S UNG -K UK K IM
Student Member
Power Conversion Lab., YeungNam University
Kyungsan, Kyungbuk, KOREA doljk@ynu.ac.kr
, http://yupcl.yu.ac.kr
Abstract -- This paper presents a non-parametric approach to failure detection of a broken rotor bar for an inverter-fed induction motors (IM). We lay the mathematical foundation for the concept of a diagnostic model of a rotor bar fault. The diagnostic model captures rotor bar high frequency (HF) characteristics which leads us to a conclusion that the HF equivalent motor resistance can be used as a direct indicator of broken rotor bars. The proposed detection technique is insensitive to other motor parameters and is effective under arbitrary load conditions. The time domain-based signature analysis enables the efficient detection and enhances fault isolation property. The identification scheme was implemented and tested on an inverter-fed 1.5 kW induction motor.
Index Terms -- Detection of a broken rotor bar, inverter-fed induction motors, rotor bar high frequency characteristics, time domain-based signature analysis, arbitrary load conditions.
J UL -K I S EOK
Senior Member negative-sequence carrier-signal current exhibits rotorposition dependent saliencies due to the broken bar. This idea seems like a good choice because it brings minimal interference with the fundamental operation and is nearly insensitive to the accuracy of motor parameters. However, the diagnosis is only effective at heavy load conditions since we can not spectrally distinguish from the harmonic caused by magnetic saturation ( 2 f e
) and the rotor-fault-related
I. I NTRODUCTION
Today, inverter-driven adjustable speed drives of induction motors (IMs) are mature and well-established technologies, used in a large variety of demanding applications. In this regard, early fault detection and diagnosis of widespread IMs are essential to ensure consistent and reliable operation without downtime in a factory. To be specific about failure monitoring, this paper focuses on a non-invasive detection of broken rotor bars in inverter-fed IMs.
The existence of 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 in the fundamental stator current is significantly affected by the operating condition such as loading conditions and the rotational speed change because operating frequency harmonics may overlap the harmonics caused by broken rotor bar faults. Thus, such spectrum-based detection schemes are bound to steady-state conditions. This method may also fail in closed-loop inverterdriven motors with a current regulator since the control loop tends to attenuate a current signature resulting from the fault.
Moreover, the need for the high precision of motor slip or rotor frequency information further complicates the accurate diagnosis task.
Another strategy for the rotor fault detection can be found in [4-5], where an open-loop high frequency (HF) voltage was injected in the stationary reference frame. The resulting harmonic ( 2 f r
) for low values of slip.
Both aforementioned methods are based on the spectrum analysis of the current signature in the stationary reference frame. The spectrum analysis requires large memories and high computational costs to achieve accurate monitoring.
Besides, both techniques are not suitable for diagnostic purposes at light loads due to load-dependent operating restrictions. This implies that the existing algorithms need large rotor currents or loadings for diagnosis under a broken bar-induced pulsating torque operation. This operation could cause secondary damage to other electrical/mechanical components as well as the running motor.
The purpose of this paper is to detect a broken rotor bar for an inverter-fed IM based on a 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 result naturally leads us to a conclusion that the HF equivalent motor resistance can be a direct indicator of broken rotor bars without being affected by magnetic saturation. Then, the HF motor resistance is determined by means of 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 fulltime domain-based scheme. In addition, the detection technique is insensitive to operating condition variations and is effective even under unloaded conditions. The developed strategy has been implemented on an inverter-fed 1.5 kW induction motor to validate the effectiveness of the proposed algorithm.
978-1-4244-5287-3/10/$26.00 ©2010 IEEE 2479

II. P
RINCIPLES OF
B
HF
AR
F
S
IGNAL
AULT
D
I
NJECTION
ETECTION
-
BASED
B
ROKEN
A. Negative-Sequence Current-based Detection
Recently, a HF signal injection-based technique was proposed to perform the rotor bar fault diagnosis procedure
[4-5]. The detection is based on an open-loop HF voltage injection, 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 2 f e
) and rotor bar faults (with a frequency of 2 f r
) as shown in Fig. 1. This approach provides some advantages over other fundamental currentbased diagnostic techniques in terms of interference with the fundamental operation of motors and the influence of the closed-loop current control. bar with a depth d , a length l , and a width of slot w , the effective impedance of the bar], shown at the bottom of the page, can be the effective impedance of the bar can be represented as [6-7].
2 f r
2 f e
(a) 20% load
Fig. 1. Saliencies detected by negative-sequence current.
However, spectrum analysis should be applied to determine rotor faults, requiring complex signal processing.
At light loads, the frequency component with 2 f r
spectrally approaches the component with 2 f e
due to a low value of slip. This makes the detection-range restriction remain.
In order to justify this assertion, two frequency spectra of the resulting negative-sequence current are shown in Fig. 2 for an IM with one broken rotor bar at 20% and 40% load, respectively. In this test, the motor was operated at 10 Hz and a HF voltage with 10 V-150 Hz was injected in the stationary reference frame. It is evident that accurate spectral quantification of faults was 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-shaped rotor
(b) 40% load
Fig. 2. Negative-sequence current frequency spectrum in the stationary reference frame (one broken rotor bar).
In (1), the term, f , represents the frequency, R r ( DC ) denotes the DC bar resistance, μ
D
indicates the permeability of air, and ρ is the resistivity of the conducting bar.
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 R e
as
[8],
Z bar
= R r ( AC )
+ jX lr ( AC )
= α dR r ( DC )
⎡
⎢⎣ sinh cosh
2 α d
2 α d
+
− sin cos
2 α d
2 α d where
+
α =
π f
ρ
μ
D j sinh cosh
2 α d
2 α d
−
− sin cos
2 α d
2 α d
⎤
⎥⎦
(1a)
. (1b)
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R r
=
2 ( 2
N
N
1
/ m
)
2 ⎡
⎢ R r ( AC )
+ R e
/
⎝
2 sin
2 ϕ
2
⎤
⎥ (2) where N
1
is the turn number of the stator winding, N is the total rotor bars number, m is the number of stator phases, and ϕ represents the electrical angular displacement between two adjacent bars. If we assume that R e
<< R r ( AC )
for all the frequency range, then,
R r
≅
2 ( 2
N
N
/
1 m
)
2
R r ( AC )
. (3)
The AC rotor bar resistance and rotor leakage reactance approach equality as the frequency or bar depth increases [6-
7]. Thus, if α d >2.5, we obtain
R r ( AC )
= X lr ( AC )
= α dR r ( DC )
. (4)
By combining (3) and (4), the healthy HF rotor phase impedance referred to the stator can be written as
R r _ hf
= X lr _ hf
=
2 ( 2
N
N
/
1
) m
2
α dR r ( DC )
. (5)
In case of n contiguous broken bars, the effective faulty
HF rotor impedance becomes
R r _ hf ( n )
= X lr _ hf ( n )
=
(
2 ( 2 N
1
)
2
N / m − n )
α dR r ( DC ) which leads to an increment due to broken bars
Δ R r _ hf ( n )
= R r _ hf ( n )
− R r _ hf
= m n
N
R r _ hf
, (6)
. (7) operator, and i e dh
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 [10].
Then, R eq
and X eq
can be estimated using a low-pass filter (LPF) as eq
=
LPF
( v e dh
LPF i e
⋅
2 dh i
( ) e dh
)
.
(9a)
LPF v
( e dh
− eq
⋅ i e dh
2
) eq
=
LPF i
( ) . (9b)
Broken rotor bars produce a non-uniform leakage flux rise in the airgap because there is no current flow in the broken bar. The non-uniform leakage flux variation provides an opportunity to identify broken bar faults that can be represented by an increase of the HF rotor leakage reactance.
Equation (5) and (6) clearly state that eq can be a fault indicator. However, eq
is found to be less adequate in this application with respect to
ˆ eq
since the stator leakage inductance changes due to magnetic saturation by the fundamental load current. Thus, in this paper, we take as a diagnostic metric because it is nearly independent of operating conditions.
Fig. 3(a) depicts a general squirrel-cage IM with n broken bars when operated with a non-zero slip of ω sl
. If a HF voltage is added on the synchronous d e
-axis, it can be viewed as rotating or scanning the rotor with a ω sl
velocity in the rotor reference frame ( d r
-axis). Thus, the resulting HF current i e dh
will carry the rotor saliency effect, as shown in
Fig. 1, due to the non-uniform rotor leakage flux. As a result, this imbalance gives rise to a sinusoidal component with double slip frequency ( 2 ω sl
) in
III. T HE P ROPOSED R OTOR B AR F AULT D ETECTION S CHEME
If the stator transient inductance is approximately equal to the total leakage inductance [9] and the injection frequency
ω h
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 v e dh
≅
=
[ (
R s
(
R eq
+
+
R r _ pL eq hf
) e
) ( i dh
L ls
+ L lr _ hf
] ) i e dh
. (8) where R s
is the stator resistance, leakage inductance, L lr _ hf
L ls
represents the stator
is the HF rotor leakage inductance referred to the stator, p denotes the differential
(8) that the fault detector resistance that is a function of temperature. Thus, the stator resistance itself and temperature variations carry a DC offset in using a high-pass filter (HPF) as
Δ r _ hf ( n )
( θ sl
) = HPF ( R eq
) . (10)
Then, we can notice that the magnitude of high-pass filtered Δ R r _ hf ( n )
in (7) as shown in
Fig. 3(b). In other words, the magnitude of Δ r _ hf ( n )
( θ sl
) is proportional to the number of broken bars and the frequency is to an existing load or a slip.
The sinusoidal signal with double slip frequency does not appear at zero slip even when a bar fault is present. However, in the real world, there is no such a zero-load because of the existence of internal friction load. This implies that the proposed detection process is not affected by external load conditions.
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sl
HF Voltage-Injection d e
-axis d r -axis
Broken bar
(a) HF voltage injection to an IM with n broken bars.
(b)
R r _ hf
AC signal represents the fact that a fault has occurred, and the
DC signal represents no fault. This alleviates the need for designing threshold values or functions for the failure detection. This simple decision rule allows the proposed approach to be a non-statistical scheme and to greatly improve the signal-to-noise ratio compared to 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 nature of rotor bar faults than current spectrum signature.
Fig. 4 shows an overall block diagram of the proposed HF voltage-injection-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 (BSF) 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.
sl
π
2
(b)
3 π
2
2 π
Δ R r _ hf ( n )
( θ sl
) by faulty bars.
Fig. 3. Broken rotor bar detection by HF voltage injection in the synchronous reference frame.
Thus, it is worth mentioning that the fault detection problem is converted into one of identifying whether
Δ r _ hf ( n )
( θ sl
) has the form of an AC or DC signal. The
IV. E XPERIMENTAL R ESULTS
The proposed algorithm was implemented on a 1.5 kW IM with 28 rotor bars described in Table I. Two-phase currents were sampled with a rate of 100 μ s and the nominal deadtime was set to 3.5 μ s. An encoder of 4096-pulse-per-revolution is mounted to one end of the IM to measure the rotor speed. The other end of the shaft was coupled with a 1.5 kW DC generator to control external loads. In experiments shown in this paper, Hall-effect current sensors and 12-bit A/D converters were used to capture the stator currents. v e dh
* rm
r _ hf
rm i e* dqs i e dqs v e * dqs v s* abcs i e ds i e qs
eq v e dh i e dh
Fig. 4. The proposed HF voltage-injection-based bar fault detection strategy.
i s abcs
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well to light load conditions.
Fig. 5. Stator and three rotors under testing.
The injection condition was fixed at 5 V-500 Hz in the daxis synchronous reference frame. In the test, the cutoff frequency of a first-order discrete-time HPF is set at 0.05 Hz.
Fig. 5 shows the stator and three identical rotors for testing.
One test was performed on a rotor with two broken bars while the external load was stepwise increased from 0 up to
15 % of the rated torque. The external load, the d-axis synchronous stator voltage command v e * ds
,
ˆ eq
, and
Δ r _ hf ( n )
( θ sl
) are plotted in Fig. 6. At the instant of the
HF voltage injection, AC signals can be observed in
Δ r _ hf ( n )
( θ sl
) . It is shown from the waveform of
Δ r _ hf ( n )
( θ sl
) that the HPF clearly decouples the DC offset resulting form the stator resistance in proposed rotor bar fault detection is capable of responding
Fig. 6. Estimated HF resistance of 2 broken rotor bars at load change test.
The performance of the proposed detection method is investigated through experiments at 300 r/min. The external load is increased from 0 to the rated load as illustrated in Fig.
7. In the absence of fault, the high-pass filtered
Δ r _ hf ( n )
( θ sl
) of Fig. 7(d) gives a clear DC signal irrespective of external load conditions. In contrast, as seen from Fig. 7(b) and (c) of the case of rotor faults, AC signals
T
L
Time
[
25 s / div
]
Fig. 7. Experimental results of the proposed bar fault detection method. (a) External load torque. (b)
Δ r _ hf ( n )
( θ sl
) of 1 broken rotor bar ( n =1). (d) Δ
Δ R r _ hf ( n )
( θ sl
) of 2 broken rotor bars ( n =2). (c) r _ hf ( n )
( θ sl
) of healthy rotor bar.
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are observed under arbitrary load conditions, including the zero external load. The designed HPF could result in a certain amount of distortions in terms of amplitude and phase of
Δ r _ hf ( n )
( θ sl
) at light loads, but it significant impact in the decision
.
does not give a
In faulty condition, the amplitude of Δ r _ hf ( n )
( θ sl
) slightly decreases as the load increases due to the magnetic saturation on the rotor leakage inductance. The experimentally measured amplitude of Δ r _ hf ( n )
( θ sl
) is plotted in Fig. 8.
0.8
0.7
2 broken bars
1 broken bar
Healthy bar
0.6
R ATINGS AND P ARAMETERS
R
TABLE I
R ATINGS AND K NOWN P ARAMETERS OF THE IM U NDER T EST s
/ R r
L m
/
@
L
25
D ls
C
V ALUE U NIT
R
ATED POWER OUTPUT
1.5 kW
R
ATED VOLTAGE
230 V
R
ATED SPEED
1435
2.47 / 0.7
134 / 10.5
Ω mH
0.5
0.4
0.3
0.2
A
CKNOWLEDGMENT
This work was supported by the Power Generation &
Electricity Delivery of the Korea Institute of
Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge
Economy. (No. 2008T100100049 )
0.1
0
-0.1
0 20 40 [ ] 60 80 100
T
L
Fig. 8. Experimentally measured amplitude of Δ R r _ hf ( n )
( θ sl
) .
The test results show that the proposed scheme achieves a reliable tracking of the rotor bar fault even under the unloaded condition where the low slip frequency is mainly resulted from the friction load.
V. C ONCLUSIONS
The purpose of this paper is to detect a broken rotor bar fault for an inverter-fed IM based on a HF model of rotor bars.
The proposed detection scheme uses a rotor leakage flux as a fault-interpreting quantity which more directly indicates the inception of broken bars while existing contributions are based on external symptoms such as rotor asymmetries or torque oscillation that mostly appear on sideband current components. As a result, the fault tracking accuracy of available approaches is significantly disturbed by external operating conditions. The proposed approach does not require the rotor speed information as well as the complicated computation of a frequency component. In addition, the detection technique is insensitive to operating condition variations and is effective under unloaded conditions. The developed strategy has been implemented on an inverter-fed
1.5 kW induction motor to validate the effectiveness of the proposed algorithm.
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