Real-Time Detection of Interturn Faults in PM Drives ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 6, NOVEMBER/DECEMBER 2011

Real-Time Detection of Interturn Faults in PM Drives Using Back-EMF Estimation and Residual Analysis Nicolas Leboeuf, Thierry Boileau, Babak Nahid-Mobarakeh, Member, IEEE, Guy Clerc, Senior Member, IEEE, and Farid Meibody-Tabar

Abstract—Interturn stator winding fault is one of the most frequent faults in permanent-magnet synchronous machines (PMSMs). In this paper, we present a new technique for online detection of this fault in PMSMs. It is based on a residual analysis improved by taking into account back-electromotive force waveform estimation, inverter model, and unbalanced inductance matrix. Then, a current residual monitoring block permits to detect the fault and its severity. The simulation and experimental results validate the proposed method and its efficiency. Index Terms—Health monitoring, interturn fault, permanentmagnet synchronous machine (PMSM), real-time fault detection.

N OMENCLATURE i v e Ω Γ Rs Ls M Ψf p J f Rf if k F

Current. Voltage. Back EMF. Rotor angular speed. Torque. Stator resistance. Stator inductance. Mutual inductance. Magnet flux linkage through the stator windings. Number of pole pairs. Inertia coefficient. Friction coefficient. Faulty insulation resistance. Fault current through Rf . Ratio between faulty turns and healthy turns. fault indicator.

Subscripts d, q Synchronous frame components.

Manuscript received January 5, 2011; revised June 12, 2011; accepted June 16, 2011. Date of publication September 22, 2011; date of current version November 18, 2011. Paper 2010-IACC-486.R1, presented at the 2010 Industry Applications Society Annual Meeting, Houston, TX, October 3–7, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Industrial Automation and Control Committee of the IEEE Industry Applications Society. The authors are with the Groupe de Recherche en Electrotechnique et Electronique de Nancy (GREEN), Institut National Polytechnique de Lorraine (INPL), Nancy University, 54510 Nancy, France, and also with the AMPERE, Université Claude Bernard, 69622 Lyon, France (e-mail: nicolas.leboeuf@ ensem.inpl-nancy.fr; [email protected]; babak.nahid@ ieee.org; [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/TIA.2011.2168929

I. I NTRODUCTION

P

ERMANENT-MAGNET (PM) synchronous machines (PMSMs) are increasingly used in transport applications such as aircrafts because of their good torque/mass ratio. Particularly in aerospace industry, they are preferred to hydraulic actuators for overcoming maintenance problems related to these latter. Within the framework of the “more electric aircraft,” PM drives are considered as a more reliable device, thanks to online diagnostic and fault-tolerant control techniques. Indeed, for such an application, PM drives should involve fault-tolerant control techniques [1], reconfigurable systems [2], and healthmonitoring methods to avoid severe failures. Several methods have been already developed for the fault detection in induction motors [3], [4] and are often based on current and voltage monitoring, spectral, or temporal analysis [5]–[10]. However, these approaches are not easily transposable to PM machines. There are also other methods which use flux sensors around the machine [11], [12], parameter identification methods [13]–[16], artificial intelligence, and neural networks [17]–[20]. To classify faults in electrical machines, two main categories can be distinguished: mechanical and electrical faults. In this paper, we focus on interturn fault in the stator winding of a PMSM. This type of fault is often the first symptom before a more important fault such as interphase short-circuit fault, phase-ground short-circuit fault [6], [7] or a demagnetization problem [21] appears. Here, the objective is to detect this fault in real time as soon as possible. The intended application is an electromechanical aileron actuator. This real-time fault detection has to detect the fault before it damages definitely the actuator. Also, no additional sensors are permitted due to certification problems. The only admitted measurements are those used for the control: stator current sensors, rotor position measurement, and dc-link voltage sensor. It is also desirable that the fault detection requires the modification of neither the current references nor the control output voltages. In summary, we have the following requirements: 1) real-time fault detection; 2) no additional sensor; 3) no signal injection. Moreover, we are looking for an indicator allowing determining the fault severity. This information may be useful for defining the corresponding degraded mode. It is of course desirable to have an indicator insensitive to the inverter irregularities and to the mechanical load variations.

0093-9994/$26.00 © 2011 IEEE

LEBOEUF et al.: REAL-TIME DETECTION OF INTERTURN FAULTS IN PM DRIVES

The proposed method in this paper allows a real-time implementation, which can be integrated in the control system of the PMSM and may be associated to a higher level online fault detection system. The PMSM considered in this study are supplied by pulse-width modulation (PWM)-controlled voltage source inverters (VSI). To better understand the behavior of the drive under fault conditions, a model of a faulty PMSM is described briefly in the next section [6]–[8]. This model takes into account an interturn fault represented by a faulty insulation resistance (Rf ). There are many studies based on this type of model, which depend on various hypotheses on the machine design such as winding distribution or saliency [22], [23]. However, it allows us simulating the actuator under a stator fault, to predict the performances of the whole drive regarding the fault and to test fault detection methods. The method proposed in this paper consists in obtaining the machine current with a healthy model and comparing it with the real current of the machine. The model has to be accurate because the difference between the two currents should only reflect the presence of an interturn short-circuit fault in faulty cases. In fact, if the model does not take into account uncertainties like real back EMF or losses in the inverter, the indicator level may exceed the alert threshold even for the healthy machine (Rf 100 kΩ). As the machine is current controlled in our application, the method exploits the unbalanced voltages and can detect a fault if the model is adequate. However, this method is not appropriate for detecting emerging faults (Rf > 1 kΩ) [24], [25] because of the original unbalance effects of the healthy machines. In this case, the interturn fault does not significantly affect the control signals and the measurements, and so, it cannot be clearly detected under the above requirements. Actually, the fault has little impact on the behavior of the system in this case so that the alert threshold is not exceeded. Whatever the fault nature is, a safe operating requires switching to a proper degraded mode once the fault is detected [26]–[28]. This is not the subject of this paper. The paper is organized into five sections. The model of the PMSM is detailed in Section II. In Section III, the detection technique is described. Simulation results and parametric studies are also presented and discussed in Section IV. Experimental tests and conclusions are given in Section V.

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Fig. 1. Electrical model of a faulty machine.

II. PMSM M ODEL U NDER FAULT C ONDITIONS After understanding the physical effects of an interturn shortcircuit fault in a PMSM, we should develop an electrical model of the faulty machine. This has already been validated using finite-element analysis and considering some hypothesis in [22]. We consider a one-slot per pole and per phase PMSM with a Y-connected stator. The saturation effects are neglected and the rotor is considered as nonsalient. As it is shown in Fig. 1, an additional resistance Rf is placed in phase a and divides it into two parts a1 (healthy part) and a2 (faulty part). Without loss of the generality, the number of pole pairs is fixed to 1 to use the one pole pair equivalent machine. The fault current through Rf is called if . Consider the following vectors: ⎧ ⎨ iabcf = [ia ib ic if ]T v = [va vb vc vf ]T ⎩ abcf eabcf = [ea eb ec ef ]T where iabcf , vabcf , and eabcf are, respectively, the phase current, the phase voltage, and the back EMF in the three phases and in the faulty part [8]. It is obvious that the faulty part supplying voltage is zero (vf = 0). Moreover, we have the resistance and inductance matrices shown in the equation at the bottom of page. Rj (j = a1, a2, b, c) is the resistance of the winding j, Lj (j = a1, a2, b, c) is the self-inductance of the winding j, Mjk (j and

⎧ ⎤ ⎡ Ra1 + Ra2 0 0 −Ra2 ⎪ ⎪ ⎪ ⎪ ⎥ ⎢ ⎪ ⎪ 0 Rb 0 0 ⎥ ⎢ ⎪ ⎪ ⎥ ⎢ ⎪ [Rabcf ] = ⎢ ⎪ ⎥ ⎪ ⎪ 0 0 R 0 ⎦ ⎣ c ⎪ ⎪ ⎪ ⎪ ⎨ −Ra2 0 0 Ra2 + Rf ⎡ ⎪ La1 + La2 + 2.Ma1a2 Ma1b + Ma2b ⎪ ⎪ ⎪ ⎪ ⎢ ⎪ ⎪ Ma1b + Ma2b Lb ⎢ ⎪ ⎪ ⎪ ⎪ [Labcf ] = ⎢ ⎢ ⎪ ⎪ Ma1c + Ma2c Mbc ⎣ ⎪ ⎪ ⎪ ⎩ −(La2 + Ma1a2 −Ma2b

Ma1c + Ma2c

−(La2 + Ma1a2 )

Mbc

−Ma2b

Lc

−Ma2c

−Ma2c

La2

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

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TABLE I E XPERIMENTAL PARAMETERS

k = a1, a2, b, c) is the mutual inductance between windings j and k. If the healthy machine is balanced, we have Ra1 + Ra2 = Rb = Rc = Rs

(1)

La1 + La2 + 2.Ma1a2 = Lb = Lc Ma1b + Ma2b = Ma1c + Ma2c = Mbc ea = ea1 + ea2 = eb = ec ef = −ea2 .

(2) (3) (4a) (4b)

Knowing that the machine is star connected, the following equation holds: ia + ib + ic = 0.

(5)

Then, taking into account (2) and (3), the cyclical inductance is given as follow: Lcy = La1 + La2 + 2.Ma1a2 − (Ma1b + Ma2b ) = La − Mab = Lb − Mbc = Lc − Mac .

(6)

Moreover, from (5), the inductance matrix can be simplified as shown in (7) at the bottom of the page, where M3×3 is a 3 × 3 matrix whose elements are all equal to Mbc . Now, we can deduce the faulty model

diabcf + eabcf . vabcf = [Rabcf ] · iabcf + Labcf · dt

(8)

This model can be rewritten as follows for separating its healthy and faulty parts: ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ va ia ea ia d ⎣ vb ⎦ = Rs · ⎣ ib ⎦ + Lcy · ⎣ ib ⎦ + ⎣ eb ⎦ dt vc ic ic ec healthy components

⎡ ⎤ α ⎣β⎦ γ

+

(9)

This shows that the fault creates residual voltages in the (abc) frame. Assuming that Ma2b ≈ Ma2c (saturation effects are neglected, one slot per pole and per phase machine), the residual voltage is quiet identical to the phases b and c whereas it is different on the faulty phase. This property can be exploited for locating the fault (phase a, b, or c). To verify the evolution of the fault severity with respect to the fault resistance, the fault current rms value is calculated as a function of Rf using the above model (parameters are given in Table I). We define k as the ratio of the faulty part of the phase a fixed to 0.5 for this test (half of the winding of the phase a is faulty). Fig. 2 shows the result. It can be seen on this figure that the fault current is negligible when Rf > 50 Ω and the fault severity grows up rapidly for Rf < 10 Ω. Similar results are obtained for different values of k. Therefore, it is really interesting to detect the fault as soon as possible when it is not yet dangerous. Finally, the above model may be useful for studying the dynamical behavior of the PMSM under stator fault conditions and for testing fault detection methods before experimental validation. The residual voltage vector [α β β]T can be considered as a fault feature. In the next section, we will use this residual term to create an indicator for detecting an interturn fault in the stator winding of a PMSM.

faulty components

with

III. D ETECTION OF PMSM I NTERTURN S HORT C IRCUITS ⎧ ⎪ ⎨ α = −Ra2 · if − (La2 + Ma1a2 ) · di β = −Ma2b · dtf ⎪ ⎩ di γ = −Ma2c · dtf .

Then, considering Ma2b ≈ Ma2c , it yields ⎧ ⎨ α = −Ra2 · if − (La2 + Ma1a2 ) · dif ⎩ β = −Ma2b · dt γ ≈ β.

Labcf = [Labcf ] −

M3×3 0

A. Principle

dif dt

(10)

dif dt

(11)

⎡

The detection technique consists in using a healthy model of a PMSM to estimate the phase current of the machine. Then, this estimation is compared to the measured current and a residual current term is obtained. This latter will be used to create our indicator. We prefer to develop a method based on the current residual instead of the voltage residual for accuracy reasons. In fact, working with integrated variables (currents) is always more stable and accurate than working with derivative

0 Lcy 0 0 Lcy ⎢ =⎣ 0 0 0 −(La2 + Ma1a2 ) −Ma2b

0 0 Lcy −Ma2c

⎤ −(La2 + Ma1a2 ) −Ma2b ⎥ ⎦ −Ma2c La2

(7)


Fig. 2.

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Fault severity as a function of Rf .

ones (voltages). Moreover, for our application, it is required that the fault should be detected in real time without any additional sensors (requirements 1 to 3 in Section I). We use the following healthy model of the PMSM: vabc = Rs · iabc + [Labc ] ·

diabc + eabc dt

(12)

with ⎧ ⎨ iabc = [ia ib ic ]T v = [va vb vc ]T ⎩ abc eabc = [ea eb ec ]T and [Labc ] = Lcy · I3 for a balanced inductance matrix (I3 as the identity matrix). It is obvious that this model is not complete. Actually, we have to define the back-EMF term eabc and to take into account the inverter model and inductance unbalanced effects. This permits us to improve the healthy model by minimizing the gap with the real healthy machine. It is described in the following. 1) Back EMF: eabc = [ea eb ec ]T is the real back-EMF vector of the healthy machine. As this vector is not measured, we have to estimate it. This estimation can be done in any working frame; we can do it in the synchronous (dq) frame as in [8] or during an offline test using the machine in generator mode. However, the contribution here is to taking into account the other back-EMF frequency components by estimating them in higher frequency synchronous frames. This permits us to get more precise back-EMF waveforms leading to decreasing the current residual term in the healthy case. Fig. 3 shows the estimated back-EMF waveforms for our PMSM at 1000 r/min. It should be noted that this estimation is only realized in the first operating cycles and the obtained back-EMF waveforms are progressively frozen. It is of course supposed that the machine and its supply are initially healthy. The freeze rate can be adjusted. It is obvious that the estimated back-EMF vector will contain not only the real back-EMF components, but also other deviations from the ideal drive model (12).

Fig. 3. No-load back-EMF of the studied PMSM at 1000 r/min.

Note-It should be noted that the Park transformation that we use for the control is the following: cos(θ + δ) − sin(θ + δ) P (θ) = (13) sin(θ + δ) cos(θ + δ) where θ is the rotor position and δ is a proper correction to this position defined often by trial and error. Actually, it is shown in [13] that when the back-EMF waveforms are not sinusoidal, we can use a modified Park transformation matrix for improving the control of the machine. 2) Inverter Model: If we use the control reference voltages, the resistance Rs is the equivalent resistance seen by the control which is a nonlinear variable parameter because of the whole system losses. We have two choices: either closing the eyes to this phenomenon and putting it with the estimated back EMF, or taking it into account and compensating it. To do the latter, an experimental law is required to describe the equivalent resistance evolution as a function of the system state variables. This can be easily done by performing offline or online tests from stand-still to Ωmax by sweeping the machine d-current from zero to the rated value and evaluating the equivalent

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4) Indicator Definition: Now, we put together (12), (14), (15) and (17) to obtain the estimated currents using the control voltages vabcref ⎡ ⎤ ⎤ ⎡⎡ ⎡ ⎤ ι varef ιa d ⎣ a⎦ −1 ιb = [Labc ] . ⎣⎣ vbref ⎦ − Rd .⎣ ιb ⎦ dt ιc vcref ιc Tm .pm .sign(iabc ) Tp ⎤⎤

− Vd .sign(iabc ) + 2.

⎤ ⎡ ea ιa −Rs . ⎣ ιb ⎦ − ⎣ eb ⎦⎦ ιc ec ⎡

Fig. 4. Model of inverter switches.

resistance from vd and id . Supposing that the IGBT devices and the diodes have the same dynamical resistance Rd and the same voltage drop Vd , we consider the following model for power switches. Then, we have [29] vabc = vabcref − Rd .iabc − Vd .sign(iabc ) where

⎞ sign(ia ) sign(iabc ) = ⎝ sign(ib ) ⎠ . sign(ic )

Fig. 4 shows the model used for the inverter switches. On the other hand, the dead time (Tm ) has also an influence on the accuracy of our results. Particularly at zero control voltage, its impact is more important than losses in the inverter. To compensate it, we modify the control voltage as follows [30]: Tm .pm .sign(iabc ) Tp

with ι abc = [ιa

ιb

ιc ]T

(14)

⎛

∗ = vabcref + 2. vabcref

(18)

(15)

where pm and Tp are, respectively, the amplitude and the period of the PWM carrier signal. 3) Unbalanced Inductances: Design or maintenance aspects have a lot of consequences on the machine behavior, particularly on the stator windings. In some cases for special machines (it is the case of our machine), the inductance matrix is unbalanced ⎤ ⎡ La Mab Mac (16) Lb Mbc ⎦ . [Labc ] = ⎣ −Mab −Mac −Mbc Lc Then, taking into account (5), and by using the cyclical inductance Lcy = La − Mab like as in (7), we obtain the following matrix: ⎤ ⎡ 0 ΔM2 Lcy (17) Lcy + ΔL2 ΔM3 ⎦ . [Labc ] = ⎣ 0 −ΔM2 −ΔM3 Lcy + ΔL3 The elements of [Labc ] are almost known and constant if the machine is not saturated. By the way, we can also do the same operation on the resistance matrix [Rabc ]. However, considering the temperature effects, unbalance effects are negligible for resistances. Hence, we will take the same value (Rs ) for all three phases.

as the estimated current vector. It should be noted that the same estimation can be done in the stationary frame (αβ)

−1 d ια = Lαβ dt ιβ vαref ι T . .sign(iabc ) − Rd . α − Vd .T32 vβref ιβ Tm T .pm .T32 .sign(iabc ) − Rs Tp ι e . α − α ιβ eβ + 2.

(19)

with

−1 −1 T = T32 .Labc .T32 ; ι Lαβ αβ = [ι α ⎡ ⎤ 1 √0 2 ⎣ −1 3 ⎦ . T32 = 2 2 √ 3 −1 − 3 2

ιβ ]T

2

In both cases, the residual currents are defined by ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ιa ia ιa ⎣ ιb ⎦ = ⎣ ib ⎦ − ⎣ ιb ⎦ . ιc ic ιc

(20)

Under fault conditions, the control voltages are unbalanced for regulating correctly the phase currents iabc . This voltage vector comes actually from the current controllers which are supposed to be efficient. Hence, the estimated currents ı abc , obtained from these unbalanced voltages, contain information on the fault. It can be deduced that the real currents are almost sinusoidal, but not ı abc because of the residual voltage vector [α β β]T [see (10)]. In this case, if the healthy model is “accurate” in terms of its back-EMF vector, Rs , ψf , [Labc ], and the inverter model, a fault in the drive can be concluded. In addition, as if grows up rapidly when Rf decreases, the residual voltage vector [α β β]T and so the residual current terms depend on the fault severity. This will be verified by simulation and then by experimentation.


Fig. 5.

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Block diagram of the fault indicator.

The block diagram of the proposed fault detection method is given in Fig. 5. The phase currents are estimated using (18). Then, the residual current vector [ıa ıb ıc ]T is calculated according to (20). Finally, a simple signal processing is applied to this residual current for determining the fault indicator. It consists in shifting the second and the third residual currents, respectively, by T /3 and 2T /3 (T is the electrical period) ιb ]t−T /3 − [ιc ]t−2T /3 ιb ]t−T /3 + [ F = ιa − [ (21) + ιa − [ιc ]t−2T /3 T = 2π/p.Ω.

(22)

Then, F is low-pass filtered. These shifts allow localizing the unbalanced phase. B. Simulation Results The simulations are performed with MATLAB/Simulink. First, we use the PMSM faulty model coupled with a VSI model including losses and voltage drops. The DC source is represented by a perfect source followed by a LC filter. Switching and sampling frequencies are fixed to 10 kHz. The drive works in a torque control scheme. Fig. 6 shows the simulation results in the healthy case and under fault conditions. The fault signal (F ), shown at the bottom, is calculated according to (21). The current references are idref = 0 A iqref = 15 A. Fig. 7 shows, respectively the control voltages, the fault current, and the fault indicator for Ω = 1000 r/min. When Rf is fixed to 50 Ω, the fault current amplitude is about 0.5 A, and no significant changes can be noticed in measured signals. In this case, the fault indicator level is low but different from zero and the fault can be detected. For Rf = 20 Ω, we can make

Fig. 6. From top to bottom: machine currents and their estimation, residual current terms, and synchronized residual current terms for the healthy machine.

a clear decision on the fault detection because the indicator level increased to about 20 (almost 50 times more than that for the healthy case). For Rf = 10 Ω, the indicator is around 40 and finally for the worst case studied here (Rf = 5 Ω), the fault current is about 5 A and the indicator is about 75 (35 points more than the previous case). It can be noticed that the indicator is close to 0.4 for the healthy machine; the sensitivity is conserved that is why we can detect a change even for a high value of Rf in simulations. In the following, the robustness of the proposed method with respect to the operating point, the parameter uncertainties, and transient periods is evaluated by simulation. 1) Influence of the Operating Point: The objective here is to observe the influence of the operating point (iq , Ω) on the fault indicator. We suppose that the evolution of the voltage drop in the inverter is almost constant (see Fig. 4) and that the direct component of the current is fixed to zero (id ∼ = idref = 0 A).

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Fig. 7. From top to bottom: compensated control voltage on phase a, fault current, and fault indicator for different values of Rf (simulation).

Fig. 8. Evolution of the fault indicator with respect to the operating point.

Fig. 8 shows the evolution of the indicator for different fault configurations regarding the operating point. Three surfaces are shown in this figure. They correspond, respectively, to the following fault configurations: Rf = 1 Ω, Rf = 10 Ω and the healthy machine. k = 0.5 for both faulty cases. These simulation results show that the fault indicator level depends on the speed, but it is almost insensitive to the current. On the other hand, the indicator is different from zero even for the healthy machine. In fact, the presence of non-ideal power switches, digital sampling with zero order hold, and numerical errors create a threshold and the surface is between −2 and 2. Nevertheless, this threshold does not prevent us to detect the fault because the fault indicator level is higher than 20 for all tested operating points. 2) Sensitivity to Parameters: In this part, we show the impact of various parameters uncertainties on the proposed indicator. Consider the following parametric errors: Lcy = Lcy ± ΔLcy (23) ψm = ψm ± Δψm Rs = Rs ± ΔRs

Fig. 9. Normalized deviations on the nominal value of the fault indicator F (see Fig. 8) with respect to parameter uncertainties (Lcy , ψm , Rs ).

where ΔLcy , Δψm , and ΔRs are fixed, respectively to 20%, 10%, and 20%. Fig. 9 shows the impact of these uncertainties on the fault indicator for several operating points. In all cases, k = 0.5 and Rf = 10 Ω. According to this figure, uncertainties on ψm have a minor impact on the fault indicator. Meanwhile, Rs and Lcy uncertainties affect the indicator, respectively, at low and high speeds. The same tests have been performed when Vd and Rd vary ±50% around their nominal values, and it was concluded that the indicator is not sensitive to these parameters. These results show that the parameter uncertainties may bias the fault indicator. Two phenomena can be distinguished: at low speeds, a rather good knowledge on Rs is required, whereas at high speed, Lcy should be relatively well known. 3) Transient Conditions: The fault detection in transient modes is often unachievable with frequently used methods based on spectral analysis because of the nature of frequency


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Fig. 12. Experimental test bench. Fig. 10. Four ramps used for transient mode tests.

because of neglected irregularities in the practical system. In steady-state operation, the obtained results show that we can detect the fault whatever the operating point is, but the fault indicator level evolves with the operating point even if these variations are less important than those of some other techniques [8]. In transient mode, the simulation results confirm that the fault can be detected if the motor speed is sufficiently high. These advantages come from the use of model (18) for deriving the fault signal. The counterpart of these advantages lies in the fact that the proposed method is relatively sensitive to some of the system parameters. In addition, an initializing phase for estimating important parameters is necessary. The authors work on this topic. IV. E XPERIMENTAL T ESTS A. Experimental Setup

Fig. 11. Simulation results in transient mode. From top to bottom: indicator response to reference4, reference3, reference2, and reference1.

analysis tools requiring steady-state operation. However, according to the definition of the proposed fault indicator in (21), the proposed method in this paper seems to be applicable in transitions. To verify it, we consider four acceleration ramps as shown in Fig. 10. For each ramp, we test the indicator for the healthy machine and for k = 0.5 and Rf = 10 Ω. It should be noted that the drive is controlled using a speed control scheme. Fig. 11 shows that the proposed method indicates the presence of the fault even in transient modes. For each reference, the indicator level does not exceed ten in the healthy case. Under fault conditions, it is always greater than 20 whatever the ramp slope. We can also notice that the indicator has its transient response due to the low-pass filtering of the fault signal (F ). However, obviously, this transient response does not prevent us detecting the fault. Finally, it is obvious that the fault detection is more efficient if the speed is higher. 4) Conclusion: The performed tests show that the proposed method is well adapted for detecting the interturn faults in PMSMs. Nevertheless, a detection threshold appears due to numerical errors, and it may be higher in experimental tests

To verify our theoretical investigations on the interturn fault detection, a test bench with a nonsalient pole PMSM supplied by a PWM controlled VSI is implemented. It is shown in Fig. 12, and its parameters are given in Table I. The machine is a 1.5 kW doubly fed PMSM. The two stator windings are connected in series to get a simple three-phase drive. Halfwinding short circuits can be realized in this manner. The drive is controlled by a TI-DSP digital control card whose sampling period is 100 μs. It sends PWM command signals to a threeleg VSI supplied by a 200 V DC source. The load is a PM synchronous generator connected to a diode rectifier. Then, the rectified DC voltage supplies a variable resistance through a buck converter in such a way that the load torque can be controlled. This allows achieving different operating points. B. Results 1) Fault Detection: At first, let us test the efficiency of the proposed method in interturn fault detection. We begin by a current control scheme with the following operating point: ⎧ ⎨ idref = 0 A ⎩

iqref = 15 A Ω = 1000 r/min.

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Fig. 14.

Test results for several operating points (experimental).

Fig. 13. From top to bottom: compensated control voltage, fault current, and fault indicator for different values of Rf (experimental).

The rotor position correction is δ = 8◦ . The dead time is fixed to Tm = 1 μs. The inverter switches are represented by a voltage drop of Vd = 1.2 V and a dynamic resistance of Rd = 0.9 Ω. Fig. 13 shows the experimental results obtained for the same tests performed by the simulation (see Fig. 7). Obviously, the stator phase currents are less sinusoidal than those in simulations. It is why the fault indicator level is greater than that in Fig. 7 for the healthy machine (Fhealthy ∼ = 42). Meanwhile, the variations of the fault indicator for low values of Rf are almost the same as in the simulation. Indeed, for Rf = 10 Ω and Rf = 5 Ω, the increase of F with respect to Fhealthy is respectively about 15 and 55. Hence, such faulty cases can be easily detected. However, due to the healthy case level of the indicator (Fhealthy ), the detection of less severe faults is strongly affected compared to the simulation. This difference between the simulation and experimental results can be explained by the fact that the healthy model of the machine is not yet accurate enough to reflect the reality. Even if the compensation terms (back EMF, inverter model, and unbalanced inductances) bring some improvements, we can consider that some other phenomena are not taken into account. Actually, mechanical losses, iron losses, and end windings configuration are ignored. The authors analyze these parameter uncertainties and measurement errors in the same manner as in [31], [32] and prepare another paper for presenting their results. 2) Influence of the Operating Point: Now, we study the impact of the operating point on the indicator level. To do that, the load torque is varied in such a way that q-current sweeps from 0 A to 5 A while the angular speed varies between 1000 r/min to 2000 r/min. For each point, the fault indicator level is evaluated and saved. The results are plotted in Fig. 14. We can notice in this figure that the indicator level is highly dependent to the angular speed, but it is almost insensitive to the q-current and so to the load torque. Also, the detection threshold (indicator level for the healthy machine) is higher than that in the simulation (see Fig. 8) as it was explained in the previous paragraph. The general shape of the surfaces matches well with Fig. 8. It is obvious from Fig. 14 that the proposed approach allows keeping a good distance between the faulty and healthy cases even at

Fig. 15. Test results in transient conditions-from top to bottom: reference1, reference2, reference3, and reference4 (experimental).

low speeds and low loads, whereas many other methods need high load and speed to be really efficient. 3) Transient Conditions: Finally, we verify our simulation results in transient mode exposed in Section III. The same four ramps in Fig. 10 are used to create a mechanical transient response. Experimental results shown in Fig. 15 reveal that the proposed approach can detect the fault for all cases. Once again, the fault indicator goes through a transition before settling to its final level. The gap between the indicator levels in healthy and faulty cases is sufficiently high for detecting the fault even if the indicator level for the healthy machine is much higher than that in Fig. 11.

V. C ONCLUSION A method for detecting interturn faults in PMSMs is presented in this paper. It is based on a current residual analysis. The difference between estimated currents obtained by a healthy model and the real currents of the machine is used to detect the fault. The healthy model is improved by several compensation terms such as inverter losses, real back-EMF waveforms, and unbalanced inductances.


The residual current is used to define the fault indicator. The simulation and experimental results confirmed the efficiency of this indicator. These tests show that the proposed method can detect an interturn fault without additional sensors in both steady-state and transient conditions. The method is tested taking into account the operating point variations and parameters uncertainties. The method does not require high CPU time and can be easily implemented in an experimental drive to give realtime results. However, other ignored irregularities should be taken into account to improve the sensitivity of the indicator to the fault. Anyway, because of the negligible impact of the fault on the system (Fig. 2), it seems to be impossible to detect the fault when Rf > 1 kΩ without violating the requirements given in Section I.

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Nicolas Leboeuf received the Engineer degree from the Ecole Nationale d’Electricité et de Mécanique, Nancy, France, in 2009. Currently, he is working toward the Ph.D. degree in the Groupe de Recherche en Electrotechnique et Electronique de Nancy at the Institut National Polytechnique de Lorraine, Nancy. His main research interests are fault detection, modeling, and control of electric machines.

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Thierry Boileau received the Master’s degree (DEA PROTEE) and the Ph.D. degree in electrical engineering from the Institut National Polytechnique de Lorraine, Nancy, France, in 2004 and 2010, respectively. Currently, he is with the Groupe de Recherche en Electrotechnique et Electronique de Nancy. His main research interests are diagnostics and control of electrical machines supplied by static converters.

Babak Nahid-Mobarakeh (M’05) received the M.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1995, and the Ph.D. degree in electrical engineering from the Institut National Polytechnique de Lorraine (INPL), Nancy, France, in 2001. From 2001 to 2006, he was with the Centre de Robotique, Electrotechnique et Automatique, Amiens, France, as an Assistant Professor at the University of Picardie. Currently, he is with the Groupe de Recherche en Electrotechnique et Electronique de Nancy at the INPL. His main research interests are in nonlinear and robust control techniques applied to power systems.

Guy Clerc (M’90–SM’10) was born in Libourne, France, on November 30, 1960. He received the Engineer’s and Ph.D. degrees in electrical engineering from the Ecole Centrale de Lyon, Ecully, France, in 1984 and 1989, respectively. He is a Professor at the Université Claude Bernard-Lyon 1, Villeurbanne, France, where he teaches electrical engineering. He carries out research on control and diagnosis of induction machines at the Centre de Génie Électrique de Lyon/ Université Claude Bernard-Lyon 1.

Farid Meibody-Tabar received the Engineer degree from the Ecole Nationale d’Electricité et de Mécanique of Nancy, Nancy, France, in 1982, the Ph.D. and “Habilitation à diriger des recherches” degrees, both from the Institut National Polytechnique de Lorraine (INPL), Nancy, France, in 1986 and 2000, respectively. Since 2000, he has been a Professor at the National Polytechnique de Lorraine (INPL), Nancy, France. His research activities in the Groupe de Recherche en Electrotechnique et Electronique de Nancy deal with electric machines, their supply, and their control.