Direct Grid Connection of Permanent Magnet
Synchronus Motor Using Auxiliary Inverter andMatrix Converter with Transition Control*Tsuyoshi Nagano, *Jun-ichi Itoh
*Nagaoka University of Technology
Nagaoka, Japanngn244@stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp

Abstract— This paper discusses a direct grid connection system
for the permanent magnet synchronous motor (PMSM). It isdifficult to connect PMSM to the power grid directly due to theresonance between a synchronous reactance and the inertia
moment. In order to solve this problem, the direct gridconnection system which consists of an auxiliary inverter ofsmall capacity and a matrix converter is proposed for PMSM.
In the proposed system, a torque vibration caused by theresonance is suppressed by the auxiliary inverter and auxiliary
windings in PMSM. Moreover, the matrix converter is used asa starter which accelerates PMSM up to synchronous speed ofa power grid. In the direct grid connection mode, the matrix
converter is matches voltage for PMSM with the grid voltage.
Besides, the rush current is suppressed by the transition
control which consists of an output voltage phase control mode
and an output voltage amplitude control mode. In the direct
grid connection mode, the matrix converter has no switching
operation. Thus, the converter loss is remarkably low in astandby mode due to no switching loss. Additionally, thevalidity of the proposed system is demonstrated in thesimulation and experimental results. From the results, the rushcurrents is suppressed to 2 A (18% of the rated current) by thetransition control and the damping control when the PMSM isconnected to the power grid.
Keywords— Permanent Magnet Synchronous Motor; Auxiliary
inverter; Matrix converter; Direct grid connection;I.

INTRODUCTION

Recently, the driving techniques for the permanent magnet
synchronous motor (PMSM) have attracted a lot of attentions
among the researchers in terms of the energy saving [1]-[3].
PMSM has high efficiency and high power density incomparison with an induction motor (IM) because PMSM does
not have the excitation circuit. On the other hands, a direct gridconnection for IM is widely utilized for fans and pumps [4]-[6].
The efficiency of the motor drive system is improved byreplacing IM with PMSM. However, it is difficult to connect
PMSM to the power grid directly because the torque vibration
occurs due to the resonance between a synchronous reactanceand the inertia moment. In order to solve this resonance, thedamping (stabilization) control that uses the current feedback
has been proposed as the motor drive technique [7-8]. Thismethod suppresses the torque vibration with adding thevibrational component in the effective current to the output

phase command of the voltage command. However, thismethod cannot be applied to the direct grid connection for
PMSM because the inverter cannot control current
corresponding to the pole position when the PMSM is directly
connected to the power grid.
Matrix converters have been studied actively recently [913]. The matrix converter does not required large electrolytic
capacitor as an energy buffer and its size is small. Besides, a
direct grid connection which connects between the power gridand the motor directly can be used by the matrix converter toreduce the switching loss. In the direct grid connection mode,the matrix converter has no switching operation. However, thevoltage transfer ratio, which is defined as output voltage/input
voltage of the matrix converter with PWM is limited up to
0.866. As a result transition control is required for the direct
grid connection. Due to the above reason, the motor current
changes widely and over current will occur without thetransition control. In addition, changing the output current willaffect the power grid because the energy buffer is notconnected between the input side (power grid) and output side.
The transition control from PWM to the direct grid connection
mode has been proposed as a control method for the matrix
converter [13]. However, this technique can be applied to onlyIM.
In this paper, a direct grid connection system for PMSM
using a small power capacity auxiliary inverter and the matrix
converter is proposed. The aim of this paper is to achieve toconnect PMSM to the power grid without the rush current. In
the proposed methods, the torque vibration is suppressed by theauxiliary inverter and auxiliary windings in PMSM. A
transition control is applied to the matrix converter used as astarter, which the output voltage gradually corresponds to the
input voltage in transiting to the direct grid connected. For theabove reason, this matrix converter is used only when PMSM
is accelerated and shifted from the acceleration mode to thegrid connection mode or vice versa. The power capacity of theauxiliary inverter is much smaller than that of the matrix
converter because the output power of the auxiliary inverter isonly used to suppress the vibration.
This paper is organized as follows; first, the configurationof the proposed system is introduced. Secondly, the control
method of the starting inverter with V/f control and thetransition control, and the auxiliary inverter with field-oriented
control (FOC) is described. Thirdly, the performance of the
proposed control is verified by detailed numerical simulation.
Finally, the experimental results demonstrate that the proposedsystem drives the PMSM with suppressing the torque vibrationand transiting the direct grid mode. The experimental results
agree with the theoretical analysis results.
II.

PROPOSED SYSTEM

A. Configuration and control strategy of the proposed system
Fig. 1 shows the configuration of proposed system. In
PMSMs, the auxiliary windings which are used in thedamping control (with the auxiliary inverter) are placed in theslots together with the main windings. The proposed system
uses two different power rating converters. The first one is thelarge power capacity matrix converter for the main windings
to start to the acceleration. This matrix converter is used only
when PMSM is accelerated and shifted from the acceleration
mode to the grid connection mode or vice versa. The second
one is a small power capacity inverter for the auxiliary
windings to suppress the torque vibration caused by theresonance between the synchronous reactance and the inertia
moment.
Fig. 2 shows a state transition diagram of the control modein the proposed system. First, in the acceleration mode (ModeI), PMSM is accelerated up to the grid frequency in starting up
by the matrix converter. When the motor frequency reaches
the grid frequency, the mode state is changed to the transition
control mode (Mode II & III). The transition control modeconsists of the output voltage phase control mode (Mode II)
and the output voltage amplitude control mode (Mode III). In
the output voltage phase control mode, the phase of the output
voltage corresponds to the phase of the input voltage gradually.
In the output voltage amplitude control mode, the amplitude of
the output voltage corresponds to the amplitude of the input
voltage gradually with operating the matrix converter as an
AC chopper. After that, the mode state is changed to the direct
grid connection mode (Mode IV). In the direct grid connectionmode, the converter loss is reduced due to no switching
operation. In the end, PMSM is connected to the grid directlyby the magnetic contactor. During all modes, the damping
control suppresses the vibration of the speed. In terms of theeffectiveness of the proposed system, it is very important thatthe power capacity of the auxiliary inverter is much smaller
than that of the matrix converter. In other words, the damping
power for the PMSM is much smaller than that of the main
drive power.
Fig. 3 shows the relationship between the motor voltage
and the motor speed. The rated voltage of PMSM is to the gridvoltage for the direct grid connection. The voltage utilizationof the matrix converter is 0.866 of the input voltage. For thisreason, when the mode state is changed from the acceleration
mode to the direct grid connection mode, the output voltage
will increase in a sudden without a proper transition control. In
addition, if the input voltage phase and the output voltage
phase are different, large rush current or overcurrent mightoccur. Moreover, large transient variation of the output current
will affect the power grid because energy buffer are notconnected between the input side (power grid) and output side

Fig. 1 Proposed system configuration.

Fig. 2 State transition diagram of the control mode.

Fig.3 Relationship between motor voltage and rotation speedin each mode.

(PMSM). In order to solve these problems, the transition
control that treats the output voltage to correspond to the input
voltage is introduced between the acceleration mode and the
direct grid connection mode.
Fig. 4 shows the control block diagram of the proposedsystem. In the proposed system, the control method of thematrix converter is based on a V/f control. On the other hand,
the FOC and the damping controls are applied to the auxiliary
inverter. The auxiliary inverter can control the current inauxiliary windings of the PMSM in order to suppress thetorque and speed vibration. Since the torque and speed
vibrations are caused by the phase difference between therotational coordinates of the inverter and that of the PMSM, it
can be suppressed by the damping control in the auxiliary

1
s

1
sTθ

Fig. 4. Control block diagram for the proposed system.

inverter. Note that postion sesor less vector control can beapplied to the auxiliary inverter when it is difficult to use
position sesor.
Fig. 5 shows the relationship between a d-q rotating frame
and a γ-δ rotating frame for a V/f control. In the control of theauxiliary invereter, the direction of the flux vector withpermanent magnet is defined as d-axis as same as theconventional FOC. In the V/f control, the output voltage
vector is defined as δ-axis, the axis which lags by π/2 rad fromδ-axis can be defined as γ-axis. The lag of the load angle ϕoccurs between the d-q rotating frame and γ-δ rotating frameas shonwn in Fig. 5. Therefore, the load angle ϕ, rotational
speed ωre and the speed command ω* can be expressed as
p ϕ = ω re − ω *(1)where p is differential operator.
When the vibration of the speed is caused by the resonancebetween the inertia moment and the synchronous reactance,
the load angle ϕ also vibrates as shown (1). Then, the changeof the load angle pϕ is the difference between the rotational
speed and the speed command. In order to compensate thechanges of the load angle pϕ, the q-axis current command iq*
is calculated from the damping controller as shown in Fig. 4.
As a result, the vibration of the speed and torque caused by theresonance are suppressed by compensating the changes of theload angle pϕ with the current controlled by the FOC and thedamping control.
The switching signal of the matrix converter is changed
corresponding four control modes. Besides, θref is the output
phase command for the output phase control used in thetransition control. Other than the transition control, the output
phase control is not used. Therefore, θref is set to θout. Control
methods of each control modes are explained in follows.
B. Mode I – Acceleration mode
In the start-up of PMSM, the mode state is changed to theacceleration mode. In this mode, PMSM is controlled in orderFig. 5. Relationship between the d-q rotating frame
and the γ-δ rotating frame. The γ-δ rotating frame lags
by the load angle ϕ from the d-q rotating frame.

to increase the motor speed up to rated speed by the V/f control
as shown in Fig. 4. In general, when PMSM is driven with only
V/f control, the resonance between the synchronous reactanceand the inertia moment of the motor causes the torque vibration.
However, PMSM can be driven stably in the proposed system
by applying the damping control to the auxiliary inverter.
C. Mode II – Output phase control mode
In transition control [11], the mode state is changed fromthe acceleration mode to the direct grid connection mode. In
order to stabilize the output current caused by a transition fromthe acceleration mode to the direct grid connection mode, it isnecessary that the output voltage corresponds to the input
voltage gradually. Thereby, first, the output voltage phase must
be corresponding to the input voltage phase using the output
phase control. Secondly, the amplitude of output voltage needs
to be corresponding to the amplitude of input voltage using an
AC chopper switching mode.
Using the output phase control, the output phase θout cancorrespond to the output phase command θref. First, thedifference between θout and θref is equaled to zero through a PI
controller which is defined by a phase gain Kθ and a phase
integral time Tθ . Next, the final value is added with anelectrical angular velocity. A transfer function from θref to θoutis represented byKθ
(1 + Tθ s )TθGθ ( s ) =K
s 2 + Kθ s + θTθ(2)Equation (2) is second order transfer function. Thus θout
corresponds to θref. Beside, Kθ and Tθ are designed by
K θ = 2ζω n
Tθ =

(3)

2ξ
ωn

(4)

where ξ is damping coefficient, and ωn is response speed of theoutput phase control.
Fig. 6 shows the vector diagram on a d-q and γ-δ rotation
frame before and after the output voltage phase corresponds tothe input voltage phase. In the proposed system, the output
voltage vector is defined as δ-axis, the axis which lags by π/2
rad from δ-axis can be defined as γ-axis because V/f control isapplied to the matrix converter. The input din axis is alignedwith U phase of the input voltage vector vin. In the output phase
control, the output voltage vector vout corresponds to the input
voltage vector vin on the input din axis.
D. Mode III – Output voltage amplitude control mode
Fig. 7 (a) shows a configuration of a V connection AC
chopper, and Fig. 7 (b) shows a control block diagram [12-14].
The output voltage is PWM waveform that the envelope curveis sinusoidal. The output frequency is same as the input
frequency. Moreover the voltage transfer ratio of the Vconnection AC chopper is from 0 to 1. Thus, switching
operation of the matrix converter is fixed to correspond to theswitching operation of the V connection AC chopper, so thatthe maximum transfer ratio of the matrix converter is improved
up to 1.

Fig. 6. Vector diagram when the output voltage phasecorresponds to the input voltage phase.

Fig. 7. V connection AC chopper. The output voltage is
PWM waveform that the envelope curve is sinusoidal. The
output frequency is same as the input frequency. Moreoverthe voltage transfer ratio of the V connection AC chopper iszero to 1.

Fig. 8 shows the control block diagram of the switchingpulse of the matrix converter in the AC chopper mode. Duty
ratio is increased from an initial value Dint to 1 in the AC
chopper mode. Dint is expressed by
2

D int =

Vγ _ int + Vδ _ int
2Vin

2

(5)

where Vin is the RMS value of the input phase voltage, Vγ_int
and Vδ_int are output voltage commands on γ-δ axis at the
moment of the operation mode changing to the AC choppermode.
The duty ratio is increased up to 1, in other words, Switches
turn on constantly. After that, the mode state is changed to thedirect grid connection mode.
E. Mode IV – Direct grid connection mode
In the direct grid connection mode, PMSM is driven by thepower from the power grid via the non-switching state of theFig. 8. Control block diagram of the matrix converter in the
AC chopper mode. The duty ratio is increased up to 1 with
operating the matrix converter as the AC chopper, in otherwords, switches turn on constantly.

matrix converter. Switches Sru, Ssv, and Stw are turned on andthe remaining switches are turned off. Moreover, if a magnetic
contactor shunting the input and output of the matrix converter
are added, the conduction loss is reduced drastically.
III.

SIMULATION RESULTS

A. Mode I- Acceleration test with damping control
Fig. 9 (a) and (b) show the simulation and experimental
models that are used to verify the operation of the proposedTable 1. Simulation condition
PMM
1500

Rated power [W]-1

Rated speed [min ]Rated current [A]Number of pole pairs
Armature resistance [Ω]d-axis inductance [mH]q-axis inductance [mH]Electro-motive force constant [Vs/rad]2

Inertia moment [kgm ]

PMA
750

1800
8.2
3
1.55
11.5
23
2.46

4
3
1.98
15.2
33.2
0.338

0.0051 0.0026

Figs. 9. Simulation and experimental model of the PMSM in
addition auxiliary windings for damping control. In order toneglect the magnetic coupling in the simulation and theexperiment, the proposed system is validated using (b).

system. Due to the reason that the mutual magnetic interference
occurs between the main and the auxiliary windings, thecontrol for the auxiliary inverter becomes complicated.
Therefore, the proposed system is validated using a model
where two PMSMs are connected in series via single shaft.
Then, the rear end of the main PMSM is connected to the load
machine. It means that the magnetic coupling is neglected in
the simulation and the experiment. Table 1 shows the details of
the tested PMSM. Simulation conditions are as follows; gridline voltage is 200 V and grid frequency is 50 Hz in thesimulation. The rated value of the tested PMSM corresponds to
the grid voltage in the simulation. The switching frequency ofthe matrix converter is 10 kHz. Parameters of the output phase
control are designed, as Kθ and Tθ are 8 and 80 msec. The
response of the output phase control is 10 rad/sec. Besides,
following results are standardized based on the rating of
PMSM in Table 1.
Fig. 10 shows the simulation results when the acceleration
mode is applied (a) without and (b) with damping control. In
Fig. 10(a), the vibration occurs in the torque and the rotational
speed during the acceleration. After the acceleration, thevibration is maintained. On the other hand, in Fig. 10(b), thevibrations in the torque and the rotational speed and the load
angle are suppressed by the auxiliary inverter which causes theauxiliary torque to neutralize the vibration of the rotational
speed. Besides, it can be confirmed that the rotational speed iswell following to the rotational speed command. However, thelargest power produced from the auxiliary inverter is only 0.5
p.u. From the results, the power capacity of the auxiliary
inverter is shown smaller than that of the main inverter.
Moreover, the auxiliary inverter only operates when the torquevibration occurs. Note that the power capacity of the auxiliary
inverter is dominated by the response time of the torquevibration suppression.
B. Direct grid connection with transient control
Fig. 11 shows the simulation results from the acceleration
mode to the output phase control mode. The mode state ischanged from the acceleration mode to the output phase
control mode at 0.1 sec, after that, the phase angle of theoutput voltage phase is gradually corresponding to the phaseangle of input voltage phase, which is completed at 0.6 sec. At
0.6 sec, the voltage phase difference decreases to zero. After
that, the matrix converter is operated as the AC chopper mode.
Fig. 12 shows the simulation results including theFigs. 10. Simulation results for a single motor drive without
and with damping control. (a) The vibration of torque androtational speed occur during the acceleration. (b) It can be
confirmed that the rotational speed is well following to therotational speed command owing to the damping control. The
vibrations in the torque and the rotational speed are suppressedby the auxiliary inverter.

transition control. At 0.1 sec, the mode state is changed to the
output amplitude control mode. In the output amplitudecontrol mode using the AC chopper, the amplitude of output
voltage is increased gradually until it matches with theamplitude of input voltage at 0.17 sec. It takes 0.07 sec tofinish the output amplitude control. At 0.17 sec, the mode stateis changed to the direct grid connection mode. As a result, thetransition process is completed within 0.57 sec. Moreover it isconfirmed that surge current does not occur during thetransition period.
IV.

EXPERIMENTAL RESULTS

In this section, the proposed control is confirmed byexperimental setup. Table 2 shows the experimental condition.
The parameters of each controller in the experiment are sameas in the simulation.

Table 2. Experimental condition
PMM
1500

Rated power [W]-1

Rated speed [min ]Rated current [A]Number of pole pairs
Armature resistance [Ω]d-axis inductance [mH]q-axis inductance [mH]Electro-motive force constant [Vs/rad]

PMA
750

1800
8.2
4
3
3
1.55
1.98
11.5
15.2
23
33.2
0.368 0.338

2Inertia moment [kgm ]0.0051 0.0026
Rotational speed in stationary state [rad/s]
900

Acceleration time

Acceleration time

0.4sec/div

Main inverter q-axis current iqm [5A/div]

Fig. 11. Simulation result of transition from acceleration
mode to output phase control mode.

00.4sec/div

Main inverter q-axis current iqm [5A/div]0
Auxiliary inverter q-axis current iqa[5A/div]

0
Rotaional Speed[1000rpm/div]

Speed command[1000rpm/div]0

Fig. 13 shows the experimental results that illustrate themotor speed vibration when the proposed system is applied (a)without the damping control and (b) with the damping control( ζ = 0.3 ) in an acceleration test. In this experiment, it isdifficult to measure the torque response directly. Therefore, thespeed vibration is evaluated instead of the torque response. In
Fig. 13(a), the proposed system is implemented without thedamping control. The speed vibration occurs during theacceleration. After the acceleration, a 400 r/min of speed
vibration and the 10 Ap-p of current vibration in q-axis of themain inverter are maintained. On the other hand, Fig. 13(b)demonstrates the experimental results, where the proposedsystem is implemented with the damping control ( ζ = 0.3 ).
The effectiveness of the auxiliary inverter from the results
confirms that the speed vibration is reduced from 400 r/min tonearly 0 r/min in compared with the acceleration test of Fig.
13(a). The 10 Ap-p of the current vibration in the q-axis of themain inverter is suppressed as well. Nevertheless, it isconfirmed that the q-axis current of the auxiliary inverter flows
only during acceleration and deceleration. Moreover, themaximum q-axis current of the auxiliary inverter is 20% of the
q-axis current of the main inverter when the damping factor is[1000rpm/div]

Speed command[1000rpm/div]0(a) without damping control.

Fig. 12. Simulation result of transition from output phase
control to direct grid connection mode.

Rotaional Speed(b) with damping control.

Fig. 13. Acceleration and deceleration test without/with
damping control in motor-generator set. (a) After theacceleration, the 400 r/min - speed vibration is maintained.
(b) The speed vibration is reduced from 400 r/min tonearly 0 r/min in compared with (a).

Fig. 14. Experimental result of the output phase control inmotor-generator set. There is no rush current in this process.

designed at 0.3. Therefore, it is confirmed that the auxiliary
inverter can suppress the speed vibration via auxiliary windings
with a small q-axis current of the auxiliary inverter even if in
the acceleration test.
Fig. 14 shows the experimental results of the output phase
control. Note that the grid line voltage is 100V and gridfrequency is 50Hz in the experiment because the tested PMSM
is general PMSM. As a result, the output voltage phasecorresponds to the input voltage phase within 0.6sec. Moreover
there is no rush current in this process.
Fig. 15 shows the experimental results of the transition
control. The input voltage phase already corresponds to the
output voltage phase due to the output phase control. During
AC chopper operation mode, it is confirmed that the output
voltage waveform is similar to the output voltage of V
connection AC chopper. Moreover, the AC chopper duty is
increased gradually, so that the output current is increased.
After that the mode state is changed to the direct gridconnection mode. Therefore the output voltage waveform
corresponds to the input voltage waveform. As a result it isconfirmed that the surge current does not occur during thetransition period to direct grid connection mode.
V.

CONCLUSION

This paper discusses the direct grid connection for PMSM
using the small power capacity auxiliary inverter and thematrix converter used as the starter. The proposed systemsolves the problem that PMSM cannot be directly connected
the power grid. The features of the proposed system arefollowing;i ) The proposed system is composed by two different
converter, which are the matrix converter to start up
and the small power capacity auxiliary inverter tosuppress the torque and speed vibration caused by theresonance between the synchronous reactance and theinertia moment.
ii ) PMSM can be stabilized by the damping control
applied to the auxiliary inverter even when the
PMSM is directly connected to the power grid.
iii ) A transition control is applied to the matrix converter,
which the output voltage gradually corresponds to the
input voltage in transiting to the direct gridconnection.
From the simulation and experimental results, it was
confirmed that the speed vibration is suppressed by thedamping control applied to the auxiliary inverter. Moreover,
the rush current does not occur when the mode state ischanged from the acceleration mode to the direct gridconnection mode.
In future work, the verification of the proposed control byexperiment with PMSM adding the auxiliary windings will beshown.
ACKNOWLEDFMENT
A part of this study was supported by industrial technology
grant program in 2011 from new energy and industrial
technology development organization (NEDO) of Japan.
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