Current Transformer Saturation Detection By Wavelet ... - CiteSeerX

Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008

Current Transformer Saturation Detection By Wavelet Transform and Compensation By Newton’s Forward Interpolation. Sukanta Das,

Gautam Bandyopadhyay

and

Prasid Syam

current is very much necessary in the secondary side to avoid malfunction of the protective devices. This demands countermeasures against saturation of a C.T.

Abstract--Protective systems require a faithful reproduction of primary current on the Current Transformer (CT) secondary side. Saturation is a common problem in a steel core CT. Saturation problem causes dreadful effects in the protection systems. This paper presents a simple solution towards detection and compensation of current transformer saturation problems. This paper describes a method in which CT saturation is detected by Wavelet Transform (WT) based Multi-resolution Signal Decomposition (MSD) technique and the compensation of saturated signal is done by Newton’s Forward Interpolation. Various case studies are made and the results obtained are very encouraging. Keywords-- Current transformer, Multi-resolution Signal Decomposition (MSD), Newton’s Forward Interpolation, Saturation, Wavelet Transform (WT)

III. REVIEW OF THE WORK Several methods are used for detecting and compensating the distortions of the CT secondary current. Conventional way [4] of tackling this problem is to choose an oversized core so that the CT can carry up to 20 times the rated current without exceeding the 10 % ratio correction. The disadvantages are increased size and extra cost involvement of the CT. In [5] a compensating algorithm is proposed which estimates the CT magnetizing current. The magnetizing current is added to the secondary current to find the actual secondary current. The major disadvantage of this technique is that it assumes the remnant flux to be zero before the occurrence of fault. In [6] a neural network based technique is used for compensation of the CT secondary current. An Auto-Regression model based approach for compensation has been used in [7]. In [8] saturation detection technique is discussed based on some important properties of saturated waveforms. This paper presents a simple solution towards current transformer saturation problem by first detecting it with the help of Wavelet based Multi-resolution Signal Decomposition (MSD) technique and then Newton’s Forward Interpolation is used to compensate the saturated signal. Various case studies have been made and encouraging results are obtained.

I. INTRODUCTION A Current Transformer (CT) is used in power system to scale down the system current signals to an allowable level. If CT characteristic is not properly selected for fault conditions, saturation will occur which may affect the protection decisions [1]-[3]. There are events where it is necessary to locate protection devices far from the CTs. In these cases, the wire resistance, which adds to the CT burden, causes CT saturation at smaller currents than when located close to the protection devices. The impact of CT saturation is different for different protective devices and protection schemes. This paper presents a method of C.T. saturation detection and compensation so as to overcome the influence of saturation on the protective relaying scheme connected to the secondary side of the current transformer.

IV. DETECTION OF CT SATURATION BY WAVELET TRANSFORM (WT) BASED MULTI-RESOLUTION SIGNAL DECOMPOSITION (MSD) TECHNIQUE: In recent years, wavelet transform (WT) techniques have been effectively used for multi-scale representation analysis of signals to demonstrate the local or detailed feature as well as smoothed feature of a particular area of a large signal. The Fig-1 shows the WT based MSD technique that decomposes a given signal C0(n) (discrete samples) into its detailed and smoothed versions up to level-2. The detailed version of the signal contains high frequency components whenever an abrupt change in waveform takes place. Using filter analogy h(n) and g(n) are used here as low pass and high pass filters respectively (Fig-1).

II. RELEVANCE OF THE WORK CT saturation is not uncommon in power system protection application. The distorted secondary current signal of CT may be asymmetrical in nature and may contain DC offset resulting in CT saturation. This leads to incorrect bus-bar differential protection and transformer differential protection in case of an external fault [2]. For this reason, most low impedance bus-bar differential relays use CT saturation detection unit to avoid false tripping for external faults which may produce large current and significant CT saturation [3]. CT saturation leads to unnecessary delay with IDMT characteristic and coordination may be compromised. It also creates error in impedance estimation in a distance relay and as a consequence a distance relay can malfunction. In short the impact of CT saturation on protection device operation is different for different protective devices and protection schemes. In all these cases a correct replica of the primary

C0(n): Original Signal, C1 (n), C2 (n): Smooth version of the signal at level 1 and 2 respectively, d1(n),d2(n): Detailed version of the signal at level1and2 respectively. Fig – 1 334

Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 Uncompensated secondary(black),Scaled Primary(blue)& WTC(green)

To detect the saturation points WT based MSD technique is used taking (Daubechies 4) ‘db4’ as mother wavelet. As ‘db4’ is compactly supported in time frame so it can detect sudden jumps in the waveform at level-1 decomposition. In Fig.-2 blue waveform represents scaled primary current and black waveform represents saturated secondary current. In ideal case these two waveforms must remain identical in all operating conditions of the CT. But in practice these two waveforms tend to deviate whenever a CT saturates as the case has been shown in the Fig.-2. Here a1, a2, etc are the beginning of saturation points and b1, b2, etc are the end of saturation points in each cycle.

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Fig-2 The CT saturation may occur either due to excessive fault current or due to overburden in the CT secondary or due to the presence of d.c. component in the primary current. The magnitude of d.c. component depends on the instant at which the fault occurs. Extensive case studies have been made considering those three different conditions. It is seen that db4 can successfully locate each of these jumps in the saturated waveforms from the scaled primary at level-1 decomposition. CASE STUDY-I VARIABLE PRIMARY FAULT CURRENT WITH FAULT OCCURENCE INSTANT KEPT FIXED AT 0 ms AND CT BURDEN AT 1 ohm. Using the saturable CT model of MATLAB (SIMULINK) different saturated waveforms have been generated by varying the CT primary fault current keeping fault instant fixed at 0 ms (i.e., when voltage passes through Zero value) and CT secondary burden fixed at 1 ohm. The generated waveforms are plotted in Fig.3. It is noticed that large change in magnitudes of Wavelet Transform Coefficients (WTC) occurs at the starting and end of the saturation points in each cycle as shown in the Fig-3 by green waveform. In each case study WTCs are multiplied by a factor for clear observation of saturation detection.

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Fig-3 Level-1 decomposition of saturated signals with db4 as mother wavelet is shown in Fig-3(a-f) by green waveforms. Larger magnitudes of WTCs occur at the starting of the saturation and at the end of the saturation points in each cycle otherwise they are almost zero. Except the detected saturation points, a high magnitude of WTC occurs at the end of first cycle where the transient condition in the primary fault current begins. The Table3.1 shows the WTCs for the first two saturated cycles. Figure WTC at a1,b1 WTC at a2, b2 a 21.38, 25.96 55.55, 20.73 b 6.54, 9.15 15.89, 12.91 c 36.42, 3.6 10.37, 5.298 d 10.96, 3.5 5.48, 3.8 e 5.7, 2.4 4.99, 0.48 f 5.8, 1.9 3.69, 1.5 Table-3.1 CASE STUDY-II VARIABLE RESISTIVE BURDEN WITH PRIMARY FAULT CURRENT FIXED AT 1444A AND FAULT OCCURENCE INSTANT KEPT FIXED AT 0 ms.

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Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 Uncompensated secondary(black),Scaled Primary(blue)& WTC(green)

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USING

Newton’s Forward Interpolation (NFI), which is basically a process of finding the non-pivotal values, is used to obtain the new approximated points in the saturated portion of the signal with the help of unsaturated points in the signal. A detail of NFI method is given in the Annexure-A. This method is applied here on two given pairs of points just before the beginning of saturation (a1, a2,..etc, Fig2)on the unsaturated portion of the signal to find the third point. The difference table is calculated taking corresponding points from a reference signal that has been generated prior to beginning of the process by taking two values from the unsaturated portion of the signal and using the discrete equation (4) for one time period. The estimated point obtained is used to calculate next point on the saturated portion of the signal. The process will continue in this way until the end of saturation (b1, b2,….etc, Fig-2) is reached. Hence the saturation process will be carried on between two points (starting and end of saturation) in each cycle.

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WTC at a1,b1 WTC at a2, b2 5.86, 1.92 3.5, 1.5 5.7, 2.62 7.89, 1.16 Unsaturated Unsaturated Unsaturated Unsaturated 1.82,2.73 Not available 5.9, 1.92 3.69, 1.5 Table-5.1 V. COMPENSATION OF SATURATION EFFECT NEWTON’S FORWARD INTERPOLATION:

WTC at a1,b1 WTC at a2, b2 5.86, 1.9 3.69, 1.5 6.7, 0.54 3.46, 1.68 15.2, 1.42 4.5, 0.31 7.66, 0.835 3.58, 2.44 36.98, 1.6 1.3, 1.6 Table-4.1 CASE STUDY-III VARIABLE FAULT OCCURRENCE INSTANT WITH RESISTIVE BURDEN KEPT FIXED AT 1 ohm, PRIMARY FAULT CURRENT FIXED AT 1444A

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Fig-5 Fig-5(a-f) show the saturated secondary current waveforms (black) for different instants of fault occurrences. Magnitude of the d.c. content in the primary fault current varies if the fault occurring instances vary. In this case also level-1 decomposition using db4 as mother wavelet successfully determines the beginning and end of saturation in each cycle. The Table-5.1 shows the WTCs for the first two saturated cycle.

Fig-4 As the burden of the CT secondary is increased the CT reaches its saturation state earlier than the normal. The green waveforms of Fig-4 (a-e) show the WTCs of the saturated signal after level-1 decomposition using db4 as mother wavelet. The large magnitude of WTC at the end of first cycle represents beginning of transient condition of the primary fault current. The Table-4.1 shows the WTCs for the first two saturated cycles.

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Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 Compensated secondary(red)& Scaled Primary(blue)

V.A. DISCRETE MODEL OF SINE WAVE An n-th harmonic sine wave component can be expressed by the following general equation, x n  t C n sin( nZ t  I n ) ………..………….(1)

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1 ª xn ( t  2T )  xn ( t T ) xn ( t T )  xn ( t ) º  « » T ¬« T T ¼»

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following Equation can be inferred. x

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n-th frequency of the system. When difference approximation is performed on a time increment ' t using a time interval ' t=T, the following equation is obtained. The first derivative of xn (t ) i.e., xn t

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In this case time can be expressed by t=kT, so that an n-th harmonic sine component can be expressed by the following model based on equation (3).

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5.37 2.87 1.58 1.12 0.88 0.72

62.10 61.99 56.79 54.92 53.62 42.92

8.99 4.71 3.06 2.80 2.47 2.88

CASE STUDY-IIA Case study-IIA is the continuation of case study-II. Each red coloured waveform of the Fig-7(a-e) shows the compensated waveforms for each saturated waveforms (black) of case study-II and blue waveforms shows scaled primary current. Composite errors are calculated for both saturated and compensated waveforms in each condition and are tabulated in Table-7.1.

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Table-6.1 Table-6.1 shows the improvement of composite errors because of compensation. Fig-6(a-f) also shows that the compensated waveforms (red) and scaled primary current (blue) are almost overlapping.

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Case Study-IA, Load in multiple (m) of rated primary current Fault instant at 0ms & Burden=1 ohm Fig. Load Composite Error, Ce (%) No. (m) Ceuncomp Cecomp

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From equation (4), it is observed that only two points in the unsaturated section is required to estimate the reference signal. So this method of compensation is effective even when saturation starts earlier. Accurate selection of reference signal plays an important role in exactly determining the tendency of movement of the original signal. As we know that the difference table for NFI method is obtained from reference signal, which actually guides the exact path to be traced by the extrapolated points. Compensation process is carried on for the cases –I, II, III during the period in which the C.T. remains saturated. CASE STUDY-IA Case study-IA is the continuation of case study-I. Each red coloured waveform of the Fig-6 (a-f) shows the compensated secondary current and the blue coloured waveforms shows the corresponding scaled primary current. Composite errors are calculated for both uncompensated and compensated waveforms in each condition and are tabulated in Table-6.1.

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Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 Compensated secondary(red)& Scaled Primary(blue)

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Fig -7 Case-IIIA, Different fault instants Burden=1ohm & primary fault current 1444A Composite Error, Ce (%) Fig. Faulty No. Instants,ms Ceuncomp Cecomp 0 62.06 3.41 a 2 51.15 3.59 b 4 1.45, unsaturated 1.45, unsaturated c 15 0.93, unsaturated 0.93, unsaturated d 17 17.84 7.65 e 20 62.06 3.41 f Table-8.1 As the instant of occurrence of fault changes the magnitude of d.c. component changes. In Fig-8c & 8d no appreciable d.c. component was present so these are unsaturated cases as such the composite errors remain unaffected. Table-8.1 shows the composite errors in tabular form.

Case-IIA, Variable resistive burden Fault instant at 0ms & Load, m=0.72 Fig. Burden Composite Error, Ce (%) No. Ohm Ceuncomp Cecomp 1 62.06 3.14 a 1.3 70.48 3.40 b 2.0 79.42 3.62 c 3.0 85.12 4.21 d 5 88.48 8.37 e Table-7.1 The Table-7.1 shows the considerable improvement in composite errors of the compensated secondary currents. The Fig-7(a-e) also justifies the same. CASE STUDY-IIIA Case study-IIIA is the continuation of case study-III. Fig8(a-f) show the compensated secondary currents corresponding to case study-III. The composite errors are also shown in tabular form in Table-8.1.

VI. CONCLUSION In our study a wide variety of saturated secondary currents have been generated by varying the primary fault current, burden and d.c. component of the fault current. A sampling frequency of 10 KHz is used to discretize the signal (C.T. secondary current). The d.c. component of the fault current can be changed by changing the instant of occurrence of fault. The extent of saturation is quantitatively expressed by composite error. The largest composite error encountered in case IA is 62.10 % when the C.T. primary current is 5.37 X 200/5 =2.148 KA. After compensation this error has come down to 8.99 %. So a drastic reduction of 53.11% in error occurs. The largest composite error encountered in case IIA is 88.48% for a secondary burden of 5 ohm. After compensation a drastic reduction of

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Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008 u u ( u 1) 2 u ( u 1)..( u  n 1) n ' y1 ... ' y1 ……………(3) y y1  'y1  1! 2! n!

80.11% (88.48%-8.37%) occurs. The largest composite error encountered in case IIIA is 62.06 % when the d.c. current is maximum. After compensation a marked improvement of 58.65% (62.06%-3.41%) occurs. From the wide variety of saturated secondary currents studied it is evident that the present saturation detection technique can successfully detect CT saturation and subsequently bring down the effect of saturation to acceptable level by providing adequate compensation using Newton’s Forward Interpolation. The whole process of saturation detection and compensation takes approximately 1.9 ms (16x0.0001+3x0.0001 sec) for 10 KHz sampling frequency. As the proposed algorithm is extensively tested by simulation, it is expected that the algorithm can be effectively implemented in real time with the help of Digital Signal Processor kit. The authors are now trying to implement this idea and also trying to develop a faster single compact technique to replace the separate methods of detection of saturation followed by compensation.

operator. To find

' i 1 yi , where i=1,2,..,5 forward difference table r

is formed. In general ' y is called r-th order forward difference of y . The table is given as follows. x

y

'y

'2 y 'y2 'y1 ' 2 y1 'y3 'y2 ' 2 y2 'y4 'y3 ' 2 y3

x1

y1

y2  y1 'y1

x2

y2

y3  y2 'y2

x3 x4 x5

y3 y4 y5

y4  y3 'y3 y5  y4 'y4

'3 y 2 ' y2 ' 2 y1 '3 y1 ' 2 y3 ' 2 y2 '3 y2

'4 y 3 ' y2 '3 y1 ' 4 y1

Here three values of y for three given x have been considered for the present interpolation technique.

VII. REFERENCES [1] Kjovic, Lj.A., “ Impact of current transformer saturation on overcurrent protection operation,” IEEE Power Engineering Society Summer Meeting 2002, Issue, 25-25 July 2002, pp.-1078-1083, vol.-3. [2] Dave, K.,“Evaluation of differential protection relay performance during transformer inrush current & CT saturation period,” 4th Int. conference on Power System Protection and Automation, 21-22 Nov-2007, New Delhi, India. [3] Zhang, Z. et al, “A novel CT saturation detection algorithm for bus differential protection,” 4th Int. conference on Power System Protection and Automation, 21-22 Nov-2007, New Delhi, India. [4] A. G. Phadke, S. H. Horowitz, Power Systems Relaying, Research Studies Press, Taunton, 1992. [5] Kang, Y. C. et al, “Development and hardware implementation of a compensating algorithm for the secondary current of current transformers,” IEE Proc. Power Appl., vol. 143, no. 1, pp.41-49, 1996. [6] Khorashadi-Zadeh H. and Pasand, M. “Correction of saturated current transformers secondary current using ANNs,” IEEE Trans on Power Delivery, vol. 21, no. 1, pp. 73-79, 2006. [7] Kang, S. H. et al, “Method of compensating for distorted secondary current of current transformer”, United States Patent, Patent No.: US 7,127,364 B2, Date of Patent: Oct. 24, 2006 [8] Murari, Saha, M et al, “Method and device for detecting saturation in current transformers”, European Patent Application, Application No.-92105169.4, Date of filing: 26.03.92 Annexure- A: NFI method If for the equation y f ( x ) , n discrete points xi and yi , where i=1,2,3,….,n are given and if xi 1  xi

x  x0 , ' represents forward difference h

where u

Annexure- B: CT specifications: 2000:5, 25VA, 50Hz Winding 1 parameters: R1 (p.u.) =0.001 L1 (p.u.) =0.04 Winding 2 parameters: R2 (p.u.) =0.001 L2 (p.u.) =0.04 Saturation Characteristics (i (p.u.), flux (p.u.)): [0.0, 0.0; 0.01, 10.0; 1.0, 10.5] Core loss resistance, Rm (p.u.) =100 ohm AUTHORS Sukanta Das, Lecturer, Department of Electrical Engineering, Birbhum Institute of Engineering and Technology, Suri-731101, Birbhum, W.B., India. E-mail: [email protected] Dr. Gautam Bandyopadhyay, Professor, Department of Electrical Engineering, Bengal Engineering and Science University, Shibpur, Howrah-711103, W.B., India. E-mail: [email protected] Dr. Prasid Syam, Professor, Department of Electrical Engineering, Bengal Engineering and Science University, Shibpur, Howrah-711103, W.B., India. E-mail: [email protected]

h then

according to NFI method for a required x (either x1