Xây dựng giải pháp chẩn đoán sự cố trong máy biến áp 3 pha sử dụng các phương pháp xử lý tín hiệu thông minh TT TIENG ANH

i
TABLE OF CONTENTS
PREAMBLE ................................................................................................................................ 1
1. THE URGENCY OF THE SUBJECT ...................................................................................... 1
2. RESEARCH PURPOSES .........................................................................................................1
3. RESEARCH METHODS .........................................................................................................1
4. RESEARCH SUBJECTS .........................................................................................................1
5. RESEARCH SCOPE ................................................................................................................ 1
6. SCIENTIFIC AND PRACTICAL MEANINGS OF THE TOPIC .............................................1
CHAPTER 1: OVERVIEW OF DIAGNOSTIC METHODS IN TRANSFORMERS ............ 2
1.1. THE IMPORTANCE OF TRANSFORMERS’ FAULT DIAGNOSIS .................................. 2
1.2. REVIEW OF METHODS FOR TRANSFORMERS’ FAULT DIAGNOSIS .........................2
1.2.1. International works .............................................................................................................2
1.2.2. Domestic works .................................................................................................................. 2
1.2.3. The limitations of reviewed diagnosis methods ...................................................................2
1.2.4. Thesis proposal ...................................................................................................................2
1.3. CONCLUSION of CHAPTER 1............................................................................................ 2
CHAPTER 2: THEORETICAL BASIS OF THE THESIS PROPOSALS .............................. 2
2.1. VIBRATION IN THE TRANSFORMER .............................................................................. 2
2.1.1. Vibration of winding ...........................................................................................................2
2.1.2. Vibration of steel core.........................................................................................................2
2.2. THE NEED TO ANALYZE THE TRANSFORMER VIBRATIONS .................................... 3
2.3. FREQUENCY DOMAIN ANALYSIS OF THE VIBRATIONS............................................ 3
2.3.1. The fundamentals of frequency response analysis ...............................................................3
2.3.2. Application scope of the method .........................................................................................3
2.3.3. Review on the method of vibration analysis in the frequency domain .................................. 3
2.4. THE FINITE ELEMENTs METHOD.................................................................................... 3
2.4.1. A general introduction to the finite elements method .......................................................... 3
2.4.2. Operation flow chart using the finite elements method ........................................................ 3
2.4.3. Generalized system of Maxwell equations for the electromagnetic field. .............................3
2.5. APPLICATION OF FINITE ELEMENTS METHOD IN ANSYS MAXWELL SOFTWARE

TO IMPLEMENT A MODEL OF TRANSFORMER...................................................................5
2.5.1. Equation of electromagnetic field........................................................................................ 5
2.5.2. System of mechanical equations .........................................................................................7
2.6. NEUTRAL NETWORK MLP ...............................................................................................7
2.6.1. The architecture of the MLP Neural Network MLP.............................................................7
2.6.2. Learning process for MLP .................................................................................................. 8
2.6.3. The steepest descend gradient algorithm .............................................................................8
2.6.4. Levenberg–Marquardt algorithm for MLP .......................................................................... 8
2.7. CONCLUSION OF CHAPTER 2 .......................................................................................... 9


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CHAPTER 3: IMPLEMENTATION OF A MODELS IN ANSYS SOFTWARE FOR
DISTRIBUTED TRANSFORMER IN SELECTED FAULTY STATES ................................ 9
3.1. GENERAL INTRODUCTION TO ANSYS SOFTWARE .....................................................9
3.1.1. Main modules of ANSYS software .....................................................................................9
3.1.2. ANSYS Maxwell as electromagnetic simulation function block .......................................... 9
3.1.3. Structural simulation function block using ANSYS Structure .............................................9
3.1.4. ANSYS design modeler and ANSYS meshing .................................................................... 9
3.1.5. ANSYS mechanical workbench .......................................................................................... 9
3.1.6. ANSYS mechanical ............................................................................................................ 9
3.2. IMPLEMENTING A 400KVA 22-0.4KV Y-Y0 DISTRIBUTION TRANSFORMER
MODEL IN ANSYS .................................................................................................................. 10
3.2.1. Working principle of a transformer ................................................................................... 10
3.2.2. Implementing a 400kVA 22-0.4kV Y-Y0 distribution transformer model ......................... 10
3.3. MODELS FOR SIMULATION OF NORMAL AND FAULTY STATES OF THE
DISTRIBUTION TRANSFORMER .......................................................................................... 11
3.3.1. The mesh for the model of transformer in normal state ..................................................... 11
3.3.2. The mesh for the model of transformer with a loosen coil ................................................. 11
3.3.3. The meshes for the model of transformer with shortages: 2-turn, 5% of total rounds, 10% of

total rounds of the high-voltage winding, phase B ...................................................................... 11
3.3.4. The mesh for the model of transformer with one coil fixing bolt loosen ............................ 12
3.4. CONCLUSION OF CHAPTER 3 ........................................................................................ 12
CHAPTER 4: NUMERICAL RESULTS OF SIMULATION AND EXPERIMENT ........... 12
4.1. DATA SETS FROM SIMULATION IN ANSYS SOFTWARE ......................................... 12
4.1.1. Normal operation of MBA, 50% load (case A-1)` ............................................................. 12
4.1.2. Case of short-circuit of two high-voltage rounds ............................................................... 14
4.1.3. Case of wire loop loosening problem ................................................................................ 14
4.1.4. Case of loosening of coil fixing bolt.................................................................................. 15
4.1.7. Review of the simulation results ....................................................................................... 15
4.2. THE RESULTS OF TRAINING OF THE MLP NETWORK .............................................. 16
4.2.1. The features extracted from the simulation data ................................................................ 16
4.2.2. Results training network MLP . ........................................................................................ 17
4.3. PRACTICAL EXPERIMENT ON ACTUAL DISTRIBUTION TRANSFORMER ............. 20
4.4. CONCLUSION OF CHAPTER 4 ........................................................................................ 23
CONCLUSIONS AND RECOMMENDATIONS ................................................................... 23
PUBLICATIONS ....................................................................................................................... 24


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PREAMBLE
1. THE URGENCY OF THE SUBJECT
During operation, transformers may encounter various problems such as insulation failure between
turns of wire, short circuit, broken wire, earth fault, equipment malfunction or user's fault, overload
condition. and aging of equipment, ... When a fault occurs in a transformer, relay protection will act
to separate the faulty element from the electrical system and eliminate the influence of the fault
elements.
Diagnosing the fault type in a 3-phase transformer is an urgent problem to help to detect and
troubleshoot a very important device in the power system. The successful development of a solution

to diagnose potential problems in transformers in general and 22/0.4kV distribution transformers in
particular will have good practical significance, if put into application, it will help operators to
recognize early transformer failures thereby avoiding economic losses due to repair or replacement of
new transformers, as well as improving power supply continuity.
2. RESEARCH PURPOSES
The thesis researches and provides solutions for fault diagnosis in 22/0.4kV 3-phase distribution
transformers. ANSYS software is used to implement a 22/0.4kV distributed transformers model. The
signals features are then processed by an MLP neural network trained with Levenberg - Marquadrt
learning algorithm to diagnose potential fault types.
3. RESEARCH METHODS
Studying research works on ANSYS software and signal processing to build a 22/0.4kV
distribution transformer model in normal and fault working states.
Simulate the transformer in normal working state and 5 fault cases in ANSYS to generate samples
of electrical signals and mechanical vibrations. These signals will be analyzed and feature parameters
extracted to train the recognition models using MLP neural networks to detect the types of potential
failure in the transformers. The training algorithm was implemented with the Levenberg - Marquadrt
algorithm and the Neural Network Toolbox library in Matlab.
Verify transformers model built on ANSYS software by experiment with device using
accelerometer to measure vibration signal of transformer in normal working mode when load
changes.
4. RESEARCH SUBJECTS
The research object of the thesis is fault diagnosis of three-phase 400kVA 22-0.4kV Y-Y0
distribution transformer to improve the efficiency of the power system.
5. RESEARCH SCOPE
Application of ANSYS software to implement 5 fault models of three-phase 400kVA 22-0.4kV
Y-Y0 distribution transformer (2-turn shortage in 1 phase, shortage of 5% of total turns in 1 phase,
short of 10% of total turns in 1 phase, loosen coils in one-phase winding, loosen winding mounting
bolts). The generated signals from the simulations in ANSYS (electrical, force, and mechanical
signals) will be used to generate sample signals for fault identification.
Selecting and building a recognition algorithm using MLP neural network to diagnose problems in

distributed transformers.
Experiment using accelerometer to measure vibration on real transformer in normal working
mode when load changes to verify the proposed approach.
6. SCIENTIFIC AND PRACTICAL MEANINGS OF THE TOPIC
 Scientific significance :
Propose a recognition algorithm using MLP neural network with simultaneous use of electrical
and mechanical signals (vibrations) to diagnose potential problems in distributed transformers.


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 The practical significance of the topic :
- The thesis contributes to early prediction of potential problems that may occur for distribution
transformers in order to improve the efficiency of power system operation.
- - The research results of the thesis are reference materials for students majoring in control and
automation, master's students and graduate students interested in research on transformers fault
diagnosis issues.
CHAPTER 1: OVERVIEW OF DIAGNOSTIC METHODS IN TRANSFORMERS
1.1. THE IMPORTANCE OF TRANSFORMERS’ FAULT DIAGNOSIS
1.2. REVIEW OF METHODS FOR TRANSFORMERS’ FAULT DIAGNOSIS
1.2.1. International works
1.2.2. Domestic works
1.2.3. The limitations of reviewed diagnosis methods
1.2.4. Thesis proposal
1.3. CONCLUSION of CHAPTER 1
Chapter 1 of the thesis has solved the following issues :
 Synthesize domestic and international studies on potential fault diagnosis methods in
transmission and distribution transformers.
 Discussed the limitations of the published methods on transformers fault diagnosis.
 Proposing a solution to diagnose distribution transformer faults by building an

transformer model in ANSYS software to generate the electrical, mechanical (vibration)
signals as a data set for identifying distributed transformer faults by MLP artificial neural
network.

CHAPTER 2: THEORETICAL BASIS OF THE THESIS PROPOSALS
2.1. VIBRATION IN THE TRANSFORMER
Vibration in transformers is caused by various forces present in
the steel core and windings inside the transformer during operation.
2.1.1. Vibration of winding
The vibration of the windings caused by the electromagnetic
forces when there is a current flowing in the coils.
2.1.2. Vibration of steel core
The vibration of the steel core is caused by a phenomenon
called magnetostriction, which is the phenomenon when metal
Figure 2.1: Magnetic circuit
objects undergo a deformation in their shape when placed in a
and transformer windings
magnetic field. Inside the transformer, the steel core, which is
made in the form of laminated plates, also experiences expansion and contraction due to flux
changes. This expansion and contraction occurs twice in an alternating cycle.


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2.2. THE NEED TO ANALYZE THE TRANSFORMER VIBRATIONS
2.3. FREQUENCY DOMAIN ANALYSIS OF THE VIBRATIONS
2.3.1. The fundamentals of frequency response analysis
The transformer is considered a complex network
of RLC elements. The contributions to this RLC
complex network come from the resistance of the

copper coil; the inductance of the windings and the
capacitance coming from the insulating layers among
the windings, between the winding and the winding,
between the winding and the steel core, between the
steel core and case, between the case and the winding.
Figure 2.2: Simplified isoval circuit
However, we can use a simplified isotropic circuit
with pooled RLC elements
with the aggregated RLC elements (illustrated in
Figure 2.2) to explain accurately the principle of
frequency response technique
The frequency response is carried out by applying a low voltage signal with variable
frequencies into the windings of transformer and measuring both input and output signals. The
ratio of these two signals gives us the required response. This ratio is called the transfer function
of the transformer. So we can obtain values of its magnitude and phase angle. With different
frequencies, the RLC network will give different impedance circuits. Therefore, the transmission
function at each frequency is a unit of measurement of the actual impedance of RLC network of
the transformer.
2.3.2. Application scope of the method
Currently, in order to detect the displacement of the transformer windings, the maintenance units
of the transformer use FRA measuring devices which are considered as a diagnostic tool to assist in
the testing of damage assessment and fault investigation. in MBAs. The FRA technique has proven to
be a powerful tool in terms of means to reliably and efficiently detect winding displacements and
other failures that affect the impedance of the transformer.
2.3.3. Review on the method of vibration analysis in the frequency domain
2.4. THE FINITE ELEMENTs METHOD
2.4.1. A general introduction to the finite elements method
2.4.2. Operation flow chart using the finite elements method
2.4.3. Generalized system of Maxwell equations for the electromagnetic field.
Table 2.1: System of Maxwell's equations

Name
Faraday's Law
Ampere's Law
Ampere's Gauss
Ampere's Gauss
(For magnetic field)

Differential form

  B
.E 
t

   D
.H  J 
t

 
.D  

 
.B  0

Integral form
  d
 
Edl

BdA
c

dt 
s
 
  d
 
Hdl

JdA

DdA
c
s
dt 
s
 
Dd

 A    dV
s

v

 
Bd

 A  0
s


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The analysis and calculation of factors in the electric and magnetic fields can be based on the
system of Maxwell's equations, The variable magnetic field generates an induced electric field and
vice versa. Electric and magnetic fields are closely related and transform each other. The concept of
the electromagnetic field was first stated by Maxwell (so they are now called Maxwell's equations):

    D
rot H  J 
t


 
B
rot E  
t
 
divB  0
 
divD  0

(2.1)



In the magnetic material environment, the relationship between B and H according to the
magnetic permeability coefficient of materials

are
 as follows:
B= H

(2.2)
In the SI system
of units, the above quantities have the following units and dimensions:

Magnetic field strength vector
A/m
H

Magnetic induction vector
T = kg/s2.A
B

Current density vector
A/m2
J

Magnetic permeability coefficient H/m
of the material

Electromagnetic induction vector
C/m2
D

Electric field strength vector
V/m
E
Napla operator: 


    

i
j k
x  y
z

(2.3)

In the coordinate system Descartes:


 A Ay A
 A  div A  x 
 z
x
y
z



i
j
k

 


rot A  x A 
x y z
Ax Ay Az





Equation rot H  J 

(2.4)

(2.5)

D
is equivalent to a system of three algebraic equations
t
 H z


 y
 H x


 z
 H y


 x

H y
z

 jx 

Dx
t
Dy

H z
 jy 
x
t
H x
D
 jz  z
y
t

For ferromagnetic materials μ is a tensor

(2.6)


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  xx  xy  xz 


    yx  yy  xz 
(2.7)
  zx  zy  zz 



2.5. APPLICATION OF FINITE ELEMENTS METHOD IN ANSYS MAXWELL
SOFTWARE TO IMPLEMENT A MODEL OF TRANSFORMER
2.5.1. Equation of electromagnetic field
The problems of electromagnetic fields can be divided into 3 different forms, each of which has a
corresponding Maxwell equations system for its solving: two cases of steady-state systems (a
stationary state, in which there is no variation of any quantity, and a steady state where all the
physical properties are cyclical) and the transient state. When the system is in the transiting state from
one steady state to another, the temporal factor associated with time will be included as the basis for
determining the instantaneous state of the system. On that basis, in order to simplify the problem in
implementing the finite element methods, in this thesis, we discussed the build of the characteristic
equations for the elements according to the above three basic states.
The systems of equations at the element nodes apply to specific analytical models are later used in
ANSYS software.
The static electromagnetic states are used only for models where only the static magnetic field
formed by permanent magnets, electromagnets in different media in 3D space is present.
The electromagnetic equations are given by the formulas
  
H  J
 
B  0
(2.8)

 


B  0 ( H  M )  0  r  H  0  M p
The 2D static magnetic state is used for models where only the static magnetic field formed by
permanent magnets, electromagnets in different media is defined for 2D space. This case applied to
problems with circular symmetric geometric structure or when the size of one dimension is much
larger than the other two dimensions, then the magnetic field derivative in one direction is zero.

The equation of the spatial variable is determined by:
  1  


J z ( x, y )    
(  Az ( x, y )) 
(2.9)
 0  r

The 3D sinusoidal variable magnetic field state applies to the class of problems on
electromagnetism in the magnetic field state generated by harmonic varying power sources, surface
effects due to the combination of magnetic fields harmonic variation and harmonic variation current
caused inside the conductor. The equation of the spatial variable at the nodes is determined by:

 1


  H   j H
   j


(2.10)

3D time-varying electromagnetic state applies to the class of problems with time-varying magnetic
fields, currents in 3D space due to variable power sources or object movement. Then the system of
spatial equations at the nodes of the elements is determined by:


6


 1   B
  H 
0

t
 
.B  0
      
 . 
  .( )  0
t 


(2.11)

The 2D time-varying electromagnetic state is similar to the 3D electric field problem, but the
derivative of the magnetic field and the current in a certain direction has zero value. Then the spatial
equation at the element node is zero. determined by:


  

 
 
A
  v  A  J s  
 V    H c  V    A
t

(2.12)

State of fixed charges: Consider the class of problems about electric field distribution in 3D space
without time variation. The spatial equation of the system is established by the system:
Apply to 2D model analysis:


.( r  0  )    v
(2.13)
Apply to 3D model analysis:


.( r  0  ( x, y ))   
(2.14)
Direct current: applied to a class of problems on analyzing conductive currents whose magnitude
and direction do not change with time. The equation of the spatial variable at the element nodes is
determined by:
For 3D model analysis



J ( x, y )   E ( x, y )   ( x, y )
(2.15)
For to 2D model analysis:
 
.( )  0
(2.16)
Harmonic variable current: Applied to the class of problems of analyzing the amperage flow in
the conductor of the harmonic variation system. Equations of spatial variables at element nodes are
determined by (applicable only to 2D problem class)
 


(2.17)
.E  j  ( x, y )   0
Current varies with time: Applied to the problem model with time-varying amperage in 3D space,
then the spatial equation at element nodes is determined by the formula
      
 . 
  .( )  0
t 


(2.18)

Method of calculating electromagnetic forces in Maxwell software: according to Lorentz's law of
electromagnetic force, the software defines a quantity called Maxwell's force tensor by the formula:

B H

H x  By
H x  Bz
 H x  Bx 

2


B H


(2.19)
 

H y  Bx
H y  By 
H y  Bz

2


B H 

H z  Bx
H z  By
H z  Bz 

2 

Accordingly, the electromagnetic force is calculated according to the formula:
dF    dA
(2.20)


7

2.5.2. System of mechanical equations
2.5.3. Linking the electromagnetic field problem and mechanical problem
2.6. NEUTRAL NETWORK MLP
2.6.1. The architecture of the MLP Neural Network MLP
MLP (MultiLayer Perceptron) network is a feedforward network built from the basic elements of
McCulloch-Pitts neurons, in which neurons are arranged into layers consisting of a layer of input
signal channels (input layer), a layer of output signal
channels (output layer), and a number of intermediate

layers known as hidden layers. Figure 2.4 is a model
of an MLP network with N inputs, one hidden layer
with M neurons and K outputs..
We generally denote the concatenation weights
between the input layer and the hidden layer as Wij
( i  1  M ; j  0  N ), denote the coupling
weights between the hidden layer and the output layer
as Vij ( i  1  K ; j  0  M ). The transfer
functions of the hidden and output layer neurons are
denoted f1 and f2, respectively. In each model, the
authors can choose different transfer functions
Figure 2.4: MLP network model with 1
according to experience and purpose. The
hidden layer
commonly used functional forms are [37]:
1
- Function logsig: logsig ( x) 
1  e x
1  e x
- Function tansig: tansig ( x) 
1  e x
- Linear function: linear ( x)  a  x  b
In this thesis, the transfer function of hidden neurons is selected as the function f1 ( x )  tansig ( x)
since this function has a range of values including both positive and negative values, it is more
general than the function logsig(), also the nonlinear function will be more general than the linear
function; The transfer function of the output neurons is the function f 2 ( x)  linear ( x ) because this
function can generate values greater than 1 (because the thesis will use the status code of the
transformer from d=0 to d=5).
Then, with the input vector x   x1, x2 ,, xN    N (fixed bias input x0  1 ), the output is
determined sequentially in the forward propagation direction as follows:

 Total input excitation of the i-th hidden neuron i ( i  1  M ) equals:
M

ui   x j  Wij

(2.21)

j 0

 Calculate the output of the i-th hidden neuron ( i  1  M ):

vi  f1  ui 
 Total input excitations of the i-th output neuron i ( i  1  K )

(2.22)


8
M

gi 

 v jVij

(2.23)

j 0

 And finally the i-th output of the network will be ( i  1  K ):

yi  f2  gi 

(2.24)

In total, the transfer function of the MLP network is a nonlinear function given the
following dependency formula:
M

yi  f 2  gi   f 2   v jVij 
 j 0



M
N  
N



 
 f 2  Vi 0   f1 u j Vij   f 2  Vi 0    f1  W j 0   xkW jk Vij  



 
j 1
j 1 
k 1
  





(2.25)

 

2.6.2. Learning process for MLP
MLP networks are usually trained using supervised learning algorithms, i.e. algorithms that train
when there are samples that include both inputs and outputs, respectively. With the sample data set
being a set of p pairs of samples given in the form of input vectors – output vectors respectively
xi , di  với i  1  p, xi  R N ; di  RK , we need to find an MLP network (including the
determination of the structure parameters and the coupling weights corresponding to the selected
structure) such that when given the vector xi into the MLP network, the output of the network will
approximate the existing target value:
i : MLP xi   di
(2.26)
Or the total error on the samples approaches some minimum value or is less than a pre-selected
threshold   0 :
E

1 p
 MLP  xi   d i
2 i 1

2

 min

(2.27)

2.6.3. The steepest descend gradient algorithm
2.6.4. Levenberg–Marquardt algorithm for MLP
Algorithms that use gradients (first derivatives) have slow convergence. When we need to improve
the convergence speed, we can use the Levenberg–Marquardt (L–M) algorithm. This algorithm is
based on Taylor to quadratic expansion. Considering the error according to formula (2.27) which is a
function that depends on all the weights of the neurons, then we expand the function E in the
neighborhood of the current weights W will be:
T

E (W  p)  E (W )   g (W )  p 

with p – the increement amount,

1 T
p H (W ) p  O p3
2

 

 E E
E 
g( W )  E  
,
, ,

Wn 
 W1 W2

(2.28)

T

is the gradient vector of the

function E with regards to all the weights (grouped in the matrix W), and H is the symmetric square
matrix of the second derivatives (also called the Hessian matrix) of E with respect to W with:


9
 2 E

 W1W1
H( W )   H ij   

 2
  E
 W W
 1 n

2 E 

Wn W1 



2 E 

Wn Wn 


(2.29)

At the minimum point (that we are looking for) of the function we would have g( W)  0 and H( W)
is positively determined. Consider the t-th iteration of the weights W ( t ) , suppose we need to find the
next approximation W ( t 1)  W( t )  p approaching the minimum point of the function, then we have:



E W( t 1)
p



  E  W

(t )

p

p





 0

(2.30)



g W ( t )  H W ( t ) p( t )  0

(2.31)

From that, the formula for determining the direction of variation of the weights vector towards the
local minimum of the error function is:





1



p (t )    H W ( t )  g W (t )





(2.32)

Adding the step factor to avoid the case of the step displacement being too large, we have the
iterative formula according to the Levenberg - Marquardt method as follows:





1



W ( t 1)  W( t )    H W ( t )  g W ( t )





(2.33)

For each set of sample data, after training is complete, the MLP network is switched to test mode
(also known as inferring mode), then the parameters of the network do not change, the network will
wait for us to input a new set of feature vector x to calculate F(x) according to formula (2.27) to
determine the state of the transformer corresponding to the feature vector x.
2.7. CONCLUSION OF CHAPTER 2
In Chapter 2, the thesis has discussed the following issues:
- Stated the theoretical basis of the vibration phenomenon of the transformer.
- Researched on the finite elements method applied in ANSYS software, where the finite elements
method is used to solve the system of Maxwell's equations and from the results of magnetic field
calculations (electromagnetic force, deformation, displacement), other feature values could be
calculated to help to determine the state of the transformer.
- The thesis has proposed the use of a nonlinear model, which is a straight-forward neural network
MLP trained with Levenberg - Marquardt learning algorithm, as a model for fault identification and
diagnosis in transformer.
CHAPTER 3: IMPLEMENTATION OF A MODELS IN ANSYS SOFTWARE FOR
DISTRIBUTED TRANSFORMER IN SELECTED FAULTY STATES
3.1. GENERAL INTRODUCTION TO ANSYS SOFTWARE

3.1.1. Main modules of ANSYS software
3.1.2. ANSYS Maxwell as electromagnetic simulation function block
3.1.3. Structural simulation function block using ANSYS Structure
3.1.4. ANSYS design modeler and ANSYS meshing
3.1.5. ANSYS mechanical workbench
3.1.6. ANSYS mechanical


10

3.2. IMPLEMENTING A 400KVA 22-0.4KV Y-Y0 DISTRIBUTION TRANSFORMER
MODEL IN ANSYS
3.2.1. Working principle of a transformer
3.2.2. Implementing a 400kVA 22-0.4kV Y-Y0 distribution transformer model
a) Basic parameters
With the ANSYS tool in this thesis, select the transformer model as shown in Figure 3.1 with basic
parameters as shown in Table 3.1
Table 3.1: Basic parameters of distributed MBA selected in the thesis
Rated power
Team Battle
Primary voltage
Secondary voltage
Window height
Window Width
Grade 1 . leg width
Leg width 2
Layer thickness 1
Layer thickness 2
Grade 1 yoke width
Grade 2 yoke width

Roll inner diameter Low pressure
Roll outside diameter Low voltage
Roll Height Low Pressure
Number of turns Low voltage
High pressure coil inner diameter
Roll Out Diameter High Pressure
Roll Height High Pressure
Number of turns of high-pressure coil

400
Y-Y0-12
22
0.4
530
302
140
120
200
40
140
120
150/250
189/289
450
22
209/309
282/382
430
2098

kVA
kV
kV
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm

Fig. 3.1. The 400kVA 22/0.4kV distribution transformer model


11

Model of transformer circuit:

LabelID=ILA

LabelID=VVHA
LabelID=IHA

+

0.78
R38

LWinding_LA

LWinding_HA

LabelID=ILB

10ohm
R24
LabelID=IHB

+

0

0.78
R41

LWinding_LB
LabelID=ILC

0

0

LWinding_HB

10ohm
R54

0

LabelID=VVHC
LabelID=IHC

+

0.78
R44

LWinding_LC

LWinding_HC

10ohm
R30

Figure 3.2: Model of the circuit transformer
3.3. MODELS FOR SIMULATION OF NORMAL AND FAULTY STATES OF THE
DISTRIBUTION TRANSFORMER
3.3.1. The mesh for the model of transformer in normal state

Figure 3.3: Meshing model and number of mesh elements MBA
3.3.2. The mesh for the model of transformer with a loosen coil
3.3.3. The meshes for the model of transformer with shortages: 2-turn, 5% of total rounds,
10% of total rounds of the high-voltage winding, phase B

The corresponding electrical circuit for transformer with shortage fault on the high voltage line
of phase B is shown on Fig. 3.4.


12
LabelID=IU_LA
+

0.78ohm
R22

LWinding_LA

0.78ohm
R25

LWinding_LB

0

0

22000*sqrt(2) V
LabelID=VV_HB
LWinding_HB

LabelID=IU_LC
+

0.78ohm

R28

5ohm
R8

LabelID=IU_LB
+

0

22000*sqrt(2) V
LabelID=VV_HA
LWinding_HA

LWinding_LC

22000*sqrt(2) V
LabelID=VV_HC
LWinding_HC

(5/2089*2) ohm
R44
LWinding_T

5ohm
R11

0

5ohm

R14

Figure 3.4: Circuit diagram for transformer in case of short circuit of high voltage line phase B
3.3.4. The mesh for the model of transformer with one coil fixing bolt loosen
3.4. CONCLUSION OF CHAPTER 3
Chapter 3 of the thesis presented the following issues:
- Simulate the transformer failures to generate the sample of electrical signals and
mechanical vibrations (mechanical signals),
- The thesis used ANSYS software to implement a distributed transformer model of
400kVA, 22-0.4kV, Y- Y0,
- Boundary conditions, excitation conditions for the coils had been defined and set up for
the simulation of the distributed transformer model 400kVA, 22-0.4kV, Y-Y0 and the original
model was modified to support different scenarios: normal working state and 05 faulty cases. The
data generated from the simulations are later used to build up a fault detection model.
CHAPTER 4: NUMERICAL RESULTS OF SIMULATION AND EXPERIMENT
4.1. DATA SETS FROM SIMULATION IN ANSYS SOFTWARE
As described in Chapter 3, a model of 400kVA, 22-0.4kV, Y-Y0 distributed transformer
model has been implemented in ANSYS software along with its modifications to simulate
different faulty states. For each scenario of faults, simulations were performed for 3 different load
levels of 50%, 80% and 100% of the norminal load. Also the simulations were performed with 10
different initial phase values to enrich the training samples data set. As results, a total of
6  3  (10  3)  234 simulations had been done.
4.1.1. Normal operation of MBA, 50% load (case A-1)`
4.1.1.1. Calculation results over time of the force components of the coils and cores
The results are given as the graph of Figure 4.1, Figure 4.2 and Figure 4.3 .

Figure 4.1: The two-end tensile force component in the radial direction of the coil HA, HB, HC


13

Figure 4.2: The two-end tensile force components in the radial direction of windings LA, LB, LC

Figure 4.3: Graph of force in 3 directions x, y, z acting on core
4.1.1.2. Displacement response analysis in frequency domain
 Displacement analysis results in the x direction of the case:

Figure 4.4: Displacement in the x-direction of the case
 Displacement analysis results in the y direction of the case

Figure 4.5: Displacement in the y-direction of the case


14

 Displacement analysis results in the z direction of the case

Figure 4.6: Displacement in the z-direction of the case
4.1.2. Case of short-circuit of two high-voltage rounds
 Displacement analysis results in the x direction of the case

Figure 4.7: Displacement in the x-direction of the case
 Displacement analysis results in the y direction of the case

Figure 4.8: Displacement in the y-direction of the case
 Displacement analysis results in the z direction of the case

Figure 4.9: Displacement in the z-direction of the case
The maximum of displacement was 0.18406mm at the frequency of 50Hz.
4.1.3. Case of wire loop loosening problem

 Displacement analysis results in the x direction of the case


15

Figure 4.10: Displacement in the x-direction of the case
 Displacement analysis results in the y direction of the case

Figure 4.11: Displacement in the y-direction of the case
 Displacement analysis results in the z direction of the case

Figure 4.12: Displacement in the z-direction of the case
4.1.4. Case of loosening of coil fixing bolt
4.1.7. Review of the simulation results
Through the simulation results, it is found that there is a difference between the electrical
characteristics and mechanical vibration, the simulation results of the working modes of the
transformer are as follows.
 Case of 50% nominal load
Displacement
(vibration
amplitude) of
Normal
the transformer
shell
6,4.10-5mm
Displacement in
at 115Hz
the x-dir.
Displacement in 4,447. 10-4 mm
at 50Hz

the y-dir.
Displacement in 6,14.10-3mm at
50Hz
the z-dir.

Shorted two
turns of high
voltage wire

Loosening of 2
Shorted 5% of
Loose problem
high-voltage
high voltage
of coil fixing bolt
coil windings
wire loop

0,00146mm
at 120Hz
0,0134mm
at 50Hz
0,18406mm at
50Hz

6,4.10-5mm
at 115Hz
4,447. 10-4 mm
at 50Hz
6,14. 10-3mm

at 50Hz

0,0036mm
at 195Hz
0,00096mm
at 195Hz
0,00054mm at
195Hz

0,0517 mm
at 120Hz
0,4823mm
at 50Hz
6,6003mm
at 50hz

Shorted 10% of
high-voltage
wire loop
0,1935mm
at 120Hz
0,74037mm
at 50Hz
10,183mm
at 50Hz


16

 Case of 80% nominal load

Displacement
(vibration
amplitude) of the
transformer shell
Displacement in
the x-dir.
Displacement in
the y-dir.
Displacement in
the z-dir.

Normal

Shorted two
turns of high
voltage wire

Loosening of 2
high-voltage
coil windings

Loose problem
of coil fixing
bolt

Shorted 5% of
high voltage
wire loop

Shorted 10% of

high-voltage
wire loop

6,8. 10-5 mm
at 115Hz
4,53. 10-4 mm
at 120Hz
6,27. 10-3mm
at 50Hz

0,775mm
at 125Hz
9,98mm
at 50Hz
136mm
at 50Hz

0,68mm
at 115Hz
0,354 mm
at 120Hz
60,27mm
at 50Hz

89,6mm
at 195Hz
21,0 mm
at 80Hz
5,79mm
at 80Hz

586 mm
at 115Hz
325mm
at 115Hz
627 mm
at 40hz

409mm
at 125Hz
316mm
at 115Hz
654mm
at 40Hz

 Case of 100% nominal load
Displacement
(vibration
amplitude) of the
transformer
shell
Displacement in
the x-dir.
Displacement in
the y-dir.
Displacement in
the z-dir.

Normal

Shorted two
turns of high
voltage wire

7,2.10-5mm

2,02.10-3mm

7,14.10-5mm

at 115Hz

at 50Hz

at 115Hz

-4

Loosening of 2 Loose problem
high-voltage
of coil fixing
coil windings
bolt

-4

-4

Shorted 5% of
high voltage wire

loop

Shorted 10% of
high-voltage
wire loop

1,35.10-2mm

2,68.10-2mm

7,5.10-2mm

at 195Hz

at 115Hz

at 135Hz

-3

4,61.10 mm

1,86.10 mm

4,61.10 mm

3,6.10 mm

0,19555mm

1,01mm

at 50Hz

at 125Hz

at 50Hz

at 195Hz

at 50Hz

at 50Hz

6,38.10-3mm

2,78.10-2mm

6,37.10-3mm at

2,02.10-3mm

2,6895mm

13,884mm

at 50Hz

at 50Hz

50Hz

at 195Hz

at 50Hz

at 50Hz

4.2. THE RESULTS OF TRAINING OF THE MLP NETWORK
4.2.1. The features extracted from the simulation data
In the thesis, it is proposed to use the characteristics of the signals to classify the status of the
transformer extracted from the above measured signals as follows:
 From the frequency spectrum of the displacement oscillations on the transformer housing
in 3 axes: use the maximum value of the spectrum on each axis, or we have:

x1 

max

 25,30,,200

 M x    ;

x2 

max

  25,30,,200

max  M z    .

 M y   ; x3  25,30,
,200

 From the variable value of the force acting on the 3 axes: using the maximum value of
the force on each axis (for phase B, the high-voltage side, the phase used in the
simulation is the phase where the failure occurs), or we have:
x4 

max

t 0,100 ms 

F

H
x

 t  ;

x5 

max

t 0,100 ms 

For the low voltage side we have:
x7  max FxL  t  ; x8  max
t 0,100 ms







t 0 ,100 ms

F

F


H
y

L
y

 t   ; x6  t max
 FzH  t  ;
0,100 ms




max  FzL  t   ;
 t   ; x9  t 0,100
ms




 From the variable value of the force acting on the radial: using the maximum value of the
force on each axis, select the wire bundle of phase B, the high-voltage side (the phase
used in the simulation is the phase where the fault occurs). ), or we have:


17

x10 

max

t 0,100 ms 

 Fcx  t   ;

x11 

max

t 0,100 ms 

 Fcy  t   ;

x12 

max

t 0,100 ms 

 Fcz  t   ;

 From the variable value of phase B current amplitude on high voltage and low voltage
side, phase B voltage on low voltage side, using the maximum value of the signals, or we
have: x13  max  I H  t   ; x14  max  I L  t   , x15  max U L  t   ;
t 0,100 ms 

t 0,100 ms 

t 0,100 ms 

Thus, the input feature vector consists of 15 components. The output of the identification system is
the status code of the MBA, which consists of 6 states considered as above:
 MBA in normal mode
 The transformer has a loosen coil fixing bolts
 The transformer has a loosen coil loop around the shaft
 The transformer has 2 shorted consecutive turns of wire (at the B phase winding, high
voltage side)
 The transformer has a shorted of 5% of the total turns of wire (at phase B winding, high
voltage side)
 The transformer has a shorted of 10% of the total turns of wire (at phase B winding, high
voltage side)
4.2.2. Results training network MLP .
The thesis uses the Levenberg - Marquadrt learning algorithm and the Neural Network Toolbox
library in Matlab to perform the computations. The test results with a feature vector of 15 inputs, 1
output and an increasing number of hidden neurons are as follows:
 With 1 hidden neuron

(a) Learning results with 180 samples

(b) Test results with 54 samples

Figure 4.13: Simulation results with 1 hidden neuron
Figure 4.13a and 4.13b presented the results of training the network with the learning
samples set and then testing it with the test samples set. The horizontal axis is the ordinal


18

number of the samples. Because the training sample set consists of 180 samples, Fig.
4.24a has a horizontal axis from 1 to 180, the test sample set includes 54 samples, so Fig.
4.24b has a horizontal axis from 1 to 54. Value points '*' (blue) are the exact target values
to be achieved for the learning process. The 'o' value points (red) are the output values of
the MLP network for each xi sample. The solid purple line represents the absolute
difference between the output of the MLP network and the target value. The black dashed
line is the y = 0.5 threshold value line for a quick assessment of the correlation between
the absolute deviation and the 0.5 threshold value. Since the target values have discrete
values (d = 1, 2, …, 6), the output value of the network will be reduced to the nearest
target value as the identification result. For example, if the output value is 2.34 then the
identification result will be the case 'd=2' (MBA is loose the coil fixing bolt). With this
method, since the target values have a minimum distance of 1, if the difference between
the output values is less than 0.5, there will be no identification error. The learning results
in Figure 4.13 show that the network has a simple structure (15 inputs, 1 hidden neuron, 1
output), so the patterns have not been successfully learned, so there are many error cases.
In which, many samples in cases 5 and 6 have failed to learn.
 With 2 hidden neurons

(a) Learning results with 180 samples

(b) Test results with 54 samples

Figure 4.14: Simulation results with 2 hidden neurons
Experimental results show that the network still has a too simple structure (15 inputs, 2 hidden
neurons, 1 output) so it has not yet successfully learned the patterns, but the number of errors is less
than the field. merge 1 hidden layer. There are still a number of cases (group 5 samples) being
mistaken for form 6. When checking with the 54 sample data set (as shown in Figure 4.14b), there are
still cases of misclassification.


19

 With 3 hidden neurons:

(a) Learning results with 180 samples

(b) Test results with 54 samples

Figure 4.15: Simulation results with 3 hidden neuron
The learning results show that the network has successfully learned all the samples, all the cases of
the learning samples and the test samples have small errors (less than 0.5 threshold).
 With 4 hidden neurons:

(a) Learning results with 180 samples

(b) Test results with 54 samples

Figure 4.16: Simulation results with 4 hidden neurons
The learning results show that just like with the network with 3 hidden neurons, the network with 4
hidden neurons has successfully learned all the samples, all the learning and test samples have small
errors (less than 0.5 threshold)

 With 5 hidden neurons:


20

(a) Learning results with 180 samples

(b) Test results with 54 samples

Figure 4.17: Simulation results with 5 hidden neurons
The learning results show that the network with 5 hidden
neurons has also successfully learned all the samples, all the
learning samples and the test samples have small errors (less
than 0.5 threshold). Therefore, it can be seen that the MLP
network with 15 inputs, 1 hidden layer with at least 3 hidden
neurons and 1 output neuron can successfully learn to
accurately identify the states of the MBA simulated in the
thesis. . The smallest network model with 3 hidden neurons
is shown in Figure 4.18 below.
The structure of the neural network selected to
recognize the feature vectors extracted from the signals of
the transformer is shown in Figure 4.18.

Figure 4.18: Structure of neural
network with 15 inputs, 3 hidden

4.3. PRACTICAL EXPERIMENT ON ACTUAL DISTRIBUTION TRANSFORMER
Vibration measuring equipment is designed, manufactured (details of design and fabrication
are as shown in the appendix of the thesis) and installed for testing at the 3rd Industrial University
Substation as shown in Figure 4.19.

(a)

(b)

Figure 4.19: Transformer at Industrial University Station 3 (a) and
the measuring device mounted on the transformer case (b)


21

It can be seen that the vibration level of the
transformer increased gradually between 10am
and 12pm. After that, it is relatively stable until
about 5 pm and increases rapidly to peak at 6 pm.
Figure 4.20 shows the vibration measurement
by accelerometer sensor at Industrial University
Station 3 from 9.00 to 18.30 on September 15,
2020. Figure 4.21 shows the results of data
collected (remotely) by Thai Nguyen Electricity
Company for the experimental transformer station
in the same time period. However, the current
values (measured remotely) are quite limited in
that they are only taken every 30 minutes to take
the instantaneous value at that time.
It can be seen that the load variation graph has
similar trends with the vibration chart. It is an
upward trend in the morning and fluctuates
(around an average) during the afternoon hours
and rapidly increases in the late afternoon. To see

more clearly the degree of correlation, in Fig. 4.22
both lines of variation have been shown, in which
the actual measured values of total P have been
normalized (linearly) in the range [0,1]. From Fig.
4.22, we can see that there is a clear correlation
between the vibration of the transformer and the
transmission power of the transformer.
Conducted spectrum analysis of the vibration
signals, the signal's spectrum was analyzed
according to the windows with length of 5 minutes,
the number of calculation windows is 90, the total
calculation time for spectral analysis is 450
minutes. The analysis results show that the
vibrational spectra have a relatively high similarity
as can be seen in Fig. 4.23 below.

Figure 4.20: Vibration measurement
by accelerometer sensor on site from
9.00 to 18.30 on September 15, 2020

Figure 4.21: Values of total P
measured by Thai Nguyen Electricity
Company for the site from 9am to
18.30 on 15/9/2020

Figure 4.22: Graph showing simultaneous
vibration and P sum signals of transformer
normalized to range [0,1] during test
measurement

22

(a)

(c)

(b)

(d)

Figure 4.23: Spectral analysis results for digital windows : 0 (a), 10 (b), 20 (c) và 30(d)
Figure 4.23 shows the amplitude of the vibration spectrum using Fourrier analysis. It can be noticed
between the graphs that there is a difference in the pitch of the spectral peaks, but the position of the
spectral peaks is quite stable. The figures have marked some spectral peaks in the vicinity of
fundamental frequencies such as 50Hz, 100Hz and 150Hz along with some non-harmonic spectral
peaks of the fundamental frequency such as peaks at 75Hz and 107.5Hz. To show more clearly the
variation of the peak positions in the spectrum over time, Figure 4.24 shows the variation of the spectral
peak in 5 frequency ranges :
 To monitor the variation of the neighboring
spectral peak at 50Hz, we determine the
extreme point of the frequency range
[37.5Hz ; 62.5Hz],
 To monitor the variation of the neighboring
75Hz spectral peak, we determine the
extreme point of the frequency range
[62.5Hz ; 87.5Hz],
 To monitor the variation of the neighboring
spectral peak 107.5Hz, we determine the
extreme point of the frequency range

[105Hz ; 110Hz] (the search band for this
spectral peak is narrower to avoid falsely

Figure 4.24: Variation of fundamental spectral
peaks with sampling time


23
detecting the spectral peak in the vicinity of 100Hz),
 To monitor the variation of the neighboring spectral peak of 150Hz, we determine the extreme
point of the frequency range [137.5Hz ; 162.5Hz].

It can be seen from Fig. 4.24 that the basic spectral peaks have quite stable positions, among the 5
observed positions, only the spectral peaks in the vicinity of 75Hz have clear fluctuations in the range
from 70Hz to 80Hz. Through this, it can be seen that in the case of normal operation, the frequency
spectrum may vary greatly in amplitude when the instantaneous power of the transformer changes, but
the main spectral peaks will have a relatively stable position.
Due to the short test measurement time, there are no conditions for testing with transformers that are
having problems and not many data for comparison, but certain conclusions can be drawn as follows:
The vibration of the transformer is greatly affected by the instantaneous transmission power of
the transformer, so to detect abnormal vibrations, it is necessary to combine both the vibration
signal and the electrical signal (measurement of the working point of the transformer).
Accelerometer sensor can be used as a solution to measure the vibration of equipment when
operating, thereby as a basis for building models to identify working modes of equipment.
In normal operating mode, when the load changes, the frequency spectrum of the actual
measured vibration signals has fairly stable spectral peak positions. This shows that when there
are unusual vibrational components (due to different incidents), it is possible to detect these
components as a basis for fault case identification.
4.4. CONCLUSION OF CHAPTER 4
Chapter 4 of the thesis presented the following issues:

- Using the transformer model built in Chapter 3 by ANSYS software to simulate 234
results of working scenarios of the transformer, including: 01 normal working case and 05
incident cases. For each case, the transformer is simulated with 50%, 80%, 100% nominal rated
load.
- Conducted evaluation and analysis showed that the electrical signals and active force
signals in the transformer can be used to detect the status of the transformer.
- Extracted the characteristic information of the received signals (from ANSYS simulation),
trained the MLP network with 15 inputs, 3 hidden neurons and 1 output to identify the working
state of the transformer. The network was trained with 180 samples and tested with 54 samples
out of a total of 234 samples collected. Study results and test results are 100% accurate.
- Developed a vibration measuring device using accelerometer and applied actual test with a
distribution transformer at the Industrial University Station 3. The initial measurement results
show that the measured vibration is consistent with the variation of the transformer's transmission
power and the amplitude spectrum of the vibration signal has a set of fairly stable spectral peaks
during normal-mode operation.
CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS
When diagnosing transformer failures in general and distribution transformers in particular,
it is very important to have complete information about transformers to help identify and
accurately diagnose transformer problems. The project has researched and successfully built a