Power transformer differential protection using neural network Principal Component Analysis and Radial Basis Function Neural Network

Simulation Modelling Practice and Theory 18 (2010) 600–611

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Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat

Power transformer differential protection using neural network Principal Component Analysis and Radial Basis Function Neural Network Manoj Tripathy * Department of Electrical Engineering, Motilal National Institute of Technology Allahabad, Allahabad 211 004, Uttar Pradesh, India

a r t i c l e

i n f o

Article history: Received 17 June 2009 Received in revised form 19 December 2009 Accepted 9 January 2010 Available online 18 January 2010 Keywords: Radial basis function neural network Digital differential power transformer protection Neural network principal component analysis Protective relaying Artificial neural network

a b s t r a c t Many methods have been used to discriminate magnetizing inrush from internal faults in power transformers. Most of them follow a deterministic approach, i.e. they rely on an index and fixed threshold. This article proposes two approaches (i.e. NNPCA and RBFNN) for power transformer differential protection and address the challenging task of detecting magnetizing inrush from internal fault. These approaches based on the pattern recognition technique. In the proposed algorithm, the Neural Network Principal Component Analysis (NNPCA) and Radial Basis Function Neural Network (RBFNN) are used as a classifier. The principal component analysis is used to preprocess the data from power system in order to eliminate redundant information and enhance hidden pattern of differential current to discriminate between internal faults from inrush and over-excitation condition. The presented algorithm also makes use of ratio of voltage-to-frequency and amplitude of differential current for detection transformer operating condition. For both proposed cases, optimal number of neurons has been considered in the neural network architectures and the effect of hidden layer neurons on the classification accuracy is analyzed. A comparison among the performance of the FFBPNN (Feed Forward Back Propagation Neural Network), NNPCA, RBFNN based classifiers and with the conventional harmonic restraint method based on Discrete Fourier Transform (DFT) method is presented in distinguishing between magnetizing inrush and internal fault condition of power transformer. The algorithm is evaluated using simulation performed with PSCAD/EMTDC and MATLAB. The results confirm that the RBFNN is faster, stable and more reliable recognition of transformer inrush and internal fault condition. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction In the literature of power transformer protection, the key issue lies in discriminating between transformer magnetizing inrush current and internal fault current. It is natural that relay should be initiated in response to internal fault but not to inrush current or over-excitation/external fault current [1]. Early methods were based on desensitizing or delaying the relay to overcome the transients [2]. These methods are unsatisfactory since the transformer may be exposed for a long unprotected time. Yet another method based on the second harmonic content with respect to the fundamental one was introduced as an identification criterion, known as harmonic restraint differential protection [3], which improved security and dependability was appreciated. However, some researchers have reported the existence of a significant amount of the second harmonic in some winding faults [4,5]. In addition, the new generations of power transformers use of low-loss amorphous material in their core, which can produce inrush current with * Tel.: +91 9412 015058; fax: +91 5332 2445101. E-mail address: [email protected] 1569-190X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2010.01.003

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lower harmonic contents and higher magnitudes [5]. In such cases, some authors have modified the ratio of second harmonic to fundamental restraining criterion by using other ratios defined at a higher frequency [6]. While other researchers proposed wave comparison and error estimation method [7], fuzzy logic based techniques [4], principal component analysis [8], and correlation analysis method [9] to discriminate internal fault condition from non-fault condition. Power flow through the transformer is also be used as an index to detect inrush current. It was said that the average power was almost zero for energizing, but an internal fault consumes large power [10]. However, all the preceding approaches share the same feature, i.e. they depend on a single index. Furthermore, to choose a proper threshold for discrimination is not easy. Artificial Neural Networks (ANN) is extremely used particularly in the field of power system protection since 1994 as this problem is subclass of pattern recognition of current waveforms. It is to be noted that ANNs were primarily used in different areas such as pattern recognition, image processing, load forecasting, power quality analysis, and data compression. The main advantage of the ANN method over the conventional method is the non-algorithmic parallel distributed architecture for information processing and inherent ability to take intelligent decision. In recent years, few works which investigate the feasibility of using ANN for power transformer differential protection has also been reported [11–18]. This paper presents two approaches to detect inrush current by recognizing its wave shape, more precisely from the wave shape of internal fault current. In this method, two different types of artificial neural networks are used to get better accuracy in classification, low computational burden and fast response of the relay. As the performance of an ANN very much depends on its generalization capability, which in turn is dependent upon the data representation. One important characteristic of data representation is uncorrelation. In other words, a set of data presented to an ANN ought not to consist of correlated information. This is because correlated data reduce the distinctiveness of data representation and thus, introduce confusion to the ANN model during learning process and hence, producing one that has low generalization capability to resolve unseen data. This suggests a need for eliminating correlation in the sample data before they are being presented to an ANN. This can be achieved by applying the Principal Component Analysis (PCA) technique [19] onto input data sets prior to the ANN training as well as testing process. In this paper, simple decision making methods based on the Neural Network Principal Component Analysis (NNPCA) and Radial Basis Function Neural Network (RBFNN) are proposed for discriminating internal faults from inrush current. The algorithm has been developed by considering different behaviors of the differential current under internal fault and inrush condition. The PCA extracts the relevant features from the differential current and reduces a training data set to a lower dimension. The presented algorithm uses a sliding data window with 12 samples per cycle at a sampling frequency of 600 Hz (for 50 Hz power systems). The algorithm considers CT saturation and changes in power system configuration. The algorithm was proven using PSCAD/EMTDC simulations considering distinct scenarios as changes in transformer load, source impedance, CT ratio, remenant flux, etc. A comparison among the performance of the Feed Forward Back Propagation Neural Network (FFBPNN), NNPCA, RBFNN based classifier and with the conventional harmonic restraint method based on Discrete Fourier Transform (DFT) method is also presented in distinguishing between magnetizing inrush and internal fault condition of power transformer. The proposed method has been observed as the best solution for power transformer differential protection. The rest of the paper has been structured as follows. Section 2 and Section 3 give an overview of the NNPCA and RBFNN, respectively. Section 4 briefly presents the simulation of various operating condition of power transformer and formulation of training and testing cases. Implementation of proposed algorithm and results of the test cases are discussed in Section 5, and Section 6 concludes the paper. 2. Neural Network Principal Component Analysis Neural Network Principal Component Analysis (NNPCA) is a kind of feed forward neural network. It is basically an adaptive non-parametric method of extracting relevant information from confusing data sets [20,21]. It expresses the data set in such a way as to highlight their similarities and differences. In 1982, Oja found a simple linear neuron model with a constrained Hebbian learning rule [20,21]. For this work, Hebbian learning is used. Generally, NNPCA is used for data reduction in statistical Pattern recognition signal processing and image compression [20]. A typical architecture of NNPCA which is defined by corresponding weights and connection scheme is shown in Fig. 1. This network architecture has multilayer structure that is one input layer, one hidden layer and one output layer. The NNPCA is trained by using back propagation method. In back propagation method, a bounded and differentiable activation function is required. The sigmoid type activation function has all these properties making it popular in this training. In the present work, the hidden unit and output unit use sigmoid type of activation function due to aforesaid advantages. For a d-dimensional input data vectors z1, z2, . . ., zd to m output of neural network s1 ; s2 . . . sm

si ¼ U

m X

wi zi

ð1Þ

i¼1

where w is the Connecting weight, wi ¼ ½wi1 ; wi2 ; . . . wim T , U is the nonlinear sigmoid activation function.The weight adapting equation for neuron i is

"

Dwij ¼ g si zi  si

j X k¼1

# wkj sk

ð2Þ

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M. Tripathy / Simulation Modelling Practice and Theory 18 (2010) 600–611

v1

X1

X2

Xd

v2

vn

h1

h2

hq

w1

w2

s

wq

Fig. 1. Typical neural network principal component analysis architecture.

where g is the learning rate, j = 1, 2, . . ., d and i = 1, 2, . . ., m.After the NNPCA model had been trained, their generalization performance was calculated based on the Mean Absolute Error (MAE) given by

E¼

P X

jT i  si j

ð3Þ

i¼1

where P is the total number of test patterns, Ti is the actual output and siis the NNPCA’s estimated output for the ith test pattern. 3. Radial Basis Function Neural Network Radial Basis Function Network (RBFN) is especial type of feed forward neural network with an input layer used as sensing unit containing n neurons through which input vector x e Rn is fed to a single hidden layer having q number of RBF-type hidden neurons and an output layer, containing L neurons. In RBF neural network model the activation of hidden unit is determined by using the radial distance between the input vector and prototype vector. Generally, Euclidean norm is used to measure the radial distance. The network is designed to perform a nonlinear mapping from input space to the hidden space, followed by a linear mapping from the hidden space to the output space. The performances of RBF network critically depends on the choice of nonlinear activation function, the centers and width factor. The centers in RBF network should be selected to minimize the total distance between the data and the centers so that the centers can properly represent the data. A simple and widely adopted square error cost function is used for network training. The square error E is defined in the following equation:

E¼

L 1X ðdk  yk Þ2 2 k¼1

ð4Þ

where dk is the desired output and yk is the output of neuron k given by:

yk ¼ ðwk ÞT  U

ð5Þ T

where wk ¼ ½wk1 ; wk2 ; . . . ; wkq  are the weights connecting the RBF hidden neurons with the output neurons and U is the output of the hidden layer. Each hidden neuron represents a single RBF and computes a kernel function of x using any one of the activation function as mentioned in this section

0

n 1X xi  cji Uj ¼ exp @ 2 i¼1 bji

!2 1 A

ð6Þ

where cj = (cj1, cj2,. . ., cjn) and bj = (bj1, bj2, . . .,bjn) are the center and width factor of the jth hidden neuron, respectively. The systematic diagram of three layered radial basis function neural network is shown in Fig. 2. The response of kernel function utilized by hidden layer neuron of RBFNN is local in nature. The number of neurons in hidden layer is fixed heuristically. The sigmoid type of activation function used in multilayer feed forward networks to train with back-propagation, does not yield the approximating capabilities for RBF networks. Following activation functions U() are in general popular for RBFNN reported in [22]. i. Gaussian function

Uðv Þ ¼ expðv 2 =2b2 Þ

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M. Tripathy / Simulation Modelling Practice and Theory 18 (2010) 600–611

w1

x1 h1

wi

xi

hi

∑

y

wq

xn hq

Hidden layer

Input layer

Output layer

Fig. 2. Typical radial basis function neural network architecture.

ii. Thin SP line function

Uðv Þ ¼ v log v 1=2 iii. Multiquadric function

Uðv Þ ¼ v 2 þ b2 Þ1=2 iv. Inverse Multiquadric function

Uðv Þ ¼ ðv 2 þ b2 Þ1=2 where v is the ||x  cj||, x is the input vector and cj is jth center, b is the width factor (real constant), and || || is the Euclidean normThe design and training of an RBFNN consist of the following three steps:

i. Determining the center, ii. Determining the widths, iii. Determining the weights. The above first two parameters of the RBFNN are determined by unsupervised learning methods. The centers are determined by using C-means clustering technique. The width factor can be determined by two methods, i.e. given as fixed center method and Moody and Darken method. The fixed center method is given as:

dmax b ¼ pffiffiffi 2M

ð7Þ

where M is the number of centers and dmax is the maximum distance between chosen centers. Moody and Darken [23] proposed width factor bj by r-nearest neighbor heuristic:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !ffi u r X 1u 2 bj ¼ t jjci  cj jj r i¼1

ð8Þ

where ci is nearest neighbor of centers cj and a suggested value for r is 2. Nabil Benoudjit et al. [24] suggested the optimal width factor as

8j ;

bj ¼ sbci

ð9Þ

where bci is the standard deviation of each data cluster obtained by Eq. (8) and s is the width scaling factor.In this paper, the above mentioned three parameters of RBFNN are designed by considering C-means clustering and optimal width factor. The weights are calculated by a supervised, single-shot process using pseudo-inverse matrices or Singular Value Decomposition (SVD) method.

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4. Simulation and training cases Power transformer operating conditions may be classified as –     

Normal condition Magnetizing inrush/sympathetic inrush condition Over-excitation condition Internal fault condition External fault condition

In the normal condition, rated or less current flows through the transformer. In this condition normalized differential current is almost zero (only no load component of current). Whenever, there is large and sudden change in the input terminal voltage of transformer, either due to switching-in or due to recovery from external fault getting, a large current is drawn by the transformer from the supply. As a result, the core of transformer gets saturated. This phenomenon is known as magnetizing inrush, or in other words, inrush can be described by a condition of large differential current occurring when either the transformer is just switched on or the system recovers from an external fault. Similar condition occurs when transformer is energized in parallel with another transformer that is already in service, it is known as ‘sympathetic inrush’ condition. Among the various faults in transformer, phase-to-ground, fault occurs most frequently. On the basis of fault current, phase-toground fault, for protective device operation view point, may be further classified as (a) Heavy faults (a) Medium level fault and (b) Low level fault In all above cases, the nature of abnormality is almost same but magnitudes of current resulting due to the fault are quite different. If the level of fault can be detected in time and corresponding protective actions are initiated, than the major damage to the protected element can be prevented. PSCAD/EMTDC simulation software is used to generate the training and testing signals under different operating condition of transformer that are normal, over-excitation, magnetizing inrush, sympathetic inrush, and fault conditions such as phase-to-phase, phase-to-ground and external fault. While simulating different operating conditions of transformer, energization angle, remanent flux in the core and load condition are considered as the magnitude and the wave shape of differential current depends on these factors. Energization angle is varied from 0° to 360° in interval of 30° and remanent flux varying from 0% to 80% of the peak flux linkages generated at rated voltage with no load and full load conditions to generate training signals, while testing signals energization angle is varied in interval of 15°. The desired remanence in un-energized transformer is modeled as controlled DC current sources in PSCAD/EMTDC model [25]. As transformers are not expected to be subjected to more than 15% over voltage, over-excitation condition is simulated by applying 115% of the rated voltage at full load. For this, three different 3-phase transformers of (a) 315 MVA, 400/220 kV, (b) 200 MVA, 220/110 kV, and (c) 160 MVA at 132/220 kV, (all at 50 Hz, delta-star grounded connection) were modeled using PSCAD/EMTP software. Fig. 3 shows the connection of power system using 315 MVA at 400/220 kV, 50 Hz power transformer. In the high voltage side, there is a source 200 MVA, 400 kV, and 10x as internal impedance; in low voltage side, there is a three-phase load of 285 MW and 137.28MVAR. The parameters used for the simulation of these transformers through PSCAD/EMTDC were obtained from M.P. State Electricity Board, Jabalpur, India. Internal fault training and testing are done by simulating fault from 1% to 99% of the power transformer winding turns. Phase-to-ground fault at different location namely at 5%, 15%, 25%, 40% and 50% of the winding as well as terminal fault are modeled. The detailed information of power transformer PSCAD/EMTDC simulation model to simulate internal fault (Fig. 14) is given in Appendix A. In [26], Eq. (10) is proposed to avoid saturation in CT and reduce the impact over the protective relays. However, in this work a reduced CT ratio of 600:5 and 1200:5 is selected to allow distortion in the waveform of the differential current as part of the stable state operation

   X  þ 1  IF  Z B  20  R

ð10Þ

315MVA XT = 0.01p.u. 10Ω 200MVA

285 MW + 137.28MVAR Fig. 3. Typical three-phase power system.

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M. Tripathy / Simulation Modelling Practice and Theory 18 (2010) 600–611

where IF is maximum fault current in per unit of CT rating, ZB is CT burden in per unit of standard burden, and X/R is the reactance/resistance ratio of power system, respectively. The test signals so obtained by simulating various operating conditions of transformer are shown in Figs. 4–8. The simulation was done at 12 samples per cycle at a sampling frequency of 600 Hz for 50 Hz power system in view of reported experience on different digital relay designs [27,13]. The developed fault detection algorithm was implemented in MATLAB on Intel P-IV processor based desktop with front side bus (FSB) speed of 400 MHz. 5. Implementation of algorithm and results The differential current is typically represented in discrete form as a set of 12 uniformly distributed samples obtained over a data window of one cycle of fundamental frequency, i.e. the sampling rate is 12 samples per cycle. These 12 samples are called a ‘pattern’. The sliding data window, consisting of one most recent and other of previous window are used to generate patterns for different operating conditions of power transformer as mentioned in Section 4. Each row of the input training matrix represents one pattern while corresponding row of target matrix represents desired output. Suppose the inrush condition signal is characterized by the following sequence:

i ¼ ½i1 ; i2 ; . . . ; ik 

Operating Signal (pu)

ð11Þ 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 0

0.04

0.08

0.12

0.16

Time (s)

Operating Signal (pu)

Fig. 4. Typical differential current waveform for normal operation.

Fault occurred here

10 8 6 4 2 0 -2 -4 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time (s) Fig. 5. Typical differential current waveform for ground fault.

Operating Signal (pu)

7

Switching-in occurred here

6 5 4 3 2 1 0 -1 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time (s) Fig. 6. Typical differential current waveform for magnetizing inrush.

0.16

M. Tripathy / Simulation Modelling Practice and Theory 18 (2010) 600–611

Operating Signal (pu)

606

4 3 2 1 0 -1 -2 -3 -4 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time (s) Fig. 7. Typical differential current waveform for over-excitation.

0.08 Operating Signal (pu)

0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 0

0.04

0.08

0.12

0.16

Time (s) Fig. 8. Typical differential current waveform for external fault.

The first row of inrush matrix takes 12 samples of i (i.e. i1 to i12) and then second row elements are from i2 to i13 and so on until all the elements of i are completed. In a similar fashion, elements of the internal fault condition matrix are also arranged for training and testing purpose. The complete training matrix contains both inrush and fault patterns. As shown in Fig. 9, two types of Principal Component Analysis (PCA) data processor had been used for the purpose. The first one is called the pre-processor, which is responsible for pre-processing input training data, to eliminate correlation in training patterns. The second is called post-processor, used to transform the validation and test datasets according to their principal components. The implementation was carried out with aid of built-in function supported by MATLAB Neural Network Toolbox. A three layered structure is used in proposed NNPCA architecture. The input layer has 12 neurons. The hidden layer consists of 11 neurons. From Fig. 10, it is clear that as the number of neurons in hidden layer increases, the error decreases. However, after certain number of neurons the error quickly increases. In this case the minimum error is obtained for 11 neurons in the hidden layer. Therefore, the number of neuron (i.e. 11) in the hidden layer is optimal for this application. The output layer consists of just one neuron as only single output (trip or not) is required. After much experimentation on various neural network architectures, the presented model is proposed which has lesser neurons in all three layers. To differentiate between the inrush and internal fault condition, the inrush condition is indicated by ‘0’ and the fault condition indicated by ‘1’. Out of 925 sets of data (patterns), 777 pattern sets are used to train the NNPCA, RBFNN and FFBPNN models. For RBFNN, three layered structure is considered so that the performance can be compared easily. Gaussian activation function is used in the proposed RBFNN classifier in view of past experience [28]. In this paper, centers are determined by C-means clustering and optimal width factor is obtained by using Eq. (9). The weights connected between the RBF units and output units are calculated by pseudo-inverse method. The RBFNN is faster to find out the connecting weights between the RBF units and output units.

Input data

Pre-

Neural

processing

network

Postprocessing output data

Fig. 9. Typical use of PCA in processing data with neural network.

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M. Tripathy / Simulation Modelling Practice and Theory 18 (2010) 600–611

30

Error (%)

25 20 15 10 5 0 0

2

4

6

8 10 12 14 16 Number of Hidden Layer Neurons

18

20

22

Fig. 10. Effect of neurons (in hidden layer) on the performance of NNPCA/RBFNN.

Out of these 777 pattern sets, 444 pattern sets are for the inrush (including sympathetic inrush patterns) and 333 are for the internal fault. The remaining 148 sets (which are not made part of training sets) are used to test the network’s generalization ability. These 148 test exemplar pattern sets contain internal fault and inrush condition only as these two conditions are very difficult to discriminate as compared to other operating conditions such as external fault, over-excitation and normal condition. Out of 148 test patterns, 74 test sets were inrush patterns and remaining 74 test sets were internal fault patterns. The inrush test patterns consists of sympathetic inrush patterns and magnetizing inrush patterns at different switching-in angles, while internal fault test patterns are made up of phase-to-ground fault and phase-to-phase fault at different locations. Flow chart of the proposed algorithm (Fig. 11) clearly indicates the steps for discriminating different operating conditions of power transformer. The discrimination between external fault and normal operating condition is made by comparing two consecutive peaks of operating signal (i.e. differential current). The over-excitation condition is determined by comparing voltage-to-frequency ratio with the rated voltage-to-frequency ratio. If this condition do not exist then inrush and internal fault condition is checked by FFBPNN, NNPCA and RBFNN models. It gives tripping signal only if internal fault condition is detected.

No: on False Positive þ No: of False Negative  100 Total Number of Test Cases Classification Accuracy ðin%Þ ¼ 100  Classification Error ðin %Þ

Classification Error ðin%Þ ¼

ð12Þ

For different conditions of the test set, fault current magnitude, load condition, remanent flux and switching angle are changed to investigate the effects of these factors on the performance of the proposed algorithm. Since the wave shape of inrush current changes with variation of switching-in instant of transformer, hence it is varied between 0° and 360°. Similarly, due to the presence of the remanence flux, magnitude of inrush current may be as high as 2–6 times of inrush current without remanence flux, although the wave shape remains same. It is found that the NNPCA and RBFNN classifier based relay is stable even with such high magnitude of inrush current caused by remanence flux whereas, the conventional harmonic based relay may mal-operate due to such high magnitude of inrush current [4,15]. A rigorous experimentation has been made to evaluate performance of the NNPCA and RBFNN model. The proposed NNPCA and RBFNN based classifier are successfully tested using relaying signals obtained by modeling the transformer on PSCAD/EMTDC and simulating various operating conditions. The proposed RBFNN have good generalization properties than the FFBPNN and NNPCA. The training required for RBFNN is faster than that required for FFBPNN and NNPCA. As an example, 1000 iterations were required for convergence in case of 12-11-1 structure of FFBPNN and NNPCA implemented by the authors, thereby giving a ratio of about 1000:11 in terms of the training time. The results of the proposed algorithm are shown in Tables 1–3. Table 1 illustrates the training and testing performances of FFBPNN, NNPCA and RBFNN model while Table 2 shows the accuracy in classification of FFBPNN, NNPCA and RBFNN type classifier which is obtained by using Eq. (11). In case of FFBPNN and NNPCA, maximum accuracy in classification is 99.32% where as in case of RBFNN it is 100.00%. Classification of RBFNN is comparatively better than the FFBPNN and NNPCA classifier. Thus, RBFNN has good generalization capability to distinguish between magnetizing inrush and internal fault condition of power transformer. Table 3 presents the number of post disturbance samples required for decision making by the FFBPNN, NNPCA and RBFNN based transformer differential protection algorithm. In light internal fault cases, all three type of neural network classifier requires nine samples after the fault occurrence that means about 15 ms are required for the fault detection while in case of inrush condition only 8 samples are required, i.e. 13.33 ms by NNPCA model while 9 samples are required by RBFNN and FFBPNN. However, it is observed that the relay operation is independent from the harmonic present in the operating signal and therefore no filtering is required in this method. In Ref. [18], Evolutionary Neural Network (ENN) was proposed and its result is compared with a multilayered ANN trained by back-propagation algorithm for power transformer differential protection rated at 200MVA, 21/400 kV, 50 Hz. The max-

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Start

Input data (Operating Signal)

Over-excitation/ Normal operation?

Yes

No

Inrush

Check for inrush or fault by NNPCA/RBFNN?

Fault

Issue Trip Signal Fig. 11. Flow chart of presented algorithm.

Table 1 Performance of FFBPNN, NNPCA and RBFNN type model classifier. Neural network topology

Training error

Max. epoch

FFBPNN NNPCA RBFNN

0.0001 0.0001 0.0000

1000 1000 11

Inrush

Fault

P

A

P

A

1.0 1.0 0.0

0.0 0.0 0.0

0.97 0.96 0.98

1.0 1.0 1.0

P, predicted, A, actual.

Table 2 Accuracy in classification of FFBPNN, NNPCA and RBFNN type classifier. Training transformer ratings

315 MVA 200 MVA 160 MVA

Accuracy in classification (%) Tested transformer ratings 315 MVA Neural network topology

200 MVA Neural network topology

FFBPNN 12-11-1

NNPCA 12-11-1

RBFNN 12-11-1

FFBPNN 12-11-1

NNPCA 12-11-1

RBFNN 12-11-1

FFBPNN 12-11-1

NNPCA 12-11-1

RBFNN 12-11-1

99.32 94.59 94.59

99.32 96.62 98.64

100.00 97.97 99.32

94.59 96.62 94.59

94.59 99.32 96.62

97.29 100.00 98.64

98.64 96.62 98.64

98.64 98.64 100.00

99.32 98.64 100.00

160 MVA Neural network topology

imum accuracy in classification for ENN is reported as 96.52% while the accuracy of multilayered ANN is 85.92% for the topological structure 32-12-1. Similarly, in Refs. [13,15] multilayered ANN trained by back-propagation algorithm was reported for discrimination between inrush and internal fault condition of transformers rated at 5MVA, 33/9 kV and 5kVA, 230/550 V, respectively. In both cases, 20 ms is required to detect internal fault for all the test cases.

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M. Tripathy / Simulation Modelling Practice and Theory 18 (2010) 600–611 Table 3 Number of post disturbance samples required for decision by FFBPNN, NNPCA and RBFNN based relay. Type of neural network

Cases

Number of samples required (actual)

Maximum samples required (logical)

FFBPNN

Magnetizing inrush (00) Internal fault (light phase-to-ground fault at 2%) Magnetizing inrush (00) Internal fault (light phase-to-ground fault at 2%) Magnetizing inrush (00) Internal fault (light phase-to-ground fault at 2%)

9 9

12 12

8 9

12 12

9 9

12 12

NNPCA

RBFNN

ratio of second to fundamental component

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.04

0.06

0.08

0.1

0.12

0.14

Time(s) Fig. 12. Ratio of second harmonic to fundamental of the differential current under typical inrush condition (inrush occurs at 0.04 s.)

Discrete Fourier Transform (DFT) based harmonic restraint method is implemented by the author, to compare performance of the proposed NNPCA and RBFNN based algorithm in power transformer differential protection. Figs. 12 and 13 show the ratio of second harmonic to fundamental of the differential current under typical magnetizing inrush and internal fault conditions, respectively. During one cycle under internal fault condition, the ratio of the second harmonic is quite high and in the same range as in case of magnetizing inrush condition. Therefore, it is difficult to discriminate between internal fault and inrush conditions by merely setting a preset threshold. From Figs. 12 and 13, it is also clear that the ratio values are fluctuating, which create problem to decide a preset threshold. Moreover, due to the presence of second harmonic during internal fault condition, digital relay will take longer time to make trip decision (one cycle or more than one cycle). In contrast, the RBFNN and NNPCA based classifier is able to detect such internal faults within 15 ms. However, the harmonic restraint method is capable to discriminate between these two conditions but does not seem to be intelligent to take decision in case of fluctuating ratio of second harmonic to fundamental of the differential current due to different loading conditions, severity of internal faults, switching-in angles, etc. and hence mal-operation of relay will occur. From the results and above discussions, it is clear that the RBFNN has better detection accuracy than the NNPCA and conventional ANNs. The detection time is less or comparable with the NNPCA and conventional ANNs. Tremendous capability of RBFNN for classification problems shows suitability for digital differential relaying protection scheme. It is free from the setting of threshold value. It is also immune from the different harmonics contained in operating signals which makes it simpler and robust than the conventional digital filtering algorithms.

6. Conclusion This paper presents two novel approach based on NNPCA and RBFNN type classifier to solve the problem of distinguishing between transformer internal fault and magnetizing inrush condition. The illustrated methods neither depend on the transformer equivalent circuit model nor the harmonic content of differential current, rather make the decision based on the current signature verification which is more accurate than traditional harmonic restraint based technique, especially in case of

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ratio of second to fundamental component

610

1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.04

0.06

0.08

0.1

0.12

0.14

Time(s) Fig. 13. Ratio of second harmonic to fundamental of the differential current under typical internal fault condition (internal fault occurs at 0.04 s).

Fig. 14. (a) Typical PSCAD/EMTDC transformer model to simulate internal fault. (b) Typical PSCAD/EMTDC transformer model to simulate internal faults at different locations.

modern power transformers which use high-permeability low coercion core materials. As the presented method is also independent of the harmonic contents of fault currents, it is especially suitable for protection of modern power transformers. The conventional harmonic restraint technique may fail because high second harmonic component may be generated during internal faults and low second harmonic component during magnetizing inrush with such core materials. In the proposed method, stability of differential relay is ensured during the magnetizing inrush, sympathetic inrush, over-excitation and external fault conditions. Hence, the differential protection reliability is enhanced. The proposed NNPCA and RBFNN used optimal number of layers and neurons. It is simple in architecture, fast in operation and robust. The presented neural network model issues tripping signal in the event of internal fault within 15 ms of fault occurrence. The classification accuracy

M. Tripathy / Simulation Modelling Practice and Theory 18 (2010) 600–611

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and the training time of RBFNN is better than the NNPCA and FFBPNN type classifier in case of power transformer differential protection. Hence, the overall performance of RBFNN is better and it can be used as a useful alternative to other methods of power transformer differential protection existing in the literature. Appendix A Fig. 14 shows a typical PSCAD/EMTDC transformer model to simulate internal faults (turn-to-turn, phase-to-ground, and phase-to-phase) at different location of transformer winding from the neutral end of the windings. In this model MVA rating, voltage rating, base frequency, leakage reactance, magnetizing current, and fault location (in %), etc. can be defined. References [1] M. Tripathy, R.P. Maheshwari, H.K. Verma, Advances in transform protection: a review, Electric Power Compo. Syst. 33 (11) (2005) 1203–1209. [2] P. Arboleya, G. Diaz, J.G. Aleixandre, C.G. Moran, A solution to the dilemma inrush/fault in transformer relaying using MRA and wavelets, Electric Power Compo. Syst. 34 (3) (2006) 285–301. [3] H.K. Verma, G.C. Kakoti, Algorithm for harmonic restraint differential relaying based on the discrete Hartley transform, Electric Power Syst. Res. 18 (2) (1990) 125–129. [4] M.C. Shin, C.W. Park, J.H. Kim, Fuzzy logic based relaying for large power transformer protection, IEEE Trans. Power Deliver. 18 (3) (2003) 718–724. [5] S.A. Saleh, M.A. Rahman, Modeling and protection of a three-phase transformer using wavelet packet transform, IEEE Trans. Power Deliver. 20 (2) (2005) 1273–1282. [6] G. Diaz, P. Arboleya, J.G. Aleixandre, A new transformer differential protection approach on the basis of space-vectors examination, Electr. Eng. 87 (2005) 129–135. [7] B. He, X. Zhang, Z.Q. Bo, A new method to identify inrush current based on error estimation, IEEE Trans. Power Deliver. 21 (3) (2006) 1163–1168. [8] E. Vazquez, I.I. Mijares, O.L. Chacon, A. Conde, Transformer differential protection using principal component analysis, IEEE Trans. Power Deliver. 23 (1) (2008) 67–72. [9] X.N. Lin, P. Liu, O.P. Malik, Studies for identification of the inrush based on improved correlation algorithm, IEEE Trans. Power Deliver. 17 (4) (2002) 901–907. [10] K. Yabe, Power differential method for discrimination between fault and magnetizing inrush current in transformers, IEEE Trans. Power Deliver. 12 (3) (1997) 1109–1118. [11] L. Yongli, H. Jiali, D. Yuqian, Application of neural network to microprocessor based transformer protective relaying, in: IEEE Int. Conf. on Energy Management and Power Delivery, vol. 2, 21–23 November 1995, pp. 680–683. [12] L.G. Perez, A.J. Flechsing, J.L. Meador, Z. Obradovic, Training an artificial neural network to discriminate between magnetizing inrush and internal faults, IEEE Trans. Power Deliver. 9 (1) (1994) 434–441. [13] P. Bastard, M. Meunier, H. Regal, Neural network based algorithm for power transformer differential relays, IEE Proc. Gener. Transm. Distrib. 142 (4) (1995) 386–392. [14] J. Pihler, B. Grcar, D. Dolinar, Improved operation of power transformer protection using artificial neural network, IEEE Trans. Power Deliver. 12 (3) (1997) 1128–1136. [15] M.R. Zaman, M.A. Rahman, Experimental testing of the artificial neural network based protection of power transformers, IEEE Trans. Power Deliver. 13 (2) (1998) 510–517. [16] A.L. Orille-Fernandez, N.K.I. Ghonaim, J.A. Valencia, A FIRANN as differential relay for three phase power transformer protection, IEEE Trans. Power Deliver. 16 (2) (2001) 215–218. [17] H. Khorashadi-Zadeh, Power transformer differential protection scheme based on symmetrical component and artificial neural network, IEEE Int. Conf. on Neural Network Application in Electrical Engineering, 23–25 September, 2004, pp. 680–683. [18] Z. Moravej, Evolving neural nets for protection and condition monitoring of power transformer, Electric Power Compo. Syst. 33 (11) (2005) 1229–1236. [19] J.E. Jackson, A User’s Guide to Principal Components, Wiley, Hoboken, NJ, 2003. [20] S. Haykin (Neural Network: A Comprehensive Foundation), Pearson Education, India, 2008. pp. 441–454. [21] C.M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, New York, 1995. pp. 310–318. [22] Dan Simon, Training radial basis neural network with the extended Kalman filter, Neurocomputing 48 (2002) 455–475. [23] J. Moody, C.J. Darken, Fast learning in networks of locally-tuned processing units, Neural Comput. 1 (1989) 281–294. [24] Nabil Benoudjit, C. Archambeau1, A. Lendasse, J. Lee1, M. Verleysen, Width optimization of the Gaussian kernels in radial basis function networks, in: ESANN’2002 Proceedings of the European Symposium on Artificial Neural Networks Bruges (Belgium), 24–26 d-side publi., ISBN 2-930307-02-1, April 2002, pp. 425–432. [25] D. Woodford, Introduction to PSCAD V3, Manitoba HVDC Research Centre Inc., 400-1619 Pembina Highway, Winnipeg, Manitoba R3T 3Y6, Canada, January 2001. [26] S.E. Zocholl, Analyzing and Applying Current Transformers, Schweitzer Engineering Laboratories, Pullman, WA, 2004, pp. 22–28. [27] M.S. Sachdev (coordinator), Microprocessor relays and protection systems, IEEE Tutorial Course Text, Publi. No. 88EH0269-1-PWR, 1988. [28] M. Tripathy, R.P. Maheshwari, H.K. Verma, RBFNN algorithm for power transformer protection, in: Int. Conf. on Computer Applications in Electrical Engineering Recent Advances I.I.T. Roorkee, Sept. 29th to 1 Oct. 2005, pp. 589–592.