Review of fundamental active current extraction techniques for SAPF

Ci a ion: Ba os, J.; So ola, V.; Bilik, P.; Ma inek, R.; Ja os, R.; Danys, L.; Simonik, P. Re iew o Fundamen al Ac i e Cu en Ex ac ion Techniques o SAPF. Senso s 2022,22, 7985. h ps://doi.o g/10.3390/s22207985 Academic Edi o : Roman So ne Recei ed: 22 Augus 2022 Accep ed: 15 Oc obe 2022 Published: 19 Oc obe 2022 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2022 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). senso s Re iew Re iew o Fundamen al Ac i e Cu en Ex ac ion Techniques o SAPF Jan Ba os 1,† , Voj ech So ola 2,† , Pe Bilik 1,† , Radek Ma inek 1, Rene Ja os 1,* , Lukas Danys 1 and Pe Simonik 2 1Depa men o Cybe ne ics and Biomedical Enginee ing, VSB–Technical Uni e si y o Os a a, 17. lis opadu 15, 708 33 Os a a, Czech Republic 2Depa men o Elec onics, VSB–Technical Uni e si y o Os a a, 17. lis opadu 15, 708 33 Os a a, Czech Republic *Co espondence: [email p o ec ed] † These au ho s con ibu ed equally o his wo k. Abs ac : The ield o ad anced digi al signal p ocessing me hods is one o he as es de eloping scien i ic and echnical disciplines, and is impo an in he ield o Shun Ac i e Powe Fil e con ol me hods. Shun ac i e powe il e s a e highly desi able o minimize losses due o he inc ease in he numbe o nonlinea loads (de o med powe ). Cu en ly, he e is apid de elopmen in new adap i e, non-adap i e, and especially hyb id me hods o digi al signal p ocessing. Nowadays, mode n me hods o digi al signal p ocessing main ain a key ole in esea ch and indus ial applica ions. Many o he bes p ac ices ha ha e been used o con ol shun ac i e powe in indus ial p ac ice o decades a e now being su passed in a o o new p og essi e app oaches. This sys ema ic esea ch e iew classi ies he impo ance o using ad anced signal p ocessing me hods in he ield o shun ac i e powe il e con ol me hods and summa izes he ex an ha monic ex ac ion me hods, om he con en ional app oach o new p og essi e me hods using gene ic algo i hms, a i icial in elligence, and machine lea ning. Synch oniza ion echniques a e desc ibed and compa ed as well. Keywo ds: ac i e il a ion; ha monic ex ac ion; shun ac i e powe il e ; synch oniza ion; o al ha monic dis o ion 1. In oduc ion The de elopmen o semiconduc o echnology has led o he massi e expansion o elec onics. These elec onic de ices a e di ec ly connec ed o he elec ical g id, whe e hey can cause p oblems because o hei nonlinea load cha ac e is ic. This nonlinea i y causes ha monic dis o ion o ol age o cu en , which leads p ima ily o economic losses and seconda ily o excessi e elec ical ne wo k o e loads [1,2]. These p oblems wi h highe ha monic componen s can be sol ed in wo ways, ia passi e o ac i e il a ion. Passi e il a ion me hods can be a sui able choice o isola ing ans o me connec ions (e.g., Del a-S a wi h lead ou neu al conduc o (Dyn) connec ion supp esses he hi d ha monic [ 3 , 4 ]), as can connec ing a esonan il e [ 5 , 6 ]. Passi e il e s ha e been widely used due o hei low cos and signi ican e iciency in supp essing ha monics. Un o una ely, hese il e s ha e mul iple disad an ages. Fo example, i he load is a con olled ec i ie , i is necessa y o compensa e only he signi ican odd ha monic componen s ( hi d and i h). In his case, he il e is op imized. Howe e , i he load dynamically changes i s ha monic spec um, he il e becomes ine icien . Ano he disad an age is ha il e ing cha ac e is ics a e signi ican ly in luenced by he impedance o he elec ical ne wo k. Wi h an unsui able design, i is possible o cause a se ial o pa allel esonance on he dis ibu ion ne wo k side. Ano he nega i e aspec o passi e il a ion is ha due o high-powe lows i is necessa y o design he componen s app op ia ely. This is e lec ed in hei size, as such il e s ake up a lo o physical space in subs a ions. Senso s 2022,22, 7985. h ps://doi.o g/10.3390/s22207985 h ps://www.mdpi.com/jou nal/senso s Senso s 2022,22, 7985 2 o 41 Fu he mo e, i is necessa y o conside ha il e s a lowe equencies ha e a capaci ance cha ac e , and he e o e compensa e he powe ac o . As s a ed abo e, ano he op ion is o use ac i e il a ion [ 7 , 8 ], which has become ele an only due o he de elopmen o swi chable semiconduc o componen s such as Ga e u n-o (GTO), In eg a ed Ga e Commu a ed Thy is o s (IGCT), and especially Insula ed Ga e Bipola T ansis o s (IGBT). In addi ion o hese componen s, de elopmen has been accele a ed by he massi e g ow h in he compu ing powe o mic ocompu e s on which i is possible o implemen a ious complex compu ing me hods. Ac i e il e s, hanks o hei unc ionali y, a e able o bypass he disad an ages o passi e il e s. Fi s o all, i is possible o eac dynamically o changes in he condi ions o he elec ical ne wo k o in he equency ha monic spec um o he connec ed load. Thus, he e is no need o design a il e o each ha monic componen sepa a ely, no is he e a need o design a il e o any speci ic load. Un o una ely, he ad an ages o ac i e il e s a e coun e ed by se e al signi ican disad an ages. Due o he cos o powe semiconduc o swi ching elemen s, ec i ie diodes, senso s, and capaci o s, he ini ial pu chase and main enance cos s a e e y high. High demands a e placed on he compu ing uni as well, which is he “b ain” o he de ice. The ask o his uni is o calcula e all ma hema ical ope a ions and o con ol he gene a ion o he compensa ion cu en signal. In addi ion, he esponse ime o his con ol sys em mus ideally be ins an aneous, o a leas minimal. Ano he nega i e aspec o ac i e il a ion is he need o p oduce a de ac o duplica e o he cu en aken wi h he opposi e sign and wi hou he undamen al ha monic componen . Thus, while powe losses a e no undesi able in e ms o unc ionali y, in e ms o cos he losses a e conside able, as all powe ou side he undamen al ha monic componen mus be p oduced wi h he opposi e sign, i.e., duplica ed. Ac i e il e s can be di ided in o se ial ac i e il e s, shun ac i e il e s, o hei combina ion. Se ial ac i e il e s a e used o sol e ol age issues in he elec ical ne wo k, such as ol age ampli ude co ec ion, compensa ion o ol age d ops, emo al o ol age ha monic componen s, o e shoo s, o powe cu s (i powe ed om backup powe sou ce), hus achie ing balanced ol age. This ype o il e does no allow compensa ion o cu en ha monics. Shun ac i e il e s a e used o esol e ongoing issues in he elec ical ne wo k, such as emo al o cu en ha monic componen s and eac i e powe compensa ion. Bo h ypes o il e s can be combined, wi h he se ial pa aking ca e o he ol age and he shun pa aking ca e o he cu en . Ac i e il e s can be combined wi h passi e il e s as well [9,10] . This combina ion is known as a hyb id il e . Such il e s educe he elec omagne ic in e e ence possible wi h ac i e il e s and p e en esonan in e ac ions be ween he passi e il e and he ne wo k, hus combining he ad an ages o bo h echnologies. Cu en ly, ac i e il e s a e on he ise; un o una ely, a p esen his de elopmen mainly conce ns academia. Howe e , s agna ion can be obse ed in he elec ical powe indus y, whe e p o en ye obsole e solu ions a e used ins ead o in eg a ing new echnologies. The elec ical powe indus y is no in a ou o inno a ion, mainly o economic easons; he deploymen o new and mo e ad anced equipmen on a mass scale is likely o equi e a signi ican inc ease in cos s, and hus a educ ion in p o i s. Ano he aspec is componen ailu e, as each senso and swi ching elemen has a limi ed se ice li e and i s eplacemen o epai inc eases cos s. The cu en end in he academic esea ch en i onmen is o design me hods ha can wo k wi h as low a numbe o senso s as possible, e.g., measu ing only wo cu en s [ 11 , 12 ] ins ead o h ee ol ages and h ee cu en s. The e o e, ins ead o six senso s, only wo senso s a e used and he emaining a iables a e calcula ed o es ima ed (see adap i e me hods). As he numbe o senso s dec eases, bo h he pu chase p ice and he se ice p ice dec ease. Howe e , his end is no ollowed in indus y; on he con a y, i is economically e icien o p oduce and use obsole e solu ions ha ha e a decla ed unc ionali y h ough ens o yea s o deploymen . A pa allel scena io a ises in o he elec ical powe ields ha do no di ec ly deal wi h cu en ha monics compensa ion. Senso s 2022,22, 7985 3 o 41 This e iew aims o p esen classical, mode n, and hyb id con ol me hods in a ious aspec s o Shun -Ac i e Powe Fil e (SAPF) con ol. These con ol me hods can be u he di ided in o wo g oups: 1. Ha monic Ex ac ion Algo i hms [ 13 – 25 ]; and 2. Synch oniza ion Techniques [26–50]. This SAPF a chi ec u e can be seen in he simpli ied diag am shown in Figu e 1. All con ol algo i hms a e implemen ed on a common powe ul con ol uni (a Field P og ammable Ga e A ay (FPGA) o Digi al Signal P ocesso (DSP)) which is able o dynamically espond o he occu ence o highe ha monics in he dis ibu ion ne wo k, and hus o compensa e hese highe ha monics in eal ime o wi h minimal delay. I is wo h men ioning ha he powe in e e i sel is a sou ce o ha monics; hus, he in e e is connec ed o he ne wo k using a low-pass LC il e . This LC il e is used o educe he highe ha monic componen s gene a ed by SAPF swi ching pulses. Synch oniza ion DC-Link Capaci o Vol age Regula ion Cu en Con ol Swi ching Con ol Ha monic Ex ac ion/ Re e ence Cu en Gene a ion × + CDC Shun -Ac i e Powe Fil e VDC Si e iDC IDC θ Supply G id a,b,c L iinj o ia,b,c PCC iL iDC iinj ia,b,c iL /// /// /// Ha monic pollu ion p oducing load Figu e 1. Simpli ied block diag am and wo king p inciple o SAPF. The ask o he Ha monic Ex ac ion Algo i hm (o en called he Re e ence Cu en Gene a ion Algo i hm in he li e a u e) is o gene a e a e e ence cu en ha co esponds o he dis o ion con ained in a ha monically pollu ed dis ibu ion ne wo k. I sepa a es he undamen al i(n) and highe ∑ih(n) ha monic componen s con ained in he cu en aken by he load iL(n). The desi ed e e ence cu en i e (n)is hen equal o he nega ion o highe ha monic componen s; hus, he label is consequen ly changed o iinj(n) . The sum o i e (n) and iL(n) is used o compensa ion, and only he undamen al componen i(n) emains in he sou ce cu en signal. The p ocedu e desc ibed abo e can be seen in he ollowing Equa ions (1)–(3): iL(n) = i(n) + ∑ih(n)(1) iinj(n) = −∑ih(n)(2) i e (n) = i(n)−iL(n). (3) The main equi emen s o il e me hods a e accu acy and speed o cu en gene a ion, whe e he gene a ed e e ence cu en mus be gene a ed as accu a ely as possible wi hin he sho es possible pe iod. O he equi emen s a e he speed o con e gence, s abili y, minimal mean squa e e o a e, and numbe o loa ing poin ope a ions in one i e a ion. Algo i hms can be di ided in o h ee basic g oups: ime domain con ol [ 13 – 16 , 18 – 20 , 22 ], equency domain con ol [ 21 , 51 ], and adap i e me hods [ 23 – 25 ]. These me hods a e desc ibed in g ea e de ail in Sec ion 2. Ano he impo an elemen o SAPF con ol is he synch oniza ion algo i hm, which has he ask o supplying in o ma ion abou he cu en phase θ( ) o he sou ce ol age in o de o he e e ence compensa ion cu en o be gene a ed co ec ly in phase. As men ioned ea lie , compensa ion is pe o med using he sum o wo cu en signals. In o de o he sum o be co ec , he cu en signals mus be in exac ly he same phase. As seen abo e, ob aining in o ma ion on he cu en phase and accu acy demands e y low Senso s 2022,22, 7985 4 o 41 la ency. Mos me hods a e based on Phase-Locked Loop (PLL) synch onize s, al hough uncon en ional me hods can be encoun e ed; see Sec ion 3on synch oniza ion me hods. O he algo i hms equi ed o SAPF add ess DC-link Capaci o Vol age Regula ion and Cu en Con ol. DC-link ol age con ol algo i hms a e necessa y o he in e e o unc ion p ope ly; when he DC-link ol age is low, he in e e is unable o gene a e an injec ion cu en o compensa e o highe ha monics. On he con a y, a highe alue can cause he in e e o swi ch o pulse ec i ie mode, which leads o an inc ease in DC-link ol age. This ol age inc ease can damage he capaci o o o he elec onic componen s o he in e e . Cu en con ol algo i hms a e used o gene a e an injec ion cu en ha combines he equi emen s o a DC-link and a e e ence cu en a he same ime. These me hods can be di ided in o wo basic g oups, Di ec Cu en Con ol (DCC) and Indi ec Cu en Con ol (ICC), acco ding o chosen ype o eedback cu en . The con ol o powe in e e s is mainly ealized using Pulse-Wid h Modula ion (PWM), a compa a i e me hod, o pola Space Vec o PWM (SVPWM). As hese algo i hms a e de ac o ela ed o he ha dwa e o he in e e ins ead o o compu ing so wa e, hey a e no co e ed in his a icle. Rele an in o ma ion abou hese me hods can be ound in [52–57]. In his publica ion, we in oduce and discuss me hods used a a ious s ages o SAPF con ol o compensa ion o undesi able ha monic componen s. The ollowing wo sec ions deal wi h he indi idual SAPF con ol blocks, and e e y sec ion p esen s he me hods ha a e used o each. The sec ions pe aining o each me hod con ain a b ie desc ip ion necessa y o unde s and i s p inciple along wi h se e al publica ions in which he me hod has been desc ibed, simula ed, o implemen ed in eal expe imen s. E e y sec ions ends wi h a summa y able whe e di e en me hods a e compa ed. He e, i is impo an o men ion ha he compa ison o indi idual me hods is a he subjec i e, as he me hods a e necessa ily implemen ed unde a ying condi ions. Pe o ming his “objec i e” compa ison unde iden ical condi ions and quan i ying “quali y” (i.e., he dynamic esponse o di e en me hods, hei To al Ha monic Dis o ion (THD), and he abili y o wo k unde non-ideal condi ions) o a ious me hods is he u u e in en ion o he au ho s. The compa isons in his e iew a e he e o e in ended o p esen he men ioned me hods o he eade , and he ables a e in ended o p o ide a basic awa eness o he ad an ages and disad an ages o a ious me hods. This publica ion ends wi h a ho ough discussion o SAPF de elopmen and concludes wi h a b ie summa y o all he esul s he ein. 2. Ha monic Ex ac ion Algo i hms Basic con ol algo i hms we e o iginally designed o ideal ol age sou ces in which balanced and sinusoidal ol ages can be assumed. Howe e , his assump ion is no me in eal condi ions; he e o e, hese me hods ha e been ei he modi ied o newly de eloped o be able o wo k p ope ly e en unde unbalanced and non-sinusoidal ol ages. A p esen , ha monic ex ac ion me hods can be di ided in o h ee basic g oups: con ol in he ime domain [ 13 – 16 , 18 – 20 , 22 ], con ol in he equency domain [ 21 , 51 ], and adap i e il e ing [23–25] . This sec ion desc ibes me hods om all h ee g oups; in Table 1, a summa y o he p ope ies o hese me hods is p o ided. 2.1. Ins an aneous Reac i e Powe Theo y This me hod (abb e ia ed as iPQ) wo ks wi h ins an aneous alues in a h ee-phase sys em. This me hod is based on he Cla k ans o m o con e ing a h ee-phase sys em abc in o s a iona y αβ coo dina es. In o al, i is necessa y o ha e h ee ol age senso s and h ee cu en senso s. Ins an aneous ac i e powe p( ) and eac i e powe q( ) a e calcula ed as ollows: p( ) = α( )×iα( ) + β( )×iβ( ), (4) q( ) = α( )×iβ( ) + β( )×iα( ). (5) Senso s 2022,22, 7985 5 o 41 Table 1. Summa y o Ha monic Ex ac ion Me hods. Algo i hm One-Phase Th ee-Phase Dis o ed Condi ions Only Cu en Meas. No Need o Se Pa ame e s Implemen a ion Complexi y (1–5) Ad an ages Disad an ages iPQ xXx x X1 Easy o implemen and co ec unc ionali y wi h balanced and sinusoidal ol age. Necessa y o measu e h ee ol ages and cu en s. Impai ed unc ion in case o unbalanced and non-sinusoidal ol ages. CVT xXx x X1 Easy o implemen and co ec unc ionali y wi h balanced and sinusoidal ol age. Elimina es neu al cu en in all cases. Same as iPQ. PQR xXx x X2 Easy o implemen and co ec unc ionali y wi h balanced and sinusoidal ol age. Elimina es neu al cu en in all cases. Two ans o ma ions a e needed. UPC xXx x X1 The powe ac o always has a alue o 1, so he ins an aneous eac i e powe is elimina ed. Me hod does no mee IEEE 1459 s anda d, and he cu en wa e o ms co espond o ol age, hus i may no co espond o IEEE 519 s anda d. PHC xX X xX1 Me hod is insensi i e o ex e nal nega i e condi ions such as dis o ed o imbalanced main ol age. Elimina es neu al cu en in all cases. Necessa y o measu e h ee ol ages and cu en s. The powe ac o does no ake he alue o 1. SRF xX X X X 2 I is no necessa y o measu e ol age. This me hod is simple o implemen and o en used. Canno be used o single-phase sys em. SDM xX X xX2 Wo ks e ec i ely in bo h balanced and unbalanced sys ems. Elimina es neu al cu en in all cases. Signi ican ly slowe han iPQ. I is necessa y o measu e h ee ol ages and cu en s. CCT X X X xX2 Me hod does no equi e any ans o ma ion, and all calcula ions a e pe o med in a-b-c coo dina e sys em. Necessa y o measu e h ee ol ages and cu en s. Senso s 2022,22, 7985 6 o 41 Table 1. Con . Algo i hm One-Phase Th ee-Phase Dis o ed Condi ions Only Cu en Meas. No Need o Se Pa ame e s Implemen a ion Complexi y (1–5) Ad an ages Disad an ages SMT X X X xX2 Wo ks e ec i ely in bo h balanced and unbalanced sys em. Elimina es neu al cu en in all cases. Necessa y o measu e h ee ol ages and cu en s. VF xX X xX2 Me hod is insensi i e o ex e nal nega i e condi ions such as dis o ed o imbalanced main ol age. Elimina es neu al cu en in all cases. Necessa y o measu e h ee ol ages and cu en s. CPT X X X xX2 Me hod does no equi e any ans o ma ion and all calcula ions a e pe o med in a-b-c coo dina e sys em. abc. Necessa y o measu e h ee ol ages and cu en s. Compu a ionally demanding. FFT & DFT X X X X x 2 Easy o implemen . Necessa y o measu e a whole pe iod o co ec es ima ion o he e e ence cu en . FFT and DFT a e sensi i e o incomple e pe iods. RDFT X X X X x 3 Me hod calcula es he e e ence cu en om N samples and does no equi e whole pe iod. Sui able o eal- ime applica ions. Less compu a ionally demanding han FFT and DFT. Necessa y o measu e a whole pe iod o co ec es ima ion o he e e ence cu en . RDFT is sensi i e o incomple e pe iods. WT X X X X x 3 Easy o implemen . Necessa y o measu e a leas one whole measu ing window TW. HT X X X X X 2Easy o implemen . Be e han FFT in case o noisy signals. No able o de e mine sho - ime and weak dis u bances. KF X X X X x 3 Easy o implemen and compu a ionally undemanding. Me hod assumes ha he sys em and obse a ion models a e linea , which does no co espond o eal sys ems. EKF X X X X x 3 Easy o implemen and compu a ionally undemanding. Can be used in nonlinea sys ems. Fil e pa ame e s dependen on measu ed inpu da a. Senso s 2022,22, 7985 7 o 41 Table 1. Con . Algo i hm One-Phase Th ee-Phase Dis o ed Condi ions Only Cu en Meas. No Need o Se Pa ame e s Implemen a ion Complexi y (1–5) Ad an ages Disad an ages ADALINE X X X X x 5 The esul s o il a ion a e independen o ex e nal condi ions and he me hod manages o il e e en dynamically changing ypes o dis o ion. High compu a ional complexi y. Sensi i e o bad se ings. S ongly heu is ic. ANFIS X X X X x 5 The esul s o il a ion a e independen o ex e nal condi ions and he me hod manages o il e e en dynamically changing ypes o dis o ion. High compu a ional complexi y. Sensi i e o bad se ings. S ongly heu is ic. LMS X X X X x 3 Easy o implemen . Necessa y o choose co ec se ings o he adap i e il e . Time o con e gence is longe han RLS. RLS X X X X x 4 Easie se up o he adap i e algo i hm han LMS. Time o con e gence is sho e han LMS. Mo e complex implemen a ion han LMS. No ch LMS xX X X x 4 The il e is used only as second o de , so he delay is one sample. Sui able o FPGA implemen a ion. S ongly dependen on he se ing o he µpa ame e . No ch RLS xX X X x 4 The il e is used only as second o de , so he delay is one sample. Sui able o FPGA implemen a ion. Mo e complex implemen a ion han No ch LMS. Senso s 2022,22, 7985 8 o 41 The ins an aneous ac i e powe p( ) is hen di ided in o he undamen al ac i e powe pa p( ) and he ha monic pa e p( ) . A e his spli ing, he undamen al pa is neglec ed and he e p( ) pa is used. Re e ence cu en s in he α and β coo dina es a e hen back-calcula ed om e p( ) and q( ) and compensa ion cu en s a e ob ained by pe o ming in e se Cla k ans o ma ion. The whole p ocedu e can be seen in Figu e 2. abc ↓ αβ abc ↓ αβ P and Q Calc. LPF + ia( ) ib( ) ic( ) a( ) b( ) c( ) iα( ) iβ( ) α( ) β( ) p( )+ − q( ) i∗ αand i∗ β e e ence cu en gene a ion i∗ α( ) i∗ β( ) αβ ↓ abc i∗ a ( ) i∗ b ( ) i∗ c ( ) Figu e 2. Block diag am o ins an aneous eac i e p-q heo y. This me hod was o iginally p oposed in 1984 by Akagi e al. [ 58 ] and has been g adually modi ied o e many yea s [ 59 – 65 ]. I s ad an ages include easy implemen a ion and, i he sys em is supplied wi h ideal ol age, excellen esul s unde s a ic condi ions. Disad an ages include he need o measu e h ee ol ages and cu en s, and i he sys em is no supplied wi h ideal ol age, he esul s a e highly dis o ed. This me hod is e y sensi i e o imbalances and high ha monic dis o ion in he ol age signals. 2.2. C oss-Vec o Theo y A simple modi ica ion o he abo e me hod c ea es a new me hod called C oss-Vec o Theo y (CVT). Unlike iPQ, his me hod conside s all componen s gained a e Cla k T ans o ma ion, ex ending he sys em o αβ 0. This ex ension akes he he o m o be e supp ession o highe ha monic componen s in he neu al conduc o . Fo his eason, i is necessa y o ex end he o e all sys em om a Th ee-Leg o a Fou -Leg in e e . The block diag am o his me hod is shown in Figu e 3. abc ↓ αβ0 abc ↓ αβ0 Calcula ion o p, qα, qβ and qL0 HP F Calcula ion o i∗ α, i∗ β, i∗ 0 i∗ a, i∗ b, i∗ , i∗ n + + ia( ) ib( ) ic( ) a( ) b( ) c( ) iα( ) iβ( ) i0( ) α( ) β( ) 0( ) qα( ) qβ( ) q0( ) P( )˜ P( ) P∗ DC ( ) i∗ 3( ) i∗ 2( ) i∗ 1( ) i∗ n( ) Figu e 3. Diag am o C oss-Vec o Theo y. In [ 18 ], he au ho s p esen ed a compa ison o he iPQ, PQR, and CVT heo ies. Thei expe imen s we e pe o med only in he MATLAB simula ion en i onmen on RC and RL loads. The esul s and conclusion show ha while all me hods a e able o educe he THD I alue o a low one, i does no all below he 5% limi . C oss-Vec o Theo y appea s o be he bes in e ms o ha ing he smalles alue o cu en lowing h ough he neu al wi e. Fu he mo e, a modi ica ion o he C oss-Vec o Theo y me hod using PLL is men ioned which led o be e esul s (abou 3% THDI). 2.3. Ro a ing PQR Theo y The PQR me hod was designed o comple ely elimina e he ze o-sequence cu en . This me hod uses wo ans o ma ion p ocesses. The i s is he ans o ma ion o ol ages Senso s 2022,22, 7985 9 o 41 and cu en s om abc coo dina es o αβ 0 coo dina es [ 15 , 66 , 67 ]. The second ans o ma ion is he ans o ma ion o cu en s om αβ 0 coo dina es o pq coo dina es, which a e o a ed ela i e o he o iginal ixed sys em by an φ angle. The me hod uses he ollowing equa ion:   ip iq i  =    α αβ0 β αβ0 0 αβ0 − β αβ α αβ 0 − 0 α αβ0 αβ − 0 β αβ0 αβ αβ αβ0      iα iβ i0 , (6) whe e αβ0=q α2+ β2+ 02 and αβ =q α2+ β2 a e he ol age ec o magni udes. F om hese cu en s in pq coo dina es, he independen a iables p , qq , and q a e calcula ed. The las s ep is double in e se ans o ma ion om pq o abc coo dina es. See Figu e 4 o a block diag am o Ro a ing PQR Theo y. abc ↓ αβ0 abc ↓ αβ0 αβ0 ↓ pq Calcula ion o p,qq, and q HPF a( ) b( ) c( ) ia( ) ib( ) ic( ) iα( ) iβ( ) i0( ) α( ) β( ) 0( ) ip( ) iq( ) i ( ) pl+ epl P∗ dc p∗ pq ↓ αβ0 ↓ abc α( ) β( ) 0( ) ql ( ) = q∗ ( ) qlq( ) = q∗ q( ) i∗ a( ) i∗ b( ) i∗ c( ) i∗ n( ) Figu e 4. Block diag am o Ro a ing PQR Theo y. Re uel a e al. [ 19 ] desc ibed a ious me hods ha we e simula ed and applied in h ee cases: sinusoidal balanced, sinusoidal unbalanced, and non-sinusoidal balanced sou ce ol age. The PQR me hod was applied o a sinusoidal balanced sou ce ol age, achie ing ze o THD U alue; o a sinusoidal unbalanced sou ce ol age, he THD U alue was app oxima ely 10%; and o a non-sinusoidal balanced sou ce ol age he THD U alue was app oxima ely 6%. Neu al cu en was elimina ed in all h ee cases. 2.4. Uni y Powe Vec o This me hod aims o conside he load in combina ion wi h he ac i e powe il e as a linea load along wi h he sou ce. I his equi emen is ul illed, he sou ce cu en a e compensa ion can be desc ibed as iS e =k× s=k×Vmsin ω , (7) whe e k is he conduc i i y o he nonlinea load and he powe ac i e il e . A e compensa ion, he sou ce cu en is sinusoidal, has he same shape as he sou ce ol age, and is in phase. In addi ion, highe ha monics a e supp essed, and he powe ac o is equal o one [16,68,69]. The e e ence cu en can be desc ibed as ollows:    iS0 e iSα e iSβ e   =k×  0 α β =~ pLαβ +~ pL0  2 0+ 2 α+ 2 βDC ×  0 α β . (8) In a s udy by Mon e o e al. [ 16 ], he UPF heo y was es ed and compa ed wi h he iPQ heo y, Synch onous Re e ence F ame (SRF), and PHC me hods. A o al o i e scena ios we e compa ed, and he me hods we e es ed unde di e en ope a ing condi ions (ideal ol age sou ce, dis o ed and asymme ical ol age sou ce, di e en ypes o load dis o ion, e ce e a). In he e alua ion o hese esul s, he cu en wa e o ms we e iden ical o hose o Senso s 2022,22, 7985 16 o 41 ans o m is eached and calcula ed [ 106 ]. When he equency spec um has been de e mined, he injec ion cu en is equal o summa ion o all sinus unc ions (wi h known ampli ude, equency, and phase). Asiminoael e al. [ 106 ] ca ied ou a compa ison o h ee me hods based on Fou ie T ans o m, DFT, FFT, and he ecu si e a ia ion o DFT. Thei compa ison was pe o med in a simula ion en i onmen , and he abo e-men ioned s a emen s abou DFT and FFT we e con i med. In addi ion, a compa ison was made wi h iPQ, SRF, and gene alized in eg a o s. The au ho s s a ed ha he main bene i o Fou ie -based me hods is a oiding he need o measu e he ol age ( educing he equi ed numbe o senso s) and he need o implemen a nume ical il e . Fu he mo e, FT me hods pe o m e y well unde dis o ed ol age condi ions. On he o he hand, he calcula ion bu den o FT me hods is e y high. 2.13. Recu si e DFT Recu si e Disc e e Fou ie T ans o m (RDFT) [ 21 , 51 ] wo ks on simila p inciples as DFT while ecalcula ing he signal spec um wi h each new sample. The Fou ie coe icien s a e es ima ed in a window o samples wi h size N which is hen shi ed by he numbe o samples in p , whe e p∈(1, N) . As such, he es ima e is calcula ed only om new samples in p . The e o e, RDFT is much less compu a ionally demanding han DFT o FFT, and is much mo e sui able o eal- ime applica ions. The disad an age o his me hod, as wi h DFT and FFT, is i s sensi i i y o noise and ansi ions be ween signal shapes. The accu acy and p ecision o his me hod depend on a sliding window. In [ 21 ], he au ho s discussed he main p ope y o RDFT, namely, ha RDFT manages composi e wa e o ms wi hou an elabo a e signal model in he equency domain hanks o he implemen a ion o loa ing-poin co ela ion. De i a ion o common indus ial pe iodic wa e o ms is possible wi hou knowledge o he physical model and i s inpu s. They u he men ioned ha wi h a sui able modi ica ion o he RDFT il e ou pu (in oduc ion o he window unc ion), leakage o he spec um can be educed. In he end, he compu a ional demands o RDFT we e said o be e y modes . Ve i ica ion o hese indings was pe o med in a simula ion. The block diag am o his me hod can be seen in Figu e 10. Fundamen al Pe iod RDFT Las Sample New Sample Rec angula Mo ing Window Figu e 10. Recu si e DFT p inciple. 2.14. Wa ele T ans o m Wa ele T ans o m can be used in combina ion wi h he SRF me hod by eplacing he LPF FIR il e by he wa ele ans o m o di ide he signal in o de ailed componen s by a High-Pass Fil e (HPF) and he app oxima ion componen s by he Low-Pass Fil e (LPF) [ 108 ]. The dominan app oxima ion componen is he undamen al ha monic componen , and he de ailed componen s con ain ha monic componen s. This me hod is used mainly due o he ac ha , unlike he FIR il e , he e is no delay. One publica ion whe e his me hod was used [ 109 ] compa ed i wi h he con en ional window me hod using he window unc ion. Fu he mo e, he me hodology o sui ably selec ing he mo he wa ele in e ms o e iciency o ansien s, low o e shoo s, and oscilla ions in he equency domain was discussed. Expe imen s we e pe o med only by simula ion, and he me hod was no e i ied on a eal SAPF. The ad an age o his me hod o e he con en ional SRF me hod is ha he esponse o he il e c ea ed by WT is an o de o magni ude as e compa ed o he con en ional FIR il e and does no su e om any o e shoo . Applying he Hamming window unc ion can u he imp o e he esul s wi h WT. Db8 (Daubechies 8) was chosen as he pa en wa e in he abo e-men ioned s udy; Senso s 2022,22, 7985 17 o 41 he au ho s no ed ha he main disad an age o his me hod is he need o know and use only one whole measu ing window TW. The p inciple o his me hod is shown in Figu e 11. D iesen e al. [ 110 ] s a ed ha he me hod is easy o implemen and combines many ad an ages om se e al con en ional me hods. Ad an ages include he ac ha he me hod can easily be used o single-phase sys ems and ha i is applicable e en unde ol age-dis o ed condi ions. In e ms o dynamics, i has a e y as esponse o ansien s. Howe e , nei he expe imen s no simula ions we e pe o med o e i y he indings. abc ↓ αβ ↓ dq PLL dq ↓ αβ ↓ abc Wa ele Fil e ing ia( ) ib( ) ic( ) a( ) b( ) c( ) i∗ a( ) i∗ b( ) i∗ c( ) id( ) iq( )e id( ) e iq( ) −θθ θ x[n] d1 a1 d2 a2 d3 a3 d4 a4e id,e iq ¯ id,¯ iq Le el 1 Le el 2 Le el 3 Le el 4 Wa ele Fil e ing Figu e 11. Wa ele T ans o ma ion p inciple. 2.15. Hilbe T ans o m The Hilbe T ans o m (HT) can be used o calcula e he ins an aneous p ope ies o a signal. I is o en used in combina ion wi h empi ical mode decomposi ion as he Hilbe –Huang ans o m (HHT). I is mos app op ia e o apply HT o he signal a e i has been p ocessed, i.e., a e noise il e ing. The ma hema ical de ini ion o HT is [ 111 , 112 ]: y( ) = P πZ 0x(τ) −τdτ, (38) z( ) = x( ) + jy( ), (39) whe e P is Cauchy p incipal alue, z( ) is he analy ic signal o med om he ini ial signal x( ) and i s HT, he pa ame e a( ) is he ins an aneous ampli ude, and φ is he ins an aneous phase [111,112]. Hilbe ans o m can be simpli ied as a con olu ion be ween he signal and 1 π . I can be implemen ed by an ideal il e wi h an ampli ude esponse o uni y and a phase esponse ha is a cons an nine y-deg ee delay. The Hilbe ans o m can be called a quad a u e il e , as i shi s he phase o he spec al componen s by π 2 [111,112]. The ad an age o HT is ha i is sui able o calcula ing he ins an aneous equency. The ins an aneous equency is an exp ession o he change in he ins an aneous phase shi , and can be calcula ed using he analy ical me hod. I is ma hema ically de ined as ollows [111,112]: φ=1 2π×d d ×φ( ). (40) Senso s 2022,22, 7985 18 o 41 Aghazadeh e al. in 2013 [ 111 ] used HT o c ea e a i ual phase and o ans o m a single-phase sys em in o a wo-phase symme ical sys em. In hei s udy, hey p esen ed a new me hod o ha monics elimina ion using a single-phase ac i e il e . Fo e alua ion, hey used THD. Simula ions we e pe o med and he esul s showed ha he new me hod in a single-phase AC ailway sys em was mo e e ec i e han he o he compa ed me hods. In 2021, Swa nka e al. [112] used HT in combina ion wi h S ockwell T ans o m (ST) o e alua e powe quali y (PQ) dis u bances in a dis ibu ion sys em wi h a ailabili y o high-pene a ion o wind powe gene a ion. Thei hyb id algo i hm was designed o iden i y PQ issues using IPI and IPL no ices. Acco ding o he esul s, he p esen ed solu ion main ained be e pe o mance han a DWT-based me hod. Hilbe ans o m was used o p ocess ol age signals du ing he e alua ion p ocess. 2.16. Kalman Fil e The Kalman Fil e (KF) is a p edic ion-es ima ion algo i hm ha es ima es he use ul componen o he signal acco ding o p e ious alues. This es ima ed signal is compa ed wi h he eal signal, and he di e ence se es o imp o e he es ima ion o u u e samples. The basic Kalman il e can be desc ibed using wo equa ions in he o m o models [113–115] . P ocess model: x(n)=A×x(n−1)+w(n), (41) whe e x(n) is a ime- a ying s a e a iable, A is a s a e ansi ion ma ix, and w(n) is a p ocess noise ec o . Measu emen model: z(n)=H×x(n)+ (n), (42) whe e z(n) is a measu ed signal, H is an obse a ion ma ix, and (n) is he obse a ion noise ec o . KF is pe o med in wo phases, p edic ion and co ec ion. The p edic ion phase is calcula ed acco ding o p e ious da a, and co ec ion is hen ca ied ou acco ding o a new measu emen . Figu e 12 shows a simple s uc u al diag am o KF. Time Upda e 1. P ojec ion o u u e s a e ahead: xk=Axk+wk 2. P ojec ion o e o co a iance ahead: P− k=Apk−1AT+Q Ini ial S a e xk,Pk−1 Measu emen Upda e 1. Compu e Kalman gains: Kk=P− kHT HP − KHT+R 2. Udpda e es ima ion wi hin measu emen cu en (xk): bxk=bxk+Kk(zk−Hbx− k) 3. Upda e he e o co a iance: Pk= (I−KkH)P− k Figu e 12. S uc u e o ecu si e calcula ion by p edic ion–co ec ion me hod. KFs may appea in di e en places in he SAPF s uc u e. The i s app oach is based on he SRF me hod, in which a low-pass (LP) il e is used o ex ac ion. The LP il e can be eplaced by a KF o inc ease he obus ness o he sys em. This is a sui able loca ion, as he LP il e is a linea sys em. This s a egy is used in [ 115 ]. The me hod was es ed in bo h a simula ed en i onmen and a eal expe imen wi h RC load, and a compa ison was made wi h a con en ional low pass il e . The esul ing THD I was 0.42%, be e han he low pass il e (wi h a alue 2.38%), and me he THDIlimi alues se by he IEEE 519 s anda d. Ano he app oach was desc ibed in [ 114 ]. This app oach uses KFs o es ima o s he e e ence cu en and ol age. The cu en es ima o wi h KF is based on he i s en odd cu en ha monics. The ou pu o he es ima o is he ins an aneous alue o he phase cu en ; il e ing ou he undamen al ha monics p oduces he e e ence cu en . The ol age es ima o wi h KF is based on he i s i e odd ol age ha monics. Toge he wi h DC-link ol age con ol, his p o ides a e e ence cu en which co esponds o he losses in he ac i e il e . Combining he wo e e ence cu en s p oduces he desi ed e e ence Senso s 2022,22, 7985 19 o 41 cu en . This me hod was es ed by simula ion in MATLAB, and i was ound ha THD I dec eased om 95.6% o 12.9%. In o he s udies [ 113 , 116 ], KF has been used o e e ence cu en es ima ion i∗ a,b,c . This solu ion achie es be e alues compa ed o iPQ. In [ 113 ], he sys em was complemen ed by obus con ol (H-in ini y). This connec ion leads o obus ness o he whole sys em, simpli ica ion o he con ol s uc u e, and educ ion o he numbe o senso s (as he e is no need o egula e he DC-link ol age using a sepa a e PI con olle ). In 2018, P ince e al. [116] used a ol age egula o o DC-link and KF o cu en ex ac ion. Acco ding o he esul s, he THDIa e compensa ion was 2.18%, compa ed o 30.56% be o e compensa ion. In 2017, Panig ahi [ 113 ] achie ed a THD I o 2.2% a e compensa ion, compa ed o 25.9% be o e compensa ion. 2.17. Ex ended Kalman Fil e Ex ended KF (EKF) is usually used o nonlinea sys ems. The nonlinea sys em unc ion is app oxima ed using linea unc ions a he poin o es ima ion (Taylo ’s de elopmen ). The basic sys em can be desc ibed by he p ocess model p o ided in Equa ion (43) and he measu emen model by Equa ion (44) [117–120]: x(n)= (x(n−1),u(n−1),w(n−1)), (43) whe e x(n) is a ime- a ying s a e a iable, is he nonlinea sys em unc ion, u(n) is an inpu , and w(n)is he p ocess noise z(n)=h(x(n), (n)), (44) whe e z(n) is hemeasu edsignal, h is henonlinea unc ion, and (n) is hemeasu emen noise. Simila o he basic KF, an EKF is di ided in o wo phases. A simpli ied diag am is shown in Figu e 13. Time Upda e (“P edic ”) 1. P ojec he s a e ahead 2. P ojec he e o co a iance ahead Measu emen Upda e (“Co ec ”) Ini ial es ima es o and 1. Compu e he Kalman gain 2. Upda e es ima e wi h measu emen zk 3. Upda e he e o co a iance KkPkHk THkPkHk TRk +� � 1– = x ˆkx ˆkK zkHkx ˆk –� �+= PkI KkHk –� �Pk = x ˆk1+ -Akx ˆkBuk += Pk1+ -AkPkAk TQk += x ˆkPk – – – –– –– – – Figu e 13. Simpli ied diag am o EKF algo i hm o pa ame e es ima ion. In [ 118 ], basic KF, EKF, and wo o he KF modi ica ions (ex ended complex KF and obus ECKF) we e desc ibed and compa ed. In all, cases THD I was educed om 24.9% o a alue below 5%. The e we e no signi ican di e ences in THD I achie ed by he di e en KF ypes (THD I= 4.79% was achie ed by KF and THD I= 4.92% was achie ed by EKF). These esul s show he o dina y linea KF pe o ming be e han he EKF, while he RECKF algo i hm achie ed he bes esul s (THDI4.46%). 2.18. Unscen ed Kalman Fil e The e a e o he a ian s o KF, o example, he Unscen ed Kalman il e (UKF). I s s a egy is no a linea iza ion; a he , i uses di ec nonlinea i y. Cu en ly, i s deploymen is no common in he SAPF amewo k. In one s udy [ 121 ], UKF was used o es ima e indi idual powe and equency componen s. UKF showed imp o ed he pe o mance, especially wi h espec o ansien phenomena in he ne wo k. 2.19. Adap i e Linea Neu on ADALINE is an abb e ia ion o Adap i e Linea Neu on, a neu al ne wo k ha has wo laye s, inpu and ou pu . I can es ima e unc ions ha ha e linea dependence be ween i s inpu and ou pu , and e ains i s unc ionali y in ce ain nonlinea eal applica ions [ 122 ]. Senso s 2022,22, 7985 20 o 41 Inpu s xi a e mul iplied by adjus able weigh s wi , hen a sum is de i ed om hese mul iples. The es ima ed ou pu y is compa ed wi h a e e ence alue g ( a ge ) and he esul ing e o e is used by he Leas Mean Squa es (LMS) algo i hm o ain he ne wo k weigh s. A design scheme o he algo i hm is shown in Figu e 14. - + P LMS g . . . . . . . . . w1 w2 wd x1 x2 xd y Inpu Ou pu Figu e 14. ADALINE schema ic. I is assumed ha he cu en lowing h ough he load iL( ) is a dis o ed signal [ 23 ], whe e 1 is a undamen al ha monic equency o he g id and ak and bk a e he ha monic sine and cosine ampli udes, espec i ely. Assuming ha he alue o 1 mus be known, he sine and cosine componen s can be easily calcula ed. Howe e , he ampli ude alues o ak and bk a e unknown a iables and mus be es ima ed using he ADALINE algo i hm. The sine and cosine componen s can be hough o as inpu s o he ADALINE equa ion, wi h he indi idual ampli udes ak and bk as ne wo k weigh s. The ou pu o he ne wo k is y , which in his case is he es ima ed cu en iL lowing h ough he load. The measu ed cu en lowing h ough he load se es as he e e ence alue g . The es ima ed cu en lowing h ough load ycan be w i en as yn= H ∑ k=1,5,7,11... an ksin (2πk 1 n)+bn kcos (2πk 1 n), (45) whe e yn is sampled by ime n=nTs (whe e n is he sample index and Ts is he sampling pe iod), k is he ha monic componen index, and H is he alue o he highes examined ha monic componen . Componen s ha a e e en o mul iples o h ee a e omi ed due o hal -wa e symme y and h ee-phase connec ion [23]. Indi idual scales a e ained by he LMS algo i hm, which is based on he op imiza ion o weigh s using G adien Descen (GD). The GD p ocess is applied o minimize he squa e o he e o be ween he e e ence gn=in L and he es ima ed ou pu yn . The c i e ion can be hen exp essed as ollows: E=1 2(en)2=1 2(in L−yn)2=1 2in L−(wn)Txn2. (46) Using he g adien alue ∇E wi h espec o he weigh ec o wn , he esul ing exp ession appea s as ollows: ∇E(wn)=−en×xn. (47) The ule o weigh adjus men hen appea s as wn=wn−1−η×∇En(w)=wn−1+η×en×xn, (48) whe e ηis he s ep size o lea ning a e o he weigh upda e. In 2011, Bha acha ya and Chak abo y [ 29 ] used ADALINE o es ima e he compensa ion cu en in o de o imp o e he con e gence ime and educe he compu a ional demands o he me hod. The THD I c i e ion was used o e alua e he quali y o il a ion. The neu al ne wo k weigh s we e adjus ed so ha he THD I eached i s local minimum. Simula ions in he SIMULINK en i onmen we e used in expe imen s pe o med unde labo a o y condi ions. The esul s con i med ha he p oposed solu ion was unc ional o bo h symme ical and asymme ical loads in a h ee-phase h ee-wi e sys em. The Senso s 2022,22, 7985 21 o 41 expe imen e ealed ha he use o wo weigh s and wo inpu ec o s helped i o con e ge e y quickly. In 1996, Dash e al. [ 123 ] used ADALINE o es ima e Fou ie coe icien s in a signal pollu ed wi h noise, highe ha monics, and DC componen s. The lea ning pa ame e s o he neu ons we e se o minimize he e o be ween he measu ed and desi ed cu en signals. The size o he weigh s was es ima ed using LMS and nonlinea weigh se ings. Using his algo i hm, an adap i e sea ch o highe ha monic componen s was easily achie ed. Compa ed o he backp opaga ion app oach, be e managemen s abili y and as e con e gence imes we e a ained. The expe imen s we e simula ed in MATLAB and e i ied on a eal pla o m. The ADALINE me hod was compa ed wi h o he algo i hms based on he Kalman il e and DFT, and showed signi ican ly be e quali y. Thanks o i s adap abili y, i was s a ed ha his me hod is sui able o inding highe ha monic componen s whe e bo h he ampli ude and he phase angle o en change. In 2007, Abdeslam e al. [ 26 ] designed and es ed a complex sys em whe e ADALINE was used in an SAPF applica ion o sol e h ee di e en p oblems, namely, ex ac ion o ol age ha monic componen s o egain a symme ical and balanced ne wo k, il e ing o highe ha monic componen s, and con ol o he SAPF powe ci cui . Using a uni ied sys em o me hods, highe e iciency was achie ed and he quali y o il a ion was imp o ed. The main ad an age o his app oach is he abili y o adap in eal ime o a ying ypes o loads. The expe imen s we e e i ied in bo h he SIMULINK simula ion en i onmen and in a eal scena io. The au ho s highligh ed he ad an ages a ising om he use o one ADALINE me hod o a ious p oblems wi hin one SAPF sys em. In a 2014 s udy, Qasim e al. [ 23 ] compa ed he ADALINE me hod wi h he eed- o wa d Mul ilaye Neu al Ne wo k (MNN) me hod, ano he equen ly used me hod o SAPF con ol. ADALINE was ained du ing ope a ion using he LMS algo i hm, while he MNN was p e- ained using he Scale Conjuga e G adien (SCG) backp opaga ion algo i hm. The ask was o ex ac he ampli ude o he undamen al ha monic componen o he cu en lowing h ough he load. Bo h algo i hms we e e i ied in simula ions as well as h ough expe imen s. Bo h he ob ained esul s and he conclusion o he s udy showed he ADALINE me hod o be mo e sui able o SAPF managemen han MNN. This was especially ue in scena ios whe e an unlea ned load was con olled; he MNN me hod ailed o ex ac he basic componen , which esul ed in o e compensa ion by he PI con olle . In con as , ADALINE can be used in any scena io, as i lea ns adap i ely du ing i s ope a ion. 2.20. Adap i e Neu o-Fuzzy In e ence Sys em The Adap i e Neu o-Fuzzy In e ence Sys em (ANFIS) is a me hod based on a uzzy expe sys em implemen ed by a mul ilaye o wa d neu al ne wo k. Func ionally, i is equi alen o a uzzy in e ence sys em o he Takagi–Sugeno [ 124 ] ype. The wo-inpu ANFIS ule basis con ains wo Fuzzy IF–THEN T-S ules o he ollowing o m: IF xis Aiand yis BiTHEN i=pix+qiy+ i(49) whe e x and y a e inpu s, Ai and Bi a e uzzy se s, i a e ou pu s o he uzzy sys em, and pi , qi , and i a e se ing pa ame e s ha a e ob ained by es ima ion du ing he lea ning p ocess. The ANFIS a chi ec u e o implemen ing hese wo ules is shown in Figu e 15 [ 125 ]. The squa es indica e a ixed node, while he ci cles indica e an adap i e one. ANFIS consis s o a o al o i e laye s; he unc ion o he nodes in a gi en le el is o he same ype. A mo e de ailed desc ip ion o he ANFIS a chi ec u e shown in Figu e 15 can be ound in [126]). The pa ame e s o se ing he FIS a e o wo ypes: non-linea in he i s laye and linea in he ou h laye . Fi s , i is necessa y o ini ialize he Fuzzy In e ence Sys em (FIS) app oxima ely, which is hen se up by he ANFIS adap i e lea ning p ocess. ANFIS uses he o iginal FIS and se s i up using a hyb id lea ning echnique combining he eedback g adien me hod and he leas squa es me hod. The esul o each i e a ion o lea ning is an e o ha is g adually educed. Lea ning ends when he se numbe o i e a ions is eached Senso s 2022,22, 7985 22 o 41 o he sys em e o is wi hin accep able limi s. The g adien me hod is usually used o se he inpu laye and he leas squa es me hod is used o op imize he pa ame e s in he de uzzi ica ion laye . A1 A2 B1 B2 Π Π N NP x y w1 w2 w1 w2 w1 1 w2 2 Laye 1Laye 2Laye 3Laye 4Laye 5 xy xy Figu e 15. ANFIS a chi ec u e schema ic wi h wo ules. In he lea ning algo i hm, each i e a ion epea s a o wa ds and backwa ds un. In he o wa ds un, aining pa e ns a e ed o he inpu ( X and Y in he gene al case), hen he ou pu s o he indi idual laye s a e g adually calcula ed, and inally he esul ing pa ame e s a e iden i ied by leas squa es es ima ion. The ou pu ec o Z o a linea unc ion has he shape Zi=miX+niY+qi. (50) In 2013, Rou h and A un [ 24 ] compa ed h ee me hods o imp o e powe quali y, supp ess he eac ance componen o he powe , and compensa e o highe ha monics a nonlinea loads. The con ol was pe o med using a PI con olle , a uzzy con olle , and ANFIS. The h ee me hods we e compa ed ia simula ions. The esul s showed ANFIS wi h he bes esul s in e ms o THD I , and i was able o compensa e o e en he la ges de ia ions. ANFIS was used in a 2013 s udy [ 127 ] o manage a h ee-phase SAPF as a cos -e ec i e solu ion o powe quali y p oblems. The il e showed good esul s a bo h he s eady s a e and unde dynamically changing condi ions. The ad an ages o he p oposed con ol sys em we e mainly he independence o he dis o ion and asymme y o he inpu sou ce ol age, as and accu a e ex ac ion o he undamen al ha monic componen unde bo h symme ical and asymme ical condi ions, and he ease and simplici y o implemen ing he a chi ec u e. The esul s showed ha SAPF was able o educe THD I o en hs o a pe cen , which ully complies wi h he IEEE-519 s anda d. I was compa ed wi h a uzzy con olle and ANFIS, wi h he esul s showing imp o emen o up o 50% compa ed o he o he con olle s. In 2013, Ma inek e al. [ 128 ] used ANFIS o con ol he d i e o mee SAPF unc ionali y. ANFIS was success ully implemen ed; i s unc ionali y in e ms o supp ession o highe ha monic componen s was e i ied and a compa ison o a ious algo i hm se ings. A o al o ou ANFIS models we e p esen ed, which di e ed in hei numbe o nodes (21–75), numbe o linea pa ame e s (12–75), numbe o nonlinea pa ame e s (12–30), and numbe o uzzy ules (4–25). The in es iga ed phases o he ne wo k eached THD I alues o app oxima ely 98%; he i s model, Model A, supp essed THD I o app oxima ely 9%, while he emaining Models B, C, and D we e able o supp ess THD I below app oxima ely 1%, which ully complies wi h IEEE-519 and IEC-61000-3 s anda ds. In conclusion, i was ound ha his me hod p o ides clea ly be e esul s han he iPQ me hod, is easie o implemen on a mic op ocesso , and can cope wi h equency changes due o ne wo k ins abili y. Sys em lea ning was pe o med o line. The au ho s u he s a ed ha he subjec o hei u u e esea ch was o adjus men he sys em o allow i o be augh du ing ac i e p ocesses, and hus become able o cope wi h new ne wo k pollu ion condi ions. 2.21. Leas Mean Squa es Algo i hm Figu e 16 shows a block diag am o an adap i e il e o use in an unknown o ime- a ian en i onmen which is unp edic ed. Fo his s uc u e, Fini e Impulse Response Senso s 2022,22, 7985 23 o 41 (FIR) o In ini e Impulse Response (IIR) a e used wi h il e s o adap i e coe icien s which a y in ime. These il e s, which a e con olled by adap i e algo i hms, a e called adap i e il e s. Va ious adap i e algo i hms [ 129 ] om he LMS and RLS amilies ha e been used in his applica ion, and a e desc ibed below. The equi ed inpu s o adap i e il e s a e he e e ence signal x(n) and inpu signal d(n) . The ou pu s om adap i e il e s a e he desi ed signal y(n)and e o signal e(n), whe e nis he numbe o i e a ions. Adap i e Algo i hm + - d(n) x(n)e(n) w Figu e 16. Schema ic o an adap i e algo i hm. The LMS algo i hm is he main ep esen a i e o a class o s ochas ic g adien algo i hms based on he Wiene heo y and he me hod o leas squa es. This me hod is widely used due o i s simplici y, low compu a ional complexi y, and obus ness. Each i e a ion o he LMS algo i hm equi es h ee di e en s eps o be pe o med in a speci ied o de [25,130,131]. The ou pu o an FIR il e y(n)is calcula ed as ollows: y(n)=~ wT(n)×~ x(n)= N ∑ i=0 wi(n)×x(n−i), (51) while he alue o he es ima ed e o e(n)is calcula ed as e(n)=d(n)−y(n). (52) In he end, he weigh s o he il e ec o ~ w(n) a e upda ed wi h espec o he ollowing i e a ion: ~ w(n+1)=~ w(n)+2×µ×e(n)×~ x(n). (53) The pa ame e µ is called he con e gence cons an o s ep size o he LMS algo i hm. I is a small posi i e cons an wi h a alue gene ally less han 1, and a ec s he adap i e p ope ies o he algo i hm. La ge s ep size alues esul in a loss o s abili y and inaccu a e il a ion. Smalle alues inc ease compu a ion ime and demands and ex end he con e gence ime. The e a e modi ica ions o he LMS algo i hm ha a e wo h men ioning, such as No malized LMS [ 132 , 133 ] and Spa se LMS [ 134 ]. The NLMS algo i hm has a a iable con e gence cons an o each i e a ion, which imp o es he con e gence a e o he adap i e il e . The SLMS algo i hm in ol es ewe mul iplica ion ope a ions han he LMS, al hough i has a slowe con e gence a e and highe s eady s a e e o . In [ 132 ], ou eam used simula ions o examine he abili y o adap i e LMS and RLS algo i hms o compensa e o highe ha monic componen s o he cu en . We assumed 100 µ s as he heo e ical delay o he in e e . A e applying he LMS algo i hm, he THD I alue was educed om 63.27% o 12.51%. The s ep size µ had a g ea in luence on he quali y o compensa ion, making i necessa y o ind a comp omise be ween he THD I alue and he con e gence ime. 2.22. Recu si e Leas Squa es The Recu si e Leas Squa es (RLS) algo i hm is he main ep esen a i e in a class o ecu si e algo i hms based on Kalman il e ing heo y and he leas squa es me hod. Unlike he LMS algo i hm, i has i s own s a is ical concep . The RLS algo i hm wo ks wi h a e age alues calcula ed om ime de elopmen s. The s uc u e o he il e emains he same as wi h he LMS algo i hm; only he adap i e p ocess is di e en , due o he use o Senso s 2022,22, 7985 24 o 41 a e ages. Each i e a ion o he RLS algo i hm equi es i e di e en s eps o be pe o med in a speci ied o de [25,130,131]. The ou pu o he FIR il e y(n)is calcula ed as ollows: y(n)=~ wT(n)×~ x(n)= N ∑ i=0 wi(n)×x(n−i). (54) The medium- ange ec o gain ~ k(n) is upda ed wi h espec o he ollowing i e a ion: ~ k(n)=P(n−1)×~ x(n) λ+~ xT(n)×P(n−1)×x(n). (55) The alue o he es ima ed e o e(n)is calcula ed as e(n)=d(n)−y(n). (56) The weigh s o he il e ec o ~ w(n) a e upda ed wi h espec o he ollowing i e a ion: ~ w(n)=~ w(n−1)+e(n)×k(n). (57) In he end, he in e se ma ix P(n)is calcula ed as ollows: P(n)=λ−1×P(n−1)−λ−1×k(n)×~ xT(n)×P(n−1). (58) The unc ionali y o he RLS algo i hm is undamen ally in luenced by he choice o he o ge ing ac o λ , aking he alues λ∈(0, 1] . Assuming ha λ= 1, i is possible o use an es ima e wi hou o ge ing. In p ac ical implemen a ion, λ om λ= 0,98 o λ= 1 is usually conside ed. The e is a modi ica ion o he RLS algo i hm called QR-RLS (o QRD RLS). This modi ica ion uses a iangula ion p ocess and has good ma hema ical p ope ies hanks o obus QR decomposi ion. In [ 132 ], ou eam examined he abili y o adap i e LMS and RLS algo i hms in simula ions o compensa e o highe ha monic componen s o he cu en . We assumed 100 µ s as he heo e ical delay o he in e e . A e applying he RLS algo i hm, he THD I alue was educed om 63.27% o 6.43%. The o ge ing ac o λ had a ce ain e ec on he quali y o he compensa ion, de e mining how many samples he algo i hm can emembe . Fo λ alues in he ange o 0.999 o 1, he e was no a signi ican di e ence in THD I o SNR alues; howe e , a a λ alue o 0.99 he e was a high THD I alue, meaning ha he sys em was uns able. 2.23. No ch LMS Algo i hm Figu e 17 shows a block diag am o a no ch adap i e il e . The adap i e il e using his a chi ec u e is able o wo k wi h mul iple e e ence inpu signals om di e ence sou ces. One ans e se FIR il e weigh o a ec o coe icien wi is needed o each e e ence inpu signal [135,136]. The no ch LMS is a modi ica ion o an LMS algo i hm o a no ch adap i e il e s uc u e. This me hod is used in a h ee-phased sys em. As wi h he LMS algo i hm, he no ch LMS algo i hm equi es h ee di e en s eps o be pe o med in a speci ied o de [135,136]: The ou pu o he FIR il e y(n)is calcula ed as ollows: y(n)=~ wT 1(n)×~ x1(n)−~ wT 2(n)×~ x2(n), (59) and he alue o he es ima ed e o e(n)is calcula ed as e(n)=d(n)−y(n). (60) In he end, he weigh s o he il e ec o s ~ w1(n) and ~ w2(n) a e upda ed wi h espec o he ollowing i e a ion: Senso s 2022,22, 7985 25 o 41 ~ w1(n+1)=~ w1(n)+2×µ×e(n)×~ x1(n), ~ w2(n+1)=~ w2(n)+2×µ×e(n)×~ x2(n).(61) In a p e ious publica ion o ou eam [ 135 ], his me hod was implemen ed on an FPGA and i s unc ionali y was e i ied in p ac ice h ough a eal expe imen . The THD I alue was educed om alues a ound 25% o alues a ound 1% a low alues o he pa ame e µ . The esul s o his expe imen showed ha he size o µ di ec ly a ec s bo h he quali y o he esul ing il a ion (THD I alue) and i s dynamics. A highe alues o µ , he adap a ion ime dec eases (highe dynamics o he sys em), howe e , he supp ession o ha monic componen s is no e ec i e (up o 13% in he expe imen ). Adap i e Algo i hm + + + + y(n) w2 w1 e(n)d(n) x2(n) x1(n) Figu e 17. Block diag am o he no ch adap i e il e . 2.24. No ch RLS Algo i hm The no ch LMS is a modi ica ion o he RLS algo i hm o a no ch adap i e il e s uc u e. This me hod is used in a h ee-phased sys em. As wi h he RLS algo i hm, he no ch RLS algo i hm equi es i e di e en s eps o be pe o med in a speci ied o de [135,136]: The ou pu o he FIR il e y(n)is calcula ed as ollows: y(n)=~ wT 1(n)×~ x1(n)+~ wT 2(n)×~ x2(n), (62) and he medium- ange ec o gains~ k1(n)and~ k2(n)a e calcula ed as ~ k1(n)=P1(n−1)×~ x1(n) λ+xT 1(n)×P1(n−1)×~ x1(n), ~ k2(n)=P2(n−1)×~ x2(n) λ+xT 2(n)×P1(n−1)×~ x2(n).(63) The alue o es ima ed e o e(n)is calcula ed as e(n)=d(n)−y(n). (64) The weigh s o he il e ec o s ~ w1(n) and ~ w2(n) a e upda ed wi h espec o he ollowing i e a ion: ~ w1(n)=~ w1(n−1)+e(n)×k1(n), ~ w2(n)=~ w2(n−1)+e(n)×k2(n).(65) In he end he in e se ma ices P1(n)and P2(n)a e calcula ed as ollows: P1(n)=λ−1×P1(n−1)−λ−1× k1(n)×~ xT(n)×P1(n−1), P2(n)=λ−1×P2(n−1)−λ−1× k2(n)×~ xT(n)×P2(n−1). (66) In [ 135 ], ou eam implemen ed no ch RLS in combina ion wi h Cla ke ans o ma ion in simula ions. We simula ed a 100 µ s delay o he in e e and examined THD I and SNR alues in a scena io whe e he cu en changed in a speci ied o de o 160 s. The ela i e imp o emen in THDIwas abou 20% and he imp o emen in SNR was abou 10%. Senso s 2022,22, 7985 32 o 41 4. Fu he Resea ch Ou eam app oached he p esen e iew mainly in he con ex o p epa ing o u u e esea ch o a p ac ical na u e. This esea ch will deal wi h he p ac ical implemen a ion o as many SAPF con ol me hods as possible unde he condi ions o a eal dis ibu ion ne wo k. Howe e , he condi ions o he dis ibu ion ne wo k will be ully unde ou con ol. Pa icula a en ion will be paid o main aining he epea abili y and uni o mi y o indi idual es s. This means ha all indi idual me hods will be subjec ed o he same condi ions and he same es s. In his way, i will be possible o objec i ely compa e all me hods and quan i y he “s eng h o he me hod” using a homogeneous c i e ion, such as he alue o esul ing THD I , ela i e imp o emen o THD I , Signal o Noise Ra io (SNR), o magni ude o he cu en lowing h ough he neu al wi e. Me hods will be implemen ed on a eal in e e o modula a chi ec u e o ou own design, wi h he indi idual pa s o SAPF able be changed independen ly o he o he s (so ha i is no necessa y o change he whole con ol sys em in o de o change he ype o synch oniza ion algo i hm). The sys em will he e o e be o an open a chi ec u e, no be a closed solu ion supplied by he manu ac u e . The “b ain” o his sys em will be a con ol sys em equipped wi h an FPGA, upon which he indi idual me hods will be g adually implemen ed and es ed. The s eng h o he FPGA solu ion lies in i s abili y o calcula e e en complex compu a ional asks in a ela i ely e y sho pe iod o ime (on he o de o uni s up o ens o µ s), which is much sho e han one pe iod o he undamen al equency (20 ms, esp. 16.66 ms). Such sho calcula ion ime pe iods a e di icul o achie e on ei he con en ional PCs o mic ocon olle s. E o s caused by poo implemen a ion o he compu a ional delay o a slow con ol sys em can hen deg ade he quali y o he esul ing il a ion, leading o he esul s conce ning he quali y o he con ol me hod being de alued. The e o e, he use o an FPGA seems o be he bes solu ion om he poin o iew o es ing and quan i ying he il a ion quali y, as i in oduces he smalles e o in o he con ol ci cui . The p ima y disad an age o his app oach is he complexi y o implemen a ion, as FPGA p og amming is disp opo iona ely mo e complex han “classic” p og amming (eg C, C], Py hon, e ce e a). The desc ibed algo i hms can be implemen ed on di e en ha dwa e pla o ms. Due o ou ex ensi e expe ience wi h Na ional Ins umen s ha dwa e, and hus wi h LabVIEW, we expec o be able o use mul iple inhouse ha dwa e solu ions. The i s op ion is a combina ion o a PC and plug-in mul i unc ion da a acqusi ion boa d, i.e., NI PCI-6221 wi h 16 × AI and 2 × AO. The esolu ion o bo h ADC and DAC is 16 bi s, and he sampling a e is up o 250 kSps. The main ad an age o his pla o m is ha he boa d can bo h gene a e and measu e da a wi hou unnecessa y bu e ing; his mode is called N-sample HW- imed, and allows o he sho es la ency be ween he measu ed and gene a ed alues, which is equal o he ecip ocal alue o he sampling a e. A second op ion is a combina ion o a PC and NI cDAQ-9185 E he ne -connec ed chassis. cDAQ is a modula measu emen and signal gene a ion pla o m consis ing o a chassis and selec able I/O modules. cDAQ-9185 is a ou -slo chassis wi h a 2 × Gb E he ne in e ace. Timing and synch oniza ion a e p o ided by a cDAQ in e nal clock. cDAQ allows an N-sample me hod mode based on a dedica ed bu e , which means ha samples a e ead/w i en in blocks. The d awback o block mode is ha he la ency is equal o he numbe o samples in a block mul iplied by he ecip ocal alue o he sampling a e. O cou se, he e is a ce ain lowes numbe o samples in a block. A hi d op ion is o use a cRIO HW pla o m. cRIO consis s o a CPU wi h an RT ope a ion sys em, FPGA, and chassis wi h ou o eigh selec able I/O modules. The b idge be ween he CPU and modules is he FPGA. The e a e wo main ad an ages o cRIO. Fi s , i he code size i s in o he FPGA, he e is no need o calcula e he samples on he CPU, as he signal p ocessing code uns on FPGA. Code on FPGA uns na i ely in pa allel and is ex emely as . As he e is no need o bu e ing, he la ency is he sho es o he h ee desc ibed me hods. Second, he cRIO uns s andalone, wi h he PC only used o pa ame e iza ion o isualiza ion. Senso s 2022,22, 7985 33 o 41 Howe e , he ollowing ca ea applies o all h ee abo e-men ioned me hods. Fo con inous ope a ion, i is necessa y o ensu e ha he compu a ion ime pe sample is sho e han he in e se o he sampling a e. The ad an ageo unning heex ac ionalgo i hmonanFPGAliesin henea -elimina ion o sys em la ency. A p ope ly implemen ed ha monic ex ac ion me hod on an FPGA can ha e he la ency minimized o alues as low as 4 µ s. Many me hods can be implemen ed as Sample-By-Sample p ocessing, and he e o e i is no necessa y o bu e da a. A majo d awback o implemen ing ex ac ion algo i hms on FPGAs is hei e y high le el o di icul y om a so wa e de elopmen pe spec i e. The p og amme canno use loa ing-poin da a ypes; all unc ions and calcula ions need o be con e ed o a ixed-poin da a ype. O cou se, while de elopmen can be ca ied ou on a sys em ha allows loa ing-poin calcula ions, in which case con e sion o FXP mus be conside ed. This is he pa o SW design whe e mos p oblems occu , because i he con e sion is no execu ed co ec ly, he da a ype will o e low, causing an e o in he ha monic ex ac ion me hod. O he p oblems include long compila ion imes and he a he complex HDL p og amming language. Because his is a gene al syn hesis o an HW ci cui , i is necessa y o ake in o accoun he ac ha he code uns in pa allel, no sequen ially. This can be used, e.g., in pipelining, whe e se e al i e a ions o he calcula ion a e un in pa allel. Howe e , i is necessa y o p og am he so-called handshaking, o o e head, which decides when he calcula ion is alid and when i is no . Ano he aim o ou s is o c ea e a da abase o signal ol age and cu en wa e o ms wi h di e en ypes o loads. Any combina ion o he indi idual wa e o ms will be clea ly desc ibed o make i clea which scena io is o be es ed (e.g., dis o ed line ol age THD Uh3 = 5%, THD Uh5 = 3%, non-symme ical na u e o load, hy is o -con olled ec i ie RL load ype XY, and o he s). The e o e, he indi idual me hods can be es ed on di e en models o he dis ibu ion ne wo k. This da abase will hen be eely a ailable o download, and o he au ho s will be able o implemen hei own new me hods o SAPF managemen and objec i ely compa e hem wi h algo i hms implemen ed by o he au ho s. The indispu able ad an age o his da ase will be, abo e all, he objec i i y o he quan i ica ion o indi idual pa ame e s o he il a ion quali y, no e bal exp ession o a subjec i e cha ac e . The key pa ame e s we in end o examine a e he con e gence speed, algo i hm s abili y, compu a ional complexi y in e ms o he numbe o ope a ions (addi ion, sub ac ion, mul iplica ion, and di ision) in one i e a ion cycle, memo y cell consump ion, Minimum Mean Squa e E o (MMSE), alue o he THD I a e il a ion, ela i e THD I imp o emen , and abili y o unc ion unde di e en es ed condi ions. Ini ial es ing and implemen a ion o he a o emen ioned me hods will be pe o med in labo a o y condi ions. The nex s ep will be implemen a ion on a eal “con olled” dis ibu ion ne wo k consis ing o he es polygon o public SMART LED ligh ing on he campus o VSB ( he Technical Uni e si y o Os a a) [ 135 , 146 , 147 ]. This polygon is used o comp ehensi e es ing o LED ligh ing in e ms o Powe Quali y [ 148 ], consump ion, and ex ended unc ionali ies (e.g., isible ligh communica ion [ 149 – 152 ], sma pa king managemen [ 153 ], sma ene gy low managemen [ 148 ], e ce e a). The subjec o ongoing esea ch is p ima ily he impac o widesp ead mass deploymen o sma echnologies on he quali y o elec ici y wi hin he ci y dis ibu ion ne wo k. The p ima y ad an age o his app oach is ha he ope a ion o he es polygon is ully unde con ol o he esea ch eam, making i possible o pe o m a ious es s wi h public ligh ing, e en du ing he day when i is no no mally li . The nex possible s ep will be o deploy he sys em on he dis ibu ion ne wo k o he en i e campus, hus con ibu ing o he ongoing p ojec o c ea e a small “SMART ci y” on he uni e si y g ounds (SMART s ee ligh ing, SMART in o ma ion boa ds, SMART ene gy low managemen , e ce e a) o deploymen o one o he indus ial companies o ou eam’s coope a ing indus ial pa ne s. Senso s 2022,22, 7985 34 o 41 5. Conclusions I is qui e ob ious ha cu en ha monics a e one o he mos impo an elemen s ha undamen ally e ec he powe quali y o elec ici y wi hin a dis ibu ion g id. G ea e o s a e cu en ly being made o compensa e o hese highe cu en componen s. One o he mos e ec i e me hods o sol ing his p oblem o supp ession o highe ha monic componen s is he deploymen o SAPF. Thei key ea u e is ha hei e iciency is di ec ly e lec ed in he speed and accu acy o con ol algo i hms. Due o he massi e deploymen o dynamically changing sys ems ( om a highe ha monic con en pe spec i e), i is necessa y o gua an ee a high deg ee o lexibili y in e ms o indi idual ope a ing scena ios. These scena ios a e co e ed by mode n con ol algo i hms hanks o he use o p og essi e signal p ocessing me hods. The de elopmen o his a ea is e oked by he a ailabili y o powe ul and a o dable semiconduc o swi ching elemen s. This esea ch has sys ema ically summa ized and compa ed exis ing SAPF con ol me hods, wi h an emphasis on mode n me hods o signal p ocessing which a e beginning o be signi ican ly applied in he ield o powe enginee ing. Thanks o he ela i ely easy a ailabili y o FPGAs, i is possible o implemen complex con ol algo i hms which, in combina ion wi h new semiconduc o swi ching elemen s, a e able o achie e high e iciency . This publica ion should help o unde s and he basic p inciple o SAPF while p o iding a subjec i e classi ica ion and compa ison o di e en con ol algo i hms ha can se e as a basis o u he esea ch in his p og essing ield. Au ho Con ibu ions: Concep ualiza ion, J.B.; me hodology, J.B. and V.S.; so wa e, J.B. and V.S.; alida ion, P.B.; o mal analysis, R.J.; in es iga ion, J.B., V.S., R.J. and L.D.; esou ces, P.B.; da a cu a ion, J.B.; w i ing—o iginal d a p epa a ion, J.B., V.S., R.J. and L.D.; w i ing— e iew and edi ing, J.B., V.S., R.J. and L.D.; isualiza ion, P.B. and R.M.; supe ision, P.B. and R.M.; p ojec adminis a ion, P.B., R.M. and P.S.; unding acquisi ion, P.B., R.M. and P.S. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: This esea ch was unded by he Minis y o Educa ion o he Czech Republic (P ojec No. SP2022/34 and SP2022/88). This wo k was suppo ed by he Eu opean Regional De elopmen Fund in Resea ch Pla o m ocused on Indus y 4.0 and Robo ics in he Os a a p ojec , CZ.02.1.01/0.0/0.0 /17_049/0008425 wi hin Ope a ional P og amme Resea ch, De elopmen and Educa ion. We hank he company B ose, Kop i nice CZ (Pe Zmij). Ins i u ional Re iew Boa d S a emen : No applicable. In o med Consen S a emen : No applicable. Da a A ailabili y S a emen : No applicable. Con lic s o In e es : The au ho s decla e no con lic o in e es . Abb e ia ions The ollowing abb e ia ions a e used in his manusc ip : ANFIS Adap i e Neu o-Fuzzy In e ence Sys em DCC Di ec Cu en Con ol DFT Disc e e Fou ie T ans o m DSP Digi al Signal P ocesso FCE Fundamen al Componen Ex ac ion FFT Fas Fou ie T ans o ma ion FIR Fini e Impulse Response Senso s 2022,22, 7985 35 o 41 FIS Fuzzy In e ence Sys em FPGA Field P og ammable Ga e A ay GD G adien Descen GTO Ga e u n-o HPF High-Pass Fil e ICC Indi ec Cu en Con ol IGBT Insula ed Ga e Bipola ansis o s IGCT In eg a ed ga e commu a ed IIR In ini e Impulse Response LF Loop Fil e LMS Leas Mean Squa es LPF Low-Pass Fil e MMSE Minimum Mean Squa e E o MNN Mul ilaye Neu al Ne wo k PCC Poin o Common Coupling PD Phase De ec o PLL Phase-Locked Loop PWM Pulse-Wid h Modula ion RDFT Recu si e Disc e e Fou ie T ans o m RLS Recu si e Leas Squa es SAPF Shun -Ac i e Powe Fil e SCG Scale Conjuga e G adien SNR Signal o Noise Ra io SVPWM Space Vec o PWM THD To al Ha monic Dis o ion VCO Vol age-Con olled Oscilla o ZCD Ze o-C oss De ec ion Re e ences 1. 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