Fault diagnosis in power transformers using the Local Statistical Approach
1
Outline
• Neural modeling and fault diagnosis is proposed for the detection and isolation of
incipient failures in electric power transformers
(i) A neural-fuzzy network is used to model the dynamics of a critical parameter
of the power transformer known as Hot Spot Temperature, in fault-free conditions
(ii) The output of the neural-fuzzy network is compared to real measurements
of the Hot Spot Temperature and residuals are generated
(iii) The residuals undergo statistical signal processing according to a
fault detection and isolation (FDI) algorithm
(iv) If a fault threshold, defined by the FDI algorithm, is exceeded then
deviation from normal operation can be detected at its early stages
and an alarm can be launched
(v) Fault isolation can be also performed, i.e. the sources of fault in the power
transformer (components subject to failure) can be also identified
(vi) Evaluation tests about the performance of the FDI method are provided
IEEE SAS 2012, Brescia, Italy
Incipient fault detection for electric power transformers
using neural modeling and the local statistical approach
to fault diagnosis
Gerasimos G. Rigatos(1)
(1) Department of Engineering
Harper Adams University College
Edgmond, TF10 8NB,
Shropshire, UK
email: [email protected]
Pierluigi Siano(2) and Antonio Piccolo(2)
(2) Department of Industrial Engineering
University of Salerno
Fisciano, 84084
Salerno Italy
email: [email protected]
IEEE SAS 2012, Brescia, Italy
Fault diagnosis in power transformers using the Local Statistical Approach
2 IEEE SAS 2012, Brescia, Italy
•Self-Healing and Adaptive
•Interactive with consumers and
markets
•Optimized to make best use of
resources and equipment
•Predictive rather than reactive,
to prevent emergencies
•Distributed across
geographical and
organizational boundaries
•Integrated, merging monitoring,
control, protection,
maintenance, EMS, DMS,
marketing, and IT
•More Secure from attack
The Smart Grid –IntelligridVision (EPRI)
Fault diagnosis in power transformers using the Local Statistical Approach
3 IEEE SAS 2012, Brescia, Italy
The Smart Grid
Fault diagnosis in power transformers using the Local Statistical Approach
4 IEEE SAS 2012, Brescia, Italy
The Smart Grid
Fault diagnosis in power transformers using the Local Statistical Approach
A modernized digital substation usually consists of:
intelligent primary devices (such as optic-electric transformers and intelligent
circuit breakers (CBs)) that can convert analog signals into digital signals completely
during the Acquisition, Transmission, Treatment and Output Process
networked secondary devices, able to implement the interoperability and
information sharing between the intelligent electronic devices (IEDs).
All of the alarm messages are collected and sent to a remote-control center.
The monitoring data of the operational devices in digital substations are displayed by
but not processed and this could lead to the inability of the operators to process
information from the data and, hence, identify what has occurred in a short time,
especially under stressed conditions such as a fault scenario.
Monitoring data for early detection of failures in electric power transformers
in digital substations
5 IEEE SAS 2012, Brescia, Italy
Fault diagnosis in power transformers using the Local Statistical Approach
The situation will be more challenging for cases with false or missing alarms.
Therefore, it is of a great significance to develop an online intelligent alarm-
processing system based on the architecture of digital substations in order to assist
the operators in making a decision for maintaining the secure and reliable operation of
power systems.
An online intelligent alarm-processing system is proposed here for the early detection
of failures in electric power transformers, it can be succeeded with neural
modeling and the Local Statistical Approach to Fault Diagnosis.
6 IEEE SAS 2012, Brescia, Italy
Monitoring data for early detection of failures in electric power transformers
in digital substations
Fault diagnosis in power transformers using the Local Statistical Approach
Failures of oil immersed power transformers
• The aging of power transformers results in increase of failures rate (Fig. 1).
• Insulation breakdown in windings is a serious failure that can generate
substantial costs for repair and financial losses due to outages.
• The onload tap changers (OLTC) and the bushings are also components prone
to failure (Fig. 2).
7 IEEE SAS 2012, Brescia, Italy
Fig. 1
Fig. 2
Fault diagnosis in power transformers using the Local Statistical Approach
8 IEEE SAS 2012, Brescia, Italy
Transformer On-Line Monitoring & Diagnostics?
•Detecting signs of failure conditions
•Reducing probability of catastrophic failure
•Reducing unscheduled outages
•Addressing specific unit or population issues
•Loading T&D equipment for maximum efficiency
•Deferring upgrade capital costs
•Managing & extending the life of equipment
•Reducing O&M costs
Fault diagnosis in power transformers using the Local Statistical Approach
9
Analytical model of the power transformer
• The stages for obtaining an analytical model of the power transformer are as follows :
• Calculate at each time step the ultimate top oil temperature rise in the
transformer from the load current at that instant, using
• Calculate the increment in the top oil temperature from the ultimate top
oil rise and the ambient temperature at each time step using the differential
equation
• Calculate the ultimate hot spot temperature rise using
IEEE SAS 2012, Brescia, Italy
1
2
3
q
LRTOUTO
R
RI
1
12
,,
TOAUTOTO
TOdt
d
,
2,, LRHSUHS I
RTO ,
TO
RHS,
Fault diagnosis in power transformers using the Local Statistical Approach
Analytical model of the power transformer
• Calculate the increment in the HST rise, using the differential equation:
• Finally, add the top oil temperature to the hot spot temperature rise to get the
Hot Spot Temperature, using:
• The model of Eq. (1)-(5), named top-oil rise model, is based on simplifying
assumptions and its accuracy can deteriorate due to parameter variations.
• As a result, in order to protect power transformers, conservative safety factors
have been introduced that prevent the transformer’s overheating.
• To assure safe operation of the transformer, the calculated maximum power
transfer may be 20-30% less or worse than the real transformer capability.
10 IEEE SAS 2012, Brescia, Italy
4
5
HSUHSHS
HSdt
d
,}{
HSTOHS
Fault diagnosis in power transformers using the Local Statistical Approach
11
Neurofuzzy modeling of the power transformer
• As shown, the analytical model of the power transformer’s Hot Spot Temperature is
represented in the generic form of nonlinear differential equations
))(),(()(
))(),(()1(
tutxhty
tutxgtx
• Alternatively, neurofuzzy models can be also used in modeling of nonlinear
dynamical systems, such as electric power transformers
• A neuro-fuzzy model consists of IF-THEN rules of the form
(x) is THEN is AND ... AND is AND is IF :
_
2211lll
nnlll zyAxAxAxR
which are extracted from numerical data using
(i) clustering methods followed by linear least squares
(ii) nonlinear least squares
);,...,( 1 yxx n
IEEE SAS 2012, Brescia, Italy
• Such black-box models capture accurately the nonlinear power transformer
dynamics without the simplifying assumptions of the analytical models
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 12
• The Hot Spot Temperature dynamics is approximated by Takagi-Sugeno
neural-fuzzy models which contain rules of the form
n
i
li
li
l
lnn
lll
Llbxwy
AxAxAxR
1
_
2211
,...,2,1 , THEN
is AND ... AND is AND is IF :
Neurofuzzy modeling of the power transformer
Fault diagnosis in power transformers using the Local Statistical Approach
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• The output of the neural-fuzzy
model is
L
l
n
iiA
L
l
n
iiA
l
x
xy
y
li
li
1 1
1 1
_
^
)(
)(
• The stages of neural-fuzzy modeling are Data
1. Structure Selection
2. Clustering
3.Extract model from data
4. Neuro-fuzzy network
simplification
5. Model Validation
accept model reject model
check similarity
measure
check Fisher
information matrix
review model
structure
Neurofuzzy modeling of the power transformer
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 14
Fault diagnosis for electric power transformers
Neural Model
nXXX ,....,2,1
nXXX ,....,2,1
0Θ
Φ
Θ
dimension
reduction
002,
01 ,...., nyyy
nyyy ,....,2,1
neee ,....,2,1
residual
Physical System
Exact Model
• The local statistical approach is used for faults diagnosis of the power transformer
• The Local Statistical Approach has been applied to Fault Detection and Isolation
of mechanical structures and rotating machinery
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 15
Fault diagnosis for electric power transformers
The neural model is used to simulate the dynamics of the Hot Spot Temperature,
both in fault and in fault-free conditions and has been extracted from input/output
data.
In order to verify the proposed method performance, the real system has been
simulated by using the so-called exact model.
In order to have the neuro-fuzzy model and the exact model with the same number
of parameters, the exact model can be also represented by a neuro-fuzzy model
extracted from input/output data of the transformer.
Therefore, when the transformer is affected by slight parameters variations,
which can lead to a fault, the output of the exact model will differ from the
output of the neuro-fuzzy model.
In other words, while the neuro-fuzzy model simulates the transformer in fault-free
conditions, the exact model simulates the transformer in all conditions.
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 16
Fault diagnosis for electric power transformers
The concept of this FDI technique is as follows.
At each time instant the neural network’s output is compared to the real condition of
the system. The difference between the real condition of the power system and the
output of the neural network is called residual.
The statistical processing of a sufficiently large number of residuals through the
aforementioned FDI method provides an index variable that is compared against a
fault threshold and which can give early indication about deviation of the transformer
from the normal operating conditions.
Therefore alarm launching can be activated at the early stages of transformer
ubnormal operating conditions, and measures can be taken.
Under certain conditions (detectability of changes) the proposed FDI method enables
also fault isolation, that is to identify the source of fault within the power transmission
system.
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 17
Neural Model
nXXX ,....,2,1
nXXX ,....,2,1
0Θ
Φ
Θ
dimension
reduction
002,
01 ,...., nyyy
nyyy ,....,2,1
neee ,....,2,1
residual
Physical
System
Exact Model
G
G
N
N
)1(^
ky
layer Gaussians Gaussians of Products layerion Normalizat
)(ky
)( nky
)(ku
)( mku
G
G
N
N
)1(^
ky
layer Gaussians Gaussians of Products layerion Normalizat
)(ky
)( nky
)(ku
)( mku
undistorted exact model (fault free
system)
distorted exact model (system subject to
fault)
Fault diagnosis for electric power transformers
• Residuals are generated between the output of the exact (fault-free) model and
the neural model that represents the present condition of the power transformer
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 18
Fault diagnosis for electric power transformers
The proposed FDI method aims at transforming complex detection problems
concerning a parameterized stochastic process into the problem of monitoring the
mean of a Gaussian vector.
The local statistical approach consists of two stages:
1. the global test that indicates the existence of a change in some parameters of
the fuzzy model, the problem of change detection with the test consists of
monitoring a change in the mean of the Gaussian variable which for the one-
dimensional parameter vector theta is formulated as:
2. the diagnostics tests (sensitivity or min–max) that isolate the parameter affected
by the change. The local statistical approach is suitable for fault diagnosis in
industrial systems.
2
),(~1 2
1
^
*
Ny
eN
XN
i
iiN
Normalized residual
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 19
• Hypothesis testing
Fault diagnosis for electric power transformers
It is noted that X is the monitored parameter for the FDI test, which means that
when the mean value of X is 0 the system is in the fault-free condition, whereas
when the mean value of X has moved away from 0 the system is in a faulty
condition.
Therefore, the model validation problem amounts to make a decision between
the two hypotheses:
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 20
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 21
• The decision tool is the Likelihood ratio
)(
)(ln)(
0
1
Xp
XpXs
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 22
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 23
Fault diagnosis tests
Fault diagnosis in power transformers using the Local Statistical Approach
Measurements of the Hot-Spot Temperature and of the Load Current
• The measurement station is formed of thermocouples to measure the Hot Spot
Temperature of the medium and voltage windings and the Top Oil Temperature
• The Hot Spot Temperature can be also measured with Optical Fiber sensors
• The manufacturer's specifications give the most probable hot-spot position.
• A hall effect current transducer is used in order to measure the load current.
24 IEEE SAS 2012, Brescia, Italy
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 25
Fault diagnosis tests
• The Hot Spot Temperature dynamics can be modeled using a neuro-fuzzy network
with output and inputs )(kHS and )1()2(),1( kIkk LTOTO
• The data for generating the exact (fault-free) model of the power system were
obtained from experimental equipment (power transformer) of the University
of Salerno
approximation of HST with
Hermite basis functions approximation of HST with
Takagi-Sugeno neurofuzzy model
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 26
• After removal of redundant rules the neurofuzzy model of the power transformer
consisted of 22 rules with 39 parameters (12 parameters in the nonlinear part
and 27 parameters in the linear part)
• The value of the change threshold was set to 39
Fault diagnosis tests
Parameters stand for the centers of the fuzzy sets which appear in
antecedent (IF) part of the fuzzy rules
that constitute the thermal model of the power transformer.
On the other hand, parameters stand for the weights variables appearing in
the consequent (THEN) part of the neuro-fuzzy model.
)(lic
)(liw
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 27
(a) Success rate of the sensitivity (x) in case of a change in linear parameter
(b) mean value (o) of the global test 2
(a) (b)
)10(1w
Fault diagnosis tests
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 28
(a) Success rate of the sensitivity tests in case of a change in nonlinear parameter
(b) mean value of the global test 2
)1(1c
(b) (a)
Fault diagnosis tests
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 29
Conclusions
• Early detection of failures in electric power transformers can be succeeded with
neural modeling and the Local Statistical Approach to Fault Diagnosis
• Neuro-fuzzy networks are proposed for modeling the dynamics of a critical parameter
of the power transformer known as Hot Spot Temperature.
• The output of the neural-fuzzy network is compared to the output of the exact model
(representing the fault-free condition of the transformer) and residuals are generated
• The residuals undergo statistical signal processing according to a fault detection
and isolation algorithm (Local Statistical Approach to FDI)
• The Local Statistical Approach consists of the global test for fault detection and
of the sensitivity and min-max tests for fault isolation
• If a fault threshold defined by the FDI algorithm is exceeded then deviation from
normal operation can be detected at its early stages and an alarm can be launched
• The proposed FDI approach can be applied to other components of the power grid,
e.g power generators, etc.
2
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 30
Thank you very much!
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 31
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 32
The deadline has been extended
until March 15 !
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 33
Selection of the model ’s structure
a. Input dimension partition b. Input space partition
1x
2x
1x
2x
: centre of input dimension partition
: centre of i-th fuzzy rule
: centre of the i-th fuzzy rule
(a) (b)
BYAxAxl ll is THEN is AND is IF : Rule 2211
Neurofuzzy modeling of the power transformer
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 34
THEN A IS ....ANDA IS AND A IS IF : 1
_
n2211
n
i
li
li
l
ln
lll bxwyxxxR
Takagi-Sugeno fuzzy model
L
l
n
iiA
L
l
n
iiA
l
x
xy
y
li
li
1 1
1 1
_
^
)(
)(
]1,0[ : )( RxiAli
output ^
y mean value estimator
membership value discrete probability
)( iAx
j
1A 2AmA
ix
jx
Neurofuzzy modeling of the power transformer
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 35
Extraction of the neural-fuzzy model from data
• Training of the fuzzy model : nonlinear least squares problem
Nonlinear
Part Linear
Part
Kalman Filter
(RLS)
Extended
Kalman Filter
Extended
Kalman Filter
e
yd y
updated
Gaussian
widths
update
Gaussian
centers
updated
linear
weights
• Extended Kalman Filter : generalization of the RLS algorithm
• Gauss-Newton, Levengerg-Marquardt training algorithms
Neurofuzzy modeling of the power transformer
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 36
• the regressor vector is
lk
lj
li v
y
c
y
w
yy......
)(
)(
1
x
x
L
iR
Ri
li
l
lx
w
y
L
lL
iR
L
jiRiRiRl
i
lii
l
lj
l
ljl xxxv
cxy
c
y
1 2
1
1
_
)]([
])()()[()(2
x
L
lL
iR
L
jiRiRiRl
i
lii
l
lk
l
ljl xxxv
cxy
v
y
1 2
1
13
2_
)]([
])()()[()(
)(2
x
weights
centers
spreads
Gradients for training of the neural-fuzzy model
Neurofuzzy modeling of the power transformer
• the sensitivity of the model’s output with respect to its parameters is
Fault diagnosis in power transformers using the Local Statistical Approach
37 IEEE SAS 2012, Brescia, Italy
Asset Optimization – On-Line Monitoring & Diagnostics
Transformer Asset Optimization Value Proposition
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 38
• Problem of fault detection and isolation (FDI)
• Solution with statistical techniques (Benveniste et al. 1987)
• Local Statistical Approach for FDI
Small parametric disturbance assumption
2
Parameter change Change in the mean of ),(~ 2NX
• Fault detection with the test
• Fault isolation with the sensitivity or min-max test
• Advantages of the Local Statistical Approach
More efficient than the RMSE and the NRMSE (sufficient statistics)
Isolation of the faulty parameter finds the faulty component
Optimal fault threshold selection
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 39
• Generation of the residuals neee ,...,, 21
• Criterion for the existence of fault : Likelihood Ratio
),...,(
),...,(ln)(
1
1
1
0
1
n
nni
yyp
yypYs
• Approximation of the Likelihood Ratio by its Taylor expansion
*)],...,,([ln 211
*
nyyypz
• Assuming a Gaussian distribution of the residuals
*)(ln 1 ii ypz
i
iii
yeeyH
^
2 )2
1(),(
• Equivalent of the likelihood ratio Normalized residual
N
i
iiN
ye
N 1
^
* 1
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 40
),(~1 2
1
*
Ny
eN
N
i
iiN
• According to the Central Limit Theorem (CLT )
under ))(,0(~ ** SNN*
p
under ))(,)((~ *** SMNNN
p *
• covariance matrix )( *S
I
i
iN
k
Tikk
N
i
Tii yHyH
iNyHyH
NS
1 1
**
1
*** ]),(),([1
]),(),([1
)(
• sensitivity matrix )( *M JJN
yHN
M TN
i
i
1),(
1)(
1
**
with Jacobian
m
NN
NN
NN
m
m
ii
ye
ye
ye
ye
ye
ye
ye
ye
ye
yeJ
...
............
...
...
21
22
2
22
1
22
11
2
11
1
11
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 41
),(~ 2NX with M and unknown
• The GRL maximizes with respect to )(
)(ln)(
0
1
Xp
XpXs
• The test for fault diagnosis 2
XSMMSMMSXt TTT 1111 )(
)( :
)( :
1
0
dimtH
dimtH
• follows a distribution 2t
• Fault existence criterion
MSM TT 1 parameter ity noncentral
5.0)( tP Fault threshold
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 42
Statistical methods for fault isolation
a. Sensitivity method b. min-max method
• Partition of the parameter vector into
• Partition of the Fisher Information Matrix into I
II
IIMSMI T 1
• Sensitivity test
XSMMSMMSXt TTT 111 )(
Perform the test for sub-groups of parameters 2
Find the sub-group with the maximum value of the test 2
Statistical projection
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 43
• min-max test
*1*** XIXt
T
XSMIIIX T 11* ][
IIIII 1*
• detect a change on the parameters sub-group
• remain robust to the changes of the non-observed parameters
Properties of the test statistics *t
• find from minimization of the noncentrality parameter *t
(transformed normalized residual)
(transformed Fisher matrix)
Minimizes non-centrality parameter
for the parameters non-suspected for
fault
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
IEEE SAS 2012, Brescia, Italy 44
• The non-detectability of changes in systems represented by neural-fuzzy models
results in singular Fisher information matrix
Success rate in fault isolation tests
(i) changes close to nominal value have increased success rate.
(ii) If the size of the test set is large then the success rate is high
(iii) If the singal to noise ratio is high then sucess rate is high
Fault diagnosis for electric power transformers
Fault diagnosis in power transformers using the Local Statistical Approach
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Fault diagnosis in power transformers using the Local Statistical Approach
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Fault diagnosis in power transformers using the Local Statistical Approach
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Fault diagnosis in power transformers using the Local Statistical Approach
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Fault diagnosis in power transformers using the Local Statistical Approach
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Fault diagnosis in power transformers using the Local Statistical Approach
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Fault diagnosis in power transformers using the Local Statistical Approach
• Condition monitoring of electrical equipment, such as oil immersed transformers,
helps in planning of maintenance schedules, obtaining knowledge of the health of
equipment, estimating the remaining service life of equipment. etc.
• Preventive maintenance of oil immersed transformers can result in savings from
proactive maintenance and can release funds for system expansions and upgrades.
Failures of oil immersed power transformers
51 IEEE SAS 2012, Brescia, Italy
Fig. 3
Fig. 4