energies

Article
Procedure for Detection of Stator Inter-Turn Short Circuit in AC
Machines Measuring the External Magnetic Field †
Remus Pusca 1, *, Raphael Romary 1 , Ezzeddine Touti 2,3 , Petru Livinti 4 , Ilie Nuca 5 and Adrian Ceban 1

1 Laboratory of Electrotechnical and Environmental Systems, University of Artois, EA 4025 LSEE,

F-62400 Béthune, France; raphael.romary@univ-artois.fr (R.R.); apceban@gmail.com (A.C.)
2 Department of Electrical Engineering, College of Engineering, University of Northern
Border, Arar 1321, Saudi Arabia; touti.these09@gmail.com
3 Department of Electrical Engineering, University of Tunis, Tunis 1008, Tunisia
4 Department of Electrical Engineering, Faculty of Engineering, University Vasile Alecsandri of Bacau,
600115 Bacau, Romania; livinti_petru@yahoo.com
5 Department of Electrical Engineering, Technical University of Moldova, MD-2004 Chisinau, Moldova;
nuca_ilie@yahoo.com
* Correspondence: remus.pusca@univ-artois.fr
† This paper is an extended version of our paper published in 2012 XXth International Conference on Electrical
Machines, Marseille, France, 2–5 September 2012; pp. 1637–1642.

Abstract: This paper presents a non-invasive procedure to detect inter-turn short circuit faults in the
stator windings of AC electrical machines. It proposes the use of the stray external magnetic field
measured in the vicinity of the machine to determine stator faults. The originality introduced by this
procedure is the analysis method presented in the paper, which when compared to usual diagnosis





 methods, does not require any data on the healthy state of the machine. The procedure uses the
Citation: Pusca, R.; Romary, R.;
magnetic unbalance created by the rotor poles and the load variation in faulty cases. The presented
Touti, E.; Livinti, P.; Nuca, I.; Ceban, method can be applied to induction and synchronous machines used as a motor or generator. It is
A. Procedure for Detection of Stator based on the variation of sensitive spectral lines obtained from the external magnetic field when the
Inter-Turn Short Circuit in AC load changes. Analytical relationships are developed in the paper to justify the proposed method
Machines Measuring the External and to explain the physical phenomenon. To illustrate these theoretical considerations, practical
Magnetic Field . Energies 2021, 14, experiments are also presented.
1132. https://doi.org/10.3390/
en14041132 Keywords: AC machines; magnetic field; non-invasive fault diagnosis; spectral analysis

Academic Editor: Anouar Belahcen

Received: 25 January 2021

1. Introduction
Accepted: 17 February 2021
Published: 20 February 2021 In recent decades the reliability and the operational safety of electrical machines
become an essential issue, so many research studies are focused on their monitoring, which
Publisher’s Note: MDPI stays neutral
is a crucial phase to prevent severe unexpected failure [1]. For that, the development
with regard to jurisdictional claims in of acquisition, analysis, and decision techniques are necessary to ensure the detection
published maps and institutional affil- and diagnosis of electrical machines. The success of these techniques requires a good
iations. knowledge of the machine and its behavior in the presence of an internal fault. Among all
the diagnosis methods used for rotating electrical machines, one can find:
• methods of appreciation, including techniques that use artificial intelligence [2,3];
• methods for the identification and estimation of physical parameters of the ma-
Copyright: © 2021 by the authors. chine [4];
Licensee MDPI, Basel, Switzerland. • methods based on modeling of signals that analyze the time variation and the spectral
This article is an open access article content of different physical quantities. The work presented in this paper concerns
distributed under the terms and that kind of analysis.
conditions of the Creative Commons
For detection of electrical and mechanical faults in electrical AC machines, different
Attribution (CC BY) license (https://
techniques have been tested as those based on spectral analysis of the machine’s vibra-
creativecommons.org/licenses/by/
tions [5] or current signature analysis [6–10]. However, the interpretation of results requires
4.0/).

Energies 2021, 14, 1132. https://doi.org/10.3390/en14041132 https://www.mdpi.com/journal/energies

Energies 2021, 14, 1132 2 of 22

an expertise level even more advanced than the method hereto described, making it dif-
ficult to ensure real democratization of those techniques. Therefore, monitoring systems
are applied only to systems that require high operational safety (for example, in power
generation plants). A reliable diagnosis technique which can detect a failure and avoid
total damage of motors or generators with a simple and non-invasive monitoring system
is of great importance. For this reason, the technology in this field is still in permanent
evolution to develop advanced methods [11–16].
In the 1970s, a new technique using the analysis of external magnetic field was devel-
oped by Penman [17]. It is a non-invasive technique and easy to implement. The drawback
of the latter is the modeling of the magnetic field which depends on the motor housings
with an important shielding effect or on the stator yoke. The determination of the external
magnetic field requires the modeling of the internal sources and the ferromagnetic influence
and the machine conducting materials. The computation of such a problem can be made
using finite element software. However, the accurate modeling requires a large computa-
tional effort [18,19], especially when 3D modeling is performed. Another approach consists
of adapting analytical solutions existing for simple geometries [20] but these methods,
based on simplified geometry and under particular hypotheses, can be hardly exploited
for electrical machines. In [21], a method based on the definition of attenuation coefficients
can be easily combined with an analytical model of the machine.
Fault detection methods using the external magnetic field analysis are based on the
property that any fault changes the magnetic field in the near vicinity of the machine.
Difficulties for modeling and in the interpretation of this variable lead to exploit only
qualitative features of the spectrum, like the appearance of sensitive spectral lines [22].
More usually, studies on the exploitation of the external magnetic field for fault detection
are generally limited to model internal consequences of the fault such as: changes in the
m.m.f. distribution [23], interaction with the slotting effect [24], magnetic of electrical
unbalance [25]. Other researchers prove that the axial field can provide additional informa-
tion [26–28]. In [29], it is shown that the analysis of the stray flux after supply disconnection
can be useful for diagnosis. Advanced exploitation has been developed to provide deeper
information: In [30], a sophisticated inverse problem is used for fault detection. In [31], it is
shown that the external magnetic field can give information concerning the location of the
fault. To improve the diagnostic process, the use of two flux sensors is proposed in [32].
Furthermore, all the diagnosis methods usually require the knowledge of the healthy state
of the machine regardless of the physical variable considered. The fault detection is then
based on the comparison of the signature for a given state with that of the presumed
healthy state by considering an indicator determined from a measurement that is known to
be sensitive to a fault. On the other hand, the machine load can be a disturbing factor for
diagnosis, because it induces several healthy states. A further difficulty lies in the fact that
the healthy state is practically never known until the failure occurs because the user never
records the healthy signature beforehand.
This paper proposes a new solution that exploits the information of the external
magnetic field measured around the machine. Generally, the load is a disturbing factor
for diagnosis methods. However, in the proposed solution, the load variation is used
to improve the diagnosis with the advantage that it does not require the knowledge of
the machine’s healthy state. The detection of a stator fault is based on a comparison
between no-load and load operating conditions. Initially, the analytical modeling of the
stray flux analysis in the presence of the stator inter-turn short circuit is proposed. Then, the
experimental validation for an induction machine (IM) working in a motor and generator
case and a wound smooth rotor synchronous generator are presented. The reliability of
the method has been tested in a self-excited induction generator (SEIG) which makes it
possible to test an unbalanced load case with large frequency slip. The experimental safety
measures that have to be taken to ensure the reliable diagnosis are also presented.
 Energies 2021, 14, x FOR PEER REVIEW 3 of 22
Energies 2021, 14, 1132 3 of 22

2. Analytical Approach for Healthy Machine

2. Analytical Approach for Healthy Machine
The analytical developments concern first a three-phase, p pole pair induction ma-
chine The analytical
with developments
Ns stator concern
slots and Nr rotor first
bars pera pole
three-phase, p pole
pair. In this pair induction
machine machine
with ns turns per
with N s stator slots and Nr rotor bars per pole pair. In this machine with ns turns per pole
pole pair, the stator coils are series connected and supplied by three-phase balanced si-
pair, the stator
nusoidal coils
voltage are frequency
with series connected andfrequency
f (angular supplied by ω).three-phase balanced
For the modeling, sinusoidal
it is assumed
voltage with frequency f (angular frequency ω). For the modeling, it is assumed that the
that the air-gap flux density content b is constant during the load variation and that the
air-gap flux density content b is constant during the load variation and that the considered
considered harmonic components are those generated by i sq sinusoidal no load currents
harmonic components are those generated by isq sinusoidal no load currents of Is0 rms, where
s
qofis the rms, where q isIn
thethe
phase number. In the
theproposed
εs air-gapmodel, the ε air-gap
forcemagneto-
s
I 0 phase number. proposed model, magnetomotive (m.m.f)
generated by the stator winding is multiplied by the λ per area unit air-gapper
motive force (m.m.f) generated by the stator winding is multiplied by the  area unit
permeance
air-gaptakes
(which permeance (whichthe
into account takes into account
slotting effect) tothe slotting
obtain b. effect) to obtain b.

2.1.
2.1. Air-Gap
Air-Gap Permeance
Permeance
To
To determinethe
determine theexpression
expressionofofthe air-gap
the air-gappermeance,
permeance, a specific model
a specific is considered
model as
is considered
presented by Figure 1. In this model defined in [33], the slot shape is considered
as presented by Figure 1. In this model defined in [33], the slot shape is considered rectangular
and the fieldand
rectangular linesthe
crossing the air-gap
field lines crossingaretheradial.
air-gap are radial.

Figure1.1.Geometrical
Figure Geometricalparameters
parametersof
ofthe
themachine
machineused
usedin
inthe
theanalytical
analyticalmodel.
model.

In
Inthis model,Λ
thismodel, kskr is aa permeance
kskr is permeance coefficient
coefficient that
that depends
depends on the slot geometry:

(ks rsdsπrd)sin d )
s r
  4  A sinsin(k
sr ) sin(k r r)
(kr rrd π
Λkskr kskr= 4µ A 0 sr
, , (1)
(1)
0
2k2k
s s 2k2k
r r
where 0  4107 is−7the permeability of the vacuum approximately equal to that of air:
where µ0 = 4π10 is the permeability of the vacuum approximately equal to that of
rds slsd =
air:r / (llses/l(sd l)s, +psls)l,se p/ 5s ,=rdrls/5,  ldrl)r ./(lr + lr ).
ldr /r(lrer =
d d e d e d d e d
In(1)(1)the thecomponent,
component,AA srsr is defined as:
In is defined as:
eM  e
AsrA sr= 4p4p
s rp eM2 + se r
s r
p 2 seer e e, , (2)
(2)
π ee e eM M
where es  e  ps , er  e  pr , e  e  ps  pr .
where es = e + ps , er = e + prM, eM = e + ps + pr .
As the
As the field
field lines
lines never
never join
join the
the bottom
bottom of of the
the slots,
slots, practically,
practically,the
theair-gap
air-gapcan
canbe
be
modeled considering fictitious slots with a depth equal to the fifth of their
modeled considering fictitious slots with a depth equal to the fifth of their opening. With opening. With
that assumption,λcan
thatassumption, can bebedefined
definedas:
as:

+∑∞ Λkskrkskrcoscos [(( ksN

ksN ss  krN r )rp s s pkrN r  r,
 
∞
+
(3)
λ= ∑ ks   kr  
+ krN ) pα − pkrN θ ], (3)
ks=−∞ kr =−∞
where θ represents the angular position of the rotor tooth 1 axis relatively to the stator
where θ represents
referential ds tied tothe
the angular position
phase 1 axis, of the
ks and rotor
kr are tooth 1null,
negative, axisorrelatively to the stator
positive integers, αs is
referential ds tied to the phase 1 axis, ks and kr are negative, null, or positive integers, αs
the angular abscissa of considered point M in the air-gap related to ds, and kskr is a per-
s , and Λ
ismeance
the angular abscissa
coefficient thatofdepends
considered
on thepoint
slotMgeometry.
in the air-gap related to
Considering thed slip kskr isap-
s which a
permeance coefficient that
pears in IM, θ is defined as: depends on the slot geometry. Considering the slip s which
appears in IM, θ is defined as:
θ = (1 − s)ωt/p + θ0. (4)
θ = (1 − s)ωt/p + θ0 . (4)
Energies 2021, 14, 1132 4 of 22

2.2. Healthy Machine m.m.f

In the healthy machine, the m.m.f ε calculated relatively to the stator ds can be ex-
pressed as:
ε = I0s ∑ Ashs cos(ωt − hs pαs ), (5)
hs

where Ashs is a function which depends on the winding coefficient corresponding to the
rank hs defined by: hs = 6k + 1, where k varies between −∞ to +∞.

2.3. Air-Gap Flux Density

The calculus developments lead to define b = εs λ in the reference frame related to ds
as the following:

(1 + krN r (1 − g))ωt
 
b= ∑ b̂hs kskr cos
− p(h + ksN s + krN r ) as + krN r pθ0
s , (6)
hs ,ks,kr

with:
b̂hs kskr = I0s Ashs Λkskr . (7)
After regrouping the components of the same frequency and same polarity, it comes:

b= ∑ bK,H , (8)
K,H

where bK,H is an elementary component of K frequency rank, and H pole pair number
defined as:
bK,H = b̂K,H cos (Kωt − Hαs − ϕK,H ), (9)
and:
K = 1 + krN r (1 − s)

. (10)
H = p(hs + ksN s + krN r )
The frequency rank K only depends on the rotor rank permeance kr. kr = 0 leads to
define the fundamental (K = 1), kr = ±1 leads to the first slotting harmonics.

2.4. Transverse Field

The stray external magnetic field is obtained from leakage flux created by the different
elements of the machine. It is the result of its combination of transverse and axial compo-
nents. The transverse field measured in the plane perpendicular to the machine axis is an
image of the b attenuated by the stator yoke and the axial field located in a plane containing
the axis of the machine and created by the overhang effects of the winding. The attenuation
caused by the external machine frame will not be taken into account. According to the
position of the sensor, the measured field does not come from the same source, and does
not result from the same physical phenomenon. Therefore, the measured signal will be
sensitive to different field components and it will depend on the position of the sensor
around the machine periphery. So, in practice, it is possible to measure mainly the trans-
verse field by choosing an adequate position of the sensor so that the effects of the axial
field are minimal. This position corresponds roughly to the middle of the sheet package.
Figure 2 presents a simplified geometry of the machine with the main geometrical
parameters which appear in the analytical model with a smooth air gap [34].
 Energies 2021, 14, x FOR PEER REVIEW 5 of 22
Energies 2021, 14, 1132 5 of 22
Energies 2021, 14, x FOR PEER REVIEW 5 of 22

Flux coil sensor

Stator
Flux M
B xcoil sensor
x Stator
B M 
Bx x M
bBn
bt M  s   0s
bn sy
bt Rint
 0s   0s ds
sy
Rint 0
Rotor ds
sy
Rext
Rotor
sy
Rext Stator yoke Airgap
(laminations)
Stator yoke Airgap
(laminations)
Figure 2. Geometrical parameters of machine used in the analytical model.

Figure 2.
Figure 2. Geometrical parameters
parameters of
of machine
machine used
used in
in the
the analytical
analytical model.
model.
In the analytical model used to determine the flux density, only the normal
component
In of the traverse field tois determine
considered. theIt flux
takes into consideration thecomponent
attenuation
In the
theanalytical
analytical model
modelused used to determine density,
the flux only the normal
density, only the normal
coefficient
of the C
traverseH related to the stator yoke that influences the magnitude of bK,H component.
field is considered. It takes into consideration the attenuation coefficient
component of the traverse field is considered. It takes into consideration the attenuation
CIt depends on the magnetic permeability μr influenced by the bK,Hstator lamination, H pole
H related to
coefficient CHthe stator
related toyoke that
the stator influences
yoke thatthe magnitude
influences theof magnitude component. It depends
of bK,H component.
s s
Itpair
on thenumber, on and
magnetic
depends the geometrical
permeability
the magnetic parameters
µr influenced
permeability inner
μrbyinfluenced
the statorRintby andthe outer
lamination, statorHRlamination,
poleradius
ext and
pair number, can
H pole
and the geometrical s s
parameters inner Rint and outer Rsext radius and scan be defined as
be defined
pair number, asand
follows
the [35]:
geometrical parameters inner Rint and outer Rext radius and can
follows [35]:
be defined as follows [35]:C H  2 2 .
CH = 
 
s  /Rint
s s  H 1
 s H 
s | H |− 1 . (11)(11)
r
µr  ( Rint ( R s / R−| H )|− 1 (
−2 ( RintR
s /R / R
int s ext ) 1 
 ext ) ext )
ext
CH .
rH (pole s  H 1 H 1  (11)
s
 ( Rint
s s
71.6mm
Rint / Rext )
Theevolution
The evolutionofofCCHHversus
versus H pole pair number
pair number with/RRR
with s )
s ext
int =
int  71.6 mm, Rextsext 121
, R s
= 121 and
mm mm
and
μr =µr = 1000
1000 is presented
is presented in inFigure
Figure3.3.One Onecan cannotice
notice that that value of the attenuation
The evolution of CH versus H pole pair number with Rints the  71.6 value
mm ,ofRextthe
s attenuation
 121 mm and
coefficient
coefficientdecreases
decreaseswithwiththetheincrease
increaseofofH. H.
μr = 1000 is presented in Figure 3. One can notice that the value of the attenuation
coefficient decreases with the increase of H.
Attenuation coefficient CH

0.00104
Attenuation coefficient CH
0.00084
0.00104
0.00064
H

0.00084
CH C

0.00044
0.00064
0.00024
0.00044
0.00004
0.00024
0 1 2 3 4 5 6 7
0.00004
0 1 2 3 H 4 5 6 7

H
Figure3.3.Attenuation
Figure Attenuationcoefficient
coefficientevolution
evolutionCCH versus pole pair number H.
H versus pole pair number H.

Figure 3. Attenuation coefficient evolution CH versus pole pair number H.

AAphysical
physicaljustification
justificationofofthe
theevolution
evolutiongiven
givenininFigure
Figure33can
canbebedone
donebybyconsidering
considering
the
theline
linefield
fielddistribution.
distribution.Actually,
Actually,flux
fluxdensity
densitycomponents
componentsofofhigh highpolarity
polarityhave
haveaaline
line
A physical justification of the evolution given in Figure 3 can be done by considering
field
fieldconcentrated
concentrated at the levellevelofofthe
theair-gap
air-gapwhereas
whereas those
those of of
lowlow polarity
polarity havehave a line
a line field
the line field distribution. Actually, flux density components of high polarity have a line
field
that that spreads
spreads on on
thethe whole
whole stator
stator core.This
core. Thiscoefficient
coefficientinfluences
influences the amplitude
amplitude of ofthe
the
field concentrated at the level of the air-gap whereas those of low polarity have a line field
traverse flux field.
traverse flux field.
that spreads on the whole stator core. This coefficient influences the amplitude of the
traverse
2.5. flux field.
2.5.Measurement
Measurementofofthe theTransverse
TransverseField
Field
For the proposed
For the proposed diagnosis method,
method,the
diagnosisField thenormal
normalcomponent
componentofofthe thetraverse
traversefield
fieldisis
2.5. Measurement of the Transverse
measured
measured with flux sensors. The sensors are placed in the closed vicinity of the yoke,
with flux sensors. The sensors are placed in the closed vicinity of the stator stator
For the proposed diagnosis method, the normal component of the traverse field is
measured with flux sensors. The sensors are placed in the closed vicinity of the stator
Energies 2021, 14, x FOR PEER REVIEW 6 of 22

Energies 2021, 14, 1132 6 of 22

yoke, allowing to consider in the model only the CH coefficient. Supposing the sensor
s
placed at radius x = Rext , the normal traverse flux density bx is defined as:

bx  
allowing to consider in the model C H bˆthe
only K , H cos ( Kt  H s  Supposing
CH coefficient. K,H ) . the sensor placed(12)
at
radius x = Rext , the normal traverse flux density bx is defined as:
s K , H

Let us introduce bKxx the harmonic of K rank of bx at the given point M’ in the closed
b = ∑ CH b̂K,H cos (Kωt − Hαs − ϕK,H ). (12)
,    0s ), corresponding to the center of the wound flux
sK,H s
vicinity of the stator (x = Rext
x
Let b
sensor. us can be defined
K introduce harmonic of K rank of bx at the given point M’ in the closed
bKx theby:
vicinity of the stator (x = Rext , αs = αx 0s ), corresponding
s to the center of the wound flux
bK  bˆK cos ( K t   Kx ) .
x
sensor. bKx can be defined by: (13)
x
b̂K can be computed by introducing complex quantities:
bKx = b̂Kx cos (Kω t − ϕKx ). (13)
 j ( H 0s  K , H )
bˆK   C H bK , H e ˆ
x
b̂Kx can be computed by introducing complex quantities:
. (14)
 H 
 
At given  0s , the resulting ∑density
s
b̂Kx =flux e− j( Hα0 + ϕK,Hat) Kω
CH b̂K,Hharmonics . angular frequency is com-
(14)
 
H 
posed of several elementary components of different polarity H.
At given α0s , the resulting flux density harmonics at Kω angular frequency is composed
3. Analytical Approach
of several elementary for Faulty of
components Machine
different polarity H.
3.1. Structure of the Faulty Machine
3. Analytical
In orderApproach
to determine for Faulty Machineof the faulty turns in the change of the flux
the influence
3.1. Structure
density, of theconsidering
a model Faulty Machine
a three-phase stator winding was developed. In this model,
In order tothat
it is supposed determine
“y” turns thefrominfluence
the n’ ofs turns
the faulty
of anturns in the change
elementary sectionofbelonging
the flux density,
to the
aphase
model considering
q are a three-phase
short-circuited and thatstator winding
y is small was developed.
compared with pns, the In this
totalmodel,
number it is
of
supposed that “y” turns from the n’ s turns of an elementary section belonging to the phase
turns per phase. Therefore, it can be assumed that the current remains unchanged and has
qtheare short-circuited
same values in each and phase thatin y the
is small
faultycompared with pns , the
case. This hypothesis cantotal number
therefore of turns
characterize
per phase. Therefore, it can be assumed that the current remains
the short circuit thanks to a model that preserves the original structure of the machine. unchanged and has the
same
This model assumes that the stator winding in presence of the fault is equivalent to the
values in each phase in the faulty case. This hypothesis can therefore characterize the
short
healthy circuit thanks
winding, to a model
associated to that
“y” preserves
independent the turns
original structure
in which theof the machine.
short-circuit This
current
model assumes
circulates. It willthatbethe stator winding
assumed that these in presence of thehave
two circuits fault independent
is equivalent to the healthy
running. The
winding, associated to “y” independent turns in which the
healthy part of the winding generates therefore the same flux density components without short-circuit current circulates.
It will be assumed that these two circuits have independent running. The healthy part of
fault.
the winding
The model generates therefore
of a faulty the same
winding flux density
is presented incomponents
Figure 4 where without the fault.
whole phase
The model of a faulty winding is presented
winding is composed of an elementary healthy section and one with short in Figure 4 where the whole phase winding
circuit turns.
is
For both structures, it is assumed that the magnetic reaction of the rotor is such thatboth
composed of an elementary healthy section and one with short circuit turns. For only
structures,
the fundamental of the stator currents for a running at no load will be consideredthe
it is assumed that the magnetic reaction of the rotor is such that only to
fundamental of the stator currents for a running at no load will be considered to characterize
characterize the air-gap flux density. This way, the resulting air-gap flux density b * is equal
the air-gap flux density. This way, the resulting air-gap flux density b* is equal to the initial
to the initial one, b, to which the flux density bsc generated by the “y” turns flowing
one, b, to which the flux sdensity bsc generated by the “y” turns flowing through by the
throughisby: the
current b ∗ = current
b + b sc
: b*  b  bsc is added.
iisqscadded.
qsc

s s
iqsc iqsc
iqs iqs
= +
iqs  iqscs  ns turns y s.c.turns

Figure 4.
Figure 4. Proposed model
model for
for aa faulty
faulty winding.
winding.

The
The short
short circuit
circuit current
current is
is defined
defined as as follows:
follows:
√
qsc I
s s Is 2 cos(t   ) .
isqsc i= sc sc2 cos(ωt − ϕsc
sc ). (15)
(15)

ϕsc is the phase lag between the short circuit current and the phase 1 current as shown
in Figure 5. This phase actually depends on several parameters such as the impedance
 Energies 2021, 14, x FOR PEER REVIEW 7 of 22

Energies 2021, 14, x FOR PEER REVIEW 7 of 22

sc is the phase lag between the short circuit current and the phase 1 current as shown
Energies 2021, 14, 1132 in Figure 5. This phase actually depends on several parameters such as the impedance 7 of 22

thatsclimits
is thethe
phase short
lag circuit
between current, thecircuit
the short shortcurrent
circuit and
winding, and1the
the phase position
current of the
as shown
infundamental
Figure 5. This air-gap
phaseflux density
actually relativeon
depends to several
the phase q current such
parameters (depending
as the on the load).
impedance
that limits the
that limits the short
short circuit current, the short circuit winding, and the positionofofthe
circuit current, the short circuit winding, and the position the
s
fundamental i
fundamentalair-gap
1
air-gapflux
fluxdensity
densityrelative
relativetotothe
thephase
phaseqqcurrent
current(depending
(dependingononthe
theload).
load).
 sc
iqscs i1 s

 sc
iqscs
Figure 5. Current diagram in faulty case.

Figure 5. Current
3.2. Faulty Turns diagram
m.m.f ininfaulty
faulty case.
Figure 5. Current diagram case.
3.2. Faulty Turns m.m.f
The magnetomotive force  qscs
generated by the “y” short circuit turns, shifted of
3.2. FaultyThe Turns m.m.f
magnetomotive force ε s generated by the “y” short circuit turns, shifted of αsq
 qs from ds, is shown on Figuresqsc 6 in the case of a 4 poles machine. It also shows the m.m.f
from Theds,magnetomotive force6 in
is shown on Figure the case of a 4 poles machine. It also shows the m.m.f
qsc generated by the “y” short circuit turns, shifted of
εsqel
ss
qelgenerated
generated byby
thethe
healthy
healthyelementary
elementary winding.
winding.εsqscis
s
qscan
isunidirectional m.m.f
an unidirectional and and
m.m.f can
be from ds, is shown
q decomposed in on Figure
rotating 6
fields in the
that case
rotateof
ina 4 poles
opposite machine. It also
directions. In ashows
stator the m.m.f
referential,
can be decomposed in rotating fields that rotate in opposite directions. In a stator
s s can be written as follows:
εqelqsc generateds by the healthy elementary winding.  qsc is an unidirectional m.m.f and

s
referential, can be written as follows:
qsc
can be decomposed in rotating fields that rotate in opposite directions. In a stator
εsqsc = sIsc
s
∑
 I sc 
s
sA 0 h cos (ω(tt −
A'hs cos
s
 s − hϕ) h. ).
 hhα (16)
referential,  qsc can be written as follows:
s qsc
h (16)
h

 qsc
s
 I sc
s
 A'hs cos ( t  h s   h ) . (16)
 s
qel
h
s
i q
ns
2
 qel
s 2
is s 0 s
ns sq iq
 n2
2 2
(a)
0 s
 qsc
s
i s
 n iqsc
s qs

y 2 2
4 (a)
0 s s
is  qsc
3iyqsc
s qsc

y 4  qs 2
4 (b)
s
iqsc
0 s
Figure
3y
 qs by the faulty turns.
4 6. m.m.f generated
(b)
A0shs is a function that can be determined from the Fourier series of εssqsc and h is a
Figure A'm.m.f
6.
non-null is agenerated
h relative function
integer, that
by the can
which becan
faulty determined
turns. from the Fourier
take consequently series of
all the values of hsqsc and φ
. Here, h isisa
h
defined
non-nullas: φh = hα
relative s
q + φscwhich
integer, . can take consequently all the values of hs. Here, h is
'hs as:
AAs
defined bissca =
h λε
s s, the
function that .can be determined
q  sccalculus
 hqsc developments fromleadthe toFourier
defineseries
this of  qsc
s
quantity and h isref-
in the a
s
erence frame related
non-null relative integer, to which can take consequently all the values of h . Here,  is
d . A grouping of parameters with same polaritys and same
As bsc
frequency   qsc
provides:
s
, the calculus developments lead to define this quantity inh the
defined as: h  hq  sc . s
s

sc ∑ A 0 h cos
s s
reference frame related toε qsc d s. =
A Igrouping ω t − hαs − ϕ
of(parameters h ), same polarity and same
with (17)
As
frequencyb   s
sc provides:
qsc , the calculus developments
h lead to define this quantity in the
reference frame related bsc =to ∑ ds. Ab̂scK
grouping
s
 scI sc
sc ,H
qsc
s
 Aof
cos parameters
('hsKcos ( −
sc ωt hscsαswith
t H − same polarity and same
h ) ϕsc,Ksc ,Hsc ), (18)
(17)
frequency provides: Ksc ,Hsc h ,
with:  qsc
s
 I sc
s
 A'hs cos0 (r t  h s   h ) (17)
K = h1 + kr N (1 − s)
bsc   bˆsc sc
K sc , H sc cos 0( Kssct 0 H sc  s, .  sc, K sc , H sc ) (18)
(19)
K sc , H scHsc = h + p(ks N + kr N r )
,
ˆ
where ks0
with:
are
bsc 
the 
and kr0
permeance bsc rank
K sc , H sc
of
cos
x
the
( K sc 
rotort and
H sc  s

stator  which
sc , K sc , vary
H sc
) from −∞ to(18)
+ ∞,
equivalent to ks and krKdefined
sc , H sc in (10). bsc,Ksc calculated at the point M’ is, the harmonic of
x
K rank, of magnitude b̂sc,K : K sc  1  kr ' N r (1  s) 
with: sc . (19)
H sc  h  p(ks' N s  kr ' N r )
' N r ((1Kscs)ω t − ϕsc,K
x
bsc,Ksc K= sc,K
sc b̂ 1x sckrcos x
), (20)
 . sc (19)
H sc  h  p(ks' N  kr ' N )
s r
and  
 
− j( Hα0s + ϕsc,Ksc, Hsc ) 
b̂sc,Ksc = ∑ CH b̂sc,Ksc ,Hsc e
x
. (21)

H 
Energies 2021, 14, 1132 8 of 22

By comparing the values of the frequency rank Ksc given by (18), which appears in the
case of short circuit with frequency value taken by K in healthy case defined by (10), we can
notice that, there is no bring new frequency in the signal spectrum. Therefore, to detect the
failure, the classic diagnosis method which analyzes the increase (or decrease) of already
existing lines needs to know the amplitude value in the healthy case as a reference, thus
limiting their practice application. Concerning the polarities H and Hsc , one can observe
that Hsc can take all positive and negative integers whereas H is a multiple of p. Hsc can
especially be equal to ±1 corresponding to components that are weakly attenuated by the
stator iron. In the following, the properties relating to the dissymmetry generated by such
components will be exploited.

3.3. Searching for Sensitive Components

The harmonic at Kω angular frequency is composed of several components of various
polarities. The ones that have the highest contribution can be found by searching the lowest
values of hs , h, ks, kr, k’s, k’r, leading to the smallest possible H (or Hsc ) corresponding to
the less attenuated components.
Let us consider an induction machine with p = 2, Ns = 24, Nr = 16, supplied by
50 Hz power source. Tables 1 and 2 give the magnitude of the components relative to the
magnitude of the fundamental for the healthy and faulty machines respectively. The short
circuit current rms value is three times that of the line current: Issc = 3Is0 .

Table 1. Components generated by the healthy induction machine.

x x
kr ks hs K H f(Hz) K × f (Hz) CH b̂K,H /b̂11
−1 1 −5 −15 6 50 −750 5.08 × 10−5 1.48 × 10−5
−1 1 −11 −15 −6 50 −750 5.08 × 10−5 4.04 × 10−6
1 −1 7 17 −2 50 850 4.71 × 10−4 1.41 × 10−4
1 −1 13 17 10 50 850 2.66 × 10−6 2.81 × 10−7
−2 1 7 −31 −2 50 −1550 4.7 × 10−4 −1.28 × 10−4
−2 2 −17 −31 −2 50 −1550 4.71 × 10−4 2.82 × 10−5

Table 2. Components generated by the faulty induction machine.

x x
k’r k’s hs KSC Hsc Ksc × f(Hz) CH b̂sc /b̂11
Ksc ,Hsc

−1 1 −10 −15 6 −750 5.08 × 10−5 9.2 × 10−6

−1 1 −13 −15 3 −750 2.56 × 10−4 −3.52 × 10−5
−1 1 −14 −15 2 −750 4.71 × 10−4 −1.02 × 10−4
−1 1 −15 −15 1 −750 0.00107 −1.84 × 10−4
−1 1 −18 −15 −2 −750 4.71 × 10−4 9.1 × 10−5
−1 1 −19 −15 −3 −750 2.56 × 10−4 2.61 × 10−5
−1 1 −21 −15 −5 −750 8.62 × 10−5 −5.8 × 10−6
−1 1 −22 −15 −6 −750 5.08 × 10−5 −4.07 × 10−6
1 −1 10 17 −6 850 5.08 × 10−5 9.32 × 10−6
1 −1 11 17 −5 850 8.62 × 10−5 1.12 × 10−5
1 −1 14 17 −2 850 4.71 × 10−4 −1.02 × 10−4
1 −1 15 17 −1 850 0.00107 −1.9 × 10−4
1 −1 17 17 1 850 0.00107 1.82 × 10−4
1 −1 18 17 2 850 4.71 × 10−4 9.1 × 10−5
1 −1 21 17 5 850 8.62 × 10−5 −5.8 × 10−6
1 −1 22 17 6 850 5.08 × 10−5 −4.07 × 10−6
−2 1 17 −31 1 −1550 0.00107 −1.52 × 10−4
−2 1 21 −31 5 −1550 8.62 × 10−5 5.04 × 10−6
−2 1 22 −31 6 −1550 5.08 × 10−5 3.26 × 10−6
−2 2 −26 −31 6 −1550 5.08 × 10−5 1.92 × 10−6
Energies 2021, 14, 1132 9 of 22

In Tables 1 and 2, it can be observed that the highest components in the external
magnetic field are mainly issued from air-gap components of the lowest polarity. In healthy
conditions, the first slotting harmonics are obtained for:
Kr = 1, ks = −1, hs = 7 lead to K = 17, H = −2 (f = 850 Hz); kr = −2, ks = 1, hs = 7 lead
to K = −31, H = −2 (f = −1550 Hz); and kr = −1, ks = 1, hs = −5 lead to K = −15, H = 6
(f = −750 Hz).
In faulty conditions, the same harmonics are obtained for:
kr’ = 1, ks’ = −1, h = 15 lead to Ksc = 17, Hsc = −1 (f = 850 Hz); kr’ = −1, ks’ = 1, h = −15
lead to Ksc = −15, Hsc = 1 (f = −750 Hz),
and kr’ = −2, ks’ = 1, h = 17 lead to Ksc = −31, Hsc = 1 (f = −1550 Hz) with frequencies
given for s = 0.
In the following, one will consider the harmonics of rank K = Ksc = 17 (f = 850 Hz)
because it is generated by components of the lowest polarity in healthy and faulty con-
ditions (H = −2, Hsc = −1). These components are highlighted in grey in Tables 1 and 2
and they will be considered as the sensitive components for the inter-turn short circuit
fault. The sensitivity has been shown in previous works [24]. It can also be noticed that
for the healthy machine, only one predominant component can be associated to one given
harmonic whereas for the faulty machine, one given harmonic is generated by several
components of different polarity and of similar magnitude. In this case, the components
with the highest magnitudes has the polarity Hsc = +1 and Hsc = −1. Moreover, these
components, weakly attenuated by the stator frame, have a magnitude similar to that of
the component related to the healthy machine as those highlighted in yellow in Table 2.
Therefore, the fault does lead to a significant change in the magnitude of the spectral line
at 850 Hz in the external magnetic field. In order to improve the detection, the analysis will
be focused on the load-induced variation of sensitive spectral lines measured at two points
in the transverse external magnetic field.

3.4. Influence of the Load

Only the sensitive components defined in the previous section are now considered:
bKx relative to the healthy machine and bsc,K
x
sc
relative to the faulty machine. They both merge
together to generate the resulting harmonic flux density bK∗ x . According to the hypothesis
related to the rotor magnetic reaction, it will be assumed that b̂Kx does not change when the
load increases. The same hypothesis will be considered for b̂sc,K x . Actually, only the phase
sc
lag ϕsc and consequently φh change with the load. Consequently, for position 1 (Pos.1)
defined for αs = 0, and position 2 (Pos. 2) defined for αs = π, the resulting harmonic bK∗ x
can be expressed as follows:

Pos. 1 : bK∗ x1 = b̂Kx cos (Kω t − ϕKx ) + b̂sc,K

x
sc
x
cos (Ksc ω t − ϕsc,K sc
), (22)

Pos. 2 : bK∗ x2 = b̂Kx cos (Kω t − ϕKx ) − b̂sc,K

x
sc
x
cos (Ksc ω t − ϕsc,K sc
). (23)
Considering resulting harmonics, bK∗ x obtained from (22) and (23), their difference con-
x
sists in the sign of the second term bsc,K which changes in the faulty case as a consequence
sc
of the polarity Hsc = 1 in the expression of cosines ((cos(γ + π) = −cos(γ)), contrary to
polarity H = 2 of the healthy term when it does not change (cos(γ + 2π) = cos(γ)). This dis-
symmetry, generated by the fault in (22) and (23) is, from a physical point of view, the base
of the proposed detection procedure. Figure 7a gives the associated time phasor diagram
∗ x1 ∗ x2
for ϕKx = 0. It clearly shows that the magnitudes of the complex quantities bK and bK
are different. If the load changes, then a variation of ϕcc leads to a variation of ϕsc,Kx .
sc
x
Figure 7b gives the time phasor diagram after a variation of ϕsc,Ksc . It can be observed that
the resulting magnitude has increased in Pos. 1 (b̂K∗ x1 ) and has decreased in Pos. 2 (b̂K∗ x2 ).
The theoretical approach neglects the phase variation, which leads to a partial justification
of the physical phenomenon.
 K are different. If the load changes, then a variation of cc leads to a variation of
 sc , K . Figure 7b gives the time phasor diagram after a variation of  sc
x x
, K sc . It can be
sc

observed that the resulting magnitude has increased in Pos. 1 ( b̂*Kx1 ) and has decreased in
Energies 2021, 14, 1132 Pos. 2 ( b̂*Kx2 ). The theoretical approach neglects the phase variation, which10leads
of 22 to a par-
tial justification of the physical phenomenon.

bscxK1 bK* x1
sc
 x bscxK1 bK* x1
scK sc
bKx 
sc x
scK sc
x2
bscK sc bKx
*x2
b K
x2 *x2
b scK sc b K

(a) (b)
Figure
Figure 7. Phasor
7. Phasor diagram
diagram variation
variation (a)(a)
nono loaded
loaded condition
condition (b)(b) loaded
loaded condition.
condition.

The different directionsdirections

The different of variationof between
variationthe magnitudes
between of the b̂K∗ x inoffaulty
the magnitudes the bˆcase
*x
K in faulty
allow one to propose the presented procedure:
case allow one to propose the presented procedure:
• In the healthy case:
• In the healthy case:
The air-gap flux density does not change when the machine is loaded compared to
Theandair-gap x
flux bdensity ∗ x1
the no load case the term sc,Ksc is does
null. not change
In this case,when the machine
the amplitudes of theis loaded
terms b̂compared
K to
∗ x2
and b̂K themeasured x * x1
no loadin Pos.
case and 1 and Pos. 2bkeep similar
the term values or at least evolve in the same
sc , K sc is null. In this case, the amplitudes of the terms b̂K
way if the load of the machine change.
and b̂*Kx2 measured in Pos. 1 and Pos. 2 keep similar values or at least evolve in the same
• In the faulty case:
way if the load of the machine change.
In loaded conditions, the magnitude of the component at Kω angular frequency
measured • in Pos.
In the1 faulty case:2 will evolve in opposed directions and this particularity is
and Pos.
proposed to beInexploited in the analysis
loaded conditions, theofmagnitude
the harmonic of Kω
the as a fault indicator.
component at Kω Compared
angular frequency
to another existing proposed methods, one does not require the
measured in Pos. 1 and Pos. 2 will evolve in opposed directions and knowledge of the
thishealthy
particularity is
state to be applied.
proposed to be exploited in the analysis of the harmonic Kω as a fault indicator. Compared
to another existing proposed methods, one does not require the knowledge of the healthy
3.5. Application to a Salient Pole Synchronous Machine
state to be applied.
Different kinds of synchronous machines exist, they differ only by the structure of
their rotor:
3.5.wound salient,
Application to aorSalient
wound smooth
Pole rotor (turbo
Synchronous alternator), surface mounted, or
Machine
interior permanent magnet rotor. The modeling of the intact synchronous machine and the
Different kinds of synchronous machines exist, they differ only by the structure of
faulty one is deduced from the studied induction machine where the slotting effect created
their
by the dampers rotor: wound salient,
is neglected. or wound
Since the smooth
stator has rotorstructure
the same (turbo alternator), surface mounted,
for both machines, in or
the analytical model, it is considered that the effect created by the saliency rotor and wound
smooth rotor of the synchronous machine is similar to the rotor slots of the induction
machine. Consequently, if the rotor is a wound smooth rotor, the components generated by
a healthy and faulty synchronous machine are given by (10) and (18) with particularity s
= 0. For a salient rotor, as the pole number is equal to the rotor saliencies of the machine,
the frequency ranks and pole pair numbers given by (10) can be likewise considered in the
case of a synchronous machine, with Nr = 2 and s = 0:

K = 1 + 2kr
. (24)
H = p(hs + ksN s + 2kr )

For a faulty machine, (18) becomes:


Ksc = 1 + 2kr 0
. (25)
Hsc = h + p(ks0 N s + 2kr 0 )

Tables 3 and 4 give the magnitude of the components relative to the magnitude of
the fundamental respectively for the healthy and for the faulty synchronous machines
with 4 poles, and Ns = 18. The short circuit current rms value is three-time that of the line
current: Isc s
s = 3I0 .
Energies 2021, 14, 1132 11 of 22

Table 3. Components generated by the healthy synchronous machine.

x x
kr ks hs K H K × f (Hz) CH b̂K,H /b̂11
6 0 −5 13 14 650 7.2 × 10−6 6.04 × 10−3
6 0 1 13 26 650 8.19 × 10−8 3.43 × 10−3
7 0 −5 15 18 750 1.63 × 10−6 13.5 × 10−3
7 0 1 15 30 750 1.83 × 10−8 10.8 × 10−3
−7 0 −5 −13 −38 −650 9.19 × 10−10 2.21 × 10−3
−7 0 1 −13 −26 −650 8.19 × 10−8 2.29 × 10−3
8 0 −5 17 22 850 3.65 × 10−7 11.8 × 10−3
8 0 1 17 34 850 4.01 × 10−9 8.8 × 10−3
−8 0 −5 −15 −42 −750 2.05 × 10−10 4.91 × 10−3
−8 0 1 −15 −30 −750 1.83 × 10−8 10.3 × 10−3

Table 4. Components generated by the faulty synchronous machine.

x x
kr ks hs K H K × f (Hz) CH b̂K,H /b̂11
6 0 −5 13 19 650 1.12 × 10−6 5.13 × 10−4
6 0 1 13 25 650 1.19 × 10−7 3.64 × 10−4
7 0 −5 15 23 750 2.51 × 10−7 2.13 × 10−3
7 0 1 15 29 750 2.66 × 10−8 1.82 × 10−3
−7 0 −5 −13 −33 −650 5.90 × 10−9 7.9 × 10−4
−7 0 1 −13 −27 −650 5.60 × 10−8 9.8 × 10−4
8 0 −5 17 27 850 5.60 × 10−8 1.2 × 10−3
8 0 1 17 33 850 5.90 × 10−9 4.8 × 10−4
−8 0 −5 −15 −37 −750 1.33 × 10−9 1.46 × 10−4
−8 0 1 −15 −31 −750 1.26 × 10−8 1.52 × 10−4

The results are similar to those of induction machine. It appears that each harmonic at
given kr mainly originates from the components of lowest polarity. It also appears that the
sensitive harmonics are:
kr = 7, ks = 0, hs = −5 lead to K = 15, H = 18 (f = 750 Hz); kr = 7, ks = 0, hs = 1 lead to
K = 15, H = 30 (f = 750 Hz);
and kr = 8, ks = 0, hs = −5 lead to K = 17, H = 22 (f = 850 Hz). In faulty conditions, the
same harmonics are obtained for:
kr = 7, ks = 0, hs = −5 lead to K = 15, H = 23 (f = 750 Hz); kr = 7, ks = 0, hs = 1 lead to
K = 15, H = 29 (f = 750 Hz),
and kr = 8, ks = 0, hs = −5 lead to K = 17, H = 27 (f = 850 Hz).
In the proposed method, which is the same as in the induction machine, the harmonics
obtained for kr’ = ±7 and ±8 can be analyzed. The choice between two harmonics must be
made taking into account as practical measurements of harmonics amplitudes

4. Experimental Results
4.1. Presentation of the IM Test Bench
The tests are performed using a three-phase squirrel-cage induction machine with
4 poles, 50 Hz, 11 kW, 380/660 V, 22.3/13A, 1450 rpm, 48 stator slots, and 32 rotor bars
(Ns = 24, Nr = 16). This machine presented in Figure 8a is supplied by the grid and is
specially modified to enable inter-turn short circuits. For measurement of the external
magnetic field, the sensors are 180◦ spatially shifted around the frame of the machine
(Figure 8b). The output connections to the terminal box can short-circuit an elementary
section housed in a slot, which corresponds to 12.5% of the full phase winding for the
induction machine (Figure 8c).
The equipment above the machine makes it possible to simulate a fault by short-
circuiting the coils. The machine can operate under no-load or various loading conditions.
For the induction machine, the short circuit current is limited to 15.3 A using an external
 15, H = 30 (f = 750 Hz);
and kr = 8, ks = 0, hs = −5 lead to K = 17, H = 22 (f = 850 Hz). In faulty conditions, the
same harmonics are obtained for:
kr = 7, ks = 0, hs = −5 lead to K = 15, H = 23 (f = 750 Hz); kr = 7, ks = 0, hs = 1 lead to K =
Energies 2021, 14, 1132 15, H = 29 (f = 750 Hz), 12 of 22
and kr = 8, ks = 0, h = −5 lead to K = 17, H = 27 (f = 850 Hz).
s

In the proposed method, which is the same as in the induction machine, the harmon-
ics obtained for kr’ = ±7and ±8 can be analyzed. The choice between two harmonics must
rheostat. Figure 8b displays locations 1 and 2 of the flux sensors required for the method.
be made taking into account as practical measurements of harmonics amplitudes
The tests consist of measuring and analyzing the magnetic field outside the machine in
order to validate the proposed diagnosis method. The measurements are performed using
4. Experimental Results
two identical manufactures wound flux sensors, placed against the machine. It has been
4.1. Presentation
checked that theofwirethe IM Test Bench
current from the machine to the terminal block does not disturb the
measurement.
The tests are Asperformed
announcedusingin thea previous
three-phasesection, the position
squirrel-cage of sensors
induction mustwith
machine be on 4
the one
poles, 50hand
Hz, 11 α1s kW,
= 0 380/660
(Pos. 1)V,and, on the 1450
22.3/13A, otherrpm,
hand,48as accurately
stator as possible
slots, and 32 rotor in α2s (N
bars = sπ=
with
24, Nrthe input
= 16). This(Pos. 2) so that
machine the measurements
presented in Figure 8acould be interpreted
is supplied in the
by the grid andcontext of the
is specially
proposed to
modified method.
enableFor both measurements,
inter-turn short circuits.theFor
sensor signal measured
measurement of theby the PULSE
external in the
magnetic
input Signal 1 and Signal 2 is placed in the middle of the machine to reduce
field, the sensors are 180° spatially shifted around the frame of the machine (Figure 8b). the influence
of end
The windings.
output connectionsTeststohave been performed
the terminal on the two induction
box can short-circuit an elementarymachines
sectionfor three
housed
operating conditions (motor, generator connected to the power system,
in a slot, which corresponds to 12.5% of the full phase winding for the induction machine and self-excited
induction
(Figure 8c).generator).

Energies 2021, 14, x FOR PEER REVIEW 13 of 22

(a) (b) (c)

operating conditions (motor, generator connected to the power system, and self-excited
Figure 8.
8. Experimental
Experimental test
test bench
bench with
withspecial
specialinduction
induction machine
machine modified
modified to
to enable
enable inter-turn
inter-turn short
short circuits
circuits (a)
(a) test
testbench,
bench,
induction◦generator).
(b) flux sensors spatially shifted at 180
180°,, (c) stator with a short circuit box and output connections.

4.2.
4.2. Induction
Induction Machine
Machine in
in Motor
Motor Case
Case
The equipment above the machine makes it possible to simulate a fault by short-cir-
cuitingThe
Thethetime variation
coils.
time The machine
variation of
of the electromotive
the can operate under
electromotive force (emf)
(emf) and
forceno-load the
the spectrum
or various
and loadingof
spectrum the signal
ofconditions.
the signal
delivered
delivered
For by
by the
the inductionthe sensor
sensor in
machine,in the
the case
case
the of
of the
short the healthy
healthy
circuit induction
currentinduction machine,
to 15.3measured
machine,
is limited measured
A using an in the
the near
in external
near
vicinity of the
the machine
machine are
are shown
shown in
in Figure
Figure 9a
9a where
where the
the magnitudes
magnitudes
rheostat. Figure 8b displays locations 1 and 2 of the flux sensors required for the method. are
are presented
presented in
in dB.
dB.
The first
The first tooth
teststooth
consist harmonics
harmonics
of measuring at 750 and
at 750 and 850 850 Hz can
Hz can the
analyzing be clearly
be clearly
magnetic observed
observed in
in Figure
field outside Figure 9b.
9b.machine
the The studyThe
in
study
order is validate
is focused
to focused on proposed
on the the
line the lineHz,
at 850 atdiagnosis
850 Hz,
where where
the the
theoretical
method. theoretical
The analysis analysis
shows
measurements aare shows
polarity a polarity
lower
performed than
using
lower
two ofthan
the that
that identical line of the
at 750 line
manufacturesHz. at 750isHz.
This
wound Thissensors,
reflected
flux is by
reflected
a greaterby amagnitude
placed greaterthe
against magnitude
of ofItat
the line
machine. the
has line
850 at
Hz,
been
850 Hz, athat
a property
checked property
that
theiswirethat
measuredis measured
current experimentally.
experimentally.
from the machine to the terminal block does not disturb the
measurement. As announced in the previous section, the position of sensors must be on
the one hand 1s  0 (Pos. 1) and, on the other hand, as accurately as possible in  2s  
with the input (Pos. 2) so that the measurements could be interpreted in the context of the
proposed method. For both measurements, the sensor signal measured by the PULSE in
the input Signal 1 and Signal 2 is placed in the middle of the machine to reduce the influ-
ence of end windings. Tests have been performed on the two induction machines for three

(a) (b)
Figure
Figure 9.
9. Signal
Signal delivered
delivered by
by PULSE
PULSE acquisition
acquisition system;
system; (a)
(a) emf
emf delivered
delivered by
by flux
flux coil
coil sensor,
sensor, (b)
(b) signal
signal spectrum
spectrum delivered
delivered
for
for the
the healthy
healthy machine.
machine.

It
It should
shouldbebekept
keptininmind
mindthat inin
that practice, thethe
practice, lineline
studied cancan
studied move withwith
move the slip, but
the slip,
will be identified
but will as the
be identified as line at 850
the line Hz.Hz.
at 850 TheThe
results obtained
results for for
obtained thisthis
machine operating
machine operatingas
a motor in healthy and short-circuit fault conditions are presented, taking into account the
variation of the spectral line at 850 Hz under the load influence. Figure 10a gives the var-
iation of the spectral line at 850 Hz on the signal delivered by the sensor in Pos. 1 and
Figure 10b by the sensors in Pos. 2.
 (a) (b)
Figure 9. Signal delivered by PULSE acquisition system; (a) emf delivered by flux coil sensor, (b) signal spectrum delivered
Energies 2021, 14, 1132 for the healthy machine. 13 of 22

It should be kept in mind that in practice, the line studied can move with the slip, b
will be identified as the line at 850 Hz. The results obtained for this machine operating
as a motor in healthy
a motor and short-circuit
in healthy fault conditions
and short-circuit are presented,
fault conditions taking into
are presented, account
taking into account t
the variation ofvariation
the spectral
of the spectral line at 850 Hz under the load influence. Figure 10athe
line at 850 Hz under the load influence. Figure 10a gives gives the v
variation of the iation
spectral linespectral
of the at 850 Hzlineonatthe
850signal
Hz ondelivered
the signalbydelivered
the sensor
byin Pos.
the 1 and
sensor in Pos. 1 a
Figure 10b by the sensors
Figure 10b in
byPos. 2.
the sensors in Pos. 2.

(a) (b)
Figure 10.Figure
Harmonic components
10. Harmonic at 850 Hz under
components at 850both measurement
Hz under positions for positions
both measurement healthy motor and load
for healthy variation (a)
motor
measurement in position 1, (b) measurement in position 2.
and load variation (a) measurement in position 1, (b) measurement in position 2.

Figure 10 showsFigure
that a10 shows that
difference a difference
appears appears
between between theof
the amplitudes amplitudes
significantoflines
significant lin
at 850 Hz for the healthy machine in positions 1 and 2. Actually, due
at 850 Hz for the healthy machine in positions 1 and 2. Actually, due to the real geometry to the real geome
of the machine, the elements that lead to the attenuation are not exactly the same allthe same
of the machine, the elements that lead to the attenuation are not exactly
around
around the machine. the machine.
However, However, as in
as aforementioned aforementioned in the analytical
the analytical development, onedevelopment,
finds o
finds the same direction of variation (positive) of this component for both positions wh
the same direction of variation (positive) of this component for both positions when the
the machine is loaded.
machine is loaded.
For the faulty machine (Figure 11), the presence of the shorted turns introduces two-
pole flux density components that will be combined with those presented for the healthy
machine. Analyzing the results presented above, it can be seen that:
• in healthy conditions, the lines at 850 Hz evolve in the same direction with the change
of the load,
• in faulty conditions, the lines at 850 Hz in position 1, compared with those in position
2 vary in opposite directions.
• the value of the short circuit current Isc can influence the evolution of the lines

4.3. Induction Machine in Generator Case

A second test of the proposed method is carried out in the case where the machine is
used as a generator connected to the grid. The results are shown in Figure 11.
For this kind of operation, the angle ϕsc of short-circuit undergoes a phase change of
approximately π compared to motor operating mode. As in the case of motor operation,
the obtained results show that for a healthy machine, the magnitudes of lines at 850 Hz
increase with the load (Figure 12a). In both measurement positions, they vary in the
same direction. For the faulty machine with the short-circuit current Isc limited to 8.2A
(Figure 12b) harmonics magnitudes change the variation, its decrease in position 1 for 3.3
kW power load and increase in position 2. Figure 12c,d gives a zoom in the evolution of
flux harmonics at frequency 850 Hz measured in Pos. 1 and Pos. 2. The experimental
results confirm that the proposed method can be applied also as an induction machine
operating as a generator.
 For the faulty machine (Figure 11), the presence of the shorted turns introduces two-
pole flux density components that will be combined with those presented for the healthy
machine. Analyzing the results presented above, it can be seen that:
• in healthy conditions, the lines at 850 Hz evolve in the same direction with the change
of the load,
Energies 2021, 14, 1132 • 14 of 22
in faulty conditions, the lines at 850 Hz in position 1, compared with those in position
2 vary in opposite directions.
• the value of the short circuit current Isc can influence the evolution of the lines

(a) (b)

(c) (d)
Figure 11. Harmonic components at 850 Hz under both measurement positions for faulty motor and load variation (a)
Figure 11. Harmonic components at 850 Hz under both measurement positions for faulty motor and
short-circuit current Isc limited at 8.2 A, (b) short-circuit current limited at 15.3 A, (c) load variation for a sensor in position
1 andload variation
Isc = 15.3 (a)variation
A, (d) load short-circuit current
for a sensor Isc limited
in position at=8.2
2 and Isc 15.3A,A.(b) short-circuit current limited at 15.3 A,
(c) load variation for a sensor in position 1 and Isc = 15.3 A, (d) load variation for a sensor in position
2 and Isc = 15.3 A. Induction Machine in Generator Case
4.3.
Energies 2021, 14, x FOR PEER REVIEW 15 of 22
A second test of the proposed method is carried out in the case where the machine is
used as a generator connected to the grid. The results are shown in Figure 11.
For this kind of operation, the angle sc of short-circuit undergoes a phase change
of approximately  compared to motor operating mode. As in the case of motor operation,
the obtained results show that for a healthy machine, the magnitudes of lines at 850 Hz
increase with the load (Figure 12a). In both measurement positions, they vary in the same
direction. For the faulty machine with the short-circuit current Isc limited to 8.2A (Figure
12b) harmonics magnitudes change the variation, its decrease in position 1 for 3.3 kW
power load and increase in position 2. Figure 12c,d gives a zoom in the evolution of flux
harmonics at frequency 850 Hz measured in Pos. 1 and Pos. 2. The experimental results
confirm that the proposed method can be applied also as an induction machine operating
as a generator.

(a) (b)

(c) (d)
Figure 12. Harmonic components at 850 Hz under both measurement positions for generator operating at load variation
Figure
in healthy faultyHarmonic
and 12. components
case: (a) healthy at case,
case, (b) faulty 850 (c)
Hzvariation
underinboth
faultymeasurement positions
case for measurement for 1,generator
in position (d)
operating
variation at load
in the faulty variation
case for in healthy
measurement and
in position 2. faulty case: (a) healthy case, (b) faulty case, (c) variation
in faulty case for measurement in position 1, (d) variation in the faulty case for measurement in
4.4. Synchronous Machine
position 2.
In order to test the efficiency of the proposed method, the following tests are per-
formed on a synchronous machine operating as a generator. This machine is a 4 poles
wound smooth rotor (cylindrical rotor) with concentric rotor windings presented in Fig-
ure 13 and the following characteristics: 10 kVA, 230/400 V, 25/15 A, 50 Hz, 54 stator slots,
(Ns = 27), Nr = 16, R sint  113.5 mm , R sext  165 mm .
 (c) (d)
Figure
Energies 2021,12.
14,Harmonic
1132 components at 850 Hz under both measurement positions for generator operating at load variation15 of 22
in healthy and faulty case: (a) healthy case, (b) faulty case, (c) variation in faulty case for measurement in position 1, (d)
variation in the faulty case for measurement in position 2.

4.4.
4.4.Synchronous
SynchronousMachine
Machine
InInorder
orderto to test the
theefficiency
efficiencyofofthethe proposed
proposed method,
method, the the following
following teststests are per-
are performed
formed on a synchronous
on a synchronous machine machine operating
operating as a generator.
as a generator. This machine
This machine is a 4wound
is a 4 poles poles
smoothsmooth
wound rotor (cylindrical rotor) with
rotor (cylindrical rotor)concentric rotor windings
with concentric presented
rotor windings in Figurein13Fig-
presented and
the13following
ure characteristics:
and the following 10 kVA, 230/400
characteristics: 10 kVA,V,230/400
25/15 A,
V, 50 Hz,A,
25/15 5450
stator slots,
Hz, 54 (Nsslots,
stator = 27),
Nsr==27),
(N Rsint
16, N r ==16,113.5
R sint mm, Rsext
 113.5 mm = ,165  165 mm .
R sextmm.

Figure 13. Concentric rotor winding.

Figure 13. Concentric rotor winding.
Energies 2021, 14, x FOR PEER REVIEW AApicture
pictureofofthe
thetest
testbench
benchisisshown
shownininFigure
Figure1414where
whereaaDC
DCmachine
machineisisused16as
used ofaa
as 22
prime mover and external flux sensors are placed around the synchronous generator
prime mover and external flux sensors are placed around the synchronous generator frame.
frame.

Figure14.
Figure 14.Experimental
Experimentaltest
testbench
benchwith
withspecial
specialsynchronous
synchronous generator
generator modified
modified to to enable
enable inter-
inter-turn
turn short circuits.
short circuits.

Fordiagnosis,
For diagnosis, we weuse
usedata
dataobtained
obtainedfromfromthethesignals
signalsdelivered
deliveredby bytwotwoflux
fluxsensors
sensors
which are 180°◦ spatially shifted around the frame of the machine
which are 180 spatially shifted around the frame of the machine as shown in Figure as shown in Figure 8b.
Here, the load induces a variation of the spectral line delivered by both
8b. Here, the load induces a variation of the spectral line delivered by both sensors at sensors at 750 Hz.
For Hz.
750 presented results, aresults,
For presented single turn is short-circuited
a single (0.26%) in(0.26%)
turn is short-circuited phase Ainofphase
the stator. Fig-
A of the
ure 15aFigure
stator. gives the
15avariations
gives the of the line inofhealthy
variations the lineconditions
in healthyand Figure 15b,
conditions andinFigure
faulty ones.
15b,
Figure
in faulty15c,d
ones.shows the15c,d
Figure zoomshows
of harmonics
the zoom variation in the faulty
of harmonics variationcaseinfor
thesignals
faultymeas-
case
ured
for in Pos.
signals 1 and Pos.
measured 2. One
in Pos. can Pos.
1 and notice2. in
Onea healthy
can notice caseinan identicalcase
a healthy evolution of the
an identical
spectral line
evolution withspectral
of the load variation.
line withInload
the faulty case, In
variation. it isthe
measured an increase
faulty case, in position
it is measured an
2 and a wave variation in position 1. This asymmetry evolution is in agreement
increase in position 2 and a wave variation in position 1. This asymmetry evolution is in with (22),
(23), and phasor
agreement diagram
with (22), presented
(23), and in Figurepresented
phasor diagram 7. For theinexperimental
Figure 7. Fortests, the synchro-
the experimental
nous the
tests, machine has been
synchronous modified,
machine haspermitting
been modified,a small short-circuit
permitting fault.
a small short-circuit fault.
 For presented results, a single turn is short-circuited (0.26%) in phase A of the stator. Fig-
ure 15a gives the variations of the line in healthy conditions and Figure 15b, in faulty ones.
Figure 15c,d shows the zoom of harmonics variation in the faulty case for signals meas-
ured in Pos. 1 and Pos. 2. One can notice in a healthy case an identical evolution of the
spectral line with load variation. In the faulty case, it is measured an increase in position
Energies 2021, 14, 1132 2 and a wave variation in position 1. This asymmetry evolution is in agreement
16 of 22with (22),
(23), and phasor diagram presented in Figure 7. For the experimental tests, the synchro-
nous machine has been modified, permitting a small short-circuit fault.

(a) (b)

(c) (d)
FigureFigure
15. Harmonic components
15. Harmonic at 750 Hz under
components at 750both measurement
Hz under positions for synchronous
both measurement positions forgenerator operating at
synchronous
Energies 2021, 14, x FOR PEER REVIEW
variable load: (a) healthy case, (b) faulty case, (c) faulty case in position 1, (d) faulty case in position 2. 17 of 22
generator operating at variable load: (a) healthy case, (b) faulty case, (c) faulty case in position 1,
(d) faulty case in position 2.

Self-Excited Induction
4.5. Self-Excited Induction Generator
To confirm
confirmthetheapplicability
applicabilityofofthe
theproposed
proposed method,
method, another
anothertesttest
hashas
been carried
been out
carried
withwith
out an induction machine
an induction operating
machine as a self-excited
operating induction
as a self-excited generator
induction in a balanced
generator in a and
bal-
unbalanced
anced load as it is load
and unbalanced indicated inindicated
as it is Figure 16.inThis machine
Figure is a machine
16. This three-phaseis asquirrel cage
three-phase
induction
squirrel generator
cage inductionwith 4 poles, 50
generator Hz,4 3poles,
with kW, 380/660
50 Hz, 3V,kW,
7.3/4.2 A, 1420
380/660 rpm, 54
V, 7.3/4.2 A,stator
1420
slots, 54
rpm, and 36 rotor
stator slots,bars
and(Ns = 27, Nr
36 rotor bars= (Ns
18). = 27, Nr = 18).

Figure 16. Self-excited

Self-excited induction generator connected to a resistive balanced and unbalanced load.

This machine
This machine does
does not
not offer
offer the
the possibility to create
possibility to create artificial
artificial faults,
faults, but
but tests
tests with
with
variable frequency
variable frequencyand andthe
theunbalanced
unbalancedloadload
waswas carried
carried outout in order
in order to estimate
to estimate the
the reli-
reliability of the method in case of an unbalanced load. Actually, the aim is
ability of the method in case of an unbalanced load. Actually, the aim is to check that the to check
that the method
method providesprovides
a healthya healthy
responseresponse in unbalanced
in unbalanced operatingoperating conditions.
conditions. For IM
For IM operat-
operating as SEIG, the frequency changes with load and reactive power. If
ing as SEIG, the frequency changes with load and reactive power. If an unbalanced loadan unbalanced
load appears,
appears, the symmetry
the symmetry of theof the magnetic
magnetic field around
field around the machine
the machine will bewill be disturbed.
disturbed. How-
However, this dissymmetry should not be confused with that created by a
ever, this dissymmetry should not be confused with that created by a stator short-circuitstator short-
circuit fault.
fault.
For the tests, a resistive load star connected is used and the unbalanced case is ob-
tained by disconnecting phase A of the SEIG from the load. The reactive power is kept
constant and the flux sensors are placed 180° spatially shifted around the machine frame.
In this case, the frequency changes with the slip which is negative in generator oper-
ating condition (s < 0). Figure 17a shows the harmonic evolution for the load variation in
 Figure 16. Self-excited induction generator connected to a resistive balanced and unbalanced load.

This machine does not offer the possibility to create artificial faults, but tests with
variable frequency and the unbalanced load was carried out in order to estimate the reli-
ability of the method in case of an unbalanced load. Actually, the aim is to check that the
Energies 2021, 14, 1132 method provides a healthy response in unbalanced operating conditions. For17IM of operat-
22
ing as SEIG, the frequency changes with load and reactive power. If an unbalanced load
appears, the symmetry of the magnetic field around the machine will be disturbed. How-
ever, this dissymmetry should not be confused with that created by a stator short-circuit
For the tests, fault.
a resistive load star connected is used and the unbalanced case is obtained
by disconnecting phase ForA the
oftests, a resistive
the SEIG fromloadthestar connected
load. is used power
The reactive and the is
unbalanced case is ob-
kept constant
tained by disconnecting
◦ phase A of the SEIG from
and the flux sensors are placed 180 spatially shifted around the machine frame.the load. The reactive power is kept
constant and the flux sensors are placed 180° spatially shifted around the machine frame.
In this case, the frequency changes with the slip which is negative in generator operat-
In this case, the frequency changes with the slip which is negative in generator oper-
ing condition (s <ating
0). Figure
condition 17a
(s <shows the17a
0). Figure harmonic
shows theevolution for the load
harmonic evolution variation
for the in in
load variation
balanced mode. Here, themode.
balanced line atHere,
564 the
Hzline
(corresponding to s = −3.5%,
at 564 Hz (corresponding to s =kr = −1krand
−3.5%, = −1funda-
and funda-
mental harmonic mental
frequency 32 Hz)
harmonic evolves
frequency 32 in
Hz)the sameindirection
evolves when the
the same direction load
when theincreases.
load increases.

(a) (b)
Figure 17. Amplitude variation for SEIG harmonic components at load variation: (a) healthy machine with balanced re-
Figure 17. Amplitude variation for SEIG harmonic components at load variation: (a) healthy machine
sistive load, (b) healthy machine with unbalanced resistive load.
with balanced resistive load, (b) healthy machine with unbalanced resistive load.
In practice, the studied line moves with the slip, but here it will be identified as the
In practice, the
linestudied
at 564 Hz.line
The moves with of
time variation thetheslip, but here force
electromotive it will be identified
measured by both as the and
sensors
line
Energies 2021, 14, at 564PEER
x FOR Hz.REVIEW
The
the time variation
spectrum of the
of the signal electromotive
delivered by sensor force measured
1 in a balanced caseby
areboth sensors
presented in Figure
18 of 22
and the spectrum18. ofWethecan
signal
noticedelivered by curves
identical emf sensormeasured
1 in a balanced case are
by flux sensors presented
in Pos. in2. As
1 and Pos.
Figure 18. We can notice identical emf curves measured by flux sensors in Pos. 1 and Pos.
2. As in 11 kW IM, in the
11 kWanalyzed harmonics
IM, the analyzed is chosen
harmonics to take
is chosen intointo
to take account (10)
account (10)and
and the
the highest
highest measured value. measured value.

(a) (b)

(c)
Figure 18. Signals measured by the flux sensors for balanced load: (a) emf measured in position 1, (b) emf measured in
Figure 18. Signals measured by the flux sensors for balanced load: (a) emf measured in position 1,
position 2, (c) signal spectrum delivered from flux sensor in position 1.
(b) emf measured in position 2, (c) signal spectrum delivered from flux sensor in position 1.
Figure 17b shows the magnitude of the line at 617 Hz (36 Hz for the fundamental
Figure 17b shows the frequency)
harmonic magnitude in of
thethe
caseline at 617 Hzresistive
of unbalanced (36 Hz load
for the fundamental
connected at the SEIG out-
harmonic frequency) in the case of unbalanced resistive load connected at the
put. In this case (which is not a faulty case), the lines show the sameSEIG output.
variation in the two
measurement positions although the emf curves shown in Figure 19 are not identical.
 (c)
Figure 18. Signals measured by the flux sensors for balanced load: (a) emf measured in position 1, (b) emf measured in
position 2, (c) signal spectrum delivered from flux sensor in position 1.
Energies 2021, 14, 1132 18 of 22

Figure 17b shows the magnitude of the line at 617 Hz (36 Hz for the fundamental
harmonic frequency) in the case of unbalanced resistive load connected at the SEIG out-
put. In this
In this casecase (which
(which is not
is not a faulty
a faulty case),
case), thethe linesshow
lines showthe
thesame
samevariation
variationin
in the
the two
measurement positions although the emf curves shown in Figure 19 are not identical.
identical.

(a) (b)
Figure 19. Signals
Figure 19. Signals measured
measured by
by the
the flux
flux sensors for unbalanced
sensors for unbalanced load:
load: (a)
(a) emf
emf measured
measured in
in position
position 1,
1, (b)
(b) emf
emf measured in
measured in
position 2.
position 2.

This test confirms

This test confirmsthat
thatthe
theproposed
proposedmethod
method is is sensitive
sensitive to to field
field disturbance
disturbance gener-
generated
ated byshort-circuit
by the the short-circuit current
current and isand
notissensitive
not sensitive to frequency
to frequency variation
variation or unbalanced
or unbalanced load.
load.
4.6. Practical Precautions
The method is applicable for the diagnosis of all AC machines (motors and generators)
uses in an industrial process, except 2 pole machines because it does not generate a
dissymmetry in the phase winding. It uses the stray external magnetic field which is an
image of the air-gap flux density attenuated by the stator magnetic circuit. By measuring
the field, a difference can be observed which appears between the specific amplitudes
(850 Hz, 750 Hz) of the magnetic spectrum in two specific positions around the machine.
As the difference appears in the faulty machine but also in the healthy case, the load (which
generally is a disturbing factor) is used here for discrimination. The method consists in
comparing the signals delivered by each sensor during of the load variation. As shown in
Figure 12a, the sensitive harmonic increases in the healthy case for Pos. 1 and Pos. 2 when
the load increases. Whereas, in the faulty case, the increase of the load leads to a decrease
followed by an increase (Figure 12c). This asymmetric amplitude variation between Pos. 1
and Pos. 2 is used for diagnosis and it does not require a high level of expertise to analyze
the data. It concerns:
• the kind of sensor: the sensor has to be small enough so that one can consider that
the measured value of the flux density is the same as the flux density at the center of
the sensor. In order to get an acceptable value of the output voltage, the small size
has to be compensated by the number of turns. But as the increase of the number of
turns decreases the resonance frequency of the sensor, this latter has to be checked
with an impedance analyzer to get sure that the frequency resonance is far from the
analyzed frequency. The used sensors are 3.2 cm diameter and 1200 turns, which leads
to a resonance frequency at 93 KHz.
• the location of the sensors: both sensors have to be placed symmetrically from the
machine axis, approximately in the middle of the stator, between the end bells. Con-
cerning the accuracy of the symmetry of the sensors, it increases when the pole pair
number p of the machine is high. Actually, an error in the sensor alignment will be
multiplied by p and it could not be possible to consider that the first terms of (22) and
(23) are the same, leading to a disturbance in the diagnosis method.
• the number of measurements: practical tests have shown that when the sensors
are far from the axis of the damaged coil, the results give the impression that the
machine is healthy because the magnitudes at sensitive spectral lines always vary
in the same direction with the load variation. Theoretically, this can be taken into
 number p of the machine is high. Actually, an error in the sensor alignment will be
multiplied by p and it could not be possible to consider that the first terms of (22) and
(23) are the same, leading to a disturbance in the diagnosis method.
• the number of measurements: practical tests have shown that when the sensors are
Energies 2021, 14, 1132 far from the axis of the damaged coil, the results give the impression that the machine 19 of 22
is healthy because the magnitudes at sensitive spectral lines always vary in the same
direction with the load variation. Theoretically, this can be taken into account con-
sidering all the elementary components of Tables 2 and 4 instead of the predominant
account considering all the elementary components of Tables 2 and 4 instead of the
components grey highlighted. To avoid this confusion, it is necessary to perform sev-
predominant components grey highlighted. To avoid this confusion, it is necessary
eral
to measurements
perform such as at leastsuch
several measurements one isascloser to one
at least the faulty winding
is closer to the than the
faulty healthy
winding
winding, among the p windings that constitute a whole phase.
than the healthy winding, among the p windings that constitute a whole phase.Consequently, the
minimal number of measurements should be 2p, but to increase
Consequently, the minimal number of measurements should be 2p, but to increasethe probability of
fault
the detection,ofwe
probability recommend
fault detection,3p
wemeasurement.
recommend 3p Ofmeasurement.
course, in a practical point
Of course, in of
a
view, the locations of the sensors have to take into account the non-accessible
practical point of view, the locations of the sensors have to take into account the non- areas,
e.g., the areas
accessible ofe.g.,
areas, the mounting
the areas ofbase
the or the terminal
mounting base box (Figure
or the 20).box (Figure 20).
terminal

Figure 20.Illustration
Figure20. Illustrationof
ofthe
the33measured
measuredpositions
positionsof
ofthe
thesensors
sensorsaround
aroundthe
themachine.
machine.

Then, when the obtained results give at least one position with opposed magnitude
variations with the load, then a fault can be suspected. AI methods can be also used to
limit the number of measurements [36].
• case of inverter fed: it should be checked that the chopping frequency is higher than
the sensitive one.

5. Conclusions
This paper presents the application and the reliability of a noninvasive procedure
for the detection of inter-turn short-circuit faults in the stator winding of induction and
synchronous machines. This procedure uses the stray external magnetic field measured
in the vicinity of the AC machines by two sensors placed at a specific angular shift to
extract information about the faulty state of the machines. The analysis is carried out
considering the change of the transverse field obtained from the air-gap flux density which
brings up the properties related to the characteristics of the flux density components being
found in the transverse external field. The new contribution of the proposed diagnosis
method is the analysis strategy which eliminates the main disadvantage presented by other
diagnosis methods using the comparison with a healthy state assumed to be known before
the fault appears. Moreover, the described procedure is non-invasive and inexpensive,
characterized by the exploitation of the spatial dissymmetry of the field created by a
short circuit current in the area where the fault appears. This dissymmetry modifies the
rotor slotting harmonics and induces specific signatures in the external magnetic field
spectrum which are analytically demonstrated, identified, and presented in this paper. In
order to eliminate the constructive dissymmetry which exists practically, the presented
diagnosis method proposes a procedure where the external field is measured in the vicinity
of the electrical machine in the two cases: loaded and not-loaded machine. In order to
test the reliability of the method, different Isc levels and an unbalanced load are tested.
The paper shows that the proposed procedure can be applied to induction and synchronous
machines with wound smooth rotor, considering specific spectral lines for each machine,
with frequencies depending on the number of rotor slots. These specific frequencies
facilitate the use of this procedure in the presence of other magnetic fields as is the case
in an industrial environment. It is also shown that unbalanced operating conditions does
disturb the procedure, especially in the healthy case.
Energies 2021, 14, 1132 20 of 22

Author Contributions: Data curation, E.T., I.N.; Formal analysis, R.P., R.R. and A.C.; Funding
acquisition, P.L. All authors have read and agreed to the published version of the manuscript.
Funding: University Agency of Francophonie” (UAF), the Institute of Atomic Physics Bucharest
and LSEE.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Acknowledgments: The authors would like to thanks the “Francophone University Agency” (FUA)
(Agence Universitaire de la Francophonie) and the Institute of Atomic Physics Bucharest for the
financial support brought by Contract No. 19-AUF.
Conflicts of Interest: The author declared no potential conflicts of interest with respect to the research,
authorship, and/or publication of this article.

Abbreviations

p number of pole pair

f supply frequency
ns number of turns in series for a whole phase
n’s number of turns in an elementary section
y number of shorted turns
Ns , Nr number of stator and rotor slots per pole pair
I0s rms value of the no load stator current
s
Isc rms value of the short circuit current
ε air gap resultant m.m.f—healthy machine
λ air gap permeance
b air gap flux density- healthy machine
bx external radial flux density—healthy machine
h, hs m.m.f rank
ks,kr permeance rank
bhs kskr elementary component of air-gap flux density
bKH component of air gap flux density
K frequency rank of a flux density component
H pole pair number of a flux density component
bKx rank K harmonic of bx
CH attenuation coefficient
s , Rs
Rint inner and outer radius of the stator
ext
All the parameters and variables with “sc” lower index are related to the short
circuit turns.

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