Academic Edi o : Guille mo
Villanue a
Recei ed: 11 Sep embe 2025
Re ised: 1 Oc obe 2025
Accep ed: 29 Oc obe 2025
Published: 3 No embe 2025
Ci a ion: Be i, C.; Tina elli, R.;
Pe e o, L.; Mingo i, A. Expe imen al
Valida ion o Simple Powe Quali y
Indices o F equency Con en
Assessmen up o 150 kHz. Senso s
2025,25, 6716. h ps://doi.o g/
10.3390/s25216716
Copy igh : © 2025 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/).
A icle
Expe imen al Valida ion o Simple Powe Quali y Indices o
F equency Con en Assessmen up o 150 kHz
Ch is ian Be i , Robe o Tina elli , Lo enzo Pe e o and Alessand o Mingo i *
Depa men o Elec ical, Elec onic and In o ma ion Enginee ing, Guglielmo Ma coni Alma Ma e S udio um,
Uni e si y o Bologna, Viale del Riso gimen o 2, 40136 Bologna, I aly; [email p o ec ed] (C.B.);
obe o. ina [email p o ec ed] (R.T.); [email p o ec ed] (L.P.)
*Co espondence: alessand [email p o ec ed]
Abs ac
The powe sys em is e ol ing wi h he in eg a ion o new echnologies, including elec onic
de ices and enewable ene gy sou ces, which a e inc easingly used o suppo new applica-
ions, educe dependence on ossil uels, and d i e sys em inno a ion. Howe e , his shi
b ings a signi ican d awback: a educ ion in powe quali y (PQ). The li e a u e ex ensi ely
discusses he impac o poo PQ on elec ical asse s and explo es po en ial solu ions o
his new challenge. Building on his ounda ion, his pape in oduces new PQ indices
de i ed om exis ing me ics and alida ed on bo h syn he ic and eal signals o assess
hei e ec i eness. The aim is o p o ide esea che s and sys em ope a o s wi h simple and
e icien ools o he clea iden i ica ion o PQ issues in moni o ed ne wo ks. These new
indices a e designed o be lexible and independen o acquisi ion condi ions, making hem
sui able o a wide ange o equencies (e.g., 50 Hz–150 kHz) and applica ions. A e an
o e iew o he PQ landscape, he pape demons a es he use o hese indices on a ious
ol age wa e o ms, including a case s udy om a measu emen campaign. The p omising
esul s indica e ha , when combined wi h exis ing indices, hese new me ics can o m a
s ong ounda ion o a deepe unde s anding and mo e accu a e classi ica ion o PQ issues
in powe ne wo ks.
Keywo ds: powe quali y; ins umen ans o me s; sup aha monics; indices; high
equency; ha monic dis o ion
1. In oduc ion
The in eg a ion o enewable ene gy sou ces (RESs) and he p oli e a ion o elec onic
de ices (EDs) a e ha ing a signi ican impac on powe quali y (PQ) in mode n powe
sys ems [
1
]. RESs, such as sola pho o ol aics (PV) and wind u bines, use swi ching powe
elec onics—in e e s— o con e di ec cu en (DC) o al e na ing cu en (AC). Al hough
hese de ices a e essen ial o e icien ly connec he RESs o he g id, hey also in oduce
ha monic dis o ions ac oss a wide equency spec um. As in e e s ope a e in disc e e
pulses, hey cause ha monic cu en injec ions ac oss a wide equency spec um [
2
]. These
dis o ions lead o non-sinusoidal ol age and cu en wa e o ms, especially in he mid- o-
high- equency anges, such as om 9 kHz o 150 kHz [
3
]. Addi ionally, he widesp ead use
o EDs in households, comme cial buildings, and indus ies also con ibu es o PQ issues.
In ac , many mode n de ices, such as LED ligh ing, compu e s, and elec ic ehicles [
4
],
inco po a e swi ching powe supplies and o he elec onic componen s ha d aw non-
linea cu en om he g id. These de ices gene a e ha monics and o he dis u bances
Senso s 2025,25, 6716 h ps://doi.o g/10.3390/s25216716
Senso s 2025,25, 6716 2 o 21
in bo h low- and high- equency anges [
5
]. Toge he , he non-linea na u e o RESs and
EDs in oduces a ious dis u bances, including ha monic dis o ion, licke , and ol age
luc ua ions. These dis o ion phenomena c ea e non-ideal ope a ing condi ions, leading
o physical impac s on elec ical asse s such as o e hea ing, ib a ion, and insula ion
deg ada ion in mo o s, ans o me s, and cables [
6
,
7
]. Mo eo e , sensi i e equipmen , such
as con ol sys ems, medical de ices, and da a se e s, is especially ulne able o poo PQ.
Vol age sags, su ges, and licke can cause equen shu downs, educe ope a ional s abili y,
and lead o da a losses o inaccu a e measu emen s [
8
]. Ul ima ely, low le els o PQ impac
he e iciency, longe i y, and eliabili y o powe dis ibu ion; consequen ly, economic
implica ions a ise, such as highe sys em main enance cos s and ines and economic losses
in case o powe ou ages [
9
]. Consequen ly, due o he accele a ing end owa d RESs,
dis ibu ed gene a ion, and EDs, de eloping new indices o e alua e hese PQ issues ac oss
all equency anges has become a c ucial ask o sys em ope a o s in o de o ensu e a
s able and esilien powe sys em o mode n needs.
O e all, his wo k aims o in oduce simple PQ indices designed o assess he spec al
con en o a signal, selec i ely ocusing on speci ic po ions o he spec um. These indices
a e demons a ed p ima ily in he 50 Hz–150 kHz equency ange bu a e no limi ed o
i . The indices a e o s aigh o wa d implemen a ion, and hey p o ide an immedia e
indica ion o he signal’s quali y and “heal h”, speci ying in which equency ange he
c i icali ies a e ound. O cou se, se e al PQ indices a e de ined in he li e a u e and in
es ablished in e na ional s anda ds, all add essing speci ic needs and p o iding a obus
amewo k o ha monic analysis (see he dedica ed sec ion in wha ollows). Howe e , he
added alue o he p oposed indices, hence o he wo k, is o ha e a simple and p ac ical
diagnos ic ool o an immedia e e alua ion o he signal spec al con en and, in pa icula ,
he iden i ica ion o he ce ain equency band in which he dis o ion is mos p ominen .
Fu he mo e, a e desc ibing hem, he indices a e es ed in wo di e en condi ions.
Fi s , a alida ion in a simula ion en i onmen wi h syn he ic signals is un. Such signals a e
ep esen a i es o po en ial ol ages and cu en measu ed in he powe sys em. Second, he
indices a e es ed on signals ob ained wi hin a measu emen campaign aimed a acqui ing
ol ages signals gene a ed by a PV sys em. Bo h es ing p ocedu es con i m he lexibili y,
eliabili y, and ease o use o he p oposed PQ indices. No e ha he p oposed indices
could, in p inciple, be es ed ac oss housands o scena ios in ol ing di e en mix u es o
ha monic and equency componen s, as hey a e lexible and applicable o all such cases.
Howe e , hei alida ion has been p esen ed using a single case s udy, which is conside ed
su icien ly gene al and obus o demons a e hei e ec i eness.
The emainde o he ex is s uc u ed as ollows: Sec ion 2ou lines he con ex o
his pape , analyzing he exis ing indices and s anda ds. Sec ion 3in oduces he p oposed
indices and hei meaning. In Sec ion 4, he indices a e es ed in he simula ion en i onmen .
The expe imen al alida ion, ins ead, is ully desc ibed in Sec ion 5. Finally, Sec ion 6
con ains he conclusion o he wo k.
2. S a e o he A
This sec ion s a s wi h he analysis o he exis ing and ypical PQ indices. A e wa ds,
a b ie discussion on ins umen ans o me s (ITs) is p o ided o cla i y hei c ucial ole.
2.1. Powe Quali y E alua ion
2.1.1. S anda ds
Many s anda ds on PQ a e a ailable. Some o hem p esc ibe es s, some de ice
speci ica ions and limi s, and o he s ocus on he use o manu ac u e pe spec i e. This
e iew ocuses speci ically on he ele an s anda ds ha de ine measu emen me hods
Senso s 2025,25, 6716 3 o 21
and indices o quan i ying wa e o m dis o ion o p o ide a con ex in which o compa e
he indices p oposed by he au ho s. Among hem, some o he mos popula a e he IEC
61000-4-7 [
10
] and he IEC 61000-4-30 [
11
], in which he o al ha monic dis o ion (
THD
) is
used oge he wi h g ouping echnique in oduced. The THD is de ined as
THD =
q∑h_max
h=2Y2
H,h
YH,1
(1)
whe e
YH,h
is he ms alue o he conside ed quan i y
Y
a he ha monic componen
o o de
h
.
YH,1
is he ms alue o he undamen al componen . In [
10
], he pa ial
weigh ed ha monic dis o ion (
PWHD
) is also in oduced, which is a weigh ed e sion
o he
THD
. Ano he documen indica ing an index is he IEC 63191 [
12
], in which he
o al dis o ion a io (
TDR
), also known as o al wa e o m dis o ion (
TWD
), and he o al
demand dis o ion a e used (TDD). They a e de ined as
TWD =
qY2
H−Y2
H,1
YH,1
(2)
TDD =
q∑h_max
h=2Y2
H,h
YH,1,max
(3)
whe e
YH
is he o e all ms o he quan i y
Y
, and
YH,1,max
is he max demand alue.
Then, he IEEE 519 [
13
] se s some limi s o he ha monic componen s o he cu en , bu
he only index used is he elephone in e e ence ac o (TIF), whose use is limi ed o
he communica ion assessmen . Finally, e . [
14
] p o ides comp ehensi e and de ailed
guidance on a wide ange o ol age sag indices, anging om single e en cha ac e is ics
(such as sag ene gy) o si e indices (such as SARFI-X), while e . [
15
] o e s indices o
measu e he se e i y o he licke in he sho and long e m, Ps and Pl , espec i ely.
O e all, he guidelines o he s anda ds p o ide an excellen s a ing poin o he PQ
e alua ion, bu he e is plen y o space o imp o emen s.
2.1.2. Li e a u e Re iew
S udying he s a e o he a , some examples o new in e es ing indices can be ound.
Fo example, e . [
16
] in oduced a so o a io e o using he THD alues. In [
17
], he PQ
e alua ion app oach is based on he a ic ligh echnique. The au ho s in [
18
] in oduce a
dis o ion index a e applying a wa ele -based app oach. In [
19
], a so o e iew o some
indices is gi en (all o which ha e been al eady men ioned). The same concep has been
applied in [
20
], whe e he sho comings o he exis ing indices ha e been highligh ed. As
o [
21
], he p oposed solu ion is speci ic o e alua ing he impac o pho o ol aic sou ces
and non-linea loads. Meanwhile, e . [
22
] ocuses on he p oposal o indices ha can be
used o cha ac e izing he beha io o elec ic d i es. Then, e . [
23
] p oposes no el PQ
indices ha , by means o powe decomposi ion me hod, assess PQ phenomena in case o
using LED lamps. Finally, e . [
24
] in oduces a sho ime e sion o he THD, he STDE,
which quan i ies he dis o ion by conside ing he ene gy o all equency componen s.
Conside ing he abo e, wha is p oposed ollowing his sec ion clea ly ep esen s he alue
his adds o he scien i ic communi y.
2.2. Ins umen T ans o me s
This pa ag aph aims o emphasize he impo ance o ITs in PQ e alua ion. In ac ,
any PQ index would be useless i he inpu p o ided is inaccu a e o e en w ong. Hence,
conside ing ha ITs a e he key link be ween he elec ical quan i ies and he compu a ion
Senso s 2025,25, 6716 4 o 21
o pa ame e s/indices, hey ha e a undamen al ole. T adi ional ITs a e gene ally designed
o undamen al equency measu emen s (50 o 60 Hz) and may ail o accu a ely cap u e
he highe - equency componen s in oduced by mode n loads. This gap in measu emen
capabili ies can esul in inaccu a e moni o ing, inadequa e con ol esponses, and a limi ed
unde s anding o PQ issues in high- equency anges, such as om 9 kHz o 150 kHz.
The e o e, he e is a p essing need o specialized ITs capable o measu ing and analyzing
hese equency componen s o enable accu a e PQ assessmen . This need is con i med
by he la es e sion o he main IT s anda d documen , he IEC 61869-1 [
25
], and he
mos ecen li e a u e [
26
,
27
], as well as he inancing o wo Eu opean p ojec s, IT4PQ
(19NRM05) [
28
] and ADMIT (22NRM06) [
29
], which aimed o s udy he equency esponse
o ITs up o 9 kHz and 150 kHz, espec i ely.
3. P oposed Indices
This sec ion p esen s he indices and he me ics de eloped as a simple and immedia e
diagnos ic ool o e alua ing he ha monics ha a e a ec ing he sys em unde analysis.
The s anda d
THD
calcula ion p o ides a global measu e o wa e o m dis o ion bu ails o
isola e he con ibu ion o di e en spec al egions. The e o e, o o e come his limi a ion,
his wo k in oduces a se o modula indices designed o quan i y he agg ega ed dis o ion
ene gy wi hin speci ic and p ede ined equency bands. By calcula ing a
THD
alue o
dis inc spec al anges, a sys em ope a o can quickly de e mine whe he he dominan PQ
issues o igina e om classic low-o de ha monics, high- equency swi ching componen s,
o o he sou ces. The i s se o h ee indices includes
THDPQ
,
THDEX
, and
THDSH
. They
a e de ined as
THDPQ =
q∑50
h=2Y2
H,h
YH,1
(4)
THDEX =
q∑180
h=51 Y2
H,h
YH,1
(5)
THDSH =
q∑450
h=181 Y2
H,h
YH,1
(6)
whe e he subsc ip s PQ, EX, and SH e e o powe quali y, ex ended PQ, and sup a-
ha monics. In ac , he h ee equa ions in oduce a so o
THD
dedica ed o a speci ic
pa o he equency spec um, as ou lined in [
10
,
11
]. Hence,
THDPQ
e alua es ha monic
componen s up o 2500 Hz;
THDEX
conside s he equency ange [2550–9000 Hz], and
THDSH
is speci ic o he equencies [9050–150,000 Hz]. Equa ions (4)–(6) a e w i en in a
gene al o m ha indica es hin he sum as he ha monic o de conside ed. Howe e ,
•
The 50 Hz esolu ion is ypically no adop ed by he s anda d [
10
], and i does no
allow us o app ecia e in e ha monic componen s.
•
In his pape , he analysis a a 50 Hz esolu ion is in eg a ed wi h o he esolu ions o
u he suppo he esul s. In ac , inc easing he esolu ion allows us o in oduce he
ou h index as
THDSUB =
q∑9/10
h=1/10 Y2
H,h
YH,1
(7)
whe e subsc ip SUB e e s o he subha monic componen s om he DC o he undamen al
one (bo h excluded). The supe sc ip and subsc ip o he summa ion e lec he case o
5 Hz esolu ion ( o example). In conclusion, he ele an in o ma ion p ese ed is he e o e
he agg ega ed ha monic dis o ion o each equency band unde analysis. In his wo k,
Senso s 2025,25, 6716 5 o 21
he indices quan i y and isola e he agg ega ed dis o ion wi hin he p e iously de ined
equency bands (PQ, EX, SH, SUB).
To u he suppo his app oach, new me ics a e de ined s a ing om he p e ious
indices. Such me ics a e
ρPQ =
THDPQ
TWD (8)
ρEX =
THDEX
TWD (9)
ρSH =
THDSH
TWD (10)
ρSUB =
THDSUB
TWD (11)
in which all he elemen s we e p e iously de ined. The p oposed me ics aim a highligh -
ing he con ibu ion o each po ion o he spec um wi h espec o he o e all dis o ion
o he signal. The a ionale below hose me ics consis s o e alua ing he “weigh ” o
he dis o ion, in which 1 ep esen s he maximum alue, caused by each po ion o he
spec um. This p ocedu e p o ides sys em ope a o s wi h a p ac ical, high-le el diagnos ic
ool o help wi h he quick iden i ica ion o he oo cause o powe quali y deg ada ion. A
no e on he DC componen : The e is no p oposed index conside ing he DC. This is because
he measu emen and subsequen mi iga ion/ emo al o such componen is ypically i -
ial, and i does no ep esen a challenge. A inal me ic ha weighs he na u e o he PQ
deg ada ion ha is a ec ing he powe ne wo k unde analysis is de ined as
ρ=
THD
TWD (12)
In ac , a alue equal o 1 o his index implies ha he ha monics a e he main cause
o he de ia ion o he wa e o m om i s ideal sinusoidal shape; consequen ly, o he ypes
o dis u bances, such as in e ha monics and noise, ha e a minimal con ibu ion o he
o e all dis o ion o he measu ed signal.
Finally, he p oposed indices and me ics, which will be implemen ed in he ollowing
sec ion, a e simple and lexible enough o be implemen ed in any compu a ion sys em
using da a collec ed wi h any equency esolu ion.
4. Valida ion by Simula ion
4.1. Syn he ic Signals
To alida e he p oposed indices and me ics, a es case was designed in ol ing wo
syn he ic signals, called S1 and S2, whose composi ions a e de ailed in Tables 1and 2.
Speci ically, a 50 Hz signal was gene a ed wi h a ol age o 15/
√
3 kV o emula e a medium-
ol age (MV) sys em. Subsequen ly, h ee se s o ha monics we e added as speci ied in
Table 1, each co esponding o a pa icula ange de ined in he p e ious sec ion (PQ, EX,
and SH). The ha monic ampli udes, ela i e o he undamen al componen , we e chosen as
2.5%, 1%, and 0.25% o he h ee se s, espec i ely. These ampli ude alues we e selec ed
o simplici y and cla i y, as hey do no a ec he alida ion o he indices. Signal S1 was
u he augmen ed wi h addi ional equency componen s lis ed in Table 2, which include
in e ha monics wi hin he PQ, EX, and SH anges, as well as subha monics. In con as ,
signal S2 is iden ical o S1 bu excludes he equency componen s om Table 2. This
dis inc ion be ween S1 and S2— he i s one encompassing a b oade ange o dis u bances
and he second one con aining only ha monic componen s—ensu es a mo e ho ough
alida ion o he p oposed indices and me ics.
Senso s 2025,25, 6716 6 o 21
Table 1. Ha monic con en o signal S1 and S2.
Range [-] F equency [Hz] % o Fundamen al
PQ
150 2.5
250 2.5
350 2.5
450 2.5
550 2.5
800 2.5
1000 2.5
1250 2.5
2000 2.5
2500 2.5
EX
3000 1
3750 1
4500 1
5000 1
5750 1
6250 1
7000 1
7750 1
8300 1
9000 1
SH
22,500 0.25
37,500 0.25
50,000 0.25
62,500 0.25
75,000 0.25
100,000 0.25
112,500 0.25
125,000 0.25
137,500 0.25
150,000 0.25
Table 2. In e ha monic con en o signal S1.
Range [-] F equency [Hz] % o Fundamen al
SUB 17 1.25
25 1.25
PQ
720 1.25
1329 1.25
2275 1.25
EX
2835 0.5
4259 0.5
6120 0.5
7330 0.5
8740 0.5
SH
10,210 0.125
50,020 0.125
90,029 0.125
120,060 0.125
147,480 0.125
The ime domain ep esen a ion o he signal S1 is depic ed in Figu e 1. Signal S2 is
no plo ed o he sake o b e i y.
Senso s 2025,25, 6716 7 o 21
Figu e 1. Time domain ep esen a ion o signal S1.
4.2. Resul s
To alida e he indices desc ibed in Sec ion 3, hey a e applied on signals S1 and S2,
desc ibed abo e. In pa icula , he signal is assumed o be sampled wi h ime windows
o 1 s, 200 ms, and 20 ms o ec ea e he condi ion o a equency esolu ion o 1 Hz, 5 Hz,
and 50 Hz, espec i ely. No e ha , in he conside ed case o a cons an signal, he e is
no dynamici y in he equency componen s. The e o e, he ime window is solely used
o change he equency esolu ion and no o assessing speci ic ime- a ying equency
componen s. Finally, o ob ain he equency spec um o he sampled signal in he ime
domain, he Fas Fou ie T ans o m (FFT) is applied o each ime window. Then, o he
calcula ion o he p oposed indices and me ics, only he ampli ude alues o he complex
FFT a e used. The phase in o ma ion is no conside ed in his analysis, and he ampli ude
alues a e used o he calcula ion o he ollowing indices (p esen ed in Sec ion 3).
The
TWD
o he wo signals is lis ed in Table 3, which highligh s he sligh di e ence
in he ha monic con en be ween he wo signals. Acco ding o he de ini ion o he
TWD
,
i is independen o he equency esolu ion.
Table 3. TWD o signals S1 and S2.
Index [%] S1 S2
TWD 9.07 8.55
The
THD
,
THDPQ
,
THDEX
,
THDSH
, and he
THDSUB
o signal S1, o each e-
quency esolu ion, a e p esen ed in Table 4. The i s commen is on he
THDSUB
, which
does no ha e a alue o he 50 Hz esolu ion o ob ious easons. Second, as expec ed,
he highe he equency esolu ion (i.e., smalle equency s eps), he highe he de ail
wi h which he equency componen s can be analyzed. Howe e , he mos in e es ing
commen is he hi d. In ac , ocusing on a single- equency esolu ion, i can be seen how
he con en o he signal can be judged a a glance. In he case o S1, he p oposed indices
p o ide a simple and clea indica ion o a signi ican dis o ion in he PQ equency ange,
and a modes in luence o high- equency componen s.
Simila ly, he esul s o he indices’ implemen a ion o S2 a e p esen ed in Table 5.
These esul s highligh he well-es ablished p inciple ha he absence o in e ha monic
componen s (including subha monics) ende s equency esolu ion i ele an o he sig-
nal’s equency analysis. Ne e heless, in his simpli ied example, he p oposed indices
pe o m as e ec i ely as hey do wi h he mo e complex signal, S1.
Senso s 2025,25, 6716 8 o 21
Table 4. Di e en THD indices esul s, o each equency esolu ion, o S1.
Index [%] F equency Resolu ion [Hz]
50 5 1
THD 8.55 8.96 9.07
THDPQ 7.91 8.10 8.20
THDEX 3.16 3.31 3.35
THDSH 0.79 0.83 0.84
THDSUB - 1.25 1.77
Table 5. Di e en THD indices esul s, o each equency esolu ion, o S2.
Index [%] F equency Resolu ion [Hz]
50 5 1
THD 8.55 8.55 8.55
THDPQ 7.91 7.91 7.91
THDEX 3.16 3.16 3.16
THDSH 0.79 0.79 0.79
THDSUB ---
A inal commen on his i s se o esul s is abou he equency esolu ion. I is
known ha he s anda d [
5
] sugges s sampling he signal collec ing 10 o 12 pe iods o
he undamen al componen (50 Hz o 60 Hz). Howe e , i is no always possible due o
he a ailable ins umen a ion, du a ion o he signal, o he du a ion o he phenomena
o in e es . The e o e, he lexibili y and simplici y o he indices become c ucial o hei
widesp ead adop ion.
Looking a he me ics
ρPQ
,
ρEX
,
ρSH
, and
ρSUB
, de ined in Sec ion 3, i applied o he
esul s in Tables 4and 5, hey p o ide he esul s p esen ed in Table 6.
Table 6. Applica ion o he new me ics o signals S1 and S2.
Index [-] Signal [-] F equency Resolu ion [Hz]
50 5 1
S1 0.943 0.989 1
S2 1 1 1
ρPQ
S1 0.871 0.893 0.903
S2 0.924 0.924 0.924
ρEX
S1 0.348 0.365 0.369
S2 0.369 0.369 0.369
ρSH
S1 0.087 0.091 0.092
S2 0.092 0.092 0.092
ρSUB
S1 - 0.137 0.194
S2 - - -
The me ics in Table 6p o ide a clea in o ma ion on he weigh o each po ion o
he equency ange on he o e all dis u bance a ec ing he signal. Once again, he highe
he equency esolu ion, he be e he analysis o he p esen ha monic componen s. I is
in e es ing o highligh ha , e en in he case o a low- equency esolu ion; o example,
in he case o analysis o sho du a ion phenomena, he me ics s ill p o ide a use ul
indica ion abou he loca ion o he dis u bance.
Senso s 2025,25, 6716 9 o 21
A inal no e on he numbe o digi s o he esul s: Tables 3–6con ain alues om
simula ions ha , e en i epea ed, would no lead o di e en alues. The e o e, he numbe
o digi s ep esen ed is a ealis ic alue ha could be possibly ob ained in in- ield ondi ions.
5. In-Field Valida ion
5.1. Scena io
A e alida ing he p oposed indices h ough a simula ion, i is essen ial o e alua e
hei pe o mance unde mo e ealis ic condi ions. The subsequen chap e s de ail he
measu emen se up, which comp ises he elec ical sys ems on which he es s a e con-
duc ed o acqui e he signals and apply he indices. Speci ically, a p e iously cha ac e ized
measu emen se up was ins alled a he si e o a PV plan ins alled a he Facul y o En-
ginee ing o he Uni e si y o Bologna, pa icula ly on he in e e used o injec powe
in o he ne wo k. The ou pu ol age o he in e e was measu ed, and he indices we e
subsequen ly calcula ed.
5.2. Measu emen Se up and Powe Sys em Unde Analysis
The sys em con igu a ion o he elec ical sys em unde analysis consis s o
•
PV gene a ion: The PV plan a chi ec u e con ains 72 modules. Each module has a
peak powe a ing o 400 Wp. The e o e, he nominal peak powe o he PV sys em is
equal o 28.8 kWp. The modules a e elec ically connec ed in o se en s ings.
•
Powe condi ioning sys em: Powe con e sion and managemen a e handled by wo
in e e s—a 20-kW sola in e e p ocessing he ou pu om ou s ings and a 10-kW
hyb id in e e p ocessing he ou pu om h ee o he s ings and a ba e y.
•
Ene gy s o age: An elec ochemical ba e y sys em p o ides an ene gy capaci y o
27.6 kWh.
•Loads: Mainly o ices and class ooms.
•G id.
•
Moni o ing and p o ec i e sys em: An elec ical panel in eg a es ci cui b eake s,
p o ec i e de ices, and a sma me e o sys em moni o ing and g id connec ion.
Wi h he help o Figu e 2, he unc ioning o he sys em unde analysis can be sum-
ma ized as ollows: he powe gene a ed by he PV is managed by wo in e e s and
depending on he load demand, i is di ec ly consumed by his load, s o ed in he ba e y
o ed in o he g id.
The measu emen se up, used o acqui e he in e e ou pu ol age, consis s o he
ollowing elemen s:
•
A Hall e ec senso ea u ing (i) p ima y nominal ms ol age o 700 V, (ii) ans o -
ma ion a io o 10, (iii) accu acy o 2%, (i ) equency bandwid h om DC o 500 kHz,
and ( ) ex e nal powe supply ol age equi ed.
•
NI DAQ 9222 da a acquisi ion boa d ea u ing (i) ADC o 16 bi s, analogue inpu
ol age ange o ±10 V, and a maximum sample a e o 500 kSa/s.
•
Lap op ha manages he au oma ic acquisi ion o ol age wa e o ms wi h dedica ed
unning so wa e.
The acquisi ion sys em is con igu ed in he ollowing way: e e y hou , a ol age
wa e o m o 1 s du a ion is acqui ed a 500 kSa/s. The acquisi ion is au oma ed by means
o he Ma lab 2024 so wa e, and he acqui ed wa e o ms a e sa ed in lap op memo y. To
be e cla i y wha has been acqui ed, he eade can e e o Figu e 2, in which i has been
highligh ed ha he Hall e ec senso acqui es he ol age ha he in e e p oduces and
ha he inal use would use.
Senso s 2025,25, 6716 16 o 21
Figu e 14. THD index o he 20 ms ime window.
Figu e 15. THDPQ index o he 20 ms ime window.
Figu e 16. THDEX index o he 20 ms ime window.
Senso s 2025,25, 6716 17 o 21
Figu e 17. THDSH index o he 20 ms ime window.
Figu e 18. TWD index o he 20 ms ime window.
Figu e 19. ρindex o he 20 ms ime window.
Senso s 2025,25, 6716 18 o 21
Figu e 20. ρPQ index o he 20 ms ime window.
Figu e 21. ρEX index o he 20 ms ime window.
Figu e 22. ρSH index o he 20 ms ime window.
Figu es 14–17 ep esen he
THD
,
THDPQ
,
THDEX
and
THDSH
, espec i ely. As
expec ed om he use o a sho e analysis window, he indices displayed a gene al decline
Senso s 2025,25, 6716 19 o 21
in alue due o a lowe p esence o leakage. E en in his case o a sho e window, he PQ
band is he p edominan one and causes he g ea es ha monic pollu ion o he ne wo k.
Howe e , he p esence o bo h s a ic con e e s and a s o age sys em leads o a clea
p esence o high- equency ha monics in he sup aha monic (SH) equency ange, which
exhibi luc ua ing beha io h oughou he day.
F om Figu e 19, he me ic
ρ
is almos uni a y. The eason is clea when compa ing
he
THD
and
TWD
indices, ep esen ed in Figu es 14 and 18, espec i ely, which a e e y
simila in alue.
Simila ly o wha is seen in Figu es 11–13, Figu es 20–22 show he p oposed indices
o each selec ed equency band in he case whe e he signal is analyzed o e a 20 ms ime
window. Again, he PQ band, as expec ed, is he band ha con ibu es mos o ha monic
pollu ion o he ne wo k compa ed o he o he wo bands (EX and SH). In conclusion, he
p oposed indices o e a clea and de ailed insigh in o he signi icance o each pa o he
spec um. Fu he mo e, hanks o hei modula na u e, hese new indices enable use s
o analyze hei ne wo k o e cus omizable equency anges— o example, based on he
con e e echnology used and i s co esponding swi ching equency.
A e p esen ing all esul s, a commen on hei a iabili y and accu acy is needed.
Fi s , i is commonly di icul o pe o m epea ed measu emen s on eal ne wo ks due o
lack o s abili y o he signal. The e o e, he s a is ical app oach o educe unce ain y canno
be used. Second, in his case, he in o ma ion ha is ecei ed om he ins umen a ion
is c ucial. In ac , as p esen ed in [
30
], he au ho s guide he use o he calcula ion o
he unce ain y associa ed wi h THD indices wi h a closed- o m exp ession ha uses he
collec ed wa e o ms as a s a ing poin .
As a inal no e, accu a e signal analysis depends on many ac o s—such as he acqui-
si ion window, esolu ion, windowing echnique, il e s, and ins umen a ion. Howe e ,
he app oach p esen ed in his esea ch can be applied independen ly o hese aspec s. In
o he wo ds, i is lexible enough o adap o all such a iables, which makes i pa icula ly
aluable o eal in- ield applica ions.
6. Conclusions
This pape in oduces a se o simple ye e ec i e powe quali y (PQ) indices aimed
a imp o ing he e alua ion o ha monic dis o ions ac oss a wide equency ange
(1 Hz–150 kHz).
Add essing cu en gaps in me hodologies and s anda ds, he p oposed
indices a e lexible and obus , cap u ing key cha ac e is ics o powe dis u bances inde-
penden ly o acquisi ion condi ions. Thei pe o mance is demons a ed h ough alida ion
on bo h syn he ic and eal signals, con i ming hei capabili y o iden i y and quan i y
con ibu ions om dis inc spec al componen s, including ha monics, in e ha monics, and
subha monics. Beyond simpli ying PQ analysis, hese indices suppo p ac ical decision-
making o sys em ope a o s by pinpoin ing he equency anges ha mos signi ican ly
con ibu e o signal dis o ion. Thei s aigh o wa d implemen a ion also ensu es adap -
abili y o di e se measu emen sys ems and equency esolu ions, making hem sui able
o widesp ead adop ion. Collec i ely, hese esul s ad ance powe quali y moni o ing
and mi iga ion s a egies, pa icula ly in mode n elec ical sys ems ma ked by enewable-
ene gy in eg a ion and he p oli e a ion o non-linea loads.
Au ho Con ibu ions: Concep ualiza ion, A.M. and C.B.; me hodology, R.T.; so wa e, C.B.;
alida ion, L.P.; o mal analysis, A.M.; in es iga ion, C.B.; esou ces, L.P.; da a cu a ion, R.T.;
w i ing—o iginal d a p epa a ion, C.B.; w i ing— e iew and edi ing, L.P. All au ho s ha e ead
and ag eed o he published e sion o he manusc ip .
Senso s 2025,25, 6716 20 o 21
Funding: The p ojec 22NRM06 ADMIT ecei ed unding om he Eu opean Pa ne ship on Me ol-
ogy, co- inanced by he Eu opean Union’s Ho izon Eu ope Resea ch and Inno a ion P og amme and
by he Pa icipa ing S a es. The pape was also pa ially unded by G idDa a, EURAMET—Me ology
o eliable powe g id da a analy ics—24DIT05.
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 : Da a is una ailable due o p i acy.
Con lic s o In e es : The au ho s decla e no con lic s o in e es . The unde s had no ole in he design
o he s udy; in he collec ion, analysis, o in e p e a ion o da a; in he w i ing o he manusc ip ; o
in he decision o publish he esul s.
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Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
