chapter 5 a new current transformer...
TRANSCRIPT
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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
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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.