Glossary of Symbols

This paper presents an original non-invasive procedure for the diagnosis of electromagnetic devices, as well as AC electrical rotating machines using two external flux coil sensors that measure the external magnetic field in the machines’ vicinity. The diagnosis exploits the signal delivered by the two sensors placed in particular positions. Contrary to classical methods using only one sensor, the presented method does not require any knowledge of a presumed machine’s healthy former state. On the other hand, the loading operating is not a disturbing factor but it is used to the fault discrimination. In order to present this procedure, an internal stator inter-turn short-circuit fault is considered as well.


Introduction
The productivity, reliability and safety of installations using electrical rotating machines are directly influenced by the "healthy" state of these electromechanical converters. Generally, these requirements concerning the operating quality are achieved thanks to an adapted maintenance policy which is often associated with monitoring systems that measure specific parameters like noise, vibrations, temperature or currents [1,2]. The implementation of such systems is expensive and can be justified only in critical cases (power plants). In order to anticipate the failure of a machine, that avoids its replacement or repair during unscheduled periods of maintenance, the machine user needs inexpensive, reliable and easy to implement methods. This aspect justifies the scientific interest to carry out investigations relating to the diagnosis of electrical machines.
Previous works in the field of electrical machine diagnosis are multiple and generally oriented towards the research of specific signatures able to identify or to predict some kind of failure [3][4][5][6][7][8][9]. These studies essentially concern the supply current analysis and, more particularly, some harmonic components of the same. Unfortunately, in practical cases, electrical machines are not equipped with convenient systems able to measure and to analyze the current on line. Consequently, noninvasive methods, relating in particular to the exploitation of the data contained in the external magnetic field, can be an alternative to the traditional ones. Another aspect, which characterizes the exploitation of the external magnetic field, concerns the possibility of acquiring information about the failure localization. The studies performed in this field for various kind of machines [10][11][12][13][14], have brought to the fore the specific signatures corresponding to different kind of defects (inter-turn short-circuit in the stator or in the rotor windings, rotor broken bars, eccentricity, etc).
Methods which use the external magnetic field of the machine are generally based on the comparison between a reference spectrum corresponding to a healthy state and a given one measured during the machine operating. In some cases, when the fault leads to generate new spectral lines (sideband) then the analysis may be performed without comparison with the healthy signature, but in other cases sensitive indicators may exist even in the healthy machine. Then, their variations, often their increase, give information on the presence of a defect. Moreover, the machine loading operatings, can disturb the diagnosis because it induces other harmonics. These harmonics appear as consequence of the load and they can be confusing with a faulty signature. An additional difficulty is that the presumed healthy state is practically never known before the failure because the machine user has not recorded the corresponding features which characterize the healthy state.
In order to free oneself from these analysis problems, a new noninvasive diagnosis method, which does not require any knowledge of a presumed healthy former state of the machine, is suggested. This method exploits the external magnetic field and more particularly its space variations measured using two flux sensors. Its main interest consists in the fact that the loading operating does not constitute any more, as previously evoked, a perturbing factor but rather it corresponds to an essential state allowing failure discrimination. The procedure presented concerns the detection of a stator inter-turn short-circuit on Salient Synchronous and Induction Machines which will be denoted respectively SSM and IM. The basis of this methodology is an analytical study followed by measurements in both kinds of machines. As a conclusion, the limits of this method are analyzed and commented.

Choice of the Sensor
As the method is based on the analysis of the external magnetic field existing in the vicinity of a rotating electrical machine, sensors for magnetic field measurement are used. They can be classified into three categories: based on the Hall Effect, those that exploit the magneto-resistive phenomenon, and those which used specific coils. As the behavior of the external magnetic field harmonic components tied to the slotting effect are considered, the corresponding frequencies are in a medium frequency range going from the hundredth to the thousandth of hertz. Consequently, a coil sensor is more convenient because it induces electromotive force (emf) and this derivative effect amplifies the medium frequencies. The used sensor is circular of S area    Figure 1(a) presents the sensor symbol. Figure 1(b) gives the sensor frequency response, especially the modulus z and the phase of the sensor impedance Z  measured with an impedance analyzer. It can be observed that a resonance appears at 559, 7 kHz . This resonance is tied to the inter-turn capacitive effect combined with the inductive effects. The considered frequency range is lower (some kHz ) compared to resonance frequency, meaning that this sensor is well suited for the intended application. The drawback of a coil sensor is that it does not give localized information but an average value over the sensor area, so in order to have the most localized information possible, the sensor has to be small compared to the machine size. However, use of a small sensor leads to a decrease of the sensitivity, which can be compensated by increasing c n , but a high number c n decreases the resonance frequency. Consequently a compromise has to be made in the choice of sensors.

Principle of the Method
The use of the proposed diagnosis method requires at least two sensors, located symmetrically about the machine axis (180° spatially shifted) and placed close to the motor frame between the end bells, roughly in the middle of the machine. The principle consists in the comparison of the delivered sensor signals according whether the machine runs under no-load or loading conditions. The analysis concerns the magnitude of the specific harmonics of the induced coil emf. One will be interested in the magnitude of the third rank harmonic for SSM and the rotor slotting harmonics for IM. The principle of the method can be described considering a load increase:  if the harmonic amplitudes measured on both sides of a machine vary in the same direction, then the stator winding does not present an inter-turn short circuit fault,  if they vary in opposed directions, then this particular failure can be suspected.
Let us point out that the amplitude of the measured harmonics strongly depends on the fault severity and the location of the sensor in relation to the machine.

Considerations on the Machine External Field
The stray external magnetic field results from the combination of its axial and transverse components. The axial field is in a plane that contains the machine axis; it is generated by the end overhang effects. The transverse field is located in a plane perpendicular to the machine axis. It is an image of the air-gap flux density b which is attenuated by the stator magnetic circuit (sheets package with length L) and by the external machine frame. On the other hand, the eddy currents introduce a phase change which differs according to the considered component. It is however possible to measure mainly the transversal field by choosing an adequate position of the sensor such as the effects of the axial field are minimized. This position corresponds roughly to L/2 as shown in Figure 2. In the following, from a theoretical point of view, only the transverse field is considered. In order to identify its harmonic components, the b air-gap flux density, which results from the product between the  air-gap permeance and the  resulting magnetomotive force (mmf), has to be determined.

Air-Gap Flux Density Modeling
To determine b , the following assumptions are formulated: the iron permeability is supposed to be infinite, -the p pole pair, three-phase stator winding, made up of diametrical opening coils, is energized by a balanced three-phase sinusoidal currents system s q i  

Air-Gap Resulting Magnetomotive Force (mmf)
The s  mmf generated by a healthy stator relatively to s d can be expressed as:  which represents the mmf generated by the rotor but defined relative to s d . Consequently,  is given by:

Air-Gap Permeance
The  air-gap permeance expressions, different according to the kind of machine, defined relative to s d , are deduced from the general Equation (3) [15]: This relationship concerns an IM taking into account the interaction between the stator and the rotor teeth [16]. s N and r N are the stator and rotor per pole pair tooth numbers.  s r k k is a coefficient which depends on the ranks s k and r k and the air-gap geometry. Let s denote the slip,  is given by: For the SSM, it suffices to adapt the parameters taking into account that 2 r N  and 0 s  .

Air-Gap Flux Density
, the calculus developments lead to define b in the reference frame related to s d as follows: , , An elementary component , is characterized by two parameters: K and H . When only one indicator appears in the variable, it corresponds to K . A flux density component is thus characterized by its pulsation K and by its pole pair number H .

Transverse External Magnetic Field
The transverse external flux density is deduced from b through an attenuation coefficient as previously mentioned. This coefficient, denoted ,  (5) and (6), at comes: , with: and:

Measurement
The measurements are performed with a flux sensor presented in section 2.1 placed in 0 s    . The K component of the flux linked by the coil sensor results from: The result of this integration depends of the sensor parameters   , c n S , but also H and x .
Introducing these parameters in the coefficient x Among the components which constitute x K  only few of them, relative to low pole number (low H ), have a significant contribution [18]. The other components will be absorbed by the ferromagnetic parts of the machine. The x e delivered by the sensor is given by: with:

Stator Inter-Turn Short-Circuit Modeling
Let us consider the 2 p  , three-phase stator winding given in   In this way, the resulting air-gap flux density b  can be expressed as: b is given by Equation (5) Figure 6(a). The Figure   6(b) gives the mmf generated by the faulty turns.  leads to determine this quantity is identical to that formulated in Section 3.

Theoretical Developments
Let us consider a SSM where the rotor winding is energized by a J DC current. One assumes that r d is confounded with a north rotor pole axis. . These properties make difficult the diagnosis by analysis of the changes in the amplitudes of the measured components. In the following the properties relating to the dissymmetry generated by the fault will be exploited.

Presentation of the Proposed Method
The measurements are carried out in two diametrically opposed positions: position 1 in The respect of these constraints leads to consider the spectral line at  angular frequency   1 K  of magnitude 1,1 b . However, this component corresponds to the fundamental of the air-gap flux density which generates the main energetic effects: with H different from 1. It results that 1 b will be not very sensitive to the components defined for 1 H  . Consequently, the analysis will be focused on the spectral lines related to 3 K  . If one considers a four pole machine   2 p  , the flux density components that contribute to this harmonic are defined as follows:  To solve this problem, the method can be extended thanks to the exploitation of a test in load. The method can be refined as following.
 Under healthy conditions: When the machine is loaded, the stator current increases but, at given supply voltage, the air-gap flux density stays practically identical to that obtained at no-load. As the external elements responsible of the attenuation act in the same way in positions 1 and 2 for the no-load and for the load tests, the amplitudes (1) keep similar values or at least evolve in the same way when the machine is loaded.
 Under faulty conditions: In loading conditions, 3 x sc b varies taking into account the model chosen to characterize the short-circuit (the loading current contributes to the definition of the fictitious current which circulates in the damaged coil). Consequently, according to (23) and (24), the magnitude of the component at 3 angular frequency in positions 1 and 2 will evolve in opposed directions. The variations of the lines at 3 are thus an indicator of defect. The advantage of the method is that it does not require any knowledge of a healthy state to detect the fault.

Experimental Tests
The tests are carried out on a SSM characterized by: 7.5 , 50 , 2, 230 / 400 , 18 This machine has been rewound so that the terminals of the different stator elementary sections are extracted from the winding and are brought back to a connector block which is fixed above the machine as indicated in Figure 7. So it is possible to produce short-circuits between elementary coils.
The tests carried out when the SSM is connected to the grid, consist in measuring and analyzing the emf delivered by the sensors in order to validate the suggested procedure when an elementary coil is short-circuited (what corresponds to 16, 6 % of the whole winding of a phase). In order to avoid damaging the winding, the short-circuit current is limited by an external resistance R .    The measured spectra under loading conditions for the healthy machine and the faulty one are given respectively in Figures 9(a,b). It can be observed in Figure 9(a) that the differences between the amplitudes measured in positions 1 and 2 for the lines at 50 Hz and 150 Hz still exist under loading conditions. The difference is relatively important for the amplitudes of the lines related to the fundamental ( 50 Hz ). Figure 9(b), relating to the faulty machine, shows that a small difference characterizes the amplitudes of the lines at 150 Hz for the both positions. Consequently, the analysis of the difference between the two positions is not enough to detect the fault because it depends on a high number of parameters: inaccurate position of the sensor, value of the short-circuit current, number of short-circuit turns, state of load, machine's design, etc.. In order to minimize these effects, the suggested method consists in combining the tests at no-load and in load operating conditions.    For the faulty machine the variations of the 150 Hz harmonic are given in Figures 11(a,b). It can be seen that the magnitudes in the both positions vary in an opposite way when the machine is loaded. The results are in accordance with the theory, what validates the diagnosis procedure. This procedure has been also test on an interior permanent magnet synchronous machine. The same results were found.  This method is thus applicable to IMs, confirming the universal quality of this diagnosis method.

Conclusions
The proposed new diagnosis procedure is reliable, inexpensive and simple to implement. This noninvasive method uses two flux coil sensors diametrically located to measure the external magnetic field. This technique eliminates the principal disadvantage of other methods which use only one coil sensor that needs to compare the signature relative this one corresponding to a healthy prerequisite known state. The proposed method presented does not require the knowledge of the healthy signature.
It is based on comparison that concerns the state at no-load and load operations.
Actually, this diagnosis procedure can be applied independently if asynchronous or synchronous machine are considered, on condition to choice the suitable spectral component of the observed external magnetic field. This constitutes in our opinion, from an industrial point of view, a considerable added-value.
Practically, all faults can be modeled by a balanced three-phase system to which is added a single-phase system which takes into account the fault. This single-phase system introduces an imbalance on the air-gap magnetic field which is at the origin of the suggested diagnosis procedure. For this reason, this method has been qualified as universal. During the development, implicitly, the need to consider a machine which comprises saliencies on the rotor seems to be a condition in order to apply this method. Studies are at the moment in progress to analyze the possibility of adapting this method for machines with smooth rotor as, for example, synchronous machines with permanent magnets on the rotor surface. Another way of investigations concerns the 2 poles machines.