Random Generation of Arbitrary Waveforms for Emulating Three-Phase Systems

Random Gene a ion o A bi a y Wa e o ms o Emula ing Th ee-Phase Sys ems Juan-Ca los Mon año, Senio Membe , IEEE, Ca los León, Senio Membe , IEEE, An onio Ga cía, An onio López, Iñigo Monede o, and En ique Pe sonal, S uden Membe , IEEE Abs ac —This pape desc ibes an appa a us o gene a ing a signal ep esen a i e o s eady-s a e and ansien dis u bances in h ee-phase wa e o ms o an ac elec ical sys em as desc ibed in IEEE S d 1159-09. I can be con igu ed as a syn hesize o andomly dis o ed signals o di e en applica ions: o es ing he e ec s o dis u bed g id on equipmen and o gene a e pa - e ns o elec ical dis u bances o he aining o a i icial neu al ne wo ks, which a e used o measu ing powe quali y asks. Fo he i s pu pose, ol age and cu en ampli ie s a e added in he ou pu s age, which allows he gene a ion o dis u bed signals a g id le el. Index Te ms—AC gene a o s, a i icial neu al ne wo k (ANN), educa ion, load modeling, powe ha dwa e in he loop (PHIL), powe quali y (PQ), powe sys em simula ion, signal syn hesis, es equipmen . I. INTRODUCTION MOST o oday’s ins umen a ion o h ee-phase sys ems used in he indus y is ocused and designed o es ing and measu ing powe supply sys ems and equipmen connec ed he e o [1]. Eme ging me hods o ad anced expe imen a ion exis , such as he powe ha dwa e-in- he-loop (PHIL) simula- ion [2], [3] whe eby a piece o powe ha dwa e, o example, an ene gy-powe me e o a powe elec onic d i e, is ope a ed om a i ual g id, simula ed in eal ime wi h he necessa y powe capabili ies h ough p ecision powe ampli ie s. PHIL simula ion me hod can be applied oo o esea ching he eal- ime beha io o con olle and p o ec ion equipmen . All o hese applica ions ha e a posi i e and economic impac on indus y. In ano he con ex , i is well known ha an e ec i e way o es ing equipmen seems o be ha o supplying hei ol - age and cu en inpu channels wi h p io unknown signals andomly gene a ed [4], [5]. I he es is epea ed a gi en numbe o imes and a new se o es signals is andomly gene a ed a each epe i ion, each new es shows di e en andomly gene a ed es wa e o ms, and he e o e, he beha io o equipmen unde es is likely o be e i ied in eal condi ions o e y close o he eal ones. This wo k was suppo ed in pa by he esea ch p ojec e . C03-056 and in pa by he esea ch p ojec s CICYT/FEDER DPI2006-15467-C02-01 and CICYT/FEDER DPI2006-15467-C02-02. The au ho s a e wi h he Elec onic Technology Depa men , Uni e - si y o Se ille, Escuela Poli ecnica Supe io , 41011 Se ille, Spain (e-mail: [email p o ec ed]; [email p o ec ed]; [email p o ec ed]; [email p o ec ed]; imonede o@ us.es; [email p o ec ed]). In his pape , we de eloped an appa a us capable o gen- e a ing ealis ic wa e o ms ep esen a i e o many indus ial powe applica ions. Con ol and con igu a ion o he uni is e y in ui i e owing o he use o sel -explana o y g aphical in e ace. Ins ead o compe ing wi h comme cial sys ems, i is designed o p o ide a e y low cos al e na i e o eal- ime ha dwa e-in- he-loop applica ions while main aining ac- cep able speci ica ions. In he li e a u e, he e a e some examples o equipmen simila o he andom gene a o desc ibed in his pape , bu in some cases only is i possible o gene a e a limi ed numbe o dis u bances [6] o he g aphical in e ace is no use - iendly and has low con igu a ion possibili ies [7]. The ollowing sec ions will discuss he p oposed p ocedu e and p o ide he de ails o a labo a o y p o o ype speci ically de eloped: 1) wi hou ou pu ampli ie s: a) a bi a y and andom gene - a ion o aining pa e ns o op imal design o a i icial neu al ne wo ks (ANNs) [8] and b) a bi a y gene a ion o low- ol age and low-cu en le els (scaling-down e - sion o h ee-phase powe sys ems) in sepa a ed channels o aining o eaching; 2) wi h ou pu ampli ie s: c) a bi a y and andom gene a- ion o elec ical pa e ns a high-powe le els o es ing he e ec s o powe -line dis u bances on equipmen [5] and d) a bi a y gene a ion o high- ol age and high- cu en le els in sepa a ed channels o ep esen ing dy- namic beha io s o a powe sys em. II. AWG Acco ding o he conside a ions in he p e ious sec ion, he p oposed solu ion o es ing equipmen unde common wo k- ing condi ions o o aining ANNs is based on he gene a ion o andomly dis o ed wa e o ms o he ol age and cu en signals. This can be done in a ela i ely simple way employing a digi al- o-analog con e sion (DAC) boa d connec ed o a p og ammable de ice, such as a digi al signal p ocesso o PC. A. So wa e Based on his concep , LabVIEW and Tes S and so wa e (Na ional Ins umen ) we e used o p og am an au oma ic signal gene a o ha allows comple e con igu a ion o he pa e ns e- qui ed. Fi s , a i ual ins umen (VI), ha we called Pando a, was implemen ed in LabVIEW [9]. This VI mainly gene a es a pa e n based on he pa ame e s de ined by he use ; hus, Fig. 1. F on panel o Pando a 3ph. s eady-s a e o ansien -s a e dis u bances we e modeled as desc ibed he eina e . In a i s s age, he sys em was designed o be used manually, so he use needed o speci y he pa- ame e s o he pa e n o e e y simula ion. Then, Tes S and was included in o de o p o ide au oma ion. This so wa e ool can help he use o de elop au oma ed es and alida ion sys ems, i.e., i can de elop es sequences ha in eg a e code modules w i en in any es p og amming language. Sequences also speci y execu ion low, epo ing, da abase logging, and connec i i y o o he en e p ise sys ems. Finally, es sys ems o p oduc ion wi h easy- o-use ope a o in e aces can be o ga- nized [10]. Se e al algo i hms we e p og ammed in Tes S and o launch he Pando a VI acco ding o di e en goals ( andom ha monic con en s pa e ns, noisy signals, ansien dis u bances, e c.). Gene a ed pa e ns can be sa ed as ex iles o be used o line o ANN aining o ins ance o sen o he DAC boa d in li e expe imen s (as in es pu poses). The on panel o h ee-phase Pando a VI is shown in Fig. 1. A ypical sequence consis s basically o a se up ope a ion, whe e all he a iables ese o hei de aul alues, and he main ope a ion whe e pa ame e s and inpu s ha de ine he new ex- pe imen a e modi ied and Pando a VI is execu ed. Then, wi h all hese alues, epo s o he esul s a e gene a ed. Finally, he cleanup ope a ion is execu ed, whe e he a iables a e ese again o de aul alues. The e o e, he Pando a VI consis s o he main p ocesses o Fig. 2. Fi s , inpu s and pa ame e s a e collec ed om manual use o Tes S and au oma ic sequences. Second, he signal is buil acco ding o hese speci ica ions, and hi d, he pa e n is sen o a ile o o he DAC boa d. The main ea u e o he de eloped a chi ec u e is ha i is a laye -based model. I dis inguished h ee dis inc pa s o laye s p og ammed in LabVIEW ha ca y ou asks ha a e essen ially di e en . 1) Laye 3: This module is esponsible o managing he use in e ace ca ying ou he display o he windows on each case. On he o he hand, i allows he use o Fig. 2. Gene al diag am o gene a ion wi h Pando a. en e all he in o ma ion necessa y o he edi ion o he desi ed signal. The e o e, his laye is ocused on ga he ing in o ma ion ha comes om he p og am’s con ols, g ouped acco ding o some da a s uc u e, and ans e s i o laye 2. 2) Laye 2: I is he eal engine o he applica ion. F om he da a en e ed by he use and ha e p e iously been man- aged h ough laye 3, laye 2 pe o ms all calcula ions necessa y o gene a e he da a signal o be edi ed. This is whe e he a ious models a e implemen ed in each o he dis u bances ha we s udied p e iously. The ou pu o laye 2 is a se o nume ical da a co esponding o he edi ed signal. These alues a e ans e ed o laye 1. 3) Laye 1: This block pe o ms all he communica ions wi h he sc een, iles, and da a ca d. In his block, we p ope ly ake ca e o displaying he use in e ace. On he o he hand, i condenses he implemen a ion o all he unc ions necessa y o expo he da a signal ecei ed om laye 2 o a da a ile ha ollows a s anda d o ma . Mo eo e , i pe o ms all he communica ion wi h he ha dwa e ins alled o pe o m he physical gene a ion o he edi ed signal h ough he da a ca d gene a ion. The scheme o he laye -based model p og ammed in Lab- VIEW is shown in Fig. 3. 1) Cons ain s o Random Gene a ion: Using his sys em, i is possible o syn hesize any kind o wa e o ms in he equency ange o in e es o he emula ion o ac ual powe sys ems. O cou se, a pu ely andom gene a ion o he dis o ion com- ponen s is no likely o ep esen he eal ope a ing condi ions o ac ual powe sys ems. The sys em is designed o p og am dis u bances as desc ibed in powe quali y (PQ) s anda ds (i.e., IEEE S d 1159-09). The e o e, a numbe o cons ain s mus be conside ed by he gene a ion algo i hm. In pa icula , he ollowing cons ain s ha e been conside ed. 1) Highes ha monic o de is gi en o he syn hesize as an inpu pa ame e so ha he desi ed bandwid h is no exceeded. 2) Maximum allowed dis o ion is imposed as an inpu pa ame e in e ms o maximum allowable o al ha monic dis o ion (THD) ac o , sepa a ely o he ol age and cu en signals. 3) Fundamen al componen o he ol age signal, U1, can be se o any alue in he ange [0.9U1,1.1U1], whe e U1is he a ed ol age [1]. 4) Fundamen al componen o he cu en signal can be se o any desi ed pe cen age o he a ed cu en , and i s phase shi wi h espec o he undamen al componen o Fig. 3. LabVIEW a chi ec u e o Pando a. he ol age signal can be se o any alue, ei he leading o lagging. 5) Fundamen al equency can be se o any alue in he ange [0.98 n,1.02 n], whe e nis he a ed equency [1] (whe e n=50o 60 Hz). Taking in o accoun he a o emen ioned cons ain s, a an- dom numbe o s eady-s a e and ansien -s a e dis u bances can be emula ed. 2) S eady-S a e Dis u bances: • Ha monics Ha monic componen s, andomly dis ibu ed be ween he undamen al componen and he maximum desi ed ha monic o de , can be gene a ed. The cu en wa e o m always has he same ha monic compo- nen s as he ol age wa e o m. I also has addi ional ha monic componen s ha , when p o ided by he andom gene a ion, accoun o he p esence o nonlinea loads. Ampli ude and phase shi a e andomly gene a ed o each o he ha monic componen s de e mined in he p e ious s ep. A check is pe o med so ha he maximum desi ed THD ac o is no exceeded. I a sui able numbe o di e en andomly gene a ed dis- o ed signals a e used o supply he uni unde es (UUT), i is possible o assume ha a signi ican numbe o possible wo king condi ions ha e been ep oduced so ha he UUT can be hypo he ically es ed in i s eal wo king condi ions. The ollowing ma hema ical model was implemen ed: C( )=A+ N  n=1 Ansin(2πn 1 +ϕn)(1) whe e Ais he dc e m (V o A), Anis he ampli ude o he n h ha monic o he signal (V o A), 1is he undamen al equency (Hz), ϕnis he phase o he n h ha monic ( ad), and nis he ha monic o de (n=1,...,N). • Flicke Flicke is conside ed an ampli ude modula ion o he ca ied signal C( ), which changes in unc ion o he modula ing signal F( )[11]. The modula ing signal has sinusoidal o m wi h p e- ixed andom ampli ude, equency (usually a ound 30 Hz), and an ini ial phase. The equa ion which de ines he ma hema ical model implemen ed by he emula o is Z( )=F( )C( )=[1+A ksin(2π k +ϕ k)] C( )(2) whe e A k, k, and ϕ k a e he licke ampli ude, licke e- quency, and licke phase, espec i ely. • Unbalance: S eady-s a e symme ical componen s The me hod o symme ical componen analysis akes i s o igin om [12]. I p esen s a ma hema ical app oach o he analysis o an asymme ical polyphase sys em (unde s eady- s a e condi ions) by ans o ming i in o a se o symme ical se- quence ne wo ks called posi i e-, nega i e-, and ze o-sequence ne wo ks. I Fa,Fb, and Fcdeno e he co esponding o iginal phaso s o phases a, b, and c o a h ee-phase sys em, hen ⎡ ⎣ Fa Fb Fc ⎤ ⎦=⎡ ⎣ F+ a F+ b F+ c ⎤ ⎦+⎡ ⎣ F− a F− b F− c ⎤ ⎦+⎡ ⎣ F0 a F0 b F0 c ⎤ ⎦(3) whe e +,−, and 0 deno e posi i e-, nega i e-, and ze o- sequence componen s, espec i ely. Since each se o sequence componen s is balanced, one can deduce [13] ⎡ ⎣ F0 a F+ a F− a ⎤ ⎦=1 3 ⎡ ⎣ 11 1 1ββ 2 1β2β ⎤ ⎦⎡ ⎣ Fa Fb Fc ⎤ ⎦(4) whe e β=exp(j2π/3). 3) T ansien -S a e Dis u bances: • O e ol age, swell, unde ol age, and sag In hese kinds o dis u bances, he ampli ude o he signal ises (o e ol age o swell) o alls (unde ol age and sag) a ce ain alue along a ime in e al. In he de elopmen o he dis u bance gene a o , a ape- zoidal model o he ampli ude e olu ion (lineal slope) was conside ed. The model makes i possible o app oxima e he ampli ude dis u bances mos equen ly encoun e ed in powe sys ems. Fig. 4 shows a g aphic o he model used o o e ol - ages o swells (in e se apeze o unde ol ages and sags); he ollowing pa ame e s a e de ined: pini ial sample o he dis u bance; pip slope o he ini ial amp; p p slope o he inal amp; n1numbe o samples o he ini ial amp; n2numbe o samples o he inal amp; bnumbe o samples a he bo om; M o al numbe o samples. • Oscilla o y ansien s Fig. 4. Sag model. The elec ical pa e n gene a o (EPG) models ansien as a damped sine h ough a supe posed exponen ial unc ion, which is added o C( )a a ce ain poin . The implemen ed ma hema ical model is exp essed as T( )=e−a A sin(2π +ϕ )(5) whe e ais he oscilla o y- ansien exponen , A is he ampli- ude o he ipple (V o A), is he equency o he ipple (Hz), and ϕ is he ini ial phase o he ipple ( ad). •Noise The gene a o makes i possible o add an addi i e whi e Gaussian noise in o de o simula e mo e ealis ic signals o he powe line. B. Ha dwa e The emula o design is based on gene a ing h ee-phase ol ages and ou line cu en s o emula e a low- ol age powe sys em. Gene a ed da a se s a e ob ained om a hos PC in he o m o da a iles wi h Ame ican S anda d Code o In o ma ion In e change o ma compa ible wi h he mos popula da a- analysis ools (Ma lab, Ma hcad, e c.). The hos PC is equipped wi h a NI PXI 6733 boa d wi h eigh analog ou pu s a up o 1 MS/s, 16-b esolu ion, and ±10-V ou pu ange. Se en ol age signals a e a ailable: h ee p opo ional o he h ee phase-neu al ol ages (Va,Vb, and Vc) and ou p opo ional o he h ee line cu en s (Ia,Ib, and Ic) and neu al cu en (In). A he inal s age, he ampli ie sec ion b ings he ol age signals o he g id le el. The numbe and ype o ampli ie s depend on he applica ion o he sys em. The ol age ac oss he load and/o he cu en lowing h ough he load o UUT can be simula ed. Fig. 5 shows he simpli ied h ee-phase powe emula ion ci cui . 1) Ampli ie Sec ion: A e y c i ical issue in he design o he es sys em is he ampli ie sec ion since i mus ensu e accu- a e and cons an gain and phase shi on he whole bandwid h equi ed. On he o he hand, he ampli ie ype depends on he selec ed applica ion. Two op ions ha e been conside ed. Op ion 1. A powe ampli ie o es ol ages a g id le el In his ype o applica ion, dis u bed ol age signals a g id le el a e gene a ed o es ing equipmen unde eal condi ions Fig. 5. Simula ion o an ac ual ol age sou ce (Op ion 1): Vol age gene a o wi h p og ammed dis u bances and powe ampli ie . Fig. 6. Simula ion o a comple e sys em (Op ion 2): (a) Powe sou ce wi h p og ammable dis u bances applied o an a bi a y load and (b) ol age and cu en gene a o wi h p og ammable dis u bances and ampli ied ou pu s. (see Fig. 5). In his case, gene a ed ol age signals can be con- igu ed o single-phase o h ee-phase sys ems. The ampli ie sec ion consis s o one o h ee ol age ampli ie s wi h he powe capabili y necessa y o supply he UUT. A labo a o y p o o ype has been implemen ed o es ing single-phase sys ems. The Paci ic Powe Sou ce Model 320 was used as a powe ampli ie o ul ill all he p oposed equi emen s: 1) ou pu ol age up o ±600 peak ol s; 2) maximum ou pu powe : 1.2 kVA; 3) bandwid h (30–5 kHz) a ull powe ; 4) THD <0.2%. Op ion 2. A high- ol age ampli ie and a high-cu en anscon- duc ance ampli ie o es ol ages and load cu en s a g id le el (see Fig. 6) . In his second ype o applica ions, i is necessa y o gene a e bo h ol ages and cu en s a g id le els o simula e a comple e sys em wi h high- ol age sinusoidal supply sou ce wi h added dis u bances and a bi a y load. In hese applica ions, common UUT (powe me e s, powe analyze s, p o ec ion elays, e c.) Fig. 7. Labo a o y p o o ype o he p oposed es sys em wi h ol age and cu en ampli ie s. measu es he ol ages and/o cu en s h ough independen inpu s. These inpu s ypically ha e high-inpu impedance o ol age measu emen s and low-inpu impedance o cu en measu e- men s, so i is no necessa y o ampli y he ou pu signals wi h high-powe capabili ies. Vol age ampli ie s (A )ha e been designed using Apex PA05 high- ol age low-powe ope a ional ampli ie s wi h some impo an speci ica ions: 1) ou pu ol age up o ±600 peak ol s; 2) maximum ou pu cu en =5mA; 3) bandwid h (dc o 50 kHz); 4) THD <0.1%. Cu en ampli ie s (Ai)ha e been designed using ope a ional ampli ie s and disc e e ansis o s as high-cu en low-powe ansconduc ance ampli ie s. Thei main cha ac e is ics a e as ollows: 1) ou pu cu en up o ±50-A peak; 2) maximum ou pu ol age =±8V; 3) bandwid h (dc o 50 kHz); 4) THD <0.2%. Fig. 7 shows he implemen ed labo a o y p o o ype o he p oposed es sys em, wi h he wo ypes o ampli ie s. III. APPLICATIONS The single-phase o h ee-phase powe a bi a y wa e o m gene a o (AWG), wi hou o wi h he ampli ie s age con- igu ed acco ding o Op ion 1 o Op ion 2, allows a se o applica ions equi ing he use o high-powe o low-powe sou ces. A. T aining Pa e ns o Op imal Design o ANNs The AWG has been de eloped as an auxilia y ool o gene a e elec ic pa e ns o ANNs, i.e., we ha e con igu ed he AWG as an EPG. Pa e n ecogni ion in ANNs gene ally equi es p ep ocessing o da a, ea u e ex ac ion, and inal classi ica ion [16]–[19]. One o he mos impo an asks in he design and de elopmen p ocess o an ANN is o gene a e an adequa e numbe o aining pa e ns in o de o app oxima e u u e inpu s. Some imes, an op imal design o he ANN is ound, bu he limi ed numbe o aining pa e ns does no gi e good esul s. In pa icula , in PQ measu emen , a g ea numbe o elec ical pa e ns is necessa y due o he mul iple combina ions o di e en dis u bances which can coincide in one o a ious samples. Thus, in o de o ex ac he signal ea u es, ANNs a e usu- ally combined wi h ma hema ical analysis, such as Fou ie and wa ele ans o ms, o he gene a ion o signal ea u es which se e as inpu s o he ne wo k [8]. Thus, wi h he help o hese ma hema ic ools, he de ec ion o he elec ical dis u bances has ended o be easy, bu hei classi ica ion is s ill a di icul ask in which ANNs play an impo an ole [14]–[16]. Ano he addi ional p oblem wi h ANNs applied o PQ is he impossibili y o ob aining eal use ul aining pa e ns di ec ly om he powe g id due o he i egula appa i ion o hese dis u bances and he di icul y o cap u e hem. In u n, i is e y di icul o ge access o da abases o elec ical dis u bances and, once achie ed, o adjus he ea u es o he ob ained elec- ical pa e ns o he equi emen s o he sys em o be designed (in pa ame e s such as sample ime and ol age ange de ined o each ype o dis u bance). Thus, o he ask o aining ANNs o he de ec ion and classi ica ion o elec ical dis u bances, he EPG gene a es an unlimi ed numbe o pa e ns o be used by a classi ica ion sys em. The ypes o dis u bances include o e ol age, swell, unde ol age, sag, oscilla o y ansien s, ha monics, licke , unbalance, equency a ia ions, and in e up ions. Fo he applica ion desc ibed in [8], o e 27 000 signal iles ha e been gene a ed, including one-dis u bance signals and wo-dis u bance signals, and ied o sweep all he ypes o dis u bances. B. T aining o Teaching Tool Ano he impo an applica ion o he emula o sys em is as eaching and/o aining ool. Th ee-phase powe can be augh in a sa e labo a o y en i onmen using he h ee-phase powe emula o wi hou exposing he s uden o dange ous high ol ages and cu en s. Ano he impo an conside a ion o he emula ion sys em is he low cos o build and main ain. An a o dable low-cos emula ion sys em can be e y help ul o schools wan ing o imp o e hei labo a o y equipmen and eaching echniques. The s uden s can lea n abou phase-angle ela ionships by edi ing he ou pu wa e o ms, which a e dis- played on he sc een ia he moni o ing p og am. C. Tes ing Equipmen Using Op ion 1, i is possible o es di e en ypes o sys- ems in he p esence o supply ol age dis u bances a g id le el. The ou pu ol ages should be used o d i e he UUT wi hin he powe limi s o he powe ampli ie [14], [15]. In his kind o applica ions, i is possible o es he equipmen unde ol age dis u bances [20], [21], esea ching he eal- ime beha io o con olle and p o ec ion equipmen [4], [22] o es ing and Fig. 8. Labo a o y se up o es ing a powe me e . compa ing sys ems and/o echniques o dis u bance analysis [23]–[26]. This ype o applica ion has been implemen ed in he case s udy desc ibed in Sec ion IV o his pape . D. Scaling-Down Ve sion o Th ee-Phase Powe Sys ems Finally, sys em designe s and manu ac u e s can use he h ee-phase powe emula o o build and es a scaled-down e sion o he sys em being conside ed. S udying scaled-down e sions o he p oposed equipmen can g ea ly aid he designe in es ing and pe o ming sys em al e a ions by sa ing ime and cos . T oubleshoo ing can be con olled and easy o pe o m wi h smalle manageable sys ems. Once he small-scale model is ully unc ional, he sys em is eady o ull-scale assembly. IV. EXAMPLE OF REAL APPLICATION Fig. 8 shows an example o a eal expe imen al se up o es ing an ene gy-powe me e (powe line communica ion) unde condi ions o g id dis u bances. The accu acy in he measu emen o ol age, cu en , ac i e and eac i e powe , and powe ac o , wi h di e en kinds o load (linea Ro RL and nonlinea ) and pe iodical dis u bances ( licke , ha monics, combined, ansien , e c.), has been analyzed. Pando a sys em combined wi h a comme cial powe ol age ampli ie has been used o gene a e a single-phase ol age sig- nal a g id le el wi h an added se o common dis u bances. This signal had been applied o a digi al ene gy/powe me e (UUT) wi h di e en loads: linea ( eal o complex) and nonlinea (swi ched powe egula o ). The ou pu da a alues o he UUT ha e been compa ed, o di e en loads and dis u bances, o a e e ence powe -analysis sys em consis ing in a calib a ed senso ca d equipped wi h ol age and cu en senso s (bo h TABLE I EXPERIMENTAL RESULTS based on Hall e ec ) and a PC equipped wi h an analog- o- digi al acquisi ion boa d and con olled by da a-analysis so - wa e de eloped in LabVIEW. Fig. 9. Example 1—Ha monic dis u bance (Tes ID 17). (a) Pando a’s on panel. (b) Pando a’s ha monic se up. (c) Measu es om he e e ence powe - analysis sys em ( he measu ed cu en , whi e signal, is scaled by 20). Table I summa izes he esul s o es s in ac i e powe measu emen s. Because he measu es a e loca ed in he lowe ange o he UUT (<1kW), he p ac ical ou pu esolu ion is limi ed o wo digi s. Wi h hese p ecision limi s, we conclude ha he UUT is p ac ically no a ec ed, in he measu e o he ac i e powe , by he dis u bances es ed. Howe e , he e a e signi ican di e ences in he eac i e powe , and powe ac o , measu ed when he cu en has high- equency ha monics. This may be caused by a swi ching load o by he p esence o high- equency ha monics in ol age applied on a esis i e load. Figs. 9–11 show he on panel o Pando a and he co e- sponding sc een o he powe -analysis sys em o h ee ypes o dis u bance: ha monics, licke , and ansien . Fig. 10. Example 1—Flicke dis u bance (Tes ID 6). (a) Pando a’s on panel. (b) Measu es om he e e ence powe -analysis sys em ( he measu ed cu en , whi e signal, is scaled by 20). Fig. 11. Example 3—Gene a ion o a ansien dis u bance (Tes ID 25). (a) Pando a’s on panel. (b) Measu es om he e e ence powe -analysis sys em ( he measu ed cu en , whi e signal, is scaled by 20). This eal applica ion demons a es he lexibili y and ease o use ha he sys em Pando a in ol ed in his ype o applica ion. V. C ONCLUSION This pape has desc ibed an AWG o signals ep esen a i e o s eady-s a e and ansien dis u bances in single- o h ee- phase wa e o ms o elec ical sys ems, as desc ibed in IEEE S d 1159-09. The sys em has di e en po en ial applica ions: aining pa e n gene a ion o ANN design, aining o eaching ool, equipmen es ing, o scaling-down e sion o h ee-phase powe sys ems. Depending on he applica ion, i is possible o use he sys em wi h o wi hou an ou pu ampli ie . In ha case, he e a e wo possible op ions. The i s one consis s in a powe ampli ie o es a g id- ol age le el. The second op ion combines a low- powe high- ol age ampli ie and a high-cu en ansconduc- ance ampli ie o es g id- ol age and load-cu en le els. An example o a eal equipmen es ing applica ion is de- sc ibed in o de o demons a e he sys em lexibili y and ease o use. 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