BR102015028907A2 - SATURATION DETECTION METHOD IN CURRENT TRANSFORMERS USING SAVITZKY-GOLAY FILTER - Google Patents

Abstract

method for detecting saturation in current transformers using the savitzky-golay filter method for detecting electromagnetic saturation of the core of a current transformer (tc) using signal processing techniques applied to the samples of the electrical current signal of its circuit secondary (2). upon fault detection (9), the secondary circuit current signal (2) is filtered (13), processed by the savitzky-golay 2nd order differential filter (14) and compared to an adaptive threshold (15). The results of this comparison allow the detection of start points (4) and end points (5) of saturated regions (3). This method can be used in mitigation processes of the effects caused by the saturation of tcs in the protection devices of the electric power systems.

Description

(54) Title: METHOD OF SATURATION DETECTION IN CURRENT TRANSFORMERS USING THE SAVITZKY-GOLAY FILTER (51) Int. Cl .: G01R 35/02; G01R 12/31 (73) Holder (s): FEDERAL UNIVERSITY OF JUIZ DE FORA, FEDERAL UNIVERSITY OF ITAJUBÁ, RESEARCH FOUNDATION OF THE STATE OF MINAS GERAIS FAPEMIG (72) Inventor (s): CARLOS AUGUSTO DUQUE; PAULO MÁRCIO DA SILVEIRA; BRUNO MONTESANO SCHETTINO (57) Abstract: METHOD FOR SATURATION DETECTION IN CURRENT TRANSFORMERS USING THE SAVITZKY-GOLAY FILTER Method for detecting electromagnetic saturation of the core of a current transformer (CT), using signal processing techniques applied to the samples of the electric current signal from its secondary circuit (2). After fault detection (9), the current signal from the secondary circuit (2) is filtered (13), processed by the 2nd order differentiating filter from Savitzky-Golay (14) and compared to an adaptive threshold (15).

The results of this comparison allow the detection of the start points (4) and end points (5) of the saturated regions (3). This method can be used in processes to mitigate the effects caused by the saturation of the CTs in the protection devices of the systems

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DESCRIPTIVE REPORT

METHOD FOR SATURATION DETECTION IN TRANSFORMERS

CHAIN USING THE SAVITZKY-GOLAY FILTER

Technical Sector [001] The present invention belongs to the technical sector of Digital Signal Processing (PDS), applied to the protection of Electric Power Systems (SEP). More precisely, this invention relates to a method for detecting electromagnetic saturation of the core of a current transformer (TC), using PDS techniques applied to the electrical current signal extracted from its secondary circuit.

State of the Art [002] CTs play a fundamental role in the protection of Electric Power Systems (SEP), since they allow access to the high currents of the primary circuit through their small scale replicas at their secondary terminals, in such a way obtain current levels acceptable for the use of protection devices. However, under certain fault conditions, the high currents in the primary circuit can cause the CT to saturate, causing distortions in the secondary current waveform. This phenomenon occurs due to the nonlinear magnetic characteristics of the CT core. In summary, when the CT core saturation occurs, the secondary current is no longer a true scale copy of the primary current, which can significantly affect the performance of the protection devices. To assist in elucidating the topic addressed, figure 1 will be used, which shows the current of the primary circuit (1) and the current of the secondary circuit (2) distorted by saturation, for a typical situation of CT saturation due to the occurrence of a asymmetric fault at the end of the first sampled cycle.

[003] There are several reasons that lead to saturation of the CT core, among them:

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1) High components a.a. of the primary current, caused by bad dimensioning of the CT or by faults in the SEP;

2) Presence of d.c. exponential decay in the primary current, which arise due to asymmetric faults;

3) Use of high impedance loads in the secondary of the CT;

4) Presence of magnetic flux remaining in the CT core due to the network reclosing process.

[004] One way to avoid saturation of the CT core would be to oversize it, that is, use CTs with ferromagnetic cores of sufficient cross-section to support the most unfavorable situations possible. However, this procedure leads to CTs with high financial costs and physical dimensions, which usually makes this type of solution unfeasible.

[005] Another proposed solution to mitigate the effects caused by the saturation of the CT core is to sample and analyze the secondary circuit current (2) distorted by the saturation, using methods to correct it in order to recover current information the primary circuit (1), promoting compensation for the effects caused by saturation. In this way, it would be possible to correct the current signal before using it in protection devices. This solution can be implemented either in a device that is located between the secondary of the CT and the protection device or simply through a method based on signal processing incorporated in the protection device itself, when it is a processed digital protection device , as is the case with current numerical relays. In the latter case, the saturation compensation method would belong to an initial pre-processing stage of the signal, preparing it for the subsequent stages already existing in the numerical relay processing algorithm.

[006] Studies around the world have been carried out with the objective of recovering information from the primary circuit current (1) through samples of the secondary circuit current (2) distorted by CT saturation. However, to make such a correction, accurate knowledge of the

3/18 current curve region where there is distortion, hereinafter referred to as saturated regions (3). Thus, methods for detecting the start points (4) and end points (5) of the saturated regions (3) of current are usually incorporated into the distortion correction techniques. Some methods of detecting saturation of CTs that make up the state of the art are described below:

[007] Document SE468189B presents a method and device for detecting CT saturation, which use the simultaneous combination of criteria related to the instantaneous values of the secondary current and its first derivative. This method stands out for the inventor's perception of the fact that the behavior of the first derivative can signal the presence of saturation, and can be considered one of the first methods based on derivative filters, also called derivative methods.

[008] The document US6617839B2 presents another derivative method to detect the saturation of the CT, based on the observation of the second or third derivatives of the current signal of the secondary circuit (2), estimated through the finite difference method. The peaks reached by the derivatives correspond to the start (4) and end (5) points of the saturated regions (3).

[009] The method proposed in document FR2835319A1 is based on an association of two criteria, to be simultaneously satisfied, for the detection of CT saturation. The first criterion is related to the comparison of an estimated instantaneous value of secondary current with the real value of the sample, such estimation being based on a prediction through a second order autoregressive sine mathematical extrapolation model. When the absolute value of the difference between the estimated and actual values exceeds a threshold, the first detection criterion is considered satisfied. The second criterion is based on the estimation of the magnetic flux of the CT core, which is proportional to the integral of the secondary current, and on its comparison with two thresholds, one positive and the other negative. To make the

4/18 According to a criterion independent of the characteristics of the CT, the referred thresholds are adaptively defined, in function of the maximum and minimum reached by the integral of the secondary current in conditions of permanent regime. However, there is a need to insert a margin at these thresholds, related to the remaining flow, this margin being stipulated according to the TC class in question. The inventors do not suggest a sampling rate or mention the influence of noise on the behavior of the proposed detection method, describing only a previous stage of anti-aliasing filtering to eliminate harmonic interference.

[010] The Hilbert-Huang transform.or Hilbert-Huang transform (HHT) is the basis of the method proposed in CN103050942A. HHT is a time and frequency signal decomposition technique developed especially for the analysis of non-stationary and non-linear signals. Unlike Fourier decomposition, which uses orthogonal bases defined a priori (sinusoides parameterized in amplitude and frequency), HHT uses base functions defined a posteriori, called intrinsic mode functions, or 'intrinsic mode functions' (IMF). MFIs are empirically extracted from a signal data set, using a method called empirical mode decomposition, or empirical mode decomposition (EMD). Once the MFIs are obtained, a Hilbert spectral analysis (or '' Hilbert spectral analysis '' - HSA) can be performed, calculating the instantaneous frequencies of the MFIs and representing the signal through an energy-tempofrequency distribution, called a spectrum Hilbert. The detection method is initially based on a previous off-line stage of determining MFIs using the EMD method, using a data set previously acquired under real conditions of CT operation. Thereafter, the MFIs are used to carry out the HSA of the current signal, and the instantaneous frequencies are calculated for each new sample acquired. Finally, a comparison logic is instituted to determine the occurrence of saturation through the temporal evolution of the Hilbert spectrum. The inventing authors describe

5/18 additionally a way of implementing the method in hardware with a sampling frequency of 4 kHz.

[011] In CN103245860A proposes a saturation detection method that brings together Wavelet Transform (WT) and Mathematical Morphology (MM) tools, with the objective of improving noise immunity. A technique for obtaining the current signal morphological gradient, for each sample, based on the wavelet theory, generates a detailed output signal that contains information about transients of the original signal, but with a lot of noise interference. Then, morphological filters are used using the expansion and erosion operators, accompanied by the morphological top-hat transform, whose output corresponds to a signal that highlights the start and end points of saturation due to the occurrence of peak values at these points. However, it is necessary to consider the high computational effort required by the different stages involving the proposed detection process.

[012] In BR1020130340065, a derivative saturation detection method was developed, developed with the objective of dealing with noisy signals in a more effective way than conventional derivative methods. It was chosen as a starting point a filter developed by Cornelius Lanczos (1956), whose main characteristic is the fact that it is a first-order derivative filter that attenuates signal noise. Such a filter became known in the scientific community as a low noise Lanczos differentiating filter. From there, to accentuate the transition points between the saturated and unsaturated regions, a filter was created whose coefficients are obtained through the first difference function of the low noise Lanczos filter. Observing the output of this filter, when the input corresponds to the secondary current signal, allows to precisely locate the start and end points of the CT saturation. The authors also developed the equations for calculating the most appropriate threshold to be used in the detection process, depending on the SNR and the characteristics of the anti-aliasing filter used in the stage prior to the Analog-to-Digital (A / D) conversion.

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Technical Problems Existing in the State of the Art [013] The saturation detection methods in CTs existing in the state of the art can present some (s) of the three basic problems now listed:

1) Dependence on knowledge of characteristics such as the CT magnetization curve, the remaining flux in the core, the secondary load impedance (burden), the primary circuit time constant, etc. The dependence on these characteristics makes the generalization of such methods unfeasible, making their practical application difficult, since these characteristics are not always available or can be easily estimated;

2) Some methods present in the state of the art require high computational effort for their execution, due to the complexity of calculations involved in the process. Still, in certain methods there is a need to use several current samples, contained in a very extended time window. In any of these cases, the processing and response time precludes the use of such methods in real time, a fundamental condition for use in practical applications in the area of SEP protection;

3) The sensitivity of the saturation detection methods in relation to the presence of noise, since it impairs the detection process, contaminating the information contained in the range of the frequency spectrum present in the transitions between saturated (3) and unsaturated regions . Even with the insertion of an initial filtering stage in the detection process, the efficiency of such methods is compromised for signals affected by high noise levels.

Objectives of the present invention

7/18 [014] The present invention consists of a method to detect the saturation of the CT core by processing samples from the current of its secondary circuit (2). The main objective is to determine precisely the start points (4) and the end points (5) of the saturated regions (3) of the secondary circuit current signal (2) distorted by saturation.

[015] The method consists, briefly, in processing a moving window of the secondary current sampled signal (2) through a differentiating filter 2 ^to Savizky-Golay order to be presented in detail below and comparing the result with an adaptive threshold appropriately calculated , also to be detailed below. At the start points (4) and at the end points (5) of the saturated regions (3) the output value of said filter exceeds said threshold, thus establishing the criterion for detecting said points.

[016] The main advantage of the method object of the present invention compared to other methods covered by the state of the art is in the improvement of noise immunity. Furthermore, the proposed method does not depend on characteristics such as the CT magnetization curve, the remaining flux in the core, the secondary load impedance (burden) and the primary circuit time constant. Finally, the implementation of the presented method requires low computational effort, as it requires that few algebraic operations be carried out each iteration, allowing the present method to be embedded in the current numerical protection relays without restrictions regarding processing and other hardware resources.

[017] A contribution of the present invention to the state of the art lies in the use of ^the Savitzky-Golay 2nd order differentiating filter applied to the secondary current signal (2) to detect CT saturation. Another contribution is made in the development of the appropriate adaptive threshold, responsible for giving the method immunity to a wide range of noise levels. The figures presented in the drawings are listed below, accompanied by a brief description.

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List of Figures Presented in the Drawings [018] Figure 1 - Graph showing the behavior of the electrical current passing through the primary circuit of the CT and the electrical current produced in its secondary circuit, showing the effects caused by the saturation of its core.

[019] Figure 2 - Block diagram of the simulation experiment carried out to compare the proposed detection method with one of the existing detection methods in the state of the art.

[020] Figure 3 - Graph showing the behavior of ^the Savitzky-Golay 2nd order differentiating filter (t / e / 25g [«]) revealed in the present invention and its comparison with the first difference function of the low Lanczos filter noise (dellan [laughs]) already belonging to the state of the art.

[021] Figure 4 - Flowchart representative of the saturation detection method in CTs object of the present invention.

[022] Figure 5 - Graph showing the ROC (Receiving Operating Characteristic) curves of the saturation detection method in CTs based on ^the Savitzky-Golay 2nd order differentiating filter (efe / 25g [«j) revealed in the present invention and the saturation detection method in CTs based on the first difference function of the low noise Lanczos filter (dellan [n \) already belonging to the state of the art.

Description of the Invention [023] The present invention, as already discussed, refers to a method of detecting saturation of the core in a CT, with special application in situations where the electrical current of the secondary circuit (2) is immersed in noise. For the perfect description and understanding of this invention, it is unnecessary to develop two concepts that make up the core of the method: The families of Savitzky-Golay filters, with special focus on differentiating filters Family 2 ^to order Savitzky-Golay, and the adaptive threshold.

a) Savitzky-Golay filters

9/18 [024] A. Savitzky and MJE Golay proposed in their work “Smoothing and differentiation of data by simplified least squares procedures, published in the Analytical Chemistry Journal (vol. 36, n ° 8, pp. 1627-1639, 1964) method to smooth or differentiate discrete noisy data obtained from chemical spectrum analyzers based on a local least squares (LS) polynomial approximation. They showed that the coefficients c = [c ₀ ci c ₂ ... c _p ] ^T of the polynomial of degree p adjusted by LS in a data window containing 2m + l consecutive samples y = [y- _m jP-magnet-n ... jo -.- ym-i>'m] ^T (for p <2m + l) can be obtained using the equation c = (a ^t .a) ”', A ^T .y = A * .y _{( 1]} where

(-1) ° 1 1 ° (-1) '0 1' (-1) ² 0 l ² [2] (-p) ^m - (-1) 0 1

On the other hand, since the relationship between the order derivative </ (for d <p) of the polynomial in the center of the data window, represented by / ^d (0), and the coefficient c _d is fW = d \.

[3] it can be seen that the lines of matrix A * define a set of finite impulse response filters (FIR), called Savitzky-Golay filters, in which each member is able to estimate the signal value (smoothing filter ) or its derivatives (differentiating filters) in the center of the data window. Once p and w are chosen, which are related to the degree of the polynomial and the size of the window respectively, the coefficients of the FIR filters remain fixed as the data window moves in time.

10/18 [025] Simulations and experiments indicate that Savitzky-Golay 2 ^- order differentiating filters (d = 2) are the most appropriate for the detection of CT saturation. Particularly, in a preferred embodiment of the invention, a third degree polynomial (/ 7 = 3) and a window of seven samples (2m + 1 = 7) were used to obtain, through equations [1], [2] and [3] the differentiating filter 2 ⁱⁿ order Savitzky-Golay defined by del2sg equation [n) = ^ - {5 / [η] - 3 / J '- 2] - 4i _s [n - 3] - 3 / Jw - 4] + 5i _s [n - 6]}, pq where í ' _s is the sampled signal of electric current from the secondary circuit (2) of the TC and n is the index of the samples.

[026] Tests were also carried out with windows of 9 and 11 samples with polynomials of 3 °, 4 ° and 5 ° degrees, achieving satisfactory results. However, the larger the window size, the greater the computational effort required to implement the filter.

[027] Figure 2 shows the experiment carried out to prove the efficiency of the use of ^the Savitzky-Golay differentiating filter (del2sg) in the precise detection of the start points (4) and end points (5) of the regions saturated (3), where an SEP was modeled in a digital simulator in real time (Real Time Digital Simulator or RTDS). A CT installed in one of the feeder phases was also modeled in the RTDS and a phase-to-ground fault was simulated, in such a way as to produce saturation in the core of the CT. The simulated data of the secondary circuit current signal distorted by saturation (õ? Ros [«]) were captured from RTDS and inserted in MATLAB, where they were added to a white Gaussian noise (WGN), called w [«]> with respect to 40 dB signal-to-noise ratio (SNR). This noisy signal, shown in figure 3a, was subjected to a preliminary filtering stage through a Butterworth anti-aliasing low-pass filter (6), commonly found in commercial relays, and was then processed using equation [4], the result being ΔA? 2sg [«] shown in figure 3b.

[028] For comparison, the same filtered noise signal was processed using the equation

11/18 dellan [n] = i _s [«] - 9i _s [η -1] + 8/5. [n - 2] + 8i _s [«- 3] - 9i _s [« - 4] + i _s [«-5], which represents the first difference function of the low noise Lanczos filter, already known from the state of the art . The result dellan [n] is shown in figure 3c.

[029] The peak values reached by deÍ2 $ g [n] in figure 3b exactly in the samples where the start points (4) and end points (5) of the saturated regions occur (3) indicate that this function has the desired detection capability. In addition, the comparison of the results obtained by de / 2sg [n] and deJtan [n], in figures 3b and 3c, makes it clear that the first function is more robust to noise than the second, and should produce a saturation detection method more efficient.

[030] The next step is to obtain a safe value for 0 threshold that will be used as a comparison to define in which samples of / 2sg [n] detected the start points (4) and the end points (5) of the saturated regions ( 3), to be detailed below.

b) adaptive threshold

b.1) calculating [031] To use the threshold differentiating filter of order 2 Savitzky-Golay (del2sg} as an indicator the detection process, the values assumed by the output of this filter off the starting points (4) and end points (5) of the saturated regions (3) must be found.The module of the maximum value assumed under these conditions can be used as a threshold above which the start points (4) and end points (5) of the saturated regions (3). Initially disregarding the presence of noise, it can be said that, in the unsaturated regions, the current of the secondary circuit (2) of the CT is a faithful copy (on a reduced scale) of the fault current that passes through of the primary circuit of the CT. From the state of the art, it is known that, in the case of maximum asymmetry, the expression that represents the current of the secondary circuit (2),

12/18 in its digitized form with the sampling period r _S) equivalent to jV samples per cycle, is:

AM ^- Ã, 'Fmax <2π cos —nlv

[6] where l _S F max θ the peak value of the ac component of the secondary circuit current (2) and τ is the time constant of the dc component of the system fault current. Replacing [6] in [4]:

del2sg [laughs] = ~ · J _SFmax {5 cos w) - 3 cos (n - 2))

- 4cos («- 3) J - 3 cos (« - 4) ^ + 5 cos0 ^ (n - 6)

-exp ^^ J [5-3exp ^ j-4exp ^^ -3exp (^] ₊ 5exp (^)]}.

[032] In the study of transient behavior, a large number of samples per cycle is normally necessary, such that the sampling period 7 _S assumes values much smaller than the time constant τ. Assuming this hypothesis to be true, we have for T _s «τ:

exp f27 ^ <37; .j <47Ώ <67p exp ^{= 6ΧΡ} Ι \ = 1, [8] eliminating the exponential term of [7], [033] After some algebraic manipulations and using some trigonometric identities, [8] reduces up to £ / e / 2 <n] = ^ -7 _SFmax (2π á (2π «cosl —n + /? sin - n where [9] [10]

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(12τγΛ a = 5-3cos - -4 cos - -3cos - + 5 cos l / V J l n j

β = - 3sin ί 4π ^λ Λ ·

-4sin

3sin $ π

Ν + 5sin. <12 / τ [11] [034] Since ο objective is to find ο maximum value of del2sg [laughs], the derivative of [9] must be null in relation to η. The value of n that maximizes the function, called « _max , can be found by the expression

N = —arctan 2π [12]

Finally, the maximum output value del2sg [n], in the unsaturated region, can be approximated by:

max {<7e / 25g [n]} 42

Sf max acos

I n (^ ^π + B sin —n „I [13] [035] Equation [13] can be used as a threshold in the saturation detection process. However, it is necessary to adopt a margin factor (k) to adapt to the effects of noise, leading to an adaptive threshold (Tsh)

Tsh = - · kJ

SF max <2 COS

2π

I f 2π + Z? Sin —n [14] [036] In summary, the following steps should be used to obtain the adaptive threshold (Tsh) \

1) Once the sampling rate and consequently the number of samples per cycle (Ν) has been defined, the value of a and β are calculated using [10] and [11];

2) With the values of a and β, the value of n _ma x is obtained using [12];

3) Finally, the adaptive threshold is found using the value of n max in [14].

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As an example, for a sampling rate of 200 samples / cycle, the steps above lead to the following calculation for the adaptive threshold:

Tsh = 0.0009862.A. _[15] [0371 The margin factor (k) gives the threshold the adaptive characteristic, as it is related to the signal-to-noise ratio (SNR) present in the secondary current signal (2). The next step shows how to calculate the margin factor.

b.2) Calculation of the margin factor [038] The margin factor (k) is directly related to the noise output variance (σ ^,). This in turn can be obtained by the noise of the input variance (σ ² ΝΙΠ), attenuated by passage through the low-pass filter (6) in cascade with the differentiating filter 2 ⁱⁿ order Savitzky-Golay, as shown figure 2.

[039] Let eh _d (j &) be the transfer functions in the frequency domain of the low-pass filter and the 2 ^- order differentiating filter of Savitzky-Golay, respectively. As in a linear time-invariant system (LTI) the convolution in the time domain is equivalent to multiplication in the frequency domain, the cascading of the two systems can be represented by an equivalent system with a transfer function G (je>), also LTI , given by

G (y'o) = H _b (jü) \ H _D (j (0). [16]

Assuming that the noise is WGN, its power spectral density is constant and then the variance of the system output can be obtained through the energy coefficients of the G (/ o) impulse response, that is, g [n], as Follow:

=, [17] —oo where Δ is the variance gain. Using Parseval's relationship, we have:

[18]

15/18 οο 1 *

Δ = X (g [«]) ² = - J | G (») | ² άω [040] A good degree of precision can be achieved in the calculation of the margin factor assuming that the noise at the output does not exceed an amount equivalent to three times the standard deviation. In the Gaussian distribution, the probability of noise being below ^ σ _Νοια is 99.87%. Therefore, the adaptive threshold relates to the maximum output value of the

2 ^the order of Savitzky-Golay by the expression

Tsh = max {del2sg [n \} + 3rd _Nouí . _[19]

Using the well-known expression of SNR,

SNR = 20.log ¹ SF max ^σ Νίη;

[20] and considering the previous calculation of 200 samples per cycle, equations [15], [17] and [20] can be replaced in [19], obtaining, after some algebraic manipulations, + 3042 ·

[21] [041] The value of Δ to be used in [21] for calculating the edge factor is obtained by numerical integration [18] based on filter transfer functions Butterworth and differentiating filter 2 ^to order Savitzky -Golay, easily estimated by mathematical software, such as MATLAB.

[042] The margin factor (k) and, consequently, the adaptive threshold (Tsh) can be calculated for any situation, following the steps shown in sections b.1) and b.2). As an example, considering a system with a frequency of 50 Hz, a sampling rate of 10 kHz (equivalent to N = 200 samples / cycle), a low-pass Butterworth filter of

16/18 second order with a cutoff frequency of 500 Hz and the peak value of the ac component of the secondary circuit current (2) ZsF _max = 20 pu, we obtain, for SNR = 50 dB, values of k = 1.1427 and Tsh = 0.0225 pu. For SNR = 40 dB we get k = 1.4513 and Tsh = 0.0286 pu and for SNR = 30 dB we get k = 2.4271 and Tsh = 0.0479 pu

[043] To avoid unnecessary computational effort involving these calculations, the adaptive threshold values can be pre-calculated for different SNR levels and saved in a lookup table (LUT). Thus, in real-time applications, the SNR value can be predicted and continuously estimated, using methods that already belong to the state of the art, keeping updated to obtain the most appropriate adaptive threshold for detecting CT saturation as soon as a fault occurs. in the system.

The proposed method [044] Figure 4 shows the flowchart of the proposed method, which detects CT saturation through the following steps:

• Initially, there is the acquisition of the current signal from the secondary circuit of the TC, through an analog digital converter (DAC). The signal sampling (8) must be carried out at a sample rate per cycle (N) sufficient to provide the digital signal resulting from a level of resolution sufficient to allow the detection of saturation;

• The next step involves a fault detector (9), already present in the state of the art. While a fault is not detected, the SNR value is estimated (10), updated and stored in a memory unit (11). Once a fault is detected, the CT saturation detection process is effectively started;

• Using the updated SNR value and stored in the memory unit (11), the adaptive threshold value (12) is determined by reading a LUT previously built and also stored in the memory unit (11);

17/18 • The digital signal is filtered by a low-pass filter (13), to attenuate the effects of noise and harmonic components possibly present in the digitized current signal;

• The filtered signal is processed by a differentiating filter of order 2 Savitzky-Golay (14), obtaining the value of del2sg [ri \\ del2sg • The value of \ n \ is compared (15) with the adaptive threshold (Tsh), with three possibilities:

- If del2sg [n] <Tsh, the sample analyzed does not correspond to a start point (4) or an end point (5) in the saturated region (3);

- If del2sg [n]> Tsh and it is an event whose occurrence is odd (17) (1 ^a, 3 ^a, ... cases), it is detected that the entered CT saturation (18), or a starting point (4) of the saturated region (3) is detected;

- If del2sg [n]> Tsh and it is an event occurring is even (17) (2, 4 ^th, ... cases), it is detected that the CT saturation left (19), or an end point (5) of the saturated region (3) is detected.

• The entire process is then repeated with each new sample of the secondary circuit current signal (2).

[045] To attest to the high accuracy obtained by the detection process object of the present invention, several secondary current signals distorted by CT saturation were generated in RTDS, combining different scenarios with different values of fault angles, remaining flow in the CT core , burden (modulus and power factor) and primary time constant. These signals were then added to WGN with a 30 dB SNR and subjected to the saturation detection method in CTs based on ^the Savitzky-Golay 2nd order differentiating filter (del2sg [n]} revealed in the present invention and the detection method of saturation in CTs based on the first difference function of the low noise Lanczos filter (dellan [n]) already belonging to the state of the art, for comparison purposes. The start points (4) and the end points (5) of the regions saturated (3) of the first two cycles after the occurrence of the fault were classified by the “confusion matrix”, where the true positive rate (TPR),

18/18 true negatives (TNR), the false positive rate (FPR) and the false negative rate (FNR) for a wide range of thresholds. These data enabled the construction of the ROC curves for the two compared methods, which is shown in figure 5. It is observed that the proposed detection method surpasses the state of the art when applied to signals with a high level of noise.

[046] The CT saturation detection method revealed here was the start points (4) and end points (5) of the saturated regions (3) of current tested through RTDS fault simulations. The results showed that the method has high detection efficiency for noise with SNR up to 30 dB, maintaining excellent results regardless of the characteristics of the CT, the burden, the remaining flow and the type of fault. In addition, the simplicity of operations requires low computational effort, enabling implementation in real time. The test results were satisfactory for sampling rates ( A / V) between 100 and 400 samples / cycle, and using various types of low-pass filters, including a Butterworth filter of second order with cutoff frequency between 3 and 10 times higher than the system frequency value (50 Hz or 60 Hz).

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Claims (4)

1) METHOD FOR SATURATION DETECTION IN CURRENT TRANSFORMERS USING THE SAVITZKY-GOLAY FILTER comprising the steps of: sample (8) the secondary current signal (2) from the CT; detect the occurrence of a fault (9); filter (13) the secondary current signal (2) with a low-pass filter and further characterized by: determining the adaptive threshold value (12); process the filtered signal through the 2 ^- order differentiating filter Savitzky-Golay (14); compare the output value of the differentiating filter from 2 ^to Savitzky-Golay with the adaptive threshold and, through this comparison, detect a start point (4) or end point (5) of the saturated region (3). 2) METHOD FOR SATURATION DETECTION IN CURRENT TRANSFORMERS USING THE SAVITZKY-GOLAY FILTER, according to claim 1, further characterized by the fact that determining the adaptive threshold value (12) comprises: previously calculate the values of said threshold as a function of the SNR; build a LUT with the calculated values and store it in a memory unit (11); continuously estimate the SNR value (10) and keep it updated until the fault is detected (9); use the estimated SNR value to find in LUT the corresponding adaptive threshold value. 3) METHOD FOR SATURATION DETECTION IN CURRENT TRANSFORMERS USING THE SAVITZKY-GOLAY FILTER, according to claim 1, still characterized 2/2 due to the fact that the sampling step (8) the signal is performed at a sampling rate between 100 and 400 samples / cycle. 4) METHOD FOR SATURATION DETECTION IN CURRENT TRANSFORMERS USING THE SAVITZKY-GOLAY FILTER according to claim 1, further characterized by the fact that the filtering step (13) the signal is carried out with a low-pass Butterworth filter cut-off frequency between 3 and 10 times higher than the frequency of the electrical power system. 51 METHOD FOR DETECTION OF SATURATION IN CURRENT TRANSFORMER USING Savitzky-Golay Filter according to any one of the preceding claims, characterized in that the differentiating filter coefficients of the second order of Savitzky-Golay correspond to the choice of a interpolator polynomial with degree between 3 and 5 and a data window with size between 7 and 11 samples. 1/4 DRAWINGS