Elimination of broken rotor bars false indications in induction machines

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ScienceDirect Mathematics and Computers in Simulation 167 (2020) 250–266 www.elsevier.com/locate/matcom

Original articles

Elimination of broken rotor bars false indications in induction machines O. Guellouta ,∗, A. Reziga , S. Touatib , A. Djerdirc a

L2EI Laboratory, Jijel University, BP 98 Ouled Aïssa 18000, Jijel, Algeria b Nuclear Research Centre of Birine, Birine, Djelfa, Algeria c FEMTO-ST Laboratory, University of Technology Belfot-Montbélliard, 90010, Belfort cedex, France Received 31 January 2019; received in revised form 26 May 2019; accepted 16 June 2019 Available online 2 July 2019

Abstract This work illustrates a method to detect and separate the broken rotor bars (BRBs) from load torque oscillations (LTOs) in motor’s line current signature. The LTOs (due to mechanical load condition abnormalities, load fluctuations like speed reduction couplings or a defective transmission) can introduce similar symptoms as the rotor cage breaks do. The proposed policy is based on the set of two rotating coordinates (same and inverse angular velocity as the current’s fundamental frequency ω) for the stator current vector, and its decomposition into positive and negative components. The extracted components of the positive sequence allow to separate the similar effects produced by rotor defects and the oscillating load . The detection and separation process is performed through the demodulation of the amplitude modulating signal due to BRBs and the phase modulating signal due to LTOs. An experimental test bench has been conducted to validate the simulation results and demonstrate the effectiveness of the proposed approach. c 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights ⃝ reserved. Keywords: Load torque oscillations; Broken rotor bars; Fault detection/diagnosis; Condition monitoring; Induction machine

1. Introduction Electric motors are widely used in transportation (Electric vehicles, trains. . . etc.), medical treatment and different industrial and military operations, it is also considered as crucial instruments for renewable energy applications [21]. A failure during a machine’s work could lead to its total interruption. Subsequently, it will directly affect the system’s sustainability, and can exhibit human’s life to danger or lead to costly material damages. Therefore, countless research works have dealt with motor condition monitoring and fault detection, trying to comprehend the machine’s behaviour during and before failure incidence and therefrom, to reduce maintenance costs, prevent unscheduled downtimes and avoid harmful and devastating consequences [9]. In particular, a large amount of proposed schemes has dealt with motor current signature analysis (MCSA) as a mainstream fault detection method, providing reliable results for diagnosis of faults, such as; broken rotor bars, end rings fissures, abnormal levels of air-gap eccentricity, shorted turns in low voltage machines and several mechanical problems [27]. In fact, MCSA is simple and effective ∗

Corresponding author. E-mail address: [email protected] (O. Guellout).

https://doi.org/10.1016/j.matcom.2019.06.010 c 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights 0378-4754/⃝ reserved.

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under suitable operating conditions such as steady state. Furthermore, low-cost tools are used for the diagnostic operation and tests are realized online without interrupting production. Hence, MCSA can be used as a predictive maintenance tool for detecting common motor faults at early stage and prevent expensive catastrophic failures, production outages and extend motor lifetime [4,13]. From all faults that could affect the induction machines (IMs), the problem of broken rotor bars (BRBs). This last has been given a special interest. Because, it represents a considerable percentage from the whole faults range. As soon as a rotor cage winding asymmetry takes place, a backward-rotating field is produced. Therefore, an induced electromotive force (EMF) shows up in the stator windings. Consequently, a stator current amplitude modulation (AM) will appear coming up with two sideband components around the fundamental at frequency (1 ± 2s)f [24], where f is the current supply frequency, s is the rotor slip of the machine. Likewise, rotor position dependent loads applications (like speed reduction couplings and centrifugal compressors as well as defective mechanical loads couplings) frequently introduce load torque oscillations (LTOs) to the rotor’s shaft [23]. LTOs have a significant impact over the machine, appearing as a sinusoidal phase modulation of the stator current and exhibiting similar indications as the BRBs fault do (sideband components at frequency; f±fr ) [2,3]. As a result, this false positive rotor fault indication may lead to misinterpreted signals and, thus, incorrect diagnostic steps [18]. Particularly, when the BRBs fault and LTOs occur simultaneously, their indications are shown to be barely inseparable without a preliminary knowledge of the spatial position of the fault and the LTOs characteristics with respect to the rotor [22,25]. Furthermore, their harmonics overlap at adjacent or same frequency (2sf≈fr ) and interact to add or cancel out depending on their relative phase angle [8]. Therefore, the fault detection and severity estimation process results using the MCSA under these circumstances become suspicious and doubtful. Consequently, the appearance of two sidebands components around the current’s fundamental spectrum becomes a non-prominent symptom proving BRBs fault incidence, since it can be attributed to mechanical oscillations as well. Hence, giving rise to false indication occurrence possibility, which can lead to unnecessary inspection, and thus, valuable industrial production losses, and makes rotor fault detection and severity estimation operations more challenging [28]. In order to distinguish the two events (BRBs and LTOs signs), numerous research papers addressing similar problem have proposed some solutions and attempted to achieve a high accuracy of diagnostics. In this regard, authors in [26] have summarized some previously proposed techniques like the Model Reference Estimation [22], which suggests the current change evaluation, with reference to an ideal machine model. These techniques inconveniences are the machine parameters estimation dependency and the large processing time need. Later on, instantaneous stator current positive and negative sequences [25]. Some authors have based on unconvincing theoretical background, which makes the obtained results implausible. Thereafter, several papers in the literature addressed the same problem. For instance, the Vienna Monitoring Method [17], by means of the calculated torque values from both current and voltage models (A model-based technique), afterward, authors in [3] proposed a method based on the stator currents decomposition into active and reactive components using the p–q theory, [1]. After that, De Angelo, Ch. et al. [7] tried with the stator instantaneous complex apparent impedance. Then, the study of Concari, et al. [6] shows the angular displacement of the active and reactive Current’s Space Vector, in order to distinguish external torque ripple from rotor faults. Recently, G¨oktas¸, et al. [11] used a method named; Analytical Signal Angular Fluctuation (ASAF). Also, Kim, et al. [16] suggested two alternative options to discriminate the two-overlapped indications (BRBs and LTOs) via Space Harmonics-based MCSA and Start-up Current Analysis techniques. In addition to the Instantaneous Active and Reactive Power Signature Analysis proposed by Drif, et al. [8]. Finally, G¨oktas¸. & Arkan. [10] have extracted the BRBs and LTOs indications sidebands components appearing around the current and voltage fundamentals. Accordingly, the main weaknesses of most techniques are the estimation of the phase shift between voltages and currents and the need of both voltage and current sensors to perform the required process, in spite of their complexity and the large processing times which makes the online fault detection too difficult. For the aim of BRBs detection and elimination of false indication in case of LTOs presence purpose, the paper proposes a stator synchronous reference frame MCSA based technique. Furthermore, some trigonometric implementations are used in order to demodulate each phenomena components separately. Accordingly, the main improvements that the proposed technique in this paper provides are; the machine’s parameters independence, where there is no preliminary knowledge of the BRBs spatial position need, nor the LTOs characteristics. The process only requires two phase currents to perform the whole process with no need to the phase shifts estimation. In addition to its simplicity, each of the BRBs and LTOs indications are distinguished straightway from the direct and quadrature

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Fig. 1. Phase-a current in presence of 1 broken rotor bar.

components spectrums (idpos and iqpos ) and gives more significant signs (frequency and amplitude). Therefrom, all these gathered features make this method advantageous to be a promising tool for faults detection and false alarms elimination. The paper is organized as follows: an overview of the broken rotor bars and cyclic loads effects over the machine’s line currents is explained in Section 2. Afterwards, the rotating reference frame based system used for both phenomena’s effects analysis has been discussed in the third section. Later, the simulation results are illustrated in the 4th section in addition to the experimental validation, results comparison and the signatures separation chart. Lastly, a conclusion and the suggested future work are presented in the last section. 2. Fault and load oscillations effects on machine’s line currents Active faults are defined as being every turning fault at a defined frequency causing one or multiple current harmonic components as a result of its effect including broken rotor bars and end rings, eccentricity, etc. Some external factors may introduce false indications seen as the same BRBs fault symptoms appear. Therefore, this study has been established to discern the LTOs effects from the BRBs fault in order to eliminate any false indications in case of symptoms similarity that may cause invaluable investigations and misleading diagnostic steps. 2.1. Broken rotor bars characteristics The reasons for the rotor cage winding failure occurrences such as broken rotor bars are various, including overloads, too-frequent starts, which cause high electro-mechanical stresses. As long as such a failure exists, rotor currents will be redistributed, and an additional backward rotating field at slip frequency will be present. Accordingly, the air gap flux density will redistribute as well, therefrom, a voltage and thus, a current in the stator windings will be induced at a frequency flsb = (1 − 2s)f. And, because of the current cyclic variation, a torque and a corresponding speed oscillation will be induced at a frequency of (2sf). Therefore, an upper sideband current component will appear at fusb = (1 + 2s)f. So, a twice components at sidebands frequencies will appear around the stator current fundamental as it is shown in Fig. 1, calculated as fsb = (1 ± 2s)f, where fsb presents the sidebands frequencies of the components generated by fault, f is the supply frequency and s the rotor slip [20,24]. The modulated currents due to the broken rotor bars or end ring fault in one phase is written as [12]: i (t) = I sin (ωt − ϕ) + Iu sin[(1 + 2s) ωt − ϕ] + Il sin [(1 − 2s) ωt − ϕ]

(1)

where I and ω are the max value of the stator current, the fundamental angular velocity (ω = 2π f). ϕ, Iu and Il are the phase shift, the max values of the upper and lower current sideband components respectively.

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Fig. 2. Phase-a current in presence of LTOs at fs = 5 Hz.

2.2. Load torque oscillations Under mechanical load condition abnormalities, an induced load torque oscillations appear in the related instantaneous torque of the machine. In this case, the general load torque at steady state has the following form [2,3]: TLoad (t) = Tresist + Tr cos(ωr t)

(2)

where Tr is the torque oscillation component’s max value and ωr = 2π fr is the oscillation angular velocity, TLoad is the machine’s related load torque and Tresist is the resistant torque. Blodt, et al. 2006 [2] have analytically studied the LTOs effect over the magneto-motive forces (MMFs) induced in the stator windings. The latter has a direct influence over the currents, starting from the torque fluctuation in the steady state and extending to the resulted oscillating speed and rotor mechanical position which occurs later. The latter leads to a phase modulation (PM) of the rotor MMF by its role. As a result, a sinusoidal phase modulation of the stator current arises, which is seen in the related frequency spectrum as sideband components at f±fr (Fig. 2.), with f and fr are the fundamental and the load oscillations frequencies respectively. Due to this event, the stator current in an arbitrary phase can be written in a general form as: ( ) i (t) = I sin ωt + ϕ ′ + Ir sin [ωt + β cos (ωr t)] (3) where I and Ir are the max values of the stator current and the oscillating current respectively.ϕ ′ , ω and ωr are the phase shift, the fundamental angular velocity (ω = 2π f), the angular velocity of the oscillating load torque (ωr = 2π fr ). The modulation index β = JpTωr2 r J is the total inertia of the machine and the load, p is the pole pair number. For physically reasonable values J, Tr and ωr , the approximation β is held ≪1 in most cases [2]. 2.3. LTO with BRBs interaction and false indications It has been reported in many literature case histories that cyclic loads is one of the typical causes that can cause rotor cage winding breaks false positive indications by introducing low frequency load oscillations (LOs) to the motor shaft [18,23]. This incidence effects appear in the current spectrum as sideband components around the fundamental at frequency (f ± fr ). In a similar way that BRBs fault reacts as it is illustrated in Figs. 1 and 2.

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In case of the two phenomena simultaneous presence, BRBs fault and LTOs related harmonics overlap at adjacent or same frequency (2sf ≈ fr ) and interact to add or cancel out depending on their relative phase angle [8]. In contrast, they are shown to be barely inseparable without a preliminary knowledge of the spatial position of the fault and the LTOs characteristics with respect to the rotor [22,26]. This may result in false indications or doubted fault severity estimation, giving rise to misinterpreted signals during the machine’s diagnosis process, and may lead to a substantial financial loss due to unnecessary inspections and maintenance efforts as well as the industrial production interruptions. In such circumstances, a discerning technique is crucial, and the proposed idea is to perform a demodulation of the amplitude modulated signal due to BRBs fault and frequency modulated signal due to LTOs using basic synchronous reference frame. The theoretical study as well as the simulation with experimental validation are presented in the next sections. 3. Rotating reference frame definition for faults detection and separation Reference frame theory has been studied and shown to be an effective analytical tool for Machines modelling, control, condition monitoring and fault detection. In this paper, this theory is used to extract the BRBs and LTOs effects over the machines line current. The main proposed idea is to perform a demodulation of the amplitude modulated signal due to BRBs fault and frequency modulated signal due to LTOs separately basing on rotating reference frame at the currents main frequency. Accordingly, the process is done through the use of two load types, static and oscillating to see the impact of the LTOs over the healthy and BRBs affected machine. 3.1. Healthy machine The healthy machine term is said with referring to the BRBs fault. The LTOs is considered as an external factor. 3.1.1. Healthy machine with a static load torque The introduced torque to the machine’s shaft in this case is considered constant, thus, there is no speed oscillations. In steady state, the flowing currents in a healthy machine’s stator windings are as follows: ⎧ ⎪ i (t) = I sin (ωt − ϕ) ⎪ ⎨a ) ( (4) −ϕ ib (t) = I sin ωt − 2π 3 ⎪ ⎪ ( ) ⎩ 2π ic (t) = I sin ωt + 3 − ϕ where I denotes the max current value, ω = 2π f is the angular velocity of the current and f is the current supply frequency. Using Concordia’s transformation, for a balanced three-phase system, currents can be written as: √ { iα = 26 I sin (ωt − ϕ) √ (5) ( ) iβ = 26 I sin ωt − π2 − ϕ with π2 presents T4 . (T is the fundamental cycle) Currents iα and iβ can be represented by mutually perpendicular instantaneous vectors (Fig. 3). The resulting vector i is an instantaneous rotating vector expressed as: ⃗ı = ı⃗α + ı⃗β

(6)

Based on the double synchronous reference frame (DSRF) Method, an orthogonal rotating coordinates is defined, where ipos represents the instantaneous positive sequence component of the current vector i and the angular velocity of ω. ineg represents the instantaneous negative sequence component of the current vector i at the angular velocity of –ω (Fig. 4) [14,15]. Since the currents phase shift is calculated with reference to the related voltages, and in order to simplify the coming calculations, ϕ and ϕ ′ are equal and considered null. α -β to dpos − qpos Reference Frame Transformation: The main purpose of this transformation is to get free of the fundamental current. This will enable us deal with the sideband-harmonics from a midpoint to see them as unified components in frequency and amplitude. From [14,15] the transformation form from α-β to dpos -qpos rotating reference frames is: [ ] [ ][ ] idpos sin (ωt) − cos (ωt) iα = (7) iqpos − cos (ωt) − sin (ωt) iβ

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Fig. 3. Instantaneous current vector.

Therefrom; { idpos = iα sin (ωt) − iβ cos (ωt) iqpos = −iα cos (ωt) − iβ sin (ωt) By replacing (5) into (8) and using trigonometric manipulations, it can be straightforwardly arrive to: { √ idpos = 26 I iqpos = 0

(8)

(9)

From the previously cited equations, and after the α-β to d–q transformation, it can be noticed that the AC fundamental component of the currents is missing. Therefore all the components of the signal will be reconstructed referring to the fundamental harmonic component frequency (ω = 2π f), and the side bands fault related harmonic will appear as a signal presenting the fault. Thus, the positive sequence seems adequate for the demodulation process of the low frequency harmonics. α -β to dneg − qneg Reference Frame Transformation: Using the same steps of Section 3.1.1: [ ] [ ][ ] idneg − sin (ωt) − cos (ωt) iα = iqneg − cos (ωt) sin (ωt) iβ Therefrom; { idneg = −iα sin (ωt) − iβ cos (ωt) iqneg = −iα cos (ωt) + iβ sin (ωt) By replacing (5) into (11) and using trigonometric manipulations: √ { idneg = 26 I cos(2ωt) iqneg =

√ − 6 2

(10)

(11)

(12)

I sin(2ωt)

From the results of the two sequences, it can be noticed that the negative sequence will show every side band harmonics components around its fundamental, which has a two times frequency of ia.b.c currents related one, i.e.; 2ω. Thus, it shows the BRB and LTO as similar signs, although, the separation of the two incidences could not be possible. This makes the extraction of the BRBs from the LTOs index impossible. On the other hand, the positive sequence is likely more convenient for the process. Since the frequency of the new coordinate system is the same as the fundamental component, the latter keeps just its DC component. From this mid-point, the sideband harmonics will appear as unified components in frequency and amplitude, as it will be demonstrated through the theoretical study in the next section.

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Fig. 4. Instantaneous current vector in new (d–q) coordinates.

3.1.2. Healthy machine with an oscillating load torque By applying an oscillating torque to the machine’s shaft and according to Section 2.2, the stator currents form in the case of Load torque oscillations presence is described as follows: ⎧ ⎪ i (t) = I sin (ωt) + Ir sin [ωt + β cos (ωr t)] ⎪ ⎨a ( ) [ ] (13) ib (t) = I sin ωt − 2π + Ir sin ωt + β cos (ωr t) − 2π 3 3 ⎪ ⎪ ( ) [ ] ⎩ 2π 2π ic (t) = I sin ωt + 3 + Ir sin ωt + β cos (ωr t) + 3 Consequently, iα and iβ will take the form; √ √ { iα = 26 I sin (ωt) + 26 Ir sin [ωt + β cos (ωr t)] iβ =

√ − 6 2

I cos (ωt) −

√

6 I 2 r

sin [ωt + β cos (ωr t)]

(14)

The demodulation process will be done by projecting iα−β into the dpos −qpos rotating reference frame as follows. α − β to dpos − qpos Reference Frame Transformation: By replacing (14) into (8), and performing some trigonometric simplifications: √ √ { idpos = 26 I + 26 Ir cos [β cos (ωr t)] iqpos =

√ − 6 Ir 2

sin [β cos (ωr t)]

(15)

Since the amplitudes variation between min and max values of i d pos and i q pos can represent the fault index; the amplitudes variation range difference between both functions shows the fault index firmness. By putting θ = β cos (ωr t), it is well known that the function, −1 ≤ cos (ωr t) ≤ 1, therefrom; the variation of the angle is −β ≤ θ ≤ β. it is also known that β ≪ 1.

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For a small change of the angle (θ < π2 ), and because of cos(θ ) = cos(−θ ), the amplitude variation of i d, pos is cos (β) < Idpos < 1. On the other hand, the amplitude variation of i q, pos is sin (−β) < Iq pos < sin(β). It is shown sin(β) in [19] that limβ→0 1−cos(β) = +∞, therefore, the amplitude variation of i d pos is negligible comparing with i q pos . Therefrom, the two functions can be rewritten in the form; √ { idpos = 26 I √ (16) iqpos = −2 6 Ir sin [β cos (ωr t)] As a result of the mathematical development, it is noticed that the modulating signal due to LTOs appears properly in the positive sequence and extracted from the fundamental. Therefrom, the appearance of an AC component in i q pos signal can be considered as a strong LTOs indicator. 3.2. Machine with broken rotor bar fault The sidebands appearance in the machine’s line current spectrum during its surveillance may receive false rotor fault alerts caused by external perturbations. With an accord to the study of the BRBs and LTOs interference, the main purpose of the chosen analytical method use consists of the two phenomena separation and the elimination of the fault false indications in case of symptoms resemblance. 3.2.1. Broken rotor bar with a static load torque In order to analyse the broken bars effect over the machine line’s currents, the modulated currents due to the fault should be defined. If only the sideband components around the supply current fundamental considered, the machine currents in steady state are written as: ⎧ ia (t) = I sin (ωt) + Iu sin [(1 + 2s) ωt] ⎪ ⎪ ⎪ ⎪ + Il sin [(1 − 2s) ωt] ⎪ ⎪ ⎪ ⎪ ⎨ib (t) = I sin (ωt − 2π ) + Iu sin [(1 + 2s) ωt − 2π ] 3 [ 3 ] (17) ⎪ + Il sin (1 − 2s) ωt − 2π ⎪ 3 ⎪ ( ) [ ] ⎪ ⎪ 2π 2π ⎪ ⎪ ⎪ic (t) = I sin ωt[ + 3 + Iu sin (1] + 2s) ωt + 3 ⎩ + Il sin (1 − 2s) ωt + 2π 3 Assuming that the upper and lower sidebands have the same amplitude, Iu = Il = Is and by putting 2sω = ωs , (17) can be rewritten in the following form; ⎧ ia (t) = I sin (ωt) + Is {sin [(ω + ωs ) t] ⎪ ⎪ ⎪ ⎪ + sin [(ω − ωs ) t]} ⎪ ⎪ ⎪ ⎪ ⎨ib (t) = I sin (ωt − 2π ) + Is {sin [(ω + ωs ) t − 2π ] 3 3 [ ]} (18) 2π ⎪ + sin − ω t − (ω ) s ⎪ 3 ⎪ ( ) { [ ] ⎪ ⎪ 2π 2π ⎪ ⎪ic (t) = I sin ωt + 3 + Is sin (ω + ωs ) t + 3 ⎪ [ ]} ⎩ + sin (ω − ωs ) t + 2π 3 By following the same steps leading to (5), iα and iβ in the BRB fault affected machine can be written as; √ √ ⎧ 6 6 ⎪ ⎪iα = 2 I sin (ωt) + 2 Is {sin [(ω + ωs ) t] ⎪ ⎪ ⎨ + sin [(ω − ωs ) t]} √ (19) ( ) √ { [ ] ⎪ ⎪ iβ = 26 I sin ωt − π2 + 26 Is sin (ω + ωs ) t − π2 ⎪ ⎪ [ ]} ⎩ + sin (ω − ωs ) t − π2 α-β to dpos − qpos Reference Frame Transformation: The transformation of the two currents iα and iβ into the synchronous coordinates idpos and iqpos allows the extraction of the BRBs signal from the fundamental. By replacing (19) into (8). With some trigonometric

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simplifications: { √ √ id,pos = 26 I + 6 Is cos(ωs t) iq,pos = 0

(20)

From (20), the idpos signature is a BRBs fault frequency and amplitude dependent, and has the same fault form. Besides, it is totally independent from the fundamental frequency. Therefore, √ the demodulation process has been analytically proved with success. The fault amplitude rises up with a value of 6 comparing with the fault signature in the line basic current Iabc and the double of the values of iα or iβ . The idpos component at the frequency of 2sf can be considered as a powerful sign for BRBs fault detection. 3.2.2. Broken rotor bar with an oscillating load torque During the BRBs occurrence while the machine shaft is exhibited to an oscillating torque, the related harmonics of the two incidences overlap at adjacent frequencies. The proposed method is adequate to extract the indication of each phenomena separately. Pursuing the same steps, the resulted signal due to the two simultaneous incidences would be the sum of the two effects and the fundamental: ⎧ √ √ 6 6 ⎪ ⎪iα = 2 I sin (ωt) + 2 Is sin [(ω + ωs ) t] ⎪ √ ⎪ ⎪ ⎨ + sin [(ω − ωs ) t] + 26 Ir sin [ωt + β cos (ωr t)] √ √ (21) 6 − 6 ⎪ ⎪ i = I cos − I cos [(ω + ωs ) t] (ωt) β ⎪ 2 2 s ⎪ √ ⎪ ⎩ + cos [(ω − ωs ) t] − 26 Ir sin [ωt + β cos (ωr t)] α-β to dpos − qpos Reference Frame Transformation: The dpos − qpos components have the advantage to demodulate the BRBs and LTOs signatures separately from the fundamental signal. Following the same previous steps, by replacing (21) into (8): { √ √ idpos = √6 I + 6 Is cos(ωs t) (22) iqpos = −2 6 Ir sin [β cos (ωr t)] The analytical results show clearly the success of the two phenomena signals separation procedure. Where the idpos signature represents the amplitude modulating signal due to BRBs, whereas iqpos represents by its role the phase modulating signal due to LTOs. Accordingly, the process is done through the demodulation of the amplitude and frequency modulating signals from the fundamental. Whereas, the negative sequence is still limited in the low frequency fault identification. The practical results discussion in the next section will validate the theoretical study. 4. Simulation results and experimental validation 4.1. Test facilities and experimental setup A transmission system experimental bench at Electrical Engineering research Lab, CRNB1 as shown in Fig. 5, has been conducted to validate the proposed method for BRBs fault and LTOs detection and separation results. It consists of the set of a 4poles, 1.5 kw and 50 Hz squirrel cage induction motor, its speed with the rated load is 1410 rpm and a rated voltage and currents of 200 V–230 V and 4 A respectively. An adjustable powder break load with a voltage controlled of a Vmax = 20 V, Tmax = 20 N.m and maximum speed of 3000 rpm. The test bench consists of currents, voltages, speed and torque sensors. The data are collected at a sampling rate of 25 kHz and a time duration of 1 s (minimum frequency of 1 Hz) through a 16-bit National Instruments-LabVIEW data-acquisition board. The Data acquisition system passes by the three phase’s current sensors of the machine. The data were treated offline under Matlab environment. Throughout the practical study, the phases order should be respected, otherwise, a sequence change will occur, and the procedure must be reversed. During the data acquisition process, the periods and the number of the points must be adjusted to cover the low frequencies, i.e.; time >0.2 s. Moreover, due to the mechanical system shaft alignment imperfection, stator slots, variable speed drives which can give rise to unconsidered harmonics or any 1

CRNB: Centre de Recherche Nucl´eaire de Birine, Djelfa, Algeria.

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Fig. 5. The used experimental test bench.

Fig. 6. (a) LTO waveform. (b) Broken bar in the rotor cage of the used machine.

kind of related components may appear. However, it will not affect the effectiveness of the proposed technique, since the related currents components of the faults appear in low frequencies. Hereby, it gives satisfying results, as it is shown in the presented results. In order to verify the proposed task to separate the two incidences signatures, one broken bar fault is created in the rotor of the used machine. On the other hand, we resort to generate an external oscillating torque. The operation is done by generating a sinusoidal voltage wave to the input voltage of the powder brake load. A low frequency voltage generator is required as it is shown in Fig. 6

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4.2. Machine simulation under faulty conditions To simulate the behaviour of the three-phase squirrel cage induction motor under fault and load oscillations conditions, a mathematical model of an ideal machine ( machine parameters in appendix), based on the Coupled Circuit Approach [5] has been implemented under Matlab environment. The impact of broken rotor bars is modelled by creating an asymmetry of the resistance in rotor phases. The inductance changes are neglected due to its insignificance influence compared to the resistance changes. For simplicity, the air gap, the stator resistances and inductances stay unchanged [5]. Therefore, a resulted amplitude-modulating signal due to BRBs will be present with a 1% amplitude of the fundamental current max value and a 6 Hz modulation frequency. Since the sidebands due to the BRBs appear around the fundamental spectrum at frequency (1 ± 2s)f, the slip s speed − Rotor speed is calculated as: s = Synchronous , which equals in our case to ≈ 6.66%, so the fault frequency will Synchronous speed turn around the 6 Hz. Regarding the simulation of LTOs effects, the mechanical equations are edited by adding a sinusoidal component to the resistant torque. However, the additional component has a convenient frequency and amplitude with the desired study. Thus, the resistant torque will have the form described in Eq. (2). In order to study the LTOs and BRBs interactions, the LTOs frequency is adjusted to 5 Hz to coincide with the BRB fault frequency, and fits the study aims to separate the two phenomena indications. In the steady state, a resulted phase-modulating signal due to LTOs will be present with an amplitude of a 3% of the fundamental current max value, a frequency of 5 Hz and a calculated factor of β = 0.3. 4.3. Study results 4.3.1. Healthy machine 4.3.1.1. Healthy machine with static torque. The torque is set with a constant value of around 10 N.m. The results in Figs. 7 and 8 show clearly the absence of any sign of fault or abnormal behaviour at the required frequencies (weather in time or spectral curves). In contrast, components at low frequencies may appear with small amplitudes due to the misalignment and imperfection of the system shaft. 4.3.1.2. Healthy machine with LTOs. LTOs are created in the machine’s rotor shaft as a sinusoidal resistant torque in the form of Tresist + Tr cos(ωr t) by adjusting the low frequency voltage generator at the required amplitude and frequency to feed the powder break load. The frequency of the oscillating torque is chosen to coincide with the related one of the BRB fault, which suitably accord to our study aims. The LTOs amplitude is chosen to be 40% of the total resistant torque. According to Fig. 10 the presence of the LTOs can be observed from the additional component at frequency fr in iqpos signature. Furthermore, it appears in iqpos with a higher amplitude than the one in Ia spectrum (Fig. 9) with a very small indication inidpos which can be neglected. Therefrom, the modulating signal due to torque oscillations is successfully demodulated from the fundamental (frequency of 50 Hz) and validate the theoretical study of Section 3.1.2. Therefrom, the component appearance over iqpos signature can be considered as a strong LTOs indicator. 4.3.2. Faulty machine As it is already mentioned, the term faulty is referred to the BRB incidence. 4.3.2.1. Broken rotor bars with static load torque. In this section, only the BRBs is considered. The torque is set with a constant value around 10 N.m. According to Fig. 11, the two sidebands around the fundamental represent the BRB effect. However the information provided from idpos signature in Fig. 12. show clearly the √ presence of the BRBs at its proper frequency fs , with a higher amplitude comparing with the one in Ia spectrum ( 6 theoretically). Whereas, iqpos shows nothing nearby the supposed fault frequency (around 6 Hz). The experimental study matches with the simulation and validates the theoretical part by extracting the amplitude modulating signal of the BRB fault. Therefrom, idpos signature can be considered as a powerful BRB fault indicator for the fault detection process.

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Fig. 7. Stator current of a healthy machine with static torque.

Fig. 8. Positive sequence currents i dpos and i qpos , healthy machine.

4.3.2.2. Broken rotor bars with oscillating load torque. In this section, the simultaneous presence of the BRBs and LTOs at adjacent frequencies with the signatures separation results are presented. As a consequence of the broken rotor bar fault incidence, an amplitude modulating signal is produced, appearing as sidebands at the fault frequency around the fundamental spectrum. On the other hand, the LTOs at an adjacent frequency as the BRBs fault cause a phase modulating signal appearing as the same signs as Fig. 13 shows. According to Fig. 14, the appearance of the same signature in i d pos and i q pos spectrums proves the existence of the two incidences simultaneously at the same frequency ( f s = fr ). Fig. 13 shows how the classical FFT spectrum is limited in such case. The simulation and practical results in Fig. 14 show how the proposed technique is adequate for demodulation and the two signatures separation process. A global chart of the proposed approach has been represented in Fig. 15.

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Fig. 9. Line current of the phase a with a load torque oscillations (10 Nm, 1400 rpm, LTOs 5 Hz) time and frequency domains.

Fig. 10. Positive sequence currents i d pos and i q pos in the presence of the LTOs (10 Nm, 1400 rpm, LTOs 5 Hz).

5. Conclusion This paper presents a technique of eliminating one of the root potential BRBs false positive indications that could be made by the low frequency LTOs. A synchronous reference frame of the fundamental current is used to discern the two phenomena effects. However, it consists of the projection of the affected machine’s stator current vector over two rotating coordinates (same and inverse angular velocity as the current’s fundamental frequency ω). The theoretical study shows that the BRBs and the LTOs impacts appear independently in the positive sequence coordinates components of the current ( idpos and iqpos respectively). Furthermore, it allows the demodulation of the amplitude modulating signal due to the BRBs and the phase modulating one due to the LTOs from the fundamental

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Fig. 11. Line current of the phase a with a one Broken rotor bar in time and frequency domains. (10 Nm, 1400 rpm 1 BRB).

Fig. 12. Positive sequence currents i d pos and i q pos in the presence of the one Broken bar (10 Nm 1400 rpm).

separately (with idpos and iqpos respectively). And, the theoretical study is validated through the experimental study results section. On the other hand, the negative sequence components is still limited for such use. This technique brings together many advantages comparing to the existing works in the literature, such as; its independence on the machine’s parameters and the preliminary knowledge of the spatial position of the fault or the LTOs characteristics, since it only requires the currents to perform the whole process. In addition to its simplicity, the frequencies are distinguished directly from the direct and quadrature components spectrums, which gives more significant indications (frequency and amplitude) during the machine condition monitoring. Therefore, both of the

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Fig. 13. Line current of the phase a with a one Broken rotor bar and LTOs in time and frequency domains (Ia 9.6 Nm, 1400 rpm, LTOs 5 Hz and 1BRB).

Fig. 14. Positive sequence currents i d pos and i q pos in the presence of the one Broken bar and LTOs (9.6 Nm, 1400 rpm, LTOs 5 Hz and 1BRB).

resulted signatures (idpos and iqpos ) are suitable to use as powerful patterns of the BRBs and LTOs and to distinguish the false indication. Finally, the proposed policy can be considered as a decent tool that allows discerning the BRBs and LTOs signatures interference and can be used as an optimal fault detection instrument to achieve an optimal accuracy of diagnostics.

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Fig. 15. BRB Fault and LTOs detection and separation chart.

Table 1 Motor parameters. Rotor resistance Rr Stator resistance Rs Iron resistance R f e Stator Inductance L s Rotor Inductance Lr Mutual Inductance M Moment of inertia J coefficient of friction fr Number of rotor bars Number of notches

3.57  5.43  1452.15  0.40 0.65 0.5 0.00561 Kg.m2 0.00488 N.m.s/rad 28 36

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