Quick Compensation Method of Motor Phase
Current Sensor Offsets without Motor Parameters
for PMSM Drive
Koroku Nishizawa, Jun-ichi Itoh, and Yoshinobu Nishizawa,
Nagaoka University of Technology
Department of Electrical, Electronics and Information Engineering
Nagaoka, Niigata, Japan
koroku_nishizawa@stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp, yoshinobu_n@stn.nagaokaut.ac.jp
Abstract—This paper proposes a quick PMSM torque ripple
reduction method caused by current sensor offsets. The proposed
method consists of two novel offset compensation methods without
any motor parameters. The first method estimates the current
sensor offsets from output voltage references. Meanwhile, thesecond method estimates the current sensor offsets from detected
output currents. By selecting the compensation method whose
completion time of the compensation is shorter than the other
under the different conditions of the PMSM drive, the quick
compensation is achieved in the proposed method. It contributes
to the application where the offsets vary in a short time, such as a
HEV application. The effectiveness of the two compensation
methods is confirmed by experiments. Moreover, it is confirmedthat the completion time of the current sensor offset compensationis shortened by 12.0 seconds at most by accurately selecting one oftwo proposed methods of the current sensor offset compensation
method.
Keywords—Current Sensor Offset Error Compensation, PMSM
Drive.

I. INTRODUCTION
Recently, hybrid electric vehicles (HEVs) are rapidly
becoming more common due to an increase in global
environmental regulations. A HEV is an automobile that has anelectric power train (EPT) added to its engine [1]-[10]. The EPT
system consists of a battery, a voltage source inverter (VSI), anda permanent magnet synchronous motor (PMSM). The driving
force of HEV is generated by the EPT. The motor torque rippleof the PMSM must be reduced in order to improve the riding
quality of the HEV. There are several causes of the motor torqueripple, e.g. spatial harmonics of a permanent magnet flux of the
PMSM, a dead-time of the VSI, and motor phase current sensor
offsets.
Motor torque ripple reduction methods have been developedwith focusing on the motor configurations [11]-[19]. In thesolution with focusing on the motor configuration, an increaseof the production cost for the motor is inevitable. Thus,
approaches to the torque ripple reduction based on the motor
control have also been considered. The torque ripple reduction
methods which cancel out the effect of a dead-time of the VSI

have been developed [20]-[22]. However, these methods cannot
reduce the torque ripple caused by offsets of the motor phasecurrents. Generally, the motor current sensor offsets arecompensated by adjusting the detected motor phase current
values to zero during the motor is stopped, i.e. an off-line
compensation method. However, the off-line compensation
method cannot compensate the motor current sensor offsets,
which dependently vary by the variation of temperature during
the rotation of the motor.
So far, some on-line compensation methods have been
proposed to compensate for the current sensor offsets during thedrive of the motor with no motor parameters [23]-[26]. The
methods in [23]-[24] compensate the motor current sensor
offsets based on the output voltage references. Meanwhile, themethod in [25] directly compensates the motor current sensor
offsets based on the detected current values. In the HEV
application, the current sensor offsets vary quickly due to thevariation of the temperature because the load and speed of the
PMSM are widely changed by the drive conditions. Therefore,
the completion time of the current sensor offset compensation isrequired to be as short as possible. However, the completiontime of the offset compensation has not been discussed yet. In
particular, the completion time of each compensation method
depends on the bandwidth of the current regulator in the PMSM
drive system and the rotational speed. Thus, it is necessary toapply the compensation method whose the completion time of
the compensation is shorter than the other under the different
conditions of the PMSM drive.
This paper proposes the quick compensation method using
two different compensation techniques in order to shorten thecompletion time of the compensation. At first, the two current
sensor offset compensation methods in [23] and [25] areexperimentally demonstrated. In addition, the completion timeof the current sensor offset error compensation of the two
methods are estimated by the simulation. Based on these results,
by selecting the method whose completion time of thecompensation is shorter than the other under particularconditions of the PMSM drive, the completion time of thecompensation will be shortened.

+

id*

II. TORQUE RIPPLE CAUSED BY CURRENT SENSOR
OFFSET ERROR

-

+

iq*
ids

Fig. 1 shows the general control block diagram for an
IPMSM drive in the HEV. The current sensors are mounted into
UVW-phases respectively. In order to simulate the effects of thecurrent sensor offsets, the detected output phase current values(ius, ivs, iws) are obtained by intentionally adding the current
sensor offsets (iuoerr, ivoerr, iwoerr) to the true output phase current
values (iutr, ivtr, iwtr) as

vu*

vd*
Automatic
Current v *Regulator q

-

iqs

dq

uvw v

*
w

ius  iutr  iuoerr

uvw

ivs  ivtr  ivoerrdq

iws  iwtr  iwoerreFig. 1.

Voltage
SourceInverter

vv*

p

PS

Load

IPMSM

General control block diagram for IPMSM drive in HEV.

ius  iutr  iuoerr
ivs  ivtr  ivoerr 
iws  iwtr  iwoerr





In this paper, the errors in the gain of the current sensors are notconsidered and these gains are all regarded as 1.
The detected d-q- axis current values (ids, iqs) are obtained as
ids  idtr  idoerr

iqs  iqtr  iqoerr





by performing the transformation from three-phase to d-q
rotational frame, where idtr and iqtr are the true d-q- axis current
values, whereas idoerr and iqoerr are the current sensor offset
components in d-q- axis currents, respectively. Then, each termof (2) is expressed as

idtr 

2
2π 
2π 


iutr cos θe  ivtr cos θe    iwtr cos θe  
3
3
3 




iqtr  

2
2π 
2π 


iutr sin θe  ivtr sin  θe    iwtr sin  θe  
3
3 
3 



idoerr 

2
2π 
2π 


iuoerr cos θe  ivoerr cos θe    iwoerr cos θe  
3
3 
3 



iqoerr  

2
2π 
2π 


iuoerr sin θe  ivoerr sin  θe    iwoerr sin  θe  
3
3 
3 





In the general control system of the IPMSM, the detected dq- axis current values shown in (2) is regulated to the d-q- axis
current reference values (id*, iq* ) by the operation of theautomatic current regulator (ACR). As a result, the true d-q- axis
current values are transformed from (2) as
idtr  ids  idoerr  id*  idoerr
iqtr  iqs  iqoerr  iq*  iqoerrT  p aiqtr  Ld  Lq idtr iqtr 







where p is the number of pole pairs, φa is the magnet flux linkage,and Ld and Lq are the d-q- axis inductances, respectively. By
substituting (3) and (4) to (5), the influence of the current sensor
offsets for the motor torque can be observed by (6).

 
 

 p  i  L  L i i  p L  L  i i
i i



T  p  a iq*  iqoerr  Ld  Lq iq*  iqoerr id*  idoerr



*
a q

d

d

q

q

* *
d q

*
d qoerr*q doerr idoerr iqoerr   a iqoerr

The first term of the right-hand side of (6) means the torquereference. The second term of the right-hand side of (6) means
the torque ripple component caused by the current sensor offset
error. The fundamental frequency of the torque ripple is the sameas an electric angle frequency of the rotor position of the IPMSM.

where θe is the electric angle.

Then, the torque of the IPMSM is calculated asIII. COMPENSATION METHODS FOR CURRENT SENSOR OFFSETS
A. Method I : Compensation for current sensor offsets byusing output voltage references [23]Fig. 2 shows the control block diagram of the compensation
method for the current sensor offsets by using output voltage
references [23]. When the detected output phase currents havethe current sensor offsets (iuoerr, ivoerr, iwoerr), the voltage offsets
occur in the output voltage references in order to cancel thesesensor offsets, i.e. by the operation of the ACR. Therefore, thepolarities of the current sensor offsets and the offsets in thevoltage references (v*uoff, v*voff, v*woff) are opposite. The method I
indirectly estimates the current sensor offsets from the voltage
references by using this relationship.
Fig. 3 shows the calculation processes of the offsets from thevoltage references. First, by applying discrete Fourier transform(DFT) to the inverter output voltage reference, the DC voltage
reference is calculated as

id*
iq*

+
-

Automatic
Current
Regulator+

idcp iqcp

OffsetError
woerr Estimation

uvw
dq



dq

vq*

v w*

uvw

*
vuoff
*
vvoff
*
vwoff

IPMSM

p

iucp - +ivcp - +ius  iutr  iuoerr

Motor parameters
Pn = 5.5 [kW]Nn = 1500 [r/min]
Vn = 400 [Vrms]
In = 20 [Arms]
Pairs of poles = 3
Ra = 215 [mΩ]
Ld = 4.3 [mH]
Lq = 10.2 [mH]iwcp

iws  iwtr  iwoerr

ivs  ivtr  ivoerr

- +

Load

PS

Discrete
MovingFourier & Average
Transform
FilterControl block diagram of method I for compensating current sensor offsets by using output voltage references.

v

*
udc



N sample 1*un v ( n) N sample

Fig. 4 shows the estimation process of the method I for thecurrent sensor offsets. The current sensor offsets are estimatedby subtracting the offsets in the voltage references, which ismultiplied by an integral gain for the offset estimation, from theprevious values of the estimated current sensor offsets as*iˆuoerr  iˆuoerr.old    vuoff
Inverter output
voltage referencevu*

where Nsample is the number of sampling during one period of theelectric angle frequency. Then, by applying the moving averagefilter (MAF) to the calculation results of (7), the offsets in thevoltage references are calculated. The reason of using MAF is tosuppress the variation of the calculation results of the offsets inthe voltage references, which occur when the torque referenceor the rotational speed reference is changed.



iutr
Voltage
ivtr
SourceInverter iwtr

vv*

e
iˆuoerriˆvoerriˆFig. 2.

vu*

vd*

Calculation startCalculated resultof DFT*
vudc

Moving average filter
processing

Caluculated offset
voltage reference*
vuoffTime [s]Fig. 3.

Calculation processes for offset in voltage references.
Estimation start

where, α is the integral gain for the offset estimation. Finally, by
subtracting the estimated current sensor offsets from thedetected output phase current, the compensation for the current
sensor offsets is finished.
B. Method II : Compensation for current sensor offsets byusing detected output currents [25]Fig. 5 shows the control block diagram of the compensation
method for current sensor offsets by using detected output
currents. The method II directly estimates the current sensor
offsets from the detected output currents by using the multistage
DFTs.
Fig. 6 shows the estimation process of the method II for thecurrent sensor offsets. By applying the multistage DFTs on thedetected output phase currents, the current sensor offsets can bedirectly estimated from the detected output phase currents. The
calculation process of each DFT is same as the method I, shownas (7).

Calculation by Eq. (7)Calculated offset
voltage reference*
vuoff

Estimation finish
*
vuoff
=0

0
[s]
*

Estimated current
sensor offset error 0iˆuoerr

Fig. 4.

× vuoffiˆuoerr = iuoerr

iuoerr[s]

Estimation process of method I for current sensor offsets.

IV. SIMULATION AND EXPERIMENTAL RESULTS
Table I shows the motor parameters of the IPMSM for the
test. In order to confirm the validities of the method I and method
II, simulations are run under the same parameters.
Fig. 7 shows the simulation results of method I at thedifferent rotational speeds. At the low rotational speed of 300
r/min., the completion time of the offset error compensation is
19 s. On the other hand, at high rotational speed of 750 r/min.,the completion time is 8 s. in the high-speed region, thecompletion time is shorter than the completion time of 300 r/min.

id*
i

*
q

+
-

vd*

Automatic
Current
Regulator+

idcp iqcp

vq*

v

iutr
Voltagei
Source vtr
Inverter iwtr

*
v

v w*

uvw

e
iˆuoerriˆvoerr
iˆ

woerr

uvw
dq

Fig. 5.

vu*
dq

IPMSM

p

PS
Motor parameters
Pn = 5.5 [kW]Nn = 1500 [r/min]
Vn = 400 [Vrms]
In = 20 [Arms]
Pairs of poles = 3
Ra = 215 [mΩ]
Ld = 4.3 [mH]
Lq = 10.2 [mH]Multistage Discrete
Fourier Transform

iucp - +ivcp - +ius  iutr  iuoerr

iwcp

iws  iwtr  iwoerr

ivs  ivtr  ivoerr

- +

Load

Control block diagram of method II for compensating current sensor offsets by using detected output currents.

Fig. 10 shows the experimental results of the method II in a
steady state at a rotational speed N of 300 r/min, a ωci of 500
rad/s, a d-axis current command id* of 0 A and q-axis current
command iq* of 4 A. The current sensor offsets are preset to iuoerr= 1.0 A, ivoerr = -0.6 A, and iwoerr = -0.4 A, respectively. The
current sensor offsets are estimated from the detected output
currents and compensated. As a result, the torque ripple isreduced by 1.0 Nmp-p by applying the method II.
Fig. 11 shows the simulation results of the completion timeof the offset compensation with two methods at the angularfrequency of ACR (ωci) of 500 rad/s. The horizontal axis of Fig.
9 is the ratio of the angular frequency of ACR to the electric
angular frequency of the IPMSM (ωe). In the method I, thehigher rotational speed is, the shorter the completion time of theoffset error compensation becomes, because the repetition
frequency of the estimation and compensation process, shownas Figs. 3 and 4, becomes higher when the rotational speed ishigh. On the other hand, the method II has an opposite
characteristic of the completion time of the compensation
against the rotational speed compared with the method I. The
repetition frequency of the estimation process of the method II,
shown as Fig. 9, also becomes higher when the rotational speed

Sampled valueius

iuoerr0

 m   / 2

Calculation
Calculation result
result of 1st DFTof last DFT

Fig. 9 shows the experimental results of the method I in
steady state at a rotational speed (N) of 750 r/min, the angularfrequency of ACR (ωci) of 500 rad/s, a d-axis current command(id* ) of 0 A and-q- axis current command (iq* ) of 4 A. The
current sensor offsets are preset to iuoerr = 0.7 A, ivoerr = 0.3 A,
and iwoerr = -1.0 A respectively and the integral gain for error
estimation (α) is 0.05. The current sensor offsets are estimatedfrom the output voltage references and compensated. As a result,
the torque ripple is reduced by 1.4 Nmp-p by applying the method
I.

Detected output phase current

Fig. 8 shows the simulation results of method II at thedifferent rotational speeds. At the low rotational speed of 300
r/min., the completion time of the offset error compensation is
5.5 s. On the other hand, at the high rotational speed of 750
r/min., the completion time is 14 s, longer than the completiontime of 300 r/min. It is confirmed from Figs. 7 and 8 that thecompletion time of the offset error compensation of the method
I and method II depend on the rotational speed. Furthermore, thecompletion time characteristics of the method I and method II
are inversely related.

Fig. 6.

0iˆuoerr

iuoerr0

Rotor position  m [rad]Estimation processes of method II for current sensor offsets.

TABLE I.
Symbol
Pn
Vn
In
Nn
p
R
Ld
Lq
φa
id*
iq*
iuoerrivoerriwoerrωciαiuoerrMOTOR PARAMETERS OF IPMSM AND SIMULATION AND
EXPERIMENTAL CONDITIONSMeaning
Rated motor power
Rated voltage of motor
Rated current of motor
Rated rotational speed
Number of pole pairs
Winding resistanced-axis inductanceq-axis inductance
Back EMF constantd-axis current reference
q-axis current reference
U-phase current sensor offset error
V-phase current sensor offset error
W-phase current sensor offset error
Angular frequency of ACR
Integral gain of offset estimator in method I

Value
5.5 kW
400 Vrms
20 Arms
750 r/min.
30.215 Ω4.3 mH
10.2 mH
0.284 V/rad/s
0A
4A
0.7 A
0.3 A
-1.0 A
500 rad/s
0.05 A/V

Estimation and compensation start

Finishiucp [A]Estimation and compensation start
Finishiucp [A]0.742 Aiuoerr = 0.7 A

0.798 Aiuoerr = 0.7 A
iˆuoerr [A]iˆuoerr [A]T [Nm]

T [Nm]
0.276[Nmp-p]1.69 [Nmp-p]

0.500 [Nmp-p]
1.69 [Nmp-p]

19 sec.

8 sec.

Time [s]Time [s](a) N = 300 r/min.
(b) N = 750 r/min.
Fig. 7.
Simulation results of method I at different rotational speeds, ωci = 500 rad/s, id* = 0 A, iq* = 4 A, iuoerr = 0.7 A, ivoerr = 0.3 A and iwoerr = -1.0 A. The
integral gain for error estimation (α) is 0.05.
Estimation and compensation start
Finishiucp [A]iuoerr = 0.7 A

Estimation and compensation start
Finishiucp [A]0.724 Aiuoerr
= 0.7 Aiˆuoerr [A]

0.692 Aiˆuoerr [A]T [Nm]

T [Nm]
0.189 [Nmp-p]

1.69 [Nmp-p]
5.5 sec.

1.69 [Nmp-p]
14 sec.

Time [s]Fig. 8.

0.275 [Nmp-p]

Time [s](a) N = 300 r/min.
(b) N = 750 r/min.
Simulation results of method II at different rotational speeds, ωci = 500 rad/s, id* = 0 A, iq* = 4 A, iuoerr = 0.7 A, ivoerr = 0.3 A and iwoerr = -1.0 A.

is high. Furthermore, in the method II, the current sensor offsets
are estimated directly from the detected current values.
Therefore, when the rotational speed is high, the estimatedvalues of the current sensor offsets oscillate and it takes a longtime for the estimated values to converge. By selecting between

the method I or method II, whose completion time of thecompensation under the particular conditions of the PMSM
drive is short, the completion time of the compensation isshortened by up to 12.0 s.

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Estimation and compensation start
Preset current sensor error : iuoerr = 0.7 [A]iˆuoerr :[1 A/div.]

00.5 [A]

iucp :[4 A/div.]0

Calculated torque T :[4 Nm/div.]
1.4 [Nmp-p]

2.8 [Nmp-p]

0[2 s/div.]

Fig. 9.
Estimation of current sensor offsets and reduction of motor torqueripple with method I in steady state at N = 750 r/min, ωci = 500 rad/s, id* = 0 A,
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Estimation and compensation start

iucp :[4 A/div.]0

Preset current sensor error : iuoerr = 1.0 [A]iˆuoerr :[1 A/div.]0

Calculated torque T :[1.7 Nm/div.]
0.68 [Nmp-p]

1.7 [Nmp-p][1 s/div.]

0

Fig. 10. Estimation of current sensor offset error and reduction of motor
torque ripple with method II in steady state at N = 300 r/min, ωci = 500 rad/s,
id* = 0 A, iq* = 4 A, iuoerr = 1.0 A, ivoerr = -0.6 A and iwoerr = -0.4 A.
20
Completion time of offset
error compensation [s]In this paper, two compensation methods for the current
sensor offset compensation without using the motor parameters
are experimentally demonstrated. In addition, the completion
times of the compensation of both methods were also assessedand compared by the simulation. By selecting the one of them,whose completion time of the compensation is shorter than theother depending on the particular conditions of the PMSM drive,the torque ripple caused by the current sensor offsets is quickly
reduced. It was confirmed that the completion time wasshortened up to 12.0 s by applying the proposed method. It willcontribute the improvement of a riding quality of the HEV,
because the proposed method quickly suppress the vibration
caused by the torque ripple owing to the current sensor offsets
depending on the temperature.

ci = 500 rad/s

Method I

16
Shortend by
12.0 sec.

Shortend
by 6.0 sec.

12

8
4

Method II

0
1

2

3

4

5

6

Angular frequency of ACR ci / Electric angular frequency of IPMSMe [-]Fig. 11. Completion time of offset error compensation of method I andmethod II under different condition of rotational speed. The angular frequency
of ACR (ωci) is 500 rad/s.

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