g model article in press - pdfs.semanticscholar.org · cite this article in press as: s.r. mohanty,...

A

P

Sa

b

a

ARRAA

KJESI

1

lrTnittafpeatfrt

drtcgC

1d

ARTICLE IN PRESSG ModelSOC-1250; No. of Pages 9

Applied Soft Computing xxx (2011) xxx–xxx

Contents lists available at ScienceDirect

Applied Soft Computing

j ourna l ho mepage: www.elsev ier .com/ locate /asoc

erformance evaluation of distance relay with CT saturation

oumya R. Mohantya,∗, V. Ravikumar Pandib, B.K. Panigrahib, Nand Kishora, Prakash K. Raya

Department of Electrical Engineering, NIT, Allahabad, IndiaDepartment of Electrical Engineering, IIT, Delhi, India

r t i c l e i n f o

rticle history:eceived 27 July 2009eceived in revised form 7 May 2011ccepted 17 July 2011vailable online xxx

a b s t r a c t

The decision of digital distance relay is very important for making the protection scheme in the trans-mission system more reliable. As the current signal is taken from the output of the current transformer,the distortion introduced by the saturation in it affects the performance of the distance relay. In thiscontext proper nonlinear modeling of current transformer is necessary and a suitable compensation

eywords:iles–Atherton CT modellman neural network-transformmpedance trajectory

should be carried out to nullify the distortion introduced by it. In this paper Elman neural network basedcompensation scheme is proposed and the trip decision due to distorted secondary and compensatedsecondary current is made to have a comparative assessment of the trip decision of the relay is also done.The impedance trajectory with and without the compensation with quadrilateral trip boundary is alsoshown in this paper using S-transform to have an understanding of the proposed approach. The series ofsimulation result reflects the improved performance of the distance relay.

. Introduction

Electric power systems are subjected to a variety of disturbancesike transients due to switching operations and lightning, faults,outine operations such as line energization and de-energizations.his leads to a redistribution of energy which cannot occur instanta-eously and power system must go through a transient state before

t reaches a new steady state. During the first few cycles followinghe power system fault, high speed protective relays are expectedo make a correct decision in order to preserve the system stabilitynd minimize the extent of equipment damage. The dynamic per-ormance of these relays depends to a larger extent on the signalsroduced by instrument transformers. Generally these transform-rs are designed to faithfully reproduce the current or voltage with

reduced magnitude during normal operations. However duringransients and fault conditions when the magnitude as well as therequency of the line current/voltage change the secondary cur-ents/voltages gets distorted. Designing low distortion instrumentransformer for all occasions is not economically viable.

As line current exhibits more transients than the line voltages,istortions introduced by a current transformer (CT) plays a vitalole in the trip decision of the distance relay. In the distance protec-ion impedance seen by the relay depends upon the amplitude of

Please cite this article in press as: S.R. Mohanty, et al., Performance evJ. (2011), doi:10.1016/j.asoc.2011.07.003

urrent and voltage samples. So impedance seen by the relay willet modified. For normal operating current the magnetic core of theT operates below the saturation flux and exciting current drawn

∗ Corresponding author. Tel.: +91 6742370149.E-mail address: [email protected] (S.R. Mohanty).

568-4946/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.asoc.2011.07.003

© 2011 Elsevier B.V. All rights reserved.

by it is very small. But the transient performance of CT is influencedby a number of factors with most notably exponentially decaying dccomponent of primary current. Its presence influences the buildupof core flux, a phenomenon which is likely to cause saturation andsubsequently substantial errors in the magnitude and phase of gen-erated signal. So in order to determine the proper operation ofrelays, correct representation of the current transformer and theirbehavior under all possible operating conditions is important.

The distortion and saturation of the secondary current of currenttransformer affects the performance of the distance relay. In thiscontext, the Jiles–Atherton (JA) CT model [1–3] is based on Ferro-magnetic hysteresis, which considers the multi-valued relationshipbetween the magnetic flux density and the field intensity has beenconsidered for analysis. Although the CT model based on the abovetheory is available in the literature, we have applied the conceptin order to get the exact reflection of distorted secondary current.This model of a CT has been chosen for analysis but our main aimis focused for design of compensators using Elman recurrent net-work (ERN) in order to improve the performance of the distancerelay due to CT saturation. The compensation for hysteresis andeddy current on CT is analyzed in [4]. The compensation for CT sat-uration effect is also modeled in [5,6]. The back propagation (BP)algorithm has established itself as the most popular method for thedesign of neural networks. However, a major limitation of standardBP algorithm is that it can only learn input–output mapping that isstatic. In particular, how one can extend the design of a feed for-

aluation of distance relay with CT saturation. Appl. Soft Comput.

ward network so that it assumes a time-varying form and thereforewill be able to deal with time-varying signals and sequences. Elmannetwork is very powerful in processing the voltage and current astemporal input signals. ERN based compensator can compensate

dx.doi.org/10.1016/j.asoc.2011.07.003

dx.doi.org/10.1016/j.asoc.2011.07.003

http://www.sciencedirect.com/science/journal/15684946

www.elsevier.com/locate/asoc

mailto:[email protected]

dx.doi.org/10.1016/j.asoc.2011.07.003

ARTICLE IN PRESSG ModelASOC-1250; No. of Pages 9

2 S.R. Mohanty et al. / Applied Soft Computing xxx (2011) xxx–xxx

tTtcmdMrs

iAcadstto(cctit

2

ewgdniomrfmosrttvsti

Fig. 1. The block diagram of protection scheme.

he distorted secondary current even in deep saturation in the CT.his paper evaluates the performance of the distance relay duringhe CT saturation. An Elman recurrent neural network (ERN) basedompensator is designed to have a true reflection of the CT pri-ary current into the secondary for the decision making of the

istance relay. On the other hand, its performance with that ofarquardt–Levenberg (ML) algorithm [6] is compared and its supe-

ior tracking capability of true secondary current is shown throughimulation results.

Further, the performance of the distance relay is analyzed by thempedance calculation from the phasor estimation of the signal.s the phasor estimation using wavelet transform (WT) is sus-eptible to noise unlike S-transform (ST) and provides distortedmplitude and phase even with SNR 30 dB. There are few literaturesescribing the use of WT and ST for the protection of transmis-ion line [7,8]. The concept of S-transform [7–10] is proposed forhe impedance calculation. The impedance trajectory of the dis-ance relay is generated by extracting the fundamental componentf the voltage and the compensated current using S-transformST). Over all the suitable design of compensator using ERN forompensation of CT secondary current is addressed. Further, theomparative performance evaluation of the distance relay by dis-orted and compensated secondary current through evaluation ofmpedance trajectory by S-transform followed by the response ofhe relay is also supplemented to the contribution in this paper.

. CT modeling

The distortion introduced by the CT can substantially influ-nce relaying under fault conditions. In order to analyze theseaveforms in primary and secondary, large currents need to be

enerated under steady state as well as possible transient con-itions in the laboratory. Experiment with such high power CTeeds instrumentation setups with formidable price and complex-

ty. With present state of art mathematical model seems to be thenly solution. The model is based on current physical theories ofagnetic domains of ferromagnetic material [1–3]. The concept

eported in [3] has been taken for the modeling of current trans-ormer. But the anhysteretic magnetization (Man) presented in the

odel takes care of domain wall bending as well as translationf the magnetic domains. Langvein function (L) has been used toimulate the effects of domain wall bending and translation, i.e.,eversible and irreversible domain wall motion which is necessaryo model M–H curve. The distorted secondary current due to satura-ion is obtained using the concept of the JA theory. If the ratio of theoltage to current magnitude is taken to calculate the impedance


een by the relay, an error will be introduced due to the CT satura-ion. This leads to the design of a CT compensation scheme whichs discussed in the next section.

Fig. 2. The Elman network architecture (z−1 represents for unity delay).

3. CT compensation using Elman recurrent network

When the signal supplied by the CT is distorted by saturation,the rms value sensed by the relay will be much lower than theactual fault current. This leads to inaccurate current measurementand, therefore, may cause malfunction of the protective relays andcontrol devices that use current as the input signal. Due to distortedcurrent waveform distance relays may experience both overreachand underreach problems in fault impedance calculations. At thesame time when CT saturation is higher, it can even prevent relaytripping. All the methods of fault detection, classification and loca-tion of distance relay rely heavily on the instantaneous line currentsamples. The distorted waveforms may result in misclassification offaults and incorrect decisions. Therefore, compensators/equalizersshould be employed to counter the distortions introduced by theCT.

3.1. Elman recurrent network

Elman recurrent network (ERN) [11–13] is a two-layer feed for-ward network with the addition of a recurrent connection from theoutput of the hidden layer to its input. The delay in this connectionstores values from the previous time step, which can be used in thepresent time step. This feedback path allows the Elman network tolearn to recognize and generate temporal patterns, as well as spa-tial patterns. The advantage of ERN over fully recurrent networks isthat back propagation is used to train the network while this is notpossible with other recurrent networks where the training algo-rithms are more complex and therefore slower. The architecture ofthe Elman network is shown in Fig. 2.

The network is augmented at the input level by additional units,called context units. These units are also hidden in the sense thatthey interact exclusively with other nodes internal to the network,and not the outside world. The augmented input units, includingboth the input units and the context units activate the hidden units.The hidden units feed forward to activate the output units as wellas they feed back to activate the context units. This feedback pathallows the Elman network to learn to recognize and generate tem-poral patterns, as well as spatial patterns The number of context


units is equal to the number of hidden units. Activations are copiedfrom hidden layer to the context layer on a one-to-one basis withfixed weights of 1.0. The context unit values at time step t + 1 are

dx.doi.org/10.1016/j.asoc.2011.07.003

ARTICLE ING ModelASOC-1250; No. of Pages 9

S.R. Mohanty et al. / Applied Soft Co

et

3

srb

x

t

x

w

y

l

wrhl

h

f

N

w

I

x

y

y

u

x

Fig. 3. Structure of the proposed Elman recurrent network.

xactly the same as the hidden unit values at time step t. Therefore,he context units provide memory to the network.

.2. Formulation

In the structure of the proposed Elman recurrent network (ERN)hown in Fig. 3, the output of the context layer xc(k) and the recur-ent layer of the hidden layer x(k) in the Elman network is describedy

c(k)=x(k − 1) (1)

The multi-input–multi-output Elman network can be written inhe state space model as

i(k) = f

⎧⎨⎩

N∑j=1

wxi,jxj(k − 1) +

M∑m=1

wui,mum(k − 1)

⎫⎬⎭ (2)

here i = 1...N and N: total number of hidden layer neurons.

l(k) =N∑

i=1

wyi,l

xi(k) (3)

= 1 . . . L

here wxi,j

, wui,m

, wyi,l

are the weights between ith hidden layer neu-on and jth context layer neuron, mth input layer neuron and ithidden layer neuron, and the ith hidden layer neuron and lth output

ayer neuron yl(k), respectively.f(·) is the activation function in hidden layer neurons which is a

yperbolic tangent function, i.e.

(x) = 11 + e−x

(4)

ow three weight matrices are given as

x = [wxi,j]N×N

, wu = [wui,m]

N×M, wy = [wy

i,l]N×L

(5)

n vector form state equation and output is written as

(k) = f (wxx(k − 1) + wuu(k − 1)) (6)

(k) = wTy x(k) (7)

(k) = [y1(k) . . . yN(k)]T

(k − 1) = [u1(k − 1) . . . um(k − 1)]Tn∑

X2


i=1

i

(k) = [x1(k) . . . xN(k)]T

PRESSmputing xxx (2011) xxx–xxx 3

In the following, let f(x) = x be the linear activation function in (4),then

x(k) = [wxx(k − 1) + wuu(k − 1)] (8)

y(k) = wTy x(k) (9)

In the present case secondary current is the input u to the Elmannetwork. y is the reconstructed secondary current.

4. Distance protection scheme with S-transform

The S-transform is an extension to the ideas of wavelet trans-form, and is based on a moving and scalable localizing Gaussianwindow and has characteristics superior to wavelet transformsand Fast Fourier Transform (FFT) [7–10]. The S-transform isfully convertible from the time domain to two-dimensional fre-quency translation domain and to then familiar Fourier frequencydomain. The amplitude frequency–time spectrum and the phase-frequency–time spectrum are both useful in defining local spectralcharacteristics. The superior properties of the S-transform are dueto the fact that the modulating sinusoids are fixed with respectto the time axis while the localizing scalable Gaussian windowdilates and translates. As a result, the phase spectrum is absolutein the sense that it is always referred to the origin of the time axis,the fixed reference point. The real and imaginary spectrum can belocalized independently with a resolution in time, correspondingto the basis function in question and the changes in the absolutephase of a constituent frequency can be followed along the timeaxis and useful information can be extracted. The phase correctionof the wavelet transform in the form of S-transform can providesignificant improvement for impedance calculation.

The ST falls within the broad range of multiresolution spectralanalysis, where the standard deviation is an inverse function ofthe frequency, thus reducing the dimension of the transform. Thelocalizing Gaussian function g(t) is defined as:

g(t) = 1�

√2�

exp[−t2f 2/2�2] (10)

where � is the standard deviation. The multiresolution ST is definedby

S(f, �, �) =∞∫

−∞

h(t)g(� − t, �)e−i2�ftdt (11)

This falls within the definition of the multiresolution Fouriertransform. The Gabor transform � (f, �) is a particular case of S (f,�, �) with � held constant. The primary purpose of the dilation (orscaling) parameter is to increase the ‘width’ of the window func-tion g(t, �) for lower frequency and vice versa, and is controlled byselecting a specific functional dependency of � with the frequencyf. Thus, the width of the window is inversely proportional to thefrequency and by varying the width of the window; the requiredspectral (frequency) components can be picked up. Also we havechosen the width of the window to be proportional to the periodof the co sinusoid being localized. Thus, the width the window isgiven as:

�(t) = T = ˛|f | (12)

where ‘T’ is the time period. The choice of ̨ is important as a small ̨ means improved time resolution and loss of frequency resolu-


tion. The vice versa is true for large value of ̨ which improvesthe frequency resolution, but reduces time resolution. Conse-quently, identification of the whole event can be compromisedwith ̨ < 1. A choice of ̨ = 0.4 is good enough for fault detection

dx.doi.org/10.1016/j.asoc.2011.07.003



ac

S

Fw

given by

Fig. 4. Scaled primary and secondary current.

nd identification, keeping both time and frequency resolution intoonsideration. ST may be written as

(f, �) =∞∫

h(t) |f |√2�

e−((�−t)2f 2/2)e−i2�ftdt (13)


−∞

or the discrete ST, h(t) can be written in discrete form as h[kT],here k varies from 0 to N − 1 and is known as discrete time series

0 0.01 0.02 0.03 0.04

-2

-1

0

1

2

Time (s

Cur

rent

am

plitu

de (p

.u.)

True secondaryCompensated secondary using ERNDistorted secondaryCompensated secondary using ML

Fig. 6. Comparative assess

0.02 0.022 0.024 0.026 0.028

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time

Cur

rent

am

plitu

de (p

.u.)

Compensated secoCompensated secoTrue secondaryDistorted secondar

Fig. 7. Zoom plot for comparative

Fig. 5. The error convergence plot for training the recurrent network.

of the signal h(t). Discrete Fourier transform of the sampled timeseries h[k] (omitting T) can be expressed as:

H(n) = 1N

N−1∑k=0

h[k]e−2�nk/N (14)

where n = 0, 1, . . ., N − 1. The ST of the discrete time series h[k] is


S[n, j] =N−1∑m=0

H[m + n] e−2�2m2˛2/n2ei2�mj (15)

0.05 0.06 0.07 0.08ec)

ment of ERN and ML.

0.03 0.032 0.034 0.036 0.038(sec)

ndary using MLndary using ERN

y

assessment of ERN and ML.

dx.doi.org/10.1016/j.asoc.2011.07.003

IN PRESSG ModelA

oft Computing xxx (2011) xxx–xxx 5

wi

h

T

A

a

˚

Flmasamdtw

cbeetmaivub

Z

was

Z

wa

5

stsTaacrosCrdr

ARTICLESOC-1250; No. of Pages 9

S.R. Mohanty et al. / Applied S

here j, m and n = 0, 1, . . ., ,N − 1. The discrete inverse of S-transforms obtained as

(k) = 1N

N−1∑m=0

N−1∑j=0

S[n, j]ei2�nk (16)

he S-amplitude and phase spectra are given by

(n, j) =∣∣S(n, j)

∣∣ (17)

nd

(n, j) = a tan(

Im[|S(n,j)|]Re[|S(n,j)|]

)(18)

rom the above analysis it is quite evident that not only S-transformocalizes the faulted event but also peak amplitude and phase infor-

ation of the voltage and current signals can be obtained, whichre important for impedance calculations. It is found that the pha-or estimation using S-transform with SNR up to 20 dB providesccurate estimation in magnitude and phase. But the phasor esti-ation using wavelet transform is susceptible to noise and provides

istorted amplitude and phase even with SNR30 dB. This indicateshe robustness of S-transform for phasor estimation compared toavelet transform.

The impedance seen by the relays are calculated from the coeffi-ients of S-transform matrix. Here in this work the moving windowased S-transform is implemented with one sample movement atach time. For the protection purpose the faster relay operation isxpected when the fault occurs. The absolute of S(t, f) matrix giveshe magnitude of the signal in different time and frequency. The

aximum of the magnitude and its corresponding angle is takens the fundamental amplitude and phase angle of the correspond-ng phase. Similarly we will get the magnitude and phase of all threeoltage signals and all three current signals. These values are thentilized by the impedance calculation part. In this impedance seeny the distance relay is obtained as follows:

For phase to ground fault

ph = Vphase

Iphase(1) + Iphase(2) + k × Iphase(0)(19)

here Vphase is the estimated amplitude of the phase voltagend Iphase(1), Iphase(2), Iphase(0) are the positive, negative and zeroequence currents of estimated amplitude.

For phase faults

ab = Va − Vb

Ia − Ib(20)

here Va and Vb are the estimated voltage amplitude and Ia and Ibre the estimated current amplitude.

. Results and discussion

One line diagram of 230 kV interconnected power system is con-idered for the simulation of this work as shown in Fig. 1. To presenthe case of CT saturation using the JA method, a three phase fault isimulated in the transmission line at a distance of 80 km from Bus 1.he fault resistance considered is 10 �, fault inception angle is 70◦

nd simulation step size is taken as 5 �s. The current waveformsre shown in Fig. 4 demonstrates distortion of the CT secondaryurrent. After the onset of fault at 0.1120 s the secondary currenteferred to primary does not follow the primary current becausef hysteresis along with saturation. The dotted waveform repre-ents the ‘true secondary’ which is the reflection of the primary


T current assuming there is no saturation and the ratio of the CTemains constant. The solid line is the actual CT secondary currentue to the saturation. As simply observed from the figure if theatio of the voltage to current magnitude is taken to calculate the

Fig. 8. (a) Phase A current. (b) Impedance trajectory plot. (c) Trip decision of therelay.

impedance seen by the relay an error will be introduced due to theCT saturation. The following current transformer data as shown inTables 1 and 2 [3] has been used to simulate the above model.

5.1. Compensation by ERN


The present and past samples of the distorted secondary currentwith reference to the Jiles–Atherton model of the CT constitute setof input for recurrent neural network. The output of the network is

dx.doi.org/10.1016/j.asoc.2011.07.003



Fig. 9. (a) Phase A current. (b) Phase B current. (c) Impedance trajectory for relay AB. (d) Trip decision of the relay.

Table 1Electrical parameters of CT.

No. of p-turns No. ofs-turns

Area of thecore (m2)

Resistance of thes-winding (�)

Inductance ofs-winding (mH)

20 200 2.61 × 10−3 0.5 0.8

Table 2Magnetic parameters of CT.

Inter domaincoupling (˛)

Saturationmagnetization (Ms)

Materialconstant (K)

C A

tslb

N

Tcom

in Wb/(Henry m)

2.5 × 10−5 1.53 × 10−6 7 × 10−5 0.1 8

he compensated secondary current, which is compared with trueecondary current available with the current transformer. The fol-owing network structure has been chosen by trial and error for theest performance.

umber of inputs = 10; Number of nodes in the Hidden layers

= 15; Number of outputs = 1


he inputs are the present and 9 delayed versions of the secondaryurrent samples. The output is the desired (compensated) sec-ndary current. The interval between two consecutive samples isaintained at 1 ms for training the neural network. This is achieved

by down sampling the original data by a factor of 20. It has beenfound that about 500 training sets are sufficient to stabilize theweights. The convergence plot has been shown in Fig. 5. The totaltraining error of 0.001 is sufficiently accurate considering the mag-nitude in p.u.

The performance of the proposed scheme for the distance relayperformance is studied for a variety of fault cases in the systemunder study. But due to the space limitations the performance offew cases is reported in this section. The waveforms of true sec-ondary current assuming true reflection of the CT primary currentin the secondary according to CT ratio, distorted secondary currentconsidering CT saturation and the compensated secondary currentis shown as in Fig. 8(a), 9(a) and 10(a) for comparison purposeand the effect of these three cases on the distance relay trippingcharacteristics is studied. It is observed that in the post fault condi-tion there is a mismatch between the true secondary and distortedsecondary current due to CT saturation. If the uncompensated sec-ondary current is fed to the relay then there may be a false trippingor no tripping under the faulty condition. Thus there is a need forthe compensation to have an accurate tripping decision. The ERN istrained for a large variety of fault currents so that the compensatedcurrent produce by the ERN is trying to track the true secondary


current. The relay status due to all the three cases of waveformis demonstrated for few fault cases and it is observed that the tripdecision made by true secondary current and compensated currentis almost same.

dx.doi.org/10.1016/j.asoc.2011.07.003


S.R. Mohanty et al. / Applied Soft Computing xxx (2011) xxx–xxx 7

Table 3Analysis of reconstruction of CT secondary current.

Sl. No. Reconstructionmethod

No. of samples/cycles

Error (%) Responsetime (m s)

1 ML 20 4.2 4.82 ERNN 20 1.5 0.5

5w

osMaig

�

wwvwFccfaof

ptttFctctsrOtfczTr

TC

.2. Comparative assessment of compensation scheme of ERNith ML algorithm

In this section, the comparative assessment of compensationf distorted secondary current due to CT saturation is pre-ented using ML and ERN algorithms through simulation results.arquardt–Levenberg (ML) algorithm is a nonlinear least square

lgorithm applied to the learning of the multilayer perceptron ands an approximation to Newton’s method. The ML update rule isiven by [6]:

W = (JT J + �I)−1

JT e (21)

here J is the Jacobian matrix of derivatives of each error to eacheight, � is a scalar, and e is an error vector. If the scalar � is

ery large, the above expression approximates gradient descent,hile if it is small, then it becomes the Gauss–Newton method.

or designing the ML neural network, 10 inputs and 1 output wereonsidered. The sampling rate was chosen to be 20 samples perycle with 50 Hz frequency. Numbers of the neurons consideredor the hidden layers were 6 and 4, respectively. For the network,

tangent-sigmoidal function was used as the activation functionf the hidden layer neurons while a linear function was consideredor the output layer.

With various system changing condition in the inter-connectedower system such as fault inception angle, change in fault resis-ance, change in frequency has been taken as the possible conditiono constitute the primary current. To demonstrate the compara-ive assessment of all the algorithms, the current is normalized.urther, in the simulation results, the primary current has beenreated by taking fault at 20 km from relay end with fault incep-ion angle 0◦ and fault resistance of 1 �. The distorted secondaryurrent and the actual secondary current have been normalizedo have clarity in the comparative assessment scheme. From theimulation, it is clearly reflected that the estimated secondary cur-ent tracks the actual secondary current with least possible error.n contrary, Marquardt–Levenberg (ML) algorithm could not track

he actual secondary current to a remarkable extent. As a matter ofact, ERN based compensation was found to be most suitable. Theomparative assessment is shown in Fig. 6 and the correspondingoom plot is shown in Fig. 7 to clearly visualize the efficacy of ERN.

Please cite this article in press as: S.R. Mohanty, et al., Performance evaluation of distance relay with CT saturation. Appl. Soft Comput.J. (2011), doi:10.1016/j.asoc.2011.07.003

he performance analysis of ML and ERN in terms of %error andelay response time (time taken by the relay to operate after the Fig. 10. (a) Phase A current. (b) Impedance trajectory. (c) Trip decision of the relay.

able 4omparative assessment of the relay status.

Sl. No. Case study Fault resistance (�) Occurrence of fault (s) Tripping time (s)

True secondary Compensatedsecondary

Secondary

1 Case 1 (LG fault at phase-A at70 km from source side)

10 0.1120 0.1123 0.1124 0.1128

2 Case 2 (LL fault at phase-A and B at10 km from source side)

20 0.1120 0.1125 0.1126 0.1132

3 Case 3 (LLLG fault at phase-A, B, Cand G at 60 km from source side)

10 0.1120 0.1130 0.1132 0.1135

dx.doi.org/10.1016/j.asoc.2011.07.003

ING ModelA

8 oft Co

ou

E

wc

5

ozto1

I

k

TZr

t

CectiiFdcsw

Copfttac

CsAcso

ro

tpmsC

6

s

[

[

[

[

tute of Technology (IIT), Delhi, India. Currently he is thepost doctoral fellow at Masdar Institute, Abu Dhabi, UAE.His research interest includes evolutionary and soft com-puting techniques and its application to various powerengineering problems.



ccurrence of fault) is shown in Table 3 where error is calculatedsing the following formula:

rror (%) = max{

Iestimated − Itrue

Itrue

}× 100 (22)

here Iestimated and Itrue refer to the estimated and true CT secondaryurrent, respectively.

.3. Impedance trajectory by S-transform

After calculating the impedance seen by the relay the relay willperate if and only if the impedance trajectory enters into trippingone. Here the quadrilateral relay characteristics are assumed toake care of different fault impedances. The Polygon characteristicsf the all relays are considered as: P1 = (0, 0); P2 = (70, 0); P3 = (150,50); P4 = (0, 150), where

0 = 13

(Ia + Ib + Ic) (23)

= Z0 − Z1

Z1(24)

he values of Z1 and Z0 considered in this study is1 = 0.0358 + j0.5027 �/km and Z0 = 0.3520 + j1.3509 �/km,espectively. Hence the value of k is k = 1.7236− j0.5063.

The following cases are studied to demonstrate the efficacy ofhe proposed scheme.

ase 1. A LG fault in phase A is simulated at 70 km from the sourcend of the line with a fault resistance of 10 �. The true secondaryurrent of the CT, actual CT secondary current under saturation andhe compensated CT secondary current (output of ERN) is shownn Fig. 8(a). The impedance trajectory and the trip decision of thempedance relay for the above current conditions are shown inig. 8(b) and (c), respectively. As observed from Fig. 8(c) a tripecision is produced for all of the cases but due to uncompensatedurrent the trip decision is delayed for samples (ms). The trip deci-ion for true secondary and compensated secondary is nearly sameith a delay of only samples.

ase 2. A LL fault between phase A and B is simulated at 10 kmf the line from the source end with a fault resistance of 20 �. Thehase current of phase A and phase B are shown in Fig. 9(a) and (b)or all the three cases. Fig. 9(c) and (d) demonstrates the impedancerajectory and the trip decision. As observed the trip decision dueo the true secondary and compensated secondary is same wheres the trip decision is delayed due to the uncompensated secondaryurrent.

ase 3. A LLLG fault is simulated at 60 km of the line from theource end with a fault resistance of 10 �. The current of phase

is shown in Fig. 10(a) from which it is observed that the faulturrent magnitude is very high due to LLLG fault. This results inaturation of the CT and thereby results highly distorted CT sec-ndary current. The impedance trajectory and the trip decision are

eported in Fig. 10(b) and (c), respectively, demonstrating the needf compensation for accurate and fast trip decision.

Further, the comparative assessment of the relay status dueo true secondary, secondary and compensated secondary isresented in Table 4. It is concluded from this table that the perfor-ance of the relay status due to true secondary and compensated

econdary is almost same and there is a delay in time in distortedT secondary current.


. Conclusion

Detailed mathematical modeling of current transformer is con-idered through Jiles–Atherton (JA) theory in this paper. The

PRESSmputing xxx (2011) xxx–xxx

distortion in the current waveform is compensated with ERN designand its improved tracking performance over ML algorithm is alsostudied. Further, the performance of the distance relay is ana-lyzed by evaluation of impedance trajectory using S-transform.A comparative assessment of the impedance trajectory for truesecondary, secondary and compensated secondary current enter-ing the trip zone is shown through series of simulation results.As a matter of fact, the correct performance of the distance relaycan be evaluated and its malfunction can be avoided to a greaterextend.

References

[1] D. Jiles, D.L. Atherton, Theory of ferromagnetic hysteresis, J. Magn. Magnet.Mater. 61 (1986) 48–60.

[2] D.C. Jiles, J.B. Thoelke, M. Devine, Numerical determination of hysteresis param-eters using the theory of ferromagnetic hysteresis, IEEE Trans. Magnet. 28(1992) 27–35.

[3] U.D. Annakkage, P.G. McLaren, E. Dirks, R.P. Jayasinghe, A.D. Parker,A current transformer model based on the Jiles–Atherton theory offerromagnetic hysteresis, IEEE Trans. Power Delivery 15 (1) (2000)57–61.

[4] Nicola Locci, Carlo Muscas, Hysteresis, Eddy, Hysteresis and eddy currents com-pensation in current transformers, IEEE Trans. Power Delivery 16 (2) (2001)154–159.

[5] Pan Jiuping, K. Vu, Y. Hu, An efficient compensation algorithm for currenttransformer saturation effects, IEEE Trans. Power Delivery 19 (4) (2004) 1623–1628.

[6] H. Khorashadi-Zadeh, M. Sanaye-Pasand, Correction of saturated current trans-formers. Secondary current using ANNs, IEEE Trans. Power Delivery 21 (1)(2006) 73–79.

[7] H. Osman, O.P. Malick, Transmission line distance protection basedon wavelet transform, IEEE Trans. Power Delivery 19 (2) (2004)515–523.

[8] S. Samantray, P.K. Dash, Transmission line distance relaying using a vari-able window short time Fourier transform, Electr. Power Syst. Res. 78 (2008)595–604.

[9] R.G. Stockwell, M. Manisha, Localization of complex spectrum, S-transform,IEEE Trans. Signal Proc. 44 (2001) 998–1001.

10] C.R. Pinnegar, L. Mansinha, The S-transform with windowsof arbitrary and varying shape, Geophysics 68 (1) (2003)381–385.

11] X. Li, G. Chen, Z. Chen, Z. Yuan, Chaotifying linear Elman networks, IEEE Trans.Neur. Netw. 13 (5) (2002) 1193–1199.

12] M. Sanaye-Pasand, O.P. Mallick, High speed Transmission system directionalprotection using an Elman network, IEEE Trans. Power Delivery 13 (4) (1998)1040–1045.

13] O. Nells, Nonlinear System Identification from Classical Approaches to NeuralNetworks and Fuzzy Models, Springer, 2000.

Soumya R. Mohanty received the Ph.D. degree fromIndian Institute of Technology (IIT), Kharagpur, India. Cur-rently, he is an Assistant Professor in the Department ofElectrical Engineering, Motilal Nehru National Institute ofTechnology (MNNIT), Allahabad, India. His research areaincludes digital signal processing applications in powersystem relaying and power quality, pattern recognitionapplications in power system and distributed generations.

V. Ravikumar Pandi has completed his Ph.D. degree fromthe Department of Electrical Engineering, Indian Insti-


dx.doi.org/10.1016/j.asoc.2011.07.003

ING ModelA

oft Co

National Institute of Technology (MNNIT), Allahabad,India. His research area includes distributed generations,renewable energy resources and digital signal processingapplications in power system, robust control applicationsin power system and power quality.



B. K. Panigrahi is working as Associate Professor in theDepartment of Electrical Engineering, Indian Institute ofTechnology (IIT), Delhi, India. The research interest ofDr. Panigrahi is evolutionary computing techniques andits application to power system planning, operation andcontrol. His research interest also includes digital signalprocessing techniques and its application for power qual-ity monitoring and power system protection.

Nand Kishor received the Ph.D. degree from Indian Insti-tute of Technology (IIT), Roorkee, India. Currently, he isan Assistant Professor in the Department of Electrical


Engineering, Motilal Nehru National Institute of Technol-ogy (MNNIT), Allahabad, India. His research area includesArtificial Intelligence (AI) applications in power system,distributed generations, wireless and sensor network anddigital signal processing applications in power system.

PRESSmputing xxx (2011) xxx–xxx 9

Prakash K. Ray is currently pursuing Ph.D. degree inthe Department of Electrical Engineering, Motilal Nehru


dx.doi.org/10.1016/j.asoc.2011.07.003

g model article in press - pdfs.semanticscholar.org · cite this article in press as: s.r. mohanty,...

Documents