximum module voltage of the MMC.In Fig. 5, the resulting field strength amplitude is shown for the transformer with the highest potential. The max-imum field strength occurs between the secondary winding and the coupling winding(s) in the epoxy potting/theinsulation layer of the winding-wires (3.6MV/m) and near the field shielding tube of the primary winding in air(1.761MV/m). These values are in the same range as the ones given in [2], such that the setup is also free ofpartial discharges.

7 Experimental ResultsIn this section, experimental results for the proposed concept based on the mechanical setup shown in section 5are presented. The test case are three modules operating at a power consumption of 10W, where one of the threemodules performs a load step of 10W at t ≈ 0.

Output voltages [V] Coupling currents [A]

t [ms]t [ms]

V o1

V o2

V o3

Ic,12

Ic,23

Fig. 8: Experimental results for the proposed MMC auxiliary supply with 3 modules/outputs. The power consumptions of allmodules is approximately 10W. At t = 0 the third module performs a load step of 10W. As a result, coupling currents in bothcoupling windings start to flow.


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Vo,1

Vo,2

Vo,N

Diode recifiers

Cr

Rectangularvoltage source(e.g. full bridgeconverter)

Cr

Cr

b)a)

RAC,1

RAC,2

RAC,N

Lm

Lm

Lm

Input N Outputs

Vo,AC,1

Vo,AC,2

Vo,AC,N

Vin

Ip

Vi,1

Vi,2

Vi,N

Fig. 9: Possible alternatives for a stable output voltage with unbalanced loads: (a) Saturable transformer cores. (b) Parallelconnection of the transformers’ primary sides.

A simplified schematic of the experimental setup is shown in Fig. 7. Switched voltages regulators (buck converters)feeding a resistive load for each output are used to implement the constant power sinks modelling the powerconsumption of the MMC modules.Fig. 8 shows the waveforms of the three rectified secondary voltages Vo,1/2/3 and the two coupling currents Ic,12/23(cf. Fig. 4a)). The voltage of the module, which is performing the load step drops by 1.05V, where the othervoltages increase by 0.45V. Thus, the voltage balancing does not work as perfect as in the simulation resultsshown in section 4, but the stabilisation works fine. The voltage differences are rather small considering thatmodule 3 consumes twice the power of the other modules. Possible reasons for the voltage differences are (possiblydiffering) resistive and inductive elements in the secondary and coupling windings which are not included in thesimulation model (results presented in section 4).When the load step of module 3 occurs, the coupling currents start flowing at the same time. Just like in thesimulations, current Ic,23 through the coupling winding closer to the module that consumes more power than theothers is approximately twice the current Ic,12 through the other coupling winding.

8 Alternative ConceptsAs mentioned in the introduction, there are alternative solutions balancing the output voltages. In the following,two promising variants are shortly discussed and compared to the proposed setup.

Saturable TransformersA possibility to stabilize the output voltages of the series connected transformers under unbalanced secondaryloads is to use saturable transformers. Fig. 9a) shows the equivalent circuit for the operation of the resonant tankat resonance frequency, where the impedances of the capacitor and the leakage inductance cancel each other. Asexplained in section 2, a higher output power of output k compared to the other outputs x results in a permanentlydecreasing RAC,k. Therefore, also the part of the primary voltage Vi,k of output k decreases as shown in (1). Forall other outputs x, the voltage Vi,x increases. If the transformers would now saturate at a specific voltage, theimpedance of the magnetizing inductances Lm,x would drop, such that the absolute value of the parallel connec-tion’s (ωLm,x‖RAC,x) decreases. As a result, the voltage stops to increase for the outputs x and therefore also stopsto decrease for output k.This may seem elegant and uncomplicated, but note that it requires the ’normal’ operation close to saturation.When operating a core material close to (or even within) its saturation, high hysteresis losses have to be expected.To provide an example, the losses with the cores used in the proposed setup (data provided in [11]) are evaluatedfor an operation close to the saturation: Compared to the operation point for the proposed system (< 50mT), a fluxdensity of 200mT, results in more than 20 times more core losses.

Parallel ConnectionOne could overcome the instability problem by avoiding the series connection of the primary transformer windingsand connect them in parallel instead. In Fig. 9b) the schematic for this alternative is shown. Each transformer nowrequires a dedicated resonance capacitor to compensate for possibly different resonance frequencies due to differentleakage inductances of the individual transformers. Alternatively with good matching of all leakage inductances,


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Primary windings

Ring core

Secondary windingMechanicalfixationof the field shaping tubes

Aluminium fieldshaping tubes

b)

Primary winding(current direction marked)

Ring cores

Plastic housing for ring cores

Mechanical fixationof the field shaping tubes

Aluminium field shaping tubes

a)

97 mm 97 mm

97 mm

67 mm

97 mm

z

xy

Fig. 10: (a) Front view of the proposed series connection’s mechanical setup. Note, that the 67mm of height are mostlydefined by the module hardware (IGBTs) and is does not represent the minimum possible for the auxiliary supply concept. (b)Exemplary mechanical setup for the parallel connected primary windings. The module stack would be placed behind the shownassembly (in y-axis direction/where the secondary winding is shown). The construction achieves the field distribution as theproposed series connection. Therefore, the distance of each core to the field shaping tubes is kept at 97mm.

one can also supply all parallel transformers from one resonance capacitor with N times larger capacitance value.The input voltage is only 1/N compared to the series connection of N transformers, therefore the current fed bythe rectangular voltage source must be N times higher.Fig. 10b) shows a possible mechanical setup for such parallel connected transformers. In Fig. 10a) the front viewof the proposed series connection setup is shown to compare the mechanical outlines with the parallel connectedalternative. In order to achieve similar insulation characteristics, each transformer now needs two field shapingtubes shielding the primary winding. If the secondary sides should be arranged in a similar way as shown for theseries connected primary sides (cf. section 5), the cores also have to be arranged displaced to each other (alongthe x-axis) in order to decrease the height difference required in between the individual secondary sides/modules.It is assumed that for keeping the electrical field distribution equal to the one shown for the series connectionsetup (in section 6) the distance between the individual field shaping tubes and the transformer cores/secondarywindings has to be kept. Thus the required height (size in z-axis direction as denoted in Fig. 10b)) per module is97mm instead of 67mm resulting with the proposed series connection setup (Fig. 10). The depth (size in y-axisdirection) of the series connection setup is dominated by the outer core diameter (110mm), where the depth of theparallel connection setup consists of half of the outer core diameter plus the distance between two field shapingtubes, resulting in 148mm. The width (size in x-axis direction) of the series connected setup is 194mm, where, ifa 67mm slot width per core is kept, the parallel setup has a minimum width of 134mm (2 ·67mm). The requiredboxed volume per output is thus 1.924dm3 for the parallel and 1.326dm3 for the series connected setup, whichcorresponds to a volume increase of about 45%. Apart from that, the mechanical complexity is much higher dueto the many field shaping tubes and the displacement of the cores.

9 ConclusionIn this paper, the output voltage stability problems resulting from the series connection of transformers in an LLCresonant setup have been analysed. A novel coupling method using two coupling windings per output to coupleeach transformer to its neighbour(s) is introduced and simulation results proving the concept are shown. Thecoupling guarantees output voltage stability for any load distribution at the individual outputs. An exemplarymechanical setup using the introduced topology as an auxiliary power supply for MMCs is presented. Based onthis, the insulation design is verified by FEM simulation (experimental results for a very similar setup are presentedin [2]). Measurement results are presented which show that the coupling windings keep the output voltages stablebut cannot balance them perfectly due to parasitics in the secondary and coupling circuits (5% output voltagedifference compared to 3% in the simulation). Finally, two alternative solutions have been shortly analysed as abenchmark. In comparison to the proposed solution, they either result in very high losses in the transformers orrequire significantly more space and mechanical construction effort.


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References[1] F. F. A. Van Der Pijl, J. A. Ferreira, P. Bauer, and H. Polinder, “Design of an inductive contactless power

system for multiple users,” in IEEE Industry Applications Conf. 41st IAS Annual Meeting, 2006.

[2] D. Peftitsis, M. Antivachis, and J. Biela, “Auxiliary power supply for medium-voltage modular multilevelconverters,” in 17th Europ. Conf. on Power Electronics and Applications (EPE, ECCE-Europe), 2015.

[3] J. Gottschlich, M. Schafer, M. Neubert, and R. W. D. Doncker, “A galvanically isolated gate driver with lowcoupling capacitance for medium voltage SiC MOSFETs,” in 18th Europ. Conf. on Power Electronics andApplications (EPE, ECCE-Europe), 2016.

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[6] B. Wunsch, J. Bradshaw, I. Stevanovic, F. Canales, W. V. der Merwe, and D. Cottet, “Inductive power transferfor auxiliary power of medium voltage converters,” in IEEE Applied Power Electronics Conf. and Exposition(APEC), 2015.

[7] L. Luo, Y. zhang, L. Jia, and N. Yang, “A novel method based on self-power supply control for balancingcapacitor static voltage in MMC,” IEEE Trans. on Power Electronics, vol. 33, no. 2, pp. 1038–1049, Feb.2018.

[8] S. Fuchs and J. Biela, “Transformatorenanordnung und isolierter Konverter mit mehreren galvanisch getren-nten AC- und/oder DC-Ausgangen fur einen grossen Leistungsbereich,” Swiss Patent P4506CH, Dec 12,2017.

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[10] A. Tiranuchit and R. J. Thomas, “A posturing strategy against voltage instabilities in electric power systems,”IEEE Trans. on Power Systems, vol. 3, no. 1, pp. 87–93, Feb 1988.

[11] Kaschke Components. (2018, May) Ringkern R 102/65,8/15. [Online]. Available: http://www.kaschke.de/fileadmin/user upload/documents/datenblaetter/Ringe/R102a.pdf

[12] ——. (2018, May) Material K 2006. [Online]. Available: http://www.kaschke.de/fileadmin/user upload/documents/datenblaetter/Materialien/MnZn-Ferrit/K2006.pdf


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Output Voltage Stability of Series Connected Transformers ... · creasing blocking capabilities of...

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