Poltoranina, O. A.

Rogovyh, A. V.

Vasilevskaya, E. S.

Electronic archive of Tomsk Polytechnic University

XI ぜñ¢ÑÜÖíëÜÑÖí　 ÖíÜôÖÜ-äëí¡öóôñï¡í　 ¡ÜÖâñëñÖîó　 ïöÜÑñÖöÜç, íïäóëíÖöÜç ó ½Ü¿ÜÑ▲ê Üô、Ö▲ê «ぜÜ¿ÜÑ、¢á ó ïÜçëñ½ñÖÖ▲ñ óÖâÜë½íîóÜÖÖ▲ñ öñêÖÜ¿ÜÇóó» ___________________________________________________________________________  396 DIGITAL SIGNAL PROCESSING IN PULSE METHOD FOR MEASURING FREQUENCY RESPONSE FUNCTION OF HIGH-CURRENT SHUNT O.A. Poltoranina, ん.V. Rogovyh, ぎ.S. Vasilevskaya  Tomsk Polytechnic University Lenina Avenue, 30, 634050, Tomsk, Russia E-mail: nastya_rogovyh@mail.ru  Introduction Current shunts are employed to measure high cur-rents under significant electromagnetic interference conditions [1, 2]. Investigation of dynamic behavior of the current shunt requires to measure small imped-ance of the order of dozens or hundreds of mi-croohms [3]. Classical methods for measurement of small impedances need rather expensive metrological equipment, which is available to a limited number of specialized laboratories. There are also so called pulse methods characterize high current shunt dynamic be-havior. In this approach, the shunt input is affected by a short current pulse [4]. The input and output shunt signals are measured by means of reference current to voltage transducer and a digital oscilloscope. Then a frequency response functions are calculated using a digital signal processing algorithm. The latter method provides reduced requirements to a source of the input test pulse signal of the shunt.  The object of this paper is the description of digi-tal signal processing method for measuring frequency response function of high-current shunt.  Determination of frequency response functions In order to measure the frequency response func-tion of high-current shunt, a short current pulse is applied to the shunt input; input and output signals of the shunt are recorded in a digital oscilloscope memory; then spectra of these two signals are com-puted. In practice, the test signal must be piecewise continuous. The recorded input and output shunt sig-nals are presented by N-element sequences readouts of input signal x(tk) índ output signal y(tk), where tk is an acquisition time for k-th sequence eleЦОЧЭ (1≤ k ≤ N). Discrete Fourier transform, being applied to the signals, produces spectra of the signals as complex number vectors X(fk) and Y(fk) as follows:       1 11Nj kk j NjX f x t f   ,       1 11Nj kk j NjY f y t f   ,  (1) 212i NNf e , where fk is a vector of frequencies corresponding to complex vectors X(fk) and Y(fk) obtained using the sampling length and Nyquist frequency; i is imaginary unit. Then, the shunt frequency response K(fk) can be determined by means of the expression   ( ) kkkY fK fX f.  (2) Then modulus of K(fk) is the frequency response and argument of K(fk) is the phase response. In order to determine the moving averaging time windows for the input WX and output WY shunt sig-nals, one should apply Fourier series expansion of the sequences x(tk) and y(tk). Next stage is determination ШП ЭСО ЬЩОМЭЫКХ ЛКЧНЬ 〉FX КЧН 〉FY at level -10 dB. Averaging time windows are inversely proportional to the spectra bands. That is, we have the following ex-pressions: 1XXWF, 1YYWF.  (3) Then the smoothed initial signals are calculated by the following formulae:    221XXWkj kWX k kx t x tW   ,    221YYWkj kWY k ky t y tW  .  (4) The discrete Fourier transform applied to the smoothed signals allows to have their spectral compo-sition:       1 11Nj kk j NjX f x t f   ,       1 11Nj kk j NjY f y t f   .  (5) Consequently, the accuracy of the proposed meth-od can be increased by means of uniform ensemble averaging over realizations of the smoothed signal spectral components ( )kX f and  kY f at fixed fre-quencies fk. When carrying out n measurements of the input and output shunt pulse signals, averaged spec-tral signals components ( )kX f and ( )kY f  can be found by using the following expressions:    11arg11( )nj kji X fnnk j kjX f X f en  ,    11arg11( )nj kji Y fnnk j kjY f Y f en  .  (6) Then, from expression (5), the shunt frequency re-sponse (1) can be rewritten as follows: ( )( )( )kkkY fK fX f .   (7) Uncertainty of the method for measuring shunt frequency response can be estimated by calculation of ЭСО МШСОЫОЧМО ПЮЧМЭТШЧ けxy between the spectral densi-ties output signal and the test signal as proposed in [4]: XI ぜñ¢ÑÜÖíëÜÑÖí　 ÖíÜôÖÜ-äëí¡öóôñï¡í　 ¡ÜÖâñëñÖîó　 ïöÜÑñÖöÜç, íïäóëíÖöÜç ó ½Ü¿ÜÑ▲ê Üô、Ö▲ê «ぜÜ¿ÜÑ、¢á ó ïÜçëñ½ñÖÖ▲ñ óÖâÜë½íîóÜÖÖ▲ñ öñêÖÜ¿ÜÇóó» ___________________________________________________________________________  397       2*122 21 1( )nj k j kjxy k n nj k j kj jX f Y ffX f Y f   , (8) where *jX  is a j-th conjugate complex value of the averaged signal spectral component.  Experimental studies of high-current shunt frequency and phase responses The proposed method was applied to experimen-tally determine frequency response for a coaxial high-current shunt that was designed for measurement of ЩЮХЬО МЮЫЫОЧЭ ЮЩ ЭШ β0 ¡ん [2]. The resistance of the shunt is about 170 Ohm. For this experiment, a simple pulse current source was designed. Pulse current source yields a current pulse up to 20 kA with duration 150 s. The experi-mental setup is shown in Figure 1. Shunt under testPulse current sourceComputerOscilloscopeReference currenttransformerI VSVT Fig. 1. The experimental setup diagram to determine the shunt frequency response  Figure 2 shows typical waveforms obtained from outputs of the reference current transformer (curve 1) and shunt under test (curve 2); for the sake of clarity the signals in Figure 2 are reduced to the same scale. 10 ½¡ï/Ññ¿100 ゑ/Ññ¿ (1)200 ½ゑ/Ññ¿ (2)1 2 Fig. 2. Output waveforms of reference current trans-former (curve 1) and shunt under test (curve 2)  Further, according to the proposed algorithm aver-aged spectra of signals from outputs of the reference current transformer (curve 1) and shunt under test (curve 2) were determined. These spectra are shown in Figure 3. 10 20 50 100 200 500-80-60-40-200204060Frequency, kHzSpectrum, dB 12 Fig. 3. Spectra of the signals of reference current transformer (curve 1) and shunt under test (curve 2)  Figure 4 shows final outcomes of application of the proposed algorithm to the experimental data; it can be seen that in the bandwidth up to approx. 200 kHz the shunt under test has a linear gain about -75.5 dB. a)10 20 50 100 200 500-77-76.5-76-75.5-75-74.5-74Frequency, kHzAmplitude, dB b)10 20 50 100 200 500-100-80-60-40-200Frequency, kHzPhase, degree Fig. 4. Frequency (a) and phase (b) response func-tions of the high-current shunt  Conclusion Pulse method for analysis of high-current shunts dynamic behavior has been proposed and experimen-tally investigated. The method includes ensemble av-eraging of spectral components of the pulse signals that results in increase of shunt frequency response measurement accuracy.  References 1. S.V. Muravyov, V.N. Borikov, N.M. Natali-ЧШЯК, “A МШЦЩЮЭОЫ ЬвЬЭОЦμ ЦОКЬЮЫОЦОЧЭ ШП аОХНТЧР XI ぜñ¢ÑÜÖíëÜÑÖí　 ÖíÜôÖÜ-äëí¡öóôñï¡í　 ¡ÜÖâñëñÖîó　 ïöÜÑñÖöÜç, íïäóëíÖöÜç ó ½Ü¿ÜÑ▲ê Üô、Ö▲ê «ぜÜ¿ÜÑ、¢á ó ïÜçëñ½ñÖÖ▲ñ óÖâÜë½íîóÜÖÖ▲ñ öñêÖÜ¿ÜÇóó» ___________________________________________________________________________  398 ЬЮЫРО МЮЫЫОЧЭЬ”, Measurement and control, vol. 42, no. 3, pp. 44–47, 2009. 2. S.V. Muravyov, V.N. Borikov, S.A. KКвЬКЧШЯ, “CШЦЩЮЭОЫ ЬвЬЭОЦ ПШЫ ЦОКЬЮЫОЦОЧЭ ШП welding procesЬ ЩКЫКЦОЭОЫЬ”, Proceedings of the XVIII IMEKO World Congress (September 22-27, 2006, Rio de Janeiro, Brazil), 2006. 3. I.A. εОЭаКХХв, “CШКбТКХ-Cable Wound Rogowski Coils for Measuring Large-Magnitude Short-DЮЫКЭТШЧ CЮЫЫОЧЭ PЮХЬОЬ”, IEEE Transactions on Instrumentation and Measurement, vol. 62, no. 1, pp. 119-128, 2013. 4. Mathews J., Fink K. Numerical Methods us-ing MATLAB, Prentice Hall, Upper Saddle River, New Jersey, 1999.  でごでどぎぜん がごでどんぞぴごだぞぞだざ とんずごゐづだゑとご でづぎがでどゑ ごげぜぎづぎぞござ で ごでぢだずぽげだゑんぞごぎぜ どぎびぞだずだゎごご ゑごづどばんずぽぞぼび ぢづごゐだづだゑ LABVIEА びÜÑÜÖÜÇÜçí ず.ご. どÜ½ï¡óú äÜ¿óöñêÖóôñï¡óú ÜÖóçñëïóöñö 6γ4050, づÜïïó　, Ç. どÜ½ï¡, äë-ö ずñÖóÖí, γ0 E-mail: likhud@tpu.ru  ゑçñÑñÖóñ ぢñëïäñ¡öóçÖ▲½ Öíäëíç¿ñÖóñ½ ç íçöÜ½íöó£í-îóó ½ñöëÜ¿ÜÇóôñï¡óê óïï¿ñÑÜçíÖóú 　ç¿　ñöï　 Ñó-ïöíÖîóÜÖÖí　 ¡í¿óßëÜç¡í ïëñÑïöç ó£½ñëñÖóú. がó-ïöíÖîóÜÖÖí　 ¡í¿óßëÜç¡í äëñÑÜïöíç¿　ñö ï¿ñÑÜ0-àóñ âÜÖ¡îóÜÖí¿áÖ▲ñ çÜ£½Ü¢ÖÜïöó [1]:  ÜÑí¿ñÖÖÜñ Üäëíç¿ñÖóñ ó£½ñëóöñ¿áÖ▲½ ÜßÜëÜÑÜçíÖóñ½ ó ñÇÜ ½ÜÖóöÜëóÖÇν  äëÜçñÑñÖóñ ó£½ñëñÖóú Öí ïöÜëÜÖñ ¡¿óñÖ-öí, Üäëíç¿ñÖóñ ¡ÜöÜë▲½ó äëÜóïêÜÑóö ÑóïöíÖîó-ÜÖÖÜ ï äÜ½Üàá0 ïäñîóí¿áÖÜÇÜ ¡í¿óßëÜçÜôÖÜÇÜ ÜßÜëÜÑÜçíÖó　. ゎ¿íçÖ▲½ ÖñÑÜïöíö¡Ü½ ½ÖÜÇóê ïóïöñ½ ¡í¿óß-ëÜç¡ó 　ç¿　ñöï　 öÜ, ôöÜ ÜÖó äëñÑÖí£ÖíôñÖ▲ Ñ¿　 äëó½ñÖñÖó　 ¿óüá ç ¡ÜÖ¡ëñöÖ▲ê ÜëÇíÖó£íîó　ê Ñ¿　 ¡í¿óßëÜç¡ó ¡ÜÖ¡ëñöÖÜÇÜ ÜßÜëÜÑÜçíÖó　, í íÑíäöí-îó　 äëÜÇëí½½ÖÜÇÜ ÜßñïäñôñÖó　 öí¡óê ïóïöñ½ ¡ ÑëÜÇó½ äëóßÜëí½ ÖñçÜ£½Ü¢Öí ¿óßÜ £íöëÜÑÖóöñ¿á-Öí. ゑ ÑíÖÖÜú ïöíöáñ äëñÑïöíç¿ñÖí ïóïöñ½í ÑóïöíÖ-îóÜÖÖÜú ¡í¿óßëÜç¡ó ïëñÑïöç ó£½ñëñÖóú, ëñí¿ó£Ü-çíÖÖí　 ï äÜ½Üàá0 öñêÖÜ¿ÜÇóó çóëöÜí¿áÖ▲ê äëó-ßÜëÜç δКЛVIEА.  だäóïíÖóñ ïóïöñ½▲ ÑóïöíÖîóÜÖÖÜú ¡í¿óß-ëÜç¡ó ゑ ÖíïöÜ　àññ çëñ½　 Öí ¡íâñÑëñ とÜ½äá0öñëÖ▲ê ó£½ñëóöñ¿áÖ▲ê ïóïöñ½ ó ½ñöëÜ¿ÜÇóó (とごでぜ) どぢば ëñí¿ó£ÜçíÖí ïóïöñ½í, äÜ£çÜ¿　0àí　 äëÜçÜ-Ñóöá ÑóïöíÖîóÜÖÖÜ0 ¡í¿óßëÜç¡Ü ïëñÑïöç ó£½ñëñ-Öóú ~¿ñ¡öëóôñï¡óê çñ¿óôóÖ.  だïÖÜçÖ▲½ó ¡Ü½äÜÖñÖöí½ó ïóïöñ½▲ 　ç¿　0öï　μ ¡í¿óßëÜñ½Üñ ïëñÑïöçÜ ó£½ñëñÖóú – îóâëÜçÜú ½Ü¿áöó½ñöë NI PXI-407β, ëíßÜôóú ~öí¿ÜÖ – ÜÖó-çñëïí¿áÖ▲ú ¡í¿óßëíöÜë FХЮФО 55β0A, äñëïÜÖí¿á-Ö▲ú ¡Ü½äá0öñë (ぢと) ïÜ ïäñîóí¿ó£óëÜçíÖÖ▲½ äëÜÇëí½½Ö▲½ ÜßñïäñôñÖóñ½ (ぢだ) – äëÜÇëí½½Üú, ëí£ëíßÜöíÖÖÜú Öí ¡íâñÑëñ とごでぜ Ñ¿　 äëÜçñÑñÖó　 ÑóïöíÖîóÜÖÖÜú ¡í¿óßëÜç¡ó. ゑ£íó½ÜÑñúïöçóñ ½ñ¢-ÑÜ ¡í¿óßëÜçÜôÖ▲½ ÜßÜëÜÑÜçíÖóñ½ ó ぢと ÜïÜ-àñïöç¿　ñöï　 ôñëñ£ GPIB óÖöñëâñúï. でóïöñ½í ç▲äÜ¿ÖñÖí ç íëêóöñ¡öÜëñ «¡¿óñÖö-ïñëçñë», äÜ£çÜ¿　0àñú ÜëÇíÖó£Üçíöá äëÜçñÑñÖóñ Öñ£íçóïó½▲ê ó£½ñëñÖóú Öí ÜÑí¿ñÖÖ▲ê ó£½ñëóöñ-¿　ê ï ÜÑÖÜÇÜ ¡Ü½äá0öñëí ó Üß½ñÖ ¡í¿óßëÜçÜôÖÜú óÖâÜë½íîóñú. づíßÜôññ ½ñïöÜ ¡¿óñÖöí ç¡¿0ôíñö ç ïñß　 öÜ¿á¡Ü ぢと ï ¡¿óñÖöï¡Üú ôíïöá0 äëÜÇëí½½▲. ぞí ïöÜëÜÖñ ïñëçñëí ÖíêÜÑ　öï　 ó£½ñëóöñ¿áÖÜñ ÜßÜ-ëÜÑÜçíÖóñ ó ぢと ï ïñëçñëÖÜú ôíïöá0 äëÜÇëí½½▲. ゑÖñüÖóú çóÑ ïóïöñ½▲ ÑóïöíÖîóÜÖÖÜú ¡í¿óßëÜç¡ó ½Ü¿áöó½ñöëí NI PXI-407β, ëíßÜöí0àñÇÜ ç ëñ¢ó½ñ ó£½ñëñÖó　 äñëñ½ñÖÖÜÇÜ Öíäë　¢ñÖó　, äëñÑïöíç¿ñÖ Öí ëóïÜÖ¡ñ 1.  づóï. 1. ゑÖñüÖóú çóÑ ïóïöñ½▲ ÑóïöíÖîóÜÖÖÜú ¡í-¿óßëÜç¡ó ½Ü¿áöó½ñöëí NI PXI-407β äÜ äñëñ½ñÖ-ÖÜ½Ü Öíäë　¢ñÖó0  ぢëÜÇëí½½í Ñ¿　 ïóïöñ½▲ ÑóïöíÖîóÜÖÖÜú ¡í-¿óßëÜç¡ó ÖíäóïíÖí ç ïëñÑñ ëí£ëíßÜö¡ó LabVIEW ДβЖ. ぢëÜÇëí½½í ç¡¿0ôíñö ç ïñß　 Ñçí çóëöÜí¿áÖ▲ê äëóßÜëí (ゑぢ)μ «でñëçñë-ゑぢ», £íäÜï-¡íñ½ÜÇÜ Öí ぢと, ÖñäÜïëñÑïöçñÖÖÜ ïÜñÑóÖñÖÖÜ½ ï ó£½ñëóöñ¿áÖ▲½ ÜßÜëÜÑÜçíÖóñ½, ó «と¿óñÖö-ゑぢ», ¡ÜöÜë▲ú £íäÜï¡íñöï　 Öí ëíßÜôñ½ ½ñïöñ ¡¿óñÖöí.  が¿　 ¡Üëëñ¡öÖÜú ëíßÜö▲ «でñëçñë-ゑぢ» ïñëçñë-Ö▲ú ぢと öëñßÜñö ÜïöíÖÜç¡ó äëÜÇëí½½ÖÜú ïëñÑ▲ δКЛVIEА ï ÖíßÜëÜ½ ïäñîóí¿áÖ▲ê ÑëíúçñëÜç Ñ¿　 ¡ÜÖ¡ëñöÖÜÇÜ ÜßÜëÜÑÜçíÖó　, ÜôíïöçÜ0àñÇÜ ç äëÜ-îñïïñ ¡í¿óßëÜç¡ó. がëíúçñëí ÖíêÜÑ　öï　 ç Üö¡ë▲öÜ½ ÑÜïöÜäñ ó ½ÜÇÜö ß▲öá ÖíúÑñÖ▲ Öí ïíúöñ ¡Ü½äíÖóó National Instruments (NI) [3]. «と¿óñÖö-ゑぢ» ½Ü¢ñö ß▲öá Üö¡ë▲ö ó £íäÜàñÖ Öí ¿0ßÜ½ ¡Ü½äá0öñëñ, ó½ñ0àñ½ ç▲êÜÑ ç ごÖöñëÖñö. ぢëó ~öÜ½ ¡¿óñÖöï¡óú ぢと Öñ öëñßÜñö ÑÜäÜ¿Öóöñ¿á-ÖÜú ÜïöíÖÜç¡ó ¡í¡ÜÇÜ-¿óßÜ ぢだ ó¿ó ÑëíúçñëÜç.  ずÜÇó¡í ç£íó½ÜÑñúïöçó　 ïñëçñëÖÜú ó ¡¿óñÖö-ï¡Üú ôíïöó äëÜÇëí½½▲ Üäóï▲çíñöï　 ï¿ñÑÜ0àó½ 

Digital signal processing in pulse method for measuring frequency response function of high-current shunt

http://earchive.tpu.ru/bitstream/11683/70301/1/conference_tpu-2013-C04_p396-398.pdf

Digital signal processing in pulse method for measuring frequency response function of high-current shunt

Abstract

Similar works

Full text

Available Versions

Electronic archive of Tomsk Polytechnic University