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

APPLICATION OF FINITE ELEMENTS METHOD IN ANSYS MAXWELL SOFTWARE TO IMPLEMENT A MODEL OF TRANSFORMER.... RESEARCH METHODS Studying research works on ANSYS software and signal processing

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

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

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

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

 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

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

objects undergo a deformation in their shape when placed in a

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

Figure 2.1: Magnetic circuit and transformer windings

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

However, we can use a simplified isotropic circuit

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 Differential form Integral form

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):

00

D

t B rot E

t divB

Current density vector A/m2

 Magnetic permeability coefficient

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

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:

0

y x A y

x

r z

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:

0 ) (

.

0

0 1

(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:

t

A J

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:

(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)

  E  j (x,y) 0

(2.17)

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

Figure 2.4: MLP network model with 1

hidden layer

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 W ij

(i  1 M; j 0N), denote the coupling

weights between the hidden layer and the output layer

as V ( ij 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

according to experience and purpose The

commonly used functional forms are [37]:

e tansig x

- Linear function: linear x( )   a x b

In this thesis, the transfer function of hidden neurons is selected as the function f x1( )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 x2( )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x x1, 2,,x NN (fixed bias input x  ), the output is 0 1determined sequentially in the forward propagation direction as follows:

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

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

x d với i, i i 1 p, xiR N;diR K, 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:

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:

g W E  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:

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 ( )t

W , suppose we need to find the next approximation W(t 1) W( )t p approaching the minimum point of the function, then we have:

( )t   ( )t  ( )t

p H W g W (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)t  ( )t   ( )t  ( )t

W W H W g W (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

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

Roll outside diameter Low voltage 189/289 mm

High pressure coil inner diameter 209/309 mm

Number of turns of high-pressure coil 2098

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

Model of transformer circuit:

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

10ohm R30

LabelID=IHA

LabelID=IHB

LabelID=IHC

0.78 R38

0.78 R41

0.78 R44

LabelID=ILA

LabelID=ILB

LabelID=ILC

10ohm R54

0 0

0 0

5ohm R11

5ohm R14

+ 22000*sqrt(2) V LabelID=VV_HA

+ 22000*sqrt(2) V LabelID=VV_HB

+ 22000*sqrt(2) V LabelID=VV_HC

0.78ohm R22

0.78ohm R25

0.78ohm R28

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