Halt Sequence for Matrix Converter to Suppress
Increase of Snubber Capacitor Voltage during Motor
Regeneration
Tsuyoshi Nagano, Jun-ichi Itoh
Nagaoka University of Technology
Nagaoka, Japanngn244@ stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp

Abstract— This paper proposes a halt sequence for a matrix
converter to overcome the overvoltage and overcurrent
problems in the case of grid faults in regeneration. The
proposed halt sequence short-circuits PMSM to avoid theregenerating current which flows into the snubber capacitor.
The proposed method consists of two sequences; Sequence I
controls the q-axis current to reach zero and PMSM becomes in
the flux-weakening region. Then, Sequence II short-circuits
PMSM to avert the regenerating current flowing into thesnubber capacitor. In Sequence II, the current direction of thebi-directional switches is restricted by gate signal in order toachieve to cut the current off automatically at the zero-crossing
point of the motor current. The experimental results
demonstrate that the rise of the snubber capacitor voltage is lessthan 16% of the rated snubber voltage.
Keywords— Permanent Magnet Synchronous Motor; Matrix
converter; Halt sequence; Dynamic braking circuit;I.

INTRODUCTION

Recently, power converters in regenerative adjustablespeed drive system such as a crane, an elevator and a flywheel
energy storage system are required from the view point of the
improvement of long life time and the reduction of the volume[1-6]. A matrix converter, which is one of the AC/AC directconverters, is expected to achieve smaller volume, higher
efficiency and longer lifetime than a back-to-back (BTB)
system which consists of a three-phase PWM rectifier and athree-phase PWM inverter [7-9]. Therefore, the matrix
converter is used for above regeneration systems. When a film
capacitor or a ceramic capacitor with a small capacitance is used
as a snubber capacitor in the snubber circuit, the reduction of
the volume and the extension of lifetime are achieved. However,the snubber capacitor voltage increases rapidly in case that all
bi-directional switches in the matrix converter are turned off
simultaneously when the grid faults halt the matrix converter
which has the snubber capacitor with small capacitance whilein the regeneration. Then, when the snubber capacitor voltage
exceeds the rated voltage, the switching devices are broken.
Therefore, it is necessary to suppress the rise of the snubber
voltage when grid faults happen.
As one of the conventional solutions to suppress theincrease of the snubber voltage, a dynamic brake circuit isconnected in parallel with the snubber capacitor [9]. When thesnubber voltage is over the threshold voltage, the resistance inthe brake chopper circuit consumes the regeneration energy.
Nevertheless, the dynamic brake circuit requires a largecapacity resistance and a switching device. Furthermore, it isundesirable that the cost and volume of the dynamic brakecircuit in the regenerative adjustable-speed system.
The authors have proposed a halt sequence that shortcircuits the terminal of PMSM according to the motor current
when the grid is cutoff during the regeneration [10]. Thismethod avoids the overvoltage of the DC-link capacitor, andalso prevents the overcurrent problem in the BTB system.
However, when each switching device is turned off aroundzero-crossing point of corresponding motor current during theshort-circuit of PMSM of this technique, the snubber voltage isincreased by the surge current because it is difficult to detectcorrectly the zero-crossing point of motor current. Therefore,
this technique directly cannot be applied to the matrix converter
without modifications.
This paper proposes a halt sequence for the matrix converter.
The proposed halt sequence consists of two sequences;
Sequence I controls the q-axis current to reach zero without acurrent regulator and achieves the flux-weakening operation to
reduce the output terminal voltage whereas the hysteresis
control in Sequence I maintains the filter capacitor voltage
within a certain range. After Sequence I, Sequence II shortcircuits PMSM to prevent its current flowing into the snubber
circuit and turns each bi-directional switch off each time when
the current reaches zero. This paper is organized as follows;
first, the principle of the proposed halt sequence method is
introduced. Next, the fundamental operation is confirmed in thesimulation. Finally, the effectiveness of suppressing theincrease of the snubber capacitor voltage in the proposed halt
sequence is evaluated in experiments.
II.

PRINCIPLE OF HALT SEQUENCE FOR MATRIX CONVERTER

A. Overvoltage problem
Fig. 1 shows the system configuration of the motor drive
system using the matrix converter in order to control aSnubber circuit
Csnb

Rbrk

Braking circuit

Sequence 2

Start

Short-circuit mode

Parallel-off

Power station

Sru
Ssu
Stu

Regeneration
current

Srv
Ssv
Stv

iu

Srw
Ssw
Stw

iw

iv

No
Single phase mode

Detecting thedirection of current

B. Proposed halt sequence
The regeneration power P from PMSM depends on therotating speed and the braking torque of PMSM.
P  T(1)
where  is the rotational speed and T is the torque of the PMSM.
In addition, the output torque of the PMSM is given by (2).



Zero-crossing current

PM

Permanent Magnet Synchronous Machine (PMSM). In general,the matrix converter includes the snubber circuit to absorb asurge current and a surge voltage. When the surge current flows
or the surge voltage occurs, the snubber capacitor Csnb insnubber circuit absorbs the surge current and the surge voltage.
In addition, a magnetic contactor is placed between the grid sideand the matrix converter for the protection. The dynamic brakecircuit is connected in parallel with the snubber capacitor tosuppress the rise of the snubber capacitor voltage whichhappens eventually due to the absorption of the surge voltage
and the surge current. However, when the grid faults halt thematrix converter with the snubber capacitor during motor
regeneration suddenly, it is difficult to suppress the rise of thesnubber capacitor voltage by only using the discharge
resistance because a large regeneration current flows to thesnubber circuit. Therefore, in order to suppress the rise of thesnubber capacitor voltage during above accident, a braking
circuit is added to the snubber circuit. However, it is preferable
that the cost and volume is increased due to the dynamic brakecircuit.



No

Yes

Yes

Others
Input filter Matrix converter
Fig. 1. Configuration of the matrix converter for a motor drive system.
The snubber circuit includes a braking circuit which consists of aswitching device and a large-capacity resistance.

T  Pn iq 3e  Ld  Lq id

Relay is open(2)

where e is the linkage magnetic flux of armature by permanent
magnet, Ld is the d-axis inductance, Lq is the q-axis inductance,
Pn is the number of the pairs of poles, and id and iq are the dand q-axis current. From (2), it is understood that the negative
torque causes the rise of the snubber capacitor voltage if the qaxis current flows into negative direction. Thus, the q-axis
current should reach zero in the halt sequence as fast as possible
in order to preclude the overvoltage at the snubber capacitor
voltage.
Fig. 2 shows the operation flow chart of the proposed halt
sequence. Sequence I controls the q-axis current to reach zeroand achieves the flux-weakening operation to reduce the output
terminal voltage without using a current regulator whereas thehysteresis control, which selects the switching patterns tocharge and discharge the filter capacitor, maintains its voltage
within a certain range. After the q-axis current becomes zero,Zero-crossing current
NoYes

iq = 0Yes
Zero current mode

No
Detection of filter
capacitor voltage

Current does not flow?
Yes
All gate off mode

Decision of CSR
switching patternbased on Table 1

No

End

Vc>Vupper_limit

Yes

No
Vc<Vlower_limit
No

Output of signal

Yes
Charge mode
(Decision of
VSI switchingpattern basedon Table 2)

Discharge mode
(Decision of
VSI switchingpattern basedon Table 2)

Vupper_limit : upper limit voltage
Vlower_limit : lower limit voltage
Sequence 1

Fig 2. Flow chart of the proposed halt sequence for the matrix converter.

Sequence II is implemented in order to conduct the short-circuitmode until the motor current is interrupted by Sequence II. It
has been observed that Sequence II alone can achieve to preventthe snubber capacitor from the rapid voltage rise, because theregeneration current is circulating in the matrix converter.
However, the short-circuit current will increase by the highelectromotive force of PMSM drastically in high speed region.
In the worst case, the irreversible demagnetization of the
PMSM happens because of the large short-circuit current. In
addition, it is necessary to implement with higher current rating
switching devices in the matrix converter. Therefore, Sequence
I is introduced before Sequence II in order to preclude the large
short-circuit current with the reducing the output terminal
voltage. Sequence I suppresses the maximum current to below
three times of the rating current of PMSM, and then generally
the irreversible demagnetization in PMSM does not occur.
Fig. 3 shows an example of Sequence I. The magnetic
contactor is off because of the grid faults before Sequence I
starts. Therefore, the filter capacitor voltage is maintained byonly the charge and discharge current which flows from PMSM.
Besides, this proposed halt sequence selects the switchingpattern based on the virtual AC/DC/AC conversion.

Sru

I

Ssu
Stu
Srv
Ssv
Stv

R
S
T

II

III

IV

V

VI

II

III

IV

V

VI

vcr
vcs

0

vct

PM
I

Srw
Ssw
Stw

Edc

Input filter Matrix converter
Fig. 3. Example of Sequence I.

0Fig. 5. Input voltage, virtual DC-link voltage and state number.
Srp Ssp Stp

Table 1. Switching pattern of the current source rectifier at Sequence I.

Spu Spv Spw

EDC

Max/Mid/MinPMvcr vcs vct
Ssn Stn

Snu Snv Snw

Input filter
AC/DC/AC converter
Fig. 4 Virtual AC/DC/AC converter which generates same input
and output waveform with the matrix converter in Fig. 3

Fig. 4 shows the virtual AC/DC/AC conversion system
which is constructed by a current source rectifier (CSR) and a
voltage source inverter (VSI). The virtual AC/DC/AC control
method separates the input current control strategy and theoutput voltage control strategy because the matrix converter isconsidered as a virtual CSR and a virtual VSI to obtain
designated switching pulse commands [8]. The switching statesin Fig. 3 can be expressed by that in Fig. 4. Equation (3)expresses the formula for the switching states in the matrix
converter.
 S ru S su Stu   Sup Sun  S rp S sp Stp 
S
 
(3)
 rv S sv Stv    Svp Svn   S
S sn Stn rn S rw S sw Stw   S wp S wn 
where, Sij is the switching function of the switch Sij in the virtual
AC/DC/AC converter.
Fig. 5 shows the relationship between the filter capacitor
voltage and the state number. Table 1 shows the switching tableof the virtual CSR. The bi-directional switch, which isconnected to the medium phase voltage, is off in Sequence I. In
other words, the matrix converter acts as two-level inverter
which has a DC-link voltage equaling to the difference between
the maximum phase voltage and the minimum phase voltage.
Fig. 6 shows the output voltage vector of the charging modeand the discharging mode toward the motor current vector in
Sequence I. The instantaneous power pout does not occur when
the output voltage vector crosses the motor current vector at theright angles as shown in Fig. 6. Nevertheless, the instantaneous
power pout cannot always become zero because the matrix
converter which acts as the two-level inverter has only six
active voltage vectors. The six active voltage vectors of thematrix converter separates the charging voltage vector anddischarging voltage vector. Therefore, Sequence I selects theswitching pattern to charge and discharge the filter capacitor tokeep its voltage according the current direction while theinstantaneous power pout is adjusted to reach zero. Finally, theq-axis current turns zero and PMSM is in the flux-weakening
region because the the energy stored in the q-axis inductance is

I
II
III
IV
V
VI

vr
MAX

vs
MID

vt
MIN

State of switch of rectifier
Srp

Ssp

Stp

Srn

Ssn

Stn

ON OFF OFF OFF OFF ON
MID MAX MIN OFF ON OFF OFF OFF ON
MIN MAX MID OFF ON OFF ON OFF OFF
MIN MID MAX OFF OFF ON ON OFF OFF
MID MIN MAX OFF OFF ON OFF ON OFF
MAX MIN MID ON OFF OFF OFF ON OFF

q
(110)

(010)
Charging
voltage vector

pout>0(100)(011)
Discharging
voltage vector

pout<0Motor current
(001)

d

(101)

Fig. 6. Output voltage vector of the charging mode and the discharging
mode toward the motor current vector in Sequence I.
Table 2. Switching pattern of the voltage source inverter at Sequence I.

Direction ofcurrent
iu
iv
iw

Discharge

Srn

Charge

R
S
T

+
+

-

+
+
+

-

+

-

+
+
+

-

+
+
+

-

+
+
+

-

+
+
+

-

State of switch of inverter
Spu

Spv Spw Snu

Snv Snw

ON OFF ON OFF ON OFF
OFF OFF ON ON ON OFF
OFF ON ON ON OFF OFF
OFF ON OFF ON OFF ON
ON ON OFF OFF OFF ON
ON OFF OFF OFF ON ON
OFF OFF ON ON ON OFF
OFF ON ON ON OFF OFF
OFF ON OFF ON OFF ON
ON ON OFF OFF OFF ON
ON OFF OFF OFF ON ON
ON OFF ON OFF ON OFF

stored to the d-axis inductance by the charging and discharging
vectors in the matrix converter.
Table 2 shows the switching table of the virtual voltage
source inverter. The discharging mode selects the voltage
command vector which is delayed by a 30 to 90 degrees toward
the motor current vector. Similarly, the charge mode selects theoutput voltage vector which is delayed by a 90 to 150 degrees
toward the motor current vector. The output voltage vector
which is applied to PMSM is delayed a 60 to 120 degree toward
the motor current vector by alternating the charging mode with

(b)

(c)

(d)

Table 3 Switching pattern of Sequence II.

(e)Direction ofcurrent
iu
iv
iw

iv
0

+
+

iu

iw

(a) Example of current waveform
Sur ONSur ON

U
Sru

R

U
Sru

Svr

V
ON Srv

Swr ON

Swr ON

W
Srw

W
Srw

(b) Short-circuit mode(c) Single-phase mode

Sur ONSur OFF

U
Sru

U
Sru

Svr

R

Svr

V R
ON Srv+Svr

V R
ON SrvV
OFF Srv

Swr ON

Swr OFFW
Srw(d) Zero-current mode-(e) All gate off mode

Fig. 7. Operational modes in Sequence II of the proposed halt
sequence. The matrix converter interrupts the motor current by using
the turn-off of the freewheel diode in Sequence II.

the discharging mode. Sequence I ends when the q-axis current
reaches zero.
Fig. 7 illustrates Sequence II that is utilized to prevent thesnubber capacitor voltage from the rise by circulating the motor
current inside the matrix converter. The switching state in thematrix converter turns a short-circuit condition to suppress therise of the snubber capacitor voltage in Sequence II. The
following represents the switching states of the matrix
converter. First, the switching pattern of two IGBT in the bidirectional switch is decided corresponding to the direction ofcurrent when Sequence II starts. Table 3 shows the switchingpattern. For instance, when U-phase current flows to load side
as shown in Fig. 7(a), Sur is turned on and Sru is turned off inorder not to interrupt U-phase current. U-phase current flows to
load side via the freewheel diode of Sru and IGBT of Sur.
Similarly, other IGBTs which are connected to R-phase ( Srv,
Svr, Srw and Swr ) are decided corresponding to the direction ofcurrent. In addition, the bi-direction switches which areconnected to S-phase and T-phase are turned off. Then, thematrix converter is short-circuited as shown in Fig. 7(b). The
switching state of the short-circuit mode avoids theregeneration current flowing into the snubber circuit. Then,
when one of the three-phase currents reaches zero, thefreewheeling diode is turned off automatically as shown in Fig.
7(b). Thus, the matrix converter turns the condition of a single
phase mode. Then, the zero-current mode also turns theremaining two freewheel diodes off naturally when the current
is zero, severally as shown in Fig. 7(c). Finally, all bidirectional switches are turned off as shown in Fig. 7(d).
Therefore, because Sequence II averts the regeneration current

Sxu Sux Sxv Svx Sxw Swx- - ON OFF OFF ON OFF ON- + ON OFF OFF ON ON OFF- + OFF ON OFF ON ON OFF+ + OFF ON ON OFF ON OFF+ - OFF ON ON OFF OFF ON+ - ON OFF ON OFF OFF ON

Table 4 Simulation and experimental condition.

Rated motor power
Rated motor voltage
Rated current
Rated speed
Number of poles
Winding resistanced-axis inductanceq-axis inductanceBack-electromotive force
Snubber voltage
Threshold over-voltage

W
Srw

State of Phase 2

3.7 kW
180 Vrms
14.1 Arms
1800 rpm
6 poles0.693 W
6.2 mH
15.3 mH
141 Vrms@1800rpm
283 V
480 V

Gate interruption Dynamic braking
Input current
ir is it[A]

it

Filter capacitor
voltagevcr vcs vct
[V]

vcs
vcr
vct

ir

is

Snubber
capacitor
voltage
[V]

180V

iw

Output current
iu iv iw
[A]

iv
iu
id

dq-axis current
id iq
[A]

iq
Time [s]Fig. 8. Simulation result of the gate interruption. After all switches areturned off at the same time, the snubber voltage increases by 180 V

flowing into the snubber capacitor, the suppression of thesnubber voltage rise can be achieved.
III.

SIMULATION RESULTS

Fig. 8 shows the simulation result of the gate interruption.
In the simulation, the magnetic contactor is opened and the gateinterruption, which is interrupts the gate signals, turns all
switches off simultaneously. In Fig. 8, the snubber capacitor
voltage increases by 180 V after the gate interruption. After thesnubber capacitor voltage reaches 460 V, the dynamic break
circuit is operated to ensure that the snubber voltage do not
exceed the designed threshold voltage. The snubber capacitor

Filter capacitor
voltagevcr vcs vct[V]it

Snubber voltage [V]Phase II (Short-circuit)
Input current
ir is it
[A]

ir

is
vcs
vcr
vct

340

iq = -1.0, id = 0.0

320

300
280
0

0.2

0.4

0.6

0.8

1

Rotational speed [p.u]Fig. 11. Snubber voltage rise when PMSM is not the flux-weakening region
Snubber
capacitor
voltage[V]

Table 5 Experimental condition.

Output current
iu iv iw
[A]

iw iu

dq-axis current
id iq[p.u.]

id

55A

iv

iq

2.9 p.u.
Time [s]Fig. 9. Simulation result of only Sequence II. The motor current
increases to 55A after PMSM is short-circuited.
Phase I Phase II
Input current
ir is it[A]
Filter capacitor
voltagevcr vcs vct
[V]

it

ir

is
vcs
vcr
vct

Snubber
capacitor
voltage[V]
Output current
iu iv iw[A]
dq-axis current
id iq
[A]

20V
iw
iv
iu
id
iq
Time [s]Fig. 10. Simulation result of the proposed halt sequence. The matrix
converter interrupts the motor current by the turn-off of the freewheel
diode. The fluctuation of the snubber capacitor voltage is suppressed toless than 20V.

voltage is reduced instantly by the brake resistance which
consumes the regeneration energy after the dynamic break
circuit is operated. The large-capacity resistor to consume theregeneration energy is essential for this method in order toprevent the snubber capacitor from the overvoltage problem.
Fig. 9 shows the simulation result of only short-circuit modeof Sequence II. If the output current of 3.0 p.u. flows in theexperimental system, it is possible to cause the burnout and theirreversible demagnetization. In Fig. 9, the motor current
increases to 55A because PMSM is short-circuited without
Sequence I. Even if the overcurrent protection works, theRated motor power
Rated motor voltage
Rated current
Rated speed
Number of poles
Winding resistanced-axis inductanceq-axis inductanceBack-electromotive force
Rated snubber voltage
Threshold over-voltage
Filter indactance
Filter capacitance
Filter resistance
Snubber capacitance

3.7 kW
180 Vrms
14.1 Arms
1800 rpm
6 poles
0.643 W
7.5 mH
15.1 mH
151 Vrms@1800rpm
283 V
400 V
2 mH
37 mF
47 W
100mF

snubber capacitor voltage rises drastically. Therefore, thismethod is not practical.
Fig. 10 represents the simulation results of the proposed halt
sequence. In Fig. 8, the magnetic contactor is opened at 20 ms.
Then, the matrix converter implements the switching patterns inTable 1 and Table 2 depending on the current direction and the
input voltage. After the q-axis current reaches zero and PMSM
is in the flux-weakening region at approximately 28 ms,
Sequence II short-circuits PMSM. From the result, the proposed
halt sequence can suppress the motor current to below 2.1 p.u of
the rated current. In addition, Sequence I suppresses the rise of
the snubber capacitor voltage to below 0.1 p.u. of the rated
voltage.
Fig. 11 shows the snubber voltage rise in the speed rigion
which does not include the flux-weakening region. The snubber
voltage is below 400V when the snubber voltage is larger than
the terminal voltage of PMSM below 1523 r/min (= 0.846 p.u.).
IV.

EXPERIMENTAL RESULTS

Table 3 shows the detail of the experimental condition. The
proposed sequence is implemented in DSP. Therefore, due tothe operation switching period of Sequence I, the filter
capacitance is large than the general one in this experiment. The
d- and q- axis current is calculated by DSP.
Fig. 12 shows the experimental waveform of the gateinterruption. In Fig. 12, the snubber capacitor voltage increases
by 100 V after the gate interruption. After the gate interruption,
the switching device of the dynamic break circuit is turned on.
Because the brake resistance is consuming the regenerationenergy, the snubber capacitor voltage drops rapidly after thebrake register begins consuming the regeneration energy.

Fig. 13 represents the experimental results of the proposed
halt sequence. In Fig. 13, the snubber capacitor voltage vibrates
during from t1 to t2 because the hysteresis control of Sequence I
maintains the the snubber capacitor voltage. Sequence II shortcircuits PMSM when the q-axis current turns positive at t2. In
addition, the maximum snubber capacitor voltage rises to 45 V
during Sequence I. The rise of the snubber capacitor voltage isapproximately 50% lesser than Fig. 12. On the other hand, themaximum output current is suppressed to below three times of
the rated current. From Fig. 13, it is confirmed that the proposed
halt sequence can suppress the rapid voltage rise of the snubber
capacitor and the short-circuit current without the dynamic brakecircuit.
V.

Gate interruption Dynamic braking
Filter capacotor
vtr vstvoltage
0 v
rs
vrs, vst, vtr
500V/div
Snubber voltage
EDC
50V/div
300

Output current
iu, iv, iw 0
20A/div

CONCLUSION0
Output current
id, iq1p.u./div

[2]

[3]

[4]

[5]

[6]

[7]

[8]

iw
iv
iu

2ms/div

id
iq
2ms/div
t1 t2

Fig. 12. Experimental results when all gate signals are interrupted as
the halt sequence. The snubber capacitor voltage rises byapproximately 100 V after the magnetic contactor is opened and all
switches are turned off.
Phase 1 Phase 2
Filter capacotor
vrs
voltage0
vst vtrvrs, vst, vtr
2ms/div
500V/div

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100V
2ms/div

This paper proposes the halt sequence for the matrix
converter which suppresses the rising of the snubber capacitor
voltage by avoiding the motor current flowing into the snubber
circuit. The proposed halt sequence interrupts the regeneration
current by using the short-circuit and suppresses the snubber
voltage rise without the the additional parts. The proposed halt
sequence suppresses the snubber voltage rise within 45V
without the dynamic brake circuit in the experiment. The
simulation and experimental results demonstrated theeffectiveness of the proposed sequence.
[1]

2ms/div

Snubber voltage
EDC
50V/div
300

45V
2ms/div

Output current
0iu, iv, iw
20A/div

Output current 0
id, iq1p.u./div

iu
iv

20 A

iw

2ms/div

id1.25 p.u.

iq

2ms/div
t1

t2

t3

Fig. 13. Experimental results when the proposed halt sequence isapplied. It is confirmed that the rise of the snubber capacitor voltage
is 45 V during the Sequence I and Sequence II.
[9]

C. Klumpner, F. Blaabjerg: "Short Term Braking Capability During
Power Interruptions for Integrated Matrix Converter-Motor Drives",
IEEE Trans. Power Electron., Vol. 19, No. 2, pp. 303-311 (2004)[10] T. Nagano, K. Orikawa, J. Itoh, A. Toba: "Simplification of Halt
Sequence to Suppress Increase of DC-link Voltage during Motor
Regeneration", 9th International Conference on Power Electronics, TuC23, pp.337-344 (2015).