CT Compensation of Numerical Distance Relaying (Documento)

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:09 No:09 20

1917091-IJECS-IJENS © October 2009 IJENS I J E N S

CT Compensation of Numerical Distance Relaying

Algorithm

Abdullah Assuhaimi Mohd Zin , Nur ‘Ain Maiza Ismail , Zaniah Muda and Mohamad Jalalian 1,2,3,4

Faculty of Electrical Engineering Universiti Teknologi Malaysia from Johor, Malaysia [email protected],

[email protected],

[email protected]

Abstract— In this paper a prototype algorithm for Numerical

Distance relay is developed in order to pre vent mal -operation

of relays when Current Transformer (CT) saturation occurs.

Saturation of CT causes errors in reproduction of the current

fundamental harmonic. The design of CT(s), which never saturate would end in bulky and expensive units. Therefore

most of the protective CTs that are in service saturate during

severe transients. Distorted secondary current due to CT

saturation is detected and compensated by the algorithm in

order to obtain correct operation of Distance relay in saturation area. Third-difference function and Auto Regressive

(AR) model are employed in developing the saturation

detection and compensation algorithm. The algorithm is

developed using C++ language. Then the performance of the

algorithm is evaluated through simulation of case studies in Alternative Transient Program (ATP) simulator. Finally, the

Numerical Distance Relaying algorithm with CT saturation

compensation is successfully developed.

Index Term-- Numerical Distance Relay; CT saturation; CT

compensation; ATP

I. INTRODUCTION

Numerical t ransmission line d istance protection systems

have been widely applied in recent years. This is due to their

monitoring and communications capabilities as a protection

system. Typically, t ripping t imes for d igital d istance relays

range from one to three cycles. Meanwhile, relays using

analogue signal processing techniques offer tripping times of one-quarter to one cycle [1]. Recent developments in

combination of adaptive algorithms and higher sampling rates have lead to the development of secured high-speed

protection, which is not availab le in prev ious distance protection systems [1, 2, 3]. Improvement of the distance

protection system is made both in the area o f phasor calculation and the p rotective algorithm implementation [1].

Improvements are made due to the protective relays demand on a reasonable accurate replica of the primary current and

voltage especially during fau lt event. Therefore, for this

reason current transformer (CT) is employed in the distance protection system in order to perform primary current

reduction for the relays usage [2, 3].However, relay performance is affected by CT installat ion. Rat io error

becomes severe during CT saturation condition which leads to mal-operation of protective relay. The conventional way

employed by earlier researchers is by over dimensioning the

core of CT. It is said that the CTs can carry up to 20 times the rated current without exceeding 10% of rat io correction

[3]. On the other hand, the large cross-section area of CT creates space and economic problems as it results in bulky

CTs.

As mention previously, the mal-operation of protection relay

is caused by ratio error which occurs due to the CT

saturation condition. Therefore, the mal-operation of

distance protection relay can be avoided by preventing the

saturation of CT. This can be achieved by constructing

compromise algorithms for the distance protection system,

[4, 5].Th is paper describes a design of suitable CT

Compensation algorithm for Distance Relay, which is used

to overcome the saturation effects and prevents the mal-

operation of a Distance Relay. The design algorithms will

include current compensation, anti-aliasing filter, dc-

removal and digital filter. Besides that, this paper describes

the simulation test conducted using ATP power simulator in

order to evaluate the proposed designed algorithm

performance under various faults conditions.

II. METHODOLOGY

The proposed algorithms start with the process of voltage

and current sampling. After sampling process, inflection

points are detected by saturation detector. If saturation level

is sensed to be more than the threshold value and inflection

point detected is the first inflection po int, the current is

compensated by current compensation and return the values

to the main program. However, if second point of inflection

is sensed and confirmed by end of saturation detection then

the compensation algorithm would end and continue to the

main program. After that, anti-aliasing filter is implemented

to remove all harmonics higher than sixth harmonic and,

Direct Current (DC) removal is applied to eliminate the DC

components in sampling data. The basic fundamentals of

current and voltage are extracted using DFT function.

Calculating the sine and cosine elements of current and

voltage performs DFT function. Finally, the developed

program ends with calcu lation of monitoring point

impedance.

A. Sampling Rates

Generally, dig ital relays sample waveforms between 4 and

64 t imes per cycle. A high sampling rate will produce more

accurate result. However, there must be enough time

between samples to perform relay calculation. Normally, the

implementation of all steps in Distance Relay takes longer

time compared to the sampling period in order to let the

program to analyze all sampling data.

B. Current Saturation Detection and Compensation

Normally, when CT saturation occur the magnetizing

current increases and causes severe ratio error [4]. The

higher ratio error increases the probability of distance relay

to mal-operate. Therefore, the saturation current needs to be

compensated in order to obtain minimum ratio error.

Besides that, compensation process is needed to provide

correct RMS current during saturation condition. The Auto

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Regressive (AR) model is employed in this paper to

compensate the saturation current.

Unfortunately, the saturation area needs to be determined

before compensation process can be performed. The third-

difference function is employed in determin ing the

saturation area. The third-difference function converts the

inflection points sensed at the waveform of secondary

current into pulses. The first inflection point indicates the

start of saturation condition where compensation algorithm

will begin. Then, the second inflect ion point sensed by the

compensation algorithm will end the compensation process.

In other words, the point of inflection determines the

saturation area and also starting and ending of compensation

algorithm.

In this proposed algorithm, the saturation detection area is

identified using equation (1), meanwhile the RMS current

during saturation is determined from equation (2). Equation

(1) is obtained from third-difference function and equation

(2) is computed from the simplified equation of AR model.

The last three samples of current are used to compute the

value of third differential of sample (del3[i]) and current

during saturation condition (I[i]).

del3[i]= I[i]-3I[i-1]+3I[i-2]-I[i-3] (1)

I[i]=2.9683117.I[i-1]-2.94647423.I[i-2]+0.97794999.I[i-3]

(2)

C. Anti Aliasing Filter

The anti-aliasing filter of a dig ital relay removes the

unwanted frequencies from a sampled waveform. Normally,

the anti-aliasing filter removes harmonics above ω0N/2 to

prevent corruption of the desired phasor which is based on

Nyquist frequency theorem [1, 7]. There are two issues that

need to be considered in selecting the anti-aliasing filter [1].

The first issue is the frequency response of the filter, and the

second issue is the time domain response of the filter. A

sharp frequency response of filter is desirable to completely

remove the unwanted harmonics. However, as the frequency

response of a filter becomes sharper, the time domain

response becomes worse. Therefore a balance must be

achieved between the frequency and time domain response

of the filter.

In this proposed algorithm, a fifth order Butterworth filter is

designed as anti-aliasing filter using WFILTER-filter design

software. The order of the Butterworth filter is obtained

based on the distorted secondary current data. From the

data, the sixth harmonic is determined to be less than 5% of

the fundamental frequency, which results to 300 Hz of cut

off frequency. The system is assumed to be operated at 50

Hz. The other design specifications of Butterworth filter are

tabulated in Table I. Meanwhile, the filtered current

produced by the Butterworth anti-aliasing filter is calculated

based on the last five samples of current as in equation (3).

]5[[5582.0]4[1159.3]3[9779.6

]2[8385.7]1[41821.4])5[]4[5

]3[10]2[10]1[5][(000044529.0][

iIiIiI

iIiIiIiI

iIiiIiIiI

fff

ff

f

𝐼𝑓𝑖=0.0000044529.𝐼𝑖+5𝐼𝑖−1+10𝑈𝑖−2+10𝑖−3+5𝐼𝑖−4+𝐼𝑖−5+4.4182𝐼𝑓𝑖−1−7.8385𝐼𝑓𝑖−2+6.9779𝐼𝑓𝑖−3−3.115

9𝐼𝑓𝑖−4+0.5582𝐼 (3)

T ABLE I

T HE ANTI-ALIASING BUTTERWORTH FILTER SPECIFICATIONS Selectivity Low-pass

Approximation Butterworth

Implementation IIR (digital)

Pass band gain (dB) -0.01

Stop band gain (dB) -40.0

Pass band freq (Hz) 50.0

Stop band freq (Hz) 300.0

Sampling freq (Hz) 3200.0

D. DC Removal

When faults or disturbances occur, a dc-offset is generated

in an electrical power system. The generated dc-offset will

affect the accuracy of the DFT algorithm results [8].

Therefore, the DC removal algorithm is designed in o rder to

eliminate the dc-offset. The dc-offset component is assumed

to be in exponential form when a fault occurs.

In this algorithm, the dc-offset is removed by computing the

value of sampled current after anti-aliasing filtering and dc-

removal; Ifdc. Value of Ifdc is calculated using equation (4)

with an assumption of sampling interval (∆t) of 0.00031 and

time constant (τ) of 0.04653.

nkfdc ayiI /][ (4)

Where;

)1

22)/(

)/(

)/(

/(tan

,)(),/2sin(]./1[

),/2cos(]./1[1),]1[

(][

nnn

nnnt

n

tnt

f

fk

EF

FEaNneF

NneEe

iIiIy

𝐼𝑓𝑑𝑐𝑖=𝑦𝑘𝑎Where, 𝑦𝑘=𝐼𝑓𝑖−𝐼𝑓𝑖−1𝑒E. Discrete

Fourier Transform (DFT)

In a distance relay system, the impedance value detected

will determine the distance relay operation. In this design,

the impedance value is computed from the magnitude of

basic fundamental of current and voltage. The magnitude of

basic fundamental of current and voltage is extracted using

DFT method.

The complete flow chart of the developed distance relay

algorithm is shown in Appendix 1. The constructed C++

language of numerical distance relaying algorithm with

current compensation is based on the flow chart.

III. CASE STUDY

In order to evaluate the performance of the developed

algorithm, two case studies have been setup. The case

studies are conducted during normal and saturation

condition for all types of faults. Both of the case studies

employed ATP in generating the transients current and

voltage.

Power system model in Fig. 1 is used to evaluate the

performance of developed algorithm during normal



condition. The sampling frequency employed for the

simulation is 3200 Hz or 64 samples per cycle in a 50 Hz

system with total length of 200 km. Besides that, the value

of positive and zero sequence of line impedance have been

fixed to Z0= (30.34+j123.6) Ω and Z1= (3.347+j56.15) Ω

respectively.

Fig. 1. Power system configuration in normal condition

Fig. 2. Power system configurations for CT saturation simulation

Fig. 2 is used in evaluating the proposed algorithm

performance under saturation condition. The saturation

condition is created by adding a synchronous generator to an

existing bus to replace a weak source. This is because high

magnitude of fau lt current with DC components is produced

during high X/R rat io, which leads to CT saturation.

Therefore, a 15750 V synchronous ALESTOM generator

connected to Y-Y step-up transformer has been selected as a

power source. The output voltage subjected to the secondary

part of the Y-Y transformer is 132000 V.

IV. SIMULATION RESULT AND DISCUSSIONS

All results obtained for the designed distance relaying

algorithm with current compensation are presented here.

A. During Normal Condition

Fig. 3 shows the fault current during the occurrence of

three-phase fault on the system. Meanwhile, the current after

filtering and dc-removal is shown in Fig. 4. Comparing both

figures (Fig. 3 and Fig. 4), it can be seen that the current has

been smoothen and balanced after the application of an anti-

aliasing filter and dc removal. Therefore, the designed

algorithms have removed the high frequency and DC-offset

components occurred in the system successfully.

Fig. 3. Current before anti-aliasing and DC removal

Fig. 4. Current After Anti-Aliasing and DC Removal

The voltage waveforms for the three phase faults before and

after the application of anti-aliasing low-pass filtering are

shown in Fig. 5 and Fig. 6. The occurrence of h igh harmonic

components in the voltage waveform can be seen clearly in

Fig. 5. But, after the filter is applied, the harmonics

components have been filtered out as shown in Fig. 6.

Therefore, Fig. 6 reveals the filter effect in removing the

high frequency components. The phase delay can be seen

from the two figures (Fig. 5 and Fig. 6).

T ABLE II MEASURING IMPEDANCE IN NORMAL CONDITION

Fig. 5. Voltages before filtering (symmetrical fault)

Fault Type

Current RMS(A)

Voltage

RMS(V)

Measured Z(Ω)

Real Z (Ω)

Error (%)

A-B-C-G

61953.8 1056.22 58.6561 56.4040 3.9928

A-G 914.933 66726.3 51.000 56.4040 9.5808

A-B 1889.78 105021 55.5731 56.4040 1.4731



Fig. 6. Voltages after filtering

Fig. 7 shows the measuring impedance according to the

previous voltage and current. Meanwhile, Table II indicates

the measured impedance and the error for symmetrical and

unsymmetrical fau lts in normal condition. As it can be seen,

the maximum error is 9.58%, which occurred during the

single phase faults.

Fig. 7. Measuring impedance by algorithm for three phase fault

B. Saturation Condition

Fig. 8 depicts the results obtained after the implementation

of compensation algorithm with the signal which comprises

of the dc-offset and power frequency component. The first

graph shows the scaled primary current (a) and the

measured secondary current (b). Meanwhile, the second and

third graphs show the detection signal and the transient error

compensated secondary current and scaled primary current.

Based on the transient error graph, it can be stated that the

maximum transient error is less than 0.2%.

Fig. 8. Compensated current and transient error

The basic fundamental phasor of current and voltage is

shown in Fig. 9 and Fig. 10 respectively. The waveform is

obtained by DFT algorithm which has extracted the basic

fundamental phasor of current and voltage after the

compensation process has been completed.

Fig. 9. Current phasor for single phase fault in saturation condition

Fig. 10. Voltage phasor for single phase fault in saturation condition

The results for saturation condition including RMS

values of compensated current and measured impedance are

displayed in Table III and Table IV. These tables display the

results and verify the performance of Distance Relay

algorithm. Furthermore, it shows the valid ity of the

proposed algorithm in compensating the saturation current

for Distance Relay applicat ion. Based on both tables (Table

III and Table IV), it can be seen that the value of error is

very small (1.15% for compensated current and 1.1723% for

measured impedance).

T ABLE III. T HE REAL AND MEASURED CURRENT RMS VALUES ONE AND HALF CYCLE

AFTER FAULT Fault Type Real Current

RMS Compensation Current RMS

Error (%)

A-B-C-G 25.8916 25.5919 1.1575

T ABLE IV T HE REAL AND MEASURED IMPEDANCE FOR THREE PHASE FAULT

ONE AND HALF CYCLE AFTER FAULT Fault Type Real Z(Ω) Measured Z( Ω) Error (%)

A-B-C-G 39.0158 39.4727 1.1710

CONCLUSIONS

DISTANCE RELAY OPERATION DEPENDS ON THE VALUE OF

FAULT CURRENT AND FAULT IMPEDANCE. THE SMALL VALUE



OF IMPEDANCE ERROR SHOWS THE HIGH SENSIT IVITY OF THE

PROPOSED NUMERICAL DISTANCE RELAY ALGORITHM IN

FAULT DETECTION. MEANWHILE, SMALL CURRENT ERROR

INDICATES THE ABILITY OF THE PROPOSED ALGORITHM IN

PREVENTING THE MAL-OPERATION OF DISTANCE RELAY

EVEN DURING SATURATION CONDITION. THEREFORE, AS A

CONCLUSION, A C++ NUMERIC DISTANCE RELAY

ALGORITHM WHICH IS IMMUNED FROM CT SATURATION

CONDITION HAS BEEN SUCCESSFULLY DEVELOPED.

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Schenectady NY. Advancements in Adaptive Algorithms for Secure High Speed Distance Protection T.S

[2] E. E. CONNER, E. C. WENTZ and D. W. ALLEN. Methods for Estimating Transient Performance of Practical Current Transformer for Relaying. IEEE PES Summer Meeting & Energy Resources Conf. July 14-19, 1974. Anaheim, Cal:IEEE. 1974. 116-122.

[3] Y. C. Kang, S. H. Kang, J. K. Park, A. T . Johns and R. K. Aggarwal. Development and hardware implementation of a compensation algorithm for the secondary current of current transformers .IEE. 1996. 143(1): 41-49.

[4] Sidhu, M.Hfuda and M. S. Sachdev. A Technique for Generating Computer Models of Microprocessor–Based Relays. Conference on Communication Power and Computing. May 22-23, 1997. Winnipeg: IEEE .1997.191-196.

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[7] Chul-Hwan Kim. Myung-Hee Lee. Raj K. Aggarwal and Allan .T .Johns. Educational Use of EMTP MODELS for the study of Distance Relaying Algorithm for protecting Transmission Lines. IEEE. 2000. 15(1): 9-15.

[8] T.S.Sidhu, X.Zhang, F.Albasri and M.S.Sachdev. Discrete-Fourier-Transform Based Technique for Removal Of Decaying Dc Offset From Phasor Estimates, IEEE Proc-Gener. Transm. Distrib, 2003. 150(6): 745-752

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INDEX 1

S

[23] ransformer Models For Protective Relay Transient Study. IE

nded

End of saturatio

n

Sampling of voltage and current

Saturation

detection

Saturation

level>TH

Second

Inflection

point

Current

compensation

Anti aliasing filter

DC Removal

Enter new sample and remove the old one 𝑉𝑛=𝑉𝑛+1 𝐼𝑛=𝐼(𝑛+1)

Calculation of sine and cosine elements of voltage and current

𝑉1𝑠=1𝑛Σ𝑤𝑛𝑠 𝑉1𝑐=1𝑛Σ𝑤𝑛𝑐

𝐼1𝑠=1𝑛Σ𝑤𝑛𝑠 𝐼1𝑐=1𝑛Σ𝑤𝑛𝑐

𝑉<𝜙𝑣=𝑉1𝑠2+𝑉1𝑐2∠𝛼 𝑡𝑎𝑛𝑉1𝑠𝑉1𝑐 𝐼<𝜙𝐼=𝐼1𝑠2+𝐼1𝑐2∠𝛼 𝑡𝑎𝑛𝐼1𝑠𝐼1𝑐

𝑍=𝑉𝐼 ; ∅=∅𝑉−∅𝐼 𝑋= 𝑍𝑠𝑖𝑛∅ ; 𝑅=𝑍𝑐𝑜𝑠∅

YES

NO

YES

YES

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CT Compensation of Numerical Distance Relaying (Documento)