Expansion of FRT Operation Range and Reduction ofGrid Current Distortion for Grid-Tied Matrix
Converter
Jun-ichi Itoh, Kyota Asai, Keisuke Kusaka, Satoshi Nagai
Department of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp, k_asai@stn.nagaokaut.ac.jp, kusaka@vos.nagaokaut.ac.jp, satoshi_nagai@stn.nagaokaut.ac.jp
Abstract— This paper proposes a fault-ride-through (FRT)
control method to expand a FRT operation range for a grid-tied
matrix converter. In the conventional method, the grid reactive
current is limited because the generator q-axis current iscirculated in only the generator side. Consequently, the matrix
converter cannot satisfy the FRT requirements due to thelimitation of the grid reactive current. On the other hand, theproposed method circulates the q-axis current between thegenerator side and the grid side in order to increase the grid
reactive current. This increases the maximum grid reactive
current by 14% as compared to that of the conventional method.
As the experimental result, the proposed method expands the
FRT operation range from 44 % to 100%, whereas a grid current
with a low THD of 9.69% during the FRT operation is obtained.
Keywords—matrix converter; fault ride through; generator;
reactive current; three-phase voltage sag

I. INTRODUCTION
Nowadays, wind turbine systems, distributed power
generation systems, and low-head hydropower systems haveattracted many attentions as sustainable energy systems [1]. In
these systems, fault-ride-through (FRT) requirements for the
grid-tied converters are applied in many countries in order toavoid a power interruption in a large scale when only a local
grid fault occurs [2]. A power converter for the grid-tiedsystem employed must satisfy the FRT requirements asfollowing: 1) the grid-tied converter needs to continue tooperate during the grid voltage sag when the remaining voltage
and its duration are within a limitation defined by the grid
requirements; 2) a reactive current is delivered to the grid
dependently on the remaining voltage. Furthermore, the gridtied converter also requires the following capability aside fromthe FRT requirements: 3) the grid-tied converter has tomaintain the generator torque during the grid voltage sag assame as that in the normal operation. In the wind turbine
system, the generator torque needs to be maintained regardlessof the grid state in order to avoid unexpected acceleration andvibration of the wind turbine [3]. Similarly, in the distributed
power generation system and the low-head hydropower system,
the generator cannot react to a quick torque disturbance causedby the grid voltage sag [4].

Meanwhile, a matrix converter has also attracted many
attentions as a high-performance AC-AC converter [5-6]. The
matrix converter is expected to achieve higher efficiency,
smaller size and longer life-time compared to a conventional
back-to-back (BTB) system. In previous works, grid-tiedsystems using the matrix converter for the wind turbine or the
distributed power generation system have been reported [7].
However, generator terminal voltage of the grid connectedmatrix converter is forced to be lower during the grid voltage
sag because the matrix converter is a step-down converter.
Thus, the matrix converter cannot satisfy the FRT requirements.
Several literatures have discussed the FRT method for thematrix converter [8-11]. A conventional FRT control method
for the matrix converter has been proposed to achieve 1) thestable FRT operation, 2) the grid reactive current control and 3)
the generator torque control in the same time during the voltage
sag [11]. The problem in the past work is that the grid current
amplitude during the FRT operation is limited by 0.88 p.u ofthat during the normal operation, because the conventional
FRT method circulates the generator q-axis current in only thegenerator side. Consequently, the matrix converter cannot
satisfy the FRT conditions when the voltage sag of more than
44% of the normal grid voltage occurs in the grid.
This paper proposes an improved FRT control method to
expand a FRT operation range for a grid-tied matrix converter.
The q-axis current is flown into the snubber circuit and the daxis current is flown into a voltage source inverter (VSI) of an
indirect matrix converter (IMC). The original idea of this paper
is that the proposed method circulates the q-axis current insnubber circuit at both the generator side and the grid side
during the FRT operation in order to increase the grid current.
The originality in this paper is that the proposed method
achieves both the expansion of the FRT operation range andthe reduction of the grid current distortion. In consequence, thegrid reactive current is increased to 1.0 p.u. as compared to
0.88 p.u. of the conventional method. As a result, the range of
the FRT operation becomes 100% in this paper. In addition, theproposed method also achieves the grid current control withlow distortion by using two kinds of the VSI vectors when the
VSI connects a current source rectifier.

This paper is organized as following; first the control
strategy of the grid-tied matrix converter during the FRT
operation is explained. Second, the control of the dq-axis
current in the generator to increase the grid reactive current is
explained. Finally, the effectiveness of the proposed method is
confirmed by experiment.
II. CIRCUIT CONFIGURATION
Fig. 1 shows the matrix converter which is used as aninterface converter between the power grid and the generator.
During the voltage sag, the active power supplied from thegenerator to the grid becomes zero because only the reactive
current is flown to the grid. However, the same torque of thegenerator should be maintained as same as that before thevoltage sag. Therefore, a brake system consisting of an IGBT
and a braking resistor is employed in order to absorb the active
power provided from the generator. In particular, the IGBT in
the brake circuit is turned on during the voltage sag and theactive power provided from the generator is consumed by thebraking resistor Rbrk. Note that this braking circuit is required
not only in the system employing the matrix converter but also
in the conventional BTB system. Hence, the advantages of thematrix converter compared to the conventional BTB systemdoes not degrade. In the conventional method, the snubber
circuit is only connected the generator side in order to preventthe grid active current from circulating. On the other hand, inthe proposed method, the snubber circuit is connected in both
the generator side and the grid side because the proposed
method circulates the q-axis current in snubber circuit at both
the generator side and the grid side.
III. FAULT-RIDE-THROUGH CONTROL METHOD FOR GRID-TIED
MATRIX CONVERTER

Fig. 2 shows a circuit diagram of an indirect matrix
converter (IMC) which is used to employ the proposed FRT

control method. The modulation method for the matrix
converter during the voltage sag uses a virtual indirect control
method [5]. The virtual indirect control treats the matrix
converter illustrated in Fig. 1 as the IMC which consists of acurrent source rectifier (CSR) and the voltage source inverter(VSI). This replacement simplifies a consideration about themodulation method during the voltage sag. Note that the LC
filters is eliminated and the snubber circuit is composed of adiode bridge and a DC voltage source in Fig. 2. Then, in orderto yield the same waveforms between the matrix converter andthe IMC at the input and output terminals excluding an effectof the LC filter in Fig. 1, (1) should be satisfied.
 sru
s
 rv
 srwstu   sup
stv    svp
stw   swp

ssu
ssv
ssw

sun 
 s
svn   rpsswn   rn

ssp
ssn

stp 

stn 



Fig. 3 shows a modulation block diagram of the matrix
converter for the FRT operation. A single-phase modulation is
employed to the CSR in order to modify the grid power factor
reference during the voltage sag [5]. This results in the same
modulation scheme of the CSR in both the grid normal
operation and the voltage sag. On the other hand, the VSI has
to change the modulation strategy in response to the grid state.
Fig. 4 shows the operation of the VSI in the voltage sag. In
the conventional method, the matrix converter cannot satisfy
the FRT requirements due to the limitation of the grid reactive
current. Therefore, in the proposed method, the grid reactive
current is increased by flowing the q-axis current in snubber
circuit from the generator side to the grid side. In order toincrease the grid reactive current, the control of the matrix
converter is separated into three modes; a) the generator power
factor control mode (only one phase is open), b) the DC-link
conduction mode, and c) the freewheeling mode. In a) the

Snubber circuit
Brake circuit

Rbrk

Csnb
Vsnb

Power
grid

ir
is
it Lf

LC filter Cf

Sru
Ssu
Stu
Srv
Ssv
Stv
Srw
Ssw
Stw
Bidirectional switches

Vsnb
Lg

idc

iu

Srp

Ssp

edc

iv

Srn
iw
Generator

Fig.1. Circuit configuration of a matrix converter.

Sup Svp Swp

Stp

Power
grid

Ssn

Stn

Current source
rectifier (CSR)

Lgvuv
Sun Svn Swn

Generator

Voltage source
inverter (VSI)

Fig.2. Circuit diagram of indirect matrix converter.

vu*
vv*
vw*

3f

3

ab
k1
k2 2

idc_rip*

Carrier
generator

vα*
vβ*
2

q

3

6

6

VSI pulses

3
VSI modulation

Duty cal.
Eq. (2)(3)(4)

3

Pulse
pattern3
conversion 6

Table 1

Line tophase
conversion

Sectordecision

3

CSR pulses

Carrier

MAX

ir*
is*
it*

ABS

CSR modulation

Freewheeling mode
DC-link conduction mode
Generator power
factor control mode
1
VSI carrier

dX+dY+dlink
dX+dY
dX

x
PLL

vr
vs
vt

3

0

dfw

Fig.3. Modulation block diagram in FRT mode.

dlink

Ssn

Sup Svp Swp

Stp

Stn

dY

dlink

dfw

idc
Srp

iu
iv
iw

edc
Srn

dX

Vsnb
idc

Ssp

dX

Fig.4. VSI operation in short voltage sag.

Vsnb

Srp

dY

Ssp

M

Sun Svn Swn

Sup Svp Swp

Stp
edc

Srn

Ssn

Stn

iu
iv
iw

M

Sun Svn Swn(a) In conventional method, active q-axis current circulates(b) In proposed method, q-axis current is controlled
only in snubber circuit at generator side.
in order to circulate between generator side and grid side.
Fig.5. Current path in generator power factor control mode.

generator power factor control mode, the dq-axis currents ofthe generator are controlled. In b) the DC-link conductionmode, the VSI and the CSR are connected in order to let thegrid reactive current circulate in the matrix converter. On theother hand, c) the freewheeling mode let the reactive current
circulate only in the VSI.
A. Mode 1: Generator power factor control mode
Fig. 5 shows the current path in the generator power factor
control mode. In this mode, the q-axis current is flown into thesnubber circuit and the reactive d-axis current is flown into the
IMC. In the conventional FRT method, the active q-axis
current circulates only in snubber circuit at the generator side.
On the other words, the grid reactive current in theconventional method is always zero. Consequently, the matrix
converter cannot satisfy the FRT requirements for the grid
reactive current. On the other hand, in the proposed method,
instead of let q-axis current circulate only in the generator-side
snubber circuit, the q-axis current is controlled in order tocirculate between the generator side and the grid side. This
enables the increase of the grid reactive current.
Table I shows the VSI pulse generation based on the
conduction states of the diode rectifier during the generator
power factor control mode. By selecting the short-circuit
pathway of the generator, the current direction flow into thediode rectifier and the generator voltages are controlled, i.e. thecontrol of the dq-axis currents. In particular, the conduction
states of the diode rectifier define six space vectors from V1 to
V6. The VSI controls the generator power factor by a current
regulator (ACR) as following; two vectors from V1 to V6
which are adjacent to the voltage references vα*, vβ* are selected.
Then the duties dX , dY of the output voltage vector vX , vY are
expressed by (2) and (3) based on these two selected vectors.
d X  va vYb  vYa vb

vXa vYb  vYa vXb Table I. Virtual VSI pulse table.
Conduction state ofdiode rectifier[D u , D v , D p ]VSI pulse(S u , S v , S w )Conduction state ofdiode rectifier[D u , D v , D p ]VSI pulse(S u , S v , S w )V1 [1 0 0]

(X 0 0)V4 [0 1 1]

(X 1 1)V2 [1 1 0]

(1 1 X)

V5 [0 0 1]

(0 0 X)

V3 [0 1 0]

(0 X 0)V6 [1 0 1]

(1 X 1)

Note: 1:Upper arm (Dxp, Sxp) ON 0:Lower arm (Dxn, Sxn) ON X:OPEN
x = u,v,w

Vsnb

Vsnb

idc

idc
Srp

Ssp

Sup Svp Swp

Stp

iv
iw

edc
Srn

Ssn

Stn

Srp

iu

Ssp

M
Ssn

Stn

iu
iv
iw

edc
Srn

Sun Svn Swn

Sup Svp Swp

Stp

M

Sun Svn Swn(a) All generator current injects to virtual DC-link.
(b) Part of generator current circulates at virtual VSI.
Fig.6. Current path in DC-link conduction mode.

dY  vXa vb  va vXbvXa vYb  vYa vXb 

B. Mode 2: DC-link conduction mode
Fig. 6 shows the current path in the dc-link conduction
mode. During the off-state period of the diode bridge rectifier,the VSI outputs the vector based on the conduction states ofthe diode bridge rectifier, which is selected by the generator
power factor control mode. In particular, the VSI outputs thevector based on the ratio between the duties dX，dY and thesum of dX，dY. In Fig. 6(a), the dc-link current idc becomesthe u-phase current iu. This switching pattern achieves the
maximum idc. However, idc depends on the generator current,
and the matrix converter is not control the grid current to thesinusoidal waveform. Therefore, in the generator current sameas Fig. 6(a), the VSI outputs the switching pattern of Fig. 6(b)instead. Consequently, a part of the generator current
circulates in the VSI. Due to this operation, idc is obtained by
two kinds of the VSI vectors of the generator current
independently. In this mode, the average voltage of the dc-link
is zero every 1/6 of the grid period. In conclusion, by thismode, the constant dc-link current is obtained and thegenerator terminal voltage equals to the dc-link voltage,
because all phases of the generator side are connected to the

dc-link. This mode is controlled by the dc-link conduction
duty dlink expressed by (4).
dlink  (k1  k 2 )(1  d X  dY ) * idc _ rip

*





where k1 and k2 are the ratio between the duties dX ,dY and thesum of dX , dY. Note that the multiplication of idc_rip* is to matchthe ripple of idc to the frequency of the grid current and tocontrol the grid current to sinusoidal waveform. The value of k1,
k2 are expressed by (5) and (6).

k1  d X (d X  dY ) 





k 2  d Y (d X  d Y ) 





C. Mode 3: Freewheeling mode
Fig. 7 shows a current path in the freewheeling mode. In
this mode, a zero vector is chosen to obtain a circulating pathfor the generator current. Consequently, the dc-link voltage
and the generator terminal voltage become zero. This mode iscontrolled by the freewheeling duty dfw expressed by (7).

d fw  1  d X  dY  dlink 





IV. FEEDBACK CONTROLS DURING VOLTAGE SAG
Fig. 8 shows a feedback control block diagram for the FRT
operation. As shown in Fig. 1, it is required to control thesnubber voltage and the generator current stably during thevoltage sag in order to obtain a stable FRT operation and adesired generator torque. Hence, this paper uses two feedback
controls for the snubber voltage and the generator current. In
particular, the snubber voltage control is defined as an outer
loop and the generator current control is set as an inner loop.
When the braking IGBT is turned on during the voltage sag,the snubber voltage reference Vsnb* is determined according to
the active power consumed by the braking resistor Rbrk, whichis equivalent to control the generator torque. On the other hand,
inner loop controls the generator dq-axis current according to
the voltage sag. PI controllers are employed in to the snubber
voltage and the generator current controls. By introducing these
feedback controls, the stable FRT operation and the generator
torque control are achieved during the voltage sag.
V. SIMULATION RESULTS
Table II and III show simulation conditions and control
parameters. This session presents simulation results using thecircuit depicted in Fig. 1 to confirm the FRT capability, thegrid reactive current and the generator torque controls with theproposed FRT method. Note that inductors and an AC voltage

source are used instead of the generator and q-axis current of
the inductors is evaluated as the generator torque in simulation.
The voltage sag amplitude is set to 100%, i.e. the remaining
voltage of 0%. Note that, during the voltage sag, the power
factor of the generator is limited from 1 to cos /6 due to theoperation of the diode bridge rectifier. Therefore, in the
proposed method, in order to output the maximum grid reactive
current, the d-axis current of the generator is regulated at thelimitation of the power factor of the generator, i.e. cos /6.
Fig. 9 shows the simulation results of the matrix converter
during the FRT operation under the ideal condition (ideal
commutation and no delay of the voltage dip detection). The
red waveforms of the generator terminal voltage (U-V) in Fig.
9 show the averaged waveforms by using a low pass filter witha cut-off frequency of 1 kHz. In Fig. 9, the voltage sag of 100%
occurs and the matrix converter operates with the proposed
FRT method during this period. During the FRT operation, thegrid active current is reduced to almost zero and the grid
reactive current is generated by the zero power factor
modulation of the virtual CSR and the DC-link conduction
mode of the virtual VSI. The grid current, the generator
terminal voltage (U-V) and the generator current during thevoltage sag are sinusoidal waveform, whereas the grid current
THD is 5.84%. Note that the q-axis current during the voltage
sag is kept to 1 p.u. during both the normal state and the FRT
operation. This results in the constant generator power of 1500
W, i.e. the constant generator torque. On the other hand, theproposed method increases the d-axis current of the generator

Vsnb
id*

idc
Srp

Ssp

Sup Svp Swp

Stp

Srn

Ssn

Stn

iu
iv
iw

edc

Vsnb*

PI
dq

Sun Svn Swn

dq

vq*

3f

3f

3

vu*
vv*
vw*

iu
iv
iw
Vsnb

Fig. 8 Feedback control block diagram for FRT operation.

Input line voltage

200 V

FRT duration

100 msRated power

1500 W

Carrier frequency

10 kHzSnubber capacitor

150 mF

Brake resistor

110 W

Grid side
filter L (Lf)

2.15 mH(2.53%)

Generator
back e.m.f.

140 V

Generator
inductance (Lg)vd*

3

Table II Conditions of simulation and experiment.

6.60 mF(5.54%)

iq*M

Fig.7. Current path in freewheeling mode.

Grid side
filter C (Cf)PIPI

3.86 mH(9.28%)

Table III Feedback control parameters.

Normal mode
(Field oriented control)

FRT
mode

Snubber voltage
control

d-axis current reference

0 p.u.

q-axis current reference-1.0 p.u.

Proportional gain

1.2 p.u.

Integral time

26.6 ms

Voltage reference

400 V

Proportional gain

2.0 p.u.

Integral time

16.5 msd-axis current reference -0.577 p.u.
Generator
current control

Proportional gain

1.2 p.u.

Integral time

1.65 msNormal mode

FRT mode

Normal mode

Grid phase voltage 250V/div
0
Grid current 10A/div
0
Snubber voltage 250V/div

Reactive
Active0020ms/div

Generator current 10A/div

Fig.10 Operation waveform.
Normal mode
480

FRT mode

Normal mode

Snubber voltage reference (400V) 160V/div

320
160

Snubber voltage 160V/div00d-axisq-axis-0.4 Generator q-axis current 0.4p.u./div
-0.8
-1.2
Generator q-axis current reference 0.4p.u./div

Fig. 9 Simulation results.
in order to obtain the power factor cos /6, i.e. the condition toachieve the maximum grid reactive current. Therefore, theexpansion of the FRT operation range is achieved by the
proposed control.
VI. EXPERIMENTAL RESULTS
Table II shows experimental conditions. This session
presents experimental results using a prototype depicted in Fig.
1 to confirm the FRT capability, the grid reactive current andthe generator torque controls with the proposed FRT method.
Note that inductors and an AC voltage source are used insteadof the generator and q-axis current of the inductors isevaluated as the generator torque in experiments. The voltage
sag amplitude is set to 100%, i.e. the remaining voltage of 0%.
Note that, during the voltage sag, the power factor of thegenerator is limited from 1 to cos /6 due to the operation of
the diode bridge rectifier. Therefore, in the proposed method,in order to output the maximum grid reactive current, the d-

20ms/div

Fig.11 Responses of snubber voltage and generator q-axis
current.
axis current of the generator is regulated at the limitation of
the power factor of the generator, i.e. cos /6.
Fig. 10 shows the operation waveform of the matrix
converter during the three-phase voltage sag. In Fig. 5, thevoltage sag of 100% occurs and the matrix converter operates
with the proposed FRT method during this period. During the
FRT operation, the grid active current is reduced to almost
zero and the grid reactive current is generated by the proposed
control method. The grid current and the generator current
during the voltage sag are sinusoidal, whereas the grid current
THD is 9.69%.
Fig. 11 shows the responses of the snubber voltage and thegenerator q-axis current. The snubber voltage reference is set
to 400 V in order to obtain the same generator torque as before
the voltage sag by using the braking resistor. As shown in Fig.
12, the snubber voltage and the generator q-axis current follow
their references. As a result, a stable FRT operation is
confirmed by the proposed control.

Normal mode

FRT mode

Normal mode

Generator d-axis current reference 0.2p.u./div
Generator d-axis current 0.2p.u./div

-0.4

1.00
0.88

-0.8

0.50

-1.2
Generator q-axis current 0.2p.u./div
20ms/div
Generator q-axis current reference 0.2p.u./div

Fig.12 Generator dq-current response.

Fig. 12 shows the dq-axis current responses of the generator.
The q-axis current reference during the voltage sag are kept to1 p.u. in both the normal mode and the FRT operation in orderto maintain the constant torque of the generator. As mentioned
above, the active power generated from the generator during
the FRT operation is transferred to the braking circuit bysetting the snubber voltage reference to 400 V. Consequently,
it is confirmed that the proposed FRT method obtains the samegenerator torque as before the voltage sag. Note that the ripple
component in the dq-axis currents is caused by a zero-phasevoltage fluctuation due to a two-phase modulation. On theother hand, the proposed method increases the generator d-axis
current of 0.577 p.u. in order to obtain the power factor cos /6,
i.e. the condition to achieve the maximum grid reactive current.
The effectiveness of the proposed control method in theexperiments is confirmed as same as the simulation. In
particular, the proposed method expands the FRT operation
range for the grid-tied matrix converter.
Fig. 13 shows the relationship between the voltage sag andthe reactive current requirement. The FRT operation is notapplied in the voltage dead band, when the grid voltage sag is
below 10% of the nominal value of the grid voltage.
According to the grid requirements, the reactive current needs
to be injected by 0.02 p.u. in response to each 1% of the gridvoltage sag. The applicable range of the conventional FRT
method is 44% or less, whereas the applicable range of the
proposed method is extended to 100%.
VII. CONCLUSION
This paper proposed the FRT method for the grid-tied
matrix converter in order to expand the FRT range. The
proposed method circulated the q-axis current in the snubber
circuit at both the generator side and the grid side during the
FRT operation. This increased the grid reactive current, which
expanded the FRT range. It was confirmed from theexperimental result that the proposed method achieved thestable FRT operation during the voltage sag of 100%.
Furthermore, the maximum value of the grid reactive current

0Voltage dead band

Reactive current requirement [p.u.]
FRT regulation

0

0.10

ExpandConventional
methodProposed method0.44 0.50

1.00
Voltage sag [p.u.]

Fig.13 Relationship between voltage sag and reactive current
requirement.
was increased by 14% as compared to that of the conventional
method. Consequently, the range of the FRT operation was
expanded from 44 % or less to 100%.

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