Academic Edi o : Michael
Negne i sky
Recei ed: 2 June 2025
Re ised: 25 June 2025
Accep ed: 30 June 2025
Published: 4 July 2025
Ci a ion: Ma isco i, A.; Salles, R.S.;
Rönnbe g, S. Unsupe ised
Segmen a ion and Classi ica ion o
Wa e o m-Dis o ion Da a Using
Non-Ac i e Cu en . Ene gies 2025,18,
3536. h ps://doi.o g/10.3390/
en18133536
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
Unsupe ised Segmen a ion and Classi ica ion o
Wa e o m-Dis o ion Da a Using Non-Ac i e Cu en
And ea Ma isco i 1,* , Ra ael S. Salles 2and Sa ah K. Rönnbe g 2
1
Depa men o Elec ical, Elec onic and Telecommunica ions Enginee ing, and Na al A chi ec u e (DITEN),
Uni e si y o Geno a, 16145 Geno a, I aly
2Elec ic Powe Enginee ing G oup, Luleå Uni e si y o Technology, 93187 Skelle eå, Sweden;
[email p o ec ed] (R.S.S.); sa ah. onnbe [email p o ec ed] (S.K.R.)
*Co espondence: and [email p o ec ed]
Abs ac
Non-ac i e cu en in he ime domain is conside ed o applica ion o he diagnos ics
and classi ica ion o loads in powe g ids based on wa e o m-dis o ion cha ac e is ics,
aking as a wo king example se e al eco dings o he pan og aph cu en in an AC ailway
sys em. Da a a e p ocessed wi h a deep au oencode o ea u e ex ac ion and hen
clus e ed ia k-means o allow iden i ica ion o pa e ns in he la en space. Clus e ing
enables he e alua ion o he ela ionship be ween he physical meaning and ope a ion o
he sys em and he dis o ion phenomena eme ging in he wa e o ms du ing ope a ion.
Euclidean dis ance (ED) is used o measu e he di e si y and pe inence o obse a ions
wi hin pa e n g oups and o iden i y anomalies (abno mal dis o ion, ansien s, ... ).
This app oach allows he classi ica ion o new da a by assigning da a o clus e s based
on p oximi y o cen oids. This unsupe ised me hod exploi ing non-ac i e cu en is
no el and has p o en use ul o p o iding da a wi h labels o la e supe ised lea ning
pe o med wi h he 1D-CNN, which achie ed a balanced accu acy o 96.46% unde no mal
condi ions. ED and 1D-CNN me hods we e es ed on an addi ional unlabeled da ase
and achie ed 89.56% ag eemen in iden i ying no mal s a es. Addi ionally, G ad-CAM,
when applied o he 1D-CNN, quan i a i ely iden i ies he wa e o m pa s ha in luence
he model p edic ions, signi ican ly enhancing he in e p e abili y o he classi ica ion
esul s. This is pa icula ly use ul o ob aining a be e unde s anding o load ope a ion,
including anomalies ha a ec g id s abili y and ene gy e iciency. Finally, he me hod has
been also success ully u he alida ed o gene al applicabili y wi h da a om a di e en
scena io (cha ging o elec ic ehicles). The me hod can be applied o load iden i ica ion and
classi ica ion o non-in usi e load moni o ing, wi h he aim o implemen ing au oma ic
and unsupe ised assessmen o load beha io , including ansien de ec ion, powe -quali y
issues and imp o emen in ene gy e iciency.
Keywo ds: anomaly de ec ion; deep lea ning; elec omobili y; ene gy e iciency; load
signa u e; non-in usi e load moni o ing; ac ion powe sys ems
1. In oduc ion
The p oblem o iden i ying ha monic sou ces has been a subjec o discussion o a
long ime, and a ious app oaches ha e been p oposed. Classical app oaches used be o e
he ad en o neu al ne wo ks (NN), deep lea ning (DL) and a i icial in elligence (AI) we e
mos ly based on ha monic signa u es using ac i e, eac i e and dis o ion powe o cu en
Ene gies 2025,18, 3536 h ps://doi.o g/10.3390/en18133536
Ene gies 2025,18, 3536 2 o 27
quan i ies [
1
,
2
]. Elabo a ed ans o ms ha e been explo ed as ools o ex ac all aluable
in o ma ion om aw signals. These include Fou ie ans o m and i s sho - ime e sion,
S- ans o m [
3
,
4
] and i s adap i e e sion [
5
], wa ele ans o m (WT) [
4
,
6
] and empi ical
mode decomposi ion (EMD) [
7
]. Such me hods a e pa icula ly a ac i e when dealing
wi h ansien phenomena [
5
,
8
,
9
], al hough he e a e app oaches ha in ol e eeding
such ansien s di ec ly o he NN [
10
–
12
]. We emphasize ha hese app oaches ha e been
p oposed as ools o classi y di e en powe -quali y ansien s [
10
,
11
] om a p ede e mined
lis ; only [
12
] add esses anomaly de ec ion applied o he ailway en i onmen ; howe e , i
ocuses on ansien s iden i ied by he Hilbe ans o m and uses a supe ised me hod, like
a 1D-CNN. This demons a es he no el y o he p esen app oach, which co e s anomalies
no p e iously iden i ied and quan i ied wi h an unsupe ised app oach.
Despi e he p e alence o a ocus on he equency domain in esea ch p oduced un il
he las decade, ime-domain (TD) app oaches ha e been also p oposed and ha e become
mo e popula o use in combina ion wi h DL [12–14].
Non-in usi e load moni o ing (NILM) and dis o ion classi ica ion aim a imp o ing
he a ailabili y, quali y and sa e y o mode n g ids [
15
–
17
] bu ace signi ican challenges
in p esence o highly dynamic loads and non-ideal g id esponse. Whe eas pu e NILM
ocuses on ene gy disagg ega ion o appliances, he use o dis o ion classi ica ion p o ides
impo an suppo o disambigua ing ypical scena ios in ol ing con empo a y swi ching
e en s, simila V-I pa e ns, e c. Load moni o ing and classi ica ion can in gene al suppo
he ollowing ea u es:
•
g id p o ec ion and managemen (including s abili y) ha a e applicable a la ge scales
(e.g., in dis ibu ion), bu also a he small scale o a mic og id, including enewables
and highly dynamic o suscep ible loads [18,19];
•
con ol o powe low o imp o e he quali y o se ice, in pa icula in e ms o
ol age luc ua ions and ansien s [20];
•
powe -quali y con ol encompassing bo h adi ional ha monic dis o ion and dis u -
bance a highe equency, which a e eme ging oday as possible h ea s o g id con ol
and me e ing ha di ec ly a ec powe -line communica ion p o ocols [
21
–
24
]; pas
s udies demons a e ha in e e ence wi h he me e ing unc ion can occu a a ious
equency anges wi hin he ha monic and sup aha monic domains, a ec ing no only
he o e all in ensi y, bu also speci ic pa s o he wa e o m, as in he case o pulsed
dis u bances [22];
• ene gy e iciency om a mul i ude o pe spec i es:
–
iden i ica ion o ene gy-was ing de ices o , in gene al, de ices wi h less- han-
ideal powe p o iles [25];
–demand managemen and load balancing as pa o g id con ol;
–
iden i ica ion o powe losses in suscep ible g id elemen s (namely ans o me s
and cables) and in he loads hemsel es ha occu as a consequence o exces-
si e dis o ion;
–
co ec accoun ing o ha monic powe losses in he es ima ion o powe abso p-
ion and ene gy e iciency [26];
•
ai a i ing and billing, associa ing a iable a i s wi h he le el o load “ i uosi y”
as soon as a load is connec ed o he g id; his includes linking a i s po en ially
dis up i e e en s ha may cause economic losses and also may incen i ize imp o e-
men s in ene gy e iciency and educe associa ed losses. Con e sely, a he use le el,
usage egula ion encou ages he use o low-p ice ime slo s, a change suppo ed by
he use o sma me e s [25].
Ene gies 2025,18, 3536 3 o 27
Ano he in e es ing applica ion is he moni o ing and e alua ion o long- e m unsu-
pe ised powe -quali y (PQ) measu emen s as a o m o big-da a analy ics [
27
]. A p e ious
applica ion in ol ing ansien emo al om eco ded da a in powe g ids is epo ed
in [28].
E en accu a e and sophis ica ed DL me hods can su e om in insic a iance in
inpu da a ( his will be add essed in his wo k by e alua ing he e ec s o noise in inpu
da a) and om he p esence o new unlabeled da a [
29
,
30
] (e.g., a new ype o load o an
un o eseen ope a ing condi ion).
Focusing on AC ailways as a ne wo k ea u ing mo ing loads ( he olling s ock, RS)
wi h a iable powe ing and ope a ing condi ions (OCs), his s udy emphasizes single-poin
moni o ing me hods applied a he pan og aph in e acing po . While ol age d ops can
a ec ol age alues along he con ac line (and hus a ec he calcula ed powe e ms
depending on he measu emen loca ion in he ne wo k), analysis o he pan og aph cu en
alone o e s an ad an age because he pan og aph cu en can be di ec ly ela ed o he
line cu en sou ced by he T ac ion Powe S a ion (TPS), which ep esen s he in e nal
coupling poin . In o he wo ds, he e is a mo e accu a e and di ec ela ionship be ween
he TPS cu en and he RS pan og aph cu en .
RS, wi h i s abso p ion peaks du ing ac ioning and in ense e e se powe low du -
ing b aking, ep esen s a challenging load, wi h highly dynamic beha io and con inuously
changing eeding line impedance as i mo es [
31
], which cause he ol age-cu en ela-
ionship o change con inuously, especially a high equencies. Complex and a ying
ha monic pa e ns occu depending on he a iable OCs [
32
] and a e in luenced by he TPS
dis o ion and nea by ains [33].
Basic signal-p ojec ion and -classi ica ion echniques applied o AC ailway da a we e
e alua ed in [
34
], explo ing he bene i s o each me hod (p incipal componen analysis
(PCA) and pa ial leas squa es eg ession (PLSR)), and discussing TD ea u es use ul o
load moni o ing and dis o ion acking (a e age and ex eme alues, slope, in e sec ions,
e c.) [35].
The numbe o candida e ea u es ha can be ex ac ed wi h “classical” me hods is
la ge. AI echniques can o e signi ican suppo o syn hesizing pools o highly in o ma-
i e ea u es [
36
]. Such echniques go h ough sui able p ojec ions and da a-dimensionali y
educ ion, which a e ollowed by clus e ing and classi ica ion, including iden i ica ion
o anomalies and ou lie s [
27
,
36
]. Fo example, image-p ocessing echniques may be
equally applicable o equency-domain spec a [
36
] and TD wa e o ms, including V-I
ajec o ies [13,32,37,38].
In o ma ion a ailable in TD wa e o ms can be u he exploi ed by ocusing on wa e-
o m pa s ha con ey he mos ele an in o ma ion. The ad an age o TD wa e o ms
lies in hei close ela ion o load ope a ion, which imp o es comp ehensibili y and in-
e p e abili y o he use . The combina ions o in o ma ion ex ac ed om he TD aw
da a and possible clus e ing and classi ica ion app oaches a e coun less. Mode n a i icial
in elligence me hods may help educe his complexi y, p o iding e ec i e dimensionali y
educ ion on he one hand and p o i able iden i ica ion o in o ma i e ea u es on he o he
hand [39].
This pape abandons he mo e classical equency-domain dis o ion indexes and
discusses he ollowing poin s:
•
Non-ac i e cu en (NAC) p o ides good classi ica ion pe o mance and cha ac e iza-
ion o wa e o m dis o ion (WD).
•
Classi ica ion o unlabeled highly-dimensional WD da a wi h a wo-s ep me hod: i s ,
dimension educ ion using deep au oencode (DAE) and clus e ing o OC cha ac-
e iza ion, labeling and anomaly de ec ion (AD); second, clus e assignmen based
Ene gies 2025,18, 3536 4 o 27
on Euclidean dis ance (ED) o segmen a ion o new unlabeled da a (no clus e ed o
ained); his classi ica ion is unsupe ised and has diagnos ic and in e p e a i e uses.
•
Al e na i ely, clus e ca ego iza ion can be u ilized o labeling he da a, allowing
supe ised DL algo i hms o ain and pe o m moni o ing asks, since such me hods
depend on eliable labeling o pe o m well a e aining and alida ion. Fo ha
pu pose, a 1-D CNN is employed as a benchma k o supe ised DL in classi ica ion
asks, highligh ing he po en ial o clus e -based labels.
•
Clus e ing e eals pa e ns associa ed wi h WD cha ac e is ics and sys em dynamics,
including anomalies, hus suppo ing he iden i ica ion o ou lie s wi hou he need
o a speci ic p io c i e ion. This is a poin o no el y wi h espec o he majo i y
o p e ious s udies and is demons a ed also by conside ing an addi ional example,
speci ically, cha ging o elec ic ehicles (EVs).
•
Assessmen o bo h classi ica ion me hods using new unseen da a om he same sys-
em ha a e no labeled, bu a e assigned an OC by inspec ion o da a cha ac e is ics.
•
Iden i ica ion o in o ma i e wa e o m ea u es o p o ide added alue o he su-
pe ised classi ica ion, ocusing on he 1-D CNN and using g adien -weigh ed class
ac i a ion mapping (G ad-CAM).
The objec i e is no so much he gene al classi ica ion o PQ dis u bances in a powe
g id, bu he cha ac e iza ion o load ope a ion and i s changes in OCs o allow he iden i i-
ca ion o di e en loads and he sepa a ion o anomalous cases, as well as o new, p e iously
unseen loads. This wo k cha ac e izes WD by segmen ing he associa ed mechanisms wi h
OC a ia ions, allowing unsupe ised load cha ac e iza ion. ED allows quan i ying he con-
sis ency o pa e ns o igina ing om he same load, including applica ions o diagnos ic
pu poses, such as iden i ing ou lie s and anomalous cases.
The o e all s uc u e and he main con ibu ions o his wo k a e g aphically desc ibed
in Figu e 1.
Figu e 1. O e all g aphical desc ip ion o he pape s uc u e and o ganiza ion.
Ene gies 2025,18, 3536 5 o 27
2. Elec ic Sys em and Rela ed Powe Theo y
This sec ion cla i ies he app oach o NAC ex ac ion and he cha ac e is ics o he
s udied elec ic sys em, which will be ele an in he la e discussion o clus e ing and
inge p in ing.
2.1. Time-Domain Non-Ac i e Powe
Based on F yze’s heo y [
40
,
41
], a TD decomposi ion was applied o he measu ed
i( )wa e o ms.
S a ing om he ac i e cu en componen
ip( )
, he NAC
iq( )
is hen he di e ence
be ween he o al cu en
i( )
and
ip( )
. The componen s
ip( )
and
iq( )
a e o hogonal, so
ha hey can be summed in quad a u e.
ip( ) = G ( )G=P
V2(1)
whe e he ac i e powe
P
is di ec ly de e mined om i s TD de ini ion o a sinusoidal
signal o pe iod T:
P=1
TZ 0+T
0
( )ip( )d (2)
The NAC iq( )is calcula ed as he di e ence:
iq( ) = i( )−ip( )(3)
2.2. Desc ip ion o he Elec ic Powe Sys em
Elec i ied ailway sys ems (ERSs) ea u e long line b anches (wi h powe dis ibu-
ion mos ly h ough o e head conduc o s) ed by one o mo e TPSs. In AC ailways,
adi ional TPSs p o ide powe o he line h ough ans o me s, whe eas mo e mode n
con e e -based TPSs in e ace di ec ly and a e a cause o inc eased backg ound dis o -
ion. AC ailways may wo k in synch ony wi h he na ional g id (a 50
Hz
o 60
Hz
), o
au onomously a 16.7 Hz (in cen al Eu ope), using hei own ansmission g ids [42].
The elec ical in e ac ions among he a ious elemen s (na ional and ansmission
g ids, TPSs, o e head lines, e u n cu en ci cui s, signaling sys ems, RSs, e c.) can be
complex. RSs a e mo ing loads ha ope a e dynamically wi h ac ion and b aking in e als
bu also include coas ing and s ands ill. Besides con e e -based TPSs, hey a e he o he
majo sou ce o dis o ion due o a a ie y o s a ic powe -con e sion sys ems ha ope a e
onboa d ( o ac ion and auxilia y loads) and ha e emissions o e lapping he backg ound
dis o ion [43].
Iden i ica ion and assessmen o RS dis o ion has he ollowing echnical objec i es:
•
compliance wi h dis o ion limi s aims a p e en ing damage o he dis ibu ion sys em
and in e e ence wi h o he loads [44];
•
dis o ion limi s a e also se o limi in e e ence wi h signaling ci cui s, such as ack
ci cui s [45];
•
ac ion line s abili y and limi a ion o o e ol ages igge ed by RS emissions [
46
,
47
].
3. Segmen a ion and Classi ica ion Me hod
In his wo k, he DAE is applied o he
iq( )
pa o he pan og aph cu en , and
his s ep is ollowed by clus e ing. In [
32
], he DAE was applied o ind pa e ns in
WD da a o pan og aph quan i ies, showcasing he po en ial o unsupe ised DL and
clus e ing echniques (see Figu e 2). While ha me hod e ec i ely cha ac e ized WD
sho - e m a ia ions and hei ela ion wi h OCs, some aspec s we e no in es iga ed,
namely he ollowing:
Ene gies 2025,18, 3536 6 o 27
•
how o deal wi h a iabili y o di e si y wi hin a clus e and how o use i o e i y
new unlabeled da a;
•
he shape and compac ness a ound he clus e s’ cen oids may be used o iden i y
anomalies and p o ide in o ma ion o diagnos ic pu poses.
Figu e 2. DAE applica ion o pa e n ecogni ion in WD da a.
This wo k goes beyond he simple classi ica ion ask by quan i a i ely assessing
he in o ma ion con eyed by he a ious da a ea u es, s a ing he p ocess om he
achie ed clus e s uc u e in o de o p o ide segmen a ion o WD da a, including AD.
This no el app oach no only suppo s obus labeling o da a, bu also in oduces wo
unique classi ica ion me hods:
•
one me hod is based on he ED o DAE ea u es and p ede e mined clus e s, e alua ing
he capaci y o ans e ing segmen a ion knowledge om he unsupe ised lea ning
amewo k o new unlabeled da a;
•
he o he me hod uses a mo e adi ional 1-D CNN, ensu ing ha labeling can be
explo ed wi h o he DL echniques o independen alida ion.
3.1. DAE and Clus e ing o Da a Segmen a ion and Labeling
DAE, an unsupe ised lea ning model, is designed o lea n a compac inpu da a
ep esen a ion, cap u ing i s signi ican cha ac e is ics and pa e ns [
36
]. This enables he
model o achie e dimensionali y educ ion and ea u e lea ning. The a chi ec u e consis s
o an encode , la en space and a decode .
The choice o DAE o e o he mo e adi ional me hods, such as p incipal componen
analysis (PCA), is ela ed o i s capaci y o modeling complex/complica ed non-linea
unc ions wi h high-dimensional da a [
48
]. While DAE uses non-linea ac i a ion unc ions,
PCA is limi ed o a linea ans o ma ion o da a and hus has una oidable limi a ions.
The encode , a se o eed- o wa d il e s, ans o ms he inpu da a in o he la en
space, whe e a educed dimension and a de ined numbe o ea u es ep esen he da a [
49
].
Simul aneously, he decode , a se o e e se il e s, p oduces he inpu econs uc ion. By
a ge ing he inpu and pe o ming back-p opaga ion du ing aining, he model lea ns he
unde lying ele an ea u es o he da a. The di e ence be ween he econs uc ed inpu
and he ac ual inpu upda es he e o e m, using me ics like mean squa ed e o (MSE)
o cosine simila i y (CS), in case o highly-dimensional and noisy da a.
The encoding s ep is desc ibed by (4):
z= ({W,b};u) = σ(Wu +b)(4)
Ene gies 2025,18, 3536 7 o 27
whe e he inpu ea u e ec o
u
is ep esen ed by he coded ea u e ec o
z
, which
p opaga es h ough he hidden laye s. Wa e he weigh s o he ne wo k, bis he ne wo k
biases, and σis an ac i a ion unc ion.
The decoding s ep is desc ibed by
(5)
, whe e he coded ea u e ec o
z
is mapped
back o he highe dimension econs uc ion y.
y= (W′,b′;z) = δ(W′z+b′)(5)
Table 1desc ibes he a chi ec u e and he hype -pa ame e s used in he DAE. The CS
is desc ibed by
(6)
: i assesses he simila i y be ween wo ec o s,
A
and
B
, by calcula ing
he cosine o he angle be ween hem, esul ing in almos uni y alues o simila ec o s
and owa ds 0 o dissimila o o hogonal ec o s [50].
CS =A·B
∥A∥∥B∥=∑n
i=1AiBi
q∑n
i=1A2
iq∑n
i=1B2
i
(6)
Table 1. Au oencode A chi ec u e and T aining Hype -pa ame e s.
Laye Type Desc ip ion
Inpu Laye Inpu shape: (15,000)
Dense (Encode ) 64 uni s, ReLU ac i a ion
Dense (Encode ) 32 uni s, ReLU ac i a ion
Dense (Encode ) 16 uni s, ReLU ac i a ion
Dense (Decode ) 32 uni s, ReLU ac i a ion
Dense (Decode ) 64 uni s, ReLU ac i a ion
Dense (Decode ) 15,000 uni s, Linea ac i a ion
Hype pa ame e s Op imize : Adam; Epochs: 150; Lea ning Ra e: 0.001
As illus a ed in Figu e 2, k-means clus e ing is applied o he la en space ep e-
sen a ion o he da a ha a e sepa a ed based on he WD cha ac e is ics ex ac ed by he
DAE. The esul ing clus e s ep esen he da a segmen a ion and also p o ide da a labeling,
con eying in o ma ion ela ed o he RS OCs and WD.
The k-means clus e ing algo i hm o ganizes da a in o a p elimina y assigned numbe
o clus e s
Nc
[
51
]. I measu es simila i y using ED and employs cen oids o ep esen each
clus e [
51
,
52
]. I s choice is mo i a ed by i s simplici y o in e p e a ion and implemen a ion,
oge he wi h he capaci y o good pe o mance wi h la ge da ase s, scalabili y, and
sui abili y o mul iple domains [53].
This app oach esembles ha used in [
54
] o he classi ica ion o PQ ansien s wa e-
o ms, al hough dimensionali y educ ion is achie ed he e wi h he DAE i sel and no
by applying PCA a he au oencode ou pu . The PCA and CS we e combined in [
54
] o
associa e da abase labels wi h he clus e cen oids om he obse ed da a. Th ough his
app oach, manual analysis o de ining he e en s associa ed wi h he clus e s is a oided.
Howe e , his p ocess equi es a da ase wi h p ede e mined and eliable labels, and he
esul an classi ica ion o he clus e s is made as e . I is a good al e na i e o PQ e en s
wi h such highly dis inguishable and sepa a ed cha ac e is ics, bu i is much less e ec i e
when only WD cha ac e is ics wi hou labels a e subjec o analysis. Add essing a ia ion
o spec al con en in he ime domain equi es ha he ea u es cap u ed by he DAE
can dis inguish unlabeled pa e ns (no known a p io i) wi h a measu able diagnos ic
pa ame e , as p oposed in he p esen wo k. This p ocess enables he c ea ion o new labels
associa ed wi h WD ea u es and sys em cha ac e is ics (such as RS ype o i s OC). The
app oach in [
54
] is app op ia e when he objec i e is o iden i y pa e ns and segmen a-
Ene gies 2025,18, 3536 8 o 27
ion wi h classi ica ion based on one ype o e en (e.g., ol age a ia ions o di e en
magni udes, such as dips, swells, in e up ions, e c.).
Since he DAE p o ides da a dimensionali y educ ion, he p ede e mined numbe o
clus e s o be used in k-means
Nc
is de e mined using he Calinski–Ha abasz c i e ion [
55
].
The ED me ic used by k-means will be u he e alua ed o AD.
3.2. Sui abili y o NAC o Finge p in ing
Good and consis en pe o mance is p o ided by he ac i e powe index (API), which
calcula es he ac i e powe componen
Ph
a each spec um equency bin and is able o
ack he di e en beha io s o each componen o each ype o dis o ion. The use o
a ious non-ac i e powe e ms has also been discussed in he li e a u e as an indica o o
he iden i ica ion o dis u bing loads, bo h in he equency domain [
56
,
57
] and in he ime
domain [58,59].
The p oblem o selec ing in o ma i e pa s o he spec um o RS classi ica ion was
in es iga ed in [34], wi h he ollowing esul s:
•
Ac i e powe s. equency
Ph
p ese es he sign o powe abso p ion, dis inguishing
be ween ac ion and b aking condi ions, and has good classi ica ion pe o mance,
al hough i s pe o mance is no always be e han hose o ha monic eac i e powe
Qhand ha monic cu en Ih;
•
Acco ding o he esul s o P incipal Componen Analysis (PCA), a small numbe o
he componen s o he ac i e powe spec um
Ph
accoun o he o al ene gy, whe eas
he componen s o he eac i e powe spec um
Qh
a e mo e dispe sed: he amoun o
in o ma ion con ained in
20–28 Qh
componen s is equi alen o ha con ained in jus
3Phcomponen s;
•
Pa ial Leas Squa e Reg ession (PLSR) has in gene al be e pe o mance han PCA,
al hough no in all cases;
•
Classi ica ion based on ha monic cu en
Ih
is consis en ly be e han ha based on
Qh
componen s, as was also demons a ed by he calcula ion o he “ a iable impo ance
in p ojec ion” pa ame e o PLSR.
In [
34
], he esul s o he con usion ma ices o a wide ange o cases (144 o Swiss
and Ge man RS) showed ha using
Ih
may ne e heless imp o e
Ph
i he da a a e sui ably
p ojec ed and pos -p ocessed, po en ially achie ing be e pe o mance han PCA and PLSR.
The use o DAE in he p esen wo k is a s ep in his di ec ion. A simila app oach is ollowed
in [59], whe e he ocus is on he i s h ee odd cha ac e is ic ha monic wa e o ms.
Conside ing he cu en quan i y as he inpu o moni o ing, an app oach using
diagnosis and classi ica ion has he ad an age o being a ailable a he TPS (o , mo e
gene ally, in an indus ial o esiden ial con ex a he poin o common coupling), whe e
indi idual load cu en e ms a e agg ega ed. In addi ion, using he cu en alone and
igno ing he ol age makes i possible o ollow he in o ma ion om he loads o he sou ce
almos unal e ed, whe eas he line ol age is a ec ed by una oidable ol age d ops.
The ocus on using TD in o ma ion ( hus p ese ing he wa e o m shape) shows
ha
iq( )
shows p omise o dis o ion classi ica ion, as i is dep i ed o he p eponde an
ac i e cu en e m. The in es iga ion o he use o
iq( )
in [
58
] was limi ed o showing
V-I diag ams o i , which we e compa ed o he comple e V-I diag ams o he whole
inpu cu en
i( )
. The use o DL echniques makes i possible o use a b oade ange o
classi ica ion and diagnosis capabili ies, as discussed below.
3.3. ED o AD and Segmen a ion o New Da a
The ED be ween an obse a ion o a clus e and i s cen oid may indica e simila i y
o he iden i ied pa e n. I is in ac in ui i e ha poin s in he clus e space a he away
Ene gies 2025,18, 3536 9 o 27
migh di e mo e signi ican ly om he ypical pa e ns cha ac e izing ha clus e . Such
abno mal ED a ia ions may also indica e he p esence o an anomaly (o ou lie ) in he
p o ided da a. Thus, one possible applica ion is ha o da a sc eening, in pa icula o
long- e m eco dings.
Obse a ions wi h g ea e dis ances wi hin a clus e migh di e om he expec ed
pa e n ep esen ed by ha g oup, and one should be able o de e mine whe he hose
a ia ions a e due o he ac ual di e si y o he clus e o whe he hey ep esen anomalies
wi hin he da a. This wo k p oposes anomaly-de ec ion AD based on he ED me ic, as
shown in Figu e 3.
Figu e 3. P ocedu e o ind anomalies wi hin he assigned clus e s.
AD consis s on inding ou lie s based on ela i e ED wi hin each clus e pe he
ollowing s eps: calcula e ED o each obse a ion o he cen oid; calcula e he z-sco e o
such ED alues; de e mine which obse a ion dis ance ep esen s an ou lie by median
absolu e de ia ion (MAD). As is known, wi h he median being a obus es ima o o
loca ion, MAD is a obus measu e o he a iabili y and scale o a da a sample [
60
].
Obse a ions wi h a dis ance om he median g ea e han 3
×MAD
a e conside ed
anomalies, ollowing he c i e ion se o h in [
61
], who indica ed a ac o o 3 as a “ e y
conse a i e” choice, as also discussed in [62].
Fo a ec o
Y
made up o
N
scala obse a ions, MAD is de ined as in
(7)
o
i=1, 2, . . . , N.
MAD =median(|yi−median(Y)|)(7)
Besides al eady labeled da a, new unlabeled da a may be sc eened o anomalies wi h
ED calcula ion. Based on he same ED, new da a may be assigned o an exis ing clus e ,
a e which he cen oid will be upda ed o he nex new obse a ion and i s ED alue.
The p ocess is desc ibed in Figu e 4.
Figu e 4. Classi ica ion me hod based on ED and p ede ined clus e s o unlabeled da a.
3.4. 1-D Con olu ional Neu al Ne wo k (CNN)
A mo e adi ional supe ised-lea ning me hod may be adop ed using a 1-D CNN
o ha po ion o da a ha is labeled (as shown in Figu e 5). The da ase is sepa a ed o
aining, alida ion and es ing, allowing assessmen o classi ica ion pe o mance o he
a ge classes (using con usion ma ix and balanced accu acy quan i ica ion). La e , he 1-D
CNN is also e i ied on unlabeled da a as pa o i s es ing.
DL models based on 1-D CNN a e usually composed o he inpu laye , mul iple
hidden laye s, al e na ed con olu ional and pooling laye s, a ully connec ed laye , and an
ou pu
laye [63].
In an analog o he popula 2-D CNN, he 1-D CNN allows lea ning and
Ene gies 2025,18, 3536 16 o 27
in he new da a, whe e 4 a e o C1, 69 a e o C2, 37 o C3, none o C4, and 11 o C5.
F om a pa e n iden i ica ion iewpoin , hose esul s a e in e es ing since hey can be
ob ained h ough he well-de ined quan i y ED, ans e ing p e ious knowledge and da a
classi ica ion o new unlabeled da a.
(a) (b)
Figu e 13. Classi ica ion esul s based on ED and p ede e mined clus e s: (a) classi ica ion based on
he p ede e mined clus e s (ci cles o e iden mis-classi ica ion); (b) classi ica ion wi h AD (a ea
iden i ied by he dashed ho izon al lines).
4.3. Classi ica ion by 1-D CNN wi h Clus e -Based Labels
The esul s o se 1, based on clus e ing and AD, suppo he c ea ion o labels ha
impose classes on he da a, ca ying he associa ion o OCs and WD. The p esence o labels
opens up he oppo uni y o ain mo e adi ional algo i hms like 1-D CNN, as desc ibed
in Sec ion 3.4. Two poin s a e discussed he e: he alida ion o he labeling p ocess based
on DAE ea u e ex ac ion and clus e ing, and he pe o mance o he 1-D CNN. A e
success ully using 80% o he da a o aining and 10% o alida ion, he emaining 10%
was used o classi ica ion and o es he 1-D CNN pe o mance (see he con usion ma ix
in Figu e 14a). The 1-D CNN pe o ms well wi h he gi en labels conside ing he ollowing
poin s: i is an unbalanced se o labels and da a wi h high dimensionali y. Conside ing
balanced accu acy (BA), since he e is a signi ican unbalance be ween classes, he sys em
pe o med wi h BA = 89.4% o he es se , in which he anomaly class p e alen ly pushes
down he pe o mance (excluding i , BA = 96.5%).
(a) (b)
Figu e 14. 1-D CNN es ing esul s: (a) es clus e -labelled da ase based on con usion ma ix
( ow-no malized) (b) new unlabelled da ase (squa es indica e e iden misclassi ica ion).
Figu e 14b shows he esul s o he second se 2 o 3444 wa e o ms o new unlabeled
da a. Lacking labels o use as e e ence o e i ica ion, compa ison wi h he ac i e powe
dis ibu ion o clus e s allows o check ha he 1-D CNN classi ica ion is easonable
Ene gies 2025,18, 3536 17 o 27
and cohe en . A ew esul s de ia e om he expec ed OC associa ed wi h ha clus e
(indica ed by squa es). Compa ing he wo me hods, as in Figu e 15, 84.66% o he 1-D
CNN p edic ions a e in ag eemen wi h he ED me hod, wi hou conside ing anomalies.
Figu e 15. Con usion ma ix ( ow-no malized) compa ing 1-D CNN and ED classi ica ion me hods.
F om a gene al s andpoin nea ly 90% o accu acy, 96.5% excluding anomalous cases,
using eal da a in unsupe ised lea ning condi ions, is a signi ican pe o mance, i we
compa e o o he p e ious wo ks also using TD wa e o ms, bu in supe ised lea ning
condi ions:
•
Re . [
13
] epo s qui e a a iable accu acy o he a ious classes o he PLAID da ase ,
ending in 81% o balanced accu acy;
•
Re . [
37
] shows alues o a e age accu acy be ween 96.6% and 97.2% when wo king on
he LIT-SIM 5 da ase , ha may be conside ed he closes example in ha publica ion
o he p esen case; o he pas app oaches epo ed in [
37
] ange be ween 77.2%
and 95.4%.
I is no ewo hy he abso p ion o anomalies iden i ied by he unsupe ised ED me hod
in o he class C2 o he 1-D CNN me hod. This is a he base o he di e en sco ing o
pe o mance wi h and wi hou he anomaly ca ego y.
Fo mo e insigh in he pe o mance o he 1-D CNN model, he g adien -weigh ed
class ac i a ion mapping (G ad-CAM) [
68
] can be employed o in e p e a ion, by highligh -
ing he da a segmen s ha a e key o classi ica ion [
69
], measu ing hei in o ma i e con en .
Figu e 16 shows h ee examples o co ec p edic ion o C1, C3 and C4.
In he case o he C1 p edic ion (see Figu e 16a), he highes impo ance is highligh ed
in pa icula o he op and in e media e pa s o he wa e o m shape, indica ing ha
hose
iq( )
segmen s a e mo e impo an o de e mine C1 p edic ion. The highes alue o
G ad-CAM impo ance is 1.84, while he a e age is 0.68. In ha case, 53.4% o he inpu
signal is abo e he mean alue. Tha signal cha ac e is ic can be associa ed wi h he high
le els o hi d ha monic in HT condi ions, impac ing signi ican ly on he TD shape. I is
ema kable ha he bo om pa o each wa e o m pe iod is no picked up by G ad-CAM:
he symme y o he wa e o m can be obse ed, so ha p obably ha pa o he wa e o m
is jus specula and does no add any inno a i e in o ma ion.
Looking a he C4 case (see Figu e 16e), he mos meaning ul wa e o m segmen
iden i ied by he G ad-CAM is he ze o c ossing and an almos 50% o ampli ude ange
a ound i . Tha migh be associa ed wi h he change in he ze o c ossing di ec ion due
o egene a i e b aking; he p ominen dis o ion a ound he ze o c ossing is sha ed in
eali y wi h C3 (see Figu e 16c), which has he la ges dis o ion o he poin ha he
wa e o m shape is qui e di e en almos comple ely domina ed by he 3 d ha monic. Fo
Ene gies 2025,18, 3536 18 o 27
C4, he highes impo ance alue was 10.25, wi h an a e age o 1.56. Al hough he a e age
is signi ican ly lowe han he peak, only 26.6% o he wa e o m exceeds he a e age,
indica ing ha hese segmen s ha e a s ong in luence on he p edic ion.
(a) (b)
(c) (d)
(e) ( )
Figu e 16. Explana ion o some es p edic ion o he 1-D CNN using G ad-CAM o co ec classi ica ions:
(a) ue p edic ion o C1, (b) alse p edic ion o C1, (c) ue p edic ion o C3, (d) alse p edic ion o C3,
(e) ue p edic ion o C4, ( ) alse p edic ion o C4.
All he h ee inse s on he le side o Figu e 16 discussed abo e o C1, C3 and C4
a e sided by an example o alse p edic ion (o , misclassi ica ion), showing he simila i y
and closeness o he wa e o m shape and dis o ion ea u es. Al hough he wa e o ms
o C3 in Figu e 16c,d may appea isually simila o jus i y he assignmen o he same
class (namely C3), Figu e 16d ac ually ma ks he ansi ion o a new ope a ing s a e
(i.e., C4), as can be e idenced by he inc eased peak ampli udes and sligh change on
wa e o m dis o ion. This pa is pa icula ly challenging due o he simila i y o i s
cha ac e is ics o hose obse ed a he limi s o no mal ope a ing condi ions, leading o
g ea e con usion du ing classi ica ion by supe ised models as 1-D CNN. I is impo an o
emembe ha he used labels a e no de i ed om an ex e nal o p ede ined c i e ion, bu
Ene gies 2025,18, 3536 19 o 27
a e ins ead he esul o clus e ing based on ea u es ex ac ed by he DAE. This inhe en ly
in oduces a deg ee o imp ecision in o he labeling p ocess, as p e iously demons a ed
wi h “diagnosis” based on ED. In he case o he C4 class and i s co esponding alse
p edic ion (
Figu es 16e and 16 ,
espec i ely) i is possible o see ha an appa en ly C4
wa e o m was classi ied as “Anomaly”, possibly because o la ge high- equency con en ,
isible in he double “ oo h” in he hump abo e he ze o c ossing, whe eas only one la ge
oo h is isible in he C4 wa e o m on he le .
These G ad-CAM examples show ha he 1-D CNN model can unde s and nuances
wi hin he inpu da a signals and exploi hem o classi y, while p o iding an indica ion o
he ela i e impo ance o e en small wa e o m po ions. They also demons a e how he
model can shi i s a en ion ac oss he signal, which can be insigh ul o complex mul i-
class classi ica ion asks. The a en ion aspec s, associa ed wi h WD iden i ica ion, u he
enhance he explicabili y o he analysis (c ucial aspec wi hin mul i-domain applica ion,
as poin ed ou in [70] o a simila applica ion ega ding powe sys em ansien s).
4.4. Noise and Noise E ec
Some conside a ions a e p o ided on he noise concep o he me hod. The expe i-
men al da a u ilized in he wo k a e al eady cha ac e ised by hei own in insic elec ic
noise ha is e alua ed in he ollowing o suppo he s a emen ha he p oposed me hod
is obus o da a noise. Shi ing o a equency-domain in e p e a ion, he NAC spec um is
e alua ed o he cha ac e is ic ha monic componen s compa ed o he adjacen incohe en
spec al equency bins, assessing wha is he amoun o noise p esen in he da a as inpu
o he DAE (see Figu e 17).
I is possible o see in Figu e 17c ha he undamen al and low-o de ha monics a e
cha ac e ized by a 25–35 dB a e age SNR, whe eas beyond he 17 h componen , included,
he SNR se les o abou 20
dB
going down smoo hly o abou 10
dB
. This is con i med by
he his og am o alues in Figu e 17b, whe e al oge he hey span be ween
5 and 40 dB
,
excluding he wo all bins a ound 0.
These SNR alues demons a e how he p oposed unsupe ised me hod can deal
wi h a signi ican amoun o in insic noise in he da a. The nega i e alues occu ing
a low powe le els a e due o he ope a ion o he ac ion con e e s in an i ele an
ope a ing egion, ea u ing an o e lap o dis o ion caused by onboa d auxilia ies ha is
no associa ed wi h he main cha ac e is ic ha monics. The many ou lie s (shown as ed
c osses in Figu e 17c) demons a e he highly a iable dynamic condi ions.
The wo classi ica ion me hods explo ed in his wo k we e hen e alua ed by injec ing
addi ional a i icial incohe en noise (whi e noise), he eby wo sening he SNR alues
and assessing he consequen pe o mance. The a ec ed componen s we e hose wi h he
la ges SNR alues, he eby educing he SNR alues globally o less han 20 dB (18
dB
on
a e age, o be p ecise), implying a deg ada ion o 12 ±5 dB.
The aim is o obse e any possible shi s in he decision c i e ia and label assignmen
du ing he segmen a ion o he “unlabeled da a” in se 2 (see Figu e 18). The esul s
compa ing he ED-based classi ica ion wi h and wi hou addi ional noise a e illus a ed
in Figu e 18a. Addi ionally, he ED classi ica ion is compa ed again o he ou pu o he
supe ised 1D-CNN model, and he esul s a e p esen ed in Figu e 18b.
Ene gies 2025,18, 3536 20 o 27
(a) (b)
(c)
Figu e 17. Signal- o-noise a io (SNR) dis ibu ion in o m o box-plo s o he inpu NAC da a: (a) SNR
s. inpu ac i e powe ; (b) his og am o SNR alues; (c) SNR dis ibu ion o he odd ha monics
o he spec um up o ha monic o de 119 (in he boxplo he blue box ex ends om he i s o he
hi d qua ile, he ho izon al ed dash in he middle is he median, and he emaining ed c osses
a e ou lie s).
(a) (b)
Figu e 18. Con usion ma ices o ED unsupe ised me hod ope a ion a e injec ion o addi ional
noise educing he SNR alues below 20
dB
: (a) compa ison wi h pe o mance wi hou noise injec-
ion (o iginal SNR); (b) compa ison wi h he 1D-CNN classi ica ion bo h wi h he said addi ional
injec ed noise. Colou s a e chosen o isually dis inguish he wo cases and da ke nuances unde line
highe alues.
As shown in Figu e 18a he e is subs an ial ag eemen on he class assignmen s, wi h
a maximum de ia ion o 2.1%. Anomalies a e ins ead mo e dispe sed, wi h some “leakage”
Ene gies 2025,18, 3536 21 o 27
(al hough less han 10%) o he classes C1 h ough C5 as a esul o o noise hi ing speci ic
wa e o m po ions, such as he op- and ze o-c ossings.
Compa ed o 1D-CNN, Figu e 18b is almos unal e ed compa ed o he p e ious
Figu e 15; he la ges a ia ion is in he co espondence be ween class C3 o ED and class
C4 o 1-D CNN, wi h a di e en o abou 6%; all he o he alues a e nea ly he same, being
wi hin 0.3% o each o he .
4.5. Compu a ional Times
This b ie sec ion discusses he compu a ional ime needed o he p oposed unsupe -
ised DAE me hod using ED, including a compa ison o he compu a ional ime needed
o he 1D-CNN. Resul s a e shown in Figu e 19 and show ha he p oposed me hod is
much as e and sui able o a eal- ime implemen a ion, wi h he mos likely alue being
3.4
ms
; all alues a e wi hin 9.3
ms
, wi h a maximum alue o 6.9
ms
a 99% p obabili y. The
dispe sion o compu a ional imes is caused by o he concu en p ocesses on he hos ing
compu e , so he as es imes (which also co espond o he mode o he dis ibu ions)
p o ide he bes es ima e o he compu a ional e o o he algo i hm alone.
Figu e 19. Dis ibu ion o he compu a ional imes o 1000 es s o he unsupe ised DAE me hod
and 1D-CNN e e ence me hod.
4.6. Applica ion wi h EV Cha ging Da a o Valida ion
As addi ional e i ica ion, he me hod has been applied o da a measu ed on he
AC side o a 150
kW
CCS cha ging s a ion o a win e ca - es ing cen e in he no h o
Sweden [71]
. Se e al cha ging sessions las ing se e al days we e eco ded by sampling
a 40
kHz
om he AC eeding lines ups eam: he incoming powe and associa ed NAC
we e hen analyzed. Depending on he model o he cha ging EV, powe may a y be ween
25
kW
and 150
kW
; he cha ging imes a y om as as as 6 min o 3 h. Da a we e
eco ded as sho 500
ms
eco ds e e y minu e using Rogowski cu en senso s. In o al,
3338 snippe s we e cap u ed and used in he p oposed me hodology. The objec i e is
o alida e he me hod discussed so a by applying i o a comple ely new scena io, EV
cha ging, which ca ies signi ican applicabili y po en ial.
Clus e ing was pe o med on ou classes, which led o he iden i ica ion o one class
in ol ed in he cha ging a he highes powe le el (C1), wi h he wo o he s in ol ed a
lowe powe le els (C3 and C4). The backg ound noise wi h no EV cha ging was cap u ed
by C2. The in- eed ac i e powe is plo ed s. ime in Figu e 20c, oge he wi h he ou
iden i ied TD pa e ns. I is possible o see ha C2 consis en ly ags all backg ound noise
samples, whe eas C1 is ese ed o high-powe cha ging, occu ing jus abo e 100
kW
;
he cha ging session on 10 Feb ua y, ca ied ou up o 100
kW
, in ac , did no yield any
C1 pa e n.
Ene gies 2025,18, 3536 22 o 27
(a)
(b)
(c)
Figu e 20. Ve i ica ion o EV CCS cha ging sessions o 3 consecu i e days using he p oposed
me hod: (a) 100
ms
long pa e n wa e o ms o each NAC clus e (sample numbe on he ime
axis); (b) co esponding cu en spec um up o 10
kHz
; (c) dis ibu ion o clus e s o e he ac i e
powe p o ile.
The spec a o he o al cu en up o 10
kHz
o he espec i e clus e s a e also il-
lus a ed. I is possible o see ha C3 and C4 a e e y simila , wi h a sligh ly la ge
high- equency con en o C4. C1 is cha ac e ized by he la ges emissions, hese being
app oxima ely ou imes la ge han hose o C3 and C4 o he i s cha ac e is ic ha mon-
ics ( he 5 h, 7 h and 11 h a e pa icula ly isible in Figu e 20b). The backg ound noise in
be ween he ha monics o he undamen al is almos he same o all modes when cha ging
akes place (C1, C3 and C4), wi h a sligh educ ion o C1 be ween 800 Hz and 2 kHz.
Classi ica ion is consis en o he whole 3 days o ope a ion used and epo ed
as an example.
5. Conclusions
The wo k explo ed F yze’s TD NAC
iq( )
o assess he signa u e o dis o ing loads
(AC ailway RS and i s onboa d con e e s in he s udied case, wi h he inclusion o an
Ene gies 2025,18, 3536 23 o 27
addi ional case o a CCS EV cha ging s a ion o con i ma ion). The challenging aspec s
a ise om he RS’s highly dynamic beha io , as i passes h ough a wide ange o powe
le els while ac ioning and b aking. Peculia WD can be associa ed wi h he a ying OCs,
as con i med by he analysis o he equency spec a.
Unsupe ised deep lea ning was used wi h
iq( )
wa e o m samples as inpu . This
is a i s poin o no el y, as i ocuses on he in o ma i e NAC a he han using he
en i e V-I ajec o y. The explo a ion o an unsupe ised me hod using unlabeled da a
is also no ewo hy, in pa icula as i conside s he achie ed high classi ica ion sco e,
p o iding an in e es ing solu ion o he managemen o new loads, like hose seen in
elec omobili y scena ios.
The applica ion o DAE and clus e ing has iden i ied pa e ns associa ed wi h RS OCs,
he eby showing he sui abili y o
iq( )
o pa e n iden i ica ion and ad anced moni o ing.
ED was explo ed o e alua e clus e dispe sion, and a new me hod was p oposed o
iden i ying anomalies, inpu WD samples wi hou de ined c i e ia (so, “ou lie s”), and
unusual shapes. New da a a e hen classi ied based on ED. Resul s we e alida ed by
showing he dis ibu ion o classi ica ion indexes o e he RS OCs; his way, one can
con i m he co ec ness o he da a segmen a ion by i s e iden cohe ence wi h ope a ion
and plausibili y.
La e , he da ase [
65
] wi h clus e -based labels was used o supe ised lea ning
wi h he 1-D CNN o compa e esul s based on ED. BA achie es 96.5% ag eemen using
he es ing po ion o his da ase . When exposed o new unlabeled da a, he 1D-CNN
achie es 89.6% ag eemen wi h he ED-based me hod o no mal s a es. Addi ionally,
G ad-CAM was applied o he 1D-CNN model o quan i y he impo ance o wa e o m
segmen s o p edic ion and highligh he di e en a en ion mechanisms depending on
he obse ed OC.
We he e highligh ha he wo k uses clus e ing and ED o e alua e eal-wo ld PQ
measu emen s and ha he p oposed me hodology is capable no only o inding pa e ns
in WD da a, bu also o add essing unce ain y and inhe en a iabili y o he da ase .
In o he wo ds, i is possible o quan i y he quali y and consis ency o obse a ions,
sc eening o isola e bad, wei d o simply unusual da a (a ea u e ha is ex emely use ul
wi h unsupe ised measu emen and moni o ing and big-da a analy ics). In he s udied
case, a ew eco ds we e iden i ied as ha ing anomalous shapes ha we e no caugh ea lie
by he manual check ca ied ou o build he o iginal da ase in [
65
], he eby demons a ing
he p ac ical alidi y o he me hod.
In addi ion, by classi ying new da a, his wo k showed he po en ial o his app oach
o ans e ing knowledge and ea u e lea ning o o he simila da ase s.
Possible applica ions o his me hod include NILM aimed a he iden i ica ion and
classi ica ion o loads by hei dis o ion signa u es, as well as he e alua ion o PQ om
unsupe ised long- e m measu emen s o iden i ica ion o ou lie s and wei d da a. The
ange o high-powe dis o ing loads and sou ces encompasses indus ial d i es, such as
hose o la ge ans, pumps, comp esso s and o he mo o applica ions. They a e in e aced
o he AC g id wi h con e e s ha a e ei he mo e adi ional diode o hy is o ec i ie s
o ad anced ac i e ec i ie s o he same ype as he RS 4QC conside ed he e.
Fo mode n enewable sou ces, such as pho o ol aic pa ks, he AC g id in e ace
is implemen ed wi h an in e e wi h a g id- o ming o g id- ollowing ope a ion. The
p inciple o ope a ion is qui e simila o ha o he 4QC, ha ing simila modula ion and
swi ching pa e ns.
As an icipa ed, he me hod has been success ully applied also o a di e en scena io
o u he e i ica ion: he cha ging pa e ns o a CCS cha ging s a ion we e consis en ly
classi ied o e sessions las ing se e al days. This p o ides e idence o con idence in
Ene gies 2025,18, 3536 24 o 27
applying he me hod o he o hcoming es campaigns o he Me 4EVCS p ojec [
72
],
which ocus on conduc ed emissions and dis o ion caused by EV cha ging s a ions.
Besides he ad an ages isualized by he esul s, some conside a ions ela ed o
possible limi a ions and nega i e aspec s a e highligh ed below.
•
Clus e -based labels a e e ec i e in cap u ing he ope a ional s a es and load cha -
ac e is ics, enabling o he classi ica ion algo i hms o bene i om he s uc u ed
da a. Howe e , he anomaly ca ego y should be used wi h cau ion, as i is based
on p e iously known anomalies and may no ep esen new o p e iously unseen
e en s. In such cases, he p oposed ED-based classi ica ion me hod becomes impo an
again, as i allows he iden i ica ion o new anomalies ha do no con o m o exis ing
clus e bounda ies.
•
Addi ionally, he success o clus e -based segmen a ion and labeling emains highly
dependen on he clus e ing algo i hm used, which in u n is de e mined by he da a
cha ac e is ics and he dis ibu ion o he da a in he ea u e space.
•
O he limi a ions can be no ed ega ding he WD signa u e used. NAC is mo e
sui able o loads wi h s ong non-linea beha io , so i s pe o mance may be limi ed
in sys ems wi h low non-linea i y and dis o ion. On examina ion o he esul s in
he li e a u e, i is easy o see ha , cu en ly, he ca ego y o dis o ing loads is much
b oade han ha o linea loads, which a e mos ly limi ed o hea ing elemen s, some
home appliances, and a ew o he s.
Au ho Con ibu ions: Concep ualiza ion, A.M., R.S.S. and S.K.R.; me hodology A.M., R.S.S. and
S.K.R.; alida ion, A.M. and R.S.S.; o mal analysis, A.M. and R.S.S.; in es iga ion, A.M. and R.S.S.;
esou ces, A.M., R.S.S. and S.K.R.; da a cu a ion, A.M. and R.S.S.; w i ing—o iginal d a , A.M.
and R.S.S.; w i ing— e iew and edi ing, A.M., R.S.S. and S.K.R.; isualiza ion, A.M. and R.S.S.;
supe ision S.K.R.; p ojec adminis a ion, A.M. and S.K.R.; unding acquisi ion, A.M. and S.K.R. All
au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding: The wo k he e p esen ed has ecei ed unding om EPM (Eu opean Pa ne ship on
Me ology) SRTi03 Me 4EVCS. The p ojec SRTi03 Me 4EVCS has ecei ed unding om he Eu opean
Pa ne ship on Me ology, 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. This wo k is also pa ially unded by he
Swedish T anspo Adminis a ion.
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 a e con ained wi hin he a icle.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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