Induction Drive Health Assessment in DSP-Based Self ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 5, MAY 2011

Induction Drive Health Assessment in DSP-Based Self-Commissioning Procedures Carlo Concari, Member, IEEE, Giovanni Franceschini, and Carla Tassoni, Senior Member, IEEE

Abstract—This paper investigates the effect of different asymmetries on the results of the usual self-commissioning procedures for induction drives, as well as the further possibilities given by a digitally controlled inverter. It is shown that, even at a standstill, it is possible to detect some fault conditions of the machine. In particular, a specific supply scheme is proposed that, through the machine response, allows outlining the rotor conditions. This technique implements the IEEE Standards single-phase rotor test on a DSP-controlled converter, allowing the detection and the quantification of the rotor fault conditions. Index Terms—AC machines, automatic test equipment, fault diagnosis, induction motor drives, inverters, magnetic anisotropy, modeling, parameter estimation.

N OMENCLATURE Rs , Rr ls , lr M N, n P ξ Vf If is , ir , im τf , τs ¯ Z(s) τr z f , z r , pr ω α, β a δ V Is I rα , I rβ Zs

Stator and rotor resistances. Stator and rotor leakage inductance. Magnetizing inductance. Rotor bar number and broken rotor bars. Motor pole pair number. Pitch factor. Stator voltage step amplitude. Steady-state stator current (voltage step response). Stator, rotor, and magnetizing currents. Fast and slow time constants (voltage step response). Total machine impedance. Rotor time constant. Machine model zeroes and pole. Supply pulsation. Rotor orthogonal axes (β aligned with fault). Stator reference axis. Rotor angle (angular displacement between α and a). Sinusoidal voltage supply amplitude. Stator current phasor. Healthy and faulty rotor current phasors. Stator winding impedance.

Manuscript received January 26, 2010; revised May 8, 2010, July 20, 2010, and August 26, 2010; accepted September 3, 2010. Date of publication October 7, 2010; date of current version April 13, 2011. The authors are with the Department of Information Engineering, University of Parma, 43100 Parma, Italy (e-mail: [email protected]; giovanni. [email protected]; [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/TIE.2010.2084976

Z rα , Z rβ Z r , Zr ΔZ r , ΔZr k h Is ΔIs v vp , vn Vm Vm , θ Λk , αk B0 xslot xecc

Healthy and faulty rotor impedances. Average rotor impedance phasor and amplitude. Rotor impedance ripple phasor and amplitude. Nonnegative integer. Generic asymmetry pole pair number. Average stator current. Amplitude of stator current ripple. Stator voltage space vector. Positive and negative sequence components of stator voltage. Stator voltage phasor. Amplitude and angle of V m . Amplitude and angle of permeability kth harmonic. Amplitude of flux density fundamental component. Quantity x due to rotor slotting. Quantity x due to eccentricity. I. I NTRODUCTION

E

FFECTIVE parameter estimation is mandatory for controlled systems based on machine models. As far as induction-motor-controlled drives are concerned, a small error in parameter estimation could result in a mismatch between the estimated and actual flux values causing a detuned control structure. This problem is central in case of a field-oriented control based on a flux observer [1]. The machine model parameters can be obtained by automatic self-commissioning procedures. Traditional selfcommissioning is based on the processing of voltage and current waveforms while the machine is at natural standstill operation mode. A stator phase winding, if the neutral connection is available, or two series-connected phases are supplied with suitable signals provided by the inverter and synthesized through a DSP-based digital control board [2]. An ideal machine presents a behavior independent of phase permutations while, in an actual machine, nonidealities lead to different response modes to the test signals. Specifically, any asymmetry of stator windings, rotor cage, or magnetic core may lead to differences in parameter values. These parametric differences are outlined in IEEE Standards for mains supplied machines. In particular, [3] lists, among various maintenance tests, the phase balance ac frequency test and the single-phase ac rotor test to verify the condition of stator windings and rotor squirrel cages. In order to quicken the parameter estimation and health assessment procedures, automatic or quasi-automatic approaches

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CONCARI et al.: INDUCTION DRIVE HEALTH ASSESSMENT IN DSP-BASED SELF-COMMISSIONING PROCEDURES

to self-commissioning are very attractive. The further possibilities and flexibility derived from supplying the machine through a digitally controlled power converter can be utilized as well. Diagnostic procedures can be performed during selfcommissioning using the Motor Current Signature Analysis (MCSA) online methods as well [4]. At a standstill, the shortcomings linked to the correct detection of slip and to possible transient conditions are avoided so that the usual fast Fourier transform (FFT) analysis can be used [5], [6]. An analytical model must be chosen for the induction machine. The reference model must be the four parameters one usually adopted for control schemes, because models with more parameters developed to diagnostic aims, such as those proposed in [7] and [8], are redundant for control, and the additional parameters are not included in self-commissioning procedures. A simple possibility is the use of a symmetrical three-phase supply with a voltage amplitude low enough to prevent the motor from starting [9], [10]. The machine condition is obtained through the torque modulation in [9] or through the negative sequence component of the current space vector in [10]. This technique is not recommended because the fault-indicating current spectral lines can be present due to different causes such as rotor or stator asymmetry, supply voltage asymmetry, and eccentricity [11]. Moreover, it is not obvious how low the voltage must be to prevent the motor from starting, and finally, the need for low-amplitude excitation signals has a negative effect on the signal-to-noise ratio. Exploiting the potential of digitally controlled power converters, other techniques to state the machine conditions by standstill tests have been proposed. In [12], a discrete interval binary sequence is utilized as an excitation signal, and a parameter identification algorithm, applied to phase voltage and current data sets, allows the construction of a faulty space vector chosen to represent the machine asymmetry. Multifrequency waveforms with a minimized crest factor are used as excitation signals through the spectrum components of stray flux, while current components are not significantly affected [13]–[15]. The experiments show the dependence of the flux spectrum components on the fault severity, but no relationships linking the cause and effect are developed. The following section of this paper investigates the effect of different machine asymmetries on the usual selfcommissioning procedures; the method precision is taken into account in order to assess the possibility to detect faults through parameter variations, extending the considerations reported in [16]. Experimental results are reported. Section III focuses on the single-phase test in order to compare it with the proposed self-commissioning procedure, described in Section IV, which automates the operation by digitally generating a quasi-stationary pulsating field moving along the motor air gap, according to recent proposals [16]– [18]. It will be shown that, even when the motor is at a natural standstill, it is possible not only to detect the presence of rotor faults but also to diagnose their severity through the machine current analysis. Experiments to validate the assertions are reported as well.

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Finally, Section V concludes this paper with a summary of the obtained considerations and results. II. S ELF -C OMMISSIONING P ROCEDURES : A N A SSESSMENT In this section, the usual self-commissioning procedures for the determination of the machine electric parameters will be recalled in order to assess their precision. These methods are often grouped in the category of offline self-commissioning as opposed to online self-commissioning, which regards procedures to tune the drive following parameter variation with load conditions and temperature [1], [2], [19], [20]. Other online procedures extend their aim to the determination of inverter parameters such as the nonlinear behavior of the inverter [21], [22], or mechanical parameters of the machine [23]. The four parameters of the usual induction machine equivalent circuit are the total leakage inductance (lr + ls ), the magnetizing inductance M , and the stator Rs and rotor Rr resistances. These parameters allow computing the values needed for the control, such as the rotor time constant (lr + M )/Rr and the ratio M/(lr + M ), where it is assumed lr = ls . The signal sets useful for parameter identification can be grouped as follows: 1) dc voltage step signals [19]; 2) single-phase variable frequency signals [21], [24]; 3) specific signals for parameter identification [2], [25]–[27]. The first two classes comprise the classical tests, which are applicable in turn to all the motor phases as well and therefore able to compare the different phases’ results. They will be briefly recalled in the following paragraphs, discussing their precision and reporting the experimental results obtained on a test machine. The machine under test is a 1.5-kW, 400-V, 4-A, 50-Hz, 2-pole-pair off-the-shelf induction machine, with the star point available and two rotors, one healthy and one with two contiguous broken bars. The rotors have N = 28 slots. The stator has 36 slots, 3 slots per phase per pole, with full-pitch series-connected lap windings. The self-commissioning procedures have been tested on the healthy rotor because, in case of rotor fault, the parameter values would depend on the fault location. A. DC Voltage Step Test A dc voltage step of fixed amplitude Vf is applied in turn to the motor phases. Fig. 1 reports the current response of a phase to different voltage step values. To determine the machine parameters, the rotor skin effect is neglected, and the rotor is modeled as a single-cage rotor with lumped parameters. Because the pole is due to iron losses at a high frequency, it does not affect the dynamic response, and these losses are neglected as well. Since the leakage inductance is much lower than the magnetizing one, the current time response can be split into two distinct transients. In the former, named fast transient, since the magnetizing current iM can be neglected, the equivalent circuit of Fig. 2(a) holds. In the latter, named slow transient,

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Fig. 1. Phase current response to a voltage step test of the healthy machine at different steady-state current values If . (a) If = 0.8 p.u.. (b) If = 1.375 p.u..

Fig. 2. “T” equivalent circuit of the induction machine used for the voltage step test. (a) Fast transient. (b) Slow transient.

Fig. 3. Voltage step test: Shape of time constants measured on the different motor phases versus steady-state current. (a) τf . (b) τs .

the voltage drop due to stator and rotor leakage inductances can be neglected [see Fig. 2(b)] obtaining, for the fast τf and slow τs time constants, respectively τf =

lr + ls Rr + Rs

τs =

(2/3)M (Rr + Rs ) . Rr Rs

(1)

The analytical expression of the current can, therefore, be written as the superposition of two exponential functions, and by means of a least mean square (LMS) algorithm, the time constants τf and τs can be computed. Changing the applied dc voltage Vf modifies the results owing to the influence of saturation. Fig. 3 reports the time constants as functions of the steady-state p.u. current. Repeating the

procedure on the three phases, the curves of Fig. 3, which are fairly superimposed, are obtained. The stator resistance Rs can be computed directly from the steady-state current and voltage. The direct measurement approach involved in the application of a voltage step as presented in [28] avoids the problems linked to the inverter nonlinearity [21].

B. SSFR Test During a standstill frequency response (SSFR) test, one phase of the stator is supplied with a sinusoidal voltage at a variable frequency. Recording the values of the voltage and current during a frequency sweep, the modulus and phase angle


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TABLE I AVERAGE OF M OTOR PARAMETERS O BTAINED U SING D IFFERENT E STIMATION M ETHODS

Fig. 4. Experimental results of the SSFR test on the healthy machine. Measured transfer function Z(s) modulus.

¯ of the operational impedance Z(s) of the machine are obtained as functions of frequency. Under linear assumptions, it is possible, by the frequency response, to determine the number of poles and zeroes and their position (see Fig. 4). From the number of poles and zeroes, a suitable equivalent circuit can be obtained, and from their position, its parameters can be determined. The equivalent circuit of a double-cage or single-cage machine, with or without the iron loss branch, can be selected as a reference. Choosing the single-cage equivalent circuit without iron losses, the machine model has two zeroes zf = 1/2πτf and zs = 1/2πτs and one pole pr = 1/2πτr , where τr = (lr + M )/Rr . The frequency sweep must start at a very low frequency (below 10 Hz) because, for small- to medium-size machines, typical values of the highest frequency zero zf are around 30 Hz, while the low-frequency zero zs and the pole pr are around 1 Hz. A stator resistance measurement, to identify the usual four equivalent circuit parameters, is required as well. The test must be applied in turn to all the phase windings in order to compute the average value of the parameters. C. About the Precision of Parameter Estimation Procedures The recalled procedures show clearly why the exact determination of parameters is a very critical issue. The nonlinearity of the machine influences both the response of the machine to a dc voltage step signal and its transfer function. Table I reports the average of the three phases’ results at a rated current. Standard no-load and locked-rotor test results have been reported for comparison as well, which were performed at a rated frequency and at rated voltage and current, respectively, in order to account for saturation. The magnetizing reactance ωM was computed by a no-load test once half of the global leakage reactance and the dc stator resistance were subtracted. The locked-rotor test overestimates the rotor resistance, due to the high value of slip frequency and the consequent increase of resistance due to the skin effect. In order to obtain a more effective rotor resistance value to compare, a load test has been performed at a rated operating load. This allows to compute the parameter Rr measuring the air-gap power, rotor speed, and input current [29]. An assessment of the parameter estimation uncertainties affecting the different methods is necessary to determine if they

might be able to detect machine faults. The error should be compared with the minimum detectable fault threshold. Implementing the voltage step method on a digitally controlled inverter, the stator resistance can be determined as Rs = Vf /If . Supposing the bus voltage can be measured and assuming the usual A/D resolution of 8 equivalent bits, the approximation on Rs , taking into account compound errors, can be estimated at around 1% in the worst case. Considering stator winding diagnostics performed by comparing the phase parameters, the resistance is affected by the uncertainties arising from the stator winding shape: wound or random wound and concentric (shorter length of the inside turns) or lap wound (ends reshaped in flatter form to make room for the crossover, without affecting the length). Considering a low-voltage motor with a few hundreds of stator turns per phase, a single shorted turn (worst case [11]) leads to a resistance variation of less than 1% and is not detectable. Regarding the computation of the short-circuit impedance and leakage inductances, the parameter estimation is obtained fitting a transient response by an LMS algorithm to calculate the series and the parallel of the parameters or by the pole position in a Bode diagram: It is difficult to obtain a precision better than 10%. The uncertainty prevents associating the result obtained from the different phases to an actual winding fault. Although no specific standards have been established, the generally accepted healthy machine unbalance is up to 10% [3], and this prevents any possibility to detect short circuits involving a few turns. Regarding the magnetizing inductance M , magnetic asymmetries (static or dynamic eccentricity which is undistinguishable at a standstill) can modify the measured value; this issue will be addressed in the next section. The approximation on M , which is greatly affected by saturation, can be estimated around 10%, although, for the small-size machine under test, the approximation is even higher (see Table I). The rotor resistance is the parameter mostly affected by uncertainty, which is dependent on the chosen procedure. Several phenomena such as skin effect and temperature variation, as well as the measuring method, lead to differences of around 20%. This difference can greatly increase in larger size machines with deep rotor slots. Table I shows that the average between the results of the two considered self-commissioning procedures is a good approximation of the best estimation of Rr , which is obtained by the load test. Table II summarizes the relative precision obtained with the different estimation methods. About the possibility to detect rotor failures, the effect of at least one broken bar causes an expected relative variation of rotor parameters of the 1/N minimum [11]. Adopting the same

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TABLE II VALUES OF M OTOR PARAMETERS O BTAINED U SING D IFFERENT E STIMATION M ETHODS W ITH R ELATIVE P RECISION

self-commissioning procedure, the same voltage values, at the same temperature and changing the phase under test (the rotor position is fixed), the location of rotor breakage relative to the supplied stator phase axis influences the measured parameters. The possibility to detect rotor faults is, therefore, strictly linked to the total bar number N . For small machines (N < 20 bars, 1/N > 5%), in the case of the axis of the supplied stator phase aligned with the broken bar, the rotor parameters should result 5% greater than those measured through the other two phases. For different broken bar locations, the parameter increase would be smaller as it spreads over two phases. Recalling that the use of typical 8-equivalent-bit A/D converters leads to a worst case precision of about 1%, the detection of a single broken bar can be extended to medium-size machines with a larger number of rotor bars. From the aforementioned analysis, it appears that the considered self-commissioning procedures are not generally able to detect machine failures. Only the detection of broken rotor bars may be possible in the case of small-size machines. III. S INGLE -P HASE AC T EST ACCORDING TO IEEE S TANDARD 1415-2006 The single-phase rotor test described in IEEE Standard 14152006 [3, Sec. 4.3.23] is a method to evaluate rotor bar damage. The test is relatively simple and requires a single-phase ac voltage of approximately 20% of the rated value. The rotor is turned slowly by hand, and the stator current is observed. A significant change in the ac current or in the impedance is an indication of either broken rotor bars or broken connections between the bars and the end ring. Then, the phase balance ac frequency test compares the results obtained from the motor phases: The variation of parameter averages is used to assess the stator winding conditions. The test result is a pass/fail response with reference to a “significant change” of 10% or more. This change seems very high, and some authors have brought forth advances, offering a more complete analysis of motor health [30], [31]. Six “fault zones” have been proposed using a combination of online and offline tests. Regarding the “rotor fault zone,” the inductance is measured (being the resistance already measured by a dc test), and the inductance values are plotted with respect to rotor position; then, the test is repeated supplying the other phases. According to the authors, the inductance waveforms, typically displayed as sinusoidal, provide a valuable tool to determine the overall health of both the rotor and stator. The reactance amplitude variation leads to classify the motor as a “low-influence” rotor or “with-influence” rotor. Changing the

phases, the waveform results shifted in phase: A change in the mean amplitude of the different phases’ reactance waveforms indicates a stator winding asymmetry. Some shapes of inductance are reported, and the authors conclude that a healthy rotor should present a variation of inductance of less than 7% for wound motors and less that 12% for random wound motors. An “air-gap fault zone” is also proposed using standstill tests. Eccentricity (static and dynamic eccentricities are undistinguishable at a standstill) causes a nearly sinusoidal variation of the inductance, again with differences among phases if the supplied phase is changed. No machine model is introduced in the papers, and the periodicity of the inductance waveform, which is useful as a signature of the different affecting phenomena, is not addressed. The results of the single-phase test are deeply investigated in [32] utilizing the rms stator current as a function of rotor position. Fig. 5 reports the experiments made on the tested machine with the healthy rotor (a) and with two broken bars (b). In the former, the rotor slotting modulation of the rms stator current versus rotor position, obtained with the resolution of one mechanical degree, is clearly visible. In the latter, its superposition with the broken bar modulation is visible, while no sign of magnetic asymmetry appears. The rated frequency is applied, while the voltage amplitude is reduced in the same range used for the voltage step test. The experiments of Fig. 5 refer to a voltage that causes an rms current of 0.8 times the rated one. The technique of sinusoidal supply with manual rotor rotation presents a good signal-to-noise ratio since a power inverter is not required. Therefore, the results are so clear that the effects of phenomena that are different from rotor faults, such as permeance variations by rotor slotting or eccentricity, may be recognized and studied through dedicated machine models. Each phenomenon can be individually considered, and a suitable monoharmonic model can be developed, obtaining simple relationships linking the cause and effect [33]. Let us start from the effect of rotor asymmetry. In stationary conditions, the stator can be modeled as a single-phase circuit supplied by a voltage with amplitude V and pulsation ω, producing a magnetic flux with the axis fixed in space and the amplitude sinusoidally modulated. The rotor can be modeled by two circuits in quadrature, named α and β, with axis β aligned with the position of the rotor fault. In the stator reference frame, the angular displacement of the rotor α axis is the generic rotor location δ. Fig. 6(a) corresponds to a generic displacement δ, and Fig. 6(b) corresponds to δ = 0 (therefore, to the maximum amplitude of the stator current phasor), while Fig. 6(c) corresponds to δ = π/2, i.e., to the minimum amplitude. The electrical displacement is P δ in the case of a machine with P pole pairs. Naming Z rα and Z rβ the healthy and faulty rotor winding impedances and introducing Z r = (Z rα + Z rβ )/2 and ΔZr = (Z rβ − Z rα )/2, a phasor model can be written V 0 0

jωM + Zs = jωM cos P δ jωM sin P δ

jωM cos P δ jωM + Z rα 0

jωM sin P δ I s I rα . 0 jωM + Z rβ I rβ (2)


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Fig. 5. Experimental results obtained through the single-phase supply test with manual rotation: RMS stator current versus mechanical rotation angle. (a) Healthy rotor. (b) Two broken bars.

first harmonic is [32] Zr n ΔIs . 2 Is Zs + Zr N

Fig. 6. Rotor fault model with single-phase stator and asymmetric two-phase α-β rotor (axis β aligned with the rotor fault). Phase configurations for (a) a generic stator–rotor angular displacement δ, (b) δ = 0, and (c) δ = π/2.

The relationship between the stator voltage and current can be obtained from (2), adopting some simplifications. Being ωM |Z rα | and ωM |Z rβ | and supposing |Z rβ − Z rα | |Z r |, we obtain [16] ΔZ r V Is cos 2P δ . 1+ (Z s + Z r ) Zs + Zr

(3)

The spatial FFT of the current data can be used in order to study the component at spatial periodicity 2P . Alternatively, disregarding the effect of higher order harmonics, the amplitude of the current ripple can be obtained as the difference between the maximum (at 2P δ = 2kπ, i.e., cos(2P δ) = 1) and minimum (at 2P δ = (2k + 1)π, i.e., cos(2P δ) = −1) values of the current phasor. Using (3), we can calculate the ratio between the current ripple and its mean value [16] ΔIs 1 ΔZr . Z s + Z r Is

(4)

n contiguous broken bars cause an additional impedance ΔZr = 2(n/N )Zr ; therefore, the expected amplitude of the

(5)

The model accounts for the first spatial harmonic only; obviously, further harmonics are present, and this leads to the asymmetry of the curve of Fig. 5(b). From Fig. 5(b), the difference between the maximum and minimum values of the current envelope referred to the average is ΔIs /Is = (2.85 − 2.45)/(2.85 + 2.45) = 0.075. The impedance ratio |Z r /(Z s + Z r )| is not easily determined. The difficulties in splitting the total reactance between the stator and rotor are added to the considerations reported in Section II. The impedance ratio can be approximated by 0.5, and 2|Z r /(Z s + Z r )| can be approximated by one. The rotor with n = 2 and N = 28 has n/N = 0.071, and the values are therefore consistent with (5). This allows quantifying the broken bar number as Z s + Z r ΔIs . (6) nN 2Z r Is Changing the supplied phase, similar shapes shifted by a 2π/(3 · 2P ) electrical angle are obtained. These further two measurements provide indications about the stator winding asymmetry: The single-phase model (2) can still be used assuming Z rα = Z rβ . For each phase, there are different values of Z s and M (the former is dominant in a short-circuit test). As expected, no difference among the phases has been found because the machine has lap windings that ensure fairly equal phase impedances. The results obtained by a pseudo-single-phase test in which the field position is moved along the air gap instead of moving the rotor itself are analyzed in [17] and [18]. The equivalent circuit adopted to justify these results is obtained representing the effect of the forward and backward magnetic fields. The circuit is then simplified for the standstill conditions, obtaining the usual three-phase equivalent circuit. The use of a single circuit in case of rotor asymmetry leads to parameter variations as the field vector sweeps along the air gap. The curves of motor parameters, such as equivalent resistance and reactance, and of variables, such as current modulus and active and reactive power versus the relative field to rotor angle, are reported. The

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ripple can be used. The average and the amplitude of the first spatial harmonic are computed through the minima and maxima of the current amplitude, and their ratio is 1 Z r ΔMslot ΔIsslot . (9) Isslot 2 jωM M Fig. 7. Rotor slotting effect: Magnetic coupling variation versus rotor position.

peak value of the fundamental component of these parameters or variables, extracted from the Fourier transform, is proposed as an index to estimate the fault severity. Nevertheless, no analytical relationship between the asymmetry degree and its effect has been developed. To explore the full information obtained by the single-phase test shown in Fig. 5, further machine models can be developed. A model suited to account for rotor slotting and eccentricity starts from the consideration that any permeance variation along the air gap can be expressed as Λk cos(khδ + αk ), where Λk is the amplitude of the kth harmonic of the permeability, αk is its displacement from the stator winding axis, and h is the pole pair number of the considered type of asymmetry (N for the rotor slotting, one for the eccentricity). Two new magnetic field components arise (1/2)Bo Λk cos [(ωt − (P ± kh)δ ± αk ] where Bo is the fundamental component of the flux density. The equivalent pole number P ± kh is different from the stator winding pole number; therefore, this mismatch cancels out these components unless the pitch factor ξ = sin(((P ± kh)/P )(π/2)) is different from zero [34], [35]. This is true only if the ratio (P ± kh)/P is odd. As far as the first harmonic of rotor slotting is concerned, being N = 28 and P = 2 for the tested machine, (P ± N )/P is odd, and its effect appears. In the equivalent model, the magnetizing reactance is modeled by a component ΔMslot varying with the angular position with the period 2π/N , as shown in Fig. 7. The amplitude depends on slot-opening/air gap depth ratio and on the distribution factor. Taking into account this magnetizing inductance variation, a system similar to (2) can be written for the healthy rotor machine, obtaining (7), shown at the bottom of the page. The stator current assumes the form Zr V (1 + ΔMslot % sin N δ) . (8) Is 1+ jωM Zs + Zr Relationship (8) can be used to quantify the amplitude of the magnetizing reactance variation due to rotor slotting. With analogy to the procedure used for the extraction of the first spatial harmonic followed in case of rotor fault (3), the current

V 0 0

jω(M − ΔMslot sin N δ) + Z s = jω(M − ΔMslot sin N δ) cos P δ jω(M − ΔMslot sin N δ) sin P δ

From Fig. 5(a) the difference between the maximum and minimum values of the current envelope referred to the average is ΔIsslot /Isslot = (2.86 − 2.74)/(2.86 + 2.74) = 0.021. The impedance ratio |Z r /(jωM )|, using the parameter values reported in Table I, results to about 0.08; using (9), the percentage value of the magnetizing reactance variation due to rotor slotting results to jωM ΔIsslot 2 ΔMslot = 2 ¯ 0.021 0.53. (10) M I 0.08 Zr sslot This value corresponds to a ratio of the slot-to-air-gap width of 0.65 [29], which is in agreement with the tested machine design. Therefore, (10) can be used to obtain information about the rotor slotting effect that is useful for sensorless control [35]. Concerning the eccentricity, the first harmonic of the air-gap permeance gives no contribution, being (P ± 1)/P fractional. The lower harmonic whose contribution differs from zero has order 2P [36], [37]. A relationship similar to (8) holds V Zr ΔMecc sin kδ . (11) Is 1+ 1+ Zs + Zr jωM M In this case, the magnetizing reactance component ΔMecc , due only to the upper harmonics of permeance, is very low; therefore, it is not possible to detect it in the experiments. The current shape of the healthy machine [see Fig. 5(a)] shows only a very small modulation with period 2π/2P , due to the intrinsic electric rotor asymmetry, superimposed to the effect of rotor slotting which has period 2π/N . IV. Q UASI -S TATIONARY F IELD M OVING A LONG THE A IR G AP The possibility to automatically realize a pseudo-singlephase test moving the field position along the air gap instead of the rotor itself, keeping the motor at a standstill, is very attractive. Many excitation signals are possibly exploiting the flexibility of a voltage inverter supply [12]–[18]. Keeping the motor at a standstill during the procedure can be achieved in several ways, including the generation of null or sufficiently small mean torque in order to avoid overcoming the starting friction. In this way, a test can be implemented to detect the rotor asymmetry with the remarkable difference, with respect to the single-phase test, in which, in this case, all motor

jω(M − ΔMslot sin N δ) cos P δ jω(M − ΔMslot sin N δ) + Z r 0

jω(M − ΔMslot sin N δ) sin P δ I s I rα 0 jω(M − ΔMslot sin N δ) + Z r I rβ

(7)


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v can be decomposed in two counterrotating vectors vp =

Fig. 8. Pulsating voltage vector v = (Vm cos(ωt))ejθ applied to the machine under test. (a)–(d) θ = 0◦ . (e)–(h) θ = 10◦ . (a) and (e) ωt = 0. (b) and (f) ωt = π/4. (c) and (g) ωt = 3/4π. (d) and (h) ωt = π.

phases are simultaneously involved. It is not possible, therefore, to perform separate tests on the different stator phases. A pulsating field with its axis moved through sequential stationary conditions was adopted for the experimental tests. In order to generate a null mean torque, a field pulsating between a prefixed direction and the opposite one was synthesized (see Fig. 8). Sinusoidally pulsating voltage space vector v (t) is generated passing through the sequence of positions of Fig 4(a)–(d) and back v (t) = V m cos(ωt) = (Vm cos(ωt)) ejθ

(12)

where phasor V¯m = Vm ejθ is oriented along the axis of the pulsating field v and θ is the angle of V¯m relative to a fixed reference frame.

1 V m ejωt , 2

vn =

1 V m e−jωt . 2

(13)

This ensures, theoretically, a zero torque. In an actual motor, unavoidable manufacturing asymmetries cause an uneven machine response to the two counterrotating fields so that a small amount of torque (1%–2% of the rated one) can be expected. Being the torque proportional to the square of the applied voltage, the use of a reduced voltage decreases the generated torque to less than the friction breakout value, and the rotor does not move. Nevertheless, the operating voltage can be kept an order of magnitude higher than in the case of the symmetrical three-phase supply (see Section I), obtaining a higher signal-tonoise ratio. The pulsating space vector v is applied with a fixed angle θ for a time interval long enough for the electrical transient to subside so that the machine impedance along the α axis can be estimated through the acquisition of the current space vector. For small-size motors such as the one used for the experimental tests, the electrical time constants are in the range of tens of milliseconds, so 200 ms is used. Subsequently, the axis of v is rotated by a fixed quantity, which is dependent on the desired precision (one electrical degree was used in this case), and the impedance measurement is repeated on the newly identified axis [see Fig. 8(e)–(h)]; this procedure is repeated until the pulsating vector sweeps a full 360◦ electrical period. As the pulsating vector sweeps along the air gap, the current space vector, and thus the estimated impedance, varies with the rotor circuit angular position relative to the supplied voltage vector. The full procedure consists of a sequence of stationary conditions; turning off the pulsating vector for an equal time interval (200 ms) between the increments of the sweep angle θ ensures that no torque is generated [16]. Since the test voltages are produced in a feedforward manner, the injected space vectors are affected by inverter nonidealities such as dead times; this does not pose a problem because the diagnostic procedure is based on the resulting current ratio. A similar proposal was presented in [17] and [18] in which square wave voltage pulses were used instead of sinusoidal waveforms to excite the rotor at multiple circumferential locations, causing the presence of the entire chain of odd harmonics. Moreover, the spatial resolution appearing from the presented results is of 5 electrical degrees, and this introduces an undersampling of the shapes of variables as functions of the pulsating field position. The experimental setup is depicted in Fig. 9 and is built around a desktop computer with a dSPACE rapid prototyping system installed. The dSPACE board generates the pulsewidth modulation signals required to implement the proposed technique through a voltage source inverter which, in turn, drives the motor under test. The dSPACE system is used to acquire and record the phase currents as well. Applying the proposed technique to the test machine, whose specifications are reported in Section II, the results shown in Fig. 10(a) have been obtained with the healthy rotor, while Fig. 10(b) refers to the rotor with two broken bars. In order

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Fig. 9. Block diagram of the experimental setup.

Fig. 11. Comparison of experimental results obtained with a quasi-stationary field moving along the air gap. Shape of the stator current space vector amplitude (rms value) versus supply angle δ for (dark trace) healthy rotor and (light trace) two broken bars.

Fig. 10. Experimental results obtained with a quasi-stationary field moving along the air gap. Shape of the stator current space vector amplitude (rms value) versus supply angle δ for (a) healthy rotor and (b) two broken bars.

to retain the validity of the usual assumptions about the magnetizing reactance value with respect to the other machine parameters and to compare the results with those obtained by the single-phase test, the machine was supplied, through the digital inverter, with voltages that realize a stationary magnetic field pulsating at ω = 314 rad/s. The peak amplitude of the voltage space vector was chosen in order to obtain the same current (0.8 rated current). Supplying the motor through an inverter generates a relatively high noise level, and signal filtering is required. As a consequence, the rotor slotting is buried in noise, and Fig. 10(a) shows only a small amplitude modulation of the current as an effect of intrinsic asymmetry. The two-broken-bar machine exhibits a broad modulation of the stator current as the test field scans the air gap [see Fig. 10(b)]. The modulation caused by the fault is a periodic function whose period is 1/2 of an electrical revolution. Equations (5) and (6) can be applied both to the healthy and to the faulty machine. For the healthy machine, from Fig. 10(a) ΔIs /Is = (2.81 − 2.77)/(2.81 + 2.77) = 0.0072 and from (6), n = 0.2. This result can be interpreted as an intrinsic rotor asymmetry equivalent to 20% of a broken bar. For the faulty rotor, from Fig. 10(b) ΔIs /Is = (2.9 − 2.5)/(2.9 + 2.5) = 0.074 i.e., n = 2.07, which is in good agreement with the two broken bars and with the results obtained in Section III. Comparing the healthy and faulty machine curves, a phase displacement can be observed (see Fig. 11), depending both on

the random standstill rotor position and on the location of the rotor asymmetry relative to the fixed angular reference. In the amplitude of the faulty rotor machine, a low component with electrical period 2π appears as well, probably due to the unavoidable different mechanical conditions obtained by disassembling and reassembling the machine to change the rotors. As far as rotor conditions are concerned, Fig. 10(b) gives the same results as Fig. 5(b). This confirms the possibility to add the proposed technique as a fault diagnosis stage during selfcommissioning procedures implemented in a digital inverter, obtaining the same information given by the single-phase test with manual rotation. Obviously, in this case, the signal injection concerns all the three phases, and stator phase asymmetries cannot be detected. The presence of interbar currents prevents a correct diagnostic of rotor conditions. Similarly to other MCSA-based techniques, by the proposed procedure, it is not possible to determine the presence of interbar currents; only differential diagnostic procedures can reliably detect the presence of such currents [38]. V. C ONCLUSION The problem of detecting abnormal electric and magnetic conditions of induction machines through standstill tests during self-commissioning procedures has been considered. To this aim, the precision of the usual self-commissioning procedures has been investigated to estimate the parameter identification uncertainties in which the aforementioned methods incur. The minimum visible fault threshold seems too small to recognize incipient faults, and a further procedure based on injected signals has been proposed. In particular, exploiting a digitally controlled inverter, it is possible to perform automatic tests which give information similar to the “single-phase test” of the IEEE Standard 1416-2006. A particular stationary magnetic field has been realized whose axis moves along the air gap changing its linkage with the rotor circuits. By this signal, it is possible not only to detect rotor nonidealities but also to state their severity as well, as demonstrated by the experimental results.


This confirms the possibility to add a specific signal injection to the self-commissioning procedures implemented in a digital inverter obtaining, as far as rotor diagnosis is concerned, the same information obtained by the single-phase test. Obviously, with this procedure, the injection concerns all the three phases simultaneously, and no information about the stator asymmetry can be obtained. R EFERENCES [1] J. Holtz, “Sensorless control of induction motor drives,” Proc. IEEE, vol. 90, no. 8, pp. 1359–1394, Aug. 2002. [2] T. M. Wolbank, M. A. Vogelsberger, R. Stumberger, S. Mohagheghi, T. G. Habetler, and R. G. Harley, “Autonomous self-commissioning method for speed-sensorless-controlled induction machines,” IEEE Trans. Ind. Appl., vol. 46, no. 3, pp. 946–954, May/Jun. 2010. [3] Guide to Induction Machinery Maintenance Testing and Failure Analysis, IEEE Std. 1415-2006, 2006. [4] M. El Hachemi Benbouzid, “A review of induction motors signature analysis as a medium for faults detection,” IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 984–993, Oct. 2000. [5] 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. [6] A. Bellini, A. Yazidi, F. Filippetti, C. Rossi, and G. Capolino, “High frequency resolution techniques for rotor faults detection of induction machines,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4200–4209, Dec. 2008. [7] S. Bachir, S. Tnani, J. Trigeassou, and G. Champenois, “Diagnosis by parameter estimation of stator, rotor faults occurring in induction machines,” IEEE Trans. Ind. Electron., vol. 53, no. 3, pp. 963–973, Jun. 2006. [8] C. H. De Angelo, G. R. Bossio, S. J. Giaccone, M. I. Valla, J. A. Solsona, and G. O. García, “Online model-based stator-fault detection and identification in induction motors,” IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4671–4680, Nov. 2009. [9] A. Kral, F. Pirker, and G. Pascoli, “Detection of rotor faults in squirrelcage induction machines at standstill for batch tests by means of the Vienna induction machines monitoring method,” IEEE Trans. Ind. Appl., vol. 38, no. 3, pp. 618–624, May/Jun. 2002. [10] B. Akin, S. B. Ozturk, H. A. Toliyat, and M. Rayner, “DSP-based sensorless electric motor fault-diagnosis tools for electric and hybrid electric vehicle powertrain applications,” IEEE Trans. Veh. Technol., vol. 58, no. 5, pp. 2150–2159, Jun. 2009. [11] 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. [12] P. J. Chrzan, G. Champenois, P. Coirault, and J. C. Trigeassou, “Diagnosis of induction machine in standstill conditions,” in Proc. IEEE SDEMPED, 1999, pp. 497–501. [13] A. Mpanda Mabwe Badileshi, D. Cristian, G. A. Capolino, and H. Henao, “Detection of induction machines anomalies using stand-still tests,” in Conf. Rec. IEEE IAS Annu. Meeting, Salt Lake City, UT, Oct. 2003, pp. 1855–1860. [14] A. Mpanda Mabwe Badileshi, D. Cristian, and G. A. Capolino, “Broadband excitation signal techniques for electric machines diagnostics,” in Proc. IEEE SDEMPED, Atlanta, GA, Aug. 2003, pp. 236–241. [15] D. Cristian, A. Mpanda Mabwe Badileshi, H. Henao, and G. A. Capolino, “Detection of induction machines rotor faults at standstill using signal injection,” IEEE Trans. Ind. Appl., vol. 40, no. 6, pp. 1550–1559, Nov./Dec. 2004. [16] C. Concari, G. Franceschini, and C. Tassoni, “Self-commissioning procedures to detect parameters in healthy and faulty induction drives,” in Proc. IEEE SDEMPED, Cargese, France, Aug./Sep. 2009, pp. 1–6. [17] S. B. Lee, J. Yang, J. Hong, B. Kim, J. Yoo, K. Lee, J. Yun, M. Kim, K. Lee, E. J. Wiedenbrug, and S. Nandi, “A new strategy for condition monitoring of adjustable speed induction machines drive system,” in Proc. IEEE SDEMPED, Cargese, France, Aug. 2009, pp. 1–6. [18] B. Kim, K. Lee, J. Yang, S. B. Lee, E. J. Wiedenbrug, and M. R. Shah, “Automated detection of rotor faults for inverter-fed induction machines under standstill conditions,” in Proc. IEEE ECCE, Sep. 2009, pp. 2277–2284. [19] W. Leonard, Control of Electric Drives. Berlin, Germany: SpringerVerlag, 1996.

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[20] G. L. Cascella, N. Salvatore, M. Samner, and L. Salvatore, “On-line simplex-genetic algorithm for self-commissioning of electric drives,” in Proc. EPE, Dresden, Germany, 2005, pp. 1–10. [21] J. Holtz and J. Quan, “Sensorless vector control of induction motors at very low speed using a nonlinear inverter model and parameter identification,” IEEE Trans. Ind. Appl., vol. 38, no. 4, pp. 1087–1095, Jul./Aug. 2002. [22] G. Pellegrino, P. Guglielmi, E. Armando, and R. I. Bojoi, “Selfcommissioning algorithm for inverter nonlinearity compensation in sensorless induction motor drives,” IEEE Trans. Ind. Appl., vol. 46, no. 4, pp. 1416–1424, Jul./Aug. 2010. [23] T. M. Volbank, M. A. Volgelsberger, R. Stumberger, S. Mohagheghi, T. G. Habetler, and R. G. Harley, “Autonomous self commissioning method for speed sensorless controlled induction machines,” in Conf. Rec. IEEE IAS Annu. Meeting, Sep. 2007, pp. 1179–1185. [24] M. O. Sonnaillon, G. Bisheimer, C. De Angelo, and G. O. Garcia, “Automatic induction machine parameters measurement using standstill frequency-domain test,” IET Elect. Power Appl., vol. 1, no. 5, pp. 833– 838, Sep. 2007. [25] M. Globevnik, “Induction motor parameters measurement at stand still,” in Proc. IEEE IECON, Aachen, Germany, Aug./Sep. 1998, pp. 280–285. [26] J. Godbersen, P. Thogersen, and M. Tonnes, “A practical identification scheme for induction motors at standstill using only a VS inverter as the actuator,” in Proc. EPE, 1997, pp. 3370–3374. [27] C. B. Jacobina, J. E. C. Filho, and A. M. N. Lima, “Estimating the parameters of induction machines at standstill,” IEEE Trans. Energy Convers., vol. 17, no. 1, pp. 85–89, Mar. 2002. [28] S. Bolognani, L. Peretti, and M. Zigliotto, “Commissioning of electromechanical conversion models for high dynamic PMSM drives,” IEEE Trans. Ind. Electron., vol. 57, no. 3, pp. 986–993, Mar. 2010. [29] P. L. Alger, The Nature of Poliphase Induction Machines. New York: Wiley, 1951. [30] D. L. McKinnon and N. Bethe, “Fault zone analysis: Identifying motor defects using the rotor fault zone,” in Proc. Elect. Insul. Conf., Oct. 2005, pp. 400–407. [31] D. L. McKinnon, “Using a six fault zone approach for predictive maintenance on motors,” in Proc. Elect. Insul. Conf., Oct. 2007, pp. 253–264. [32] A. Bellini, G. Franceschini, N. Petrolini, C. Tassoni, and F. Filippetti, “Online diagnosis of induction drives rotor by signal injection techniques: Faults location and severity classification,” in Proc. IEEE SDEMPED, 2001, pp. 435–441. [33] A. Bellini, F. Filippetti, G. Franceschini, C. Tassoni, and T. J. Sobczyk, “Unique classification of single frequency induction motors features introduced by different anomalies,” in Proc. IEEE SDEMPED, Grado, Italy, Sep. 2001, pp. 435–440. [34] A. Ferrah, P. J. Hogben-Laing, K. J. Bradley, G. M. Asher, and M. S. Wooldson, “The effect of rotor design on sensorless speed estimation using rotor slot harmonics identified by adaptive digital filtering using the maximum likelihood approach,” in Conf. Rec. IEEE IAS Annu. Meeting, New Orleans, LA, Oct. 1997, pp. 128–135. [35] A. Bellini, F. Filippetti, G. Franceschini, N. Petrolini, and C. Tassoni, “Sensorless speed detection in induction machines,” in Proc. ICEM, 2002, pp. 1–6. [36] T. J. Sobczyk, P. Vas, and C. Tassoni, “A comparative study of effects due to eccentricity and external stator and rotor asymmetries by monoharmonic model,” in Proc. ICEM, Hut, Finland, Sep. 2000, pp. 946–950. [37] N. Arthur and J. Penman, “Induction machines conditioning monitoring with high order spectra,” IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 1031–1041, Oct. 2000. [38] C. Concari, G. Franceschini, and C. Tassoni, “Differential diagnosis based on multivariable monitoring to assess induction machine rotor conditions,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4156–4166, Dec. 2008.

Carlo Concari (S’98–M’06) was born in San Secondo Parmense, Italy, in 1976. He received the M.S. degree in electronics engineering and the Ph.D. degree in information technology from the University of Parma, Parma, Italy, in 2002 and 2006, respectively. Since 2006, he has been an Assistant Professor with the Department of Information Engineering, University of Parma. His research activity is mainly focused on power electronics, digital drive control, and electric machine diagnostics.

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Giovanni Franceschini was born in Reggio Emilia, Italy, in 1960. He received the M.S. degree in electronic engineering from the University of Bologna, Bologna, Italy. Since 1990, he has been with the Department of Information Engineering, University of Parma, Parma, Italy, where he was an Assistant Professor and is currently a Full Professor of electric machines and drives. His research interests include highperformance electric drives and diagnostic techniques for industrial electric systems. He is the author or coauthor of more than 120 technical papers and is the holder of three industrial patents.

Carla Tassoni (SM’97) was born in Bologna, Italy, in 1942. She received the M.S. degree in electrical engineering from the University of Bologna, Bologna, in 1966. She was with the University of Bologna first as an Assistant Professor and, then, an Associate Professor of electrical machines in the Department of Electric Engineering. She is currently a Full Professor of electrical engineering with the University of Parma, Parma, Italy. She is the author or coauthor of more than 150 scientific papers. Her main research interests include the simulation and modeling of electric systems and the application of diagnostic techniques.