Non-Invasive Detection of Rotor Short-Circuit Fault in Synchronous ...

IEEE TRANSACTIONS ON MAGNETICS, VOL. 52, NO. 7, JULY 2016

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Non-Invasive Detection of Rotor Short-Circuit Fault in Synchronous Machines by Analysis of Stray Magnetic Field and Frame Vibrations Mauricio Cuevas1,2, Raphaël Romary1 , Jean-Philippe Lecointe1 , and Thierry Jacq2 1 Laboratoire

Systèmes Electrotechniques et Environnement, Artois University, Béthune F-62400, France 2 Électricité de France Research and Development, Clamart F-92141, France

This paper concerns a coupled analysis of the stray magnetic field and the external housing vibration of a synchronous machine to detect rotor short-circuit faults. Indeed, in addition to the possibility to measure these parameters with non-invasive equipment, these two measures depend on the air-gap flux density that is directly impacted by the short circuits of any nature. Hence, correlating these two quantities, it is achievable to confirm or discard an eventual motor fault. This method allows both to develop an analysis of non-invasive manner and to establish the magnetic state of a synchronous generator in normal operation. The experimental survey of stray magnetic field and housing vibration spectrum is shown as a promising alternative at low cost and easy to implement and to determine, for instance, rotor turn-to-turn winding faults. Faulty and healthy signatures are drawn from the measured spectra to determine a degree of healthy state of the synchronous machine. Index Terms— Diagnosis faults, magnetic signature, spectral analysis, synchronous generator.

I. I NTRODUCTION

D

ESPITE numerous technological innovations carried out by electric power companies, it still remains to improve the availability of generation parks of nuclear, thermal, and hydraulic plants. Optimization of the production capacity requires greater reliability. It is well known that the efficiency of the production plant is strongly linked to the failures of their generators, especially for turbo generators and salientpole synchronous machines. In addition, to reduce the machine breakdown probability, an optimized maintenance plan and a fitted monitoring have to be established. Hence, a constant monitoring of generator conditions is essential for an optimal production [1]. Nevertheless, among the most developed techniques, interruption of production or introduction of invasive sensors is required. The first challenge of this paper is to diagnose machines during their operation by a non-invasive way and respecting safety standards. Non-intrusive diagnosis must guarantee a simple implementation of measuring devices located around the machine. Among the most used parameters that fulfill these requests, external magnetic field and vibration of the housing frame appear promising. Statistics show that both the stator and rotor winding short circuits can cause irreversible damage to the machine [2]. Therefore, as soon as a short circuit appears, the electromagnetic flux content is modified in a different manner in function of the magnetic and mechanical parameters of the machine. Section II presents a description of electromagnetic models of the healthy machine and explanations of the stray field [3], [4] and the Maxwell forces. In Section III, a model

Manuscript received November 6, 2015; revised December 22, 2015; accepted December 30, 2015. Date of publication January 12, 2016; date of current version June 22, 2016. Corresponding author: M. Cuevas (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2016.2514406

Fig. 1.

Slotting scheme of a rotor salient-pole synchronous machine.

of rotor turn-to-turn winding faults in a synchronous machine is given. In Section IV, some experimental results obtained are shown in order to verify the theoretical model described and to define the spectral lines that are sensitive to a short-circuit fault. Section V provides the discussion. II. H EALTHY M ACHINE M ODELING The basis of this study relies on the air-gap flux density determination. Assuming that the relative permeability of the magnetic circuit is much larger than the unit and multiplying the air-gap permeance P per surface unit by the equivalent magnetomotive force (m.m.f.) ε of the machine [5], the air-gap flux density is given by b = P · ε.

(1)

A. Air-Gap Permeance Slots in an electrical machine are represented using a simple scheme of rectangular teeth, as shown in Fig. 1. Therefore, supposing that magnetic field lines are radial, the air-gap permeance is stated in P=

+∞ 

+∞ 

Pˆks kr cos[(ks Ns + 2kr ) pα s − 2kr pθ ]

(2)

ks =−∞ kr =−∞

where Pˆks kr is a coefficient that depends on the machine geometry, and ks and kr are the slotting harmonics resulting from Fourier series. Ns and p are, respectively, the stator slots

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IEEE TRANSACTIONS ON MAGNETICS, VOL. 52, NO. 7, JULY 2016

Fig. 3. (a) Scheme of stray magnetic lines around of the machine. (b) Four-hundred-turn search coil.

Fig. 2. εs and εr m.m.f. created by healthy stator and rotor windings ( p = 2 and Ns = 18).

per pole pair and pair pole number. Rotor space-angle θ and angular position of any point in the air-gap α s are related to a stator reference d s . B. Magnetomotive Forces For a healthy machine, the equivalent m.m.f. ε pattern depends on the coil distribution both into the stator and rotor slots (Fig. 1). Fig. 2 shows the m.m.f. generated by the stator (εs ) and rotor (εr ) windings in blue and green lines, respectively. Based on these patterns, two analytical expressions are formulated for stator (3) and rotor (4) healthy windings, where Ash s and Arhr are the corresponding Fourier series factors; i qs is the phase q current of the three-phase balanced stator current system and I r is the dc current εs =

3 +∞  

i qs Ash s cos{h s [ pα s − (q − 1)]}

(3)

q=1 h s = 1

h s odd +∞ 

εr =

I r Arhr cos{ p[2h r + 1][α s − θ ]}.

(4)

h r =2ν+1,ν=1

C. Equivalent Air-Gap Flux Density According to (1), bs and br air-gap flux densities corresponding to the stator and the rotor are computed multiplying (3) and (4) by (2) bs =

+∞ 

+∞ 

+∞ 

h s = 6κ + 1 ks =−∞ kr =−∞ κ=0



b = r

+∞ 

+∞ 

+∞ 

h r = 2ν + 1 ks =−∞ kr =−∞ ν=1



× cos

 (5)

Bˆ hr r ,ks ,kr

 [h r + 2kr ]ωt . −[h r + ks Ns + 2kr ] pα s

b = b s + br .

(7)

D. Stray Magnetic Field The simplicity and convenience of the stray field analysis stem from the fact of using an ordinary search coil [6], which is placed against the external housing frame (Fig. 3). The stray field radiated by an electric machine can be split up in two components. Indeed, a component comes from the winding heads and the other one originates from the air-gap flux density. E. Vibrational Content Vibration signature depends on the air-gap flux density [7]: the radial component of the flux density creates a force FM acting between the stator and the rotor, which is transmitted to the machine external housing. This force is given by FM = [b]2 /2μ0

(8)

where μ0 is the vacuum permeability. Using (7), it is achievable to extract the frequencies from the non-stationary force FM(ν) , which produces outstanding vibrations [8]. The general expression of a force harmonic component is Fˆ cos(K ωt − Mα s − ϕ). For a healthy machine, this force is characterized by three pulsations [9] f 1 = 2 f Kβ ;

f 2 = f [Kβ +Kβ  ];

f 3 = f [Kβ − Kβ  ]

(9)

β

Bˆ hs s ,ks ,kr

[1 + 2kr ]ωt × cos −[h s + ks Ns + 2kr ] pα s

harmonic amplitudes corresponding to the stator and the rotor. ω is the frequency pulsation of the power grid. Incidentally, the factors multiplied by ωt are known as rank frequencies K , and the factors multiplied by α s are known as mode-wave or pole pair number M. By superposition, the equivalent flux density is given by

(6)

Here, Bˆ hs s ,ks ,kr and Bˆ hr r ,ks ,kr , which depend on three-phase current amplitudes Pˆks kr , Ash s , and Arhr are the flux density

where Kβ and Kβ  are the β and rank frequencies of the flux density with β  = β. The mode number M F corresponds to the number of attraction points of the force. A force, to be disturbing, must have a frequency in the audible frequency range and a M F mode lower than 8. III. FAULTY M ACHINE M ODELING Modeling the rotor turn-to-turn fault in salient-pole machines requires us to set the following assumptions. 1) I r is perfectly continuous before and during the fault. 2) To disengage the short-circuit phenomenon of the healthy coil, two currents are distinguished (Fig. 4): 1) a current of the same amplitude as I r but in opposite r direction [5] and 2) some harmonic currents induced i cc s by the stator flux density b .

CUEVAS et al.: NON-INVASIVE DETECTION OF ROTOR SHORT-CIRCUIT FAULT IN SYNCHRONOUS MACHINES

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TABLE I D IAGNOSTIC F REQUENCIES FOR 4-P OLE S YNCHRONOUS M ACHINE

Fig. 4. (a) Rotor turn-to-turn fault model in a salient-pole synchronous machine. (b) Healthy coil. (c) Short-circuited coil.

Fig. 6. Fig. 5.

m.m.f. pattern generated by a rotor turn-to-turn fault.

A. Magnetomotive Force of Turn-to-Turn Fault In the reference related to the stator d s , an additional r , generated by a rotor short-circuit fault, has the m.m.f. εcc pattern shown in Fig. 5 and the Fourier series given in (10) where n rcc is the percent of turns by the pole pair that is short circuited   +∞  hr π −2n rcc I r r εcc = sin (10) cos{h r (α s − θ )}. πh r 2p

Healthy e.m.f. spectrum induced in a search coil in decibel scale.

⎫ fr1 = 2 [h r + 2kr ] f ⎬

Healthy fr2 = h r + h  r + 2kr + 2k  r f (13) rotor 

⎭ fr3 = h r − h  r + 2kr − 2k  r f ⎫ f cc1 = 2 [1 − h s + h r / p − ks Ns + 2kr ] f ⎪  ⎪ ⎪ ⎪ 2 − h s − h  s + (h r + h  r )/ p Rotor ⎬

 f f cc2 =   short-circuit + k + 2(k + k ) − k N s r  ⎪ s s r ⎪ Fault. ⎪ −h s + h s + (h r − h  r )/ p ⎪

f cc3 = f⎭   − ks − k s Ns + 2(k r − k r ) (14)

h r =1

IV. E XPERIMENTAL R ESULTS B. Flux Density in Case of Turn-to-Turn Fault r in the part of the coil that is short If the induced current i cc circuited is neglected and according to (1), the flux density r ) is given by generated by a rotor short-circuit fault (bcc r bcc =

+∞ +∞  +∞  

  r r r s Bˆ cc sin K cc ωt − Mcc α

(11)

h s = 1 h r =0 kr =−∞ h s odd r = 1 − h + h / p − k N + 2k and M r = h / p + where K cc s r s s r r cc r depends on Pˆ r r ks Ns + 2kr ; Bˆ cc ks kr , I and n cc .

C. Equivalent Air-Gap Flux Density of Faulty Machine Following the superposition principle, as in Section II, the equivalent air-gap flux density with a rotor turn-to-turn fault is the addition of (7) and (11). Hence, an alternator connected to the local power grid is characterized by the frequencies of both healthy and faulty machines (Table I). D. Vibrational Content in Faulty Machine From Table I and using the same reasoning as in Section II-E, nine faulty frequencies are found and given by ⎫ f s1 = 2[1 + 2kr ] f ⎬ Healthy f s2 = [2 + 2kr + 2k  r ] f (12) stator ⎭  fs3 = [2kr − 2k r ] f

A. Salient-Pole Synchronous Machine A 4-pole synchronous alternator 50 Hz–400 V–7.5 kVA with 36 slots in the stator is connected to the local power grid. This machine is coupled to an induction motor that provides the mechanical power on the motor shaft. To simulate a turn-to-turn fault, the rotor winding has been modified to create a 12.5% rotor short-circuit. Due to Faraday’s law, an electromotive force (e.m.f.), which is a reliable image of the external magnetic field, is induced in a coil sensor placed against the external housing. B. Case of Healthy Machine A representation of air-gap flux density is shown in Fig. 6 at low frequency, up to 1.6 kHz. Crossing marks are delineated to point out the most representative frequencies arising for a healthy machine (7). Spectral lines at low frequency are gathered selecting the combinations of kr and h r [in (5) and (6)] close to zero. For instance, 150 Hz is found with kr = 1 and h r = 1. On the other hand, ks influences only on the mode wave of the equivalent air-gap flux density for a healthy machine. At the same time, with an accelerometer that is also placed against the external housing frame, vibration measurements are recorded and shown in Fig. 7. As described in Section II-E, peak amplitudes appear every 25 Hz.

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IEEE TRANSACTIONS ON MAGNETICS, VOL. 52, NO. 7, JULY 2016

Fig. 7.

Healthy vibrational spectrum of the machine frame.

Fig. 8.

Faulty e.m.f. spectrum induced in a search coil in decibel scale.

V. D ISCUSSION The flux density spectrum lines proper of the rotor turn-to-turn fault described by (−h s + (h r / p) − ks Ns ) f = 0 have suffered significant variations. Indeed, these last lines have increased, in some cases, more than 30 dB compared with the same lines as in Fig. 6. However, the slotting lines, described by (1+2kr ) f and (h r +2kr ) f related to the healthy machine, did not vary beyond ±8 dB. Therefore, the latter frequencies are less susceptible to the present rotor failure for the external field method. Moreover, even if there are amplitude changes every 25 Hz in the vibrational spectrum, the most significant modification appears at low frequencies, especially at 225 Hz, but the healthy frequencies remain unchanged. This study allowed us to distinguish the signature of a healthy or a faulty machine by two different methods. The great advantage of the method, in addition of being totally non-invasive, relies on the simplicity of the algorithm that can be implemented into an embedded cell situated against the machine frame. ACKNOWLEDGMENT This work was supported in part by the Master of Education in Elementary Education Program through the Project entitled French National Technological Research Cluster on Electrical Machine Efficiency Increase and in part by the Région Nord Pas-de-Calais, France, and the European Funds, for the Program Electricité de France. R EFERENCES

Fig. 9.

Faulty vibrational spectrum of the machine frame.

C. Case of Rotor Turn-to-Turn Fault The more significant stray magnetic field amplitude variations between a healthy machine and a 12.5% rotor turn-to-turn fault case are highlighted with black arrows in Fig. 8. According to Fig. 6, both the rotor and stator slotting lines change within 2–32 dB compared with the same lines of the healthy machine. Indeed, the strongest variations, occurring at 25, 75, 125, 175, 250, 275, 575, and 950 Hz, increase up to 32 dB. Nevertheless, for the higher frequencies, namely, 1150, 1350, and 1450 Hz, decreasing amplitudes of 8, 10, and 11 dB are denoted, respectively. Fig. 9 shows the vibration spectrum for the faulty machine, putting emphasis on the most significant amplitude variations relative to Fig. 7. Blue down arrows point out these last frequency lines. These lines are met using the different index number combinations in (12)–(14), e.g., 225, 175, and 25 Hz, which increase between 0.15 and 1.1 m/s2 compared with Fig. 7. The lines of 225 and 175 Hz, both with M F < 4, result from the coupling of 200 Hz, which is a slotting line in the air-gap flux density, and 25 Hz lines, which is among the most modified frequencies for the faulty spectrum.

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