Error of Varhour Meter s Regstraton n the Presence of Harmoncs XU YIXUN CHENG HAOZHONG XIONG HUGANG Department of Electrcal Engneerng Shangha Jaotong Unversty 954# Huashan road, Shangha 0000, P.R. CHINA Abstract: - The mportance of meterng reactve s ncreasng wth the development of electrcty market. But there are obvous defects n reactve meterng n the presence of harmoncs manly due to mstake n phase shftng. Ths paper analyzes the phase-shft errors of common used varhour meters through sequence component analyss. The frequency response tests and harmonc reactve tests are done to nducton varhour meter and sold-state meter. The test data are analyzed by least square method. The analyss show that the error contrbuton of varhour meter s regstraton n the presence of harmoncs are due to ampltude effects and phase effects through analyss of theory and experments: the phase contrbuton wll be large to both nducton varhour meter and sold-state meter and may cause meterng errors of double harmonc apparent, the ampltude s decreased wth ncreasng harmonc order and that of the nducton varhour s decreased more dramatcally. Key-Words: - Harmonc analyss; Inducton varhour meter; Sold-state varhour meter; Frequency response; Least squares methods Introducton The mportance of reactve energy meterng s ncreasng wth the development of electrcty market. Expermental and theoretcal studes concernng the accuraces of nducton watthour meters(iwhms for no snusodal waveforms have been wdely nvestgated and reported [~5]. The energy meterng n the presence of harmoncs have obtaned consderable development through tme-doman method and frequency-doman method, through consderng the mpedance of rotator, magnetc crcut and self-brake torson. These studes conclude that most practcal loads, errors of the conventonal electrodynamcs watthour meter are manly due to harmonc and harmonc current and are small wthn commercally acceptable lmts. However, a lttle nvestgaton appears to have been conducted concernng the regstraton errors of varhour meters for nonsnusodal condtons. Both nducton and sold-state varhour meters regster the fundamental dsplacement volt-ampere hours only and do not respond to dstorton volt-ampere hours for nonlnear load drven by snusodal voltages [6]. Admttedly, one must be careful n dscussng reactve and energy n the case of dstorted waveforms. However, snce utltes often employ varhour meters n conjunctons wth watthour meters to determne factors at varous measurement ponts and because harmonc levels contnue to ncrease n many *:Ths work was supported by the Teachng and Research Award Program for Outstandng Young Teachers n Hgh Educaton Insttutons of MOE, Chna systems, t s mportant that the performances of typcal varhour meters under nonsnusodal condtons be known. Although the reactve energy meterng s dfferent only from the phase between voltage and current, there s obvous defect n phase shftng. In ths paper, the basc prncples of phase shftng of an nducton varhour meter (IVHM and a sold-state varhour meter (SVHM are frstly analyzed through dvdng the harmoncs nto postve-sequence, negatve-sequence and zero-sequence. Secondly the frequency response tests and harmonc reactve tests are done to IVHM and SVHM. In the end, the test data are analyzed by least squares method(lsm. The analyss show that the errors of varhour meter s regstraton n the presence of harmoncs are due to ampltude effects and phase effects through analyss of theory and experments: the phase errors wll be large to both IVHM and SVHM and may cause meterng errors of double harmonc apparent, the ampltude s decreased wth ncreasng harmonc order and that of the IVHM s decreased more dramatcally. Characterstc of reactve energy meterng of IVHMs are some nonlnear because of the nonlnear of characterstc of magnetzaton, the varaton of mpedance of voltage col and current col, the nonlnear of torque of frcton and self-brake. So the test data s smulated synthetcally n ths paper. The test data are not properly smulated by FFT method for IVHM and SVHM are dffcult to meter the reactve energy when the phase angle near 0, So the least squares method (LSM s appled n ths paper. The
analyss shows that there are obvous defects n reactve energy meterng n the presence of harmonc. Analyss of phase shftng The basc theory of reactve energy meterng s smlar to actve energy meterng. Varhour meters can be classfed to sne and cosne type meters n terms of the connecton types and operatng theory. The cosne Varhour meters are also named cross-phase lned or artfcal Varhour meters. Ordnary SVHMs are sne Varhour meters and IVHMs may be both type (cosne manly. To meet phase angle shftng, SVHMs delay an nterval of the voltage and make the voltage lag 90 ο (Excepton the meters of usng FFT method, sne IVHMs are seres of a resstance n voltage crcut and parallel of a resstance n current crcut (So the energy loss s enlarged. Cosne IWHMs are seres of a resstance n voltage crcut. But they may make phase shftng errors n the presence of harmoncs. The detaled analyss of phase angle shftng s presented as follow. where U..., U, U0s the postve, negatve and zero. sequence of U A respectvely; I..., I, I 0 s the postve, negatve and zero sequence of I A respectvely; θ, θ, θ0 are the phase angle between postve, negatve and zero sequence voltage and current. The rght part n the equaton s the reactve:. Q= mgs ( = UI snθ + UI sn θ + UI snθ ( a 00 0. b. Analyss of Phase angle shftng of cosne IVHM The phase of sne IVHMs n the presence of harmoncs wll change lttle wth the varaton of reactance of voltage and current crcuts. The theoretcal error analyss of cosne IVHMs s smlar wth the error analyss n the condton of asymmetry. The man cause s that the phase of negatve sequence cannot be shfted correctly. However, the harmoncs ok+ order (k s non-negatve ntegerare negatve sequence. The zero sequence s not metered for the zero sequence voltages cannot flow through. When neglectng the varaton of mpedance wth harmonc order, the metered reactve can analyze as follow: The of three phase crcuts s calculated wth the defnton of plural : The plural Ṡ can be descrbed as follow:.. *. *. * A A B B C C S = U I + U I + U I... * * * 0 = ( U + U + U ( I + I + I... * * * 0 + ( α U + αu + U ( α I + α I + I... * * * 0 + ( αu + α U + U ( α I + α I + I. *. *. * 0 0 = U I + U I + U I = UI cosθ+ UI cosθ+ UI 0 0cosθ0 + j(u I snθ + U I snθ + U0I 0sn θ0 ( c Fg.. IVHMs connecton method and the voltage phasor There are some connecton methods as follow: the three phase four lnes 90 ο connecton as shown n Fg. a, the three phases four lnes wth addtonal wndngs connecton as shown n Fg. b, the three phase three lnes 60 ο connecton as shown n Fg. c. To the connecton method of Fg. c, the voltage phasor s shown n Fg.d, The voltage phase n the voltage wndng leads the orgnal 0 ο, and the ampltude s as the /of the orgnal. So the reactve shown n Fg. can be descrbed as follow:.. *. *. * Qa = mg( S = mg( U BC I A+ U CA I B+ U AB I C ( = ( UI cos( θ 90 + UI cos( θ + 90.. * *. * * BC A B AB C B Q = mg( S = mgu [ ( I I + U ( I I ] b. *. *. * BC A CA B AB C = mg( U I + U I + U I = ( UI cos( θ 90 + UI cos( θ + 90 * * Qc = mg[ ( UBC I A 0 + UAC IC 0 ] [ cos( 90 UI θ UI cos( θ 50 = + + d (4 (5
Consdered the phase angle of the negatve sequence, t can be concluded n table. Table The phase shft statstcs of IVHM Type of varhour meter compo nent 60 ο Harmo nc order Shfted phase angle descrp ton Phase error Meterng error *k+ -90 ο correct 0 ο No error *k+ +50 ο fault 40 ο May reach tmes of harmonc apparent *k+ fault Not metered *k+ -90 ο correct 0 ο No error *k+ 80 Negatve of compo +90 ο fault ο the reactve nent 90 ο *k+ fault Not metered. Analyss of Phase angle shftng of SVHMs Dfference wth the actve meterng, SVHMs meter reactve through delayng the voltage an nterval. The nterval s based on the fundamental frequency. In the presence of harmoncs, the nth harmonc phase angle wll be shfted n*90 ο, so that only 4*k+(,5,9, order harmonc can be shfted correctly. The results of analyss are lsted n table. Table The phase shft statstcs of SVHM Harmonc Shfted descrpton Phase Meterng error order angle error 4*k+ -90 ο correct 0 ο No error 4*k+ -80 ο May reach fault, counter wth -90 ο tmes of the actve harmonc apparent 4*k+ -70 ο counter wth the reactve fault, 4*k+4 0 ο wth the actve fault,same May reach tmes of -80 ο harmonc apparent Expermental Procedure The test crcut dagram, Fg., shows the prncpal components that were used n ths study. They were the harmonc generator (SW550, the unversal analyzer (PM000A, the waveform recorder (DF04, the phase shfter, the rheostat and the IVHM (DSM9- and SVHM (DSSDIV. The make and model of IVHM was the same as those commonly employed n the feld. 90 ο May reach tmes of harmonc apparent Fg.. Equpment Confguraton for Experment The SW550 provded harmonc voltage, whle the phase shfter and rheostat adjusted the current phase angle and ampltude. The DF04 was utlzed to record the mpulse from the meter. Accordng to the average nterval of mpulses, the could be gotten. The results recorded by the PM000A provded the baselne for comparson of the accuracy of the IWHM over a wde range of frequences. The test waveforms ncluded a square shape wth a wave factor less than that of the snusod, a trangular shape wth a wave factor larger than that of the snusod, whch was the fundamental plus the rd harmonc wth an ampltude / of the fundamental and the same phase as the fundamental, whch was plus the 5th harmonc wth an ampltude /5 of the fundamental, and the same phase as the fundamental, and whch was plus the 7th harmonc wth an ampltude /7 of the fundamental and the same phase as the fundamental. The waveforms of,, and were lsted n table. The test currents were A, A and 5A. The test current phase angles were ±0 ο,±0 ο,±60 ο. The phase shfter was dsabled durng sngle-phase tests, and the voltage was connected drectly from the SW550 to the meter. Table Some test waveforms Waveform Graph Math descrpton name A[sn( ωt + sn( ωt] A[sn( ωt + sn( ωt + sn(5 ωt ] 5 A[sn( ωt + sn( ωt + sn(5 ωt + sn(7 ωt] 5 7 The processng procedure was performed as follow: Step: Preprocessng Before the analyss, the metered was multpled by a parameter n terms of the apparent, whch
was measured by the PM000A. The equaton used was: Qm = Q Sbase / S (6 where P m s the modfed ; P s the metered by the IWHM; S b s the base ; and S s the apparent measured by the PM000A. Step : Development of Equatons for Parameters wth LSM Wth the same frequency, voltage, current and vared phase angle, the follow equaton s true: Q= Asn( x+ α + B (7 where Q s reactve ; A s the ampltude of the ; x s the phase angle wth whch the voltage leads the current; α s the phase shft and B s the offset of the reactve. Accordng to the LSM, the objectve functon s: n mn [ Asn( x + α + B Q] (8 = where s the number of data ponts wth vared phase angle. Step : Programmng and Calculatng The test results were recorded n an Excel sheet, and a Vsual Basc Applcaton (VBA was appled. 4 Expermental Results Frequency response experment s utlzed to analyze the bass characterstc of varhour meters n the presence of harmoncs and harmonc reactve experment s utlzed to verfy the characterstcs. There are only sngle-phase tests wth SVHM for ts symmetrcal meterng characterstcs. 4. Frequency Response On the bass of the metered data, the mathematcal model Q= Asn( x+ α + B was appled to smulate the harmonc. The maxmum smulaton error s under 0.%, whch can be neglgble to the IVHM. The parameters are lsted n Tables 4-8 and Fgures -7. Noton: - n the frst column denote negatve sequence components; A% denotes percent to the fundamental. Table 4 Frequency response parameters of IVHM when RMS of current s 5A 50 var A% 877.47 00.00 0.4.6 756.6 86..55 7.47 69.0 7.8 6. 7.56 5 556.46 6.4. -4.95 7 4.04 6.9.49 0. 9 5.60 8.79.55 -. 0.5.97 9.5-5.70 59. 8.5 6.66-7.7 5 67.6 7.7-5.7-8. - 894.89 0.99 40.96 5.7-789.80 90.0 4.79 9.4-66.95 7.59 40.5 7.56-5 5.9 59.60 4. 0.60 Table 5 Frequency response parameters of IVHM when RMS of current s A 50 var A% Offset(var 5.59 00.00 0.8.8 448.7 85.6.8 4.57 7. 70.9 5.68 0.89 5 5.79 48.09 9.79 -.8 7 8.60 5.07 9.9 -.4 9 5.9 5.86 8.7 -.7 08.64 0.75 6.6 -.09 87.6 6.7.9 -.70 5-54.76 0.47 4.50 -.4-466.76 89.5 44.7 6.4-8.84 7. 49.50 5.50-5 7.69 5.08 54.7 -.4
Table 6 Frequency response parameters of IVHM when RMS of current s A 50 var A% 7.0 00.00 0.6-4.40 44. 8.9.85 -.75 7.54 68.4 5.7-0.96 5 79. 46.05 9.40-0.5 Fg.. Ampltude of IVHM wth postve sequence harmonc n frequency response 7 57.76.58 9.68 -. 9 4.00 5.00 8.07-0.90.7 9.8 5. -0.6 8.55 6.60.85 -.85 5.50 6.69 -.95-0.84-76.40 0.55 4. -.75-50.54 87.5 44.7 0.9 -. 7.58 49.46.08-5 8.06 48.9 54.4.84 Fg. 4. Phase shft of IVHM wth postve sequence harmonc n frequency response Table 7 Frequency response parameters of SVHM when RMS of current s 5A 50 var A% 0.79 00.00 0.0 0.6 098.7 99.7 90.0 -.97 094.7 99. 79.9-4.74 4 085.95 98.56 70.77 5.58 5 080.7 98.06 0.07.90 6 057.5 95.98 89.94-9.6 7 058.86 96.0 8.0 7.74 Fg. 5. Phase shft of IVHM wth negatve sequence harmonc n frequency response Table 8 Frequency response parameters of SVHM when RMS of current s A 50 var A%.0 00.00 0.0-0.06 0.5 99.70 90.8-0.0 8.94 99.06 80.5-0. 4 6.70 98.05 70.7.74 5 5.8 97.40 0.00 0.65 6.66 95.77 90.7.80 Fg. 6. Ampltude of SVHM n frequency response 7 09.4 94.75 80.78 0.
Fg. 7. Phase shft of SVHM n frequency response From Tables 4-8 and Fgures -7, t can be concluded that: The IVHM s phase shft n the presence of postve sequence harmoncs ncreases wth the order of the harmonc from 0 ο for the fundamental to maxmum 9.79 ο for the 5 th harmonc and then decrease wth the harmonc order and vared ο wth the vared current from A to 5A. The IVHM s phase shft n the presence of negatve sequence harmoncs are about 40 ο, as verfed the analyss of phase shftng descrbed n secton. The lttle dfference between the analyss and experment s caused manly by the varaton of mpedance of cols and magnetc crcuts. The ampltude of IVHM decreases acutely wth the order of harmonc (e.g. the metered rd harmonc s 7.8% of the fundamental; the 5 th s 6.4% of the fundamental. The ampltude of SVHM decreases a lttle wth the order of harmonc (e.g. the metered rd harmonc s 99.% of the fundamental; the 5 th s 98.% of the fundamental. The proportons of ampltude and phase shft of harmonc to fundamental frequency reman constant, and ther offsets are neglgble, when the current ampltude and phase vares. 4. Harmonc Reactve Power Test The metered reactve by nducton varhour meter was smulated by equatons as follow: Q= Q + KU Isn( θ + α (9 where Q s the smulated reactve ; Q s the metered reactve of fundamental frequency; s the harmonc order; K s the ampltude rate for th harmonc; U s the RMS of th harmonc voltages; I s the RMS of th harmonc currents; θ s the phase angle between th harmonc voltage and current; α s the phase shft of th harmonc current. The results are lsted n Tables 9, 0 as follow and descrptons of wave form are shown n table. Theta column denote the phase angle between fundamental voltage and current. Svalue column denote the smulated value. Table 9 Harmonc reactve test results of nducton varhour meter (three phases Wave Theta shape ( Metered Value (var Error to tme doman (% Error to frequency doman (% Svalue (var SError (% 0 405.77-6.40.78 4.08.56 90 80.56 -.0.96 840..7 0 77.57 -.0.55 7.0 0.6 0 40. -7.7-0.0 407.9.9 90 8.97 -.7.5 80.68 0.94 0 7.6 -.59.57 75. 0.50 Table 0 Harmonc reactve test results of sold-state varhour meter (sngle phase Error to Error to Metered Wave Theta tme frequency Svalue SError Value shape( doman doman (var (% (var (% (% 0 47.45-4.54-4.90 4. -0.97 60 950.57-6.99-0.75 955.9 0.5 70 -.49-0.0 4.7-7.8 0.9 00-958.87-6.4 0.44-956.96-0.0 0-4.94-4.6-5.5-40.0-0.90 0 45.8-47.74 -.5 45.4-0. 60 9.89 -.76-4.48 97.5 0.40 70-64.76-0.5 8.70-68.90 0. 00-90.8 -.0 -.45-97.89-0. 0-460.59-47.44 -.4-456. -0.95 0 460.8-49.65 -.9 46.47 0.4 60 90.80-4.55 -.7 895.60-0.9 70-75.5-0.70 7.45-86.80 0.9 00-89.80-5.5-4.6-896.09 0.48 0-46.44-49.90 -.9-459.94-0. From Table 9 and Table 0, t can be concluded that: Equaton (9 can express the characterstcs of nducton varhour meters and sold-state varhour meters. Addtonally, the error based on tme-doman and frequency-doman dffers acutely. 5 Concluson Ths novel test-based procedure analyzes the causes of IWHM and SVHM s regstraton error n the presence
of harmoncs. The procedure nvolves a frequency response test and a harmonc reactve test wth vared current and phase angle. Analyss of theory and experment to IVHM and SVHM n the presence of harmoncs allow classfcaton of the cause by degree of contrbuton to the total error as ampltude and phase shftng, whch are descrbed as follow: The IVHM s phase shft n the presence of postve sequence harmoncs ncreases wth the order of the harmonc from 0 ο for the fundamental to maxmum 9.79 ο for the 5 th harmonc and then decrease wth the harmonc order and vared ο wth the vared current from A to 5A. The IVHM s phase shft n the presence of negatve sequence harmoncs are about 40 ο, whch may lead an absolute error to tmes harmonc apparent. Moreover the SVHM s phase shft n the presence of negatve sequence harmoncs may lead an absolute error to tme s harmonc apparent. The ampltude of IVHM decreases acutely wth the order of harmonc (e.g. the metered rd harmonc s 7.8% of the fundamental; the 5 th s 6.4% of the fundamental. The ampltude of SVHM decreases a lttle wth the order of harmonc (e.g. the metered rd harmonc s 99.% of the fundamental; the 5 th s 98.% of the fundamental. The proportons of ampltude and phase shft of harmonc to fundamental frequency reman constant, and ther offsets are neglgble, when the current ampltude and phase vares. Ths classfcaton method s helpful n understandng the characterstcs of an IVHM n the presence of harmoncs, and smulates the reactve wth the data measured by qualty devce, when the relevant parameters have been obtaned by experments. It s strongly suggested that fundamental frequency reactve and each order harmonc reactve be metered ndvdually or the apparent be metered. Because there are defects presently n reactve meterng n the presence of harmoncs. on meterng error of nducton Watthour meter. Proceedngs of the CSEE, Vol., No.4, 00, pp. 8-4. [4] Chou C J, Lu C C, Analyss of the performance of nducton watthour meters n the presence of harmoncs: a new model approach Electrc systems research, Vol., No., 995, pp. 7-79. [5] Xu Bayu, Deng Zh, Me Guhua, Lu Chunquan, Zhang Xnjan. Influence of harmonc current on meterng error of nducton phase Watthour meters. Power System Technology, Vol 6, No.9, 00, pp. 7-4,50. [6] Cox M D, Wllams T B. Inducton varhour and sold-state varhour meters performances on nonlnear loads. IEEE Transactons on Power Delvery. Vol.5, no.4, 990, pp. 678-686. References: [] Baghzouz Y, Tan O T. Harmonc analss of nducton watthour meter. IEEE Transactons on PAS, Vol.04, No., 985, pp.99-406. [] Makram E B, Wrght C L, Grgs A A, A harmonc analyss of the nducton watthour meter's regstraton error. IEEE Transactons on Power Delvery, Vol.7, No., 99, pp. 080-088. [] Deng Zh, Xu Bayu, Me Guhua, Chen Qngqan, Zhang Zhongdong. Influence of harmonc s