IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO.

5, MAY 2013 2331

Analysis for Fault Detection of Vector-Controlled Permanent Magnet

Synchronous Motor With Permanent Magnet Defect
Takeo Ishikawa, Yutaro Seki, and Nobuyuki Kurita
Department of Electronic Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan

This paper analyzes the characteristics of a vector-controlled permanent-magnet synchronous motor (PMSM) with a permanent-
magnet defect. A method for the diagnosis of the demagnetization of the permanent magnet in PMSM is proposed. In the proposed
method, the magnetic field is calculated by the finite-element method, and then the flux linkage and and axis inductances are calcu-
lated. They are introduced into the block diagram of the drive and control system. We have manufactured interior permanent-magnet
motors, where one of four magnets is reduced by 10% and 20% in order to imitate the demagnetization. It is shown that the Fourier
and wavelet results are in good agreement with the measured ones. This paper shows that the stator current and stator voltage using the
proposed method are useful for the fault detection of demagnetized permanent magnet.
Index Terms—Demagnetization, failure diagnosis, finite-element analysis, permanent-magnet synchronous motor, vector control.

I. INTRODUCTION

P ERMANENT-MAGNET synchronous motors driven by

a sinusoidal stator current are widely used in home appli-
ances and industrial applications, such as air conditioners and
hybrid vehicles and so on, because of their high efficiency and
high-power density. In these applications, precise control is nec-
essary, and the prospect of breakdown and abnormality is be-
coming important. Permanent magnets of the PMSM can be de-
magnetized by temperature, large stator currents, large short-cir-
cuit currents produced by inverter or stator faults, and the aging
of the magnet itself. Moreover, since the permanent-magnet ma- Fig. 1. Cross section of the experimental IPMSM. (a) Motor configuration and
(b) rotor magnet defect.
terial is often magnetized after it is built in the devices, there is a
possibility that the permanent magnet is not in the state of com-
plete magnetization.
This paper deals with a less demagnetized situation. We have
There have been several research studies for detecting the de-
manufactured two interior permanent-magnet motors, where the
magnetization of permanent magnet. Rajagopalan et al. made a
thickness of one of four magnets is reduced by 10% and 20%
magnet defect by chipping off a part of the magnet and mea-
in order to imitate the demagnetization of permanent magnet,
sured stator current [1]. Yu et al. calculated a permanent-magnet
namely, the amount of 2.5% and 5% of the permanent magnet
synchronous motor (PMSM) with partial demagnetization by
is decreased [11]. Moreover, since PMSMs driven by a sinu-
the finite-elelment (FE) model [2]. Farooq et al. analyzed an
soidal stator current are usually controlled by the vector-control
outer-rotor permanent-magnet motor by a permeance network
strategy in the application of air-conditioners and hybrid vehi-
approach [3]. Urresty, Romeral, and Ortega et al. have made a
cles, this paper proposes a method for the fault detection of the
lot of contributions [4]–[10]. They analyzed the stator current by
vector-controlled PMSM with the demagnetized PM. In the pro-
the discrete wavelet analysis [4], and by the Hilbert Huang trans-
posed method, the magnetic field calculated by the FE method
form [5], and by the continuous and discrete wavelet analyses
is weakly coupled with the drive and control system. This paper
under nonstationary conditions [6], and by the Choi-Williams
investigates the stator current and the stator voltage for the de-
distribution [7]. Moreover, they analyzed a surface-mounted
magnetization detected by the proposed method. And then, this
magnet synchronous motor with uniform and local demagneti-
paper verifies the proposed method by the experiment.
zation by 2-D FEM [8], and proposed an online methodology to
detect the demagnetization based on the zero-sequence voltage
II. VECTOR-CONTROLLED PMSM WITH A
[9], [10]. In these references, one of three pairs of poles was de-
PERMANENT-MAGNET DEFECT
magnetized by 50%, namely, the amount of 8.3% of permanent
magnet was decreased. Fig. 1 shows the rotor configuration of the experimental
PMSM. This motor is a 1.5-kW, 3000 , 4.8 , 5.6-A,
four-pole machine, and the thickness of one magnet is reduced
Manuscript received November 10, 2012; revised December 30, 2012; ac- by 10% and 20% in order to imitate the demagnetization or
cepted January 11, 2013. Date of current version May 07, 2013. Corresponding imperfect magnetization. Nonmagnetic material is inserted into
author: T. Ishikawa (e-mail: ishi@el.guma-u.ac.jp).
the reduction area in order to remove eccentricity. Fig. 2 shows
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org. a typical block diagram for the simulation of the vector-con-
Digital Object Identifier 10.1109/TMAG.2013.2243135 trolled PMSM system. In this diagram, two control loops are

0018-9464/$31.00 © 2013 IEEE

2332 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 5, MAY 2013

Fig. 2. Block diagram for a brushless dc motor controlled by the vector strategy.

Fig. 3. Flux linkage and torque of the motor calculated by FEM.

used under the vector control: one is the inner loop to regulate
the stator and currents by detecting the rotor angle, and the
other is the outer loop to control the motor speed.

III. ANALYSIS METHOD FOR FAILURE DIAGNOSIS

This paper proposes a method for the fault detection of the
vector-controlled PMSM with the demagnetized PM, where the
magnetic field calculated by the FE method is weakly coupled
with the drive and control system. The magnetic field is calcu-
lated by the 2-D FE analysis, and then the flux linkage , elec- Fig. 4. Comparison of Fourier analysis of the calculated and measured stator.
tromotive force (emf) and torque are calculated. Moreover, the (a) Calculated and (b) measured.
- and -axis inductances and are calculated by using the
following equation:
duced as a load torque in the block Fcn, which is a function
(1) of rotor angle. Moreover, this paper takes the dc voltage drop
of the inverter, forward voltage drops of diode and the insu-
where , , , , , and are and axis voltages, and lated-gate bipolar transistor (IGBT) into account, along with
and are the axis currents, the stator resistance, and the differen- the resistances of the diode and IGBT in the block PWM inv2
tial operation, respectively. First, the flux linkage is obtained [12]. The dc voltage drop is taken into account as the function
by the FE analysis when the stator 0. Next, the fun- of measured -axis current, and the forward voltage drop and
damental components of and are calculated by using the resistances of power devices are taken into account by using the
electromotive force calculated by FE analysis when , , and voltage equation, where the stator current flows.
are specified at the rated values. And then, and are ob- Fig. 3 shows the calculated flux linkage and torque of the
tained by substituting these values into (1). experimental PMSM. When the stator current is 0, the funda-
The calculated flux linkage , , and are introduced into mental component of flux linkage is reduced by 4.9%, which
the block shown in Fig. 2. The cogging torque is intro- is equal to the reduction of permanent volume, that is 5%. The
ISHIKAWA et al.: ANALYSIS FOR FAULT DETECTION OF VECTOR-CONTROLLED PMSM 2333

Fig. 5. Wavelet analysis of the calculated stator current. (a) Healthy. Fig. 6. Wavelet analysis of the measured stator current. (a) Healthy. (b) Magnet
(b) Magnet demagnetized by 20%. demagnetized by 20%.

calculated result shows that the fundamental torque ripple is re- Next, this paper investigates the continuous wavelet anal-
duced by 6.2%, and that is increased by 0.62% and is ysis. Since there are several kinds of wavelet functions, we in-
increased by 0.90%. These values are introduced into Fig. 2 in vestigated three kinds of continuous mother wavelet functions;
the simulation. And then, the simulated results are analyzed by Morlet, Paul, and Derivative of Gaussian. It was shown that
the Fourier and wavelet analyses. the Morlet and Paul functions are useful, but the Derivative of
Gaussian function is not available [11]. Therefore, this paper
analyzes the continuous wavelet with the Morlet function. We
IV. COMPARISON OF THE ANALYZED AND MEASURED RESULTS
calculate the responses when the step speed reference is input,
Fig. 4(a) shows the Fourier analysis of stator current calcu- and then calculate the wavelet analysis. Fig. 5 shows the wavelet
lated by the proposed method. Here, the load torque is assumed analysis of the calculated stator current, where the number of
to be 0.4 . The fundamental component of stator current waves is six. We can find a little difference in the wavelet anal-
is of the order of the healthy motor, and the motor with the ysis of the stator current between the motor with the magnet
magnet is reduced by 10% and 20%. The measurement was car- reduced by 20% and the healthy machine, when the frequency
ried out three times, and the Fourier analysis of the measured is about 20 Hz and time is around 0.2 s. Fig. 6 shows the wavelet
stator three-phase current is shown in Fig. 4(b). Since the de- analysis of the measured stator current. Since the initial rotor po-
magnetization of the PM is very small, the measured results sition is not specified, the stator currents are different for each
are sensitive to the experimental setup. There may be little dif- measurement. The calculated wavelet results are in good agree-
ference in the mechanical loss, because the connection of the ment with the measured ones.
motor, a torque meter, and a hysteresis brake could not perfectly Since the difference shown in Figs. 5 and 6 is very slight, it is
be the same situation. In order to take it into account, an experi- difficult to distinguish the demagnetization using these equipo-
mental system was reset up in each measurement. Therefore, the tential lines of the continuous wavelet results. We investigate
measured three sets of results are a little bit different. The cal- it for a fixed frequency. Fig. 7 shows the wavelet result of the
culated results are in good agreement with the measured ones. stator current when the frequency is 21.4 Hz and the number of
Therefore, it is theoretically clarified that the Fourier compo- waves is six. It is shown that the wavelet results are on the order
nent of the stator current can distinguish the difference between of healthy, 10% and 20% demagnetized magnet. Fig. 8 shows
the demagnetization of permanent magnets. the wavelet result of the stator voltage when the frequency is
2334 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 5, MAY 2013

control system. This paper has analyzed the less demagnetized

situation, and has shown that the Fourier and wavelet results
are in good agreement with the measured ones. As a result, this
paper has shown that the stator current and stator voltage using
the proposed method are useful for the fault detection of demag-
netized PM.

ACKNOWLEDGMENT
This work was supported in part by the Japan Science and
Technology Agency (JST) and Oita prefecture.
Fig. 7. Wavelet analysis of the measured stator current, when the frequency is
21.4 Hz.
REFERENCES
[1] S. Rajagopalan, R. W. Le, T. G. Habetler, and R. G. Harley, “Diagnosis
of potential rotor faults in brushless DC machines,” in Proc. Inst. Elect.
Eng. Conf Publ., 2004, vol. 2, pp. 668–673.
[2] H. Yu, Z. Liu, and S. Cui, “Research on fault analysis and diagnosis
of PMSM in HEV,” in Proc. Int. Conf. Elect. Mach. Syst., 2011, pp.
20–23.
[3] J. Farooq, S. Srairi, A. Djerdir, and A. Miraoui, “Use of permeance
network method in the demagnetization phenomenon modeling in a
permanent magnet,” IEEE Trans. Magn., vol. 42, no. 4, pp. 1295–1298,
Apr. 2006.
[4] J. Rosero, L. Romeral, J. Cusido, and J. A. Ortega, “Fault detection
by means of wavelet transform in a PMSM under demagnetization,” in
Proc. IEEE 33rd Annu. Conf. Ind. Electron. Soc., 2007, pp. 1149–1154.
[5] A. G. Espinosa, J. A. Rosero, J. Cusido, L. Romeral, and J. A. Ortega,
“Fault detection by means of Hilbert Huang transform of the stator cur-
Fig. 8. Wavelet analysis of the measured stator voltage, when the frequency is rent in a PMSM with demagnetization,” IEEE Trans. Energy Convers.,
25.4 Hz. vol. 25, no. 2, pp. 312–318, Jun. 2010.
[6] J. R. R. Ruiz, J. A. Rosero, A. G. Espinosa, and L. Romeral, “Detection
of demagnetization faults in permanent-magnet synchronous motors
under nonstationary conditions,” IEEE Trans. Magn., vol. 45, no. 7,
25.4 Hz. It is also shown that the order of the wavelet results of pp. 2961–2969, Jul. 2009.
the stator voltage is 20% demagnetized magnet, 10% demagne- [7] M. D. Prieto, A. G. Espinosa, J. R. Ruiz, J. C. Urresty, and J. A. Ortega,
“Feature extraction of demagnetization faults in permanent-magnet
tized magnet and healthy magnet, namely, the opposite order as synchronous motors based on box-counting fractal dimension,” IEEE
that of the stator current. These frequencies are a little lower than Trans. Ind. Electron., vol. 58, no. 5, pp. 1594–1605, May 2011.
the frequency of stator current at the steady state. Therefore, the [8] J. Urresty, J. Riba, H. Saavedra, and J. Romeral, “Analysis of demag-
netization faults in surface-mounted permanent magnet synchronous
wavelet result of stator current and stator voltage can be used for motors with symmetric windings,” in Proc. IEEE Int. Symp. Diagnost.
the diagnosis of demagnetization, when the frequency is speci- Elect. Mach., Power Electron. Drives, Sep. 2011, pp. 240–245.
fied. As described in the introduction, this paper deals with the [9] J. Urresty, J. R. Riba, M. Delgado, and L. Romeral, “Detection of
demagnetization faults in surface-mounted permanent magnet syn-
less demagnetized situation than the previous paper. Therefore, chronous motors by means of the zero-sequence voltage component,”
the employed method is a successful one, though there are little IEEE Trans. Energy Convers., vol. 27, no. 1, pp. 42–51, Mar. 2012.
differences shown in Figs. 7 and 8. [10] J. Urresty, R. J. Riba, and L. Romeral, “A back-emf based method to
detect magnet failures in PMSMs,” IEEE Trans. Magn., vol. 49, no. 1,
pt. 3, Jan. 2013.
V. CONCLUSION [11] T. Ishikawa, Y. Seki, N. Kurita, and T. Matsuura, “Failure diagnosis
of brushless DC motor with rotor magnet defect,” in Proc. IEEE Int.
This paper has proposed the method for the diagnosis of the Elect. Mach. Drives Conf., May 2011, pp. 1552–1556.
demagnetization of the permanent magnet in the vector-con- [12] T. Ishikawa, T. Iida, and M. Matsunami, “Analysis of brushless DC
motor by Simulink and FEM considering DC voltage drop and in-
trolled PMSM. In the proposed method, the magnetic field cal- verter properties,” J. Jpn. Soc. Appl. Electromagn. Mechan., vol. 17,
culated by the FE method is weakly coupled with the drive and pp. 77–80, 2009.