wavelet and ann based differential protection of power transformer

8/2/2019 Wavelet and Ann Based Differential Protection of Power Transformer

1/30

SIMULATION OF TRANSFORMERS USING

SIMPOWERSYSTEMS

IINNTTRROODDUUCCTTIIOONN

Sims Power Systems extends Simulink with tools for modeling and simulating basic

electrical circuits and detailed electrical power systems. These tools let us model the

generation, transmission, distribution, and consumption of electrical power, as well as its

conversion into mechanical power. SimPowerSystems is well suited to the development of

complex, self-contained power systems, such as those in automobiles, aircraft, manufacturing

plants, and power utility applications.

Together, SimPowerSystems and Simulink provide an efficient environment for

multidomain modeling and controller design. By connecting the electrical parts of the

simulation to other Simulink blocks, we can rapidly draw the circuit topology and

simultaneously analyze the circuits interactions with mechanical, thermal, and Control

systems.

SSIIMMUULLAATTIIOONN OOFF TTRRAAIINNIINNGG CCAASSEESS FFOORR TTRRAANNSSFFOORRMMEERR::

Three-phase transformers (One power Transformer and Two distribution Transformers) of 150

MVA, 110/220 kV; 500 KVA, 11/0.433 kV; and 1000kVA, 11/0.433 kV are modelled using

MATLAB. The parameters used for the simulation of these two distribution transformers

through MATLAB were obtained from IT-BHU Substation

A Three Phase 110/220 kV power system included a 150 km transmission line, as

shown in Fig.1, has been used to produce the required test and training patterns. The

simulation was done by means of SimPowerSystems (MATLAB) software.


2/30

Fig 1Simulated power system model

Table 1represents theassociated data with this power system. Thecombination

of condition system shown in Table 2, have been produced using this system to train

the WNN (Wavelet and ANN). Faults are located at different points of transmission

line.Also,

they involve inrush current and over excitation condition with differentvoltage angles and with different loads. Here secondary current is converted to primary

side to make a common base. Breakers are connected to different positions for obtaining

data for above different conditions of power transformer. Differential current is

obtained by subtracting the secondary current to primary current.

TABLE 1 SIMULATED POWER SYSTEM PARAMETERS

Transformer nominal power

& frequency

150 MVA, 50 Hz

Transformer winding parameters R=.002 pu, L=.08 pu

Transformer core loss resistance 500 pu


3/30

TABLE 2 TRAINING PATTERNS DATA GENERATION

Condition

system

Internal fault : Transformer secondary is shorted and single

phase-ground faults and double phase-ground faults and three

phase faults

Inrush : At different voltage angles by closing the breaker

connected

Over-excitation : At different over voltages

Voltage

angle

0, 10, 20..to 180 degree

Load(MW) 20, 40, 60, 80 and 100

Line parameters (150 km) R=.2568 ohm/km, L=2e-3 H/km, c=8.6e-9

F/km


4/30

Since the network has to distinguish among five kinds of signals, 4sets of example

signals (cases) have been obtained for this purpose. These cases are normal, internal fault

current, magnetizing inrush and over- excitation condition

1. Normal case: Power system is simulated for different voltage angles and for differentloads.

2. Internal fault : Transformer terminal faults like Single phase to ground, double phaseto ground ,three phase to ground and phase to phase faults

3. Inrush condition: In this condition transformer secondary is open circuited. Circuitbreaker is connected at primary side, which is primarily open and shorted after two

cycle.

4. Over-excitation: For obtaining this condition the load side connected circuit breaker isopened at alternate cycles.

Following figures 2 show the power system models for creating the data at different

conditions.

Fig 2(a) Normal condition


5/30

Fig .2(b) internal fault condition

Fig

2(c) Magnetizing Inrush condition


6/30

Fig 2(d) Over-excitation condition

Following figures 3 show the differential currents of transformer at different conditions.

Fig-3 (a) Normal condition

Simulated event of Three phase transformer (SimPowerSystems)


7/30

Fig- 3 (b) internal fault condition

Simulated event of three phase transformer (SimPowerSystems)

Fig-3 (c) Inrush condition



8/30

Fig-3 (d) Over-excitation condition


Different cases of Normal, Fault, and Inrush and over Excitation cases are simulated. The

fundamental frequency of the current is 50Hz .The differential current waveforms generated

from using MATLAB software has a sampling frequency of 2 KHz. There are 40 samples/ cycle.


9/30

WAVELET ANALYSIS AND NEURAL NETWORK

TRAINING AND RESULTS

Design and Development of WNN (Combined Wavelet and ANN) ForDifferential Relaying:

WAVELET ANALYSIS:

There are two aspect had to consider for Wavelet analysis

1.The differential current waveforms generated from using MATLAB software

have a sampling frequency of 2 KHz. There are 40 samples/ cycle.

2. Another aspect had to be consider is no. Of current samples which will beapplied to the feature extractor (DWT) .Here half of the data cycle used as a

moving window that means 20 samples. This data would be updated by

incorporating the latest sample and discarding the oldest sample

EXTRACTING DWT COMPONENTS FOR DIFFERENT

CONDITION:

The DWT plots of differential current below demonstrate the importance of

having DWT as the feature extractor of the Neural Network classifier. Through using

the features of the DWT extracted from differential current data, the DWT can help with

the discriminating of different data clusters and groups , thus, benefit the predictive and

detective system.

Normal Condition:

The following fig shows the plots of the coefficients of the Discrete Wavelet

Transform (DWT) of differential current with 100% load


10/30

Fig: 1 (a) DWT of A-Phase differential current measured for Normal

condition

Aamax = 1.251 Damax = 0.3341

Aaavg = -0.111 Daavg = 0.0028

Naa = 4.225 Nda = 0.3969

Fig: 1 (b) DWT of B-Phase differential current measured for Normal condition

Abmax = 1.2592 Dbmax = 0.1174

Abavg

= -0.1076 Dbavg

= -0.0024

Nab = 4.230 Ndb = 0.3109


11/30

Fig:1 (c) DWT of C-Phase differential current measured for Normal condition

Acmax = 1.2517 Dcmax = 0.0395

Acavg = 0.2187 Dcavg = -3.9e^-4

Nac = 4.6876 Ndc = 0.0945

Internal Fault condition:

Single Phase to ground fault:

The following fig shows the plots of the coefficients of the Discrete

Wavelet Transform (DWT) of differential current with single phase( A-Phase) to

ground fault with zero resistance

Fig:2(a) DWT of A-Phase differential current measured for Single phase (A-

Phase) to ground fault

Aamax = 928.92 Damax = 21.38

Aaavg = 169.74 Daavg = -4.697

Naa = 1900 Nda = 80.85


12/30

Fig:2(b) DWT of B-Phase differential current measured for Single phase (A-Phase)

to ground fault

Abmax = 1.4100 Dbmax = 0.0542

Abavg = 0.0414 Dbavg = 5.42e^-4

Nab = 4.7942 Ndb = 0.1207

Fig:2(c) DWT of C-Phase differential current measured for Single phase (A-

Phase) to ground fault

Acmax = 1.4162 Dcmax = 0.0402Acavg = 0.0349 Dcavg = -1.92e^-4

Nac = 14.11 Ndc = 0.1445


13/30

Two phase fault:

The following fig shows the plots of the coefficients of the Discrete Wavelet Transform

(DWT) of differential current with two phase (R-Y) fault with 10 resistance

Fig:3(a) DWT of A-Phase differential current measured for Two phase (A-Phase

to B-Phase) fault with 10 resistance

Aamax = 813.15 Damax = 13.626

Aaavg = 222.2 Daavg = -0.4434

Naa = 1980 Nda = 33.829

Fig:3(b) DWT of B-Phase differential current measured for Two phase (A-Phase to

B-Phase) fault with 10 resistance

Abmax = 7.657 Dbmax = 27.06

Abavg = -221.98 Dbavg = 0.4416

Nab = 1980 Ndb = 33.843


14/30

Fig:3(c) DWT of C-Phase differential current measured for Two phase (A-Phase to

B-Phase) fault with 20 resistance

Acmax = 1.486 Dcmax = 0.0402

Acavg = 0.0351 Dcavg = -1.61e^-4

Nac = 15.093 Ndc = 0.0972

Three Phase Fault:


(DWT) of differential current with three phase (R-Y-B) fault with 20 resistance

Fig:4(a) DWT of A-Phase differential current measured for Three phase (R-Y-B)

fault with 20 resistance

Aamax = 840.01 Damax = 54.95

Aaavg = 162.54 Daavg = -4.339

Naa = 1780 Nda = 158.18


15/30

Fig:4(b) DWT of B-Phase differential current measured for Three phase (R-Y-B)


Abmax = 37.52 Dbmax = 33.33

Abavg = -262.09 Dbavg = -3.430

Nab = 2200 Ndb = 115.7

Fig:4(c) DWT of C-Phase differential current measured for Three phase (R-Y-B)


Acmax = 598.2 Dcmax = 111.6

Acavg = 0.2569 Dcavg = -1.08

Nac = 5360 Ndc = 285.0


16/30

Inrush condition:

The following fig shows the plots of the coefficients of the Discrete Wavelet

Transform (DWT) of differential current of 3 phases with 60 degrees

Fig:5(a) DWT of A-Phase differential current measured for Inrush condition at 60

degrees

Aamax = 855.2 Damax = 43.24

Aaavg = 162.45 Daavg = 0.6338

Naa = 1600 Nda = 57.89

Fig:5(b) DWT of B-Phase differential current measured for Inrush condition at 60

degrees

Abmax = 15.55 Dbmax = 19.88

Abavg = -100.127 Dbavg = -0.621

Nab = 1200 Ndb = 35.66


17/30

Fig:5(c) DWT of C-Phase differential current measured for Inrush condition at 60

degrees

Acmax = 9.5401 Dcmax = 13.08

Acavg = -86.11 Dcavg = 1.254

Nac = 1080 Ndc = 23.89

Over Excitation condition:


(DWT) of differential current of 3 phases with 140% of voltage

Fig:6(a) DWT of A-Phase differential current measured for 140% of voltage

Aamax = 216.90 Damax = 9.121

Aaavg = -19.116 Daavg = -0.762

Naa = 561.05 Nda = 22.0412


18/30

Fig:6(b) DWT of B-Phase differential current measured for 140% of voltage

Abmax = 223.55 Dbmax = 12.25

Abavg = 2.19 Dbavg = 0.2803

Nab = 431.11 Ndb = 27.84

Fig:6(c) DWT of C-Phase differential current measured for 140% of voltage

Acmax = 196.62 Dcmax = 22.87

Acavg = 15.17 Dcavg = 0.164

Nac = 505 Ndc = 43

In all DWT processes performed above, the Db-6 type mother wavelet (Daubechies6)

has been used. Also, the decomposition level of the DWT of these signals has been kept

at 2 In Mat lab, the some commands were used to calculate the DWT coefficients.The

maximum, normalisation and average values of detail and approximation coefficients

are used to train the neural network


19/30

d1 max = maximum value of d1[n] = max[d1[n]]

d1norm=normalisationvalue of d1[n] =norm[d1[n]]

d1avg =average value of d1[n] = avg[d1[n]]

a1max = maximum value of a1[n] = max[a1[n]]

a1norm=normalisation value of a1[n] =norm[a1[n]

a1avg =average value of a1[n] = avg[a1[n]]

For each phase 6 input values so for three phase 18 input values are used to train the

neural network

TTEESSTT RREESSUULLTTSS OOFF PPRROOPPOOSSEEDD AANNNN

A software nntool (graphical user interface) in MATLAB SIMULINK has been

used for training process. Since the network has to distinguish among four kinds of

signals, 4 sets of example signals (cases) have been obtained for this purpose. These

cases are normal, internal fault, magnetizing inrush and over- excitation. The training

functions and parameters are given in Table-1.

Table-1 Training function and parameters

Adaption learning function LEARNGM Training function TRAINGDA

Hidden layer transfer

function

TANSIG Output layer transfer

function

TANSIG

Epochs 2000 mc 0.95

Goal 0.00000011 Mu-max 100000000

Max-fail 40 Show 20

Mem_redu 1 Time Inf

Min_grad 1e-10 Learning Rate 0.7

Mu 0.001 Performance function MSE

LEARNGD-Gradient descent weight and bias learning function

TRAINGDA-Gradient descent back propagation with adaptive learning rate


20/30

For each Power transformer and distribution transformer 740 training sets of

samples (580 sets for training and 160 sets for testing purpose) generated by

SimPowerSystems in MATLAB. Signals are sampled at the sampling rate of 40

samples per cycle (over a data window of half cycle).

The Wavelet transform has been used to analyze the transients in the power

transformers. The data obtained from the simulations are given to the

MATLAB(Wavelet Analysis) software to calculate DWT coefficients of the signals..

This 580 training sets of coefficients contain 4 different conditions of power

transformer (normal, magnetizing inrush, over-excitation, internal fault ) 100 sets of

coefficients have been taken for normal, 240 sets of coefficients taken for internal fault,

140 sets of coefficients taken for inrush, 100 sets of coefficients taken for over

excitation condition.

After enough experimentation a network with 40 neurons in the hidden layer

apart from 18 inputs and 4 outputs has been found suitable for monitoring the different

conditions of power transformer. The outputs of the network have a unique set (e.g.,

1000 = normal, 0100=internal fault, 0010= inrush, 0001 =over-excitation,). This

network i.e. with 4 outputs monitors all the conditions occurring in the power

transformer and it issues the trip signal only in case of internal fault condition i.e. when

output is 0100.


21/30

Fig:8 Flowchart of ANN Training

Concerning the ANN architecture, parameters such as the number of inputs to

the network and the number of neurons in the hidden layer were decided empirically.

Performance Results for Power Transformer (110/220KV, 150MVA):

This training process involves experimentation with various network

configurations. It has been discovered that ANN with less number of input and hidden

layer perform satisfactorily using the BP training algorithm. The learning process was

terminated after 2000 cycles. The training error after 2000 epochs was 0.000097 for the

proposed network and was within acceptable limit. The network responds in a very

adequate way, performing the discrimination among normal, inrush, over-excitation,

Preparation of suitable Training

Selection of a suitable ANN

Training of the ANN

Trained

Evaluation of the trained ANN

Performance

Process Terminated

Poor

Good

Creation of Training data


22/30

and internal fault currents correctly for all cases. The competitive model and their

performance are being discussed here. Table 2 show the different ANN topologies and

their corresponding errors. On the basis of performance, networks have been classified

as very good, good, or not good. By very good performance the authors mean that the

network can be trained to achieve the error goals and can respond adequately to the test

by good the same can be achieved by increasing the

Table2

Performance of network architectures with 18 inputs, 4 outputs, and Variable neurons in

the hidden layer (Training epochs: 2000)

ANN topology Training error Training time

(seconds)

Performance

18_10_4 0.000567 71 G

18_20_4 0.000798 61 NG

18_30_4 0.000581 50 NG

18_40_4 0.000097 37 VG

18_50_5 0.000598 70 NG

NG = not good; VG = very good; G = good.

number of iterations. It has been found that a net with 18 inputs, 40 nodes in hidden

layer, and 4 outputs is capable of reducing the error up to 0.000097, which is quite

accurate for this problem. Figure 20 shows the learning error over 2000 cycles of the

architecture (18-40-4), which is continuously decreasing, whereas the same of the other

topology shows zigzag behaviour. Therefore, for these cases the performance is not

good. The response can be improved further by undertaking further extensive training,

but it is realized that the same is not desired. By Using the detail and approximate

coefficients to train the NN the training time is taken less and for testing it takes only

few milliseconds. The outputs for test and trained patterns are shown in Tables 3 and 4,

respectively. The learning errors for other topologies have been shown in in fig.


23/30

Fig:9 Learning error for 18_40_4 topology

The plot shows the mean squared error of the network starting at a large value and

decreasing to a smaller value. In other words, it shows that the network is learning.

The plot has three lines, because the 580 input and targets vectors are randomly divided

into three sets. 60% of the vectors are used to train the network. 20% of the vectors are

used to validate how well the network generalized. Training on the training vectors

continues as long the training reduces the network's error on the validation vectors.

After the network memorizes the training set (at the expense of generalizing more

poorly), training is stopped. This technique automatically avoids the problem of over

fitting, which plagues many optimization and learning algorithms. Finally, the last 20%

of the vectors provide an independent test of network generalization to data that the

network has never seen

Table 3

Trained output for the architecture

Types of

Cases

ANN

Architecture

Outputs

1

A P

2

A P

3

A P

4

A P


24/30

Normal 18_40_4 0.9776 1 0.0040 0 0.0041 0 0.00267 0

Internal Fault 18_40_4 0.00034 0 0.996 1 0.0107 0 0.000839 0

Inrush 18_40_4 0.0000016 0 0.0153 0 0.989 1 0.00051 0

Over

Excitation

18_40_4 0.000165 0 0.00094 0 0.00478 0 0.9987 1

Table 4

Tested output for the architecture

Types of

Cases

ANN

Architecture

Outputs

1

A P

2

A P

3

A P

4

A P

Normal 18_40_4 0.9776 1 0.0039 0 0.0040 0 0.0266 1

Internal Fault 18_40_4 0.0037 0 0.991 1 0.0059 0 0.00117 0

Inrush 18_40_4 0.00076 0 0.0000034 0 0.9980 1 0.000125 0

Over-

excitation

18_40_4 0.0005517 0 0.0035 0 0.00029 0 0.99900 1


25/30

Fig:10(a).Learning error for 18_10_4 topology

Fig:10(b) Learning error for 18_20_4 topology

Fig:10(c) Learning error for 18_30_4 topology


26/30

Fig:10(d) Learning error for 18_50_4 topology

Response of Relay to Internal fault:

0 0.025 0.05 0.075 0.10 0.125 0.150 0.175

0.2

Fig:11 Response of relay

From these results, it can be seen that 10 ms after the occurrence of a fault, the

protection technique developed correctly identifies internal fault.The outputs show the

satisfactory result for the architectures. The ANN recognizes the fault in all cases and

gives the trip signal output within half of cycle after the internal fault occurrence.

trip

Faultt=0.04

1

0

1


27/30

Performance Results for Distribution Transformer (11/0.433KV, 500KVA):

Table 5: Performance of network architectures with 18 inputs, 4 outputs, and Variable

neurons in the hidden layer


(seconds)

Performance

18_10_4 0.0089 71 G

18_20_4 0.011 79 NG

18_30_4 0.0092 84 NG

18_40_4 0.010 89 NG

18_50_4 0.0080 90 G

In above topologies 18_50_4 error is less than other topologies. The trained and tested

output of the 18_50_4 topology shown in Table and the learning error of the 18_50_4

topology .

Table 6 Trained output for the architecture

Types of

Cases

ANN

Architectur

e

Outputs

1

A P

2

A P

3

A P

4

A P

Normal 18_40_4 0.9427 1 8.83e-5 0 0.002 0 0.130

9

0

Internal Fault 18_40_4 0.179 0 0.942 1 0.0063 0 2.65e-

5

0

Inrush 18_40_4 0.0344 0 0.0034 0 0.997 1 0.005

6

0

Over

Excitation

18_40_4 0.048 0 1.09e-5 0 8.208e-5 0 0.960 1


28/30

Table 7:Tested output for the architecture

Types of

Cases

ANN

Architecture

Outputs

1

A P

2

A P

3

A P

4

A P

Normal 18_40_4 0.89 1 0.067 0 0.003 0 9.8e-5 0

Internal Fault 18_40_4 0.172 0 0.947 1 0.0048 0 2.67e-7 0

Inrush 18_40_4 0.0035 0 0.0004 0 0.91 1 0.023 0

Over

Excitation

18_40_4 0.168 0 2.654 0 0.074 0 0.94 1

Fig.12 Learning error for 18_10_4 topology


29/30

Performance Results for Distribution Transformer (11/0.433KV, 1 MVA):

Table 8: Performance of network architectures with 18 inputs, 4 outputs, and Variable

neurons in the hidden layer


(seconds)

Performance

18_10_4 0.0017 69 VG

18_20_4 0.0047 76 G

18_30_4 0.0039 86 G

18_40_4 0.0033 84 G

18_50_5 0.0068 91 G

In above topologies 18_10_4 error is less than other topologies. The trained and tested

output of the 18_10_4 topology shown in Table and the learning error of 18_10_4

topology is shown in fig 23

Table 9: Trained output for the architecture

Types of

Cases

ANN

Architecture

Outputs

1

A P

2

A P

3

A P

4

A P

Normal 18_10_4 0.98 1 0.006 0 0.0096 0 0.1 0

Internal Fault 18_10_4 2.2e-05 0 0.98 0 0.01 0 0.016 0

Inrush 18_10_4 0.001 0 0.02 0 0.976 1 0.003 0

Over

Excitation

18_0_4 0.00061 0 0.01 0 0.014 0 0.99 1


30/30

Table 10: Tested output for the architecture

Types of

Cases

ANN

Architecture

Outputs

1

A P

2

A P

3

A P

4

A P

Normal 18_10_4 0.842 1 0.157 0 0.011 0 0.017 0

Internal Fault 18_10_4 7.178e-07 0 0.99 1 0.019 0 0.038 0

Inrush 18_10_4 0.00067 0 0.0079 0 0.91 1 0.023 0

Over

Excitation

18_10_4 0.0061 0 0.0038 0 0.0036 0 0.9982 1

Fig.13.Learning error for 18_10_4 topology

wavelet and ann based differential protection of power transformer

Documents