A Novel Small Signal Power Line Quality Measurement System

Transcription

1 IMTC 3 - Istrumetatio ad Measuremet Techology Coferece Vail, CO, USA, - May 3 A ovel Small Sigal Power Lie Quality Measuremet System Paul B. Crilly, Erik Leadro Boaldi, Levy Ely de Lacarda de Oliveira, ad Luiz Eduardo Borges da Silva *Departmet of Electrical ad Computer Egieerig Uiversity of Teessee Koxville crilly@utk.edu, telephoe: (865) , fax: (865) Departameto de Egeharia Electroica Federal Uiversity at Itajuba Itajuba, MG 375- P.O. Box 5 Brasil leborges@iee.efei.br, telephoe: (55 35) Abstract - We ivestigate a techique to measure low level power lie harmoics usig adaptive cacellatio of the fudametal compoet. The techique reduces the effect of quatizatio oise ad exteds the dyamic rage of the aalog-todigital coverter (ADC). It also eables good accuracy with a reduced bit ADC. Keywords - Adaptive filterig, powerlie quality measuremets, power lie harmoic measuremets. I. ITRODUCTIO I order to characterize power lie quality for a 6 Hz power trasmissio lie it is ecessary to accurately ad precisely measure the voltage levels produced by the harmoic cotet of the 6 Hz sigal. This is ormally accomplished by digitizig the trasmissio lie voltage via a aalog-to-digitalcoverter (ADC) with the values fed to a computer system to be recorded ad processed. While i theory this is readily doe, i practice because the ADC has a limited dyamic rage, it is relatively difficult to ecoomically measure small sigals i the presece of a strog 6 Hz compoet. Dyamic rage is the ability of a ADC to digitize sigals of various amplitudes so that large sigals do ot overload the ADC ad either do small sigals get buried i the quatizatio oise. For example, a -bit ADC with /- volt iput has = 496 quatum levels ad thus ca accurately digitize sigals that rage from /- volts to /-.4 mv. A similar 6-bit ADC ca digitize sigals that rage from /- volts to /-.5 mv. However, the cost of the 6 bit ADC is much greater tha the bit ADC. To uderstad the difficulties ivolved, lets cosider measurig the harmoics of a, voltpeak-to-peak (V-p-p) 6 Hz trasmissio lie that has bee scaled dow by a factor of ad iputted to the above volt ADC. With a KV-p-p iput, we ca digitize harmoics as low as /-.4 V-p-p. If we had a similar 6 bit ADC, we could digitize harmoics as low as /-.5 V-p-p. II. PROPOSED SOLUTIOS There are several methods that could be employed to exted the ability of a ADC to accurately measure small voltage quatities i the presece of a large sigal. The first is usig a process kow as compadig whereby we first compress the iput sigal usig a logarithmic amplifier prior to digitizatio ad the later expad the sigal []. Compadig icreases the sigificace of small sigals ad de-emphasizes the larger sigals. However, good quality time-ivariat logarithm circuits are relatively expesive ad still may ot have the precisio we eed. Aother approach is to miimize the 6 Hz sigal altogether ad prevet it from gettig ito the ADC ad so cause the harmoics to occupy the full dyamic rage of the ADC. Assumig the 6 Hz compoet is times, greater tha the harmoics, its elimiatio would icrease our dyamic rage by a factor of ad thus i the above KV case, ad 6 bit ADCs could quatize sigals as low as.4 mv p-p ad.5 mv p-p respectively. Removig the 6 Hz fudametal compoet could be doe i two ways. The first is to use a otch filter where the 6 Hz sigal is filtered out. This solutio has several difficulties however. I our KV example, removig the 6 Hz compoet so that the harmoics occupy the full ADC dyamic rage would require a otch filter with a atteuatio factor of or 3 db. This is ot easily doe with discrete aalog compoets ad is virtually

2 impossible to do o a itegrated circuit (IC). Furthermore, its ceter frequecy is ot easily chaged ad therefore would ot be easily adaptable to situatios where the lie frequecy varies. Fially, to measure eve the smallest higher order harmoic(s) may require us to also remove ay sigificat d, 3 rd or higher order harmoic compoet. Addig additioal otch filters to do this would be relatively cumbersome. We propose usig adaptive cacellatio [] to elimiate the 6 Hz compoet from gettig ito the ADC. This system has the followig advatages over the otch filter: (a) the etire measuremet system could be put o a IC, (b) it will work i cases where the fudametal frequecy sigificatly deviates from 6 Hz, ad (c) is easily expaded to cacel out other higher order harmoics. III. ADAPTIVE CACELLATIO SOLUTIO The idea of adaptive cacellatio is to elimiate the 6 Hz compoet ad leave us the harmoic fuctio to be digitized ad measured. Let Eq. () describe a power lie sigal with harmoic cotet: x( t) = A cos(π 6 t θ ) B cos(π 6 t φ ) = () where the first term represets the 6 Hz sigal ad with A ad θ the respective magitude ad phase values. The secod term represets the power lie harmoic cotet with B ad φ the respective magitude ad phase of the th harmoic. It should be oted that we are ultimately iterested i digitizig ad measurig oly harmoics. It is possible for some deviatio i the 6 Hz frequecy to occur ad so Eq () ca be modified to be x( t) = A cos( π f t θ ) B cos(π 6 t φ ) = () where f = 6 ± is the fudametal lie frequecy ad is the amout of deviatio from 6 Hz. The uderlyig assumptio for this project is that the overall power quality is somewhat reasoable ad that we are really tryig to accurately measure trace amouts of harmoic cotet. We ca therefore say that B A. ow lets cosider the adaptive cacellatio system show i Fig. As idicated, we sythesize a replica of the 6 Hz term i Eq. () givig y( t) = M cos( π f t θ ) (3) The y( t) ad x( t ) sigals are the subtracted givig us ε ( t) = x( t) y( t) (4) = A cos( π ft θ ) B cos(π 6 t φ ) = M cos( π f t θ ) By adjustig the values of M, f, ad θ to be equal to A, f, ad θ respectively we get (5) = ε ( t) = x( t) y( t) = B cos(π 6 t φ ) Fuctio ε ( t) represets the harmoic cotet of the power lie sigal we are ultimately iterested i digitizig. It is the fed to the ADC ad computer system.

3 It should be oted that geeratig ε( t) ivolves miimizig fuctio ε ( t). This is doe by adjustig the values miimize fuctio [ ] M, f, ad θ to ε ( t) = x( t) y( t). There are several to perform this miimizatio process. If the respective fuctios are smooth ad do ot have local miima, we ca use a gradiet algorithm to solve for the respective values of M, f, ad θ that miimize ε ( t). If the fuctios are more complicated we could resort to more sophisticated algorithms such as liear ad oliear programmig, geetic algorithms or simulated aealig [3]. x(t): power lie sigal with harmoics ε(t): harmoics oly To ADC - ~ Phase adjustme t 6 Hz sie wave referece referece Frequecy adjustmet Magitude adjustme t Figure. Adaptive cacellatio filter to remove 6 Hz compoet. If the system has other sigificat compoets that are prevetig us from accurately digitizig trace harmoic cotet, we could exted the adaptive cacellatio filter to also remove these high level sigals. We merely geerate a replica(s) of the offedig sigal(s), subtract it from the power lie sigal, ad adjust the magitude(s), phase(s) ad frequecy(s) values to miimize the absolute value of the summers output. IV. EXPERIMETAL Figure describes the practical implemetatio of the adaptive cacellatio system. It works as follows. Fuctio x(t) is the 6 Hz iput sigal with the harmoics that we wish to measure. The referece sigal used to cacel out the 6 Hz compoet i x(t) is geerated via a digital source ad the coverted to aalog form usig a digital-toaalog coverter (DAC) ad a Bessel low pass filter. The relatively pure 6 Hz referece output of the Bessel filter is the subtracted from x(t) via a summig module givig us a error fuctio, ε(t). Fuctio ε(t) is the digitized givig us ε() which used by the least-mea-squared (LMS) module to adjust the refereces magitude ad phase causig the 6 Hz compoet i x(t) to be mostly caceled out. Thus, fuctio ε() cotais oly the harmoic cotet which is what we wish to accurately measure. I this particular case, it was assumed that there was oly a global miima ad therefore the LMS module uses the covetioal gradiet ad miimum measquared error algorithm to adjust the referece sigals magitude ad phase i order to miimize error term ε ( ). ote that i this particular case, we assumed that the 6 Hz lie frequecy is a give ad therefore, oly the magitude ad phase will be adjusted to cacel the 6 Hz compoet. Test sigal x(t)s spectrum is show i Figure 3. ote that the iput sigal has frequecies of 6 Hz, Hz, 8 Hz ad 4 Hz with the harmoic amplitudes beig /64 of the 6 Hz amplitude. As Figure 3 idicates, the harmoics are barely observable i the frequecy domai. Figures 4 is the ideal harmoic spectrum with Figure 5 actual result usig the system of Figure. Figure 6 is a multidimesioal plot showig error versus referece amplitude ad phase.

4 x(t) ε(t) ε() ADC - 6 Hz source DAC Bessel LPF Phase advace/ihibit Magitude adjustmet LMS Algorithm Figure. Test system for adaptive cacellatio filter to remove 6 Hz compoet. Magitude.6 Magitude Frequecy, Hz. Figure 3. Spectrum of iput sigal Frequecy, Hz Figure 4. Expected spectrum of harmoic cotet..8 Magitude ER RO 4 R Frequecy, Hz Phase (radias) Amplitude Figure 5. Actual spectrum obtaied by system. Error X Amplitude X Phase Figure 6. LMS error versus phase ad magitude.

5 V. COCLUSIOS We have described a system that causes the relatively large 6 Hz fudametal compoet to be caceled from a power lie sigal ad thereby maximizig the dyamic rage of the ADC. This i tur eables us to accurately measure these harmoics. This of course is a prelimiary ivestigatio ad more testig of the method has to be doe. We have also ot cosidered sigals that have bee corrupted by radom oise. REFERECES [] A.B. Carlso, P.B. Crilly ad J. C. Rutledge, Commuicatio Systems. ew York, Y: McGraw-Hill,. [] Widrow, B., ad Stears, S.D., Adaptive Sigal Processig. Eglewood Cliffs, J: Pretice-Hall, 984. [3] Pham, D.T., ad Karaboga, D., Itelliget optimisatio techiques. ew York: Spriger,.