incipient fault detection for electric power transformers using neural

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]



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)



The Smart Grid


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



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.


Monitoring data for early detection of failures in electric power transformers

in digital substations


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).


Fig. 1

Fig. 2



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


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


1

2

3

q

LRTOUTO

R

RI

1

12

,,

TOAUTOTO

TOdt

d

,

2,, LRHSUHS I

RTO ,

TO

RHS,


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.


4

5

HSUHSHS

HSdt

d

,}{

HSTOHS


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


• Such black-box models capture accurately the nonlinear power transformer

dynamics without the simplifying assumptions of the analytical models


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 :




• 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




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




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.




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.



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)


• 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




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



• Hypothesis testing


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:



• The decision tool is the Likelihood ratio

)(

)(ln)(

0

1

Xp

XpXs




Fault diagnosis tests


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.





• 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



• 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


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



(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




(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)




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



Thank you very much!



The deadline has been extended

until March 15 !



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




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




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




• 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


• the sensitivity of the model’s output with respect to its parameters is



Asset Optimization – On-Line Monitoring & Diagnostics

Transformer Asset Optimization Value Proposition



• 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




• 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




),(~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




),(~ 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




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




• 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




• 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



• 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


Fig. 3

Fig. 4

incipient fault detection for electric power transformers using neural

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