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High-Frequency Signal Injection-Based Rotor Bar Fault Detection of Inverter-Fed Induction Motors With Closed Rotor Slots Sung-Kuk Kim, Student Member, IEEE, and Jul-Ki Seok, Senior Member, IEEE

Abstract—This paper presents a nonparametric approach to failure detection of broken rotor bars in inverter-fed induction motors (IMs). We lay the mathematical foundation for a diagnostic model of a rotor bar fault that captures the rotor bar highfrequency (HF) characteristics. The model shows that the HF equivalent motor resistance can be used as a direct indicator of broken rotor bars. It should be emphasized that the proposed detection methodology is applicable to any shape of rotor slot design by incorporating the idea of synchronous reference frame based injection and by taking the HF resistance as the fault detector. The proposed detection technique is also insensitive to other motor parameters and is effective under arbitrary load conditions. The full time-domain-based signature process provides efficient detection and enhances fault isolation. The identification scheme was implemented and tested on an inverter-fed 1.5-kW IM. Index Terms—Arbitrary load conditions, detection of a broken rotor bar, inverter-fed induction motors (IM) with closed rotor slots, rotor bar high-frequency (HF) characteristics, timedomain-based signature analysis.

I. I NTRODUCTION

I

NVERTER-DRIVEN adjustable speed drives of induction motors (IMs) are mature and well-established technologies used in a large variety of demanding applications. Early fault detection and diagnosis of IMs are essential for consistent and reliable operation without factory downtime. Broken rotor bars are among the most common failures that affect IMs themselves and coupled mechanical equipment. Broken rotor bars can be detected by monitoring any abnormality of the spectrum amplitudes at certain frequencies in the stator current spectrum [1]–[3]; however, these frequency components are significantly affected by the operating conditions, such as the loading conditions and rotational speed

Manuscript received October 5, 2010; revised December 16, 2010 and January 27, 2011; accepted February 7, 2011. Date of publication May 12, 2011; date of current version July 20, 2011. Paper 2010-EMC-386.R2, presented at the 2010 IEEE Energy Conversion Congress and Exposition, San Jose, CA, September 12–16, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (2010-0029428). S.-K. Kim is with the AE Control R&D Lab., LG Electronics Inc., Changwon 641-713, Korea (e-mail: [email protected]). J.-K. Seok is with the School of Electrical Engineering, Yeungnam University, Kyungsan 712-749, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2011.2153171

changes, because operating frequency harmonics may overlap the harmonics caused by broken rotor bars. Thus, spectrumbased detection schemes are bound to steady-state conditions. This method may also fail in applications with closed-loop inverter-driven motors with a current regulator since the control loop tends to attenuate the current signature resulting from the fault. Moreover, the need for high-precision motor slip or rotor frequency information further complicates accurate diagnosis. Since starting stresses such as high currents and mechanical vibrations are considered as one of the major causes of rotor failure, most of the detection researches have been the focus of line-connected IMs. However, as described in [4] and [7], frequent overloading (both thermal and electrical), as well as excessive mechanical vibrations, fatigue parts, and environmental stresses caused by contamination, may result in accelerated failures of squirrel-cage rotor bars. Thus, it is believed that the rotor bars of inverter-fed IMs can be damaged by these reasons other than the starting stresses. For specific failure monitoring, this paper focuses on nonstatistical detection of broken rotor bars in inverter-fed IMs. Thus, different methods have been put forward to detect the rotor faults of inverter-fed IMs [5]–[9]. In [5], the inverter current harmonics have been employed to sense rotor faults associated with broken rotor bars. While the inverter current is introduced as a fault indicator, it still requires spectral analysis to detect broken bars. On the other hand, sophisticated multiple discriminant analysis and artificial neural networks are proposed for reliable fault detection [6]. However, the physical basis of the training process is not clear, making it hard to understand the limitations of this method. To overcome the difficulties that arise in the statistical approach, a timedomain-based diagnosis method is developed [7]. Although this approach does not require the accurate computation of a single frequency component and its amplitude, we need to implement a complicated maximum covariance method for accurate frequency tracking of the fundamental component. More attractive approaches are described in [8] and [9], where an open-loop high-frequency (HF) voltage was injected in the stationary reference frame. The resulting negativesequence carrier-signal current exhibits rotor-positiondependent saliencies due to the broken bar. This idea seems like a good choice because it produces minimal interference with the fundamental operation and is nearly insensitive to the accuracy of motor parameters. However, the diagnosis is only effective under heavy load conditions since we cannot

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KIM AND SEOK: HF SIGNAL INJECTION-BASED ROTOR BAR FAULT DETECTION OF INVERTER-FED IMS

spectrally distinguish it from the harmonic caused by magnetic saturation (2fe ) and the rotor-fault-related harmonic (2fr ) for low values of slip. Both of these methods are based on the spectrum analysis of the current signature in the stationary reference frame, which requires large memories and high computational costs to achieve accurate monitoring. Neither technique is suitable for diagnostic purposes under light loads due to load-dependent operating restrictions. This implies that the existing algorithms need large rotor currents or loading for diagnosis under a broken-bar-induced pulsating torque operation. This operation could cause secondary damage to other electrical or mechanical components as well as to the motor. Due to its injection nature, another restriction arises in diagnosing the presence of broken bars in a machine with closed rotor slots [8]. The purpose of this paper is to detect a broken rotor bar for an inverter-fed IM using the HF model of rotor bars. The presented HF model elaborates on the relationship between the HF rotor resistance and the rotor leakage inductance, which increases around faulty rotor bars. This suggests that the HF equivalent motor resistance can be a direct indicator of broken rotor bars without being affected by magnetic saturation. The HF motor resistance is determined by a d-axis HF voltage injection in the synchronous coordinate. The proposed approach does not require the complicated computation of a frequency component as it is a simple full time-domain-based scheme. In addition, the detection technique is insensitive to operating condition variations and is effective even under unloaded conditions. The developed strategy was implemented on an inverter-fed 1.5-kW IM to validate its effectiveness. The experimental evaluation of the proposed idea has demonstrated little sensitivity to the rotor slot design.

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Fig. 1. Saliencies detected by the negative-sequence current.

II. P RINCIPLES OF HF S IGNAL I NJECTION -BASED B ROKEN BAR FAULT D ETECTION A. Negative-Sequence Current Detection An HF signal injection technique was recently proposed for rotor bar fault diagnosis [8], [9]. This detection is based on open-loop HF voltage injection, which is superimposed on the fundamental voltage, in the stationary reference frame. The resulting negative-sequence current carries unbalanced signatures caused by saturation (with a frequency of 2fe ) and rotor bar faults (with a frequency of 2fr ), as shown in Fig. 1. This approach provides some advantages over other fundamental current-based diagnostic techniques in terms of interference with the fundamental motor operation and the influence of closed-loop current control. However, applying spectrum analysis to determine rotor faults requires complex signal processing. At light loads, the frequency component with 2fr spectrally approaches the component with 2fe due to a low value of slip. This restricts the detection range. To justify this assertion, Fig. 2 shows the frequency spectra of the resulting negative-sequence current for an IM with one broken rotor bar at 20% and 40% loads. In this test, the motor was operated at 10 Hz, and an HF voltage with 10 V–150 Hz

Fig. 2. Negative-sequence current frequency spectrum in the stationary reference frame (one broken rotor bar). (a) 20% load. (b) 40% load.

was injected in the stationary reference frame. It is evident that accurate spectral quantification of faults is found to be more difficult as the slip decreases. This results in complex threshold functions and may lead to higher false alarm rates. B. HF Model of Proposed Broken Bar Detection The current distribution in the shorted rotor bars may vary significantly with frequency. For a rectangular rotor bar with

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depth d, length l, and slot width w, the effective impedance of the bar can be represented as [10], [11] Zbar = Rr(AC) + jXlr(AC)  sinh 2αd + sin 2αd = αdRr(DC) cosh 2αd − cos 2αd sinh 2αd − sin 2αd +j cosh 2αd − cos 2αd

 (1)

 where α = πf μ◦ /ρ, f represents the frequency, μ◦ indicates the permeability of air, ρ is the resistivity of the conducting bar, and Rr(DC) denotes the dc rotor resistance. If the bar width is approximately equal to the slot width, the phase rotor equivalent resistance referred to the stator can be simply represented using the end-ring resistance Re [12] Rr =

 ϕ  2(2N1 )2  Rr(AC) + Re / 2 sin2 N/m 2

Fig. 3.

Plot of ΔRr_hf (n) according to the number of broken bars.

(2)

where N1 is the turn number of the stator winding, N is the total number of rotor bars, m is the number of stator phases, and ϕ represents the electrical angular displacement between two adjacent bars. If we assume that Re  Rr(AC) for all the frequency range, then 2(2N1 )2 Rr(AC) . Rr ∼ = N/m

(3)

The ac rotor bar resistance and the rotor leakage reactance approach equality as the frequency or bar depth increases [10], [11]. Thus, if αd > 2.5, we obtain Rr(AC) = Xlr(AC) = αdRr(DC) .

(4)

By combining (3) and (4), the healthy HF rotor phase impedance referred to the stator can be written as Rr_hf (0) = Xlr_hf (0) =

2(2N1 )2 αdRr(DC) . N/m

(5)

In case of n contiguous broken bars, the effective faulty HF rotor impedance becomes Rr_hf (n) = Xlr_hf (n)

2(2N1 )2 αdRr(DC) = (N/m − n)

(6)

which leads to an increment due to broken bars ΔRr_hf (n) = Rr_hf (n) − Rr_hf (0) = m

n Rr_hf (0) . N − mn (7)

For a three-phase machine, a plot of (7) to changes of n is shown in Fig. 3, where 3n/(N − 3n) is normalized to a per unit basis of Rr_hf (0) . Note that ΔRr_hf (n) is proportional to n irrespective of the number of rotor bars (N = 28, 48, and 58), which means that the rotor leakage flux grows as the number of broken bars increases.

Fig. 4. Broken rotor bar detection by HF voltage injection in the synchronous reference frame. (a) HF voltage injection to an IM with n broken bars. (b) ΔRr_hf (n) (θsl ) by faulty bars.

III. P ROPOSED ROTOR BAR FAULT D ETECTION S CHEME If the stator transient inductance is approximately equal to the total leakage inductance [13] and if the injection frequency ωh is high enough, most of the HF current flows through the rotor branch. Then, in the synchronous reference frame, the d-axis HF voltage equation at steady state can be written as e ∼ vdh = [(Rs +Rr_hf )+p(Lls +Llr_hf )] iedh = (Req +pLeq )iedh (8)

where Rs is the stator resistance, Lls represents the stator leakage inductance, Llr_hf is the HF rotor leakage inductance referred to the stator, p denotes the differential operator, and iedh indicates the resulting d-axis HF current in the synchronous coordinate. Here, we assume that the skin effect of stator parameters is negligible in the frequency range of interest (≤ 500 Hz) compared to that of the rotor parameters [14].

KIM AND SEOK: HF SIGNAL INJECTION-BASED ROTOR BAR FAULT DETECTION OF INVERTER-FED IMS

Fig. 5.

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Detectability for broken bar location of a two-pole IM. (a) Two adjacent bars. (b) Two perpendicular bars. (c) Two opposite bars.

Then, Req and Xeq can be estimated using a low-pass filter (LPF) as ˆ eq = LP F (vdh · idh ) R LP F (ie2 dh ) e



 LP F

ˆ eq = X

e



e vdh

ˆ eq · ie −R dh

(9a) 2 

LP F (ie2 dh )

.

(9b)

Broken rotor bars produce a nonuniform leakage flux rise in the airgap because there is no current flow in the broken bar. The nonuniform leakage flux variation provides an opportunity to identify broken bar faults that can be represented by an increase of the HF rotor leakage reactance. Equations (5) and (6) clearly ˆ eq can be fault indicators; however, X ˆ eq is ˆ eq or X state that R ˆ eq found to be less adequate in this application with respect to R since the stator leakage inductance changes due to magnetic saturation by the fundamental load current. Thus, in this paper, ˆ eq as a diagnostic metric since it is nearly independent we take R of the operating conditions. Fig. 4(a) shows a general squirrel-cage IM with n broken bars when operated with a nonzero slip of ωsl . If an HF voltage is added on the synchronous de -axis, it can be viewed as rotating or scanning the rotor with a ωsl velocity in the rotor reference frame (dr -axis). Thus, the resulting HF current iedh will contain the rotor saliency effect (as shown in Fig. 1) due to the nonuniform rotor leakage flux. This imbalance gives rise to a sinusoidal component with a double slip frequency (2ωsl ) ˆ eq contains the ˆ eq . Note that, from (8), the fault detector R in R unknown stator resistance, which is a function of temperature. Because of relatively large thermal inertia, the stator resistance itself and the temperature variations from motor resistances can ˆ eq . We can obtain an offset-free be treated as a dc offset in R ˆ eq using a high-pass filter (HPF) as component of R ˆ eq ). ˆ r_hf (n) (θsl ) = HP F (R ΔR

(10)

ˆ eq correThen, the magnitude of the high-pass filtered R ˆ sponds to ΔRr_hf (n) in (7), as shown in Fig. 4(b). In other ˆ r_hf (n) (θsl ) is proportional to the words, the magnitude of ΔR number of broken bars, and the frequency is proportional to an existing load or a slip. The sinusoidal signal with a double slip frequency does not appear at zero slip even when a bar fault is present. However, in real world, there is no such zero load condition because of the load from internal friction. This implies that the proposed detection process is not affected by external load conditions. Thus, it is worth mentioning that the fault detection problem ˆ r_hf (n) (θsl ) is is converted into one that identifies whether ΔR an ac or dc signal. The ac signal represents the occurrence of a fault, and the dc signal represents a no fault condition. This alleviates the need for designing threshold values or functions for failure detection. This simple decision rule allows the proposed approach to be a nonstatistical scheme and greatly improves the signal-to-noise ratio compared with other existing techniques. These benefits are explained by the suitably chosen fault detector based on the rotor leakage flux variations, which is more directly correlated with the nature of the rotor bar faults than with the current spectrum signature. Although the proposed detection method is promising, more research is required to extend its application to all types of IMs with various physical rotor disturbances, such as interbar currents, skewing, and structural rotor unbalances. The existence of the significant interbar currents may affect detection accuracy because it creates axial rotor fluxes which flow through the rotor shaft [15]. Skewing, which results in the variation of the interbar currents, and structural rotor unbalances also give rise to rotor leakage flux variations. The location of the broken rotor bars gives a direct impact on the proposed rotor fault detectability. For two broken bars displaced by 0◦ and 180◦ electrical degrees [as shown Fig. 5(a) and (c)], the rotor saliency due to the magnetic unbalances almost ˆ r_hf (n) (θsl ) compared to a single doubles the magnitude of ΔR broken bar. However, symmetric breakages separated by a half pole pitch [90◦ electrical degree; as shown Fig. 5(b)] may result

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Fig. 6. Proposed HF voltage-injection-based bar fault detection strategy.

TABLE I R ATINGS AND K NOWN PARAMETERS OF IM U NDER T EST

Fig. 8. Injection frequency effect of closed rotor slots for the negativesequence current-based method and for the proposed method.

Fig. 7. Photograph of the tested motor. (a) Stator and three rotors tested. (b) Drilled rotor with closed slots.

ˆ r_hf (n) (θsl ) in the masking of the proposed fault metric ΔR and may lead to a possible misdiagnosis. This fault scenario masks the fault index of any other existing methods using

electric and magnetic signatures [16]. Even though the fault is not diagnosed during its early stages, it gets worse, propagating toward the adjacent bars, and some symptoms enabling its easy diagnosis appear. Fig. 6 shows the block diagram of the proposed HF voltageinjection-based rotor bar fault detection strategy. In this paper, we advocate an intermittent injection scenario to reduce additional losses and acoustic noise. The resulting HF current will not affect the fundamental current regulation performance because a band-stop filter removes the HF current from the current feedback to the current controller. Here, the HPF was employed to decouple the dc offset component resulting from the temperature effect. Phase current measurement for control and protection purposes is a standard feature of inverter-fed IM drives. In addition, most drives typically have A/D converters for the current measurement with 10–12 b. This implies that no additional sensors, cabling, and A/D converters are therefore needed to implement the proposed method. Since the proposed scheme is based on a two-phase current measurement system, it is suitable in retrofitting IM drives where two current sensors are commonly used.

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Fig. 9. Frequency spectrum of the measured negative-sequence current in case of different injection frequencies with closed rotor slots (one broken bar; 40% load). (a) 150 Hz. (b) 500 Hz.

IV. E XPERIMENTAL R ESULTS The proposed algorithm was implemented on a 1.5-kW IM with 28 rotor bars, as described in Table I. Two-phase currents were sampled at 100 μs, and the nominal deadtime was set to 3.5 μs. A 4096-pulses-per-revolution encoder is mounted to one end of the IM to measure the rotor speed. The other end of the shaft was coupled to a 1.5-kW dc generator to control external loads. In the experiments shown in this paper, Halleffect current sensors and 12-b A/D converters captured the stator currents. The injection condition was fixed at 5 V–500 Hz in the d-axis synchronous reference frame. The monitoring period of motor fault diagnosis depends on the motor output capacity and its working environments or applications. It is desirable that the injection interval, which is a code to be stored in the inverter, is decided by a field personnel who has some degree of expertise on the system. In the test, the cutoff frequency of the first-order discretetime HPF is 0.05 Hz. The proposed algorithm is implemented through a signal processing method using second-order discrete-time bandpass/stop filters, two first-order discrete-time LPFs for (9a), and a first-order discrete-time HPF for (10). Each filter just requires a couple of multiplications and additions for real-time implementation. Fig. 7(a) shows the stator and three identical rotors used for testing. The rotor with closed slots was intentionally drilled to emulate the actual rotor fault, as shown in Fig. 7(b). A. Sensitivity Evaluation of the Rotor Slot Design The method in [8] and [9] injects an HF voltage in the stationary reference frame. Based on the resulting negativesequence HF current, spectral separation is required between the components at the saturation-induced frequency (2fe ) and at the rotor bar fault-related frequency (2fr ). For rotors with closed slots, however, the magnitude of the rotor bar faultrelated component at 2fr is reduced as the injection frequency increases in the range of 150–750 Hz, as shown in Fig. 8. It can be observed from the figure that it is nearly impossible to distinguish a faulty rotor from a healthy rotor over 400 Hz. The corresponding results are shown in Fig. 9, where the

Fig. 10.

Estimated HF resistance of two broken rotor bars in load change test.

frequency spectra are investigated at the injection frequency of 150 and 500 Hz, respectively. As discussed in [8], the use of the negative-sequence current-based method in the stationary reference frame for closed rotor slots has been limited over a wide range of high frequencies. In contrast, the voltage injection of the proposed method is synchronized with the synchronous reference frame or the saturation-induced frequency. This allows the proposed detection to have a reduced sensitivity to saturation-induced harmonic variations. In addition, as shown in Fig. 8, the magnitude ˆ r_hf (n) (θsl ) (marked with ) tends to increase with of ΔR injection frequency due to the skin effect. This feature provides a better signal-to-noise ratio at higher frequencies. From these observations, it can be concluded that the proposed detection technique is applicable to IMs with closed rotor slots as well as to open rotor slots. B. Rotor Fault Detection One test was performed on a rotor with two broken bars, while the external load was stepwise increased from 0% to 15% of the rated torque. The external load, the d-axis synchronous e∗ ˆ eq , and ΔR ˆ r_hf (n) (θsl ) are , R stator voltage command vds

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The test results show that the proposed scheme achieves reliable tracking of the rotor bar fault even in an unloaded condition where the low slip frequency mainly results from the friction load. V. C ONCLUSION

Fig. 11. Experimental results of the proposed bar fault detection method. ˆ r_hf (n)(θsl ) of two broken rotor bars (n = 2). (a) External load torque. (b) ΔR ˆ r_hf (n) (θsl ) ˆ r_hf (n) (θsl ) of one broken rotor bar (n = 1). (d) ΔR (c) ΔR of a healthy rotor bar.

This paper has developed a method of detecting a broken rotor bar fault in an inverter-fed IM based on an HF model of rotor bars. The proposed detection scheme uses rotor leakage flux as a fault-interpreting quantity, which directly indicates broken bars, while existing approaches rely on external symptoms, such as rotor asymmetries or torque oscillation, that mostly appear in sideband current components. As a result, the fault tracking accuracy of the available approaches is significantly disturbed by external operating conditions. The proposed approach does not require rotor speed information or the complicated computation of a frequency component. In addition, the detection technique is insensitive to operating condition variations and is effective in unloaded conditions. The developed strategy was implemented in an inverter-fed 1.5-kW IM to validate its effectiveness. By incorporating the idea of the synchronous reference frame based injection and by taking the HF resistance as the fault detector, the proposed detection becomes effective to a machine with closed rotor slots. R EFERENCES

ˆ r_hf (n) (θsl ). Fig. 12. Experimentally measured amplitude of ΔR

shown in Fig. 10. At the instant of HF voltage injection, ac ˆ r_hf (n) (θsl ). The waveform of signals can be observed in ΔR ˆ ΔRr_hf (n) (θsl ) shows that the HPF decouples the dc offset ˆ eq , and the proposed resulting from the stator resistance in R rotor bar fault detection responds well to light loads. The performance of the proposed detection method was investigated through experiments at 300 r/min. The external load increased from zero to the rated load, as shown in Fig. 11. ˆ r_hf (n) (θsl ) In the absence of a fault, the high-pass filtered ΔR of Fig. 11(d) gives a clear dc signal irrespective of the external load. In contrast, as shown in Fig. 11(b) and (c) for rotor faults, ac signals are observed under arbitrary load conditions, including a zero external load. The designed HPF could result in a certain amount of distortions in terms of amplitude and phase ˆ r_hf (n) (θsl ) at light loads, but this does not significantly of ΔR affect the diagnostic decision. In a fault condition, the ampliˆ r_hf (n) (θsl ) slightly decreases as the load increases tude of ΔR due to the magnetic saturation of the rotor leakage inductance. ˆ r_hf (n) (θsl ) is The experimentally measured amplitude of ΔR shown in Fig. 12.

[1] W. T. Thomas and M. Fenger, “Current signature analysis to detect induction motor faults,” IEEE Ind. Appl. Mag., vol. 7, no. 4, pp. 26–34, Jul./Aug. 2001. [2] J. H. Jung, J. J. Lee, and B. H. Kwon, “Online diagnosis of induction motors using MCSA,” IEEE Trans. Ind. Electron., vol. 53, no. 6, pp. 1842–1852, Dec. 2006. [3] A. Bellini, F. Filippetti, C. Tassoni, and G.-A. Capolino, “Advances in diagnostic techniques for induction machines,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4109–4126, Dec. 2008. [4] S. Nandi, H. A. Toliyat, and X. Li, “Condition monitoring and fault diagnosis of electrical motors—A review,” IEEE Trans. Energy Convers., vol. 20, no. 4, pp. 719–729, Dec. 2005. [5] B. Akin, U. Orguner, H. A. Toliyat, and M. Rayner, “Low order PWM inverter harmonics contributions to the inverter-fed induction machine fault diagnosis,” IEEE Trans. Ind. Electron., vol. 55, no. 2, pp. 610–619, Feb. 2008. [6] B. Ayhan, M. Y. Chow, and M. H. Song, “Multiple discriminant analysis and neural-network-based monolith and partition fault-detection schemes for broken rotor bar in induction motors,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1298–1308, Jun. 2006. [7] A. Bellini, “Quad demodulation: A time-domain diagnostic method for induction machines,” IEEE Trans. Ind. Appl., vol. 45, no. 2, pp. 712–719, Mar./Apr. 2009. [8] F. Briz, M. W. Degner, A. B. Diez, and J. M. Guerrero, “Online diagnostics in inverter-fed induction machines using high-frequency signal injection,” IEEE Trans. Ind. Appl., vol. 40, no. 4, pp. 1153–1161, Jul./Aug. 2004. [9] A. Bellini, C. Concari, G. Franceschini, E. Lorenzani, and C. Tassoni, “Induction drives diagnosis by signal injection: Effectiveness and severity classification,” in Proc. IEEE IEMDC, 2005, pp. 718–727. [10] P. L. Alger, The Nature of Induction Machine. New York: Gordon and Breach, 1965, pp. 265–272. [11] K. R. Cho and J. K. Seok, “Induction motor rotor temperature estimation based on a high-frequency model of a rotor bar,” IEEE Trans. Ind. Appl., vol. 45, no. 4, pp. 1267–1275, Jul./Aug. 2009. [12] A. Bellini, F. Filippetti, G. Franceschini, C. Tassoni, and G. B. Kliman, “Quantitative evaluation of induction motor broken bars by means of electrical signature analysis,” IEEE Trans. Ind. Appl., vol. 37, no. 5, pp. 1248–1255, Sep./Oct. 2001. [13] D. W. Novotny and T. A. Lipo, Vector Control and Dynamics of AC Drives. New York: Oxford Univ. Press, 1996.

KIM AND SEOK: HF SIGNAL INJECTION-BASED ROTOR BAR FAULT DETECTION OF INVERTER-FED IMS

[14] O. M. O. Gatous and J. P. Filho, “Frequency-dependent skin-effect formulation for resistance and internal inductance of a solid cylindrical conductor,” Proc. Inst. Elect. Eng.—Microw., Antennas, Propag., vol. 151, no. 3, pp. 212–216, Jun. 2004. [15] H. Meshgin-Kelk, J. Milimonfared, and H. A. Toliyat, “Interbar currents and axial fluxes in healthy and faulty induction motors,” IEEE Trans. Ind. Appl., vol. 40, no. 1, pp. 128–134, Jan./Feb. 2004. [16] G. Y. Sizov, A. Sayed-Ahmed, C. C. Yeh, and N. A. O. Demerdash, “Analysis and diagnostics of adjacent and nonadjacent broken-rotor-bar faults in squirrel-cage induction machines,” IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4627–4641, Nov. 2009.

Sung-Kuk Kim (S’10) received the B.S. and M.S. degrees in electrical engineering from the School of Electrical Engineering, Yeungnam University, Kyungsan, Korea, in 2009 and 2011, respectively. He is currently with the AE Control R&D Lab., LG Electronics Inc., Changwon, Korea. His specific research interests are high-performance electrical machine drives and ac motor fault diagnosis.

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Jul-Ki Seok (S’94–M’98–SM’09) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1992, 1994, and 1998, respectively. From 1998 to 2001, he was a Senior Engineer with the Production Engineering Center, Samsung Electronics, Suwon, Korea. Since 2001, he has been a member of the faculty of the School of Electrical Engineering, Yeungnam University, Kyungsan, Korea, where he is currently an Associate Professor. From February 2008 to February 2009, he was a Visiting Researcher with the Electrical and Computer Engineering Department, University of Wisconsin, Madison. His specific research interests are in highperformance electrical machine drives, sensorless control of ac machines, and nonlinear system identification related to the power electronics field. Dr. Seok is currently a member of the Editorial Board of the Institution of Engineering and Technology Electric Power Applications.