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CHAPTER 5

A NEW CURRENT TRANSFORMER SATURATION DETECTION

ALGORITHM

In unit protection schemes, where CTs are differentially connected, the excitation

characteristics of all CTs should be well matched. The primary current flow on each of the

CTs that are paralleled and/or differentially connected can be greatly different and thereby

the performance calculation is very difficult. Modern bus/generator/transformer protection

scheme utilizes high impedance over-voltage relays, low impedance overcurrent relays,

and medium impedance percentage restraint relays which require dedicated CTs to ensure

proper operation of relays. Still, in many cases, protection CTs are not selected and/or

matched properly. Hence, external fault current having long DC time constants leads to

saturation of CTs which in turn maloperates bus/transformer differential relays. The

subsequent sub-sections discuss

• problems encountered by different techniques,

• a new current transformer saturation detection algorithm,

• testing of the proposed CT saturation detection algorithm using field data

5.1 INTRODUCTION

The differential protection needs to trip or not within short time (ms) depends on the

transient component of fault current. This components decay very slowly during fault as

per time constant of line. Hence, in power systems, it is necessary to analyze transient

performance of CT for dedicated differential protection scheme. CT has to transform

primary current to secondary side in normal as well as faulty condition and its relative

tolerance cannot exceed the limits. However, saturation of CT may impact on its

performance during its operating state.

Most of the CTs use iron core to maximize the flux linkage between primary and

secondary windings. However, the nonlinear excitation characteristics and ability to retain

large flux (remanent flux) in cores may lead CT to saturate. Many studies on the analysis

of steady-state and transient behavior of iron-cored CTs have been reported in the

literature [105], [130], [182], [207].

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This chapter puts forward a new CT saturation detection technique which depends on

saturation detection index (Dn) that is derived using derivatives of current signals and

Newton’s backward difference formulas.

5.2 CURRENT STATE OF THE ART

Though the main function of the protective CT is to faithfully transform the

maximum possible current under normal as well as during faulty conditions, its saturation

is inevitable. The amount of saturation depends on the magnitude of fault current,

remanence flux, magnitude of the DC component, primary & secondary time constant of

CT and burden on secondary side of CT [24], [196]. Several methods have been suggested

by researchers for detection of CT saturation.

Kang et al. [200] presented an algorithm based on calculation of flux available in

core of CT using secondary current. However, the prime limitation of this algorithm is that

the value of remanence flux remains zero during initial calculation which is not true in all

situations. Thereafter, Fernandez et al. [39] proposed impedance-based CT saturation

detection algorithm for busbar differential protection. But the requirement of both voltage

and current signals for detection of CT saturation is the main disadvantage of this scheme.

Later on, Pan et al. [94] described CT compensation algorithm based on conversion of

current waveform distorted by CT saturation to a compensated current waveform.

However, this scheme is comparative slower than other schemes as it requires one and half

cycle (after inception of fault) to calculate compensated value of current. Villamagna et al.

[139] suggested a CT saturation detection scheme based on the zero-sequence differential

current gradient with respect to the bias current. However, the said algorithm may

maloperate during fault not involving ground as the amount of zero-sequence differential

current mainly depends on the involvement of ground in the fault.

Afterwards, authors of references [203] and [12] suggested a CT saturation detection

scheme based on second and third current difference function. Nevertheless, fixed value of

threshold may not be able to detect very low saturation condition and presence of noise &

harmonic during fault condition may maloperate the above two schemes. Thereafter, Hong

et al. [209], [208] presented Wavelet-based techniques for CT saturation detection. But

susceptibility of Wavelet against noise which may present during fault is the fundamental

disadvantage of the said two schemes. Later on various researchers have proposed

different techniques of CT saturation detection based on neural network (NN)/combination

of NN with other artificial intelligence (AI) techniques [47], [70], [194]. However, large

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training sets, tedious training process, and a large number of neurons are the several

disadvantages of the neural network based schemes.

Furthermore, several saturation detection techniques have also been proposed by

researchers using different approaches such as Taylor series expansion, mathematical

morphology, phasor computations, waveform analysis and difference functions of CT

secondary current samples [64], [197], [44], [13], [53]. However, most of the above

schemes may not give satisfactory results in case of involvement of decaying DC

component, noise in fault current and remanence flux in the core of CT. Moreover, the

majority of these schemes have not been tested in real time or using actual field data or in

laboratory environment.

In order to rectify the said problem, a new algorithm for CT saturation detection has

been presented in this chapter. The proposed scheme has been tested by generating various

saturation cases on CT model available in PSCAD/EMTDC software package [84].

Subsequently, the same algorithm has also been validated by developing a test bench of

CT in laboratory environment.

5.3 PROPOSED METHOD FOR CT SATURATION DETECTION

During the normal operation of power system, CT replicate fundamental frequency

component which is sinusoid in nature. However, the secondary current may distorted

during power system fault which often contain a decaying DC offset. The derivatives of

the secondary can be subsequently used to inspect the wave shape properties of the current

signal. Based on this principle, a new index has been derived to detect saturation in

various operating condition of CT. Then, the variations of this index along with filter

during typical fault current/system condition have been compared with adaptive threshold.

The subsequent sub-section describes the proposed principle and detection algorithm.

5.3.1 Proposed Algorithm

Many factors such as DC component in fault, size of core, flux density in core,

secondary burden etc, may lead to saturation of the CT core, and cause significant

distortion of the secondary current waveform [02]. Figure 5.1 shows the simplified

equivalent circuit of a CT for transient analysis with the total impedance in secondary

circuit i.e. the sum of secondary leakage impedance, lead impedance, and the load

impedance, given by Zb = (Rb + jωLb).

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Figure 5.1 Simplified equivalent circuit of a CT for transient analysis

Assume further that the magnetizing impedance Zm is a parallel combination of the

core loss resistance Rc and the magnetizing inductance Lm.

The primary current i1 (t) during transient analysis of CT can be given by,

0 t forcos)cos(I )(/

max1 ≥

−−=

Τ−

θθωPt

etti (5.1)

0 t for 0 <=

Where, Imax is the peak value of sinusoidal steady state fault current, TP is the primary

time-constant and θ is the fault initiation angle. It has been assumed that the value of pre-

fault current is almost zero before the inception of the fault (t<0).

The secondary current of CT is represented as,

ϕ−θ−ωθ

ϕωτ−

−τ−

ϕ−θ∗ϕ∗ϕ−−τ

θ=Τ−

Τ−

)t sin(*cos

cos)

T

T(e

)]cos tancos(sin T

T[e

) R+(R

R cosI(t)i

/

2/

bc

cmax2

t

t

)--tsin(*C-Be Ae(t)i//

2 ϕθωPS tt Τ−Τ− += (5.2)

Where, ωτ=ϕtan , cbmbmc RRLRLR /)( +=τ

TP and TS are primary and secondary time constant, respectively, and A & B are

constants. In equation (5.2), the first and second exponential terms decay with the time

constants TS and TP, respectively, whereas the magnitude of the sinusoidal term is given

by,

STIIIC ωϕω

ωϕϕω =

+=== tan where,

)T(1

TsincosT

2

S

SmaxmaxSmax (5.3)

The discrete–time version of i2 (t) is obtained by considering t=nH.

Rc

i1 i2

ic if

Lm

Lb

Rb

im

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)--N

2sin(*C-Be Ae

//

][2 ϕθπ

+= Τ−Τ−ni PS nHnH

n (5.4)

Where, H is the sampling interval, N is the number of samples per cycle and n is the recent

sample.

The first difference of i2 [n] is given by equation (5.5).

1]-2[][2

1i - i nnn =∇

π+

π−ϕ−θ−

π

π−

−−= −−

2N

2sin

N2sinC

e*)eB(1+e*)eA(1)H/T()(H/T)H/T()(H/T PPSS

nN

nn

(5.5)

If the sampling rate is 4 kHz (80 samples per cycle) for a power system frequency of

50Hz, the sampling interval H= 0.25ms. By considering TS = 1s and TP = 0.02s, the value

of )e(1)(H/T S− and )e(1

)(H/T P− are exponentially reduced to 0.00025 and 0.0125,

respectively [203], [64]. This indicates that the exponential terms in 1

n∇ are considerably

reduced and have negligible values since the time constants are large. These values are

further reduced for CTs of higher protection class as the secondary time constant of such

CTs are in the range of 3 to 10s [64]. At the same time, the magnitude of a sinusoid term

π

N2sinC depends on sampling rate N.

The following equations can be derived for the second, third & fourth difference of the CT

secondary current.

1

1

12

−∇−∇=∇nnn

]2[21]-2[n2[n] 2 - −+= niii (5.6)

π−ϕ−θ−

π

π−−− −−

N

22sin

N2sine)eB(1+e)eA(1=

2

(nH/Tp)2(H/Tp)(nH/Ts)2(H/Ts)n

NC

2

1

23

−∇−∇=∇ nnn

i - i 3 + i 3 - i 3]-2[n2]-2[n1]-2[n2[n]= (5.7)

π+

π−ϕ−θ−

π

π−−−= −−

2N

32sin

N2sinC e)B(1+e)eA(1

3

(nH/Tp)3(H/Tp)(nH/Ts)3(H/Ts)n

Ne

105

3

1

34

−∇−∇=∇ nnn

4]-2[n3]-2[n2]-2[n1]-2[n2[n] i +i 4 - i 6 + i 4 - i= (5.8)

π−ϕ−θ−

π

π−−− −−

N

42sin

N2sine)eB(1+e)eA(1 =

4

(nH/Tp)4(H/Tp)(nH/Ts)4(H/Ts)n

NC

Detailed analysis of saturation detection has been carried out using equation (5.5) to

equation (5.8). Here, it has been observed that the accuracy of saturation detection is

steadily increased as one move from 2- point formulas (equation-5.5) to 5- point formulas

(equation-5.8). It is true that any further increase in formulas (beyond 5-point) will

definitely reduce saturation detection error. But at the same time it will unnecessarily

increase the amount of calculation. Hence, author has derived a saturation detection index

(Dn) using equations (5.5) to (5.8) and Newton’s backward difference formulas [114].

They are given as:

∇∇∇

3+

2 +

H

1 =D

321

3nn

nn (5.9)

∇∇∇∇

4 +

3+

2 +

H

1 =D

4321

4nnn

nn Where, H is sampling interval (5.10)

Taking the difference of equations (5.9) & (5.10), a saturation detection index (Dn) can be

calculated and given by equation (5.11).

[ ]4]-2[n3]-2[n2]-2[n1]-2[n2[n]34 i 0.25 +i i 1.5 + i i 0.25H

1= DD= D −−− nnn (5.11)

Where ‘n’ is recent sample. This index (Dn) is compared with adaptive threshold

(discussed in section-5.3.2) to estimate start and end point of CT saturation.

5.3.2 Condition for CT Saturation Detection

The value of Dn is much larger than the constant term “

4

N2sin

πC ” available in

sinusoidal part of equation (5.8) during CT saturation. This term is used to derive adaptive

threshold (Th) along with several other terms such as amount of maximum fault current

(Imax) estimated using Fourier algorithm and safety factor (λ) which depends on low pass

filter.

Hence, the adaptive threshold is given as below,

4

maxhN

2sin**I*2*=T

πλ C (5.12)

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The said value of adaptive threshold is capable to detect small to heavy saturation

condition as it depends on magnitude of fault current and λ compared to the scheme given

in [203] which uses fixed threshold value.

5.3.3 Proposed Saturation Detection Flowchart

Figure 5.2 shows the flowchart of the proposed algorithm. Initially, current samples

of bay CTs are acquired by data acquisition system through first order low pass filter

which effectively removes the noise present in the secondary current. The fault detection

algorithm is used to discriminate between the fault and normal condition [170].

Figure 5.2 Algorithm of CT saturation Detection

Whenever a fault is detected by the fault detection algorithm, post fault samples of all

phases of connected bay CTs are sent to the CT saturation estimation block. In this block,

the value of Dn is calculated using five point formulas (equation-5.11) for each cycle and

is being continuously compared with adaptive threshold. When the value of Dn exceeds

Yes

No

Start

Read Current Samples (IR, IY and IB) of bay CTs

Low Pass First Order Filter

CT saturation estimation block

Computation of Dn and Th as per eq. (6.11) and (6.12), respectively

Fault Detection Algorithm

Fault

Detected?

Is

Dn > Th

Yes

CT saturation detected/begins

No

Is

Dn < Th

Next set of

samples

Yes

End of CT saturation

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threshold value, starting point of CT saturation is detected (Dn > Th) and thereafter end of

saturation is noticed when the value of Dn goes below threshold value.

5.4 SYSTEM STUDY

Figure 5.3 shows single line diagram of a portion of Indian power system network

consisting of three sources represented by Thevenin’s equivalent. These sources are

connected to the common bus through bay L1, L2 & L3, respectively. The model, as

shown in Figure 5.3, is simulated using the PSCAD/EMTDC software packages.

Figure 5.3 Single line diagram of power system model

To validate the proposed algorithm, the CTs located on bay L3 are analyzed which

uses Jiles – Atherton model [188] available in PSCAD/EMTDC software package. All the

test cases are generated by simulating faults on bay L3 with varying fault and system

parameters. These parameters are Fault Inception Angle (FIA), fault resistance (Rf), types

of fault (Ftype) and Fault Locations (FL) on line L3 (Fex1, Fex2, Fex3). The line and source

parameters are given in Appendix-E. Sampling frequency of 4 kHz, which is in the range

of the common sampling frequencies in digital relaying scheme for a system operating at a

frequency of 50 Hz, is used in this study. Moreover, the performance of CT under

transient condition is also examined with due consideration of effect of burden resistance,

remanence flux, DC offset and white noise present in current signal.

5.5 SIMULATION RESULTS OF DIFFERENT SATURATION CONDITIONS

The proposed CT saturation detection method is very fast considering adaptive

threshold. However, just after fault inception, CT secondary current has a point of

inflection. Hence, Dn may have a large value at the next sample of a fault instant; the

proposed algorithm may detect this instant as the start of saturation. To avoid

maloperation under this situation, the proposed algorithm starts after a current that exceeds

three times the rated secondary current for three successive samples [203].

In order to test effectiveness of the proposed scheme under varying system

conditions, a large numbers of simulation cases have been generated. Different parameter

Fext1

CB1

G3

L1 (80km) G1

CB2 L2 (50km) G2

CB3 L3 (100km) CT

Fext2 Fext3

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values which have been chosen to produce the transient response of CT are remanence

flux density, burden resistance and presence of DC offset & noise. Considering all these

parameter values, around 900 simulations cases were generated and the effectiveness of

the proposed scheme has been validated for all these test cases. However, the results of

some sample cases are shown in upcoming section.

5.5.1 Effect of DC Component and Secondary Burden on CT Saturation

The effect of CT saturation for any differential protection scheme is of crucial

importance particularly during a high current external fault. By changing the CT

secondary burden resistance, different degrees of CT saturation can be obtained [188]. The

performance of the proposed scheme during CT saturation is carried out by simulating

different faults on bay L3 at different locations (5 km, 10 km and 20 km) from the bus

with varying system parameters. Figure 5.4 (a) and (b) show the CT primary & secondary

current and the value of Dn & threshold (Th) , respectively, during L-g fault (R-g) on bay

L3 at 20 km without CT saturation and DC component.

Figure 5.4 Waveform of CT primary & secondary current and value of Dn & Th (a), (b)

without CT saturation (c), (d) with CT saturation, respectively

It has been observed from Figure 5.4 (b) that the magnitude of Dn remains well

below the adaptive threshold throughout the fault time and hence, no saturation is detected

by the proposed algorithm. Figure 5.4 (c) & (d) show the performance of the proposed

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scheme in presence of decaying DC component along with the value of burden resistance

Rb = 1 Ω. It is to be noted from Figure 5.4 (d) that the value of Dn crosses the threshold

value after one cycle elapse from point of fault inception (start of saturation) and remains

above the threshold value for next three successive cycles. The saturation ends when the

value of Dn goes well below the threshold value.

Further, in order to authenticate the algorithm under various degrees of saturation,

the burden resistance of CT secondary has been changed. Figure 5.5 (a) & (b) and (c) &

(d) show the performance of the proposed algorithm for L-L (R-Y) fault on bay L3 at 5 km

during burden resistance (Rb) equals to 3 Ω and 6 Ω , respectively. It is to be noted from

Figure 5.5 (b) and (d) that the proposed scheme is capable to detect severe CT saturation

condition in presence of decaying DC component.

Figure 5.5 Waveform of CT primary & secondary current and value of Dn & Th under CT

saturation condition (a), (b) for Rb= 3 Ω and (c), (d) for Rb=6 Ω, respectively

5.5.2 Effect of Remanent Flux on CT Saturation

The amount of remanent flux in the core depends on factors such as magnitude of

primary current, the burden on secondary circuit and the amplitude & time constant of

decaying DC component. Depending upon the direction of flux setup in the core during

the energization of CT in presence of remanent flux, a large part of secondary current of

CT may saturate [196]. In this situation, the performance of protective class CT is

influenced by this remanence or residual magnetism and may reach up to 90% of the

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saturation flux [82]. Figure 5.6 (a) & (b) and (c) & (d) show the primary & secondary

currents and value of Dn & threshold for a three-phase (R-Y-B) fault at 10 km on bay L3

during 0.5 Ω burden resistance with 0% and 90% remanent flux density, respectively. This

remanent flux density was set in the core of CT prior to inception of fault. It is to be noted

from Figure 5.6 (b) and (d) that the proposed algorithm is capable to detect the saturation

interval (by comparing the value of Dn and threshold) irrespective of the level of rmanence

flux previously present in the core of CT.

Figure 5.6 Waveform of CT primary & secondary current and value of Dn & Th during

(a), (b) 0 % remanence flux and (c), (d) 90 % remanence flux, respectively

5.5.3 Effect of Noise Superimposed in Secondary Current

To evaluate the proposed algorithm, acquired current signals from PSCAD/EMTDC

software are polluted with white Gaussian noise by considering different signal-to-noise

ratios (SNR) in MATLAB environment. The SNRs are set to 20db, 30db and 40dB to

pollute the original current signals. Thereafter, these noisy current signals are filtered by a

low pass first order Butterworth filter which diminishes the higher order harmonics and

noise. The proposed algorithm is tested by changing the cut-off frequency of the filter for

perfect saturation detection. Initially, cut-off frequency was set to 1600 Hz and it is

gradually decreased up to 200 Hz with sampling frequency of 4 KHz. Figure 5.7 (a) & (b)

show the primary & secondary current of CT and value of Dn & threshold during R-Y-g

fault on bay L3 at 5 km with Rb=3Ω, SNR=40 db and cut off frequency=300 Hz. It has

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been observed form Figure 5.7 (b) that the proposed algorithm accurately detects start and

end of saturation. Here, the magnitude of Dn & threshold are considerably reduced at low

cut-off frequency due to which the proposed algorithm gives more efficient results in

terms of saturation detection in the presence of harmonics and noise.

Figure 5.7 (a) waveform of CT primary & secondary current and (b) value of Dn & Th

during SNR=40db contained by CT secondary signals

5.5.4 Effect of Types of Fault and Fault Inception Angle (FIA)

The system shown in Figure 5.3 was subjected to various types of faults such as L-g,

L-L, L-L-g and L-L-L/L-L-L-g. The results are given in Figure 5.4 to Figure 5.7 of

subsection-5.5. It has been observed that the proposed algorithm detects CT saturation

condition for both balanced and unbalanced faults.

In order to identify the effect of fault inception angle (FIA) on CT saturation, various

simulation cases has been generated by varying the FIA between 0o to 180

0. Figure 5.8 (a)

and (b) show the primary & secondary current of CT and value of Dn & Th, for L-g (R-g)

fault applied at 5 km on bay L3 with Rb= 3 Ω and FIA θ=450. The simulation results for

the same fault condition with FIA θ=1350 and Rb= 5 Ω are shown in Figure 5.8 (c) and (d).

It has been observed from Figure 5.8 (b) & (d) that though the magnitude of decaying DC

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component is affected by FIA, the proposed scheme correctly identifies the start and end

points of CT saturation.

Figure 5.8 Waveform of CT primary & secondary current and value of Dn & Th during (a),

(b) FIA θ=450 and Rb= 3 Ω and (c), (d) FIA θ=135

0 and Rb= 5 Ω, respectively

5.6 PRACTICAL VALIDATION OF THE PROPOSED ALGORITHM

5.6.1 Hardware Setup

In order to evaluate performance of the proposed algorithm during CT saturation

condition, a laboratory test bench, as shown in Figure 5.9, is developed. Here, protective

class (5P10) resin cast type CT having CT ratio= 10/5 A, burden= 5 VA and voltage

rating= 660 V is used. Further, various equipments such as relay testing kit, rheostat,

switches and clamp-on meter are also used for the development of the said laboratory

prototype. Here, testing kit is used to inject high current (0-250 A) in the primary of CT

and variable rheostat is used as a secondary burden resistance. In order to record and

compare the waveform of CT secondary current, a high resolution four channel Digital

Storage Oscilloscope (DSO) is used. In addition, clamp-on type current sensor probe is

also used which converts CT secondary current signals into equivalent voltage signals.

Thereafter, these data are given to DSO where a sampling is carried out at a rate of 80

samples/cycle. Subsequently, these sampled data are loaded in MATLAB software using

USB port of DSO and further utilized for testing of the proposed CT saturation detection

algorithm.

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Figure 5.9 Hardware setup of laboratory test bench

5.6.2 Results of Prototype

In order to validate the proposed algorithm, various cases have been generated using

the said laboratory prototype by changing burden resistance from 0 Ω to 12 Ω and primary

current of CT from 10 A to 120 A. Figure 5.10 (a) shows the waveform of CT secondary

current during saturation along with zoomed view of certain portion of signal captured by

DSO during 100 A primary current and Rb=12 Ω.

Figure 5.10 (a) CT secondary current signal of DSO during 100 A primary current and 12

Ω burden resistance and (b) algorithm results in term of Dn and Th for the said condition

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The performance of the proposed algorithm in terms of Dn and Th are shown in

Figure 5.10 (b) for the zoomed view of selected portion as shown in Figure 5.10 (a). It has

been observed from Figure 5.10 (b) that the proposed scheme correctly detects severe CT

saturation condition as the value of detection index exceeds threshold value (detects only

starting point as there is no end point for the collected data).

5.7 COMPARISON OF THE PROPOSED ALGORITHM WITH EXISTING

SCHEME

It has been observed by the author that the schemes based on second and third

difference functions of the sampled current signals [64], [203] may not be able to identify

the end point of saturation. Moreover, the above two schemes may maloperate in case of

very low saturation of CT, particularly during heavy load variation. Conversely, the

proposed algorithm provides accurate result irrespective of level of saturation. This fact

can be easily understood by observing the comparative evaluation of the above two

schemes with the proposed scheme as shown in Figure 5.11.

Figure 5.11 (a) CT primary & secondary current, (b) value of del2 & Th1 during second

difference [64], (c) value of del3 & Th2 during third difference [203], (d) value of Dn and

Th for proposed algorithm

The CT primary & secondary current during B-g fault on bay L3 at 50 km with

minor CT saturation having Rb=0.06 Ω is shown Figure 5.11 (a). The magnitude of

derivative (Del2, Del3 and Dn) & threshold (Th1, Th2 and Th) during second difference of

the sampled currents (equation-5.6) [64], third difference of the sampled currents

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(equation-5.7) [203] and using five point formulas of the proposed algorithm (equation-

5.11) are shown in Figure 5.11 (b), (c) and (d), respectively. It is to be noted from Figure

5.11 (b) and (c) that the value of Del2 and Del3 remains well below the respective

threshold Th1 and Th2 under minor CT saturation condition. On the other hand, as shown in

Figure 5.11 (d), the proposed algorithm accurately detects the saturation interval.

5.8 CONCLUSION

In this chapter, a new CT saturation detection algorithm has been presented. The

proposed algorithm depends on a saturation detection index (Dn) which is derived using

derivatives of current signals and five point Newton’s backward difference formulas.

Initially, the saturation detection index (Dn) is derived using derivative of CT

secondary currents. Based on the maximum fault, sensitivity of filter and sampling rate an

adaptive threshold is decided. The calculated index is continuously compared with the

adaptive threshold (Th) to estimate start and end point of CT saturation. In order to

improve accuracy of the proposed scheme, a low-pass first order Butterworth filter is used

to suppress noise and harmonics which may present in CT secondary current. The

validation of the proposed algorithm is carried out by generating various simulation cases

considering CT model available in PSCAD/EMDC software packages. These cases are

generated by varying parameters such as remanence flux, FIA, burden resistance and

presence of DC offset & noise.

The proposed algorithm is also validated by producing various CT saturation cases in

laboratory environment using developed CT test bench. Results obtained from both

simulation and hardware setups indicate effectiveness of the proposed algorithm to detect

CT saturation condition. At the end, a comparative evaluation of the proposed algorithm is

also carried out with the existing schemes and its performance is found to be superior

compare to the existing schemes. Hence, the proposed algorithm can be practically

implemented in an existing digital differential relaying scheme.