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Transformer inrush current mitigation concept for hybrid transformers

J. Burkard, J. Biela Power Electronic Systems Laboratory, ETH Zürich

Physikstrasse 3, 8092 Zürich, Switzerland

mailto:[email protected]

Transformer Inrush Current Mitigation Concept for

Hybrid Transformers

J. Burkard and J. Biela

Laboratory for High Power Electronic Systems (HPE)

ETH Zurich, Physikstrasse 3, CH-8092 Zurich, Switzerland

Email: [email protected]

Abstract—Large inrush currents can occur when power trans-formers are connected to the grid. In the past, a wide rangeof countermeasures has been developed whereof the applicationof power electronic converters recently received more attention.With hybrid transformers combining a conventional transformerwith a power electronic converter, the elimination of inrushcurrents can be realized without considerable additional hard-ware effort. For such hybrid transformers, a novel mitigationprocedure is proposed, which is based on the injection ofa synchronous core flux before the transformer is connectedto the grid. In addition, dedicated demagnetization strategiesapplicable for grid connected converters with filter elements arepresented. The effectiveness of the proposed procedure is verifiedby comprehensive simulations and a comparison to a conventionalmethod.

I. INTRODUCTION

When a power transformer is connected to the grid, a large

inrush current could occur due to the saturation of the core.

These large inrush currents impair the transformer lifetime, the

grid power quality as well as the functionality of grid protec-

tion devices. Different concepts to reduce such inrush currents

have been developed, which can be subdivided according to

the applied mitigation mechanism as shown in Fig. 1.

Group �: By inserting current limiting elements such as

resistors or reactors in series to the transformer windings,

a limitation of the inrush current could be obtained [1],

[2]. Furthermore, a voltage source inverter (VSI) controlled

as a dynamic resistor could be applied [3]. To avoid high

conduction losses, the damping elements have to be bypassed

during normal operation which requires additional switches.

Group �: In theory, inrush currents could also be eliminated

by connecting the transformer windings of the three phases

sequentially to the grid at optimal points in time which are

defined by the residual core flux. However, circuit breakers

(CBs) with independent drives for each phase as well as the

measurement of the residual core flux would be necessary

[4]. Furthermore, the scatter of the CB closing time and

flux measurement errors deteriorate the effectiveness of this

approach [5].

Group �: In [6] a VSI is connected in parallel to the trans-

former windings in order to compensate the inrush current by

injecting a current of opposite direction. With this approach,

however, excessive currents and mechanical stresses of the

transformer windings cannot be avoided.

Inrush current mitigation concepts

Inrush currentdamping

Core flux manipulation

Inrush current compensation

Resistor

Optimizedclosing time

Reactors ShuntVSI

Constant preflux

Synchronous preflux

Series VSI

1 2 3 4

Fig. 1: The inrush current mitigation methods can be subdivided into four

groups based on the underlying mitigation mechanism. In this paper, the focus

is on the synchronous prefluxing concept.

3

MVLV

Aux

LV gridLFTHT

MV grid3

VMV

VLV

3

AC

DC

DC

ACVser

Seriesconv. A

Shunt conv. B

3

Back-to-back conv.

Fig. 2: Schematic of a HT allowing the control of VLV as well as active and

reactive power flow.

Group �: The last group of mitigation techniques relies on

the manipulation of the core flux before the transformer is

magnetized. This includes the demagnetization of the core

[7] and the injection of a defined constant residual flux by

means of a precharged capacitor. For an effective elimination

of inrush currents, the injection of a constant preflux must be

combined with an optimized grid connection instant (see group

�), which entails the mentioned requirements for the CBs [8],

[9]. As an alternative solution of group �, the application of

power electronic converters allows the injection of a sinusoidal

preflux whereby inrush currents could be completely avoided.

In contrast to the aforementioned methods, this so called

synchronous prefluxing method does neither require additional

switches nor flux measurements while the effectiveness is

independent of the closing time scatter of the CBs. Therefore,

the power electronics based synchronous prefluxing method

is the most promising solution of the mentioned alternatives.

Although the basic operation principle has been studied in

the literature, the high additional cost of the converter has

prevented a wide practical application so far [10], [11].

For hybrid transformers (HTs), which combine a power elec-

tronic converter and a conventional low frequency transformer

(LFT) to enhance grid controllability, the implementation of

Transformer Inrush Current Mitigation Concept for Hybrid Transformers BURKARD Johannes

EPE'17 ECCE Europe ISBN: 9789075815276 et CFP17850-ART P.1© assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE)

Fig. 3: 3D CAD rendering of a possible assembly of the converter and the

LFT. The HT interfaces the 20 kV MV and 400 V LV grids with a calculated

total HT system efficiency of 98%.

the synchronous prefluxing technique can be realized without

considerable additional effort. Fig. 2 shows a possible config-

uration of a HT as presented in [12]. The major share of the

power is transferred via the LFT whereas the converter is only

rated for a fraction of the LFT power (typically 10%). Thus,

the high efficiency and robustness of the LFT and the flexibility

of the power electronic converter are combined. The back-to-

back converter of the HT consists of a shunt connected side B

and a series connected side A (Fig. 2). Besides the control of

the voltage VLV as well as the active and reactive power flow,

HTs also allow active filtering and load balancing in order to

ensure a high power quality even in the presence of a high

share of renewable energy sources. Due to the connection of

converter side B to an auxiliary (Aux) winding of the LFT, a

direct magnetization of the core is possible. Fig. 3 depicts a

3D CAD rendering of a possible assembly of the converter and

the LFT. Further information about the HT concept is available

in [12] and [13].

In this paper, a novel inrush current mitigation procedure

based on synchronous prefluxing is presented which allows the

elimination of inrush currents without considerable additional

hardware effort if applied to HTs. After the presentation of

the simulation model of the HT in section II, a conventional

mitigation method is investigated as a benchmark case in sec-

tion III. The concept of the synchronous prefluxing technique

and the proposed procedure including a novel demagnetization

method are explained in section IV. Section V proves the

effectiveness of the presented procedure to eliminate inrush

currents by comprehensive simulations.

II. SIMULATION MODEL

The considerations of this paper are exemplarily carried out

for a 400kVA three-phase HT fed from a 20kV MV grid,

which supplies a radial 400V LV grid. This HT consists

of a 400kVA LFT combined with a 40kVA back-to-back

converter. The specifications of the HT are given in Tab. I.

The simulation model including an equivalent circuit of the

LFT is shown in Fig. 4. The controller for the magnetization

and demagnetization shown in this figure measures the MV

and Aux side transformer voltages VMV and VAux as well as

3

3

3

MV gridAC

De-/magnetizationcontrol

VMV

External turn-on/off

LV loadLFT model (Fig. 5) LV CBMV CB

DCVDCVAux

Conv. BLCL filter

CFB

LFBAuxLV

MV

AC

DCConv. A

3

3

Fig. 4: The simulation model of the HT includes an equivalent circuit of the

LFT as detailed in Fig. 5, CBs on both transformer sides, a controller and

the shunt connected converter B. Converter A is not required for the inrush

current mitigation and is therefore shown in grey.

TABLE I: Parameters for the model of the 400kVA, 20kV-400V HT.

Parameter Value

Sn 400kVA

VMV, VLV, VAux 20kV, 400V, 28V, RMS, line-line

Controllability ±10% of nominal VLV, P and QSconv, Vser 40kVA, 23V

Topology 2-level VSIs, back-to-back

DC-link 60V, 6.8mF

LFB1, CFB, fsw 10 μH, 100 μF, 50 kHz

the DC-link voltage VDC and controls converter B as well as

the MV and LV grid circuit breakers (MV CB and LV CB).

An external turn-on/off signal starts the process which connects

and disconnects the HT to and from the grid. Since converter A

of the HT does not influence the presented mitigation methods,

it is not considered in this model and the load of the LV

grid is directly attached to the star-connected LV winding

for simplicity. For the demagnetization and magnetization of

the transformer core, the DC-link of the converter has to be

powered by an external power supply (e.g. a battery) which is

represented by the voltage source VDC. Furthermore, an LCL-

filter consisting of the boost inductor LFB, the filter capac-

itor CFB and the Aux side transformer leakage impedance,

represented by a magnetic reluctance within the transformer

model, is considered (cf. Fig. 4). The LCL-filter is damped by a

capacitor-resistor branch in parallel to CFB designed according

to [14].

In order to simulate inrush currents, the transformer core is

modeled by saturable reluctances with hysteresis. The reluc-

tances Rc,o and Rc,m represent the outer and middle limbs as

shown in Fig. 5. The transformer limbs and the associated

windings are denoted as 1, 2 and 3 for the left, middle and right

limb. Since the residual flux Bres at the beginning of the simu-

lation cannot be directly set with the used simulation software,

an initial voltage pulse is applied to the transformer windings

to magnetize the core to different flux levels before the inrush

mitigation methods are tested. The leakage inductances on the

MV, LV and Aux side of the transformer are represented by

the reluctances Rσ,MV, Rσ,LV and Rσ,Aux. For validating the

transformer model, the MV line currents of phase 1 are given

in Fig. 6 for the case that the transformer is connected to the

MV grid without and with a residual core flux while the LV



Rc,oRc,oRc,m

R RR

RRR

Phase 1 Phase 2 Phase 3

R RR

Fig. 5: In the LFT model, the saturable reluctances Rc,o and Rc,m represent

the core limbs. The leakage reluctances are modelled by Rσ,MV, Rσ,LV and

Rσ,Aux. The windings attached to the left, middle and right limb are denoted

as phase 1, 2 and 3.

t in s 0

4

8

12

16

0.2 0.4 0.6 0.8 1

I MV

,1 /

Î n

No res. fluxWith res. flux

Fig. 6: Simulated ratio of the MV line current of phase 1 IMV,1 to the peak

value of the nominal current In for a typical connection of the LFT to the MV

grid with and without residual flux. No load is connected to the LV windings.

For the simulation with residual flux, an initial voltage pulse is applied to

magnetize the core limbs

TABLE II: Parameters of the 400kVA LFT model.

Parameter Value

Core material Cold rolled grain oriented steel

Sat. flux density Bsat 1.7 T

Rem. flux density Brem 1.5 T

Nom. flux density Bn 1.26T = 0.75 ·Bsat

Sat. field strength Hsat 127 Am

Coerc. field strength Hc 40 Am

Core cross sectional area Ac 0.025m2

Length of inner & outer limbs 0.5 m, 1.2 m

Wind. losses MV, LV, Aux 2800 W, 1500 W, 500 W (full load)

Core losses 600 W

Number of turns NMV = 2858, NLV = 33, NAux = 4

Short circuit imp. MV-LV zSC,MV−Aux = 4%

Short circuit imp. MV-Aux zSC,MV−Aux = 6.5%

circuit breakers CBLV are open. There, the specifications of

the LFT given in Tab. II are used. With the given transformer

model, the peak inrush currents are more than 10 times larger

than the peak line current during nominal operation In which

is in accordance with amplitudes for inrush currents published

in [5] and [15].

t in ms0 10 20 30 40 50 60

-1

0

1

2 Connection ofremaining phases

Connection offirst phase

-2

Initial magn. to set Bres

B in

T

Phase 2

Phase 1

Phase 3

Fig. 7: Prospective (dashed) and actual (solid) flux densities if the phases are

energized at the ideal time instants with the ”rapid closing strategy” [4]. After

the connection of the first phase, the residual fluxes in the remaining phases

are also modified.

III. CONVENTIONAL INRUSH MITIGATION CONCEPT

Inrush currents are caused by core saturation and occur if the

residual core flux Φres prior to the magnetization deviates from

the ideal DC offset-free prospective flux Φpros defined by the

applied winding voltage vwind. To avoid inrush currents, (1)

has to be satisfied at the point in time tmag when the winding

is connected to the grid. N is the number of turns of the

considered transformer winding.

Φres!= Φpros =

1

N

∫ tmag

0

= vwind︷︸︸︷V · cos(ωt)dt (1)

As a benchmark case, the optimized closing time mitigation

concept (cf. Fig. 1 �) is analysed in the following. The

performance of the proposed inrush current mitigation concept

is then compared to this conventional concept in section V.

As a first step of the optimized closing time method, the

winding attached to the limb with the lowest Φres is connected

to the MV grid when the residual and prospective fluxes

of this phase are equal, so that no inrush current occurs.

Thereby, the flux distribution of the other two limbs is also

modified. For the connection of the two remaining phases, the

so-called ”rapid closing strategy” is applied in the following.

With this strategy, the remaining phases are connected at the

next instant when the measured and prospective flux of these

phases coincide [4]. Since the optimal connection time tmag

depends on Φres, a flux measurement is required which can

be achieved by continuously measuring and integrating the

winding voltages. In Fig. 7, the waveforms of the prospective

and actual transformer flux densities are shown for the ideal

case which leads to a magnetization without inrush currents.

However, the non-ideal measurement of the flux and the clos-

ing time scatter of the CBs impede the ideal energization of the

transformer, so that the inrush currents cannot be completely

avoided. To simulate the performance of this concept including

the non-idealities, the same model as described in section II

can be used but the converter, the filter and the LV grid

are removed. In the considered case, the flux measurement



0 0.5 1 1.5tdelay in ms

0

1

2

3

4

I inru

sh /

Î n

offset / n:10% 8% 6% 4% 2% 0%

Fig. 8: Simulated inrush currents resulting with the conventional optimized

closing time method as a function of the MV CB closing time delay tdelay

reassembling closing time scatter. The relative flux measurement uncertaintyΦoffset

Φnis used as a parameter.

uncertainty is exemplarily reproduced by measuring the ideal

fluxes of the three limbs and adding flux offsets of +Φoffset

and −Φoffset to the ideal measurements of phases 1 and 3. By

delaying all MV CB closing signals by tdelay, the worst-case

closing time scatter is emulated. The adverse effect of these

non-idealities depends on Bres and on the connection instants.

For some points on the flux curve, an unprecise closing leads

to comparably high differences between the actual and the

prospective flux as has been illustrated in [4]. Fig. 8 depicts the

resulting inrush currents for the worst-case Bres, closing time

delays of 0 ≤ tdelay ≤ 1.5ms and measurement uncertainties

of 0 ≤ Φoffset ≤ 0.1 · Φn. According to [16], CBs specially

designed for this mitigation concept achieve a closing time

scatter below 1 ms. Hence, inrush currents of up to 2 · In have to

be expected if a flux measurement error below 6% is assumed.

In comparison to the connection without any inrush mitigation

method, the maximum excited currents can be significantly

reduced which proves the good performance of this method.

However, the CBs require independent drives for each phase

and a special mechanical design to minimize closing time

scatter. Furthermore, a precise measurement and integration

of the MV grid voltage is necessary to indirectly measure the

core fluxes.

IV. INRUSH CURRENT MITIGATION CONCEPT FOR

HYBRID TRANSFORMERS

In contrast to methods aiming for a connection at the optimal

time instant, the synchronous prefluxing method (cf. Fig. 1

�) induces an AC flux equal to the prospective flux prior to

the transformer connection. After prefluxing, the transformer

can be connected at any time without exciting inrush currents

so that no special CBs with reduced closing time scatter and

independent drives for each phase are needed.

A flowchart of the proposed mitigation procedure for HTs is

shown in Fig. 9. Before the individual steps are detailed in

section IV-A and section IV-B, the basic principle is explained

CBs off, Bres= 0

Close MV CB

Conv. B off

Close LV CB

Start HT control

Nominal HT operation

Open LV CB

Open MV CB

Prefluxing Demagnetization

Conv. B on

Stop HT control

Initial demagnetization (Fig. 14)

Turn

-on Turn-off

Fig. 9: Procedure of the proposed inrush current mitigation method. Before

the injection of a synchronous flux is possible, a demagnetization of the

core is required. If the HT is connected for the first time or after a sudden

disconnection, an initial demagnetization as detailed in IV-B2 has to be

performed.

in the following. At the beginning of the turn-on process, it is

assumed that the LFT is in the demagnetized state (Bres = 0).

The converter side B of the HT is used to inject a synchronous

preflux by modulating a three-phase voltage in phase with

the medium voltage grid voltage VMV as will be discussed

in section IV-A. Subsequently, the MV CB is closed and the

semiconductors of converter B are turned off which results in

a commutation of the magnetizing current from the converter

to the MV grid. Since (1) is fulfilled, no inrush currents are

excited. After closing the LV CB to supply the load, the

control of the back-to-back converter can be started which

includes synchronizing to the Aux winding voltage with a

PLL and generating the required output voltage Vser. When

the HT is turned off, the steps are repeated in reversed order.

After shutting down the HT control and opening the LV

CB, converter B applies a three-phase voltage synchronous

to VMV across the Aux windings. By opening the MV CB,

the magnetizing current commutates to the converter and a

demagnetization is performed resulting in Bres = 0 as will be

described in subsection IV-B1. If the HT should be connected

to the grid for the first time or after a sudden disconnection,

a dedicated demagnetization has to be performed before the

prefluxing is started as will be described in subsection IV-B2.

A. Synchronous Prefluxing with Power Electronic Converter

Fig. 10 shows a prefluxing strategy which is applied at the

beginning of the turn-on process when the transformer is in

the demagnetized state and all CBs are open (cf. Fig. 9). At

time t0, the converter starts to generate a three-phase voltage

in phase with VMV with linearly increasing amplitude which

induces a three-phase, DC offset-free flux in the transformer

core. At t1, the winding voltages reach the nominal value and

the core flux is identical to the prospective flux so that the

MV CBs can be closed without inrush currents at t2. This



H

B

V in

p.u

.-1

0

1

t

in p

.u.

-1

0

1

t

t1

t0

t0 t2

t1

t2


Fig. 10: Ramp prefluxing concept: Starting from the demagnetized state, the

three-phase Aux winding voltage is ramped up to the nominal value whereafter

the MV CBs are closed.

method is denoted as ”ramp prefluxing” in the following. The

slope of the voltage ramp is a compromise between speed and

effectiveness. For a fast increase of the voltage amplitude, an

accurate prefluxing cannot be ensured since the positive and

negative peak flux values differ significantly due to the ramp

up. However, for a slow increase, the required time and losses

increase.

An alternative magnetization strategy denoted as ”sequential

prefluxing” is depicted in Fig. 11 and makes use of the three-

limb construction of common distribution transformer cores.

If a flux is injected in the middle limb of the core, it splits

equally to the two outer limbs as long as the core does not

saturate. At t0, the prospective flux of the middle limb is

assumed to be zero which coincides with the actual flux since

the transformer is demagnetized. During the following quarter

period between t0 and t1, the converter applies v1 = v3 =− 12 v2

to the Aux windings where the amplitude of v2 is equal to the

nominal value. At t1, the actual and prospective fluxes of all

phases coincide and the converter applies the nominal voltages

to all windings. The MV CBs can be closed without inrush

currents at t2. With this method, the prefluxing is achieved

within a quarter of a grid period which results in a very

low energy consumption. Due to the considered LCL filter

of the back-to-back converter (Fig. 4), oscillations are excited

by the steps of the converter output voltage. For typical filter

designs, however, the occurring overvoltage does not exceed

the winding withstand voltage defined by LFT standards (e.g.

IEC 60076-3, [17]). In [18], the effectiveness of the sequential

prefluxing strategy is experimentally verified for a UPS system

feeding multiple transformers.

For both the ramp and the sequential prefluxing method, a mea-

surement of VMV is required for synchronizing the converter

output voltage. Due to the comparably low magnetization

currents, the voltage drop across the boost inductor LFB can

be neglected during prefluxing and a simple open-loop control

is sufficient.

H

B

V in

p.u

.

-1

0

1

t

in p

.u.

-1

0

1

t

t1 t2

t1

t2

t0

t0


Fig. 11: Sequential prefluxing concept: Injection of a synchronous preflux by

sequentially magnetizing first the middle and then the outer core limbs. The

prospective fluxes and voltages are shown in dashed lines.

B. Demagnetization with Power Electronic Converters

In order to induce a defined synchronous flux in the trans-

former core during turn-on, the residual flux of each limb has

to be known. By demagnetizing the transformer before the

prefluxing step, a defined initial state with Bres = 0 is reached

without an additional flux measurement.

In [7] and [19], a demagnetization method is presented which

uses a rectangular voltage source with constantly decreasing

period or amplitude to demagnetize the transformer. The

current is measured and triggers a reversal of the winding

voltage as soon as a predefined current limit is exceeded. For

power electronic converters connected to the grid, passive LC

or LCL filters are required to comply with EMI standards

during nominal operation (Fig. 4). If a converter with such a

filter is used to generate the rectangular voltage, the presence

of the capacitive filter elements limits the slope of the converter

output voltage during the voltage reversal. This reduced slope

would further increase the absolute value of the core flux

before the zero crossing of the winding voltage is reached.

At the beginning of the demagnetization procedure, where

the residual flux Φres could be close to the saturation level,

the reduced output voltage slope would saturate the core.

Considerable magnetization currents through the converter and

an inaccurate demagnetization would be the consequence. This

prevents the application of this demagnetization method if

capacitive filter elements are present as it is the case for the

HT. A further limitation of the conventional demagnetization

method is that the rectangular voltage is only applied to a

single winding even in case of three-phase transformers. As

a result, a simultaneous demagnetization of all transformer

limbs is not guaranteed. For a more efficient demagnetization,

[20] presents the possibility of additionally measuring the

core fluxes. However, this requires a very precise continuous

measurement and integration of the winding voltages which

is difficult to realize for transformers operating under harsh

field conditions. Hence, advanced demagnetization methods

are required which fulfill the following requirements:



H

B

t1

V in

p.u

.-1

0

1

t

in p

.u.

-1

0

1

t

t0 t2

t2

t1

t0


Fig. 12: Ramp demagnetization concept: After the CBs are opened at t0, the

converter continues to apply the nominal three-phase voltage across the Aux

winding until t1 after which the amplitude is ramped down to zero and the

core is demagnetized at t2. Besides the winding voltages and the core fluxes,

the B-H curve of an arbitrary core limb is depicted.

• Effective demagnetization, independent of the time

instant of disconnection and of the residual flux.

• Step changes of the winding voltage only at low

transformer flux levels to avoid core saturation.

• Demagnetization of all core limbs considering the

interdependency of the core fluxes.

• No flux measurement is required.

• Fast procedure with low energy consumption.

In the following, three new demagnetization strategies which

fulfill the mentioned criteria are presented and discussed.

1) Demagnetization After Disconnection: Starting from the

normal operation, the transformer flux has to be reduced to

zero during the demagnetization step at the end of the turn-off

process of the HT (Fig. 9). Consequently, the same principles

as for the prefluxing step presented in section IV-A can be

applied but in reversed order.

Fig. 12 demonstrates the ”ramp demagnetization” strategy.

After opening the MV CB at t0, the converter continues

to modulate the three symmetrical voltages across the Aux

winding of the transformer until it starts to linearly ramp down

the amplitude at t1. When the amplitude reaches zero at t2,

the semiconductors of the converter are turned off. As for the

ramp prefluxing strategy, the slope of the voltage ramp is a

compromise between speed and accuracy.

With the ”sequential demagnetization” strategy shown in

Fig. 13, the converter continues to modulate the nominal

three-phase voltage in phase with VMV after opening the

MV CB at t0. At t1, the voltage across the middle winding

v2 is zero whereafter the converter applies v1 = v3 = − 12 v2

to the windings for one quarter period. The transformer is

demagnetized at t2 and the semiconductors of the converter

are turned off. Since the magnetizing currents of the phases

H

B

V in

p.u

.

-1

0

1

t

in p

.u.

-1

0

1

t

t1 t2

t2

t1

t0

t0

Phase 3Phase 2Phase 1

Fig. 13: Sequential demagnetization concept: After opening the CBs at t0,

the converter continues to modulate the three-phase voltage until v2 = 0 is

reached at t1. For the subsequent quarter period of v2, the converter applies

v1 = v3 = − 12 v2 after which the transformer is demagnetized at t2. Besides

the winding voltages and the core fluxes, the B-H curve of the left core limb

(phase 1) is depicted.

have to decay to zero after t2, a minor remagnetization occurs

after the disconnection. With this procedure, a demagnetization

within a quarter of a grid period is possible which results in

low losses. As for the sequential prefluxing method, the voltage

steps applied to the outer windings do not occur at flux levels

close to saturation so that both the sequential prefluxing and

demagnetization strategy are applicable for converters with LC

or LCL filters.

A measurement of VMV is required for both demagnetization

strategies as a reference for the open-loop converter control.

2) Initial Demagnetization: An initial demagnetization has to

be performed when the HT is connected to the grid for the

first time or after a sudden disconnection for example due to

a grid fault (cf. Fig. 9). Consequently, the methods presented

in subsection IV-B1 cannot be applied. While the conventional

demagnetization procedure applying a rectangular voltage to a

winding is only applicable if the converter is coupled to the

LFT via a purely inductive filter, the demagnetization method

proposed in the following and depicted in Fig. 14 is also

applicable if capacitive filter elements are present. The basic

principle of this method is illustrated in Fig. 15.

At the beginning of the procedure, it is assumed that the

transformer is disconnected from the grid and has a residual

magnetization Bres �= 0. Converter B of the HT is used to apply

phase-to-phase voltages VAux,i (i ∈ {1,2,3}) with a variable

amplitude Vramp and variable offsets ΔVi to the Aux winding

system:⎛⎝ VAux,1

VAux,2

VAux,3

⎞⎠=Vramp ·

⎛⎝ cos(2π fdemagt)

cos(2π fdemagt − 2π3 )

cos(2π fdemagt + 2π3 )

⎞⎠+

⎛⎝ ΔV1

ΔV2

ΔV3

⎞⎠

In step � the amplitude Vramp of the sinusoidal three-phase

voltage is linearly increased (cf. Fig. 14 and Fig. 15). The

magnetizing currents of each phase are measured and com-

pared to predefined limits in step �. Depending on which limit



Increase Vramp

Transformer demagnetised, Bres= 0

Compare currents to limits, determine s1, s2, s3

Transformer disconnected, Bres 0

Calculate and add V1 V2 V3

Vramp= V1= V2= V3= 0

2

3 4 Ramp down Vramp, Set V1 V2 V3 = 0

All limits exceeded within Tramp

1

Fig. 14: Procedure of the proposed initial demagnetization method. A converter

is used to apply a sinusoidal voltage with increasing amplitude Vramp to the

transformer windings (step �). Variable offset voltages ΔVi are added such

that always the phase with the highest residual flux is demagnetized (step �)

until the DC flux of all transformer limbs is zero.

Ilim

Bres 0

I

B

I

B

I

B

I

B

-Ilim Ilim-Ilim Ilim-Ilim Ilim

Bres= 0

Steps 1 & 2 Step 3 Step 4

-Ilim

Steps 1 & 2

Fig. 15: Principle of the proposed initial demagnetization method. The B-I(H)

curve of an arbitrary transformer limb is shown. The amplitude of the

sinusoidal voltage is increased until a current limit ±Ilim is exceeded (steps

� & �). A DC-offset is added to the voltage to reduce the residual flux (step

�). When both the upper and lower limits are exceeded within one cycle, the

voltage is ramped down (step �).

is exceeded, a positive or negative DC offset is added to the

sinusoidal voltage of the respective phase for the subsequent

period Tdemag =1

fdemagin step � such that the absolute value

of the DC flux is reduced.

For the following mathematical description, the variables

s1,s2,s3 ∈{−1,0,1} are introduced which indicate whether the

magnetizing current of phase i exceeds the positive (si = 1) or

negative (si = −1) current limit. If the current either exceeds

no limit or both limits within Tdemag, the respective variable is

zero (si = 0). With the variables si, the offset voltages ΔVi are

calculated with the offset matrix M according to (2) in step �.

⎛⎝ ΔV1

ΔV2

ΔV3

⎞⎠=

=M︷︸︸︷⎛⎝m11 m12 m13

m21 m22 m23

m31 m32 m33

⎞⎠ ·

⎛⎝ s1

s2

s3

⎞⎠ (2)

Since the three voltages VAux,i have to add up to zero, the same

must be true for ΔV1, ΔV2 and ΔV3 for all values of si which is

equivalent to ∑3i=1 mij = 0 ( j ∈ {1,2,3}). The following offset

matrix complies with this requirement and is considered as an

example in the following analysis.

M =Voffset ·⎛⎝ 1 −0.5 −0.5−0.5 1 −0.5−0.5 −0.5 1

⎞⎠

With the variable Voffset, the stepwidth of the DC flux reduction

can be adjusted. By continuously repeating steps �, � and

�, all transformer limbs are gradually demagnetized. If the

magnetizing currents of all phases exceed the positive and

negative limits within Tdemag, the DC part of the flux has been

removed and all offsets ΔVi are set to zero. Thereafter, the

sinusoidal voltage is ramped down to zero and the transformer

demagnetization is finished (Fig. 14 and Fig. 15 step �).

In case of a delta connection of the Aux transformer winding,

the magnetizing currents which need to be compared to the

limits for this procedure cannot be measured directly. By

neglecting the low frequency filter capacitor currents and

taking into account that the converter does not excite circu-

lating currents in the transformer, the winding currents can be

calculated from the boost inductor currents.

With larger values for the parameters Vramp and Voffset, a faster

demagnetization with lower losses is possible. However, the

accuracy is reduced which could lead to a higher residual

flux after the demagnetization. The maximum demagnetization

frequency fdemag is defined by the maximum peak-to-peak

flux density which is required to exceed both the positive

and negative current limits at the transition to step �. If the

voltage drop across the filter inductor LFB is neglected, the

maximum core flux density Bmax which needs to be excited at

this transition can be calculated:

Bmax(Ilim,outer) =1

NAux ·Ac

∫ π2

0max(Vramp) · cos(2π fdemagt)dt

Since the amplitude of the Aux winding voltages Vramp is lim-

ited to the DC-link voltage VDC, the demagnetization frequency

fdemag has to fulfill (3).

fdemag <VDC

2π ·NAux ·Ac · Bmax(Ilim,outer)(3)

In Fig. 16, the Aux side magnetizing currents and the core flux

densities of an exemplary demagnetization with the presented

method are shown. There, fdemag = 40Hz, Vramp = 15 Vs and

Voffset = 0.4V are chosen which results in a maximum residual

of Bres < 0.1 · Bn for all initial residual flux levels after a

demagnetization phase of 4 s. Taking into account converter,

core and winding losses, a total energy of approximately 2 kJ

has to be provided from the DC-link.

Due to the shorter flux path of the middle transformer limb

compared to the outer limbs, the nominal magnetization cur-

rent of phase 2 is lower than that of phases 1 and 3. Hence,

also the current limit Ilim,middle for phase 2 is lower than the

limit Ilim,outer for phases 1 and 3.

It has to be noted that this demagnetization strategy could

also be applied during the turn-off of the HT as an alternative

to the methods described in subsection IV-B1 although this

would be unfavorable with respect to losses and duration of

the demagnetization.



I Aux

in A

-30

-10

0

10

30

t in s

0 1 2 3 4

B in

T

0

0.8

-0.8

-1.6

1.6

2.4

Step 4Repeating steps 1 , 2 and 3

Ilim,outer

Ilim,middle

-Ilim,outer

Phase 1

Phase 2

Phase 3

Limit exceeded

-Ilim,middle

Phase 1

Phase 2

Phase 3

Fig. 16: Aux winding currents IAux and core flux densities B for an exemplary

demagnetization based on the procedure given in Fig. 14. If the magnetizing

current exceeds the predefined limit (±Ilim,outer and ±Ilim,middle for the outer

and middle core limbs), a DC voltage offset is added to the sinusoidal voltage

to push the flux levels towards zero. When all magnetizing currents exceed

their positive and negative limits within one period Tdemag, the sinusoidal

voltage is ramped down and the transformer is demagnetized. The envelopes

of the waveforms are highlighted.

V. SIMULATIVE VERIFICATION OF THE PROPOSED

PROCEDURE

To verify the effectiveness of the proposed inrush mitigation

techniques, a simulation of the complete procedure according

to Fig. 9 is performed both for the ramp and the sequential

prefluxing and demagnetization strategies. The simulations are

performed with the simulation model given in Fig. 4 and the

parameters given in Tab. I and Tab. II.

Fig. 17 shows the waveforms of the MV side voltages VMV and

currents IMV as well as the flux density B for the sequential

method. Starting from the demagnetized state at t0, the core is

magnetized until t1 by applying the sequential magnetization

method shown in Fig. 11. Due to the step in the voltage

reference, oscillations of the winding voltages are excited

at t0 and t1. The amplitude and damping of the oscillations

highly depend on the chosen filter topology and the damping

elements. At t2, the MV CB and at t3 the LV CB is closed

whereupon the nominal operation of the HT starts. The MV

CB is closed without noticeable inrush currents.

At t4, the opening of the LV CB terminates the nominal

operation. Converter B starts to modulate a three-phase voltage

in phase with VMV across the Aux winding and the MV CB is

opened at t5. The sequential demagnetization method as shown

in Fig. 13 is performed between t6 and t7. As for the initial

V MV in

kV

-40

0

40

B in

T

-1

0

1

t in s0 0.06-1

0

1 Phase 1Phase 2Phase 3

0.02 0.08

I MV /

Î n

t0 t1Prefluxing t2 t3 t4Nominal op. t5 t6 t7 Demagn.

Fig. 17: Simulated voltage, flux density and current waveforms for the

procedure shown in Fig. 9 with sequential prefluxing and demagnetization.

Starting from the demagnetized state, the sequential prefluxing is performed

and the HT starts the normal operation. At the end, the core is demagnetized

sequentially.

demagnetization procedure presented in subsection IV-B2, the

residual magnetization after demagnetization is Bres < 0.1 · Bn.

Since the assumed nominal peak flux is Bn = 0.75 ·Bsat, the

core will not saturate if the proposed prefluxing procedure is

applied at the subsequent turn-on of the HT with such a low

residual flux. With the duration of a quarter of a grid period for

the prefluxing and the demagnetization steps, the net energy

which must be supplied from the DC-link including converter,

core and winding losses is approximately 50 J.

In Fig. 18, the same procedure is shown for the ramp prefluxing

and demagnetization method. Between t0 and t1 the core is

magnetized by applying a voltage with increasing amplitude

to the Aux windings. At t2, the MV CB and at t3 the LV CB

is closed whereupon the nominal operation of the HT starts.

The MV CB is closed without noticeable inrush currents.

At t4, the opening of the LV CB terminates the nominal

operation. Converter B starts to modulate a three-phase voltage

in phase with VMV across the Aux winding and the MV CB

is opened at t5. The ramp demagnetization method as shown

in Fig. 12 is performed between t6 and t7 by ramping down

the voltage applied to the Aux windings. Compared to the

first method, this procedure is more time consuming which

also reflects in the increased energy supply of 110 J. However,

a more accurate demagnetization of Bres < 0.02 · Bn can be

achieved.

The simulation results prove the effectiveness of the proposed

inrush current mitigation concept. In comparison to the conven-

tional method with the non-idealities explained in section III,



V MV in

kV

0

20

t in s

-1

0

1

-20

1

-1

0

B in

TI M

V /

Î n

0.08 0.16 0.240

t0 t1Prefluxing t2 t4t5Nominal op. t7Demagn.t3 t6

Phase 1Phase 2Phase 3

Fig. 18: Simulated voltage, flux density and current waveforms for the

procedure shown in Fig. 9 with ramp prefluxing and demagnetization. Starting

from the demagnetized state, the ramp prefluxing is performed and the HT

starts the normal operation. At the end, the core is demagnetized by ramping

down the winding voltage.

the inrush currents can be further reduced significantly from

2 · In to practically zero. In contrast to the controlled switching

method, standard CBs with a single drive for all phases and

a normal closing time scatter can be applied. For both the

conventional and the proposed concept, a measurement of VMV

is additionally required if not already present at the substation.

For the power electronics based procedure, an external power

supply or a small battery is required to supply the prefluxing

and demagnetization process.

VI. CONCLUSION

Numerous inrush current mitigation concepts have been pre-

sented in the literature whereof the power electronic based

synchronous prefluxing method is especially promising. In

this paper, it is shown that the hybrid transformer allows the

implementation of this mitigation concept without consider-

able additional effort. A complete procedure consisting of a

demagnetization and a subsequent synchronous prefluxing step

is proposed. Different alternatives for those steps optimized for

speed or accuracy of the prefluxing and demagnetization are

presented and compared. In addition, a novel demagnetization

strategy applicable for converters coupled to the transformer

via LC or LCL filters is proposed. A simulative comparison

to the conventional mitigation method based on optimized

connection instants is performed which underlines that the

inrush currents can be significantly reduced from 2 · In for

the conventional method to practically zero for the proposed

procedure.

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