Ride Through Capability of Matrix Converter for
Grid Connected System under Short Voltage Sag
Hiroki Takahashi and Jun-ichi Itoh
Dept. of Electrical Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
thiroki@stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp
Abstract—This paper proposes a FRT (Fault ride through)method of a matrix converter under three-phase short voltage
sag. The feature of the proposed method is to control grid
reactive current and generator torque at the same time. In orderto realize these capabilities, this paper describes a modulation
method dividing a control period into 3 modes. The first mode is
to turn off all switches and the second mode is a zero vector
output. By these 2 modes and utilizing a snubber circuit, thegenerator torque is controlled during the voltage sag. In the thirdmode, a non-zero vector is selected to provide the reactive
current to the grid. In contrast, this paper also proposes a
feedback control of the snubber voltage to obtain the stable ride
through operation. From experimental results, the grid reactive
current of 0.44 p.u. and the generator torque of 0.7 p.u. areachieved by the proposed method during three-phase voltage sag.
Keywords—matrix converter; fault ride through; generator;
reactive current; three-phase voltage sag

I. INTRODUCTION
Nowadays, wind turbine systems have attracted attentions
and have been introduced rapidly [1]. In a wind turbine system,a grid code is regulated in many countries in order to prevent ahuge power interruption and support rapid recovery of gridvoltage [2]. A typical topic of the grid code is following: 1) a
power converter in the wind turbine system should continue tooperate during short grid voltage sag if retained voltage and its
duration are within a defined area of the grid code; 2) the
power converter delivers reactive current to the grid dependingon the retained voltage. In addition, it is expected that thesegrid code will cover distributed power supplies such as anengine generator and a micro turbine system in the future.
On the other hand, in the wind turbine system, generator
torque should be maintained regardless of the grid state inorder to avoid unexpected acceleration and vibration of thewind turbine [3]. Moreover, in the engine generator and themicro turbine systems, the generator cannot react to a quick
torque disturbance caused by the grid voltage sag [4]. Thus, agrid connected converter should also equip the following
capability aside from the grid code: 3) the grid connected
converter should maintain the generator torque during the gridvoltage sag in the same manner as the normal operation.
In contrast, a matrix converter has attracted a lot of
attentions as a high performance AC-AC converter [5-7]. A

matrix converter promises to achieve higher efficiency, smaller
size and longer life-time compared to a conventional rectifierinverter system. In previous works, grid connected systems
using a matrix converter for a wind turbine and a micro turbine
systems have been reported [8-10]. However, generator
terminal voltage of the grid connected matrix converter isforced to be lower during the grid voltage sag because thematrix converter is a step-down converter. Thus, it is difficult
for the matrix converter to realize a ride through operation.
Some literatures about a FRT (Fault ride through) methodof the matrix converter have been published [11-17]. The FRT
methods proposed in [11-16] are able to ride through a matrix
converter during the voltage sag. In particular, [11] proposes a
simple FRT method against a small voltage dip by adjusting a
modulation index of the matrix converter. Reference [12]verifies that the proposed FRT method continues to operate thematrix converter and transfers power from a motor to a snubber
circuit in order to keep a control hardware operation. In
addition, [13] shows matrix converter topologies with added
switches for FRT. In other ways, [14] describes a FRT method
for a matrix converter driving an industrial induction motor,
which controls stator flux of the induction motor and enhances
the ride through duration. Reference [15] reports a FRT scheme
for an aircraft actuator by blocking gate pulses. Moreover, [16]represents a control method which retains grid filter capacitor
voltage during the grid failure. However, although thesemethods obtain the ride through capability during the shortvoltage sag, the reactive grid current control and the generator
torque control cannot be achieved. In contrast, [17] adds a
braking chopper in the snubber circuit of the matrix converterto convert braking energy to heat which is equal to control thegenerator torque. However, this method also cannot realize thegrid reactive current control.
This paper proposes a FRT method to achieve a stable ride
through operation, the grid reactive current control and thegenerator torque control during three-phase voltage sag in thesame time. The proposed method divides a control period into
three modes to ensure compatibility between the grid reactive
current control and the generator torque control. The stable ride
through operation without any over-voltage and over-current isrealized by using two feedback controls for the snubber voltage
and the generator current amplitude. In addition, the snubber
circuit is utilized to consume the generator power and tominimize additional component for FRT. Finally, it isconfirmed that a fine ride through capability is obtained by the
proposed FRT method in simulations and experiments.
II. CIRCUIT CONFIGURATION
Fig. 1 shows a matrix converter for an interface between apower grid and a generator. Fig 1 consists of a power grid, LC
filters, bi-directional switches, a snubber circuit including abraking circuit and a generator. During the short voltage sag,
active power delivered from the generator to the grid is zero
because the matrix converter provides reactive current to thegrid. However, the generator should be applied the same torqueas before the voltage sag. Therefore, a braking IGBT is turnedon and the active power provided from the generator isconsumed by a braking resistor Rbrk which is designed for FRT.
It should be noted that this dedicated braking circuit is used in
not only a matrix converter but also a conventional rectifierinverter system. Hence, the advantages of the matrix converter
compared to the conventional system are not degraded.

Fig. 1. Circuit diagram of the matrix converter for a grid connected
system. The snubber circuit includes a braking circuit.

III. MODULATION METHOD DURING GRID VOLTAGE SAG
Fig. 2 shows a circuit diagram of an IMC (Indirect matrix
converter) to consider the proposed FRT method. This chapter
replaces the matrix converter illustrated in Fig. 1 with a CSR(Current source rectifier) and a VSI (Voltage source inverter)as shown in Fig. 2. This replacement is based on a virtual
indirect control [7] and 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 except an effect of
the filter in Fig. 1, (1) should be satisfied.
 s ru s rv s rws su

stu   sup 
stv    s vp
stw   s wp

sun 
 s
s vn   rpss wn   rn

Fig. 2. Circuit diagram of an indirect matrix converter (IMC). The filter
is omitted and the snubber circuit uses an ideal voltage source.

the reactive current to the grid. Thus, this paper proposes a
modulation method of the VSI to overcome these two problems.
s sp

stp 

stn 



Fig. 3 shows operation of the VSI in the voltage sag. The
proposed modulation method divides a carrier period of the
VSI into three modes.

where, smn is a switching function of the switch Smn. smn is 1
when Smn is turned on and smn is 0 when Smn is turned off.

1) Mode 1: Snubber conduction mode
In this mode, all of the VSI switches are turned off and thegenerator current flows to the snubber circuit. The snubber
conduction mode is controlled by snubber conduction duty dsnb.
In addition, the dc-link current is zero and the generator
terminal voltage is equivalent to snubber voltage Vsnb. It isnoted that the generator terminal voltage between the same
current direction phases becomes zero due to the diode bridge.



s sv
s sw

s sn

Modulation methods of the CSR and the VSI in Fig. 2 arebased on a triangular carrier modulation presented in [7]. Thus,
the CSR controls grid power factor and the VSI adjusts
generator terminal voltage waveform. In order to inject thereactive current to the grid during the voltage sag, the grid
power factor reference of the CSR is set to zero. Besides, thegrid power factor reference is set to 1 in a normal mode and theactive power is delivered from the generator to the grid.
In contrast, the VSI in the normal mode controls thegenerator with a field oriented control. However, during thevoltage sag, the generator terminal voltage of the VSI becomeszero because dc-link voltage edc is zero due to the zero power
factor operation of the CSR. Hence, a modulation method tosynthesize the generator terminal voltage should be developed
to control the generator torque for the FRT. In addition, the
VSI needs to provide a constant current at the dc-link to inject2) Mode 2: DC-link conduction mode
Fig. 4 shows a space vector diagram of the VSI. This mode
select a vector (V1-V6) except two zero vectors. The dc-link
conduction mode is controlled by dc-link conduction duty dlink.
By using this mode, a constant dc-link current is obtained andthe generator terminal voltage equals the dc-link voltage
because all phases of the generator side are connected to the
dc-link. Then it should be noted that the average voltage of the
dc-link is zero per 1/6 of the grid period.
3) Mode 3: Freewheeling modeIn this mode, a zero vector V0 or V7 is chosen to obtain acirculating path of the generator current. Then, the dc-link
voltage and the generator terminal voltage become zero.
Additionally, duty of freewheeling mode is 1-dsnb-dlink.
Fig. 5 shows an equivalent circuit of the IMC in thesnubber conduction and the freewheeling modes. The
equivalent circuit consists of the VSI, the snubber circuit andthe generator because the dc-link current in these modes is zero.
Switches S1 and S2 in Fig. 5 are turned off in the snubber
conduction mode and turned on in the freewheeling mode. It is
obvious that the VSI is equivalent to an uni-directional boost
converter in these modes. Hence, the VSI modulates thegenerator terminal voltage by switching of S1 and S2 in the gridvoltage sag. Then, the generator terminal voltage becomes awaveform such as 120 deg. conduction mode and its averagevoltage Vgene_line during a positive period is expressed by (2).


Vgene _ line  d snb Vsnb Fig. 3. VSI operation in short voltage sag. The control period is divided
into three modes.

Then, dlink seems to be a disturbance in the generator terminal
voltage modulation apparently because the freewheeling mode
duty is defined as 1-dsnb-dlink although the snubber conduction
mode duty is dsnb. However, the generator terminal averagevoltage becomes zero in the dc-link conduction mode similar to
the freewheeling mode because the dc-link average voltage iszero due to the CSR operation. Thus, dlink does not act as a
disturbance of the generator terminal voltage modulation. As aresult, the generator torque control is achieved by combinationof modulating the generator terminal voltage, which uses thesnubber conduction and the freewheeling modes, and a
feedback control as described in the following chapter.
Table I shows selected VSI vectors in the dc-link
conduction mode (mode 2) and the freewheeling modes (mode3) during the voltage sag. It should be noted that generator
current vector angle ig is defined as zero when the generator
current vector corresponds to -axis in the space vector
diagram. In addition, Fig. 6 shows a current path if vector V1 isselected in the dc-link conduction mode. From Fig. 6, the dclink current idc conforms to the u-phase current iu in this pattern.
Therefore, the constant idc is obtained by changing the VSI
vector with reference to Table I. In contrast, either V0 or V7 inthe freewheeling mode is selected to turn only one switch at atransition between the modes. Furthermore, VSI dutyreferences should be given with reference to Table I because ofa relationship between the VSI vectors in the dc-link
conduction and the freewheeling modes. Then, dlink* and dsnb*
are references of dlink and dsnb. In consequence, the grid reactive
current control is realized by combination of VSI modulation
using the dc-link conduction mode and the zero power factor
modulation of the CSR. In addition, the grid reactive current
and the generator torque controls are achieved at the same time
because the dsnb* and dlink*are independent of each other.
Fig. 7 shows a modulation block diagram of the IMC. The
CSR employs a single-leg modulation proposed in [7] and themodulation scheme of the CSR is not changed because the
CSR modifies the grid power factor reference only in thevoltage sag. However, the VSI has to change the modulation
strategy in response to the grid state. Therefore, the VSI

Fig. 4. Space vector diagram of the VSI.

Fig. 5. Equivalent circuit diagram of the IMC in mode 1 and 3. S1 and S2
turn off in mode 1 and turn on in mode 3.

TABLE I.

SELECTED VSI VECTOR IN MODE2 AND MODE 3, AND VSI
DUTY REFERENCES.

0 deg .   ig  60 deg .
60 deg .   ig  120 deg .
120deg.  ig  180deg.
180deg.  ig  240deg.
240deg.  ig  300deg.
300deg.  ig  360deg.

Fig. 6. Current path of the VSI in the dc-link conduction mode when V1
is selected. In this pattern, idc corresponds to iu.

modulation block is separated into the normal mode which isbased on [7] and the FRT mode which is used during thevoltage sag only, by using a multiplexer MUX2. On the other
hand, in order to divide the dc-link conduction mode from thesnubber conduction mode, MUX1 is inserted before MUX2. In
addition, dlink** is calculated to compensate a dc-link current
ripple caused by changing the VSI vector in the dc-link
conduction mode per 60 deg. according to Table I. Moreover,dlink*** is also computed to obtain a sinusoidal grid current witha compensation of the single-leg modulation of the CSR. Thus,
the grid current amplitude Igrid is presented by using thegenerator current amplitude Igene and (3).
I grid 3*
d link I gene 
2

3
2





It should be noted that (3) is satisfied in the ideal condition
using an ideal current source instead of the generator. The gridcurrent amplitude in real system has an error compared to (3)due to the snubber diode and the generator inductance.
However, by referring Table I and using the obtained dc-link
conduction duty dlink*** and dsnb*, gate pulses of the VSI during
the voltage sag are generated.

Fig. 7. Modulation block diagram of the IMC. The VSI modulation
block is selected depending on the grid state.

IV. FEEDBACK CONTROLS DURING GRID FAILURE
Fig. 8 shows a feedback control block diagram for the FRT
duration. From Fig. 1, it is required to control the snubber
voltage and the generator current stably during the voltage sagin order to obtain a stable ride through operation and a desired
generator torque. Hence, this paper uses two feedback controls
for the snubber voltage and the generator current. The snubber
voltage control is defined as an outer loop and the generator
control is set as an inner loop from Fig. 5. Snubber voltage
reference Vsnb* is determined according to the active power
consumed by the braking resistor Rbrk, which is equivalent tocontrol the generator torque, because the braking IGBT isturned on during the voltage sag. The snubber voltage and thegenerator current controls use PI controllers respectively.
However, the generator current control does not have asufficient degree of freedom to control the generator current
phase because S1 and S2 in Fig. 5 are driven synchronously.
Therefore, only the generator current amplitude is controlled inFig. 8. In contrast, a subtraction using a feedforward term Ea,
which is amplitude of the generator induced voltage, anddivision after the PI controller for the generator current
amplitude are to calculate dsnb*. By introducing these feedback
controls, the stable ride through operation and the generator
torque control are achieved during the voltage sag.
V. SIMULATION RESULT
Fig. 9 shows a simulation result of the IMC under the ideal
condition (No LC filters, ideal AC current source load, DC
voltage source snubber, ideal commutation and no delay of thevoltage dip detection). Table II shows a simulation condition.
The feedback controls in Fig. 8 are not introduced in thischapter in order to verify the proposed modulation method. In
addition, red waveforms in Fig. 9 shows averaged waveformby using a low pass filter with a cut-off frequency of 1 kHz. In

2i  i2

Fig. 8. Control block diagram for the snubber voltage control and thegenerator current amplitude control in FRT mode.

TABLE II.

SIMULATION PARAMETERS UNDER IDEAL CONDITION.

Fig. 9, three-phase voltage sag of 90% (retained voltage of10%) occurs and the matrix converter operates with theproposed FRT modulation method shown in Fig. 7 during thisperiod. In other period, the matrix converter delivers the active
power from the AC current source to the grid. From Fig. 9, thesnubber conduction mode provides current to the snubber.
Additionally, the generator terminal voltage becomes a square
waveform such as 120 deg. conduction mode. Then, thegenerator terminal average voltage of 142 V is obtained andthis voltage is equal to a calculated result with (2). In contrast,
the dc-link current is negative value with a ripple. The dc-linkcurrent ripple is generated by the single-leg modulation of theGrid R-phase voltage [V]200

TABLE III.

0
-200
20

Grid R-phase current [A]

0
-20
1

Grid power factor

0.5
0DC-link voltage [V]

0

200 V

LVRT duration

100 msRated power

1.5 kW

LVRT voltage

30 %Grid side
filter L (Lf)

2.15 mH(2.53%)

Generator backe.m.f.

V

Grid side
filter C (Cf)

7.92 F(6.64%)

Generator
inductance (Lg)

3.86 mH(9.28%)

Snubber capacitor

300 F

Carrier frequency

10 kHzTABLE IV.

DC-link current [A]
0
-10
-20

Grid voltage

Brake resistor

200

EXPERIMENTAL CONDITIONS.

FEEDBACK CONTROL PARAMETERS.

Generator terminal voltage (U-V) [V]

200
0
-200

Generator U-phase current [A]

20
0
-20
20

Snubber U-phase current [A]

0
-20

0

0.05

0.1

0.15

0.2 s

Fig. 9. Simulation result under the ideal condition. The proposed
modulation method obtains zero grid power factor, a negative dc-linkcurrent and the rectangular generator terminal voltage.

CSR and the compensation with |igene_max|. As a result, the gridcurrent of 2.6 A and the grid power factor of zero are yielded.
The grid current amplitude corresponds to a calculated resultwith (3). Therefore, the proposed modulation method obtains
desired generator terminal voltage and desired grid reactive
current during the three-phase voltage sag.
VI. EXPERIMENTAL RESULT
Table III and IV show experimental conditions and control
parameters. This chapter presents experimental results using a
prototype drawn in Fig. 1 to confirm the ride through capability,
the grid reactive current and the generator torque controls withthe proposed 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 inexperiments. The voltage sag amplitude is set to 70% (retained
voltage of 30%) due to a commutation sequence of the matrix
converter. dlink* is calculated by dlink* = 1–dsnb* in order to earn
the maximum grid reactive current.
Fig. 10 shows grid side waveforms of the matrix converter.
The grid current during the voltage sag is sinusoidal waveformwith distortion. This distortion is caused by the generator
inductance and the diode bridge in the snubber circuit.
However, the grid active current is reduced to almost zero andthe grid reactive current of 0.44 p.u. is obtained by the zero
power factor modulation of the virtual CSR and the dc-link
conduction mode of the virtual VSI.

Fig. 11 shows control responses of the snubber voltage andthe generator current amplitude controls. The snubber voltage
reference is set to 350 V in order to obtain the same generator
torque as before the voltage sag at the braking resistor. From
the result, the snubber voltage and the generator current
amplitude follow their references. As a result, a stable ride
through operation is confirmed by the proposed control.
Fig. 12 shows dq-axis current responses of the generator.
Note that the current references during the voltage sag are kept
to ones in the normal mode. From Fig. 12, the dq-axis currents
in the normal mode follows their references by the fieldoriented control. Then, ripple component in the dq-axis
currents is caused by a zero-phase voltage fluctuation due to a
two-phase modulation. In terms of the q-axis current during thevoltage sag, the average current corresponds to the reference of
0.7 p.u.. As mentioned above, this is because the same active
power as before the voltage sag is transferred from thegenerator to the braking circuit by setting the snubber voltage
reference to 350 V. On the other hand, the d-axis current during
the voltage sag does not follow the reference and the average
current is -0.15 p.u.. This is because the feedback control of thegenerator current in Fig. 8 controls the amplitude only. In
addition, ripple component during the voltage sag is caused by
the generator inductance and the diode bridge in the snubber
circuit in the same manner as the grid current. However, it isconfirmed that the proposed FRT method obtains the samegenerator torque as before the voltage sag.
VII. CONCLUSION
This paper proposes a FRT method of a matrix converter
for a grid connected system such as a wind turbine system anda distributed power supply. The proposed method achieves theride through capability, the grid reactive current control and thegenerator torque control. From the experimental results, theproposed feedback control realizes a stable ride throughoperation with fine responses of the snubber voltage and thegenerator current. In addition, the proposed modulation scheme
ensures the virtual dc-link current of the matrix converter andthe reactive current of 0.44 p.u. is injected to the grid. Finally,
the same generator torque of 0.7 p.u. as before the voltage sag
is earned by keeping the snubber voltage and consuming theactive power at the braking resistor.
ACKNOWLEDGMENT
A part of this study was supported by research grant fromJapan Power Academy.
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[1]

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Fig. 12. Generator dq-current response. The average q-axis current is kept
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