Maximum Torque per Ampere Control Using Hill Climbing Method
Without Motor Parameters Based on V/f Control
Jun-ichi Itoh, Takato Toi, Masakazu Kato
Nagaoka University of Technology
1603-1 Kamitomioka-cho
Nagaoka city Niigata, Japan
Tel., Fax: +81 / (258) – 47.9533.
E-Mail: itoh@vos.nagaokaut.ac.jp, t_toi@stn.nagaokaut.ac.jp, katom@stn.nagaokaut.ac.jp
URL: http://itohserver01.nagaokaut.ac.jp/itohlab/index.html

Keywords«Permanent magnet motor», «Sensorless control»

Abstract
This paper proposes novel V/f control for interior permanent-magnet synchronous motors(IPMSMs) in order to achieve maximum torque per ampere (MTPA) control without motor parameterssuch as dq-axis inductance and flux linkage of a permanent magnet. The V/f control does not require
either information of a rotor position or the motor parameters in order to construct the control system.
However, the conventional MTPA control requires the motor parameters because the control
determines the compensation voltage depending on the reactive power. On the other hand, with theproposed MTPA control, a hill climbing method is utilized. The proposed MTPA control calculates
the compensation voltage depending on the output current in order to track the MTPA control point
without the motor parameters. The validity of the proposed method is confirmed by the experimental
results using a 3.7-kW IPMSM. From the experimental results, the magnitude of the phase current isdecreased by 56% at the rated speed. Furthermore, the proposed MTPA control is effective regardlessof the magnitude of the load torque.

I. Introduction
Recently, IPMSMs are widely applied to industry applications due to the attractive features; highpower density, high efficiency and robust structure [1]-[3].There are basically two IPMSM control
methods: field oriented control (FOC) and V/f control [4].
In the FOC, the identification of the pole position is necessary. Therefore, a position sensor is used
to detect the pole position. However, it is impossible to use the position sensors in applications wheresuch as a motor and a load are built-in systems. As a result, many sensorless FOC have been studied[5]-[10]. The sensorless FOC requires some motor parameters. When the motor parameters are
fluctuated and different from the nominal values, it is necessary to measure the motor parameters or
estimate them in the sensorless FOC [11]. In addition, in order to drive IPMSMs efficiently, MTPA
control is widely applied. The MTPA control based on the FOC have been studied by using various
methods such as injecting the current signal, estimating the maximum torque control frame or the
motor parameters, and on-line estimation [12]-[14]. However, these methods as mentioned above
require the motor parameters such as d-axis inductance, q-axis inductance and magnetic flux linkageof the permanent magnet. When the estimated motor parameters are different from the actual values,
the output current does not become the minimum in the MTPA control based on the sensorless FOC
because the estimated coordinate axes deviate from the actual dq-axis.
On the other hand, the V/f control does not require the identification of the pole position because thecontrol depends on the frame which is calculated in the controller of the inverter. In addition, themotor parameters are basically not used in the V/f control. Some MTPA control based on the V/fcontrol by controlling the current phase or the reactive power have been proposed [15][16]. However,the motor parameters are required in these MTPA control. Therefore, the MTPA control using the
motor parameters spoils the advantage of the V/f control.
This paper proposes the MTPA control for the V/f control with a hill climbing method in order toachieve the MTPA control without the motor parameters. It is noted that the MTPA control using thehill climbing method is not effective in the sensorless FOC because the sensorless FOC requires the
motor parameters in the control strategy. In addition, the variation of the d-axis current by the hill
climbing method disturbs the position estimation system. This paper will be organized as follows; first,
the principles of the V/f control is introduced. Next, the MTPA control based on the hill climbing
method is explained. Finally, the experimental results are shown to confirm the validity and theeffectiveness of the proposed method.

II. Maximum torque per ampere control method based on V/f control
A. V/f control
Fig. 1 shows the relationship between -frame and dq-frame on rotating frame which issynchronized to rotating speed of the motor. In the permanent-magnet synchronous motor control, thed-axis and the q-axis are generally defined as the direction of the flux vector in the permanent magnet
and the electromotive force vector, respectively. Therefore, the identification of the flux vector isimportant to apply in the FOC on dq-frame. On the other hand, the -axis is defined as the direction of
the output voltage vector of the inverter and the -axis is defined as the -axis delayed by 90 degrees.
Therefore, the -axis component represents effective components and -axis component represents
reactive components. The -frame is calculated in the controller of the inverter. In the V/f control, thepole position is unnecessary because the control algorithm utilizes the -frame instead of the dqframe [4].
The voltage equation of the IPMSM based on the dq-axis is given by (1).
vd   R  pLd vq   re Ld

re Lq  id   0 .................
  
R  pLq  iq  re m 

(1)

where vd is the d-axis voltage, vq is the q-axis voltage, re is the electric angular frequency, p is thedifferential operator, R is the armature resistance value, Ld is the d-axis inductance value, Lq is the qaxis inductance value and m is the flux linkage of the permanent magnet. Then, the voltage equationof the IPMSM based on the -axis is given by (2) [6].
v   R  1 L  pL     L  pLv   1 

1 L  pL  i 
- sin     re m R  1 L  pL  i  cos (2)where v is the -axis voltage, v is the -axis voltage, i is the -axis current, i is the -axis current, 1
is the rotating speed of the -frame and is the phase angle between the electromotive force and theoutput voltage, respectively. By definition, the output voltage vector v is aligned on the -axis and theelectromotive force rem is aligned on the q-axis. Therefore, the phase angle  is equal to the load
angle. Here, LLLLLare defined as (3) to (7).
L  L0  L1 cos 2 ..................................................
L  L0  L1 cos 2 .............................................
L  L1 sin 2 ........................................................

L0 
L1 

Ld  Lq2
Ld  Lq
2

(3)
(4)
(5)

...........................................................

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

(7)

The relationship between the -axis current and the dq-axis current is given by (8) using the phaseangle .
 id  i cos  i sin.....................................................
 iq  i sin  i cos(8)

The output torque of the IPMSM and the relationship between the electrical angular velocity and theoutput torque are expressed by (9) and (10), respectively. It is noted that the viscosity resistance isignored.
T  Pf { miq  ( Ld  Lq )id iq } ........................................

(9)pre 

(10)

Pf T  TL 
J.............................................................

where Pf is the number of pole pairs, T is the output torque, TL is the load torque and J is the inertia
moment of the motor. The phase angle  is given by (11).
p  1  re .......................................................................

(11)

Fig. 2 shows the block diagram of the V/f control based on the -frame. The control block contains
the damping control and the conventional MTPA control.
In the V/f control, the -axis voltage command v* is given by the speed command rm* which ismultiplied by the f/V conversion ratio, whereas the -axis voltage command v* is zero. The
compensation voltage v in order to achieve the MTPA control is subtracted from the -axis voltage
command v*. The conventional MTPA control is discussed in the next section in detail. Then, the frame voltage command is converted to the three phase voltage command. When a motor is controlled
by the simple V/f control based on the -frame where there is no feedback control loop, the torqueoscillation occurs due to the resonance between the synchronous reactance and the inertia moment of
the motor. Therefore, the damping control is necessary in order to achieve the stable operation.
Specifically, the damping control consists of HPF and the feedback gain K1, and uses the -axis
current as a reference to estimate the vibration component of the torque [15]. Then, the compensatedspeed command 1 is integrated in order to acquire the phase angle on -frame 1*. The phase angle
1* is utilized in order to transform the component on the -frame into the component on the threephase.
qrm*

re L i   L i 
2

d d

2

Pf

1

*

q q

v

RIa
Ia
f

MTPA
Control



rem
+

b



i

v* = 0**v * + vf/V conv. 
-

HPF

i

K1
Damping controldFig. 1. Relationship between the -frame and the dqframe. The q-axis is defined as the direction of theelectromotive force vector. The -axis is defined as the
direction of the output voltage vector of the inverter.

-

1

/3f

vu*
vv*
vw*

3f/

iu
iv
iw

v

1
s

1*
i
i

Fig. 2. V/f control based on the -frame with theconventional MTPA control. The motor iscontrolled by the V/f control with the damping
control.

B. Conventional MTPA control on V/f control

The conventional MTPA control block decides the compensation voltage v based on the reactive
power on each frame.

The reactive power on the dq-frame Qdq is given by (12).
Qdq  vqid  vd iq ...............................................

(12)

By introducing (1) into (12), the reactive power on the dq-frame Qdq can be expressed as (13).

Qdq  1 Ld id  Lqiq  mid22

 ...............................

(13)

Equation (13) can be rewritten as (14) by using the output current Ia and the current phase b.



Qdq  1 Ld I a sin2 b  Lq I a cos2 b  m I a sin b
2

2



(14)

where the current phase b when the MTPA control is applied is given by (15) [17].

    2  8 L  L 2 I 2 

m
m
q
d
a 
 ..............
4 Lq  Ld I ab  sin1 





(15)

Let define Iasin(b as X, the reactive power in the MTPA control is given as (16).







Qdq  1 Ld X 2  Lq I a  X 2  m X
2

 ............

(16)

On the other hand, the reactive power on the -axis Q is given by (17).
Q  v i .......................................................

(17)

In case that the reactive power on the -axis Qis equal to the reactive power on the dq-frame Qdq
as shown in (16), the MTPA control can be achieved. Therefore, the satisfaction of (18) achieves the
MTPA control during the V/f control.









1 Ld X 2  Lq I a 2  X 2  m X  v i .............

(18)

Fig. 3 shows the control block diagram of the conventional MTPA control method based on the V/fcontrol. In order to satisfy (18), the PI controller is implemented to regulate the -axis voltage v.
This control method does not require the information of the pole position to achieve the MTPA
control. However, the control method needs the motor parameters such as the d-axis inductance Ld, theq-axis inductance Lq and the flux linkage of the permanent magnet m.
i
i

1

Qdq* +
Qdq*
PI
calc.
Eq. (16)
Q

LPF

v

v**
Fig. 3. Conventional MTPA control block diagram. The command value of the reactive power Qdq is
calculated from (16).

III. Proposed MTPA control with hill climbing method on V/f control
Fig. 4 shows the proposed control method block diagram. In the proposed method, the MTPA
control is achieved by the hill climbing method which calculates the compensation voltage
vdepending on the output current Ia.
By introducing (8) into (1), the relationship between the dq-axis current and the dq-axis voltage inthe steady state is defined as (19).

id 
 R
1
  2
2i q  R  re Ld Lq  re Ld

re Lq  

vd



R  vq  re m (19)Here, because the -axis voltage v is zero in the V/f control, the dq-axis voltage is written as (20).
 vd  v sin................................................
vq  v cos(20)

The relationship among the dq-axis current, the output current Ia and the power factor f is given by
(21).
id 
 cos   Ia - siniq sin   sinf  ..................
cos   cosf (21)

From (19), (20) and (21), the output current Ia is expressed as (22).
Ia Z sin   Z cos   2Z sin cos v  2  Z cos  Z sin v     Z Y
2

2

2

d

q

2

2

2



2

1

m

q

2

2



1

m

2

q

2

(22)

where the valuables Zd, Zq, Z and Y are defined as (23) to (26).
Z d  R 2  1Ld  ...........................................
22

 ...........................................
Z  R L  L  ...........................................
Z q  R  1Lq
2

2

2

2

1

Y2 

q

d

1
R 2  1 Ld Lq
2..........................................

(23)
(24)
(25)
(26)

It is noted that the angular frequency re is replaced as the rotating speed of the -frame 1 because
these values are same in the steady state. From (22), the output current is adjusted by the -axis
voltage v. Therefore, the MTPA control can be achieved by subtracting the compensation voltage
vfrom voltage command v*.
In order to confirm the validity of equations, the simulation is conducted. Table I shows the motor
parameters of the IPMSM which are used in the simulation. The saliency ratio of the IPMSM is 2.5.
Fig. 5 shows the relationship between the output current Ia and the compensation voltage v of thesimulation result and the values acquired by (22). In the simulation, both results are completely
corresponded. In Fig. 5, the output current Ia has the minimum value Ia_min at the MTPA control point.
Fig. 6 shows the flowchart of the proposed MTPA control based on the hill climbing method.
Specifically, the hill climbing method is divided into four modes; Mode 1, Mode 2, Mode 3 and Mode
4. In Mode 1, the compensation voltage v is increased to find the minimum point of the output
current Ia_min. In Mode 2, the present value of the output current Ia_min is compared with the previous
value of the output current Ia. When the present value of the output current Ia is higher than thethreshold output current Ia_th, the compensation voltage v is increased in order to maintain theminimum point of the output current. In Mode 3 and Mode 4, the compensation voltage v isdecreased and the similar operation in Mode 1 and Mode 2 are implemented. In order to alleviate thefluctuation of the output torque during the MTPA control, the fluctuation amount of the output current
Ia should be less than 0.1 p.u.. Therefore, the compensation voltage vshould be decided according
to the fluctuation amount of the output current Ia.
When the output current Ia reaches the minimum point, the hill climbing method repeats Mode 1 toMode 4. When the variation value of the compensation voltage v remains constant after tracking theminimum point of the output current, the current fluctuation occurs according to the torque fluctuation.
Therefore, the variation value of the compensation voltage v is decreased in Mode 4, in order thatthe compensation voltage v converges to the MTPA control point. In addition, when the output

current Ia exceeds the minimum value of the output current Ia_min by 0.2 p.u which is caused by thefluctuating load torque TL, the parameters are initialized after waiting 1 s in order to avoid the transientstate. Then, the MTPA control is resumed in order to track the MTPA control point. In this proposed
MTPA control using the hill climbing method, the motor parameters are not necessary to achieve the
MTPA control because the -axis current is utilized.

Pf

1

f/v conv.

/3f-

MTPA control
point

v

Ia
+
Damping
control

-

v
1 1

vu*
vv**
vw

1*

0.2

Output current Ia [p.u.]rm*v* = 0
v* +

*

s

i

Fig. 4. V/f control based on the -frame with the proposed
MTPA control. The proposed method determines thecompensation voltage by using the hill climbing method inorder to achieve the MTPA control.

Rated mechanical power Pm
Electromotive force eq
Rated voltage Vn
Rated current In
Synchronous speeds

0.12Mode 3Mode 4

Ia_th
0.08

Ia_minMode 1

0.04
0

iu
iv
iw

3f/

i

MTPA control
point

0.16

Mode 2

v_Ia_min
0

0.02

0.04

0.06

0.08

Compensation voltage v [p.u.]

0.1

Fig. 5. Relationship between the output current Ia
and the compensation voltage v.The minimum
value of the output current is achieved bycontrolling the compensation voltage.

Table I. Motor parameters of IPMSM.
3.7 kW
Rated torque TeR
151 VWinding resistance Rw
180 Vd, q-axis inductance Ld, Lq
Inertia moment J
14 A
Number of pole pairs Pf
1800 r/min

19.6 Nm
.693W
6.2 mH, 15.3 mH
0.0212 kgm2
3

MTPA control start
Input
i

Calculating IaiMode 1Mode = 1
Yes
Ia_n-1 > Ia_n
Yes

Mode 2

No

No
Decision Ia_min and
Ia_thMode = 2
Yes
Ia_th < Ia_n

Mode 3No
Mode = 3
No

Yes

Yes
Mode =3

Ia_n-1 < Ia_n
Yes

Increasing v

|Ia-Ia_min|>0.2 p.u.
No

Mode = 2

Increasing v

Mode 4No

decreasing v

Mode = 4No

Yes

Decision Ia_min
and Ia_thMode = 4

Ia_th < Ia_n
Yes
decreasing v

NoNo
Mode =1
Decreasing v

Yes
Waiting 1 s
Initializing
parameters

Fig. 6. Flowchart of proposed MTPA control based on the hill climbing method. This control is divided into
four modes. The compensation voltage is decreased or increased depending on the relationship between the
output current at previous and present calculation periods. When the output current Ia exceeds the minimum
value of the output current Ia_min by 0.2 p.u, the parameters are initialized in order to resume the MTPA
control.

IV. Experimental results
Fig. 7 shows the experimental system. The tested IPMSM is driven by a two-level inverter. In
addition, a load motor is used to provide a constant torque. The information of the magnet poleposition is acquired from a Hall Effect sensor to calculate the dq-axis current. It is noted that thisinformation of the magnet pole position is not used to control the motor. The motor parameters of theexperiment is shown in Table I. The parameters are same as in the simulation.
Fig. 8 shows the experimental waveforms when the proposed method is applied at 1800 r/min (1p.u.). From Fig. 8, as mentioned above, the hill climbing method repeats Mode 1 to Mode 4 after
tracking the MTPA point. Therefore, the compensation voltage v are almost corresponded withthose of the conventional method because the fluctuation amount of the compensation voltage v isdecreased in order to prevent the output torque T from fluctuating. In order to prevent the fluctuation
amount of the output current from exceeding 0.1 p.u., the fluctuation amount of the compensation
voltage vis 0.02 p.u.. It should be noted that the motor parameters are used in the conventional
method, whereas, the proposed MTPA control is achieved by the hill climbing method without motor
parameters. Specifically, the U-phase current are reduced by 56% (from 0.18 p.u. to 0.07 p.u.) at 1.6
Nm (0.08 p.u.). Therefore, the copper loss will be reduced by 85% at most. In Fig. 8 and 9, when theload torque is increased, the compensation voltage v is slightly decreased at each load torque TL.
Fig. 9 shows the waveforms of the dq-axis current, the output current Ia and the U-phase current at
1800 r/min. From Fig. 11, it is understood that the d-axis current is drastically reduced, whereas, the qaxis current do not change after applying the proposed MTPA control. Specifically, the d-axis current
are reduced by 91% (from 0.15 p.u. to 0.01 p.u.) at 1.6 Nm. In Fig. 11, each d-axis current becomesalmost zero after applying the proposed MTPA control. Therefore, the MTPA control achieves thesame results as the zero d-axis current control in the condition such as high speed and light load withthe motor which the saliency ratio is 2.5.
Fig. 10 shows the amplitude of the output current Ia when the load torque TL is varied at the rated
speed of 1800 r/min and at 900 r/min (0.5 p.u.). From the both graphs, the amplitude of the output
current with the proposed method is almost corresponded with the theoretical value. Therefore, theproposed method achieves the MTPA control regardless of the load torque TL. At the light load, the qaxis current is relatively small against the d-axis current. When the load torque is increased, theproportion of the d-axis current to the q-axis current decreases because the q-axis current becomeslarge depending on the load torque TL. Therefore, the MTPA control is more effective at the light load
than at the heavy load.
Fig. 11 shows the waveforms of the output torque T, the rotating speed, the output current Ia and thecompensation voltage v when the load torque TL is stepped at the steady speed with the proposed
MTPA control. The rotating speed is varied 1800 r/min (1 p.u.), 1440 r/min (0.8 p.u.) and 1080 r/min(0.6 p.u.), respectively. As mentioned above, the compensation voltage v is decided in order not toexceed the fluctuation amount Ia of 0.1 p.u.. Therefore, the MTPA control is resumed when the
output current Ia fluctuates 0.2 p.u. including the current ripple. In addition, the MTPA control
should not be activated again during the transient state which is caused by the stepped load torque TL
because the output current Ia needs to be fluctuated depending on the compensation voltage v.From
Fig. 11, the MTPA control is achieved because the transient state is avoided in case that the load
torque TL is stepped up. In addition, although the transient state is not avoided, the MTPA control isalso achieved when the load torque TL is stepped down. When the load torque TL is stepped down, theoutput current decreases according to the load torque TL. Therefore, the transient state does not need tobe considered because the operating point approaches the MTPA control point automatically.
From these results, the validity of the V/f control using the hill climbing method is confirmed.
Grid

Inverter
Diode
Rctifier

IPM
motor

Coupling

Load
motor

Inverter

Grid

PWM
rectifier
Load

Fig. 7. Experimental system. The tested IPMSM is driven by a two-level inverter. A load motor is used toprovide a constant torque.

Compensation voltage [0.06 p.u./div]
With proposed method

Compensation voltage [0.06 p.u./div]
With proposed method
With conventional method
00.06 p.u.

Modes of hill climbing method1

0 0.18 p.u.

2

3With conventional method0Modes of hill climbing method

41
0 0.16 p.u.

U-phase current [0.1 p.u./div]

2

30.059 p.u.
4U-phase current [0.1 p.u./div]

0.11 p.u.

0.07 p.u.
00Reduced by 56%

Reduced by 32%
MTPA control :active

400 ms/div

MTPA control :active(b) At 2.4 Nm (0.12 p.u.).

(a) At 1.6 Nm (0.08 p.u.).

Compensation voltage [0.06 p.u./div]
With proposed method

Compensation voltage [0.06 p.u./div]
With proposed method
With conventional method0Modes of hill climbing method1

0 0.16 p.u.

2

3

400 ms/div

0.057 p.u.

Modes of hill climbing method

41U-phase current [0.1 p.u./div]

0.14 p.u.

0.056 p.u.

With conventional method

0

0

2

3

4

0.18 p.u. U-phase current [0.2 p.u./div]

0.17 p.u.

00MTPA control :active

Reduced by 6%
MTPA control :active

Reduced by 13% 400 ms/div

400 ms/div(d) At 4.0 Nm (0.20 p.u.).
(c) At 3.4 Nm (0.17 p.u.).
Fig. 8. Waveforms of the compensation voltage of each method, modes of the hill climbing method and the U-phasecurrent at the rated speed. The compensation voltage of each method is almost corresponded with the conventional
method. The U-phase current are decreased by 56%, by 32% by 13% and by 6% at the each load torque, respectively.
0.15 p.u.

d-axis current [0.2 p.u./div]

Reduced by 91%

0.11 p.u.
d-axis current [0.2 p.u./div]

0.01 p.u.

q-axis current[0.2 p.u./div]

q-axis current[0.2 p.u./div]00

Output current [0.2 p.u./div]

Output current [0.2 p.u./div]

00U-phase current [0.1 p.u./div]

U-phase current [0.1 p.u./div]

00MTPA control :active

MTPA control :active

400 ms/div

0.07
p.u.

d-axis current [0.2 p.u./div]

400 ms/div(b) At 2.4 Nm (0.12 p.u.).

(a) At 1.6 Nm (0.08 p.u.).
0.04
p.u.

Reduced by 73%-0.02 p.u.

00Reduced by 45%
d-axis current [0.2 p.u./div]-0.02 p.u.

q-axis current[0.2 p.u./div]

q-axis current[0.2 p.u./div]

00.002 p.u.

0

0

0

Reduced by 98%0

Output current [0.2 p.u./div]
U-phase current [0.1 p.u./div]0

Output current [0.2 p.u./div]

U-phase current [0.2 p.u./div]

00MTPA control :active(c) At 3.5 Nm (0.18 p.u.).

400 ms/div

MTPA control :active

400 ms/div(d) At 4.0 Nm (0.20 p.u.).

Fig. 9 Waveforms of the dq-axis current, the output current and the U-phase current at the rated speed. At the steady state,
the d-axis current is decreased by 91%, by 98%, by 73% and by 45% compared to the values without the MTPA control,
respectively.

0.30

Without MTPA control

0.25
0.20

Theoretical value

0.15 Reducedby 56%
0.10
0.05

With conventional method
With proposed method

0 0

0.1

0.2
Load torque TL [p.u.]

0.3

Output current Ia [p.u.]

Output current Ia [p.u.]

0.30

Without MTPA control

0.25
0.20

Theoretical value

Reduced0.15 by 70%

With conventional method

0.10
0.05
0

0.4

With proposed method
0(a) At 1800 r/min (1 p.u.).

0.1

0.2
Load torque TL [p.u.]

0.3(b) At 900 r/min (0.5 p.u.).

Fig. 10. Relationship between the load torque TL and the output current Ia with/without the MTPA control at
1800 r/min (1 p.u.) and 900 r/min (0.5 p.u.). The output current after applying the MTPA control are almost
corresponded to the theoretical calculation both the proposed and the conventional method regardless of theload torque TL.
Output torque [0.5 p.u./div]

Output torque [0.5 p.u./div]

0.10 p.u.
00

1 p.u.

Motor speed [1 p.u./div]

0.09 p.u.

0.38 p.u.

0Compensation voltage [0.1 p.u./div]
0.02 p.u.
0.07 p.u.

0.08 p.u.

0.10 p.u.
0.47 p.u.

0

Output current [0.5 p.u./div]

0

0

0

Motor speed [1 p.u./div]

0.08 p.u.

0.10 p.u.

0.10 p.u.
0.47 p.u.

0.8 p.u.
Output current [0.5 p.u./div]
0.08 p.u.
0.38 p.u.

Compensation voltage [0.1 p.u./div]
0.01 p.u.
0.06 p.u.
0

2 s/div

0.09 p.u.

0.06 p.u.
2 s/div(a) At 1800 rpm (1 p.u.).

(b) At 1440 rpm (0.8 p.u.).

Output torque [0.5 p.u./div]
0.10 p.u.

0.10 p.u.
0.47 p.u.

0Motor speed [1 p.u./div]00.6 p.u.
Output current [0.5 p.u./div]
0.09 p.u.

000.09 p.u.

0.38 p.u.
Compensation voltage [0.1 p.u./div]
0.01 p.u.

0.04 p.u.

0.04 p.u.
2 s/div(c) At 1080 rpm (0.6 p.u.).
Fig. 11. Waveforms of the output torque T, the rotating speed, the output current Ia and the compensation
voltage v when the load torque TL is stepped at the steady speed. The compensation v voltage is varied
depending on the load torque TL in order to track the MTPA control point.

V. Conclusion
This paper discusses the V/f control which utilizes the MTPA control based on the hill climbing
method. In the proposed method, the MTPA control without motor parameters is achieved. The
proposed MTPA control is compared with the conventional MTPA control. From the experimental
results, the phase current is decreased by 56% at the rated speed of 1800 r/min. In addition, theproposed method accomplishes the MTPA control regardless of the load torque. As a result, thevalidity of the proposed method is confirmed through the experimental results.

0.4

In future work, the relationship between the variation value of the compensation voltage vandthe hill climbing method will be clarified in order to accomplish the MTPA control in minimum
convergence time.

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