A New Calibration Method for Current and Voltage Sensors Used in Power Quality Measurements

Transcription

1 IMTC 26 Instrumentaton and Measurement Technology Conference Sorrento, Italy Aprl 26 A New Calbraton Method for and s Used n Power Qualty Measurements Pedro M. Ramos, Nuno B. Brás and A. Cruz Serra Insttuto de Telecomuncações, Department of Electrcal and Computer Engneerng, Insttuto Superor Técnco, Techncal Unversty of Lsbon Av. Rovsco Pas 1, Lsbon, Portugal Phone: , Fax: , Emal: pedro.ramos@lx.t.pt Abstract calbraton plays an mportant role n nstrument development and accuracy. Ths paper presents a method to calbrate current and voltage sensors specally dedcated to power qualty measurements whch can sgnfcantly reduce the dstortons ntroduced by the sensors. The frst approach to sensor calbraton s based on the response of sensors to DC values mposed by a calbrator. The second method s an AC calbraton, where a 5 Hz power sgnal s appled to the sensors also through a calbrator. The calbraton coeffcents are obtaned by mnmzng the output dstorton. The mnmzed output dstorton s assessed by the sgnal to nose and dstorton rato (SINAD) at the output of the sensor correcton module. Keywords power qualty, sensor calbraton, sne-fttng. I. INTRODUCTION Nonlnear loads, power utltes deregulaton and dstrbuted generaton are among the bggest contrbutors to power qualty (PQ) dsturbances [1]. The need for power qualty assessment has become consumer drven as ndustry and ndvdual consumers are becomng ncreasngly aware of the mportance of power qualty. Inexpensve, relable, flexble and accurate power qualty nstrumentaton s based on dgtal sgnal processors wth powerful algorthms for the detecton, classfcaton and measurement of the varety of PQ dsturbances. Wthn these nstruments, two very mportant components are the analog to dgtal converters (ADC) and the voltage/current sensors. calbraton s very mportant snce an ncorrect calbraton can mask some PQ events makng them undetectable by the algorthms. The easest way to mplement sensor calbraton s by applyng a correcton polynomal to the acqured samples. Ths polynomal s also responsble for the requred scalng and bascally amounts to nvertng the transfer functons of the sensors and the ADC. In ths paper, voltage and current close loop Hall effect sensors are calbrated usng dfferent methods to estmate the best coeffcents for a polynomal correcton functon of the measured ADC samples. Dfferent compensaton technques were developed for closed loop Hall Effect transducers to mprove lnearty [2]. Such technques can be combned wth the proposed calbraton method to mprove overall sensor lnearty. However, the methods developed n [2] are lmted to sensors wth a hole for the prmary wndng and are optmzed to decrease total harmonc dstorton (THD). II. THE HALL EFFECT SENSORS The calbraton method was developed usng a closed loop compensated Hall Effect current transducer (LA 25-NP [3]) and a closed loop compensated Hall Effect voltage transducer (LV 25-P [4]) both from LEM. Accordng to the manufacturers specfcatons, the voltage sensor has an overall accuracy of.9 %, lnearty error below.2 %, nomnal nput voltages up to 5 V RMS, draws a nomnal prmary current of 1 ma and outputs a nomnal current of 25 ma. The output current s fed to a 12 Ω resstor and the voltage drop n ths resstor s sampled by a data acquston board. The current sensor as an overall accuracy of.5 %, lnearty error below.2 % and s confgured to operate up to 8 A of nomnal current wth an output nomnal current of 24 ma. The sensor output s also fed to a 12 Ω resstor for current to voltage converson. The sensors are assembled n a sensor box, whose basc schematc s presented n Fg. 1. Ths setup s used to acqure smultaneously the current and the voltage suppled to a specfc load. Supply Output Output Load Fg. 1 Power network sensor box schematc contanng current and voltage sensors. The sensor outputs are voltages sutable for drect connecton to data acquston boards. The sensor box can be used to montor the current and voltage provded to a load or just to montor the power grd voltage n a specfc access pont. In ths confguraton no load s connected /6/$2. 26 IEEE 2283

2 III. CALIBRATION MEASUREMENT SETUP To calbrate the sensor box the expermental setup ncludes a PC controlled (IEEE 488.2) Wavetek 91 calbrator. The PC s also equpped wth a Natonal Instruments bt data acquston board (DAQ) to acqure the sensor outputs. The voltage calbraton archtecture s shown n Fg. 2 whle n Fg. 3 the equvalent crcut for current measurement s presented. The purpose of the calbraton procedure s to fnd a functon F( m ), to be mplemented n the correcton module, that mnmzes the error between the correcton functon output c = F( m) and the sensor nput sgnal at nstant t. A schematc representaton of the correcton procedure appled to the nput sgnal s presented n Fg. 4. Input Sgnal x() t Samplng Frequency fs DAQ m Dgtzed Samples Correcton a Coeffcents k Correcton Functon c Corrected sample values Fg. 4 Schematc descrpton of a sensor functon correcton. Fg. 2 sensor calbraton setup. The correcton functon s a polynomal functon descrbed by ( ) F x M a k k x k= = (1) where M s the order of the polynomal functon. Ths allows good results n the calbraton process and s also a smple computatonal expresson whch can be easly mplemented n DSP based nstrumentaton. IV.DC CALIBRATION METHOD Fg. 3 sensor calbraton setup. A prevously developed software platform based on LabVIEW and XML that allows easy acquston, control of the calbrator and process structured data comng from several acqustons was used [5]. An analog nput sgnal x( t ) s appled to each sensor. The sensor output s then dgtzed by the DAQ orgnatng the measured values m wth = 1 N where N s the number of acqured samples at relatve tme nstants t = ( 1) fs ( f S s the DAQ samplng rate). The dgtzed record of samples m s then fed to a correcton module that should output the value of x() t at nstant t. Ths way, the sensor and DAQ transfer functons are nverted n the correcton module to obtan an nstant estmatve of the sensor nput sgnal. The DC calbraton method conssts of controllng the calbrator to apply a set of DC voltages to the voltage sensor and determnng the a k coeffcents that mnmze the dstance between the corrected values c and the mposed DC voltages n the calbrator. The same technque s also appled to the current sensor where the calbrator now sets the DC current n the sensor box (Fg. 3). For the voltage sensor, voltages between 4 V and 4 V were appled wth the calbrator for a total of 8 dfferent test voltages. Ths voltage range corresponds to about 52 % of the DAQ range n ts ±5 V range. For each calbrator voltage, 1 samples were acqured. After the acquston, the average value was determned together wth standard devaton of the acqured samples. A weghted polynomal least-squares ft was appled varyng the order of the polynomal ft from M = 1 up to M = 9. Ths process was also performed for the current wthn the 3 A to 3 A range whch accounts for 22 % of the DAC ±5 V range. 2284

3 The valdty of the DC calbraton procedure s assessed wth a 5 Hz 23 V RMS voltage appled to the voltage sensor. 1 sets of acqustons each wth 1 samples were executed. The average power spectrum was obtaned wth the DFT and the SINAD of the corrected values was determned. It should be noted that not all of the ADC range was used, so the determned SINAD should not be used to determne the effectve number of bts of the acquston channel. However, the dfferent values of SINAD obtaned wth the dfferent order of the polynomal correcton functon can be used to compare the calbraton procedures. For the current sensor a 5 Hz, 3 A RMS current was used, and the average spectrum was also determned to estmate the SINAD and compare the dfferent order correcton polynomal usng the DC calbraton results. Fg. 5 shows the SINAD as a functon of the polynomal order ( M ). It can be seen that, for the voltage sensor, there s a steep decrease n the SINAD value for polynomal order above 2. For the current sensor, the SINAD also shows some varaton but not as relevant as the change n the voltage sensor. SINAD [db] Polynomal Order (M) Fg. 5 SINAD for the current and voltage as a functon of the polynomal correcton order for DC calbraton. The average power spectrum was obtaned from 1 sets of 1 samples. The SINAD was determned from the average power spectrum. It s clear that the SINAD s not mproved when usng hgher order polynomal correcton functons. Snce n terms of SINAD, the lnear adjustment (polynomal order M = 1 corresponds to a lnear correcton) s equvalent to not correctng the harmonc ampltudes, there are no advantages of usng hgher orders polynomals. The unmproved SINAD s mostly due to the fact that calbraton was performed at DC whch doesn t really take nto account the dstortons that the sensors ntroduce at 5 Hz. Also, the DC calbraton method s not drectly ntended to mprove the SINAD value. It merely adjusts the DC output values to the expected DC nput values. However, snce the nput sgnal s now a 5 Hz sne sgnal (ether voltage or current), t ntroduces dynamc behavor to the system (sensor and ADC) that the DC calbraton can not take nto account. V. AC CALIBRATION METHOD To take nto account the dynamc behavor of sensors and the fact that the man nput sgnal s a 5 Hz snewave, a new calbraton method was developed and mplemented. Instead of usng DC values n the calbraton step, a sne wave of 5 Hz was appled by the calbrator to the sensors. For the voltage sensor a 23 V RMS was used whle 3 A RMS were used for the current sensor. In ths stuaton, snce the nput sgnal s a 5 Hz sne, the corrected values c should correspond to the dgtzed samples of the nput sgnal at the ADC samplng rate. However, there s some nformaton mssng that s very mportant to compare the nput sgnal x( t ) wth the corrected values c. Ths nformaton s the exact value of the normalzed sgnal frequency (although the calbrator frequency s known wth very good accuracy the same does not apply to the DAQ samplng frequency) and the nput sgnal phase. In fact, snce the acquston of samples m s not trggered by the actual sgnal x( t ), the ntal phase of the samples m s a random varable wth a unform dstrbuton. In short, to compare the record c wth the samples of x( t) sampled at f S, the exact sgnal frequency of x( t ) and the phase correspondng to the frst sample must be determned. To acheve ths objectve, a four-parameter sne-fttng [6] s used to estmate the phase ( φ ) and the frequency ( f ) of the corrected values c. Afterwards a vrtual verson of the nput sgnal s now avalable () ( ) xt ˆ = A 2cos 2π ft+φ (2) RMS where A RMS s calbrator mposed value (23 V for the voltage and 3 A for the current). The polynomal correcton functon can be assessed by comparng the corrected samples c wth the sampled record of (2) at the samplng rate fs 1 f xˆ ˆ = x t = = Aef 2cos 2π ( 1) +φ. (3) fs fs To compare the records c and x ˆ, the sum of the squared errors can be used N ( xˆ ) 2 c. (4) ε= = 1 Ths cost functon amounts to quantfy the dstance between the corrected record c and the nput sne sgnal. The correcton procedure determnes the correcton functon coeffcents a k that mnmzes (4), whch s the same as maxmzng the SINAD of c. 2285

4 The optmzaton problem that leads to the best set of polynomal coeffcents can be represented by N ( ) ( ) 2 ε a,..., am = mn xˆ c (5) ak = 1 where c F( m ) =. The proposed optmzaton algorthm can be defned wth the pseudocode Algorthm Input: Acqured sensor samples ( m ) and tmestamps, ( t ) Intal estmaton of polynomal coeffcents ( a k ) for functon F( x ) Output: Coeffcents ( a k ) that mnmze the cost functon ε Body: SET ter to REPEAT INCREMENT ter CALCULATE c = F( m ) CALL SINEFIT wth t, c RETURNING φ and f f CALCULATE xˆ A 2cos 2 ( 1 ef ) fs CALCULATE ε= ( xˆ c ) 2 = π +φ N = 1 SOLVE mn () ε RETURNING new coeffcents a k a k UNTIL ( ε<εresol OR ε<εmn OR ter>maxiter) In ths algorthm, εmn s a fxed threshold for the cost functon. When ε<εmn the algorthm stops because t has acheved the desred cost functon value. εresol s the desred resoluton for the cost functon. When the algorthm fals to mprove above εresol, the algorthm stops because t has converged. The algorthm stops when the number of teratons exceeds MaxIter. Convergence depends on the ntal coeffcents. Our experence shows that, by choosng the DC calbraton coeffcents as the ntal estmates, convergence s assured. a k correcton A. SINAD Analyss In ths secton the average power spectrums of 1 sets of acqustons before and after calbraton are presented. The results were obtaned wth 991 samples per set (adjusted to reduce spectral leakage) acqured at 5 ks/s. In Fg. 6 the normalzed average power spectrum of the acqured samples c s shown. Cleary present are several sgnal harmoncs, namely the second, thrd and many more. The SINAD value s 6.1 db Fg. 6 sensor normalzed average spectrum, obtaned wth 1 sets of 991 samples each, acqured at 5 ks/s for a 5 Hz sgnal before correcton. The corrected normalzed average power spectrum s shown n Fg. 7 for the nnth order polynomal correcton functon. These results were obtaned from the uncorrected samples of Fg. 6. The frst few harmoncs wth hgher ampltudes of Fg. 6 now have much reducer ampltudes demonstratng the usefulness of the proposed correcton method. The SINAD value after correcton s 74.9 db, whch s an mprovement of 14.8 db (the equvalent of an ncrease n the number of effectve bts of 2.46) Fg. 7 Corrected voltage sensor normalzed average spectrum, obtaned wth 1 sets of 991 samples each, acqured at 5 ks/s for a 5 Hz sgnal after correcton wth 9th order polynomal functon.

5 Also note that, the hgher harmoncs have ther ampltude unchanged. Ths can be explaned by the analyss of the natural powers of a sne sgnal [7] n 1 2n 1 2n 1 2n cos( x) = cos 2 2n + 2n 1 ( n k) x 2 n 2 k = k, (6) n 2n n + 1 cos( x) = cos ( 2n 1 2k n + ) x 4 k = k. (7) Ths means that for example the 9 th power can ntroduce frequency correctons at f, 3 f, 5 f, 7 f and 9 f. Snce the power of the correcton polynomal s lmted to 9, only harmoncs up the 9 th can be corrected. In Fg. 8, the normalzed average power spectrum for the current s shown whle the corrected spectrum s shown n Fg. 9. The SINAD mproves from 59.7 db up to 68.4 db. To quantfy the mprovements, the SINAD as a functon of the polynomal order was calculated and s shown n Fg. 1, for both current and voltage sensors calbraton. SINAD [db] Polynomal Order (M) Fg. 1 SINAD value of the corrected sample values as a functon of the polynomal degree of calbraton Fg. 8 sensor normalzed average spectrum, obtaned wth 1 sets of 991 samples each, acqured at 5 ks/s for a 5 Hz sgnal before correcton. Contrarly to what happened n the DC calbraton, there s a consderable mprovement n terms of SINAD. The dfference between the mprovements obtaned n current and voltage can be consequence of the dfferent DAQ nput voltage range used n each case (42% for voltage and 3% for current) or dfferent sensor dstorton at 5 Hz. In Table I the correcton coeffcents for the voltage and current sensor obtaned wth the AC calbraton method are presented. Table I. Correcton coeffcents for the voltage and current sensor obtaned the AC calbraton method. Polynomal Coeffcent sensor a V A Fg. 9 Corrected current sensor normalzed average spectrum, obtaned wth 1 sets of 991 samples each, acqured at 5 ks/s for a 5 Hz sgnal after correcton wth 9th order polynomal functon. a A/V a V A/V 2 a V A/V 3 a V A/V 4 a V A/V 5 a6.158 V A/V 6 a V A/V 7 a V A/V 8 a9.486 V A/V

6 B. Frequency Response Analyss To assess the frequency response of the voltage sensor, a dfferent setup s used. Two Wavetek 91 are connected n seres as shown n Fg. 11. Wth ths setup t s possble to add a spurous frequency to the larger sgnal whose frequences and ampltudes can be ndependently changed. The setup s also useful to test real power qualty measurement stuatons, where a small ampltude spurous harmonc affects the power sgnal. The small ampltude spurous sgnal can also be drectly measured by a thrd dfferental channel of the data acquston board. Spurous Sgnal Ampltude [dbc] Spurous Sgnal Fg. 13 Frequency response of the spurous sgnal wth 2.3 V. The power sgnal has 23 V at 5 Hz. Clearly, the bandwdth for the spurous sgnal s much smaller than the bandwdth of the power sgnal (Fg. 12). Ths may be caused by the presence of the larger power sgnal. VI. CONCLUSIONS Fg. 11 Setup to measure the voltage sensor response to smaller ampltude spurous voltages wth ndependent control of both sgnals. Prelmnary results of the assessment of the voltage sensor nclude: () frequency response of the sensor to the large power sgnal and () frequency response of the sensor to the smaller spurous sgnal. In Fg. 12 the response of the voltage sensor to the large sgnal frequency varatons s shown. Up to 3 khz (whch s the frequency lmt of the calbrator), the frequency response of the sensor ntroduces only a maxmum loss of 2 db. Power Sgnal Ampltude [dbv] Power Sgnal Fg. 12 Frequency response of the power sgnal ampltude wthout spurous component. The frequency response of the sensor to the spurous sgnal frequency was determned wth a 23 V, 5 Hz power sgnal and a 2.3 V spurous frequency sgnal. In Fg. 13 the measured spurous sgnal ampltude s shown as a functon of the spurous frequency. A method for AC calbraton of power qualty sensors has been presented. It can mprove the measured SINAD by 14.8 db for the voltage sensor and 8.7 db for the current sensor, usng a nnth order polynomal correcton functon. The sensors bandwdth has been assessed wth a setup that allows the addton of a varable ampltude and frequency spurous sgnal. Further mprovements requre a more precse knowledge of the calbrator actual mposed sgnal to the sensors. In fact, the calbrators own THD s affectng the results snce the calbratng procedure s also tryng to correct the nput sgnal THD. However, wth the spectral composton of the nput sgnal, spectral correcton technques must be used. ACKNOWLEDGMENTS Work sponsored by the Portuguese natonal research project reference POSC/EEA-ESE/5778/24 enttled Fast and accurate power qualty measurements usng analog to dgtal converters and dgtal sgnal processng technques. REFERENCES [1] Roger C. Dugan, Mark F. McGranaghan, Surya Santoso, H. Wayne Beaty, Electrcal Power Systems Qualty, 2nd ed., McGraw-Hll, 22. [2] A Lnearzaton Method for Comercal Hall Efect L. Crstald, A. Ferrero, M. Lazzaron and R. Ottobon, Transducers, IEEE Trans. on Instrum. Meas, Vol. 5, No. 5, pp , Oct. 21. [3] Datasheet, Transducer LA 25-NP, LEM Corporaton, avalable at [4] Datasheet, Transducer LV 25-P, LEM Corporaton, avalable at [5] Nuno B. Brás, Pedro M. Ramos and A. Cruz Serra, Flexble PC measurement system based n Extensble Mark-up Language fles, 14th IMEKO Symposum on New Technologes n Measurement and Instrumentaton, Gdyna, Poland, vol. II, pp , Sept. 25. [6] Standard for dgtzng waveform records, IEEE Std , December [7] W. H. Beyer, CRC Standard Mathematcal Tables, 28th ed. Boca Raton, FL: CRC Press,