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Published in IET Electric Power Applications
Received on 21st February 2013
Revised on 12th August 2013
Accepted on 13th August 2013
doi: 10.1049/iet-epa.2013.0065
ISSN 1751-8660
Three-dimensional finite element analysis of large
electrical machine stator core faults
Choon W. Ho1,*, David R. Bertenshaw2, Alexander C. Smith3, Trina Chan4, Mladen Sasic5
1
School of Engineering, Republic Polytechnic, Singapore 738964
ENELEC Ltd, Lightwater GU18 5XX, UK
3
School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL, UK
4
Aurecon Australia Pty Ltd, Victoria 3008, Australia
5
Iris Power LP, Toronto L4 V 1T2, Canada
*
School of Electrical and Electronic Engineering, University of Manchester, Manchester, UK
E-mail: drb@enelec.org.uk
2
Abstract: Faults in the stator cores of large electrical machines can both damage local winding insulation and propagate to
catastrophic failure. This study develops three-dimensional finite element models of inter-laminar insulation faults in order to
obtain a deeper understanding of the electromagnetic behaviour of core faults and the sensitivity of sensing systems. The
problem of developing a model that adequately reflects the laminar constraints of the structure, while remaining computable is
addressed, together with eliminating images from boundaries. The model was validated by experimental measurement and
results shown to be closely matched, with the fault current distribution also predicted. The sensitivity profiles for various fault
positions and lengths were determined, which enables condition-monitoring sensors to be more specific about the location
and true threat that a fault signal may pose to the machine.
1
Introduction
In the stator cores of large ac electrical machines, a core fault
occurs when a number of laminations become short-circuited
together. Such a stator core fault (SCF) can occur from a
number of sources such as incorrect manufacture,
overheating, vibration and many faults that can damage the
interlamination insulation [1]. The SCF creates a circuit via
the building keybars that encircles the core’s magnetic flux
and allows significant induced fault current to flow. This
SCF can consequently cause dangerous local ‘hot-spots’ to
occur in the region of the damage, which even if modest,
can affect the integrity and life expectancy of nearby
winding insulation [2], and potentially develop enough
energy to melt the stator iron [3, 4].
Monitoring and maintaining the integrity of interlamination
insulation is thus an important and routine function of service
testing, with the traditional high flux test method (aka ‘Loop
Test’ and Ring Flux Test’) in use since c1952 [5]. While this
test directly detects the heating phenomena of concern, the
required power levels can be very high (>1 MVA) and
hazardous, and the test take several days to conduct. In
addition, stator windings obstruct and thus attenuate slot
and core yoke thermal defect signals.
Alternate low flux electromagnetic testing has been in use
since 1980 [6], operating at typically 4% of operating flux,
with the most common method, Electromagnetic Core
Imperfection Detector (EL CID), now in use worldwide [7].
In this test, fault currents induced in damaged areas are
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measured by sensing their magnetic potential difference (m.p.
d.) across slot teeth edges, recorded as the ‘Quad’ current. The
normal recommendation [7, 8] is that a Quad signal above
100 mA ‘should be regarded as significant and investigated
further’. The method involves inducing a toroidal flux in the
core at typically 4% of operating level, using a temporary
excitation winding inserted through the generator bore. Such a
low flux level allows the test to be conducted with normal
power sources and no heating risk. The fault currents induced
in any damaged areas are measured by sensing the m.p.d.
resulting from them with a Chattock potentiometer [9].
The Chattock is applied across the core teeth straddling
each slot and scanned axially along the slots with the
output m.p.d. resolved into components in phase (Phase)
and in quadrature (Quad) with the excitation current by a
phase-sensitive detector. Since the voltage induced in any
fault circuit is in proportion to the rate-of-change of flux,
the resultant fault current can be detected as that m.p.d. in
quadrature to the flux. Thus, the resistive (heat-producing)
element of the fault current component of the Chattock
signal is indicated by the Quad m.p.d, with the Phase signal
representing the excitation m.p.d. The signals are processed
and interpreted conventionally, as described in [6, 10, 11].
There are several alternate methods of determining
generator inter-lamination insulation damage, with the
principle offline ones surveyed by Tallam et al. [12],
however all require internal machine access to test. There
remain no successful online means of detection, although
research into potential methods is reported using external
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field sensors [13], electrical parameter variation for smaller
machines [14] and shaft voltage sensors [15]. However,
their application is likely to be limited on larger machines
since a nascent fault can produce local core heating,
damaging to nearby HV winding insulation, from an
amount of power that is extremely small by comparison
with the total core loss.
2
Modelling stator core faults
Although the electromagnetic method is proven to detect fault
currents, the Chattock only senses the resultant m.p.d. in that
region, and does not provide any information regarding the
distribution of the current. Nor is it well researched with
what sensitivity signals from different parts of the stator
core will reflect the underlying fault current. Significant
work has already been completed on two-dimensional (2D)
finite element (FE) modelling of an SCF [16–18], which
has demonstrated the ability to predict the signals seen and
their amplitudes for long faults. Furthermore, analytic 3D
work has also shown the current distribution in short faults [19].
However, simple 2D FE and analytic models always
over-estimate the detected fault (Quad) current due to
inability to accommodate a short fault length (5–50 mm).
Real faults are rarely long and are often interrupted by core
packet vents, plus there is a need to detect and correct
embryonic faults that have not yet developed into a
substantial threat. To obtain a more accurate analysis
consequently requires a 3D model of the induced currents
and fields, which adequately reflects the lamination
structure where axial conductivity and permeability is
repeatedly interrupted by fine interlamination insulation
gaps. This creates a challenging problem to develop
successful models that are computable.
Recent FE research [20–22] has proposed dual-mesh
arrangements still in development, while further work [23,
24] has shown that homogenisation techniques normally
used to resolve the problem of laminated structures can be
successfully used to simplify the modelling of stator
lamination stacks. Using these results, a fault was modelled
[25] and compared with a physical test system consisting of
a pair of axially anti-symmetric 3-slot segments of stator
core [26]. The current in a short welded fault was
constrained to just the outer-most laminations of the fault,
due to lack of connecting building bars on the core rear.
The modelled fault current however diverged substantially
from experiment and was 155% of that measured, with the
modelled EL CID signal 193% of that measured and having
poor off-centre correlation.
3
Development of a 3D FE model
This study sought to develop a more representative 3D model
of an electrical machine and successful validation of the
electromagnetic detection of a SCF, using a normal annular
stator core for both the model and experimental validation,
with normal test induction. The modelled stator core is
based on an axial section of a 48-slot 71 MVA
turbo-generator, with a 76 mm centre core packet with 10
mm outer packets separated with 10 mm vent spacers, using
M310-50A steel. The laminations have an overall diameter
of 1777 mm, bore 860 mm, and slot depth 155 mm with 12
keybars connecting the rear of all the laminations.
Calibrated length faults of known resistivity to simulate the
resistance of an SCF, were applied to tooth tip, slot side and
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Fig. 1 Fault locations
Fig. 2 3D-60° FE model
tooth and core body as indicated in Fig. 1, which thus formed
a fault circuit around fault-lamination-keybar-lamination
fault. The faults were only placed on the centre 76 mm
packet; thus only this part was modelled. A 2D model
developed using a 60° section with symmetry was extruded
38 mm axially, using axial symmetry to halve the 76 mm
packet size, with the meshed model shown in Fig. 2. The
induction current flows down the centre axis.
The ability to model a large structure to lamination level
(typically 0.5 mm thick with 0.01 mm insulation) remains
computationally prohibitive, thus the laminations were
homogenised [27] by setting the axial relative permeability
equal to the effective permeability from the stacking factor
(0.98), giving µz = 1/(1 − 0.98) = 50. Planar isotropic steel
relative permeability was set to 2950 as measured for
M310-50A steel at 0.05 T flux (all flux levels and FE
current levels are peak), being the normal electromagnetic
test level. To ensure that the fault current flow was
constrained in the lamination planes by the interlamination
insulation, the general axial conductivity σz was set to zero.
The faults identified were optionally made 10/20/40/60 mm
long (half this length in the model) by adjustment of the
fault region conductivity σz. The central excitation current
was set at the level needed to induce a mean 0.05 T flux in
the core yoke to induce current in the applied fault.
The FE software [28] solves the magnetodynamic problem
using the vector magnetic (A–V) formulation. Each end plane
boundary was enforced with the Dirichlet condition Ax = Ay = 0
with an unconstrained Az to provide uninterrupted axial
excitation current, Jz. This meant there was no z-directed
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component of flux density on the boundary surface. The outer
periphery of the model was constrained with Ax = Ay = Az = 0.
The 60° sector boundaries (e.g. A–A′) were conventional
Neumann. A post-processing algorithm sampled the model
results at 2 mm axial steps to determine the simulated Quad
Chattock signal from the imaginary component of the m.p.
d. between the tooth tips.
4
Fig. 3 Axial symmetric Chattock signals for a tooth tip fault
current of 0.8 Apk in fault_1 location
Fig. 4 Filamentary current loop FE model
Problem of images
Initial Quad scans results gave problematic results shown in
Fig. 3. The signal reached a maximum as expected in the
fault centre; however it would be expected to decay towards
zero away from the fault, whereas it is seen to asymptote to
a substantial constant value. Naturally, the Dirichlet
condition Ax = Ay = 0 on the centre axial boundary (z = 0
mm) provides the correct condition to mirror the half-length
fault current in the ‘missing’ half. It was thus suspected that
the same condition on the end boundary plane (z = 38 mm)
was causing this phenomenon to also occur here, even
though the fault current had terminated before the boundary.
With the above Dirichlet constraint, only Bx and By can
exist on the boundary plane while the flux density normal
to the plane, Bz, is zero. Therefore, in order to force the
normal flux density component to zero, an equal but
opposite Bz must exist on the other side of the boundary
[29]. This implies that there is an image of the fault current
reflected about the problem boundary to enforce this
boundary condition and is preventing the Quad signal from
reducing to zero as it approaches the boundary.
It was further suspected that the boundary condition was not
just imposing a single image, which could possibly be
analytically compensated for, but an infinite array of images.
To investigate the effect of images caused by the boundary
constraint, a filamentary current loop within a 3D air cube
FE model was created in Fig. 4, simple enough to allow a
precise analytic solution to be developed for comparison.
The six surfaces are constrained with the same conditions
Fig. 5 Equivalent open-boundary implementation of the Dirichlet plane conditions using the method of images
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imposed on the axial boundary plane on the original SCF
model and the currents away from the boundaries.
The existence of the image currents outside the boundaries
of the cube (Fig. 4) because of the Dirichlet conditions
imposed on the boundary planes were also investigated
using an analytical open-boundary model with an array of
current sources in air shown in Fig. 5. The current loop
highlighted in bold in Fig. 5 denotes the original current
source, geometrically the same as the FE model, while the
others are the image sources. Each is spaced equidistant
from the boundaries, arranged in such a manner that there is
cancellation of certain field components on the boundary
lines. Along the vertical dotted line (A–A′), the image
currents are in effect equivalent to enforcing Ay = Az = 0
with Ax unconstrained. Similarly, Ax = Az = 0 occurs on the
horizontal dotted line with Ay unconstrained. These multiple
current loop images will thus produce the equivalent
Dirichlet condition behaviour on each of the boundary
planes, allowing study of the influence of the boundary
constraints on the FE solution by comparison with the
analytical model.
The open-boundary problem was solved analytically using
Biot–Savart, where R is the distance from the required point
to the current element Idl and âR is the unit vector that
corresponds to R in (1).
dH =
Idℓ
× âR
4pR2
(1)
From this the flux density at the centre of the current loop with
current I in the x–y plane of side length L is
√
2 2m0 I
âz
B=
pL
(2)
For the multiple images model, the flux density at the same
point was solved using a development of (24) in reference
[19]. This allows the flux density at any arbitrary point in
space Bp to be found from the four current paths flowing in
different orientations using (3) for current path 1 (and with
polarity adjustment path 2), resulting in x̂ and ẑ flux
vectors. The equation can be similarly developed for paths
3 and 4, giving ŷ and ẑ flux vectors.
⎧
⎪
⎨
(yp + yf )zp
mI
0
1/2
⎪
2
2
4p xp + zp ⎩ x2p + z2p + (yp + yf )2
⎫
⎪
⎬
(yp − yf )zp
−
1/2 x̂
⎪
⎭
x2p + z2p + (yp − yf )2
⎧
⎪
⎨
(yp − yf )xp
m0 I
+
1/2
⎪
4p x2p + z2p ⎩ x2p + z2p + (yp − yf )2
⎫
⎪
⎬
(yp + yf )xp
−
1/2 ẑ
⎪
⎭
x2 + z2 + (y + y )2
p =
B
p
p
p
(3)
f
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Model
Flux at coil centre
FE Model
analytic model (no images)
analytic model (15 images)
3.9838 × 10−5 T
4.0227 × 10−5 T
4.0196 × 10−5 T
Fig. 6 Flux density Bz variation along path A–A′ in Fig. 5
Table 1, which shows both that the FE model matches the
analytic model to within 1% and that the images have
negligible effect within the current loop.
To demonstrate that the analytic model with multiple
current images produces the same result as the FE model at
the boundary, the flux density Bz normal to the plane was
computed along the Dirichlet boundary A–A′ (A = 0 m) in
Fig. 5, for just the source current loop and with 8 and 15
image current loops. Fig. 6 shows that there is a poor
correlation between the Dirichlet-enforced FE results and
the open-boundary solution without any image current
loops. However, as more image currents are included into
the
open-boundary
calculations,
the
correlation
progressively improves, with the 15 image current
correlating well with the FE solution. The trend suggests
the flux density values would converge to the FE solution
for an infinite number of images.
This confirms the conjecture that the high standing Quad
signal observed in the FE axial Chattock scan near to the
boundary edge is caused by the development of multiple
external image current sources when Dirichlet conditions
are imposed.
5
The models were validated initially by computing the value of
the flux density at the centre of the coil carrying a peak fault
current of 0.8 A and side length of 22.5 mm, in the FE model
and analytically for no and 15 images. The results are given in
4
Table 1 FE and analytic model results
Revised 3D FE model
To circumvent the effects of the 38 mm end external image
currents, the 3D FE stator core model was extended axially,
so that the fault would be minimally affected by images
because the axial boundary planes were a proportionally
large distance from the fault. The axial length of the half
core model packet was increased from 38 to 310 mm total
length (equivalent to 620 mm total core) with the fault
region maintained at the symmetric centre (z = 0 mm) of
the extended packet. To prevent any unwanted eddy
currents in the extended packet producing any field
distortion the conductivity was set to zero outside the centre
38 mm region and the mesh density outside reduced to
lessen the impact on processing time. The final 3D model
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Fig. 10 for fault_3. It can be seen the FE predictions are a
very close match to the results. The results for fault_2 were
very similar to fault_1, as would be expected due the small
positional change, and fault_2a was close to the results for
the fault on the slot base, fault_3. The error in FE
prediction at fault centre is given in Table 2 for the key
fault positions of tooth tip and slot base, for all fault
lengths. It can be seen that the errors between FE model
and experiment are small with the great majority under 10%
7
Fig. 7 Modelled Chattock Quad signals for Fault_1 lengths 10–
60 mm
consisted of 196 908 nodes that took approximately 12 h of
CPU time (2.8 GHz Xeon) to solve.
The revised model was run for the intended range of fault
lengths and positions, with little evidence of image
interference as shown for the plots of fault_1 in Fig. 7.
6
Experimental validation
A short experimental stator core of the same geometry as the
3D model, shown in Fig. 8a and described in reference [16],
was used as a validation tool. Surface faults (faults_1 to
fault_3) were imposed by pressing appropriate lengths of
0.45 mm dia. Nickel–chrome (NiCr) wire against lamination
edges solvent cleaned and prepared to achieve uniform
electrical contact, the wire having the same resistance per
unit length as the FE modelled faults. Uniform contact was
achieved by use of screw or hydraulic pressure clamps
shown in Fig. 8b. Good electrical contact down the back of
the core was ensured at the keybars.
The fault Quad signals were measured conventionally with
an EL CID system using a calibrated 175 mm Chattock, at a
flux density of 0.057 T (as established in the model),
requiring an excitation of 66 A-t pk. The EL CID Reference
was taken from the core flux rather than excitation current
to prevent error from the core loss angle between excitation
current and flux [10] since this loss was not modelled. The
resultant standing no-fault Quad value was initially
determined, then subtracted from the measurements to give
the true Quad value for the fault.
The results are compared with the FE values whose short
fault values were averaged across 4 mm to allow for the
typical Chattock coil diameter, in Fig. 9 for fault_1 and
Fault signal attenuation
The detection efficiency of the Chattock coil is known to be
highly dependent on the actual fault length, and only
approaches 100% for infinite fault lengths. Bertenshaw
et al. [19] demonstrate the analytically computed sensitivity
with surface fault length, which naturally falls to zero at
zero length. However in a real core, the laminated structure
constrains the induced fault flux and thus improves
sensitivity to short faults, a phenomena first investigated by
Sutton [30] while considering the circumferential spread of
fault potentials.
The 3D FE model allows determination of the expected
peak current in the fault and thus the ability to determine
the detection sensitivity for various lengths and position of
fault. The current in the FE model fault was determined by
integrating J.dS across the fault area to provide a family of
fault currents with fault length, shown in Fig. 11 for
fault_1. The other fault current distributions were
comparable. These current distributions are very similar to
those previously analytically modelled [19].
The sensitivities of Chattock detection of faults both in the
FE model and the experimental results were determined,
where the experimental fault current is assumed to be equal
to the modelled current. The predicted sensitivities for the
fault centre m.p.d. against centre fault current for all lengths
of fault_1 to fault_3 were plotted in Fig. 12, plus the
experimental values. The values from the 2D analytic study
[19] for fault_1 are also plotted for comparison, however
due to its use of Images to compute values, this method
cannot be used to determine signals from a fault down a slot.
8
Discussion
The 3D FE model showed a very good prediction of the
experimental results, and the aggregate error is an order of
magnitude less than the errors suffered by previous
researchers discussed in Section 3. However, there is a
Fig. 8 Experimental stator core
a Stator core section
b Fault application hydraulic clamp
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Fig. 9 Fault_1 FE and test results
a 10 mm
b 20 mm
c 40 mm
d 60 mm
Fig. 10 Fault_3 FE and test results
a 10 mm
b 20 mm
c 40 mm
d 60 mm
particular discrepancy in the 10 mm Fault_1 result, which is
believed to most probably come from experimental
limitations, such as imprecision in the length of fault wire
that actually contacted the laminations (just a − 1 mm error
would yield + 10% FE overprediction). In addition, any
fault contact resistance causes an effective shortening of the
fault because of current sharing between the end
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laminations, and further illustrates the particular sensitivity
of the shortest fault to error.
Of particular interest is the sensitivity computations for the
various faults as determined experimentally compared to the
FE model. It can be seen that the tooth tip centre fault_1 is
predicted to have best sensitivity to short faults; however, in
practice it is comparable with the tooth tip side fault_2. A
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Table 2 FE model errors to experiment
Fault length
Fault_1
Fault_3
10 mm
20 mm
40 mm
60 mm
mean absolute FE error
+21.5%
+5.8%
−4.4%
−7.6%
8.4%
+6.1%
−6.8%
−6.6%
−8.2%
Fig. 11 Fault_1 modelled fault currents
modelled sensitivities, it can be seen that the shortest (10
mm) Fault_3 fault has an approximate 24°C/100 mA
correlations. Since the threshold for service attention is 100
mA [7] this means that such defects will be detected well
before they pose a threat to the stator core.
Certain approximations have been inevitable in developing
these results. The need to eliminate the effect of images led to
the use of a very long continuous (620 mm) steel FE model,
whereas many machines have 30–50 mm long packets with
air vents isolating the packets. This may lead to some
excess spread of m.m.f. axially in the FE model and thus
attenuation of the signal from faults down the slots,
although it is seen that the shorter packet experimental
model closely matches the continuous steel FE model for
down-slot faults.
In order to rationally mesh the fault regions, the conducting
fault area was a much larger area than the experimental 0.45
mm2 NiCr wire (but with appropriately compensated
resistivity), and this is likely to affect to a small degree the
impact of lamination resistivity on the fault current value
and distributions. It is very difficult to measure the fault
current distribution without disturbing the fault, thus the
experimental fault current in the fault centre is assumed to
be comparable to the FE determined current. This may
mask some small error from, for instance, test contact
resistance.
The buried faults_4–7 are not studied since there is as yet
no ability to experimentally verify these results.
9
Fig. 12 Fault signal sensitivity with length
probable source of the difference is the aggregating effect of a
real Chattock sensor, whose coil diameter ( > 4 mm) and
spacing off the core surface (2–3 mm) will average and thus
attenuate the peaks of any short fault, beyond that allowed
for here, and also contribute to the 10 mm Fault_1
discrepancy.
The sensitivity to short faults appears to be similarly
reduced both half-way down the slot (fault_2a) and at the
base (fault_3), and interestingly they both closely match the
analytic detection sensitivity. Again the experimental values
supported the FE predictions, slightly improving on them
for longer faults.
The apparently low sensitivities however still allow
detection of embryonic short faults. The electromagnetic
Quad signal of 100 mA has been shown to correlate to
∼9 °C for a typical 15 mm long surface fault (e.g. Fault_1)
[31]. From Fig. 12 comparing relative mean experimental/
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Conclusions
A 3D FE model of a normally constructed stator core with an
SCF has been developed, which can be solved in a realistic
processing time. Although the work does not attempt to
model at lamination level, the appropriate laminar
constraints provide an adequate simulation of the
electromagnetic environment. The development of
interfering images in a geometrically limited model was
demonstrated and a technique used to avoid the effect. In
particular, the potential presence of such images in FE
models (2D or 3D) needs to be considered and
accommodated to ensure accurate results are obtained.
The model has shown that the experimental detection of
stator core faults can be closely predicted by a 3D FE
model, to a much closer degree than a 2D model. The
model has successfully predicted fault signals both on the
tooth tip and on a slot base. Analytic prediction of fault
signals for short surface faults are shown to be pessimistic
because of their inability to account for the anisotropy in
the stator core; however, they do match faults down a slot.
The variable sensitivity of the Chattock detection of the
Quad signal, as a means of measuring the fault current, is
clearly shown, ranging from 25% for 10 mm to >70% for
60 mm length surface faults. However, the sensitivity of
detection of a fault down the slot, although still on the steel
surface, is further attenuated for short faults but not longer
faults. The reason for this differing sensitivity is not clear,
and requires further research.
The model has determined the correlation between a
modelled and calibrated fault with a defined resistivity, thus
avoiding the unknown resistivity of welded connections.
This has shown that embryonic faults, not yet of the
severity of melted iron, can be readily detected, modelled
and experimentally validated. The model also provided
information on the current distribution in the fault, which is
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seen to closely match the values expected from analytic
studies. It is seen that for faults whose current is <500 mA,
the current is essentially constant with length for lengths
>20 mm, although rounded for shorter faults.
10
Acknowledgments
The authors wish to acknowledge the support for this work
provided by Iris Power LP, the Knowledge Transfer
Partnership Scheme UK, Brush Electrical Machines Ltd and
Areva T&D.
11
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