Analysis of Key Factors Affecting Electronic Transformer Calibration System Error

Transcription

1 Analysis of Ky Factors Affcting Elctronic Transformr Calibration Systm Error Mingzhu Zhang, Zhnxing Li School of Mathmatics and Statistics, Xuchang Univrsity, Hnan Provinc, China Stat Ky Laboratory of Advancd Elctromagntic Enginring and Tchnology, Huazhong Univrsity of Scinc and Tchnology, Hubi Provinc, China Abstract Rcntly, lctronic instrumnt transformrs (EIT) mt som problms such as high rror and instability in practical application, and som nw EITs and th calibration systm of lctronic instrumnt transformrs (CSEIT) ar attracting wid concrn. In this papr, som ky factors affcting CSEIT rror, including sampling synchronization, digital signals procssing and rror stimation of th calibration systm itslf, ar analysd, and th corrsponding solutions ar also offrd. Sampling synchronization is ralizd by outputting scond puls and triggr puls at th sam tim, and th lngth of pulss rspons has bn controlld in a short priod. Digital signal procssing synthsizs som spcial dsign such as FIR digital filtr, industrial frquncy masurmnt and zro-phas filtr to ovrcom th ffcts of harmonics and nois, and uss FFT intrpolatd algorithm basd on Hanning window to liminat th calculation rror whn fundamntal frquncy spctrum lakag happns. A novl rror stimation schm of CSEIT is proposd basd on th instrumnts with lowr masuring rror. Rsults of th rror stimation of th CSEIT itslf show that th systm can rach th rror of 0.0 % in magnitud and 30 scond in phas at ratd opration stat. Indx Trms Elctronic instrumnt transformr, calibration systm, intrpolation algorithm, rror stimation. I. ITRODUCTIO Elctronic instrumnt transformrs (EIT) hav bn gratly dvlopd and applid in nginring for its advantags in coping with th problm of asy saturation and scondary output signals attnuation which xist in traditional lctromagntic instrumnt transformr [, [. Howvr, th frqunt occurrnc of problms such as high rror and instability of EIT bring a larg impact on powr systm protction and control in rcnt yars [3. And ths problms hav attractd mor and mor attntion. Digital output of EIT is th main rason to chang th convntional transformr calibration systm [4. At prsnt, a lot of nginrs utiliz high-accuracy acquisition cards or instrumnts to acquir scondary output signals of EIT Manuscript rcivd May 8, 0; accptd January 6, 03. This rsarch was fundd by a grant (o. A00) from Hnan Provinc Dpartmnt of Education atural Scinc Foundation of China, and a grant (o ) from th Hnan Provinc Scinc and Tchnology Dpartmnt atural Scinc Foundation of China. [5 [7. Rfrnc [5 proposs th arlist calibration systm of lctronic instrumnt transformrs (CSEIT) on virtual instrumnt platform basd on acquisition PCI 603 card (producd by I Company). But th rror of CSEIT is big for using th card with th rror of 0.03 %. Rfrnc [6 dsigns spcial digital sampling systm as th sampling systm of rfrnc sourc signal, which stimatd rlativ uncrtainty is within in magnitud and within 40 µrad in phas. But th rror stimation of CSEIT is lack of crtain fasibility for th systm dsign is basd on th comparisons of th two sam masurmnt systms. Rfrnc [7 utilizs PCI card basd on a high-accuracy analogu-to-digital (A/D) convrtr with th rror of 0.0 % as digital sampling systm of CSEIT, whos rror xcds 0.03 % in magnitud rror and min in phas rror. But th calibration rsults chang gratly undr th condition of powr frquncy fluctuations. Although som paprs hav dscribd th ovrall dsigns of CSEIT, it is still lack of systmatic discussions for som ky tchnologis, spcially for digital signal procssing and th rror stimation of CSEIT itslf [8, [9. In this papr, som ky factors affcting CSEIT rror, including sampling synchronization, digital signals procssing and th rror stimation of th systm itslf, ar analysd, and th corrsponding solutions ar also offrd for th purpos of dsigning a CSEIT with th rror of 0.0 % which can calibrat th EITs with th rror of 0. %. II. PRICIPLE OF CSEIT A CSEIT mainly consists of thr aspcts: transformation of high-voltag rfrnc signal, synchronous sampling and communication of digital signal, and comparison btwn rfrnc signal and tstd EIT signal. Takn th CSEIT for lctronic currnt transformr for xampl, th basic principl is shown in Fig.. In Fig., th currnt boostr transforms AC 380 V into currnt sourc with rang of. tims ratd currnt of tstd EIT. Th lctronic currnt transformr (ECT) and mrging unit constitut th tstd instrumnt systm togthr. Th rfrnc currnt transformr, digital sampling systm (DSS), synchronization systm and opration platform constitut th calibration systm togthr. 39

2 Fig.. Schmatic diagram of sampling synchronization. Fig.. Schmatic diagram of calibration systm for lctronic currnt transformr. III. KEY FACTORS AFFECTIG CSEIT ERROR A. Slction of rfrnc instrumnt transformr At prsnt, th function of CSEIT is mainly basd on th comparison of two channls of signals, and th mphasis of som studis is cntralizd on th procssing of th scondary output signal. In fact, th rror of th transformation for high-voltag signal also affcts th rror of CSEIT dirctly. Although th lctromagntic currnt/voltag transformr has problms of asy magntic saturation, big siz and high cost, it has high accuracy class (0.0 % lvl or highr) and good stability undr stady stat. Hnc, th lctromagntic currnt/voltag transformr is adoptd in this papr to implmnt signal transformation of rfrnc sourc. B. Rfrnc signal sampling systm High-accuracy DSS is th ky to nsur th rationality of CSEIT dsign. Lots of paprs show that th rror of thir CSEITs can blow 0.0 % in magnitud, but th rror of sampling systm is highr than 0.0 %. It is obvious that th rror stimation of CSEIT is not nough. Th papr rcommnds som high-accuracy acquisition cards or instrumnts to dsign CSEIT for thir stability, such as HP3458A mtr with sampling prcision highr than 0.0 % and th input bandwidth as larg as 50 khz [0. C. Sampling synchronization Sampling synchronization of digital signals is critical for CSEIT. Th synchronization rror is th ky to affct th rror of CSEIT, spcially in condition that th CSEIT has diffrnt synchronization mannr of th two channl signals. Th sampling synchronization tchnology that mrging unit rcivs scond puls and DSS rcivs triggr puls is introducd for xampl. Th schmatic is shown in Fig.. ) Scond puls and triggr puls must b synchronizd in triggr puls rspons. As shown in Fig., CSEIT will choos th first scond puls ris tim aftr its start-up to triggr a low puls to stablish synchronization systm. ) Th lngth of puls rspons must b within th narrow rang. From th Fig., th lngth for two pulss is within 0 ns and th calibration rror of CSEIT for phas is lowr than 7 microsconds. D. Digital signal procssing Bsids th fundamntal wav, th input signals of th rfrnc sourc contain highr harmonic componnts and whit nois spcially whn th amplituds of th input signals ar low, th S/ ratio dcrass rmarkably and th signals rcivd by DSS contain strong intrfrnc [. Digital signal procssing should vitally bn takn into considration. Considring that not only th amplitud but also th phas of th signals ar compard in CSEIT, th phas shift of th filtr should b takn into account as wll. Th ovrall signal procssing schm is shown in Fig. 3. Fig. 3. Synchronization Schmatic diagram of digital signal progrssing. ) FIR filtr It is aimd to rmov th impact of harmonic and nois for fundamntal frquncy signals xtraction. Givn that only frquncy paramtr of th output signals nds to b obtaind, linar phas shift and signal attnuation of th filtr ar not takn into account for frquncy computing. Hnc, FIR filtr is bst undr high sampling frquncy. Th ordr and th bandwidth of FIR filtr may b slctd rasonably to gt bttr filtring rsults bcaus th CSEIT only cars about powr frquncy signal. It is rcommndd to st cut-off frquncy to 75 Hz and slct filtr ordr to 45. ) Fundamntal frquncy masurmnt Th filtrd wavform is basically sin wav. Th frquncy can b obtaind by masuring th tim intrval btwn two adjacnt zro crossing points. But th valu of th sampling points is not just qual to zro. Th tim of zro crossing can b gottn by fitting curv on th two discrt sampling points which ar bfor and bhind th zro crossing point rspctivly. Th masuring principl is shown in Fig. 4. u A u k D E u k B C Fig. 4. Th principl of frquncy masurmnt. T T u j E u j A B C D t 40

3 From th wavform in Fig. 4, th corrsponding phas angls of sampling points u k, u k, u j and u j ar small undr high sampling frquncy, and th sin wavform btwn D E can b approximatly fittd by straight lin D BE. Likwis, th sin wavform btwn D E can b approximatly fittd by straight lin D BE. Basd on similar triangl thorm, w can gt tbc tbc, t AB t AC +. Stting sampling priod ast S, tbc can b writtn as Similarly Thn () tb C t AC TS. () u j tb C TS. (3) u j u j Fig. 5. Principl of zro phas shift filtr. Th filtrd signals, compard with th original signals, ar influncd by th amplitud attnuation and phas shift. Th dsign principl of zro phas shift filtr can avoid th influnc of th phas shift, but th influnc of th amplitud attnuation must b solvd by a compnsation cofficint in dsign of IIR filtr. Th cofficint can b asily calculatd basd on th ral tim masurmnt frquncy. 4) FFT intrpolation algorithm Apparntly, powr systm frquncy cannot rmain constant. It is difficult for signal acquisition systms to maintain synchronizd sampling whn frquncy fluctuats. Whn signal sampling is synchronous, DFT frquncy spctrum at ach point coincids with spctrum of th original signal, as shown in Figur 6(a). Manwhil, thy ar not coincidnt whn signal sampling is asynchronous, as shown in Figur 6(b), whr spctrum lakag obviously xists. Window spctrum sid lob nrgy is smallr whn signals acquisition using Hanning windows, th spctrum lakag brought by convolution is lss, and th masurmnt rror would b lowr [. δ δ δ 0 0<δ < tb B ( j k) TS + tbc tbc. (4) So, th tstd frquncy can b calculatd as f. (5) tb B ( j k) TS + t BC t BC Basd on th abov analyss, th incras of th sampling frquncy is hlpful to dcras th rror of frquncy masurmnt. Furthrmor, th man valu of multipl frquncy masurmnt valus is obtaind to dcras calculation rror. 3) Zro-Phas filtr Dsign of th Zro-Phas Filtr, which has no phas shift for th fundamntal wav signals, is of grat significanc to avoid th advrs impact of phas shift on phas rror of calibration systm. Th principl shown in Fig. 5 is adoptd. It contains two idntical IIR filtrs and two dsrialization units which rvrs th tim squnc. For any frquncy componnt of x (n), if it has a phas angl of α and th first IIR filtr causs a phas shift of β, th phas angl of signal at nod A isα β. Dsrialization brings about a complx conjugat of phas angl and an additional phas shift of θ. Thus th phas angl at nod B is ( α+ β θ ). Th scond IIR filtr is th sam as th first on, so phas angl at nod C is ( α θ ). According to scond dsrialization, phas angl at nod D is xactlyα, which has no phas shift comparing with x (n). This zro phas shift charactristic rmains valid in th whol frquncy rang, which is th rason why Zro-Phas Filtr is namd. (a) (b) Fig. 6. Singl frquncy signal s spctrum: (a) synchronous sampling; (b) asynchronous sampling. From Fig. 6, (b), th fundamntal frquncy f corrsponds with digital frquncy ( P + δ ) / whn th frquncy fluctuats. In Fig. 6 (b) P is positiv intgr, is th numbr of sampl points in a priod, and 0 δ <. FFT intrpolation algorithm is introducd as follows. Supposing original input signal is j( f n+ϕ ) x(n) A, n 0,, -. (6) Th Hanning window function is w H (n) ( cos( )). (7) Th original signal X ( K ) in frquncy domain can b calculatd by DFT kn j j( f ( ) DFT[ ( ) n+ ϕ ) X K x n A n 0 ( ) sin[ ( ) j( k p ) j k p δ ϕ δ A. ( k p δ) sin[ (8) 4

4 Th signal X H (K) aftr Hanning windowing can b calculatd by DFT X H ( K) DFT[ x( n) wh ( n) DFT[ x( n)( cos( )) DFT[ x( n)( cos( )) j j + DFT{ [0.5[ x( n) x( n)( )} 0.5{ X( k) 0.5[ X( K+ ) + X( K )}. Substituting (8) to (9), th following xprssion can b obtaind) (9) sin[( K P ) ( ) δ j K P δ X ( ) { H K ( K P δ) sin[ sin[( K P ) ( δ ) δ+ j K P + 0.5[ + ( K P δ+ ) sin[ sin[( K P ) ( δ ) δ j K P jϕ + }0.5 A.(0) ( K P δ ) sin[ ( ) θ ± j Approximat quation, sin( ) θ,, can b usd whn >>. And th frquncy spctrum X H ( P ) of P point can b calculatd basd on th (0) whn K P. X H sin( δ ) [ ( δ ) jϕ sin( δ ) ( ) { P A δ ( ) δ j sin( δ ) + ( δ + ) A sin( δ ) jϕ δ ( δ ) ( ) δ + ( ) δ j ( ) δ j. } () Similarly, th frquncy spctrum X H ( P +) of ( P + ) point can b obtaind whn K P + Lt jϕ + δ A sin( δ ) X H ( P + ) () δ ( δ )( δ ) β A sin( δ) X ( ) H P δ ( δ ) X H ( P + ) A sin( δ) δ( δ )( δ) (3) Hnc δ β. (4) + β According to () and (4), th valus of industrial frquncy signal amplitud and phas angl with high prcision can b obtaind as: [δ( δ ) A X H ( P ), (5) sin( δ ) ( ) δ ϕ angl ( X H ( P )). (6) IV. ERROR ESTIMATIO OF CSEIT Th rror stimation of th dsignd CSEIT itslf is a vry important part in th dsign procss of th calibration systm. In this papr, th masuring instrumnts with highr prcision ar usd for th rror stimation of th dsignd CSEIT. A. Error stimation of magnitud Error stimation of th magnitud is ssntial to vrify th calculatd RMS valu of th rfrnc signals. Th schmatic diagram is shown in Fig. 7. Rfrnc [3 concluds that FLUKE 570A has a prcision of fiv pr tn thousand whn th output voltag is within th rang of mv to 0 mv, whil th prcision is not lowr than on pr tn thousand whn th output is ovr 0 mv. Taking output voltag U of FLUKE 570A as rfrnc and RMS valu calculatd in CSEIT U as tst subjct, th magnitud rror of CSEIT is dfind as U U rms 00%. (7) U Fig. 7. Schmatic diagram of rror stimation for magnitud. Considring th impact of frquncy rror and asynchronous sampling, th maximum, minimum and man statistical rror among 00 tsts of th rror stimation undr diffrnt frquncy (49 Hz, 50 Hz and 5 Hz) and diffrnt output voltag of Fl 570A (5 mv, 50 mv, V and 57.7 V) ar listd in Tabl I. TABLE I. TEST RESULTS OF ERROR ESTIMATIO OF MAGITUDE. Max. Man Rsults ( rms ) Min. 5 mv ,05 49Hz 50 mv V V mv ,00 50Hz 50 mv V V

5 Max. Man Rsults ( rms ) Min. 5 mv ,06 50 mv Hz V V Th rsults of rror stimation of magnitud indicat that th rror of CSEIT rachs lvl of 0.0 % in magnitud undr basic frquncy and has littl rstriction on frquncy fluctuations. B. Error stimation of phas Error stimation of phas is ssntial to vrify th tim dlay of EIT signal. Th schmatic diagram is shown in Fig. 8. BHE-I, Phas-modulation instrumnt, which provids a phas rror lowr than, outputs two idntical signals with a phas shift of ϕ btwn thm. On is capturd by oscilloscop TEK MSO3034 with high sampling rat. Th capturd phas of th oscilloscop, ϕ, is dlivrd to calibration systm. Th othr is capturd by digital sampling systm. Th phas ϕ is calculatd in CSEIT. Taking ϕ as rfrnc and ϕ ϕ as tst subjct, th phas rror of CSEIT is dfind as ϕ ϕ ) ϕ. (8) ϕ U φ U φ+ φ ( Fig. 8. Schmatic diagram of rror stimation for phas. Considring th impact of frquncy offst and asynchronous sampling, th maximum, minimum and man statistical rror among 00 tsts of th rror stimation undr diffrnt frquncy (49 Hz, 50 Hz and 5 Hz) and diffrnt output ϕ of BHE (0, ''', 5'33'' and 6'39'') ar listd in Tabl II. φ TABLE II. TEST RESULTS OF ERROR ESTIMATIO OF PHASE. Rsults ( ϕ ) Max. Min. Man 49Hz 50Hz 5Hz φ 0 0'7'' 0''' 0'5'' ''' 0'6'' -0'3'' 0'3'' 5'33'' 0'0'' -0'4'' 0'6'' 6'39'' 0'8'' -0'35'' -0'5'' 0 0'6'' -0''' 0'4'' ''' 0''' -0''' 0''' 5'33'' 0'5'' -0'3'' 0''' 6'39'' 0'5'' -0'8'' 0'4'' 0 0''' -0'4'' -0'3'' ''' 0''' -0'6'' -0'4'' 5'33'' 0'4'' -0''' -0'0'' 6'39'' -0'8'' -0'38'' -0'5'' Th rsults of rror stimation of phas indicat that th rror of CSEIT is no mor than 30 scond in phas rror undr basic frquncy and has littl rstriction on frquncy fluctuations. V. FIELD TESTS Th ntir calibration systm dsignd by this papr is applid in fild tsts of lctronic currnt transformr (ECT) and lctronic voltag transformr (EVT) in Sanxiang smart substation locatd in Guangdong, China. Th main tst rsults ar listd hr. A. Calibration of ECT An ECT with th rror of 0. % is calibratd according to th principl in Figur. Ratd primary currnt of th ECT is 300A; inhrnt dlay is 88µs. Each tst undr diffrnt input signal is tstd for 0 tims. Th statistical rsults ar listd in Tabl III. TABLE III. TEST RESULTS OF A-PHASE CURRET. Inputs Max. Min. Man 5 % Mag. Error % % % (In) Ph. Error % Mag. Error % -0.8 % % (In) Ph. Error % Mag. Error % % -0.5 % (In) Ph. Error % Mag. Error -0.0 % -0.8 % -0.4 % (In) Ph. Error % Mag. Error % -0.8 % -0. % (In) Ph. Error % Mag. Error -0.0 % -0. % % (In) Ph. Error Th rsults indicat that th magnitud rror of th ECT is lss than 0. % and th phas rror is lss than scond whn th input currnt quals to ratd valu; and th magnitud rror of th ECT is lss than 0.5 % and th phas rror is lss than 0 scond whn th input currnt unqual to ratd valu. Basd on th tst rsults and IEC standard, th rror of th tstd ECT rachs th class of 0. %. B. Calibration of EVT An EVT with th rror of 0. % is calibratd according to th principl in Figur. Ratd primary voltag of th EVT is 0kV; inhrnt dlay is 55µs. Each tst undr diffrnt input signal is tstd for 0 tims. Th statistical rsults ar listd in Tabl IV. TABLE IV. TEST RESULTS OF A-PHASE VOLTAGE. Inputs Max. Min. Man 70 %( Mag. Error 0.50 % 0.30 % 0.4 % Vn) Ph. Error %( Mag. Error 0.9 % 0.8 % 0.5 % Vn) Ph. Error %( Mag. Error % % % Vn) Ph. Error %( Mag. Error 0.78 % % 0.53 % Vn) Ph. Error Th rsults indicat that th magnitud rror of th EVT is lss than 0. % and th phas rror is lss than scond whn th input voltag quals to ratd valu; and th magnitud rror of th EVT is lss than 0. % and th phas rror is lss than 0 scond whn th input voltag unqual to ratd valu. Basd on th tst rsults and IEC standard, th rror of th tstd EVT rachs th class of 0. %. 43

6 VI. COCLUSIOS To dcras th rror of th calibration systm of lctrical instrumnt transformr, a comprhnsiv digital signal procssing mthod is proposd basd on digital filtr and FFT intrpolation algorithm. At th sam tim, th othr ky factors affcting CSEIT rror, including slction of rfrnc instrumnt transformr, rfrnc signal sampling systm, and sampling synchronization ar also discussd in this papr. Th rsults of rror stimation of CSEIT show th rror of th calibration systm basd on th proposd mthod rachs lvl of 0.0 % in magnitud and is not mor than 30 scond in phas at ratd opration stat. Th ntir calibration systm is also applid in fild tsts. Th rsults of fild tsts show that th implmntd calibration systm was succssfully applid in fild to calibrat ECT and EVT both with th rror of 0. %. REFERECES [ J. D. Ramboz, Machinabl Rogowski coil, dsign, and calibration, IEEE Transaction on instrumntation and masurmnt, vol. 45, no., pp. 5 55, 00. [Onlin. Availabl: / [ Huiqing Pan, Shulin Tian, An Adaptiv Synthsis Calibration Mthod for Tim intrlavd Sampling Systms, Mtrology and Masurmnt Systm, vol. 3, no. 3, pp , 00. [3 Ding Tao, Xu Erqiang, Masurmnt and Problm s Analysis of th On sit Error for Elctronic Transformr, Elctrical Masurmnt & Instrumntation, vol. 48, no. 3, pp , 0. [4 E. P. Suomalainn, J. K. Hällström, Onsit Calibration of a Currnt Transformr Using a Rogowski Coil, IEEE Transactions on Instrumntation and Masurmnt, vol. 58. no. 4, pp , 009. [Onlin. Availabl: TIM [5 Mi Zhi Gang, Luo Chng Mu, Dsign of Virtual Calibrator for Instrumnt Transformr, Transform, vol. 43, no. 5, pp. 5 9, 006. [6 B. Djokic, E. So, Calibration Systm for Elctronic Instrumnt Transformrs with Digital Output, IEEE Transaction on instrumntation and masurmnt, vol. 54, no., pp , 005. [Onlin. Availabl: [7 F. Pan, Y. Xu, Calibration Systm for Elctronic Instrumnt Transformrs with Analogu and Digital Outputs, in Proc. of th 9 th Intrnational Confrnc on Elctronic Masurmnt & Instrumnts, vol., 009, pp [8 Tian Qi Xu, Xiang Gn Yin, Analysis on functionality and fasibl structur of wid ara protction systm, Powr Systm Protction and Control, vol. 38, no. 3, pp , 009. [9 M. Gurbil, P. Komarnicki, Mrging unit accuracy tsting, in Proc. of th IEEE Powr & Enrgy Socity Gnral Mting, 009, pp. 6. [0 A. Brandolini, M. Faifr, A Simpl Mthod for th Calibration of Traditional and Elctronic Masurmnt Currnt and Voltag Transformrs, IEEE Transaction on Instrumntation and Masurmnt, vol. 58, no. 5, pp , 009. [Onlin. Availabl: [ Agilnt 3458A Multimtr, Usr manual. [Onlin. Availabl: 458A&smg. 000 [ F. Li, H. Wang, Ralization of high prcision harmonics analysis with plisiochronous DFT arithmtic, J Tsinghua Univrsity. vol. 39, pp , 999. [3 P. Bilski, W. Winicki, Virtual Spctrum Analyzr Basd on Data Acquisition Card, IEEE Transaction on Instrumntation and Masurmnt, vol. 5, no., pp. 8 87, 00. [Onlin. Availabl: [4 FLUKE 570A Multi Function Calibrator, Usr manual. [Onlin. Availabl: / dtail_390.html