DEVELOPMENT OF A POWER ANALYZER

Transcription

1 DEVELOPME OF A POWER AALYZER Ana M. R. Franco, M. Sc. (), Endre óh, Ph.D. (), Rosane M. Debain, M. Sc. (), Ricardo Prada, PhD. (2) () Power and Energy Laboraory (LAPE), aional nsiue of Merology Sandarizaion and ndusrial Qualiy (MERO), Duque de Caxias, CEP: , Brazil Phone (+552) , Fax (+552) lapen@inmero.gov.br (2) Ponifícia Universidade Caólica do Rio de Janeiro - PUC-RJ, Rio de Janeiro, CEP: , Brazil Phone (+552) prada@ele.puc-rio.br Absrac - hese paper gives an accoun on a new power and energy measuring sysem, based on digial sampling, ha was developed by he aional nsiue of Merology (MERO) of Brazil. he goal of he projec was o achieve he highes possible accuracy a line frequency (5 or 6Hz), even in he presence of considerable harmonic disorions, o guaranee full raceabiliy and o minimize he coss of obaining a high qualiy reference sysem. n he new sysem he programmable A/D converers of wo advanced digial mulimeers (Hewle-Packard 3458A) are used o measure he volage and curren simulaneously, by sampling mehod. he main advanage of he sysem is he high accuracy, full raceabiliy o naional sandards wihin he counry, and he possibiliy o calibrae wa-converer and wa-hour sandards also in he presence of harmonics. Principally a modified numerical inegraion mehod is applied for he calculaion of he RMS values of volage and curren, as well as ha of he acive power, power facor, apparen power and frequency, even in he presence of harmonics in he wave of volage and/or of curren. o calculae he harmonic conens a DF algorihm was developed. Currenly he new sysem is sill in a phase of ess, i has been shown very good resuls so far. 2 SRUCURE OF HE SYSEM he componens and he connecions of he sysem are shown in Figure. ROEK 8 V W C HP3458A (Volage) Keywords Sample mehods, Power, Energy, Harmonics. CH C R HP3458A (Curren) RODUCO he Power and Energy Laboraory (LAPE), linked o he Division of Elecrical Merology of he aional nsiue of Merology, Sandardizaion and ndusrial Qualiy (MERO), sill doesn' have necessary resources o reproduce he unis of power and elecric energy. he conservaion of he unis of power and energy is obained by a se of hree sandards, periodically recalibraed hrough a raveling sandard, assuring in his way he raceabiliy o S or o PB. Losses of ime and risks of damages of valuable equipmen, during he ranspor, are involved. he proposed sysem will allow he reproducion of he unis of power and elecric energy and will be direcly raceable o he oher laboraories of MERO. his sysem will enable MERO o paricipae in nernaional Comparisons of he referred unis, ogeher wih naional insiues of merology of oher counries. Due o he excellen performance of advanced A/D converers and he increasing capaciy of personal compuers, a projec, aiming a he consrucion of a Power Analyzer, based on digial sampling mehod, was iniiaed. A commercially available digial mulimeer, he HP-3458A, was applied, due o he freely programmable A/D converer of he insrumen. PC GPB Fig. - he Power Analyzer Sysem he programmable energy source is he model 8 of ROEK, responsible for he supply of he volage (V), of he curren, () and of he phase shif beween hem. W is a wameer (or wa-hour meer) o be calibraed. n he case of wa-hour meers, a pulse couner is applied ha works as a frequency meer, assuring he ime base. An auomaed swich (CH) is responsible for he connecion o he correc derivaion of he curren ransformer (C). R is an AC sandard resisor, where he volage drop on i is proporional o he applied curren. he digial mulimeers (Hewle-Packard 3458A) are used o measure he volage and curren in digiizaion mode, in DC volage (DCV) configuraion. he synchronizaion of he reading of samples is made by he conrol C. When he mulimeer ha measures he volage akes a sample, emis a pulse, forcing he oher mulimeer, ha measures curren, o ake a sample in he same ime, in a maser-slave relaionship. As Figure shows, i is possible o develop a fully auomaed sysem, wih all he componens conrolled by a personal compuer (PC). A he presen developmen sage,

2 he conrol of he volage and curren source and ha of he C is sill made manually. n he preliminary ess a resisor of Ω and a commercially available C sandard were used. Aiming a a beer performance of he sysem, a special wo-sage ransformer is being developed, which will be coupled o a sandard resisor of Ω. 3 APPLED ALGORHMS n he presen work hree algorihms were used, described as follows: 3. Swerlein Algorihm n 99 R. Swerlein [] published an algorihm, specifically for he digiizaion of sinusoidal signals, using he inernal A/D converer of he HP-3458A mulimeer. his algorihm has been esed and approved by several laboraories [2,3] and is recognized as he bes one in he direc measuremens of AC volage. During he pas decade he algorihm of Swerlein was adoped also by several naional laboraories of merology. he concep of he mehod in he algorihm of Swerlein is summarized as follows. he RMS value of a periodical volage is given by: 2 2 V = v ()d = v ( ) d C C where is he of period ime of he signal. he inegraion is execued hrough he ime or a whole muliple of i, C, where C is he number of cycles. Using he mehod of samplings, he inegral is subsiued by he sum of he samples of he digiized signal. Figure 2 shows a cycle of a sinusoidal signal, indicaing he sampling parameers. s s s Fig. 2 - A sinusoidal wave and sampling parameers On he Figure 2 s is he number of samples and s is he sampling ime (equally spaced) among hem. Generally he resoluion of he ime s is limied, inroducing errors. herefore, as shown on Figure 2, generally s s is only approximaing he ime of period. When measuring C cycles during ime τ: s s = τ C (2) () Consequenly, he error inroduced by he finie resoluion of sampling ime is given by: 2π sen τ 4π ε = sen (3) 4π τ he Swerlein algorihm is inroducing several efficien means o minimize his error. o achieve high resoluion of he inegraing A/D converer (2 bis), relaively high aperure ime is programmed, neverheless, errors occur when he signal changes during he inegraion ime. hese errors are also calculaed and compensaed. Beyond hese heoreical consideraions he acual physical parameers of he mulimeer were also aken ino accoun and correcions were inroduced wherever possible. he algorihm works well in he presence of purely sinusoidal signals, especially a low frequencies. Permissible disorion facor is max. %, highes frequency is around 2Hz. hrough comparisons wih high accuracy AC sandards, i was proven ha, in low frequencies and in low volages, he algorihm can mainain accuracies below 3 ppm [2]. n he mains frequency, up o 7 vols he accuracy doesn' exceed he limi of ± 5 ppm. niially a new version of he Swerlein algorihm was developed, inerlacing he conrol of wo HP-3458A mulimeers, making possible simulaneous measuremen of wo volages (acual volage and he oher, proporional o he curren). Wih his new algorihm he high accuracy simulaneous measuremen of he RMS value of volage and curren became possible as well as he apparen power and he acive power a uniy power facor could be calculaed. o faciliae measuremens a power facors differen from he uniy, an addiional algorihm was developed. Applying sampling mehod, he algorihm calculaes, from a se of samplings, he phase angle beween he waves of volage and curren. By his addiional algorihm reasonably good resuls could be achieved, down o ±.5 power facor. Successive ess have proven ha, for uniy power facor he new applicaion makes possible he measuremen of he acive power well wihin an uncerainy of ± 3 ppm. was also verified ha, he uncerainy of he measuremen of he phase angle is approximaely ±3 µrad, which is inroducing an addiional uncerainy of ±5 ppm a ±.5 power facor in he calculaion of he acive power. A firs he Swerlein algorihm assumed he role of a reference for he verificaion of he new mehods under developmen, however, he comparisons were resriced, because his mehod is reliable only for small phase shifs and applicable for purely sinusoidal signals. 3.2 Discree negraion For he developmen of he new algorihm, he basic idea was he following. f once a se of samples has been correcly programmed and measured, here mus be a mehod o calculae he ime of period of he signal ( or C) wih enough accuracy o saisfy he condiion of equaion (2). f i is so, an algorihm migh be developed o calculae he RMS

3 values of he volage and of he curren, as well as he acive power a high accuracy. his should be achieved wihou making effors o approximae ha he ime of measuremen be an ineger muliple of he period of he signal or o inroduce special means o minimize he residual error. he wo mulimeers, according o Figure, are programmed o measure a block of cycles of he volage and ha of he curren, respecively. he beginning of he measuremen is synchronized o a zero ransiion of he volage. hereafer, each sampling on he maser iniiaes a sampling aken by he slave. he mulimeers sore he values of samples. When compleing he measuremen of a block, he program reads and sores he samples. he seps of he algorihm for he calculaion of he RMS value of he volage, for example, are as follows. Of he block of samples an inerval is seleced ha has C complee cycles, of a samples. he algorihm makes an analysis for he whole inerval and compues he iniial and final zero crossings, applying an inerpolaion of sevenh order. he ime base (τ) of he inegraion is calculaed beween he crossings. By his he approximaion of equaion (2) becomes an equaliy: τ = sc s = C (4) where sc is usually no an ineger number of he samples (number of samples correced). For he execuion of he discree inegraion a modified rapezoidal rule was applied, by aking ino accoun ha he firs (v ) and las (v n ) samples should be correced according o he non-inegral number of samples. By applying "a" and "b" correcions, he RMS value of he volage: 2 2 = + + v v n 2 V vi (5) sc a b i= o calculae he acive power, he algorihm muliplies he corresponding samples of he volage and of he curren and applies he same mehod, as deailed above. By aking advanage of he measured RMS values and acive power, oher parameers are also calculaed, as: he apparen power, he power facor, he frequency and, in he case of sinusoidal waves, he reacive power (he power s riangle in he case of non-sinusoidal waves is no applicable). he maximum capaciy of he inernal memory of he HP-3458A mulimeer is used, allowing a oal number of 5 samples. A relaively grea number of cycles, up o C, is programmed, which faciliaes increasing he aperure ime. his allows high resoluion of he inegraing A/D converer (2 bis), assuring a resoluion of ±,5 ppm in he measuremen of he volage (or curren). he lack of sabiliy of he power source in he shor erm can also be compensaed by he increase of he number of cycles. Comparing his mehod wih he Swerlein algorihm, i should be poined ou, ha he same accuracy could be reached for sinusoidal signals, neverheless, i is possible o ensure high accuracy measuremens even in he presence of high harmonic conens. 3.3 Harmonic Analysis While he mehod of Discree negraion makes he analysis in he ime domain, his hird mehod applies he Discree Fourier ransform (DF) making he analysis in he frequency domain. f he ime of period of he signal is unknown, he soluion is o carry ou an approximaion, using he minimum squares mehod. For example, o calculae he volage V ci and V si, he equaion used is: 2 M Vc + ( 2 Vci cos( 2π if n ) + 2 Vsi sen( 2πif n ) mn = min (6) n = i= where is he number of samples m i, M is he maximum order of he harmonic componen o be calculaed and V ci and V si are he RMS values of he cosine and sine componens, respecively. he soluion of his equaion is complicaed, involving marix operaions. he paper published by Pogliano [4] suggess his mehod. As, a resul of his work, a mehod for he correc calculaion of he ime of period has been developed, his value can be applied also o calculae he harmonics. By his, simply he fundamenal formulae are applicable: V ci = m n 2π cos in = 2π Vsi mn sen in and he DC volage componen (7) (8) V = mn (9) where sc is he correced number of samples, proporional o a muliple of he period ime, according o equaion (4). has been proven ha he analysis in he ime domain and in he frequency domain resuls he same volage and curren values. he acive power is calculaed by he sum of he producs of he volages and currens of he same order: M [ Vci ci + Vsi si ] P = V + () i= 4 COMPESAO OF ERRORS he algorihms developed allow he compensaion of ampliude and phase errors, as deailed below. 4. Ampliude Error As he mulimeers are used in he configuraion of DC volage, hey can be calibraed wih an uncerainy of ± 2 ppm and he errors are used as correcions. he inegraing A/D converer of he mulimeer doesn' make he measuremen of he signal wihin an infiniely small inerval of ime, bu inegraion is carried ou during he aperure ime, a, producing a sysemaic error, given by:

4 ε sen( πif ) a = () πif where i is he order of harmonic componen. As much in he mehod in he ime domain, as in he mehod in he frequency domain, he program calculaes his error and applies his error as a correcion. he bandwidh, limied by he inpu circuis of he HP-3458A, also inroduces an error of ampliude, which is dependen on he range of volage applied. n he ranges of V and V his error is significan. his error is proporional o he frequency (f) applied and he frequency ha characerizes he bandwidh (f c ), in he form: ε = (2) 2 f + f c his error is calculable and is also considered in he correcion. he inroducion of his error is imporan especially in he evaluaion of he harmonics. 4.2 Phase Shif Errors he knowledge and he compensaion of he phase errors is very imporan for he measuremen of he power in power facors differen from uniy. he componens ha conribue o he exisence of he phase error are, as follows: he conrol of wo mulimeers, in he "maser-slave" configuraion is responsible for he exisence of a phase error, caused by he laency ime. As a resul, he slave (mulimeer o measure he curren) begins a new measuremen a bi laer han he arrival of a new rigger. As specified in he manual of he insrumen, he maximum laency ime is of 75ns, ha in power facor.5, provokes an error of 4 ppm. Addiionally, his delay is no consan, does exis a jier of ± 5 ns, resuling an uncerainy of ± 32 ppm, a power facor.5. Applying he same volage simulaneously in he wo mulimeers he phase error, due o he laency ime, can be measured and inroduced in he program, as a correcion. However, only increasing he number of repeiions can reduce he uncerainy caused by he jier. he mulimeers have aenuaors a he inpu, which also inroduce phase error. As he wo mulimeers work in differen volage ranges, heir phase errors are also differen, which will cause an addiional phase error beween he measured signals. For example, in he volage range of V he phase shif can reach 2 µrad, while in he range of V (where he oher mulimeer, measuring he curren, works) he phase error is negligible. herefore he phase shif beween he wo signals can be as much as 2 µrad. By means of a good qualiy inducive divider he phase shif in he higher volage ranges can be measured and correced in he program. he se of he curren ransformer and sandard resisor also inroduces phase errors, which are measurable and are smaller han he oher errors (wihin µrad). Experiences of he laboraory have verified ha he phase error can be measured, can be aken ino accoun as a a consan and can be inroduced in he program as a correcion. he addiional uncerainy of he measuremen, a power facor.5, is no larger han ± 3 ppm. Experiences also have shown ha he firs wo sources of error are dependen on he applied insrumens and on he connecions beween hem. 5 MPLEMEAO OF HE PROGRAM he program was wrien in language C, in he environmen of LabWindows/CV (produc of aional nsrumens). Figure 3 shows he user inerface of he conrol panel. is possible o selec he algorihm Swerlein or he algorihm DCV (Discree negraion). Figure 3 shows he resul of he laer opion. A simulaion also can be chosen, ha faciliaes he evaluaion of he accuracy of he applied algorihms. n each opion i is possible o adjus several parameers used in he algorihms. he RMS values and he powers are shown in his panel a he end of he measuremen. he resuls of he harmonic analysis are shown in an auxiliary panel. Fig. 3 - User nerface of he Power Analyzer 6 RESULS aking advanage of he bes resources of MERO, where he naional sandards are raceable o he superior laboraories, a grea number of comparisons were execued o verify he accuracy of he new sysem. n his paper only a brief summary is given of he calibraions, o demonsrae he curren level. More deails can be found in [6]. he calculaion of he uncerainies is based on he Guide for Expression of he Uncerainy of Measuremen [5] ha was adoped by MERO since 996. he resuls in he measuremen of volage, obained by he discree inegraion mehod (DCV) and by he Swerlein algorihm (SW), were compared wih he AC/DC ransfer sandard measuremens, by he model 792A of FLUKE. his sandard was calibraed by PB, and i serves as he naional sandard for he measuremen of he AC volage. he resuls are shown in Figure 4. Specified uncerainies are shown in he figure in he sandard way.

5 Error ( ppm) A SW DCV,5, Volage (V) Fig. 4 - Resuls in volage measuremens n lower volages (in he measuremen of he curren) he differences beween he sampling mehods and he 792A ransfer are inside of ± 5ppm. n higher volages he differences are bigger, bu in any condiion, hey are inside of ± ppm. he difference beween he Swerlein algorihm and he algorihm DCV is inside of ± 3ppm. he Power and Energy Laboraory has wo raceable sandards. he power comparaor K-25 (of Hamburger) is raceable o PB, while he sandard wa-hour meer RM- (of Radian) is raceable o S he RM- sandard was used o measure he acive and reacive energy. As he K-25 sandard do no measure reacive power, RM- was chosen as he reference (level zero). K-25 measures he acive power direcly, while RM- he acive energy. herefore, a high accuracy frequency meer was used o measure he frequency of he rain of pulses emied by RM-, proporional o he power. On he oher side he acive power was measured by he hree algorihms implemened in he program of Power Analyzer: he Swerlein algorihm (SW), he new algorihm using Discree negraion (DCV) and he algorihm applying Fourier analysis (DF). Figure 5 shows he resuls in he measuremen of he acive power in 2V, 24V and 48V, wih A, in uniy power facor. Error (ppm) K-25 RM- SW DCV DF 2V 24V 48V Volage Fig. 5 - Resuls in he measuremen of acive power he difference beween he hree algorihms is wihin ± 5ppm, in any condiion. he difference beween he hree algorihms and he reference (RM-) is wihin ± 5ppm a 2V and 48V and wihin ± 3ppm a 24V. As for he laer resul, currenly i is impossible o prove "which one is beer", probably he resuls of he sampling mehods are approaching he realiy beer. Figure 6 shows he resuls in he measuremen of he reacive power for 9º phase shif. Error (ppm) RM- SW DCV 2V 24V 48V Volage Fig. 6 - Resuls in he measuremen of reacive power he difference beween he resuls of he wo sampling algorihms (Swerlein and DCV) is wihin ± ppm. 7 COCLUSOS his projec has grea imporance for he following reasons. - he new mehod permis he reproducion of he unis of power and energy by resources oally raceable o naional sandards wihin he counry. nsead of a dependency of inernaional merology laboraories, MERO can paricipae in inernaional comparisons in he fuure. - A superior accuracy could be aained boh in he measuremen of acive and reacive power and ha of energy. his will faciliae he calibraion of high accuracy advanced insrumens appearing currenly on he marke. - he sysem ensures high accuracy measuremens also in he presence of disored waves, which faciliaes esing he response of power and energy meers o harmonics, according o he new inernaional sandards. he experimenal version of he program has proven he good performance and aainable high accuracy of he new mehod. he projec is coninued and currenly a compleely auomaed complex calibraion sysem is being developed, which will ensure high efficiency in he calibraion of advanced power and energy meers. REFERECES [] Swerlein R., A ppm Accurae Digial ac Measuremen Algorihm, Hewle Packard Co, Augus 99. [2] Kampik M., Laiz H., Klonz M., Comparasion of hree Accurae Mehods o Measure ac Volage a low Frequencies, 6 h EEE nsrumenaion and Measuremen echnology Conference, Venezia, 999. [3] Lapuh R., Arnsek A., Visocnik., Sveik Z., Evaluaion of Low Frequency AC Volage Measuremen Using negraing Sampling echnique, 998. [4] Pogliano U., High precision Measuremen of Elecrical Power by Means of Synchronisaion of negraive Analog o Digial Converers, 8 h nernaional Symposium on ew measuremen and calibraion Mehods of Elecrical Quaniies and nsrumens, Budapes, Hungary, 996. [5] MERO/AB/SBM and Programa RH de Merologia, Guia para Expressão da ncereza de Medição, 2 a ediion, Augus 998. [6] Franco A.M.R., Desenvolvimeno de um Analisador de Poência, Maser Degree Disseraion, PUC-RJ, February 2.