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
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Copy igh : © 2022 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
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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
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