電気学会論文誌●（●●●●●●●部門誌）
IEEJ Transactions on ●●●●●●●●●●●●●●●
Vol.●● No.● pp.●-●
DOI: ●.●●/ieejeiss.●●.●

Paper
Parallel Connected Multiple Motor Drive System Using Small Auxiliary
Inverter for Permanent Magnet Synchronous Motors
Tsuyoshi Nagano＊, Student member,

Goh Teck Chiang＊, Member

Jun-ichi Itoh＊a), Member(Manuscript received Jan. 00, 20XX, revised May 00, 20XX)
This paper proposes a parallel operation system of permanent magnet synchronous motors (PMSMs) and verifies the
suppression effect of the proposed damping control for the torque vibration caused by resonance between synchronous reactanceand inertia moment. The proposed system is composed by two types of power converters, a main inverter with a V/f control andan auxiliary inverter with the field-oriented control and the damping control. In general, PMSM cannot be driven by the V/fcontrol such as an induction motor because the speed vibration is caused by the resonance between the synchronous reactanceand the inertia moment. In the proposed system, the multiple PMSMs are driven in parallel by the main inverter with the V/fcontrol. When the motor speed vibration occurs, the damping control for the auxiliary inverter suppresses this vibration in
PMSM. From the frequency characteristics, it is clear that the power capacity of the auxiliary inverter is 10% lower than that of
the main inverter when the frequency components included in the speed command are lower than 12 rad/s. As a result, theexperimental results demonstrated that the proposed system can reduce the speed vibration from 400 r/min to nearly 0 r/min withthe damping control in our prototype of 1500-W PMSM drive system. The experimental results well agree with the theoreticalanalysis results.
Keywords : Permanent magnet synchronous motor, Auxiliary inverter, Parallel drive1.

method cannot be applied to the parallel connected PMSMs
because only one inverter cannot control each current
corresponding to each pole of the PMSMs.
There are some literatures in which two PMSMs are driven by
one power converter (10)-(15). These converters can drive two
PMSMs independently. However, these converters have someproblems. For instance, the five-leg inverter (10)-(12) and thenine-switch inverter (13)-(14) are driven at low voltage utilization
ratio in comparison with the case when one PMSM is driven bythese converters because DC-link voltage is distributed to two
PMSMs. Moreover, the current capacity of the switching device
increases because there is one common leg. The four-leg inverter
using the neutral point of the DC link capacitor utilizes fewer theswitches than other topologies (15). However, this converter
requires the capacitor voltage balancing control because thecapacitor neutral-point voltage is unbalanced by the motor current.
Therefore, it is difficult to apply these converters to several
PMSMs because the output voltage of the inverter is limited andthe number of switching devices increases.
In this paper, in order to drive PMSMs in parallel effectively, amulti-parallel PMSMs drive system based on V/f control is
proposed, and the proposed damping control is verified in theexperiment. In the proposed method, the torque vibration issuppressed by an auxiliary inverter and auxiliary windings in each
PMSM. The power capacity of the auxiliary inverter is muchsmaller than that of the main inverter because the output power of
the auxiliary inverter is only used to suppress the vibration. Notethat the proposed system assumes that the each PMSM in themulti-parallel connected PMSMs drives at same speed or

Introduction

Recently, the adjustable speed drive techniques for thepermanent magnet synchronous motor (PMSM) have attracted a
lot of attentions among the researchers in terms of the energy
saving (1)-(4). PMSM has high efficiency and high power density incomparison with the induction motor (IM) because PMSM does
not have the excitation circuit. On the other hand, IMs can be
driven in parallel by utilizing only one inverter. IM drive systems,
in which multiple IMs are driven by one inverter, are applied toindustry in terms of cost reduction and simplification of thesystem, because this system only utilizes one large power capacity
inverter to drive multiple induction motors (5)-(7).
The efficiency of the motor drive system is improved byreplacing IM with PMSM. However, it is difficult to drive theparallel connected PMSMs by using only one inverter because thetorque vibration occurs due to the resonance between synchronous
reactance and inertia moment of PMSM (8). When the parallel
connected PMSMs are driven by one inverter, the current cannot
be controlled corresponding to each pole of PMSM because thepole position of the one PMSM is different from that of other
PMSMs. Therefore, the torque vibration occurs unavoidably inthis multiple PMSMs drive system.
The damping control that uses the current feedback has been
proposed (9). This method suppresses the torque vibration byadding the vibrational component in the effective current to the
output phase command of the voltage command. However, thisa) Correspondence to: Jun-ichi Itoh. E-mail: itoh@vos.nagaokaut.ac.jp＊
Nagaoka University of Technology
1603-1, Kamitomioka-cho, Nagaoka, Niigata, Japan 940-2188© 200● The Institute of Electrical Engineers of Japan.

1Parallel Connected PMSM Drive System Using Auxiliary Inverter (Tsuyoshi Nagano et al.)independent load such as industrial fans, pumps and flywheel
energy storage systems. Different speed drive systems such as theelectric train or electric vehicles are not considered in this paper
because the motor speed of each PMSM is different from eachother.
This paper is organized as follows; first, the configuration of
the proposed parallel drive system is introduced. Next, the control
method, which is comprised of V/f control for the main inverterand field-oriented control (FOC) for the auxiliary inverter, isdescribed. Next, the stability of the proposed system is analyzed
by the root locus. After that, the suppression effect of the damping
control and the minimum power capacity of the auxiliary inverter
are clarified from the frequency characteristics of the transfer
function. Finally, the experimental results demonstrate that the
proposed system drives the PMSM with suppressing the torquevibration and the experimental results agree with the theoreticalanalysis results.

AC

PM

DC

Main inverter

AC

PM

DC
AC

PM

DC

Auxiliary inverter

AC

Fig. 1.Configuration of the proposed system that uses
the large power capacity inverter for the motors andthe small power capacity inverter for suppression of
the vibration.
vum
vvm
vwm

Main inverter control

*Proposed Multiple PMSMs Drive System

2.1
System Configuration
Fig. 1 shows theconfiguration of the proposed system. In PMSMs, the auxiliary
windings which are used in the damping control (with theauxiliary inverter) are placed in the slots together with the main
windings. The proposed system uses two different power rating
inverters. The first one is the large power capacity inverter for themain windings to control the speed of the parallel connected
PMSMs. The second one is the small power capacity inverter forthe auxiliary windings to suppress the torque vibration. In terms of
the effectiveness of the proposed system, it is very important thatthe power capacity of the auxiliary inverter is much smaller thanthat of the main inverter. In other words, the damping power for
the PMSM is required much smaller than that of the main drive
power. Moreover, the auxiliary inverter does not need to theexternal power supply depending on the operation condition
because the DC link voltage of the auxiliary inverter is controlledusing the active power. Therefore, when the capacitor can be only
connected to DC link of the auxiliary inverter depending on theoperation condition, the proposed system drives parallel connected
PMSMs. The auxiliary inverters have little effect on the systemcost because the power capacity of the auxiliary windings isenough smaller than the main windings.
2.2
Control Strategy
Fig. 2 shows the control block
diagram of the proposed system. In the proposed system, the V/fcontrol is applied to the main inverter, and the FOC and thedamping controls are applied to the auxiliary inverter. Each of theauxiliary inverter can control the current in auxiliary windings of
the PMSM in order to suppress the torque and speed vibration.
Since the torque and speed vibrations are caused by the phasedifference between the rotational coordinates of the inverter andthat of the PMSM, they can be suppressed by the damping control
in the auxiliary inverter. Note that postion sensor-less vector
control can be applied to auxiliary inverter when it is difficult touse position sensor.
Fig. 3 shows the relationship between the d-q rotating frame
and the - rotating frame for V/f control. In the control of theauxiliary invereter, the direction of the flux vector with permanent
magnet is defined as d-axis as same as the conventional FOC. In
the V/f control, the output voltage vector is defined as -axis, theaxis which lags by /2 rad from -axis can be defined as -axis.

f/V conv.

v*

1
s

q

ACR

vd*
dq
uvw

Decoupling
control

D
iq*

+
Kd

-1

ACR

+

id
iq

Damping control

Main
inverter

3f++id*= 0++others2.

Main windings
Auxiliary windings

DC

vua
vva
vwa
Auxiliary
inverter

iu
iv
iw

vq*

dq
uvw

q



PS

Auxiliary inverter control

PM

Fig. 2. Control block diagram of the proposed system.
The V/f control is applied to the main inverter. The
auxiliary inverters use the field-oriented control for thedamping control.

q
q' p





e

v



*

 : Rotational speed
*: Speed commandv : Output voltage

d' e : Electro-motive force : Load angledFig. 3. Relationship between the d-q rotating frame andthe - rotating frame. The - rotating frame lags by
the load angle  from the d-q rotating frame.
The lag of the load angle  occurs between the d-q rotating frameand - rotating frame as shown in Fig. 3. Therefore, the load
angle , rotational speed re and the speed command * can be
expressed asp  re   * ..................................................................... (1)where p is differential operator.
When the vibration of the speed is caused by the resonancebetween the inertia moment and the synchronous reactance, theload angle  also vibrates as shown (1). Then, the changes of theload angle p is the difference between the rotational speed and
2

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Parallel Connected PMSM Drive System Using Auxiliary Inverter (Tsuyoshi Nagano et al.)the speed command. In order to compensate the changes of theload angle p, the q-axis current command iq* is calculated fromthe damping controller as shown in Fig. 2. As a result, thevibration of the speed and torque caused by the resonance aresuppressed by compensating the changes of the load angle pwiththe current controlled by the FOC and the damping control.

3.

INV.

PMM

INV.

T  TM  TA pre 





RM
LM

0

0



0

R

LA

0

0

0

3 PfM  mM
cos 0
2
J
0

0

2

0



J
0

LM

 mM
LM





3
3
PfM m M iM sin   iM cos  PfA m AiAq ............ (4)
2
2





1
PfM TM  PfATA ....................................................... (5)J 3 PfM 2 mM  mM RM
 pDre  
2J
0 LdM LqM
 pD    2

 
1

 3 Pf 2 mM R M  2 J 2 L L
0
dM qM

0


2
2
3 PfM  mM  D
  re 
2 JLqM  
D 
 
0

3 Pf  mA
2 JR A02

 Dv M 0   Dv Aq  ..... (7)1  D1 

where suffix ‘0’ is the steady state value.
Above equation is the 2nd order state equation when the load angle
is zero, the -axis current is zero and the -axis current is zero in
the steady state. In addition, equation (7) assumes that the FOC isapplied with the non-interference control and the -axis voltage
command DvM* of the main inverter is zero as shown in Fig. 3.
Note that the characteristic equation can be solved as L is larger
than R from the state transition matrix A of (7). The damping
factor  and the natural angular frequency n, when the PMSM is0 mM


 1

L

M
0 mM  DiM  sin 0 0LM  DiM    Di Ad  
0

 0
  Di Aq   D  0
  re   0
2
  D  
3 PfM  mM
 0
iM 0 cos 0  iM 0 sin 0 


2
J
 0

0

sin 0cos 00RLA
2
3 PfA  mA
2

 mM

Main
(b) Simplification model

where p is differential operator, R is armature resistance, L is
synchronous reactance, Pf is the number of pole pairs of the pole,m is magnet flux linkage,  is the load angle, and J is the inertia
moment of motors. Suffix ‘A’ represents the parameter of the
motor that is connected to the auxiliary inverter, ‘M’ represents theparameter of the motor that is connected to the main inverter.
Equations (2) and (3), (4) are non-linear so that these equations
are linearized around the steady state. The state equation after the
linearization can be given by (6).
Equation (6) shows the 6th order of the state equation that iscomplicated to evaluate the stability. In order to simplify thisequation, it is assumed that the mechanical time constant is larger
than enough electrical time constant, then (6) can be approximatedas the 2nd order state equation, as (7).

Moreover, torque and speed equation can be given by0

M

Fig. 4. Simulation model of the PMSM in addition
auxiliary windings for damping control.

 re Lq A  i Ad   0 .................... (3)  
R A  pLq A  i Aq   re m A 

0

 TL

Auxiliary

Main(a) Connection diagram

On the other hand, the voltage equation of the motor that isconnected to the auxiliary inverter in d-q reference frame can begiven by

0

TA
PMA

INV.

INV.

Auxiliary  * Lq M  iM  sin      re m M  ........... (2)RM  pLq M  iM cos 

R

 M

LM

 pDiM  
 0

 
 pDiM   pDi Ad  0 pDi Aq  0 pD  
re

 
2
 pD   3 P 
fMmMsin 0
2
J

0

M

N:1

The damping control has to suppress the speed and torquevibration caused by the resonance between the inertia moment andthe synchronous reactance in each PMSM. In the proposed system,
the parallel connected PMSMs are driven while the resonance ineach PMSM is suppressed. In this chapter, the stability of the
proposed system with / without the damping control is clarified in
the root locus. Note that this chapter analyzes the case that one
PMSM is driven because the resonance occurs in each PMSM.
Fig. 4 shows the analysis model to confirm the suppression
effect with the damping control. The proposed system uses the
PMSM placed the auxiliary windings in the slots together with themain (conventional) windings, and so the mutual magnetic
interference occurs between the main and the auxiliary windings.
Due to the above reason, the control 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 neglectedin the analysis and the experiment.
The voltage equation of the motor that is connected to the main
inverter is represented as the voltage equation in the - rotating
frame because the main inverter is driven by the V/f control. Notethat the - rotating frame lags by the load angle  from the d-q
rotating frame as shown in Fig. 3. On the other hand, the voltage
equation of the motor that is connected to the auxiliary inverter isrepresented as the voltage equation in the d-q reference frame
because the auxiliary inverter control is FOC. Therefore, thevoltage equation of the motor that is connected to the main
inverter in the estimated rotating - frame is given by

v Ad   R A  pLd A 
v Aq    re Ld A

TM

PM

Stability Analysis

vM   RM  pLd M *vM    Ld M

 TL

0

LM



0
1

cos 0



0

0

0

1
LM

0

0

0

1
LA

0

0

0
0

0
0

0
1
LA
0
0


iM 0  iM 0   DvM  DvM 
0  Dv Ad   Dv Aq 
0   D * 


0 

1 

.....................................................................................................................................................................................................................................(6)3

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Parallel Connected PMSM Drive System Using Auxiliary Inverter (Tsuyoshi Nagano et al.)driven with only V/f control, can be given byD* +  0 .................................................................................... (8)

n 

-1

DiAq* ++ DvAqKi+

3 PfM mM............................................................... (9)2 JLqMDre

As mentioned above, when the PMSM is driven with only V/fcontrol, the resonance between the synchronous reactance and theinertia moment of the motor causes the torque vibration. On theother words, this vibration is unavoidable because the damping
factor  is zero. Then, the 2nd order state equation to which thedamping control is applied is derived.
Fig. 5 shows the state variable diagrams of the auxiliary inverter
control that is applied with the damping control. In Fig. 5, theq-axis voltage command DvAq*, it is assumed that the loop gain in
the current control is 1 (assuming that the current control response
is faster than the damping control response), can be given by



Kd



DiAq

Dx1

1
Ti

Fig. 5. State variable diagrams of the auxiliary inverter
control. If the current control response is faster thanthe damping control response, the loop gain in thecurrent control is 1. Therefore, the q-axis voltage
command DvAq* can be given by (10).
Table 1. Analysis and experimental conditions
PMM
1500

Rated power [W]Rated speed [min-1]
Rated current [A]Number of pole pairs
Armature resistance [W]d-axis inductance [mH]q-axis inductance [mH]Electro-motive force constant [Vs/rad]

Dv Aq   K d D *  D re .......................................................... (10)pDx1  0 ............................................................................. (11)where Kd is the damping gain.
Moreover, in Fig. 3, the -axis voltage command DvM* and the
-axis voltage command DvM* of the main inverter are given by

PMA
750

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

Inertia moment [kgm2]
0.0051 0.0026
Rotational speed in stationary state [rad/s]
900

Dv M  0 ............................................................................. (12)150

DvM   m M D * .................................................................. (13)Imaginary part

Substituting (10) and (13) into (7) yields the state equation ofpx  Ax  Bu ..................................................................... (14)where x  D re

D  , u  D

 3 PfM 2 mM

Kd
A 2
J

1

*

3 PfM  mM
2 JLqM022

 3 PfM 2 mM ,B
Kd 
J

2

1




2

 3
Kd

P
 2 fM 2


Kd=0
-50

Kd=0.946( = 1)
-300

-200

-100

0

100

Real partFig. 6. Root locus with the control structures in the
proposed system. Table I shows the evaluatedcondition. When the damping control is not applying,it shows that the proposed system is unstable. By
contrast, when the damping gain Kd increases, thepoles move into left half plane.

2

LqM 
 1 ... (16)J synchronous reactance. This resonance is caused by the drasticchange of the speed command. In this chapter, the suppression
effect of the damping control is clarified from the frequency
characteristics from the speed command to rotational speed in the
proposed system.
The transfer function is derived from the 2nd state equation of(14). The speed command D* to the rotational speed Dretransfer function is given by

At the damping gain Kd = 0, the poles are placed on the imaginary
axis as shown in (15). In other words, when the damping control is
not applied, it shows that the proposed system is unstable. By
contrast, when the damping gain Kd increases, the poles move intoleft half plane as shown in (16). Therefore, PMSM can be driven
stably in the proposed system by applying the damping control.

4.

0

-150
-400

3 PfM m M................................................................. (15)2 JLq M

3 PfM  mM
3 PfM mMs
Kd  i
2 2J
2 JLqM

50-100

Fig. 6 shows the transition of the pole placement (the root
locus) with the damping control when the damping gain Kd is
gradually changed. The poles when the proposed system is applied
without/with the damping control are given bys  iOnly V/f contol
With the damping control

100

3 Pf  m M
2
J
2

Dre

D *

Theoretical Analysis of Suppression
Characteristics

4.1
Suppression Effect of Damping Control
The
damping control has to suppress the speed and torque vibration
caused by the resonance between the inertia moment and the3 Pf  m M
3 Pf  m M
Kd s 2J
2 JLq M
2

s2 

2



2



(17)






i cos0  iM 0 sin 0mM s K d  M 0
 m M sin 0 



L

L

0
qM 0
 q M

4

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Parallel Connected PMSM Drive System Using Auxiliary Inverter (Tsuyoshi Nagano et al.)The damping factor  and the natural angular frequency n are
given by

3 PfM K d
2 2

n 

Motor
282V

PMM

LqM

....................................................... (18)J

Main inverter

3 PfM mM ........................................................... (19)2 JLqM

PMA

4.2
Minimum Power Capacity of Auxiliary Inverter
In the previous section, it is confirmed that the resonance between
the synchronous reactance and the inertia moment is suppressedby the damping control in the proposed system. However, in orderto obtain the larger suppression effect, the damping gain Kd has to
be increased, the output power of the auxiliary inverter becomeslarger. Moreover, the power capacity of the auxiliary inverter
depends on the speed command response. Thus, in this section, theminimum power capacity of the auxiliary inverter is clarified fromfrequency characteristics using the transfer function from theoutput power command, which is calculated by the speedcommand, to the output power of the auxiliary inverter. In the
proposed system, the main torque cannot be controlled directly
due to the V/f control. However, with calculating the transfer
function from the output power command to the output power, thefrequency characteristic of each output power is derived. If theelectrical and mechanical losses are neglected, the output power of
the auxiliary inverter depends on the mechanical output of the
motor. In other words, the transfer function of the output power
for the auxiliary inverter is derived from the mechanical output
transfer function of the motor. However, the mechanical output isnonlinear because the mechanical output is the product of two
variables; the rotational speed and the torque. Due to this reason,
the transfer function of the output power of the auxiliary inverter
is derived after the mechanical output is linearized. Then, thetransfer function from the speed command to the output power of
the auxiliary inverter is given by
DPA

D *

Auxiliary inverter

Fig. 7. Experimental construction in order to verify the
suppress effect of damping control
means the rate of the speed command.
The time response of the rotational speed is derived from theinverse Laplace transform of the ramp response of (17). In thissection, in order to simplify (17), it is assumed as 0 = 0, iM= 0
and iM0 = 0 in (17). Moreover, the overshoot of the rotational
speed can be derived from this time response, as given by sin nt peak 1   2 Dre _ Overshoot ............................ (23)2n 1   exp  nt peak 1t peak 
2

3 K d mA
2 J

3 PfM  mM
3 PfM  mMs 
Kd s 2J
2 JLqM222

n  2  1

3
Pf  mA K d  0 sin  n 1   2 t peak  .............. (25)2
DPaPeak  n 1   2 exp  n t peak3
 0 K d mA
2....................... (20)22
2
3 PfM  mM
3 PfM  mMs2 
Kd s 2J
2 JLqMs2

slog 2 2  1  2  2  1 
 ................................ (24)where  [rad/s2] is acceleration.
The overshoot of the rotational speed can be calculated by using(23).
Similarly, the time response of the output power of the auxiliary
inverter during the acceleration is also derived from the inverse
Laplace transform of the ramp response of (20). In this section, inorder to simplify (20), it is assumed as 0 = 0, iM= 0, iM0 = 0 in
(20). Moreover, the maximum output power of the auxiliary
inverter can be derived from this time response, as given by

The maximum output power of the auxiliary inverter can becalculated by (25).

Moreover, the transfer function from the power which is causedby the speed command to the output power of the auxiliary
inverter, it is assumed as 0 = 0, iM= 0, iM0 = 0 in (20), is given
by

DPA

DP*

Load

5. Experimental Verifications
5.1
Experimental Set-up In this chapter, in order toconfirm the effectiveness of the damping control, the experiments
are demonstrated with a motor - generator set.
Fig. 7 shows the experimental configuration to confirm theeffectiveness of the damping control in the proposed system. The
proposed system uses the PMSM placed the auxiliary windings in
the slots together with the main (conventional) windings, and so themutual magnetic interference occurs between the main and theauxiliary windings. Due to the above reason, the control for theauxiliary inverter becomes complicated. Therefore, in order toverify the proposed system, the proposed system is validated usinga model where two PMSMs are connected in series via single shaft
such as the motor-generator (M-G) set in the experiment. Note thatthe motor and generator work as main windings and the auxiliary
windings, respectively. As mentioned above, the effectiveness ofthe proposed system can be also verified with the M-G set asshown in Fig. 7.

................... (21)2where the relationship between the speed command and the power
P* which is caused by the speed command is given byD *1................................................................... (22)
DP * J0 s

4.3
Relation between Acceleration in Speed Command
and Output Power of Auxiliary Inverter
In section 4.2, theoutput power of the auxiliary inverter was discussed by frequency
characteristics. However, the acceleration or deceleration time isset as the speed command in practically. In this session, the output
power of the auxiliary inverter is discussed by acceleration which
5

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Parallel Connected PMSM Drive System Using Auxiliary Inverter (Tsuyoshi Nagano et al.)Main inverter q-axis current iqm

Main inverter q-axis current iqm[5A/div]000Deceleration time
0.2sec/div

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

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

0

Acceleration time
0.2sec/div

Deceleration time
0.2sec/div

Acceleration time
0.2sec/div

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

00
Auxiliary inverter q-axis current iqa[5A/div]

0

Speed command *[1000rpm/div]

Acceleration test

Rotaional Speed [1000rpm/div]

Rotaional Speed [1000rpm/div]

Rotaional Speed [1000rpm/div]0

Speed command *[1000rpm/div]0

Speed command *[1000rpm/div]

Rotaional Speed [1000rpm/div]0

Speed command *[1000rpm/div]

Acceleration test
Deceleration test(b) with damping control.

Deceleration test(a) without damping control

Fig. 8. Acceleration and deceleration test without/with damping control in motor-generator set. (a) After the acceleration, the
400 r/min - speed vibration is maintained. (b) The speed vibration is reduced from 400 r/min to nearly 0 r/min in comparedwith (a)n60Without the damping control

5.2
Damping Control Fig. 8 shows the experimental
results that illustrate the motor speed vibration when the proposedsystem is applied (a) without the damping control and (b) with thedamping control (  = 0.3 ) in an acceleration and deceleration test.
In this experiment, it is difficult to measure the torque response
directly. Therefore, the speed vibration is evaluated instead of thetorque response. In Fig. 8(a), the proposed system is implemented
without the damping control. The speed vibration occurs during theacceleration. After the acceleration, a 400 r/min of speed vibrationand the 10 Ap-p of current vibration in q-axis of the main inverter
are maintained. On the other hand, Fig. 8(b) demonstrates theexperimental results, where the proposed system is implemented
with the damping control (  = 0.3 ). The effectiveness of theauxiliary inverter from the results confirms that the speed vibrationis reduced from 400 r/min to nearly 0 r/min in compared with theacceleration test of Fig. 8(a). The 10 Ap-p of the current vibration in
the q-axis of the main inverter is suppressed as well. Then, theoutput power of the auxiliary inverter is suppressed to 13% of themain inverter when the damping factor is designed at 0.3. In thesame way as the acceleration test of Fig. 8(a), after the deceleration,
a 500 r/min of speed vibration and the 15 Ap-p of current vibrationin q-axis of the main inverter are maintained as shown in the
deceleration test of Fig. 8(a). In contrast, it is confirmed that, asshown the deceleration test of Fig. 8(b), the speed vibration is
reduced from 500 r/min to nearly 0 r/min and the current vibrationis reduced from 15 Ap-p to 0 Ap-p in compared to Fig. 8(a) in thesame way as acceleration test. Nevertheless, it is confirmed that the
q-axis current of the auxiliary inverter flows only during
acceleration and deceleration. Moreover, the maximum q-axis
current of the auxiliary inverter is 20% of the q-axis current of themain inverter. Therefore, it is confirmed that the auxiliary inverter
can suppress the speed vibration via auxiliary windings with asmall q-axis current of the auxiliary inverter even if in theacceleration and deceleration test.

Gain [dB]40
With the damping control ( = 0.3)

20
0

-20
Calculation

-40
-60

Experiment

1

100
10
Angular frequency [rad/s]

1000

Fig. 9. Frequency characteristics of the speed commandto the rotational speed in the proposed system. Table I
shows the evaluated condition. By applying thedamping control, the magnitude at the resonancefrequency decreases to 5 dB.
5.3
Frequency Characteristics of Proposed Damping
Control The frequency characteristics are demonstrated by theexperimental results in order to confirm the validity of thetheoretical analysis. Moreover, the suppression effect of thedamping control is discussed by comparing the peaks of theamplitude on the resonance frequency band.
Fig. 9 shows the frequency characteristic of the transfer
function (17) from the speed command to rotational speed of theV/f control. Table 1 shows the analysis and experimental
conditions. In Fig. 9, the magnitude at the resonance frequency nbecomes lower with the damping control in comparison to the
proposed system without the damping control. It means that the
suppression effect becomes higher with the proposed damping
control. Without the damping control ( = 0), the magnitude at theresonance frequency rises. By contrast, with the damping control(= 0.3), the magnitude at the resonance frequency decreases to 5
dB. The high suppression effect is obtained by increasing thedamping gain as shown (18) because the damping factor increases.
Therefore, the suppression effect of the damping control is
6

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Parallel Connected PMSM Drive System Using Auxiliary Inverter (Tsuyoshi Nagano et al.)clarified from the frequency characteristics of the transfer function(17) from the speed command to rotational speed in the proposedsystem. The proposed damping control can suppress the resonancebetween the moment inertia and synchronous reactance as show in
Fig. 9. In the experiment, when the constant speed command adds
sinusoidal wave as the speed command, the amplitude in thefrequency of the sinusoidal wave is drawn by observing the speed
response. The gain between the speed commands and rotational
speed in the experimental results has been plotted in Fig. 9 as dot
marks. The experimental results well agree with the analysis
results.
5.4
Minimum Power Capacity of Auxiliary Inverter
The power capacity of the auxiliary inverter depends on thetransient response for the speed command as described in section
4.2. In order to confirm the theoretical analysis, the frequency
characteristics between each output power and speed variation isinvestigated in the experiment.
Fig. 10 shows the frequency characteristics of the transfer
function from the power command to the output power of themain inverter, the auxiliary inverter, and the sum of the inverters
in the proposed system. In Fig. 10, the output power of theauxiliary inverter rises near the resonance frequency. On the other
hand, when the frequency components into the speed command
are lower and lower, the output power of the auxiliary inverter issuppressed more. In other words, the auxiliary inverter does notcontribute steady state i.e. constant speed. Nevertheless, although
the output power of the main inverter is constant because the main
inverter drives the motor. Note that the damping factor is designedby (18). When the frequency components included in the speedcommand are lower than 12 rad/s, the output power of theauxiliary inverter can become lower than 10% of the main inverteras shown in Fig. 10. This boundary condition is decided by inertia
moment J, q-axis inductance LqM, magnet flux linkage m and thedamping gain Kd as shown in (21). When the damping gain Kd
increases, the output power of the auxiliary inverter increase from
10% of the main inverter at 12 rad/s because the damping factor
increases. Therefore, the results show that the power capacity of
the auxiliary inverter can be designed to nearly several percent of
the main inverter when the proposed system is applied to theapplication which requires slow speed response such as fan
applications.
Fig. 11 shows the experimental waveforms that each output
power is measured at each operating point in Fig. 10 when 0.5 p.u.
of the constant speed command adds sinusoidal wave as the speedcommand. Assuming that the inverter output voltage is equal to thevoltage command, each output power is calculated from the voltage
command and the measured current. The waveforms in Fig. 11(a),(b) and (c) mention the operation at the point (a), (b) and (c) in Fig.
8, respectively. The other experimental results have been plotted inFig. 10 as dot marks. Comparing with each result, the amplitude
ratio between the output power of the auxiliary inverter and themain inverter is changed corresponding to the frequency
components included in the speed command. The experimental
results also well agree with the analysis results.
5.5
Relation between Acceleration in Speed Command
and Output Power of Auxiliary Inverter In this session, inorder to confirm the validity of proposed system in terms ofacceleration which means the rate of the speed command, therelationship between the output power of the auxiliary inverter and

(a)

60

(c)
Calculation

Sum output power
without the damping control( = 0)40

Gain [dB](b)Experiment20

Sum output( = 0.3)

0
-20
-40
-60

Main inverter( = 0.3)

Auxiliary inverter ( = 0.3)

100
1012
Angular frequency [rad/s]

1

1000

Fig. 10. Frequency characteristics of the transfer
function from power command to output power of themain inverter, the auxiliary inverter, and the sum of
the inverters in the proposed system.
1sec/div

00.4sec/div

00Power command [0.2p.u./div]

Power command [0.2p.u./div]

Power command [0.2p.u./div]

0

0

0

Sum of output power [0.2p.u./div]
Main output power [0.2p.u./div]00.2sec/div

Sum of output power [0.2p.u./div]
Main output power [0.2p.u./div]

Sum of output power [0.2p.u./div]
Main output power [0.2p.u./div]

00

Auxiliary output power[0.2p.u./div]

Auxiliary output power[0.2p.u./div]

00

Auxiliary output power[0.2p.u./div]0(a) 6.3 rad/s ( = 1 Hz)(b) 19 rad/s ( = 3 Hz)(c) 38 rad/s ( = 6 Hz)

Fig. 11. Experimental results that each output power ismeasured at each operating point ((a) is at 1 Hz, (b) is
at 3 Hz, (c) is 6 Hz) in Fig. 8 when 0.5 p.u. of theconstant speed command adds sinusoidal wave as the
speed command.

0.7

ExperimentCalculation
=n T=TRn)

0.6

=.9

Output power of the auxiliary
inverter [p.u.]

0.8

0.5
0.3

LM
J
J n

Rated acceleration [rad/s2]  n 
Rated rotational speed [rad/s]
Rated torque [Nm]

Tn
Tn

J
n
Tn

=n/4
=.9

0.2
0.1
0

3 Pf K d
2
2

Rated acceleration time [s] TRn 

=n/2
T=2TRn)=.9

0.4

Damping factor  T=4TRn)

0

=.1

=.1

=.1

0.05
0.1
0.15
0.2
0.25
Overshoot of the rotational speed [p.u.]

0.3

Fig. 12. Relationship between the output power of theauxiliary inverter and the overshoot of the rotational
speed the against speed command. Table 1 shows also
the evaluated condition. The higher suppression effectis obtained in exchange for the increase of the output
power of the auxiliary inverter because of increasing thedamping gain.
the overshoot of the rotational speed for speed command isdemonstrated in the experiment.
Fig. 12 shows the relationship among the damping gain Kd, themaximum output power of the auxiliary inverter during theacceleration and the overshoot of the rotational speed when the
PMSM is accelerated during one, half, quarter of the rated
acceleration n on the condition as shown in Table 1. The damping
gain is standardized by the damping factor  as given by (18). The
output power of the auxiliary inverter rises with the increase of the
7

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Parallel Connected PMSM Drive System Using Auxiliary Inverter (Tsuyoshi Nagano et al.)damping factor. On the other hand, the overshoot of the rotational
speed decreases with the increase of the damping factor, as shownin Fig. 12. The maximum output power of the auxiliary inverter (i.e.
the power capacity of the auxiliary inverter) depends on theacceleration factor  in the speed command as shown in Fig. 12.
The experimental results well agree with the calculation.

6.

Tm1
PM1M

Main

im2
Tm2
PM2M

Fig. 13 shows the simulation models that are used to verify theoperation of two sets of parallel connected PMSM. Since it isdifficult to construct our prototype of the drive system using two
PMSMs, the simulation is used to evaluate the validity of the
proposed controller as first step.
Fig. 14 shows the simulation results when two sets of parallel
connected PMSMs are driven by the proposed system with thedamping control. Smooth acceleration progresses are confirmed in
the two set of parallel connected PMSMs. Besides, when the rated
motor speed, load step applies to PMSM1 at 0.38s, and later also
applies to PMSM2 at 0.42s, the operation of the two auxiliary
inverters can be observed from the output power. The maximum
output power of the auxiliary inverter is approximately 0.25 p.u.
of the rated power of the main inverter. Although the power
capacity of main inverter increases with the increase of parallel
units, the power capacity of auxiliary inverter does not change
according to the numbers of parallel units.

M

PM1A

im1

INV.

Parallel Operation

1

TA1

INV.

Auxiliary

TA2

2
M

PM2A

Auxiliary

INV.

Fig. 13. Simulation model for parallel connected dual motor drive.
In order to neglect the magnetic coupling, two parallel drive of the
proposed system is validated using Fig. 8.
Acceleration time

Rated load step

1
Torque T1 [p.u.]0
Speed command * [p.u.]

Rotational Speed 1 [p.u.]

10
Rated load step
Torque T2 [p.u.]

10

7. Conclusion

Speed command * [p.u.]

This paper proposes a control technique to drive multiple
numbers of parallel connected PMSMs, and the proposed damping
control by using the small auxiliary inverter and the auxiliary
windings is analyzed theoretically and verified in the experiment.
The stability of the proposed system is analyzed and discussed by
the root locus. Moreover, the suppression effect of the damping
control and the minimum power capacity of the auxiliary inverter
were clarified from the frequency characteristics from the speedcommand to rotational speed in the proposed system.
In order to confirm the validity of the theoretical analysis, theexperiments were demonstrated with a motor - generator set. The
experimental results of the proposed system using 1.5 kW PMSM
drive system are obtained as follows;i ) The proposed system with damping control can reduce thespeed vibration from 400 r/min to nearly 0 r/min in spite ofsmall q-axis current by suppressing the torque vibration.
ii ) PMSM can be stabilized by the damping control.
iii ) The output power of the auxiliary inverter is suppressed to
10% of the main inverter when the speed response is lower
than 12 rad/s.
The experimental results well agree with the theoretical analysis
results. Thus, the validity of the proposed system is confirmed byboth the theoretical analysis and the experimental results.
In the future, PMSM added the auxiliary windings will be
designed and made. Next, the decoupling control of PMSM added
the auxiliary windings will be considered. In addition, driving two
PMSMs added the auxiliary windings in parallel with the proposedsystem will be considered and evaluated. After that, the proposedsystem will be evaluated and analyzed in detail; for example, thenecessity of external power supply connected the auxiliary inverter
will be considered in the future.

Rotational Speed 2 [p.u.]

10Main output power Pmain [p.u.]

Auxiliary output power Paux2 [p.u.]

Auxiliary output power Paux1 [p.u.]

1
0
0.0

0.2

Simulation Time [s]0.4

Fig. 14. Simulation results for parallel motor drive with damping
control. Smooth acceleration progresses are confirmed in the twoparallel connected PMSMs. After the rated motor speed, load step
applies to each PMSM, stable operation of each PMSM can be
confirmed.

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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Tsuyoshi Nagano(Student member) received his B.S. and M.S.
degrees in electrical, electronics and informationengineering from Nagaoka University ofTechnology, Niigata, Japan in 2012 and 2014,
respectively. Since 2014, he has been with Nagaoka
University of Technology as a Ph.D. degree student
His research interests include motor drives. He is a
student member of the Institute of ElectricalEngineers of Japan.

Goh Teck Chiang(Member) received his B.S. degree in electrical andelectronic engineering from Queensland Universityof Technology, Brisbane, Australia in 2004. Then, he
received his M.S. and Ph.D. degrees in electrical andelectronic systems engineering from Nagaoka
University of Technology, Niigata, Japan in 2009
and 2012, respectively. His research interests include
indirect matrix converters, PWM and motor drive.
He is a member of the Institute of ElectricalEngineers of Japan.

Jun-ichi Itoh

(Member) received his M.S. and Ph.D. degrees inelectrical and electronic systems engineering from
Nagaoka University of Technology, Niigata, Japan in
1996 and 2000, respectively. From 1996 to 2004, he
was with Fuji Electric Corporate Research andDevelopment Ltd., Tokyo, Japan. Since 2004, He has
been with Nagaoka University of Technology as an
associate professor. He received the IEEJ Academic
Promotion Award (IEEJ Technical Development Award) in 2007 and the
Isao Takahashi Power Electronics Award in 2010. His research interests
include matrix converters, DC/DC converters, power factor correction
techniques and motor drives. He is a member of the Institute of ElectricalEngineers of Japan.

9

IEEJ Trans. ●●, Vol.●●, No.●, ●●●