Verification of Parallel Connected Multiple Motor Drive System with
Numbers of Permanent Magnet Synchronous Motors
1

Tsuyoshi Nagano1 and Goh Teck Chiang1 and Jun-ichi Itoh1 and Koji Kato2
2
Nagaoka University of Technology
Sanken Electric Co., Ltd.
1603-1 Kamitomioka-machi
3-6-3 Kitano
Nagaoka city, Niigata, Japan
Niiza city, Saitama, Japan
2
Tel.: 1+81 / (258) – 47.9533.
+81 / (48) – 472.1111.
E-Mail: 1itoh@vos.nagaokaut.ac.jp 2k.kato@sanken-ele.co.jp
URL: 1http://itohserver01.nagaokaut.ac.jp/itohlab/en/index.html
2
http:// http://www.sanken-ele.co.jp/en/index.php

Acknowledgements
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.

Keywords«Permanent magnet motor», «Parallel operation», «Vector control», «AC machine».

Abstract
This paper discusses a multi-parallel drive system for permanent magnet synchronous motors
PMSMs). This system proposes to use two different functions of inverter, a main inverter with V/fcontrol to control the speed of all parallel connected PMSMs. Then, each of PMSM is individuallyconnected with an auxiliary inverter. The auxiliary windings which are used in the auxiliary inverter
are placed in the slots together with the conventional windings. In addition, implementation of thedamping control in the auxiliary inverter is discussed and the stability analysis is evaluated in order tosuppress the speed and torque vibrations which are caused from the resonance between the inertia
moment and the synchronous reactance. The simulation and experimental results demonstrate theeffectiveness of the proposed system. Moreover, the relationship between the damping gain and theoutput power of the auxiliary inverter is clarified. From the results, it can be confirmed that if theapplication that is required a slow response is applied in the auxiliary inverter, then the power capacityof the auxiliary inverter can achieve the smallest which is equivalent to 10% of the main inverter
power capacity.

1. Introduction
Recently, driving multiple motors in parallel at a time shows a good degree of interests incommunity. One of the techniques to drive multiple motors in parallel is to employ one large power
capacity inverter. One of the advantages of parallel motor drive by one large power capacity inverter is
to be able to reduce the numbers of the inverter and system cost. This application is commonly foundin the induction motor [1-2]. However, in the case of PMSMs, since each pole position of the PMSM
is different to each other, the motor current cannot be controlled to match the rotational coordinates byusing only one inverter. Therefore, it is difficult to drive the parallel connected PMSMs by using only
one inverter, due to the occurrence of the each phase differences between the rotational coordinates of
the inverter and the PMSM. In that case, the torque vibration occurs due to the resonance between a
synchronous reactance and the inertia moment of the motor. Therefore, the torque vibration needs tobe suppressed in order to drive the PMSMs in parallel.
Numerous studies have shown a number of ways to drive two PMSMs at a time, including theimplementation of a five-leg inverter [3-4] and also the implementation of a nine switches inverter [56] and so on [7-9]. However, the numbers of parallel units are limited by the number of legs in theinverter. Especially, it is not practical to drive several ten units of PMSMs by one large capacity
inverter at the same time.
The V/f control is suitable for multi-parallel drive for PMSM because the controller does not require
the information of the rotor position in the PMSM. The method that PMSM can drive by using theinformation of the current vibration is also studied [10]. However, this method cannot be applied to themulti-parallel drive system since the vibration of one motor can only be suppressed by one inverter.
In this paper, in order to drive PMSMs in parallel effectively, a multi-parallel drive system of
PMSMs based on V/f control is proposed. In the proposed methods, the vibration is suppressed byusing the auxiliary inverter. In addition, each of the PMSM is added with auxiliary windings. The
method that the iron core of the motor is used for integrating the transformer by using the auxiliary
winding is studied [11]. On the other hands, the auxiliary windings, which are connected to a small
power capacity inverter, can suppress the torque vibration. The power capacity of the auxiliary
inverter is much smaller than that of the main inverter because the power capacity of the auxiliary
windings is required to suppress the vibration. Note that the proposed system assumes that the each of
the motor in the multi-parallel connected PMSMs is driving at same speed and same load such as fans.
Different speed drive systems such as the electric train and electric vehicles are not considered in thispaper because the motor speed in each motor is different to each other.
This paper is organized as follows; first, the configuration of the proposed parallel drive system is
introduced. Next, the control method of the main inverter with V/f control and the auxiliary inverterwith field-oriented control is described. Next, the simulation and experimental results demonstrate thatthe proposed system can drive multiple of parallel connected PMSMs effectively by suppressing thetorque vibration. Then, the stability of the proposed system is analyzed and discussed by using the root
locus. Finally, the relationships among the response of the damping control, the overshoot of the motor
speed and the power capacity of the auxiliary inverter are clarified.

2. Proposed system and control structure
Fig. 1 shows the configuration of the proposed system. In PMSMs, the auxiliary windings which areused in the damping control (with the auxiliary inverter) are placed in the slots together with the main
windings as shown in Fig. 2. The proposed system uses two different power rating inverters. The firstone is the large power capacity inverter for the main windings to control the speed of the parallel
connected PMSMs. The second one is a small power capacity inverter for the auxiliary windings tosuppress the torque vibration. In term of the effectiveness of the proposed system, it is very importantthat the power capacity of the auxiliary inverter is enough small. In other words, the damping power
for the PMSM is much smaller than that of the main drive power.
Fig. 3 shows the control block diagram of the proposed system. In the proposed system, the main
inverter is applied with the V/f control and the auxiliary inverter is applied with the field-oriented
control and the damping controls. Each of the auxiliary inverter can control the current in auxiliary
windings of the PMSM in order to suppress the torque and speed vibration. Since the torque andMain windings

INV.
PM

Main inverter

INV

Auxiliary windings

Rotor
Auxiliary windings
Main windings

PM
INV
StatorPM

Auxiliary inverter

INV

Fig. 1.Configuration of the proposed system. The
proposed system uses two different power rating
inverters, the large power capacity inverter to drive
the motors and the small power capacity inverter tosuppress the vibration.

Fig. 2. Main windings and auxiliary windings. The
number of the auxiliary winding is less than thenumbers of the main windings.

*

1
s

D
Kd



q
+

id*= 0 ++v*f/V conv.

ACR
iq*

Decoupling
control

+

+

ACR

3f

vd*
dq
uvw

vq*



vua
vwa
vva
iu
iw
iv

+

id dq
uvw
iq

Damping control

vum
vwm
vvm

Main
power
converter

othersAuxiliarypower
converter

Auxiliarypower
converter

q
PS

PM

PM

Fig. 3.Control block diagram of the proposed system. The V/f control is applied to the main inverter
and the auxiliary inverters uses the field-oriented control for the damping control.

q
q' p




e



*
v

 : Rotational speed
*: Rotational speed commandd'd v : Output voltage

e : Electro-motive force : Load angle


Fig.4. Relationship between the d-q reference frame and the estimated rotating  frame. The
estimated rotating - frame lags by the load angle  from the d-q reference frame.

speed vibrations are caused by the phase difference between the rotational coordinates of the inverterand of the PMSM, it can be suppressed by the damping control in the auxiliary inverter.
Fig. 4 shows the relationship between the d-q reference frame and the estimated rtating - frame in.
a V/f control. In V/f control, the output voltage vector direction is defined as -axis, the axis whichlags by /2 rad from -axis can be defined as -axis. The lag of the load angle  occurs between the dq refrence frame and estimated rotating - frame as shonwn in Fig. 4. Therefore, the load angle  androtational speed re, the speed command * can be expressed asp   re   * ..................................................................................................................... (1)When the vibration of the speed is caused by the resonance between the inertia moment and thesynchronous reactance, the load angle  also is vibrating as shown (1). Then, notice that the changes ofload angle p is the difference between the rotational speed and the speed command, in order tocompensate the changes of load angle p, the q-axis current command iq* is calculated from thedamping controller as shown in Fig. 3. As a result, the vibration of the speed and torque caused by theresonance are suppressed by compensating the changes of the load angle with the current controlled by
the field-oriented control and the damping control.

3. Stability analysis
The damping control has to suppress the speed and torque vibration caused the resonance between
the inertia moment and the synchronous reactance. In this chapter, the stability of the proposed systemwith / without the damping control is clarified in a root locus. Besides, in the stability analysis, Surface
Permanent Magnet Synchronous Motor is analyzed in order to simplify the stability analysis. However,in the case of Interior Permanent Magnet Synchronous Motor, the same stability can be also obtained.
Fig. 5 shows the experimental system to confirm the suppression effect with the damping control.
The proposed system uses the PMSM placed the auxiliary windings in the slots together with the main
(conventional) windings, and so the mutual magnetic interference occurs between the main and theauxiliary windings. Due to the above reason, the control for the auxiliary inverter becomescomplicated. Therefore, the proposed system is validated using a model where two PMSMs are



Tm

TL

J

PM

PMM

M

 J

TA

TL
M

PMA

N:1
INV

INV

Auxiliary
windings

INV

INV

Auxiliary

Auxiliary
Main(a) Connection diagram

Main(b) Simplification modelFigs. 5. Verification model of the PMSM in addition the auxiliary windings. Due to the mutual magnetic
interference between the main and the auxiliary windings, this model is used to the verification.

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 was neglected in the simulation and the experiment.
Because it is impossible to control the current corresponding to the pole in the V/f control, thevoltage equation of the motor that is connected to the main inverter is represented as the voltage
equation in the estimated rotating - frame, which lags by the load angle  from the d-q reference
frame as shown in Fig. 4. On the other hand, the voltage equation of the motor that is connected to theauxiliary inverter is represented as the voltage equation in the d-q reference frame because theauxiliary inverter control is field-oriented control. Therefore, the voltage equation of the motor that isconnected to the main inverter in the estimated rotating - frame is given byv M   RM  pLM  * LM  iM  sin       re m M v   
 ..................................................... (2)*RM  pLM  iM cos 
 M    LM
On the other hand, the voltage equation of the motor that is connected to the auxiliary inverter in d-q
reference frame can be given by
v Ad   R A  pLA   re L A  i Ad   0 
v    
 ................................................................ (3)R A  pLA  i Aq   re m A  Aq    re L A
Moreover, torque and speed equations can be given by3
3
T  TM  TA  Pf  mM i sin   i cos  Pf  mA iq ........................................................... (4)22PfTM  TA  ........................................................................................................... (5)p re J
where p is differential operator, R is armature resistance, L is synchronous reactance, Pf is pairs of thepole, m is magnet flux linkage, and J is the inertia moment of motors, Suffix ‘A’ represents theparameter of the motor that is connected to the auxiliary inverter, ‘M’ represents the parameter of the
motor that is connected to the main inverter.
The equations (2) and (3), (4) are non-linear so that these equations are linearized in the stationary
neighborhood. The state equation after the linearization can be given bypx  Ax  Bu .................................................................................................................... (6)where x  Di M

Di M

R

 M

LM


 0



0
A

0


 3 Pf 2 msin  0
2 J
0




Di Ad

Di Aq

D re

0

0

R
 M
LM
0







D , u  Dv M
0




Dv M

m
LM

m

sin  0cos  0

0

0

R
LA

0

0

R
LA

0

0

0



3 Pf  mcos  02 J
0

0

3 Pf  m
2 J
0

2

LM

2

0

0
1

Dv Ad

Dv Aq



D * ,

 0 mLM 0 m
sin  0

LM


0
,

0


2

3 Pf  m
i cos  0  i sin  0 
2 J

0



cos  0

 1

 LM
 0


B 0


 0

 0

 0

0
1
LM

0

0

0

0

1

0

LA


i M 0  i M 0 


0 


0 

0 

1 

0
1

0

0

0

0

LA
0

0

0

0

The equation (6) shows the 6th degree of the state equation that is complicated to evaluate thestability. In order to simplify this equation, assuming that the mechanical time constant is larger thanelectrical time constant, then (6) can be approximated as the 2nd state equation, as follows:
2

P 


 pD re   0 3 f mM  mM  i M 0 cos  0  i M 0 sin  0  D re  L  pD   
2J M  D 


 1



0

 3 Pf 2 m sin 0 2 J  L
0 M

0

3 Pf  m 1

2 J
RA
0
2

2
3 Pf  m  0 L M  R M i M 0 sin  0   0 L M  R M i M 0 cos  0   Dv 



2 J
 0 2 LM  Dv q  D * 1............................................................................................................................................... (7)where suffix ‘0’ is the operating point.
In addition, (7) assumes that the field oriented control is applied with the non-interference control

D* +
Kd

-1

Dre

DiAq* +DiAq

+ DvAq

Ki

+



Dx1

1
Ti

Fig. 6.State variable diagrams of the auxiliary inverter control. If the current control response is fasterthan the damping control response, the loop gain in the current control is 1. Therefore, the q-axis
voltage command DvAq* can be given by (10).

and the -axis voltage command DvM* of the main inverter is zero as shown in Fig. 4. Notice the statetransition matrix A of (7), the characteristic equation can be solved as L is larger than R.
Fig. 6 shows the state variable diagrams of the auxiliary inverter control that is applying thedamping control. Notice in Fig. 6, the q-axis voltage command of the auxiliary inverter and the inputof the integrator in the damping control pDx1 are given by1
Dv Aq   K i K d D *  D re   K i Di Aq  Dx1 ...................................................................... (8)
Ti





pDx1   K i K d D *  D re  K i Di Aq .................................................................................. (9)However, in Fig. 6, the q-axis voltage command DvAq*, assuming 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
Dv Aq   K d D *  D re ............................................................................................................. (10)

pDx1  0 ....................................................................................................................................... (11)Moreover, in Fig. 3, the -axis voltage command DvM* of the main inverter is given by
Dv M   mM D * ........................................................................................................................... (12)Substituting the equation (10) and (12) into t (7) yields the state equation ofTable I: Verification condition
PM1&PM2

PM1 &PM2

Rated power [W]800

Synchronous inductance L M L A [mH]

3.78

-1

2000

Armature resistance R M R A [W]

0.425

3.82

Electro-motive force constant  M  A [Vs/rad]

0.233

Rated speed [min ]Rated torque [Nm]2

Rated current [A]8.2

Inertia momet J M J A [kgm ]0.018

Number of pole pairs P f

2

Rotational Speed in stationary state  0 [rad/s]

335

150
Only V/f contol
With the damping control

Imaginary part

100
50
0

Kd=0
-50

Kd=0.945905

-100
-150
-400

-300

-200

-100

0

100

Real partFig.7. Root locus with the control structures in the proposed system. Table I shows theevaluated condition. When the damping control is not applying, it shows that the proposedsystem is unstable. By contrast, when the damping gain Kd increases, the poles move into left
half plane.
2P  pD re   3 f mM K d pD    2
J

 

1


2

3 Pf  mM   mM

 i M 0 cos  0  i M 0 sin  0  D re 
2J LM  D 0 3 Pf 2 mM  sin  i 0 sin   i 0 cos  0  
 K d  mM D *
 2J
 0 LM
0




1

........................... (13)Notice the state transition matrix A of (13), assumed as 0 = 0, iM= 0, iM0 = 0, the characteristic
equation can be solved as L is larger than R, as given by

3 Pf  m
3 Pf  m
s
Kd 
2 2J
2 JLM

2

 3 K d LM 
  1 ........................................................... (14)P
 2 f 2JAs a result, Fig. 7 shows the transition of the pole placement (the root locus) when applying thedamping control when the damping gain Kd is gradually changed. At the damping gain Kd = 0, thepoles are placed on the imaginary axis. In other words, when the damping control is not applying, itshows that the proposed system is unstable. By contrast, when the damping gain Kd increases, thepoles move into left half plane. Therefore, PMSM can be driven stably in the proposed system byapplying the damping control.
2

4. Simulation for parallel drive operation
In previous chapter, the stability of the proposed system is discussed with / without the damping
control. In this chapter,
Fig. 11 shows the simulation models that are used to verify the operation of two sets of parallel
connected PMSM. As mentioned above, in order to neglect the magnetic coupling in the simulation,
the model where two PMSMs are connected in series via single shaft is used in the simulation.
Fig. 12 shows the simulation results when two sets of parallel connected PMSMs are driven by the
proposed system with the damping control as shown in Fig. 7. Smooth acceleration progresses are
confirmed in the two set of parallel connected PMSMs. Besides, when the rated motor speed, load step

Tm1

Rated load step

Main torque Tm1 [p.u.]

Auxiliary torque Ta1 [p.u.]

1 J

TA1

PM1

Acceleration timePM2

Torque T1 [p.u.]

M

INV

INV

Auxiliary

Main

Torque T2 [p.u.]

2 J

TA2

PM1

Rated load step

PM2

M

Main torque Tm2 [p.u.]

Auxiliary torque Ta2 [p.u.]

Speed command * [p.u.]

Rotaion Speed 1[p.u.]

Tm2
INV
AuxiliaryFig. 11. Simulation model for parallel connected
dual motor drive. In order to neglect themagnetic coupling in the simulation and theexperiment, two parallel drive of the proposedsystem is validated using Fig. 7 as shown in Fig.
5(b).

Rotaion Speed 2[p.u.]
Simulation Time [s]Fig. 12. Simulation results for parallel operation with
damping control based on the field-oriented control.

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 theauxiliary inverter is approximately 0.25 p.u. of the rated power of the main inverter. Although thepower capacity of main inverter increases with the increase of parallel units, the power capacity ofauxiliary inverter does not change according to the numbers of parallel units.

5. Experimental results to confirm the suppression effect with the damping
control
In this chapter, in order to confirm the effectiveness of the damping control, the experiments are
conducted with a motor –generator set.
Figs. 8 show the relationship between the simulation model and the motor-generator set in thispaper. Since the model is constructed from two PMSMs that are connected in series via single shaft asshown in Fig. 4 (b), if the load machine is removed as shown in Fig. 8 (a), then it is equal to themotor- generator set as shown in Fig. 8 (b).
Fig. 9 shows the experimental configuration to confirm the effectiveness of the damping control in
the proposed system. As mentioned above, the effectiveness of the proposed system can be verified
with the motor-generator set as shown Fig. 9. Therefore, in order to confirm the effectiveness of the
proposed damping control, the experiment is performed with the M-G set as shown in Fig. 9.
Figs. 10 show the experimental results that illustrate the motor speed vibration when the proposed
Tm

PM1

TA

 J

PM2

TL
M

Tm

PM1

Motor

TA

282V

PM

PM2
Main inverter

PM

INV

INV

Auxiliary
windings

Auxiliary
Main(a) Simplification model

INV

INV

Auxiliary inverter Load
Motor

Auxiliary
Main(b) Motor – Generator set

Figs. 8. Simulation model and motor-generator set. If theload machine is removed from (a), then it is equal to themotor-generator set as shown (b).

Load

Rated power: 1.5 kW
750 W
Rated speed:1800 r/min 1800 r/min
Rated current: 6.1 A
3A
Number of pole:33d-axis inductance : 11.5mH
15.2mHq-axis inductance : 23mH
33.2mH
Armature resistance : .522W
1.975W
Flux-linkage: 0.368Wb
0.338Wb

Fig. 9. Experimental configuration and condition

Acceleration time

Acceleration time
0.1sec/div

0.1sec/div

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

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

00

Auxiliary inverter q-axis current iqa [5A/div]
Rotaional Speed  [1000rpm/div]

0
Rotaional Speed  [1000rpm/div]

Speed command * [1000rpm/div]00

Speed command * [1000rpm/div](b) with damping control(a) without damping control

Figures 10. Acceleration 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 to nearly 0 r/min in compared with (a) by applying the damping control.

system is applied (a) without the damping control and (b) with the damping control in an acceleration
test. In this experiment, it is difficult to measure the torque response directly. Therefore, the speed
vibration is evaluated instead of the torque response. In Fig. 10 (a), the proposed system isimplemented without damping control. The speed vibration can be noticed during the acceleration.
After the acceleration, a 400 r/min of speed vibration and the 10 Ap-p of current vibration in q-axis of
the main inverter are maintained. On the other hand, Fig. 10 (b) demonstrates the experimental results,
where the proposed system is implemented with the damping control. The effectiveness of theauxiliary inverter can be noticed from the result that the speed vibration is reduced from 400 r/min tonearly 0 r/min in compared with Fig. 10 (a). The 10 Ap-p of current vibration in the q-axis of the main
inverter as shown in Fig. 10 (a) can be suppressed as well.

6. Consideration about the relationship between the damping gain and theoutput power of the auxiliary inverter
In the previous section, it is confirmed that the PMSM can be driven in the proposed system in theexperiment. However, if the damping gain Kd increases to obtain the larger suppression effect, theoutput power of the auxiliary inverter becomes larger. Thus, in this section, the relationship between
the damping gain Kd and the output power of the auxiliary inverter is clarified.
The speed command D* to the rotational speed Dre transfer function is given by2
i M cos 0  i M sin  0   mM
3 Pf  mM   mM
 i M cos  0  i M sin  0   s K d sin  0  J0
 0 LMD re 2


 LM

2
2
D *

3 Pf  mM
3 Pf  mM   mMs2 
Kd s 
 i M cos  0  i M sin  0 
2
J
2
J
 LM


............................................................................................................................................... (15)The time response of the rotational speed is derived from the inverse Laplace transform of the ramp
response of (15). In this section, in order to simplify (15), the equation (15) is assumed as 0 = 0,iM= 0, iM0 = 0. Moreover, the overshoot of the rotational speed can be derived from this time
response, as given byD re _ Overshoot t peak 

 





 sin  n t peak 1   2

 .............................................................................. (16)

 n 1   2 exp n t peak 2
2
1 log 2  1  2   1........................................................................................ (17)2n  2  1

3 Pf K d
2 2LM..................................................................................................................... (18)J

where  is acceleration [rad/s2].
The overshoot of the rotational speed can be calculated by using (16).
If the electrical 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 is nonlinear because the mechanical output is the product of two
variables, the rotational speed and the torque. Due to this reason, the output power transfer function of
the auxiliary inverter is derived after the mechanical output is linearized. The speed command D* tothe output power of the auxiliary inverter transfer function is given by
2



3
3 Pf  mM  i M cos 0  i M sin  0   mM sin  0  s  0 K d mA s 22 J 0 
LM
 
DPA


....................... (19)
2
2
D *

3 Pf  mM
3 Pf  mM   mM2
s 
Kd s 
 i M cos 0  i M sin  0 
2
J
2
J
L
M


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 (19). In this section, in order to simplify
the equation (19), the equation (19) is assumed as 0 = 0, iM= 0, iM0 = 0. Moreover, the maximum
output power of the auxiliary inverter can be derived from this time response, as given by3
Pf  mA K d  0 sin  n 1   2 t peak2............................................................................. (20)
DPaPeak  n 1   2 exp n t peak 
The maximum output power of the auxiliary inverter can be calculated by using (20).
Figs. 13 (a) and (b) show the relationship among the damping gain Kd, the maximum output powerof the auxiliary inverter during the acceleration and the overshoot of the rotational speed when the
PMSM is accelerated during one, twice, four times of the rated acceleration time on the condition asshown 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 damping factor. On the other hand,the overshoot of the rotational speed decreases with the increase of the damping factor, as shown in
Fig. 13(b). In other words, the higher suppression effect is obtained by increasing the damping gain.
However, from the point of the view of the power capacity of the auxiliary inverter, it needs todecrease the output power of the auxiliary inverter. In Fig. 13, if the output power is reduced to 0.1
p.u., the output power of the auxiliary inverter can be suppressed, under condition that the damping
factor is smaller than 0.1p.u by adjusting the damping gain. On the other hand, if the proposed system
is applied to the constant speed drive system, decreasing the power capacity of the auxiliary inverter
can be expected so that the maximum output power of the auxiliary inverter depends on theacceleration time as shown Fig. 13(a). The results show that, if the application that is required a slow
response is applied to the proposed system such as fan applications, the power capacity of theauxiliary inverter can be designed to nearly 10% of the main inverter.





1.2

=n/4(Taccel=4TR)

1.2

=n/2(Taccel=2TR)
=n(Taccel=TR)

0.8
0.6

3 Pf K d
2 2

LM
J

0.4

 

0.2

Simulation
Calculation by (20)

0

0

0.6
0.2
0.4
Output power of the auxiliary inverter [p.u.](a) Relationship between  and the output power

=n/4(Taccel=4TR)

1

Damping factor 

Damping factor 

1

Simulation
Calculation by (16)
 

0.8

=n/2

0.6(Taccel=2TR)=n

3 Pf K d
2 2

LMJ(Taccel=TR)

0.4
0.2

0.8

0

0

0.02
0.025
0.03
0.015
0.005
0.01
Overshoot of the rotational speed [p.u.](b) Relationship between  and the overshoot of the velocity

Figs. 13.Relationship between the damping factor  and the output power of the auxiliary inverter.
Table I show also the evaluated condition. n is the rated acceleration [rad/s2]. TR is the rated
acceleration time. Taccel is the real acceleration time. The higher suppression effect is obtained in
exchange for the increase of the output power of the auxiliary inverter by increasing the damping gain
However, if the application that is required a slow response is applied to the proposed system, thepower capacity of the auxiliary inverter can be designed to nearly 10% of the main inverter.

7. Conclusion
This paper discusses a control technique to dive multiple numbers of parallel connected PMSMs.
The features of the proposed system are following;The proposed system is composed by two different inverters, which are the main inverter for
speed control in parallel and the small power capacity auxiliary inverter to suppress the torqueand speed vibration.



In addition to the conventional windings (main windings) for the motor drive, each of the
PMSM is added with auxiliary windings to suppress the torque vibration.



The power capacity of the auxiliary inverter is small because the auxiliary inverter is operated
when the torque vibration needs to be suppressed.

From the stability analysis of the root locus, it was clarified that the PMSM can be stabilized byapplying the damping control in the proposed system. The experimental results demonstrated that the
proposed system can reduce the speed vibration from 400 r/min to nearly 0 r/min in spite of small qaxis current by suppressing the torque vibration by applying damping control to the auxiliary inverter.
For the experimental results, it was confirmed that the proposed system can be driven stably.
In addition, the relationship between the damping gain and the output power of the auxiliary
inverter is clarified. The results show that, if the application that is required a slow response is applied
to the proposed system such as fan applications, the power capacity of the auxiliary inverter can be
designed to nearly 10% of the main inverter.
In the future work, the internal structure of the auxiliary windings in PMSM of the proposed system
will be considered. Secondly, driving several units of motor-generator in parallel with the proposedsystem drives will be considered.

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