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

Paper
Paper

Maximum Torque per Ampere andMaximum Efficiency Control Methods based on V/f control
for IPM Synchronous Motor
Jun-ichi Itoh＊a), Member, Yuki Nakajima＊, Student Member, Goh Teck Chiang＊, Student Member(Manuscript received Jan. 00, 20XX, revised May 00, 20XX)
This paper discusses a Maximum Torque per Ampere (MTPA) and maximum efficiency control methods which are based on
the Volt per Hertz (V/f) control for an Interior Permanent Magnetic Synchronous Motor (IPMSM). The V/f control is inherently aposition sensorless method, therefore it is simpler than the conventional methods such as the sensorless vector control method. In
addition, the MTPA and the maximum efficiency controls can be achieved by controlling the reactive power without the
information of magnet pole position. The MTPA control can reduce the copper loss in IPMSM and achieve high efficiency.
Furthermore, maximum efficiency control is further improving the efficiency after implemented the MTPA, which tends toreduce both the copper and iron losses. In this paper, the validity of the MTPA methods is confirmed by simulation andexperimental results. From the experimental results, the output current is reduced by 76% after implemented the MTPA to control
the reactive power. In addition at 0.6 p.u. torque and 1.0 p.u. motor speed, the simulation results demonstrate that the maximum
efficiency control can further reduce the total losses.
Keywords : IPM synchronous motor, V/f control, maximum toque per ampere control, maximum efficiency control, reactive power

1.

control block diagram is simpler than that of the sensor less vector
control. Especially, the motor parameters are not used in thecontrol. In Ref. (14) and (15), id=0 control method based on V/fcontrol for Surface Permanent Magnetic Synchronous Motor(SPMSM) has proposed. However, for the IPMSM, id=0 control is
not effective because the reluctance torque cannot be usedeffectively.
On the other hand, the MTPA control methods based on the V/fcontrol have been investigated(16)~(17). The MTPA control method
can be achieved by regulating the current phase to control thereactive power. Therefore, the V/f control method is effective inthose applications that do not need a high response torque control
such as a fan and a pump.
However, the detail of the MTPA control method is clarified
only by simulations as reported in Ref. (16) and (17). In anotherwords, the characteristics of the MTPA in IPMSM are notevaluated practically in an experiment. Furthermore, themaximum efficiency point is different from the MTPA operation
on IPMSM. That is, the maximum efficiency control for IPMSM
based on V/f control has not been discussed so far. Furthermore inorder to apply MTPA control method based on V/f control, d andq-axis inductance values (Ld and Lq) are used. The inductanceidentification method based on V/f control is required to obtain the
motor parameters simply.
In this paper, the characteristics of the MTPA control strategy
are clarified by experimental results. Besides, the maximum
efficiency control method and the inductance identification
method based on V/f control are proposed.
This paper will be organized as follows; at first, the principle of
the V/f control for IPMSM with a damping control is introduced.
After that, the MTPA based on V/f control is described compared

Introduction

IPMSM has been intensively studied due to the attractive
features, high efficiency, high density and high speed
rotation(1)~(6).
The vector control method is widely applied to drive the
IPMSM. The vector control method is necessary to detect themagnet pole position by using a position sensor such as an
encoder and a resolver. However, the position sensors constrain
the cost in motor drive systems.
In order to remove the position sensor, several kinds ofsensorless vector control methods have been studied and proposed
for IPMSM(7)~(13). The sensorless vector control method estimatesthe magnetic pole position of the IPMSM by using the motor
voltage, the motor current and motor parameters. However, thecalculation for the position estimation is complicated. The
stabilization is difficult due to inconsistent control parameter. In
addition, the error of the position estimation occurs easily when
the parameters are mismatching between the controller and the
motor. Especially the motor parameters will change according to
the motor temperature, flux saturation and so on. As a result, it isdifficult to ensure the stability of sensorless vector control.
On the other hands, open loop control which has no current
regulator such as the Volt/Hertz (V/f) control methods for the
PMSM have been studied(14)~(17). The V/f control method does notessentially require the information of the pole position because thecontrol algorism is implemented on -flame which the -axis
corresponding to the output voltage vector of an inverter. Thea) Correspondence to: Jun-ichi Itoh. E-mail: itoh@vos.nagaokaut.ac.jp＊
Nagaoka University of Technology
1603-1, Kamitomioka-machi, Nagaoka city, Niigata, Japan 940-2188© 200● The Institute of Electrical Engineers of Japan.

1Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)to id = 0 control method. Moreover, the maximum efficiency
control considering iron loss is proposed.
Secondly, the identification methods for Ld and Lq based on theV/f control is proposed in chapter 4. These methods are
implemented with the MTPA
Finally, the MTPA control method and the maximum efficiency
control method based on V/f control method are confirmed insimulation and experimental results. The prototype uses 1.5-kW
IPMSM with a two-level inverter. In addition, the inductanceidentification method is demonstrated in the experiment. These
results indicate the validity of the proposed method.

2.

q



 re
V

i

rm*

re*
Pf

f/v conv.

v**

v* +

dq/3f

vv*
vw*

+

High
Dv*
Efficiency
Control

 1* 1

+
HPF

K1

re*

s
iu

i
Damping
control

i

3f/dq

iv
iw

Fig. 2. V/f control method based on -frame. The
motor is controlled by V/f control method with damping
control.

1 Lq  i  sin  re m  ........ (2)Ra  pLq  i cos is given on -axis. In addition, the electromotive force remoccurs on the q-axis. Therefore, the gap angular  between the
-axis and dq-frame depends on the load angular.
2.2 Damping control
Fig. 2 shows the block diagram of
the V/f control method based on -frame. When motor iscontrolled by simple V/f control method which means an open
loop control, the torque vibration is generated due to the resonancebetween the synchronous reactance and the moment of inertia of
the IPMSM as indicated in Ref. (13).
In Ref. (13), the V/f control method based on the -frame with
damping control has been proposed. The torque vibration causes
the vibration of the -axis current because the -axis current is anactive current. In another words, the vibration component of the
-axis current can be taken as a reference to assume the vibration
component of the torque. The damping control suppresses thetorque vibration with a feedback from the -axis current into theelectric angular frequency reference value re* in order to cancel
the load angular vibration. When the damping control is applied,the damping coefficient is a function to the feedback gain K1,
therefore, the stable operation can be achieved.
2.3 Maximum torque per ampere control based onreactive power control
The reactive power on dq-frame Qdq
is given by (6).

T  Pf  miq  Pf  m i sin  i cos ............................ (3)

J

vu*

v*=0

where v() is the ()-axis voltage, i() is the ()-axis current, and1 is the rotating speed of -frame. Here, the equation of thetorque and the relationship between the electric angular velocity
and the torque on -frame is given by (3) and (4) respectively. It
is noted that the viscosity resistance is ignored.

Pf T  TL 

dFig. 1. Relationship between -frame and dq-frame.
The -axis is defined as the direction of the output
voltage vector of the inverter, and the direction of the
q-axis is defined as the electromotive force vector.

where vd(q) is the d(q)-axis voltage, id(q) is the d(q)-axis current, reis the electric angular frequency, p is the differential operator, Ra isthe armature resistance value, Ld(q) is the d(q)-axis synchronous
inductance values, and m is the flux linkage of the permanent
magnet. Then, the voltage equation of IPMSM based on -frame
is obtained by (2).

pre 

Iafire Lq  id   0 .................. (1)  
Ra  pLq  iq  re m 





rem

2.1 V/f control based on the output voltage vector of theinverterFig. 1 shows the relationship between -frame anddq-frame. Generally, in the dq-frame of the IPMSM control, thed-axis is defined as the direction of the flux vector by thepermanent magnet and the direction of the q-axis is defined as theelectromotive force vector. Therefore, it is very important to
identify the flux vector in the vector control. However, the V/fcontrol method is implemented on the -frame, and the -axis isdefined as the direction of the output voltage vector of the inverter.
Therefore, the -axis is referred as the active power component
and the -axis is referred as the reactive power component.
The voltage equation of IPMSM based on dq-frame is given by(1).

v   Ra  pLd
  Lv   1 d

RaIa



High efficiency control strategy based on V/fcontrolvd   Ra  pLd vq   re Ld

 L d id 2  L q iq 2........................................................... (4)where Pf is the pairs of poles, T is the output torque, TL is the load
torque, and J is the inertia of the motor. The gap angular 
between -frame and dq-frame is given by (5).

p  1  re ................................................................. (5).
In the steady state, the rotating speed in either -frame or
dq-frame is same value. However, in transient state, the gap
angular between -frame and dq-frame occurs due to thevariation in the rotating speed. Here, the differential of isequaled to the difference between 1 and re.
From the definition of the -frame, the output voltage vector v
2

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)Qdq  vq id  vd iq ........................................................... (6)



+



2



Qdq  re Lq iq  re Lq I a  re Lq i  i222

Fig. 3. Control block diagram of id = 0 control method
based on V/f control. The Dv* compensate the -axis
voltage command v* in order to accomplish (10).

 ............. (8)i1Therefore, if v is regulated to confirm the reactive power whichis calculated from the -frame on (10), the id = 0 control can beachieved without the information from the dq-frame.



Ra

id

iod

vd





iq





vq







reLdiod

Rc

+

rem

voq
Lq

(b) q-axisFig. 5. Equivalent circuit considering the iron loss
based on dq-frame.

Equation (13) is the reactive power when the MTPA control isachieved. Therefore, if the Q as shown in (9) equals to Qdq asshown in (13), the MTPA control can be achieved. In anotherwords, the satisfaction of (14) achieves the MTPA control during
the V/f control.



ioq +

-

Qdq  re Ld X 2  Lq I a  X 2  m X ........................ (13)
2

Ra
icq

Note that the current phase becomes zero when Ld equal to Lq
i.e. it means SPMSM because 1st term equals to 2nd term. If thisis defined as Iasin () = X, then the equation of the reactive power
is obtained by (13).

Ld(a) d-axis

2


 1
m

   .... (12).
 4 Lq  Ld I a 
2






+

reLqioq

vod

Rc



where the equation of the  when the MTPA control(18)~(22) isgiven bym
  sin  4Lq  Ld I a



-

icd

Qdq  re Ld I a sin2   Lq I a cos2   m I a sin  ......(11)

1

LPF

Fig. 4. MTPA control method based on the reactive
power control for IPMSM. Qdq command value iscalculated from (13) at the Qdq* calc. block

Fig. 2 and Fig. 3 show the control block diagram of the id = 0
control method based on V/f control for IPMSM. The detail of thehigh efficiency block diagram in Fig. 2 is shown in Fig. 3.
On the other hand, when the IPMSM is controlled, thereluctance torque cannot be used if id = 0 control is applied.
Therefore, the MTPA control based on V/f control for IPMSM is
described as following.
Equation (7) can be rewritten as (11) by using the output current
Ia and the current phase.
2

PI

Q

*

v**

re Lq i 2  i 2  v i ................................................. (10)

2

Dv*

Qdq* +

Qdq*
calc.

i

Q  v i ...................................................................... (9)



LPF

v**

On the other hands, the reactive power based on -flame Q isgiven by



PI

Q

1*

At first, id = 0 control which is often used in a SPMSM to
obtain the maximum efficiency, is considered in order to compare
the MTPA for IPMSM. Equation (7) can be rewritten as (8) whenid = 0.
2

Dv*

Lq

+

i

Qdq  re Ld id  Lq iq  m id ................................... (7)
2

Qdq*
+

i

By substituting (1) into (6) the reactive power Qdq can be
expressed as (7).

-axis voltage command v* in order to accomplish (12).
2.4 Maximum efficiency control method based on V/fcontrol
The aim of MTPA control is the reduction of thecopper loss of IPMSM. However, in order to improve the motor
efficiency, the iron loss needs to be considered and analyzed. Then,the maximum efficiency control method based on V/f control is
proposed.
Fig. 5 shows the equivalent circuit considering the iron loss
based on dq-frame(23)~(24). Here, Rc is the equivalent iron loss
resistance.
The voltage equation based on dq-frame is obtained by (15) and
(16).



re Ld X 2  Lq i 2  i 2  X 2  m X  v i ................ (14)In order to satisfy the condition in (14), the PI controller isimplemented to regulate the -axis voltage v.
Fig. 4 shows the control block diagram of the MTPA control
method based on V/f control. The control block shown in Fig. 3 isthe same as the high efficiency block witch is shown in Fig. 2. In
addition, the command Qdq is calculated from (13) at the Qdq* calc.
block in Fig. 4. The high efficiency block conform Q to Qdq* by
PI controller. The PI controller outputs the -axis voltage
command compensation value of Dv*. The Dv* compensates thevd iod   Ra vod L   p  d   Ra    1 Rc voq  vq 
ioq  03

0  iod    ........ (15)Lq  ioq 

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)vod   0 
voq  Ld

 Lq  iod   0 
   
 ............................ (16)0  ioq  a reLqIa

Here, iod and ioq are given by (17) and (18).
iod  id  icd  id 

ioq  iq  icq  iq 

Lq ioq a  Ld iod 
Rc

RaIa

V

............................................ (17)

Rc

q

rem
i

Ia=iq

=f

i

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

In addition, the iron loss Wi is given by (19)d L i    L i     ................ (19)
V
W 

2

2

o

i

re

2

q oq

re

Rc

d od

re

m

Rc

Fig. 6. Vector diagram of the IPMSM driven by V/fcontrol when id = 0 control. The vector directions ofrem and RaIa become the same when id = 0

Therefore, in order to achieve the maximum efficiency control,
considering of not only the copper loss but also the iron loss isimportant.
The reactive power reference value of maximum efficiency
control method is obtained from (20).







First, (13) is transformed into (23), when Ld_est is the estimation
value of Ld.



2

*

Identification methods for Ld and Lq based on theV/f control

4.

Qdq  re Lq _ est i  i  ......................................... (21)
2

2

2







Simulation results

Qdqref _ cmp  A rm  B rm ............................................ (24)

As following, when Lq_est is equaled to Lq, id = 0 control can beachieved. Therefore, by varying the Lq_est and observing the d-axis
current, then Lq is possible to estimate.
However, during the V/f control, d-axis current cannot be
observed directly because the magnet pole position is not used. As
the result, id = 0 can be determined by (22).

v  re m  Ra I a   re Lq _ est I a2

4.1 Maximum efficiency control method based on V/fcontrol
Fig. 7 shows the simulation result when Qdqref_cmp
varies and Rc is assumed to be 300 . The minimum point of thetotal loss Wc + Wi is Qdqref_cmp = 0 p.u., when rm is 0 p.u.. On theother hand, the minimum point of the total loss is Qdqref_cmp = -0.4
p.u. when rm is 1.0 p.u. From the results, it is confirmed that thecurrent phase varies when the total loss becomes minimum since
the rotating speed of the motor is changed because the iron loss
variesFig. 8 shows the values of Qdqref_cmp that can achieve the lowest
losses subject to the motor speed. From Fig. 8, the equation of
Qdqref_cmp can be expressed by (24).

3.1 q-axis inductance identification method based on
MTPA control method
The MTPA control method based on
V/f control requires the information of motor parameters.
Therefore, if the motor parameter is different from the actual value,
the Qdq* might not become an appropriate value to minimize the Ia.
Therefore, the estimation of reactance of the IPMSM is required.
Here, by using id = 0 control method based on the V/f control, theq-axis inductance value Lq can be identified.
Here, (8) is transformed into (21), when Lq_est is the estimation
value of Lq.
*



As following, when Lq_est is equaled to Lq, the output current Ia
becomes its minimum. Therefore, by varying the Lq_est andobserving the Ia, and then the Ld can be estimated.
However, if Lq is different from the actual value, Ia might
become smaller when Ld_est is not equaled to Ld. Therefore, Lqshould be estimated by using the proposed Lq identification
method that has been discussed in this chapter.

From the MTPA control based on V/f control, it is confirmedthat the current phase can be controlled indirectly by control of thereactive power. Therefore, Qdqref is varied by the reactive powerreference compensation value Qdqref_cmp and the current phase isregulated. As the result, the maximum efficiency point can befound.

3.

Qdq  re Ld _ est X 2  Lq I a  X 2  m X ................... (23)Qdq  Qdqref _ cmp  re Ld X 2  Lq I a  X 2  m X ...... (20)2Here, in this IPMSM, A and B are -0.547 and 0.141 respectively
from the curve in Fig. 8.
Fig. 9 shows the amplitude of the total loss when the reactive
power reference value is varied by adding the error Qdqref_vary as
expressed in (25).
Qdq  Qdqref _ vary  Qdqref _ cmp.................. (25)2
  re Ld X 2  Lq I a  X 2  m X

 ........................ (22)2Equation (22) is valid only when id = 0 because the vector
directions of rem and RaIa become the same when id = 0 (shownin Fig. 6). Then, Lq_est can be assumed to be equaled to Lq. That is,
the id=0 point is found out by comparison between right term andleft term of (22) without rotor position information. Note thatthe proposed estimation method for Lq does not use Ld. Therefore,
Lq is estimated independently.
3.2 d-axis inductance identification method based on
MTPA control method
Using MTPA control method basedon V/f control, the d-axis inductance value Ld can be identified.







Here, Qdqref_cmp from (24) is substituted into (25) and Qdqref will
be compensated depending on rm. When Qdqref_vary is zero, it isconfirmed that total loss can be reach its minimum.
4.2 d and q-axis inductance identification method basedon MTPA control method
Fig. 10 shows the simulation
result of Lq identification method. Here, the horizontal axis is theratio between Lq_est and Lq, and the vertical axis is the difference
between right and left sides of (22). The simulation conditions are
4

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Copper loss Wc, Iron loss Wi
Total loss Wc+Wi [W]

Wc

Wi+Wc:Minimum
Wi
0

0.2
0.4
0.6
Reactive power referencecompensation value Q dqref_cmp [p.u.]

Wi

150
100

Wc

0
-0.6

-0.4 -0.2
0
0.2
0.4
0.6
Reactive power referencecompensation value Q dqref_cmp [p.u.](b) rm = 1.0p.u.

50

Wc

0
-0.6 -0.4 -0.2
0
0.2
0.4
0.6
Variation of reactive power reference value
Q dqref_vary [p.u.](Em+RIa)2+(reLd_estIa)2-v 2

0.2
0
-0.2
-0.4

id

-0.6
0

0.2
0.4
0.6
0.8
1
Ratio between Lq_est and Lq
Lq_est/Lq [p.u.]

1.2

Fig. 10. Relationship between Lq_est/Lq, id and thediscriminant (Load torques are 1.0 p.u. and rotating
speeds are 1.0 p.u.).

0.1
0

0.93

Output current Ia [p.u.]

Reactive power referencecompensation value Q dqref_cmp [p.u.]

Fig.7. Relationship between Qdqref_cmp and the total
loss (Load torques are 1.0 p.u.).

-0.1
-0.2
-0.3
-0.4
-0.5

Wi
100

(Em+RIa) +(reLd_estIa) -v  [p.u.]

Wi+Wc:Minimum

50

150

2

250
200

Wi+Wc:Minimum

Fig. 9. Relationship between Qdqref_vary and the total
loss with Maximum Efficiency control (Load torques
are 1.0 p.u. and rotating speeds are 1.0 p.u.)d-axis current id [p.u.]

Copper loss Wc, Iron loss Wi,
Total loss Wc+Wi [W](a) rm = 0p.u.

200

2

800
700
600
500
400
300
200
100
0

2

Copper loss Wc, Iron loss Wi
Total loss Wc+Wi [W]Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)

0

0.2
0.4
0.6
0.8
Rotating speed rm [p.u.]

1

Fig. 8. Relationship between rm and Qdqref_cmp when
the total loss minimum (Load torques are 1.0 p.u.).

0.925

Minimum

0.92
0.915
0.91
0.905

0

0.5
1
Ratio between Ld_est and Ld
Ld_est/Ld [p.u.]

1.5

Fig. 11. Relationship between Ld_est/Ld and Ia(Load torques are 1.0 p.u. and rotating speeds are 1.0
p.u.).

follows; the rotating speed command value is 1.0 p.u. and the load
torque is 1.0 p.u. When the difference between left and right sidesof (22) is equaled to 0, it is confirmed that id = 0 and Lq_est isequaled to Lq. As the result, it is confirmed that this method canestimate the Lq.
Fig. 11 shows the simulation result of Ld identification method.
The horizontal axis is the ratio between Lq_est and Lq, and thevertical axis is the output current value Ia. The simulation
conditions are follows; the rotating speed command value is 1.0
p.u. and the load torque is 1.0 p.u. When Ia becomes its minimum,

the result can confirm that Ld_est is equaled to Ld. As the result, it isconfirmed that this method can estimate the Ld.

5.

Experimental results

5.1 Maximum torque per ampere control method basedon V/f control
Fig. 12 show the schematic of theexperimental system. The IPMSM is driven by a two-level

5

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)InverterInverter
IPM
motor

Diode
RectifierCoupling

Grid

Load
motor

PWM
Converter
Load

Fig. 12.

Schematic of the experimental system.

Table 1.

Motor parameter using the experiment.

Motor Power
Rated Current
Rated Speed
Number of Poles
Winding Resistanced-axis Inductanceq-axis InductanceInterlinkage magnetic flux

1.5kW
6.1Arms
1800rpm
6poles
0.783
11.5mH23.0mH0.246V・s/rad

0.5

Minimum

0.4
0.3
0.2

-0.08 -0.04
00.04 0.08 0.12
Variation of reactive power command value
Q dqref_vary [p.u.]

Fig. 14. Relationship between Qdqref_vary and Ia with
MTPA control method (Load torques are 0.2p.u. androtating speeds are 0.2p.u.). The amplitude of the output
current becomes minimum at 0.23 p.u. when thereactive power command value is equivalent to thetheoretical value.

d-axis current value [0.5 p.u./div]0
q-axis current value [0.5 p.u./div]0

Output current Ia [p.u.]

1
Withot MTPA control
0.9
0.8
0.7
0.6
0.5
With MTPA control
0.4
0.3
0.2
0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Rotating speed rm [p.u.]u-phase output current value [5.0 A/div]0

Proposed MTPA control : on

0.6

Output current Ia [p.u.]

Grid

400 [ms/div]

Fig. 13. Variation of the dq-frame and u-phase current
by the MTPA control method based on V/f control(Load torque is 0.2p.u. and rotating speed is 0.4p.u.).
The output current can be reduced by 68 % (from 0.72
p.u. to 0.23 p.u.) after applying the MTPA control
method.

1

Fig. 15. Variation of the output current with/without
MTPA control method when rotating speed is changed(Load torques are 0.2p.u.). Even if the load condition isvarying, the proposed method can reduce the output
current.

inverter and the switching frequency is 10 kHz. In addition, theload motor is used as load machine to supply a constant torque. In
this experiment, in order to confirm the effectiveness of the MTPA
control method based on V/f control, the information of magnet
pole position is obtained from a Hall Effect sensor. However, theinformation of magnet pole position is not used in the actual motor
drive system.
Table 1 shows the motor parameters that are used in theexperiment. The IPMSM has a saliency ratio of 2.0.
Fig. 13 shows the experimental results of the IPMSM drive
operation using the two-level inverter with the MTPA control
method based on the V/f control method. The experimental
conditions are follow; the rotating speed command value is 0.4 p.u.
and the load torque is 0.2 p.u.. From Fig. 4, the output current canbe reduced by 68 % (from 0.72 p.u. to 0.23 p.u.) after applying the
MTPA control method. If the MTPA control is disabled, thereluctance torque cannot reach its maximum and the output
current becomes large. On the other hand, if the MTPA control isenabled, the reluctance torque can reach its maximum and theoutput current becomes its minimum.
Fig. 14 shows the amplitude of the output current when thereactive power is varied by adding the error Qdqref_vary as (26).









Qdq  Qdqref_vary   re Ld X 2  Lq I a  X 2  m X .. (26).
*2

In Fig. 14, the horizontal axis shows the difference between thereactive power command value and the theoretical value Qdqref. It
is confirmed that the amplitude of the output current becomesminimum at 0.23 p.u of the rated current. when the reactive powercommand value is equivalent to the theoretical value. It means thatthe reactive power command from (13) can minimize the output
current at the constant load torque. As a result, the effectiveness of
the MTPA method can be observed.
Fig. 15 shows the amplitude of output current when the loadcondition varies. Even if the load condition varies, the MTPA
method can reduce the output current. In addition, the output
current can be reduced by 76 % (from 0.96 p.u. to 0.23 p.u.).
5.2 Maximum efficiency control method based on V/fcontrol
Fig. 16 shows the experimental results to confirm theoperation of the maximum efficiency control. The schematic of
the experimental system is shown in Fig. 12. The experimental
conditions are follow; the rotating speed command value is 1.0 p.u.
6

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)d-axis current id [p.u.]

Wc : minimum
34

0.12[p.u.]
32

0.02
0.01
0

-0.02
0.25
40

(rem+RIa)2+(reLq_estIa)2-v
[V2]

30
-0.2
-0.1
0
0.1
100
V ariation of reactive power reference value[p.u.]
WQ
decleasei :dqref_cmp98

Lq_est/Lq = 0.98

-0.01

0.5

0.75

1

1.25

1.5

1.75

0.5

0.75

1

1.25

1.5

1.75

30
20

96

10

94

-20
0.25

90
-0.2
-0.1
0
0.1
Variationofreactive
power
referencevalue
132
Q dqref_cmp [p.u.]
130

0

-10

92

Ratio between Lq_est and Lq
Lq_est / Lq [p.u.]

Fig. 17. Variation of the output current with/without
MTPA control method when rotating speed is changed(Load torques are 0.2p.u.).

Wc+Wi : minimum

128

0.233

Output current Ia [p.u.]

Total loss Wc+Wi [W]Iron loss Wi [W]Copper loss Wc [W]

36

126
124
-0.2
-0.1
0
0.1
Variation of reactive power reference value
Q dqref_vary [p.u.]

Fig. 16. The relationships between the Qdqref_vary and thecopper loss, iron loss, and total loss with maximum
efficiency control (Load torques are 0.6 p.u. and rotating
speeds are 1.0 p.u.)
and the load torque is 0.6 p.u.. Here, Qdqref_cmp as expressed in (25)is set at 0.12 p.u.
The horizontal axis is the error Qdqref_vary as expressed in (25),and the copper loss, iron loss and total loss are varied by the
Qdqref_vary. When Qdqref_vary is zero, the total loss can reach its
minimum that is 125.1 W. As the result, the maximum efficiency
control can be achieved. Furthermore, when Qdqref_vary is -0.12 p.u.,
the copper loss reaches the minimum 30.8 W whereas the total
loss is not the smallest because iron loss increases. From the result,the maximum efficiency control demonstrated that the total losses
are further reduced by 2.8 W compared to the MTPA control basedon V/f control. Therefore, it is confirmed that the maximum
efficiency control can achieve higher efficiency than the MTPA
control.
5.3
d and q-axis inductance identification method
based on MTPA control method
Fig. 17 shows theexperimental result of Lq identification method. Here, thehorizontal axis is the ratio between Lq_est and Lq, and the vertical

Ia : minimum

0.232
0.231
0.23
0.229
0.228

0.5

1

1.5

2

2.5

Ratio between Ld_est and Ld
Ld_est / Ld [p.u.]
Fig. 18. Variation of the output current with/without
MTPA control method when rotating speed is changed(Load torques are 0.2p.u.).
axis is the d-axis current and also the difference between left andright sides of (22). The experimental conditions are follows; therotating speed command value is 0.2 p.u. and the load torque is 0.2
p.u. When the difference between the left and right sides of (22) isequaled to 0, it is confirmed that id = 0 and Lq_est is equaled to 0.98
Lq (22.6 mH). As the result, it is confirmed that this method canachieve to estimate the Lq.
Fig. 18 shows the experimental result of Ld identification
method. The horizontal axis is the ratio between Ld_est and Ld, andthe vertical axis is the output current value Ia. The experimental
conditions are follows; the rotating speed command value is 0.4
p.u. and the load torque is 0.2 p.u. When Ia becomes its minimum,
the result can confirm that Ld_est is equaled to 0.95 Ld (10.9 mH).

7

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)(12) M. Hasegawa, S. Yoshioka, K. Matsui, "Position Sensorless Control ofInterior Permanent Magnet Synchronous Motors Using Unknown Input
Observer for High-Speed Drives", IEEE Transactions on Industry
Applications, vol. 45, no. 3, pp. 938-946, 2009.
(13) R. Leidhold, "Position Sensorless Control of PM Synchronous Motors
Based on Zero-Sequence Carrier Injection", IEEE Transactions on
Industrial Electronics, vol. 58, no. 12, pp. 5371-5379, 2011.
(14) J. Itoh , N. Nomura , H. Ohsawa, "A Comparison between V/f Control andPosition-Sensorless Vector Control for the Permanent Magnet Synchronous
Motor", Proc. of the Power Conversion Conference PCC Osaka 2002, Vol.
3, pp. 1310-1315, 2002.
(15) JP Patent, P2000-232800A, 2000.
(16) JP Patent, P2000-262089A, 2000
(17) Shinn-Ming Sue, Tsai-Wang Hung, Jenn-Horng Liaw, Yen-Fang Li,
Chen-Yu Sun, " A new MTPA control strategy for sensorless V/f controlled
PMSM drives", 6th IEEE Conference on Industrial Electronics andApplications 2011, pp. 1840-1844, 2011.
(18) THOMAS M. JAHNS, GERALD B. KLIMAN, THAMAS W. NEUMANN," Interior Permanent-Magnet Synchronous Motors for Adjustable-Speed
Drives", IEEE Transactions on Industry Applications, vol. IA-22, no. 4, pp.
738-747, 1986.
(19) S. Morimoto, Y. Takeda, K. Hatanaka, Y.Tong, T. Hirasa, "Design andcontrol system of inverter-driven permanent magnet synchronous motors
for high torque operation", IEEE Transactions on Industry Applications, vol.
29, no. 6, pp. 1150-1155, 1993.
(20) Shinn-Ming Sue, Ching-Tsai Pan, "Voltage-Constraint-Tracking-Based
Field-Weakening Control of IPM Synchronous Motor Drives", IEEE
Transactions on Industrial Electronics, vol. 55, no. 1, pp. 340-347, 2008(21) Bing Cheng, T.R. Tesch, "Torque Feedforward Control Technique for
Permanent-Magnet Synchronous Motors", IEEE Transactions on Industrial
Electronics, vol. 57, no. 3, pp. 969-974, 2010(22) G. Foo, M.F. Rahman, "Sensorless Sliding-Mode MTPA Control of an IPM
Synchronous Motor Drive Using a Sliding-Mode Observer and HF Signal
Injection", IEEE Transactions on Industrial Electronics, vol. 57, no. 4, pp.
1270-1278, 2010(23) Roy S. Colby, Donald W. Novotny, "Efficient Operation ofSurface-Mounted PM Synchronous Motors", IEEE Transactions on Industry
Applications, vol. IA-23, no. 6, pp. 1048-1054, 1987(24) S. Morimoto, Y. Tong, Y. Takeda T. Hirasa, " Loss minimization control ofpermanent magnet synchronous motor drives", IEEE Transactions on
Industrial Electronics, vol. 41, no. 5, pp. 511-517, 1994.

As the result, it is confirmed that this method can achieve toestimate the Ld.

6.

Conclusion

This paper discussed and evaluated a maximum torque per
ampere and maximum efficiency control methods based on V/fcontrol by simulation and experimental results.
The MTPA control method is based on the control of reactive
power and as a result the information of the magnet pole position
is not necessary. From the experimental results, it can confirm thatthe output current can be reduced by 76 %.
Furthermore, the validity of the maximum efficiency control
method based on V/f control was confirmed in simulation andexperimental results. The proposed method can minimize the total
losses. From the result, the maximum efficiency control
demonstrated that the total losses are further reduced by 2.8 W
compared to the MTPA control based on V/f control.
In addition, the identification method of the Ld and Lq with the
MTPA control method was proposed. From the experimental
results, Lq_est is equaled to 0.98 Lq (22.6 mH), Ld_est is equaled to0.95 Ld (10.9 mH). That is, the estimation error is within 5% of thenominal value.
These results are shown to be benefit in the construction of highefficiency sensorless IPMSM drive system that uses a V/f control.
References(1)

K. Hiramoto, S. Morimoto , Y. Takeda, "Torque ripple improvement forsynchronous reluctance motor using an asymmetric flux barrier
arrangement", IEEE Transactions on Industry Applications, vol. 40, no. 4,
pp. 1076-1082, 2004.
(2) C.E. Nino-Baron, E.G. Strangas, "Iron and Magnet Losses and TorqueCalculation of Interior Permanent Magnet Synchronous Machines Using
Magnetic Equivalent Circuit", IEEE Transactions on Magnetics, vol. 46, no.
12, pp. 4073-4080, 2010.
(3) Yu-Seok Jeong, Yong-Jae Kim, Sang-Yong Jung, "Novel Analysis andDesign Methodology of Interior Permanent-Magnet Synchronous Motor
Using Newly Adopted Synthetic Flux Linkage", IEEE Transactions on
Industrial Electronics, vol. 58, no. 9, pp. 3806-3814, 2011.
(4) P. Sergeant, F. De Belie, J. Melkebeek, "Rotor Geometry Design of Interior
PMSMs With and Without Flux Barriers for More Accurate Sensorless
Control", IEEE Transactions on Industrial Electronic, vol. 59, no. 6, pp.
2457-2465 , 2012.
(5) 5] Roberto H. Moncada, Juan A. Tapia, Thomas M. Jahns, "Analysis ofNegative-Saliency Permanent-Magnet Machines", IEEE Transactions on
Industrial Electronics, vol. 57, no. 1, pp. 122-127, 2010(6) I. Petrov, J. Pyrhonen, "Performance of low cost permanent magnet material
in PM synchronous machines", IEEE Transactions on Industrial Electronics,
vol. PP, no. 99, pp. 1, 2012(7) M. J. Corley, and R. D. Lorenz, "Rotor Position and Velocity Estimation for
a Salient-Pole Permanent Magnet Synchronous Machine at Standstill andHigh Speeds", IEEE Transactions on Industry Applications, vol. 34, no. 4,
pp. 784-789, 1998.
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strategy for salient-pole PMSM based on extended EMF in rotatingreference frame", IEEE Transactions on Industry Applications, vol. 38, no.
4, pp. 1054-1061, 2002.
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Jun-ichi Itoh

(Member) received his M.S. and PhD degrees inelectrical and electronic systems engineering from
Nagaoka University of Technology, Nagaoka, 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. His research interests include matrix converters, DC/DC
converters, power factor correction techniques and motor drives. He is amember of the Institute of Electrical Engineers of Japan.
Yuki Nakajima(Student Member) received his B.S. degrees inelectrical, electronics and information engineeringfrom Nagaoka University of Technology, Nagaoka,
Japan in 2011. Since 2011, he has been with
Nagaoka University of Technology as a M.S. degree
student in electrical, electronics and informationengineering. His research interests include motor
drive system for Interior Permanent Magnetic
Synchronous Motor. He is a student member of theInstitute of Electrical Engineers of Japan.

8

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Maximum Torque per Ampere and Maximum Efficiency Control Methods based on V/f control for IPMSM (Jun-ichi Itoh et al.)Goh Teck Chiang(Student member) received his B.S. degree inelectrical and electronic engineering from
Queensland University of Technology, Brisbane,
Australia in 2004. Then, he received his M.S. and
Ph.D. degrees in electrical and electronic systems
engineering from Nagaoka University ofTechnology, Nagaoka, Japan in 2009 and 2012,
respectively. He is currently working as a researcher
in Nagaoka University of Technology. His researchinterests include indirect matrix converters, PWM and motor drive.

9

IEEJ Trans. ●●, Vol.●●, No.●, ●●●