Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
A ailable online 27 Sep embe 2023
2352-4677/© 2023 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-
nc-nd/4.0/).
Technique o he comp ehensi e cha ac e iza ion o sup aha monic
dis u bances (9–150 kHz) in he join ime- equency domain
Alexande Galla e a
a
,
*
, Igo Fe n´
andez
a
, Jon Gonz´
alez-Ramos
a
, Da id de la Vega
a
,
I zia Angulo
b
, Amaia A inda
a
a
Uni e si y o he Basque Coun y (UPV/EHU), Dp . o Communica ions Enginee ing, Bilbao ES-48013, Spain
b
Uni e si y o he Basque Coun y (UPV/EHU), Dp . o Applied Ma hema ics, Bilbao ES-48013, Spain
ARTICLE INFO
Keywo ds:
Elec omagne ic in e e ence
Measu emen echniques
Powe quali y
Sma g ids
Powe line communica ions
Vol age measu emen
Sup aha monic impulsi e dis u bances
ABSTRACT
The in e e -based de ices connec ed o he low- ol age (LV) g id, such as pho o ol aic panels (PVs) and elec ic
ehicle cha ging s a ions (EVCSs), a e known o gene a e sup aha monic dis o ions in CISPR Band A (9–150
kHz) ha may in e e e powe line communica ions (PLC). Cu en measu emen me hods we e designed o
p o ide esul s o he dis u bances only in he equency domain. Thus, impulsi e signals and as ampli ude
a ia ions o he dis u bances a e los in he calcula ion p ocess. This wo k add esses his issue by de eloping a
s a is ical s udy o he dis ibu ion o sup aha monic dis u bances in he join ime- equency domain, which
allows he clea di e en ia ion o impulsi e signals. The esul s show ha he ampli udes o he no malized
measu emen s can be modeled by he Loca ion-Scale p obabili y densi y unc ion (PDF), which can be used o
se a h eshold o he di e en ia ion o he impulsi e dis u bances. The s udy p oposes a measu emen me hod
and a se o me ics o he comple e cha ac e iza ion o he dis u bances p esen in he LV g id, by cha ac e izing
he noise and dis o ions as a whole and also impulsi e emissions sepa a ely. The main con ibu ion o his wo k
is ha he measu emen echnique cha ac e izes he dis u bances in he join ime- equency domain, and i is
cohe en wi h me hods below 9 kHz. The p oposed me hod is applied o some ypical g id eco dings con aining
di e en ypes o noise and emissions. The esul s demons a e ha he me hod allows he comple e cha ac-
e iza ion o he sup aha monic dis o ions p esen in he LV g id and a p ope di e en ia ion o he impulsi e
emissions in he join ime- equency domain.
1. In oduc ion
I is widely known ha he equipmen connec ed o he low- ol age
(LV) g id injec s dis u bances in CISPR Band A (9–150 kHz). Mo eo e ,
in e e -based de ices p oducing o consuming as amoun s o ene gy,
such as pho o ol aic panels (PVs) o elec ic ehicle cha ging s a ions
(EVCSs), gene a e high ampli ude dis o ions [1–3]. This equipmen has
a conside able p esence in he g id and is expec ed o be deployed on a
massi e scale in he coming yea s o educe humans’ ca bon oo p in ,
acco ding o he Clima e Ag eemen s p omo ed by he Uni ed Na ions
(UN) o Eu opean Union’s policies. In he las decade, se e al s udies
ha e been ca ied ou o classi y and pa ame ize he dis o ions in his
equency ange (commonly named as ‘sup aha monics ange’), based
on he cha ac e is ics o he wa e o ms [4–7]. Addi ionally, he impac
o hese dis u bances on he equipmen connec ed o he Low Vol age
(LV) g id has been ema ked in he li e a u e. The analyzed ad e se
e ec s include mal unc ions, he mal s ess o he p oduc ion o audible
noise in nea by equipmen connec ed o he g id [8–11]. Fu he mo e,
powe line communica ion (PLC) echnologies can be in e e ed by
sup aha monic dis u bances [12–14], as hey use he LV g id as he
p opaga ion channel o communica ions in CISPR Band A, i.e., o send
eleme y da a gene a ed by he elec ic sma me e s. Mo eo e , he
impulsi e dis u bances in he LV g id may cause he channel es ima ion
pe o med by PLC ecei e s o be inco ec , p e en ing om equalizing
and decoding he ames o e lapped wi h impulsi e emissions [15–18].
Al hough he e a e nume ous PLC echnologies a ailable in he ma ke ,
some o hem based on bu s ansmissions and o he s on con inuous
communica ions, all o hem can be in e e ed wi h impulsi e dis u -
bances. Impulsi e dis o ions in CISPR Band A a e common wa e o ms
in he LV g id and a e linked o a ious ac o s, such as he
swi ched-mode powe supplies (SMPSs), he swi ching equency o
high-powe semiconduc o componen s, he pulse wid h modula ion
* Co espondence o: Dp . o Communica ions Enginee ing, Uni e si y o he Basque Coun y (UPV/EHU), ES-48013 Bilbao, Spain.
E-mail add ess: [email p o ec ed] (A. Galla e a).
Con en s lis s a ailable a ScienceDi ec
Sus ainable Ene gy, G ids and Ne wo ks
jou nal homepage: www.else ie .com/loca e/segan
h ps://doi.o g/10.1016/j.segan.2023.101181
Recei ed 30 Ma ch 2023; Recei ed in e ised o m 18 Sep embe 2023; Accep ed 25 Sep embe 2023
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
2
(PWM), and he sho du a ion and high ampli ude ansien s [18–20].
These dis o ions a e injec ed by he in e e s o he PV panels and he
EVCS, which implemen SMPS and PWM, a he poin o connec ion
(POC) in he LV g id [21–23]. I is a hese loca ions whe e sma me e s
a e ins alled o measu e he ene gy consump ion and gene a ion o hese
de ices, so ha hey a e loca ed aside he sou ces o dis u bances.
The e o e, i is c ucial o de ec sup aha monic impulsi e dis u bances,
and hei cha ac e is ics need o be analyzed sepa a ely om he o he
wa e o ms p esen in he g id.
Impulsi e dis o ions in he LV powe g id ha e been s udied o
decades and he e a e nume ous con ibu ions in his ega d. The ma-
jo i y o he s udies a e based on he cha ac e iza ion o he empo al
beha io o dis u bances, by means o me ics in he ime domain, such
as he pe iod be ween impulses, he pulse wid h du a ion o he
ampli ude alue o impulses [24–26]. Ne e heless, in hese s udies he
dis u bances a e no di e en ia ed in equency; he e o e, he impul-
si e sup aha monic dis o ions a e analyzed oge he wi h he es o he
impulsi e dis u bances p esen in he g id ( ansien s, emissions
gene a ed by pa ial discha ges, e c.). The mos ecen con ibu ions
pa ame ize impulsi e dis u bances in he ime and equency domains,
bu sepa a ely [27–30], i.e., hey do no cha ac e ize impulsi e dis o -
ions in he join ime- equency domain (on he basis o spec og ams),
bu conside ing he ime analysis and he equency esul s
independen ly.
Cu en ly, se e al measu emen me hods a e a ailable o he
cha ac e iza ion o he sup aha monic dis u bances (9–150 kHz) p op-
aga ed h ough he LV g id. Al hough he e is s ill no s anda dized
measu emen me hod in his ange, he Annex C o IEC 61000–4–30 Ed.3
[31] ou lines h ee empo a y p oposals: he ecei e desc ibed in CISPR
16 s anda d se ies [32], an ex ension o he IEC 61000–4–7 Annex B
me hod [33] o equencies abo e 9 kHz, and an al e na i e me hod
speci ied in he same Annex C o IEC 61000–4–30 [31]. Besides, se e al
esea ch me hods ha e been desc ibed in he li e a u e: he Wa ele
App oach [34], he Subsampling App oach [35], he RM-A [36], he
Ligh -QP [37] and he S a is ical-QP me hods [38]. None heless, all
hese s anda dized and esea ch me hods deal wi h he cha ac e iza ion
o he sup aha monic dis o ions only in he equency domain and do
no make a di e en ia ed analysis be ween s able emissions o e ime o
impulsi e emissions. Addi ionally, cu en me hods a e based on
calcula ing oo -mean-squa e (RMS) and quasi-peak (QP) alues du ing
ime in e als equal o o longe han 200 ms, and look o ep esen a-
i e alues o di e en agg ega ion in e als (200 ms, 3 s, 10 min o 1
day) [31]. This implies ha impulsi e dis u bances, wi h du a ions o a
ew milliseconds, a e los in he calcula ions o a e aging and agg e-
ga ion p ocesses wi hin hese in e als.
Impulsi e dis u bances equi e speci ic pa ame e s and me hods o
analysis, di e en om hose seeking ep esen a i e alues o he
whole agg ega ion in e al. Thus, in o de o simul aneously measu e
a e age alues while iden i ying and pa ame e izing impulsi e noises,
he me ics and measu emen me hods o bo h aspec s mus be
compa ible and complemen a y.
The cu en measu emen amewo k o assessing dis o ions in he
en i e sup aha monic egion (2–150 kHz) p esen s a p incipal d awback
since he whole band has no con inui y on me ics and ampli ude limi s.
The compa ibili y le els (CL) egula ed in IEC 61000–2–2 [39], which
a e he maximum ampli ude le els o sup aha monic dis u bances
p opaga ed h ough he LV in he 2–150 kHz ange, a e de ined wi h wo
di e en and non-compa able me ics depending on he equency band.
In he 2–9 kHz ange, he CL a e de ined in he o m o RMS, which mus
be calcula ed wi h he IEC 61000–4–7 Annex B me hod. The QP alues
p o ided by he CISPR 16 me hod a e needed o assess hese limi s in he
9–150 kHz ange. These discon inui ies p esen inconsis encies in he
esul s o he sup aha monic ange, as he esul s below and abo e 9
kHz canno be compa ed.
This wo k p oposes a solu ion o he comple e cha ac e iza ion o
sup aha monic dis o ions by i s s udying he dis ibu ion o
dis o ions in he join ime- equency domain o CISPR Band A. Based
on he esul s ob ained in ha s udy, his pape p oposes a measu emen
me hod o he pa ame iza ion o all dis o ions p esen in he g id and
also o he de ec ion and sepa a e cha ac e iza ion o impulsi e dis-
u bances in he join ime- equency domain, using simple, compa ible
and complemen a y me ics o he measu emen amewo k de ined o
CISPR Band A. Mo eo e , he p oposed me hod ensu es he cohe ence in
esul in he en i e 2–150 kHz band, since i is based on an adap a ion o
he IEC 61000–2–4–7 Annex B me hod o he CISPR Band A.
This pape is o ganized as ollows. Fi s ly, a s a e o he a o mea-
su emen me hods o CISPR Band A is p esen ed. Secondly, he objec-
i es o he wo k a e desc ibed. Thi dly, he pe o mance o
sup aha monic measu emen me hods o syn he ic wa e o ms wi h
di e en epe i ion a es and ampli udes is s udied. A e wa ds, he
me hodology o he wo k is p oposed. Then, he esul s o he dis ibu-
ions ob ained o sup aha monic dis o ions a e analyzed, and he
condi ions o which a dis u bance can be conside ed impulsi e a e
p esen ed. Subsequen ly, a echnique o he comple e cha ac e iza ion
o sup aha monic dis u bances is p oposed, in which a sepa a e analysis
o he impulsi e dis u bances is p oposed based on he esul s ob ained
in he wo k. A e ha , he applica ion o he p oposed echnique o eal
measu emen s eco ded in he LV g id is shown. Finally, he conclusions
o his pape a e desc ibed.
2. Measu emen me hods o conduc ed emissions in he LV g id
This sec ion desc ibes he cu en s a e o he a o measu emen
me hods o cha ac e ize he sup aha monic dis u bances in he LV g id.
This sec ion desc ibes, i s ly, he s anda d measu emen me hods o
CISPR Band A and, secondly, he esea ch me hods a ailable in he
li e a u e.
2.1. S anda dized measu emen me hods
The measu emen me hods o cha ac e ize he conduc ed dis u -
bances ha a e p opaga ed h ough he LV g id a e no comple ely
s anda dized. As o equencies up o 9 kHz he s anda d IEC
61000–4–7 [33] de ines me ics and assessmen me hodologies, o
equencies highe han 9 kHz he e is s ill no s anda d me hod. Due o
he signi ican ele ance ha he analysis o he dis u bances in e-
quencies up o 150 kHz is gaining, he s anda diza ion bodies a e
wo king in he de elopmen o new me hods (IEC SC77A WG9) o in he
compila ion o ecen esea ch wo k (CENELEC TC219 WG11). The e-
o e, he e is a need o de ining adequa e me ics and de eloping no el
measu emen me hods in his equency ange.
On he wa ch o he de ini ion o a s anda d me hod, Annex C o IEC
61000–4–30 Ed.3 [31] sugges s h ee empo a y assessmen p ocedu es
o measu emen s in he 9–150 kHz band. Fi s ly, he me hod desc ibed
in CISPR 16 [32] s anda d se ies is p oposed, whose implemen a ion is
based on a supe -he e odyne ecei e using analog ci cui y. This
me hod p o ides QP alues in he equency domain wi h a esolu ion
bandwid h o 200 Hz a −6 dB and a high ime esolu ion due o a high
deg ee o o e lap in he ime windowing o he inpu alues. None he-
less, his me hod equi es a high compu a ional bu den and a la ge
amoun o memo y esou ces. Thus, IEC 61000–4–30 Ed.3 s anda d
s a es ha his me hod is no adap ed o on- ield su eys; on he con-
a y, i is a measu emen me hod de ined o elec omagne ic
compa ibili y measu emen s, wi h a labo a o y se up de ined in he se
o CISPR 16 s anda ds ha makes i s applica ion in ield measu emen s
impossible, mainly due o he manda o y use o a line impedance s a-
biliza ion ne wo k (LISN). Secondly, Annex C o IEC 61000–4–30 [31]
p oposes an al e na i e me hod wi h ligh e compu a ional complexi y,
whose desc ip ion is p o ided in he same annex. The me hod is de ined
o p o ide spec al esul s wi h a esolu ion bandwid h o 2 kHz by
p ocessing only 8 % o he inpu signal, i.e., 92 % o he spec al con en
is omi ed in he analysis. These aspec s gene a e a signi ican loss o
A. Galla e a e al.
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
3
e en s in he ime domain and a ough equency esolu ion, and
he e o e, his me hod is no commonly used o assess he ampli ude o
he dis u bances in he LV g id. Thi dly, he use o he p ocedu e
desc ibed in IEC 61000–4–7 Annex B [33] is p oposed o be ex ended o
he 9–150 kHz ange, al hough how o adap his assessmen me hod o a
much wide equency ange is no desc ibed in he s anda d. The IEC
61000–4–7 is a gapless me hod based on non-o e lapped ec angula
windows o 200 ms o compu e he spec al con en o he inpu da a. As
in CISPR 16–1–1, he esul s ha e a esolu ion bandwid h o 200 Hz.
Al hough he p oposal o measu emen me hods made in IEC
61000–4–30 is no ‘no ma i e’, none o hem add esses he analysis o e
ime. This implies ha ele an in o ma ion, such as impulsi e noise and
ime- a ying dis u bances, is los in he assessmen p ocess, and he e-
o e, is no shown in he inal esul s. New me hods in his band
p o iding no only good equency esolu ion, bu also he ampli ude
a ia ion o dis u bances in he join ime- equency domain a e needed
o a de ailed analysis o he sup aha monic dis u bances. These cha -
ac e is ics a e add essed in he p oposed me hod.
2.2. Resea ch measu emen me hods
Se e al esea ch me hods ha e been p oposed in he scien i ic
li e a u e, such as he Wa ele App oach, he Subsampling App oach,
he Ligh -QP, he RM-A and S a is ical-QP me hods.
The Wa ele App oach [34] analyses he spec al con en o he
sampled da a using he Wa ele Packe Decomposi ion (WPD), ins ead
o disc e e Fou ie ans o ms (DFTs). This p ocedu e il e s and
downsamples he signal ecu si ely o ob ain 740 equency bins o 200
Hz in he 2–150 kHz equency ange. The ampli ude alue o he signal
o each equency bin is ob ained by compu ing he oo -mean-squa e
o il e ed samples in measu emen in e als co esponding o en cy-
cles o he mains (200 ms).
The Subsampling App oach [35] is based on he Nyquis -Shannon
sampling heo em, which de ines ha he sampling equency mus be
a leas wice he maximum equency o he wa e o m o be analyzed.
This me hod was designed o cha ac e ize sup aha monic dis u bances
using exis ing pla o ms wi h limi ed sampling a es. This me hod im-
plemen s an analog il e bank o decompose he signal in o 10 bands o
15 kHz o analyze he en i e 9–150 kHz band. Hence, he maximum
sampling equency equi ed o cha ac e ize he conduc ed dis o ions
wi h his me hod is 30 kHz. The ou pu il e ed signals a e p ocessed
wi h DFTs using ec angula windows o 0.5 ms leng h.
The RM-A me hod [36] is an adap a ion o he IEC 61000–4–7 Annex
B o he CISPR Band A (9–150 kHz). This gapless me hod applies
non-o e lapped ec angula windows o 20 ms leng h o compu e he
DFTs. The esul an spec al alues ha e a esolu ion bandwid h and a
equency-s ep-size o 50 Hz, which a e g ouped by pe o ming an
ad-hoc ‘symme ical g ouping’ p oposed in his me hod, o ob ain a 200
Hz esolu ion bandwid h and a 100 Hz equency-s ep-size. Then, in his
me hod, he g ouped alues a e agg ega ed in ime o ob ain bo h he
maximum and oo -mean-squa e o each 200 ms and 3 s, which a e he
measu emen in e als de ined in he IEC 61000–4–30. As he dis u -
bances in he 9–150 kHz ange a e no gene a ed by dis o ions o he
undamen al, bu by he connec ed de ices, he de ini ion o hese in-
e als is no ela ed o he pe iod o he undamen al, bu o keep he
cohe ence o he me hods below 9 kHz.
The Ligh -QP me hod [37] is an al e na i e me hod o CISPR 16–1–1
ha p o ides QP alues wi h a conside ably lowe compu a ional
bu den and memo y esou ces. I is a wo-s age me hod, whe e he i s
s age is he RM-A me hod, which p o ides oo -mean-squa e (RMS)
ou pu s e e y 20 ms. These RMS alues a e p ocessed wi h a speci ic
digi al implemen a ion o a quasi-peak de ec o , o ob ain esul s simila
o he CISPR 16–1–1.
Las ly, he S a is ical-QP me hod [38] p o ides QP spec a, compa-
able o hose ob ained wi h CISPR 16, based on a s a is ical ela ionship
be ween he RMS and QP alues o CISPR Band A. This me hod uses he
ins an aneous RMS ou pu s o he RM-A me hod, a s a is ical analysis
based on pe cen iles o quan i y he luc ua ions o he dis u bances and
a simple i s -deg ee polynomial equa ion o es ima e he QP alues.
Thus, QP alues can be calcula ed o line i he ins an aneous RMS
ou pu s o he RM-A me hod a e s o ed du ing a measu emen .
As o he s anda dized measu emen me hods, none o he esea ch
me hods cha ac e ize he dis u bances in he join ime- equency
domain. None o hem ei he iden i y and analyze he impulsi e emis-
sions in he join ime- equency domain. As a esul , he as ampli ude
a ia ions a e hidden in he esul s o hese me hods, due o he
weigh ing p ocess o he de ec o s and he empo al agg ega ion
s a egies.
3. Objec i es
This wo k aims a p oposing a se o me ics and assessmen me h-
odology o he comple e cha ac e iza ion o he sup aha monic dis-
u bances p opaga ed h ough he LV g id in he join ime- equency
domains wi hin he CISPR Band A. This me hodology should cha ac-
e ize he g id dis o ions in he join ime- equency domain, as well as
o pa ame ize sepa a ely he impulsi e dis o ions in his band ha
migh a ec PLC.
Th ee main asks ha e been de ined in o de o achie e his objec-
i e. Fi s ly, he s udy pa ame izes s a is ically he ampli ude a ia ion
o he conduc ed dis u bances o e ime, o each 200 Hz- equency
band in he en i e equency ange, and o he measu emen in e als
de ined in powe quali y (PQ) su eys [31]. This s a is ical cha ac e -
iza ion is he basis o de ine a c i e ion o dis inguishing impulsi e
dis u bances in he ime domain. Secondly, a calcula ion p ocedu e o
iden i y impulsi e dis u bances is de ined, as his ype o dis u bances
may be hidden in he spec al es ima ion o e se e al seconds. Las ly,
he necessa y me ics o pa ame ize all dis o ions join ly and impulsi e
dis o ions sepa a ely a e p oposed.
4. Analysis o cu en me hods
All he me hods cu en ly a ailable we e designed o p o ide esul s
only in he equency domain. None o hem p o ide in o ma ion abou
he ampli ude a ia ions o he sup aha monic dis o ions o e ime, bu
only p o ide a weigh ed spec al esul in a measu emen in e al. As a
esul , di e en signals wi h di e en cha ac e is ics o e ime ( epe i-
ion equency, ampli ude, e c.) may gi e simila ou pu s in he e-
quency domain. The e o e, i is necessa y o de ine me ics ha p o ide
ep esen a i e esul s o he a iabili y o he emissions wi hin he
measu emen in e al. Mo eo e , hese me ics should be compa able,
o easy o ela e, o he mos commonly used measu emen me hods, so
ha he in o ma ion p o ided by hese me ics is complemen a y o he
esul s o he cu en me hods.
In o de o illus a e his easoning, he mos ele an measu emen
me hods ha e been applied o h ee LV g id wa e o ms. All he wa e-
o ms con ain a dis u bance a 132.2 kHz, in he o m o a se o non-
con inuous bu s s, bu wi h a di e en numbe and du a ion o he
bu s s: he wa e o m ‘G id-1
′
con ains 14 bu s s o 76 dB
μ
V and 54 ms
(see Fig. 1), ‘G id-2
′
con ains 6 bu s s o he same du a ion (208 ms) and
ampli ude (76 dB
μ
V) a 132.2 kHz (see Fig. 2); and ‘G id-3
′
con ains 6
bu s s o 80 dB
μ
V and di e en du a ion (be ween 108 ms and 346 ms)
a 132.2 kHz (see Fig. 3).
A selec ion o s anda dized (CISPR 16–1–1, IEC 61000–4–7) and
ecen ly published (Ligh -QP, RM-A) measu emen me hods ha e been
applied o he h ee g id wa e o ms. Al hough he a ia ion pa e n o e
he ime o he dis u bance a 132.2 kHz is no iceably di e en o he
h ee g id wa e o ms, he ou pu s a e simila in ampli ude o he same
de ec o (RMS o QP), ega dless o he me hod conside ed in he
calcula ion (see Fig. 1 o Fig. 3):
•RMS: 73 dBuV, assessed by IEC 61000–4-7 and RM-A me hods.
A. Galla e a e al.
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
4
•QP: 76 dBuV, assessed by CISPR16-1–1 and Ligh -QP.
This is a ep esen a i e example ha demons a es ha dis u bances
wi h di e en a ia ion pa e ns o ampli ude, du a ion and epe i ion
a es a e e alua ed simila ly by cu en s anda d measu emen me hods.
No el me hods ecen ly published, as RM-A [36] o Ligh -QP [37], do
no e alua e his aspec ei he . Mo eo e , he in o ma ion abou he
empo al e olu ion o he dis u bances, which can be ele an o
e alua e he impac on elec onic de ices [8] o PLC ansmissions [15],
o o iden i y he sou ce o he emission [40], is los in he assessmen
p ocedu e o he measu emen me hod du ing measu emen in e als
de ined in he s anda d [31]. This ac highligh s he need o de elop
no el echniques and me hods o cha ac e ize he dis u bances in he
join ime- equency domain and o de ine adequa e me ics o pa am-
e e ize he a iabili y o he dis o ions and, i i is he case, o iden i y
and cha ac e ize he impulsi e na u e.
Fig. 1. Spec og am and spec um o wa e o m ’G id-1
′
.
Fig. 2. Spec og am and spec um o wa e o m ’G id-2
′
.
Fig. 3. Spec og am and spec um o wa e o m ’G id-3
′
.
A. Galla e a e al.
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
5
5. Me hodology
This sec ion desc ibes he me hodology ollowed o pa ame ize he
sup aha monic dis u bances in he join ime- equency domain. Since
he measu emen me hod plays a pi o al ole in he cha ac e iza ion o
conduc ed emissions, i s ly, a me hodology o cha ac e ize he sup a-
ha monic dis u bances in CISPR Band A is p esen ed in his s udy.
Secondly, he p ocedu e o he s a is ical pa ame iza ion o he dis-
u bances in he 9–150 kHz band is desc ibed. Las ly, he p oposed
assessmen me hodology is e alua ed wi h a da ase o eco dings.
5.1. Selec ion o he measu emen me hod o he s a is ical
cha ac e iza ion
This s udy p oposes a p ocessing echnique ha is consis en wi h
exis ing me hods in he li e a u e, which allows he di ec ela ion be-
ween me hods and/o he compa ison o esul s. As he e is no
no ma i e me hod o he 9–150 kHz ange, he exis ing esea ch and
s anda dized me hods ha e been e iewed o selec he mos app o-
p ia e o be used as a basis o de eloping a mo e comple e ( ime- e-
quency domain) p ocessing echnique. Among he exis ing me hods,
only hose ha p opose esul s in he o m o RMS a e selec ed, dis-
ca ding he ou pu s o he QP, a e age o peak de ec o s. The essen ial
eason is ha he RMS ou pu is he mos widely used me ic in PQ,
because i can be easily ela ed o in en ional emissions in he same
equency band (PLC) [17], o PQ deg ada ion [3] and o physical e ec s
on he de ices ( he mal s ess and mal unc ion, mainly [11]).
In [41], an accu acy analysis o mos o he me hods men ioned in
Sec ion 2 is pe o med. This concludes ha he IEC 61000–4–7 Annex B
me hod allows he mos accu a e cha ac e iza ion o he dis o ions in
he CISPR Band A wi h RMS alues.
Recen ly, he me hod RM-A has been p esen ed wi h he pu pose o
adap ing he IEC 61000–4–7 Annex B me hod o he CISPR Band A,
p o iding good accu acy and good esolu ion in ime and equency
[36]. Compa ed o IEC 61000–4–7, in he equency domain he numbe
o esul s is wice ( om 200 Hz o 100 Hz be ween adjacen esul s) and
en imes mo e in he ime domain ( esul s e e y 20 ms, ins ead o
200 ms), o he same esolu ion bandwid h (200 Hz). This is conside ed
an op imal con igu a ion o he de ec ion o sup aha monic dis u -
bances. Fu he mo e, he RM-A me hod implemen s he ‘symme ical
g ouping’, a no el echnique o g oup he equency componen s, which
allows he be e alloca ion o high- equency dis o ions in he e-
quency domain. Las , he compu a ional bu den o his me hod is lowe
wi h espec o he es o he me hods, due o he use o non-o e lapped
ec angula windows o 20 ms leng h. Fo all hese easons, he RM-A
me hod has been selec ed as he basis o he de elopmen o a no el
me hod ha p o ides esul s in he join ime- equency domain, since i
is he me hod ha p o ides be e accu acy and cohe ence wi h he RMS
alues om he IEC 61000–4–7 me hod o equencies below 9 kHz.
Acco ding o [36], he RM-A me hod is di ided in h ee main p o-
cessing blocks: he equency analysis, he equency g ouping and he
ime agg ega ion (see Fig. 4). The ol age measu emen s pe o med in
he LV g id a e p ocessed, i s ly, wi h he sho - ime Fou ie ans o m
(STFT), using non-o e lapped ec angula windows o 20 ms leng h.
Then, he ou pu alues (Y
′
C,b
), which ha e a esolu ion bandwid h and
equency-s ep-size o 50 Hz, a e g ouped by applying he ‘symme ical
g ouping’ (see Eq. (1)) o ob ain spec al esul s wi h a esolu ion
bandwid h o 200 Hz (Y
′
B,b
).
Y
′
B,b=
1
2⋅Y2
C,b−100Hz +∑
b+50Hz
=b−50Hz
Y2
C, +1
2⋅Y2
C,b+100Hz
√
√
√
√(1)
Addi ionally, his p ocess is epea ed e e y 100 Hz o achie e a
equency-s ep-size o 100 Hz.
Finally, he ime se ies o he g ouped spec al alues a e agg ega ed
by means o he assessmen o he RMS and maximum alues in 200 ms
and 3 s measu emen in e als, acco ding o he s a emen in IEC
61000–4–30 s anda d o PQ su eys [31].
5.2. P oposed me hodology o he analysis o sup aha monic
dis u bances in he join ime- equency domain
A measu emen in e al o 3 s is p oposed in his me hodology,
which co esponds o he second agg ega ion in e al de ined by IEC
61000–4–30 s anda d. This measu emen in e al has been chosen since
he i s in e al de ined in he s anda d is 200 ms, which is oo sho o
di e en ia e he impulsi e dis o ions, and he hi d agg ega ion pe iod
is 10 min, which would imply a high compu a ional cos due o he high
numbe o DFTs ha would ha e o be calcula ed.
The p ocedu e ollowed o s a is ically pa ame e ize he dis ibu ion
o sup aha monic dis u bances in CISPR Band A is as ollows:
•Da a no maliza ion: So as o compa e all he a ailable equency
bands ob ained wi h he RM-A me hod, he alues should be
no malized. This no maliza ion is pe o med by compu ing he me-
dian and sub ac ing his alue (in dB
μ
V) o all he da a pe each
equency band. Thus, he esul ing no malized alues a e exp essed
in dB.
•Ob aining he op imal pa ame e s o each dis ibu ion: In o de o
ob ain he dis ibu ion o he no malized da a, he pa ame e s o he
p obabili y densi y unc ions (PDF) ha p o ide he maximum
likelihood es ima ion (MLE), which is an es ima ion me hod o
compu e he pa ame e s o a PDF ha be e i he inpu sample se ,
a e calcula ed.
•Selec ion o he PDF ha bes i s he inpu da a: The goodness o i
o di e en PDFs a e compa ed by compu ing he Chi-Squa ed alue,
which is used o e alua e he hypo heses abou he dis ibu ion o he
obse a ion da a. The selec ed PDF in his s udy would be he one
ha p o ides he highes MLE o i s dis ibu ion and he lowes
alue in he Chi-Squa ed alue.
Fig. 4. Schema ic o e iew o he RM-A measu emen me hod.
A. Galla e a e al.
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
6
6. S a is ical analysis o he dis u bances in he join ime-
equency domain
This sec ion desc ibes he analysis pe o med o pa ame ize s a is-
ically conduc ed dis u bances in he join ime- equency domain. Fo
ha pu pose, he PDF ha be e i s he ampli ude a ia ion o he RMS
alues o hese dis u bances o e ime and o each 200 Hz equency
band in he en i e equency ange is compu ed.
6.1. Da ase o eco dings measu ed in he LV g id
The s a is ical analysis is compu ed wi h ol age eco dings
measu ed in se e al loca ions o he LV g id. The da ase is composed o
71 signals measu ed in he POC o sma me e s (49 eco dings), EVCS
(16 eco dings) and pho o ol aic in e e s (6 eco dings).
All eco dings used in his wo k we e aken in 3 measu emen
campaigns in Spain. All POC we e loca ed be ween se e al ens and a
ew hund ed me e s om he ans o me s. Thus, mos o he measu ed
dis u bances we e gene a ed by he equipmen o he house connec ed
o he POC o he LV g id. The measu emen s aken a he POCs o he
sma me e s we e measu ed in he cabins whe e hese de ices a e
loca ed inside apa men buildings. These measu emen s we e aken in
h ee geog aphic a eas linked o loca ions dependen on LV ans-
o me s; di e en g id opologies and homes densi y can be ound in
hese h ee geog aphic a eas. These measu emen s we e ca ied ou in
u ban and u al a eas, o which 33 eco dings co espond o he i s
scena io, and he emaining 16 o he second one. The EVCSs used in his
wo k we e h ee-phase AC de ices wi h a maximum powe o 22 kW.
These measu emen s we e aken in 4 loca ions using 4 di e en EVs,
whose ba e y le el we e be ween 75 % and 90 %. In addi ion, all PV
eco dings we e measu ed in a unique ins alla ion wi h 3 connec ion
con igu a ions o 4 panels, using an in e e o 18 kW and di e en
loads.
All he measu emen s we e eco ded wi h he same measu emen
sys em, which is desc ibed in [42]. A ol age p obe is used o acqui e he
signal in he ield, which applies a gal anic isola ion and a band-pass
il e o p o ec he measu emen equipmen agains o e ol age an-
sien s and o il e he emissions ou side he 10–500 kHz band [43]. The
ou pu o he p obe is sampled wi h a sampling a e o 8.92 MHz and a
16 bi /sample esolu ion by a digi al oscilloscope and eco ded in a
lap op.
6.2. S a is ical analysis
The basis o he s a is ical analysis is he RMS alues o he spec-
og ams, which ep esen a de ailed assessmen o he noise and dis-
u bances in he join ime- equency domain o he measu emen
in e al and o he whole equency ange, as i can be obse ed in
Fig. 1, Fig. 2 and Fig. 3. As i is jus i ied in Sec ion 5.1, he me hod
selec ed o assess he spec og am is he RM-A me hod (Y
′
B,b
in Eq. (1)
and Fig. 4), which p o ides RMS ou pu s in he 9–150 kHz band, wi h a
spec al alue e e y 100 Hz, in 3 s measu emen in e als, wi h a ime
g anula i y o 20 ms. This co esponds o a ma ix o 1409 equency
bands and 150 empo al alues; he e o e, 211,350 alues a e gene a ed
o each signal, which implies a o al o 15,005,850 alues o he en i e
da ase o 71 eco dings. Fig. 5 shows he dis ibu ion o he 15,005,850
no malized alues o he en i e da ase .
The no malized alues ha e been modeled wi h 23 dis ibu ion
unc ions: Be a, Binomial, Bi nbaum-Saunde s, Bu , Exponen ial,
Ex eme Value, Gamma, Gene alized Ex eme Value, Gene alized Pa -
e o, Hal -no mal, In e se Gaussian, Logis ic, Loglogis ic, Logno mal,
Nakagami, Nega i e Binomial, No mal, Poisson, Rayleigh, Rician, S a-
ble, Loca ion-Scale and Weibull. Ne e heless, only 5 ou o he 23
dis ibu ions ha e p o ided alid esul s, since some o he dis ibu ion
unc ions do no con e ge and o he s a e no able o model nega i e
alues.
In he dis ibu ions p o iding alid esul s, he con igu a ions ha
bes i he no malized da a ha e been ob ained, which has been
nume ically e i ied, as hese con igu a ions p o ide he highes alue
o MLE (see Sec ion 5.2). The esul an dis ibu ion unc ions a e shown
in Fig. 6.
The goodness o i o di e en PDFs a e compa ed by means o he
Chi-Squa ed alue, as i epo s abou he sui abili y o he hypo heses
o he obse a ion da a. The lowes Chi-Squa ed alue ep esen s he
mos app op ia e dis ibu ion unc ion o he da ase . Table 1 con ains
he alues o he pa ame e s o each PDF ha gi e he highes MLE and
he Chi-Squa ed esul s o ha con igu a ion.
The esul s in Fig. 6 and Table 1 show ha he Loca ion-Scale is he
PDF ha bes ep esen s he dis ibu ion o he no malized inpu da a,
since i p o ides he lowes Chi-Squa ed alue. The Loca ion-Scale
dis ibu ion is de ined wi h Eq. (2) [44], whose cumula i e dis ibu-
ion unc ion (CDF) is ep esen ed in Fig. 7.
Fig. 5. Dis ibu ion o he no malized spec al alues.
Fig. 6. Dis ibu ion o he no malized da ase and he PDFs wi h he con igu-
a ion wi h highes MLE.
A. Galla e a e al.
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
7
(x;
μ
,
σ
,
ν
) = Γ(
υ
+1
2)
σ
υπ
√Γ(
υ
+1
2)(1+1
υ
(x−
μ
σ
)2)− (
υ
+1
2)(2)
Whe e x is he inpu ,
μ
is he loca ion a iable,
σ
is he scale pa ame e
and
ν
is he shape a iable.
As a esul , he CDF shown in Fig. 7 is he cumula i e dis ibu ion
ha bes ep esen s he no malized dis u bances in he LV powe g id.
The impulsi e dis u bances a e linked o he highes alues o his CDF
(close o he 100 %), as hey a e e y in equen occu ences o ampli-
ude conside ably g ea e han he median alue, co esponding o 50 %
o he CDF. Fo ha eason, he impulsi e dis u bances a e ep esen ed
by he uppe ail o he dis ibu ion, o a small pe cen age o ampli udes
se e al dBs g ea e han he median.
This CDF can be used as a basis o iden i y he impulsi e dis u bances
in he g id measu emen s. Fo his pu pose, h ee h eshold alues ha e
been de ined o di e en ia e he occasional high-ampli ude impulsi e
dis u bance om he as majo i y o he spec al componen s o s a-
iona y wa e o ms: 90 h, 95 h and 99 h pe cen iles o he CDF o he
no malized alues. Table 2 shows he ampli ude di e ence o he pe -
cen iles 90 h, 95 h and 99 h wi h espec o he median alue. The e-
sul s ob ained in Table 2 show a conside able di e ence o close
pe cen iles, since hese alues a e a he uppe ail o he dis ibu ion;
he e o e, he selec ion o he h eshold o iden i ying impulsi e dis-
o ions depends on how s ingen is he c i e ion applied o de ec he
sup aha monic dis u bances mo e p ecisely. The esul s o applying
each o hese h eshold alues is analyzed in he ollowing pa ag aphs.
7. P oposed me ics and p ocedu e o iden i y and pa ame ize
impulsi e g id dis u bances
The esul s ob ained in he p e ious sec ions show ha :
•The backg ound noise and conduc ed dis u bances p esen in he
powe g id can be s a is ically modeled as a Loca ion-Scale PDF.
•The CDF o his PDF can be used as a basis o di e en ia e impulsi e
dis u bances in he 9–150 kHz band, as hey co espond o he uppe
ale o he CDF (a small pe cen age o spo adic occu ences wi h an
ampli ude se e al dBs highe han he median alue o he PDF).
•A h eshold in he uppe ail o he CDF is p oposed as a s a is ical
p ocedu e o di e en ia e he impulse esponses in conduc ed dis-
u bances in he g id. In his wo k, h ee pe cen iles o he CDF ha e
been p oposed as a i s app oach (90 h, 95 h and 99 h).
•Once he impulsi e dis u bances a e iden i ied, a se o speci ic
me ics can be used o cha ac e ize hei ele ance, du a ion and
epe i ion a e.
•The RM-A me hod has been iden i ied as he mos app op ia e basis
o de eloping a me hod in he join ime- equency domain, wi h
me ics de ined o cha ac e ize he sup aha monic dis u bances and
iden i y and e alua e he impulsi e dis u bances sepa a ely. Mo e-
o e , he p oposed me hod main ains he cohe ence wi h he RMS
alues ob ained o equencies below 9 kHz
Based on hese esul s, a p ocedu e o he comple e cha ac e iza ion
o emission and o de ec ion and pa ame iza ion he impulsi e dis-
o ions in he CISPR Band A is p oposed and desc ibed in his sec ion.
7.1. P oposed me hod o iden i y and pa ame ize impulsi e emissions in
he powe g id
The p ocedu e o iden i ying and cha ac e izing he sup aha monic
dis u bances consis s o 3 main blocks (see Fig. 8). Fi s ly, he RM-A
me hod, desc ibed in Sec ion 5.1 is applied o pe o m he spec al
analysis o he aw da a. Secondly, he de ec ion s age dis inguishes he
impulsi e dis o ions om he non- luc ua ing emissions o e he 3 s
measu emen in e al. Finally, he cha ac e iza ion s age cha ac e izes
he ampli ude and empo al beha io o he impulsi e emissions in each
equency band.
Rega ding he i s s age o he p ocedu e, he spec og am o he
measu ed ol age (Y
′
B,b
) is ob ained by he RM-A me hod, wi h a eso-
lu ion bandwid h o 200 Hz, a 100 Hz equency-s ep-size and a ime
s ep o 20 ms (see Fig. 9).
In he de ec ion s age, he dis u bances luc ua ing o e ime a e
calcula ed. Fo his pu pose, he median alues o he spec a a e
calcula ed o each equency band and o 3 s measu emen in e als
(U_median
3 s
) and sub ac ed o he eco ding. The me ic U_median
3 s
ep esen s he median alue o he dis u bances ha a e p esen a each
equency band, wi hin he measu emen in e al o 3 s. The esul s o
he sub ac ion a e he as a ia ions o he conduc ed dis o ions and
emissions a ound he median alue.
The impulsi e dis u bances (U_impulsi e
3 s
) a e calcula ed by
applying he h eshold alues de ined in Table 2, ela ed o a speci ic
pe cen ile o he CDF o he Loca ion-Scale dis ibu ion (3.27 dB,
4.90 dB and 10.55 dB, which co espond o 90 h, 95 h and 99 h). Fig. 10
shows he esul s o he U_impulsi e
3 s
o he h ee h esholds; he
spec al componen s below he h eshold a e displayed in da k blue (see
Fig. 10):
Table 1
Pa ame e s o he highes likelihood PDF and he co esponding Chi-Squa ed
alue.
PDF Pa ame e s Chi-squa ed
alue
Ex eme Value
μ
=3.3570
σ
=10.0686 – 2.1255 ×10
82
Gene alized
Ex eme
Value
k= − 0.0204
σ
=3.3218
μ
= − 1.2343 2.4924 ×10
31
Logis ic
μ
=0.0032
σ
=1.7610 – 1.2081 ×10
7
No mal
μ
=0.3806
σ
=4.5457 – 2.7062 ×10
25
Loca ion-
Scale
μ
= − 0.0371
σ
=1.8777
ν
=2.3611 8.0053
Fig. 7. CDF o he Loca ion-Scale dis ibu ion o he no malized inpu da a.
Table 2
No malized alues o he Loca ion-Scale dis ibu ion o 3 cumula i e
p obabili ies.
Cumula i e p obabili y (%) No malized alues wi h espec he median (dB)
90 3.27
95 4.90
99 10.55
A. Galla e a e al.
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
8
•The esul s o he h eshold o 3.27 dB (90 h o he CDF) show ha i
does no co ec ly selec he impulsi e dis o ions, since nume ous
equency componen s o he backg ound noise o he LV g id emain
as impulsi e dis u bances. An example o his si ua ion is highligh ed
wi h a whi e o al in he op g aph o Fig. 10.
•The h eshold o 4.90 dB (95 h o he CDF) shows a mo e disc imi-
na ing selec ion o he impulsi e dis o ions, bu a ew equency
componen s co esponding o backg ound noise s ill emain.
Rep esen a i e examples a e iden i ied wi h whi e o als and a whi e
a ow in he cen al plo o Fig. 10.
•The esul s o he h eshold o 10.55 dB (99 h o he CDF) a e
composed only o impulsi e wa e o ms and all he backg ound noise
componen s a e p ope ly il e ed ou (see he bo om g aph in
Fig. 10). This plo does no show any spu ious equency componen s
ha may co espond o he in insic luc ua ions o he backg ound
elec omagne ic noise, which a e no impulsi e dis u bances a all.
Thus, his g aph only con ains emissions ha ha e clea ly an
impulsi e beha io .
The e o e, he h eshold o 10.55 dB (99 h o he CDF) allows he
disce ning di e en ia ion o impulsi e dis u bances, which has been
es ed wi h he 71 eco dings o he da a se . Thus, i is p oposed o use
only he h eshold o 10.55 dB in o de o co ec ly de ec impulsi e
emissions. The p oposed con igu a ion has been selec ed o a oid he
occu ence o alse posi i es, as his p ocedu e ensu es ha he ou pu s
o he ‘de ec ion s age’ co espond o impulsi e dis u bances. This
h eshold a oids including in he ‘cha ac e iza ion s age’ any emainde
o backg ound noise, as demons a ed in Fig. 10. A po en ial d awback
o his c i e ion is ha i may gene a e alse nega i es in some
Fig. 8. Schema ic o e iew o he p ocedu e o de ec and cha ac e ize he
impulsi e dis u bances.
Fig. 9. Spec og am o a eco ding measu ed in he LV g id ob ained wi h RM-
A me hod (Y
′
B,b
).
Fig. 10. Wa e o ms classi ied as impulsi e dis u bances (U_impulsi e
3 s
) o he
h esholds de ined in Table 2.
A. Galla e a e al.
Sus ainable Ene gy, G ids and Ne wo ks 36 (2023) 101181
9
ci cums ances since he selec ed ampli ude h eshold is e y high.
Ne e heless, his is no conside ed a disad an age o he me hod, as he
pu pose is he de ec ion o he highes ampli ude dis u bances. Using he
median alue o each equency bin and he h eshold co esponding o
he 99 h pe cen ile o CDF is a s able basis o he de ec ion, ensu ing
ha only he dis u bances ha ul ill his condi ion ha e impulsi e
beha io .
Finally, in he cha ac e iza ion s age, a se o me ics a e calcula ed
in o de o cha ac e ize he impulsi e wa e o ms de ec ed in he p e-
ious s age. These me ics a e de ined in he nex sec ion.
7.2. Me ics o he cha ac e iza ion o he impulsi e dis u bances
A se o me ics ha e been de ined, in o de o cha ac e ize he
impulsi e noise, in e ms o ampli ude, du a ions and epe i ion du ing
he obse a ion in e al. The app oach o his cha ac e iza ion is based
on he selec ion o simple, bu ep esen a i e pa ame e s, which gi e a
clea and di ec iew o he impulsi e emissions.
Rega ding he ampli ude cha ac e iza ion, h ee me ics ha e been
de ined o pa ame ize he impulsi e dis o ions (see Fig. 11):
•Max U_impulsi e
3 s
: maximum ampli ude o he impulsi e dis u -
bances in a 3 s measu emen in e al.
•RMS U_impulsi e
3 s
: RMS ampli ude o he impulsi e dis o ions
o e he 3 s obse a ion pe iod.
•Min U_impulsi e
3 s
: minimum ampli ude o he de ec ed impulsi e
wa e o ms on he 3 s in e al.
Fu he mo e, h ee addi ional me ics ha e been de ined o cha ac-
e ize he dis u bances p opaga ed h ough he LV g id (see Fig. 11):
•U_median
3 s
: median alue o each equency band in he 3 s in e -
al. This me ic p o ides an indica ion o he mean beha io o dis-
o ions, since i ep esen s he 50 h pe cen ile o he ampli udes.
•RM-A: U_RMS
3 s
(RMS
200 ms
): RMS alues in he 3 s in e al o he
RMS alues agg ega ed e e y 200 ms, ob ained wi h he RM-A
me hod.
•Ligh -QP: QP: QP alues calcula ed wi h he Ligh -QP measu emen
me hod.
Fo he cha ac e iza ion o he emissions o each equency band
o e he measu emen in e al, h ee me ics a e calcula ed (see
Fig. 12):
•Num. e en s: numbe o occu ences o impulsi e dis u bances
wi hin he 3 s measu emen in e al.
•To al du .: o al ime in which he impulsi e dis u bances a e p e-
sen a each 200 Hz equency band.
•Mean du .: mean du a ion o he dis u bances a each equency
band is calcula ed by di iding he o al du a ion o he impulsi e
dis u bances by he numbe o occu ences iden i ied in ha in e al.
•Mean du . be ween e en s: a e age du a ion o he ime spacing
be ween sup aha monic impulsi e dis u bances. This me ic only
shows esul s o impulsi e dis u bances whose o al du a ion is
equal o o g ea e han 100 ms, in o de o analyze he empo al
spacing o he emissions wi h he g ea es p esence in he g id.
8. Applica ion o he p oposed me hod
This sec ion shows he applica ion o he measu emen me hod o
cha ac e izing he sup aha monic emissions in he g id in he join ime-
equency domain, wi h a speci ic analysis o iden i y and pa ame ize
he impulsi e dis o ions. Two measu emen s in he LV g id whe e PLC
ansmissions a e p esen and impulsi e dis o ions can cause in e e -
ence in PLC ansmissions a e used o his pu pose.
The i s eco ding (’Rec-1
′
) con ains PLC ansmissions (highligh ed
wi h black a ows in Fig. 13), in he o m o bu s s o a ew milliseconds
in he equency ange 42–89 kHz (delimi a ed wi h wo black lines in
Fig. 13). Mo eo e , nume ous impulsi e dis o ions occupying almos
he en i e CISPR Band A can be seen in he spec og am o Fig. 13
(indica ed wi h a whi e o al). These dis o ions show high ampli ude
and as ime a iabili y wi hin he equency band designa ed o PLC,
and he e o e, hey may in e e e he ecep ion o he PLC signals.
‘Rec-1
′
has been analyzed wi h he echnique p oposed in his wo k,
and he esul s o he join ime- equency cha ac e iza ion a e shown in
Fig. 14 and Fig. 15. The impulsi e dis o ions con ained in his eco ding
ha e been di e en ia ed and assessed sepa a ely by speci ic me ics:
•The me ic ‘RMS U_impulsi e
3 s
’, which ep esen s he RMS alues
only o he impulsi e dis o ions, shows a ipple in ampli ude be-
ween 40 kHz and 85 kHz; his implies ha he impulsi e dis o ions
a e o highe ampli ude han he PLC ansmissions, which usually
show a la ampli ude spec um.
•The me ics in he join ime- equency domain clea ly iden i y he
impulsi e dis o ions in he o al numbe o e en s, whe e a highe
numbe o impulsi e e en s a e de ec ed in he same equencies
whe e he ipple in he RMS alues is obse ed.
•Mo eo e , he di e en alues in he o al du a ion o e en s o in he
mean du a ion be ween e en s ein o ce he ac o he p esence o
he impulsi e emissions al e na ing he PLC ansmissions (see
Fig. 15).
The absence o he analysis in he join ime- equency domain, his
is, he use o only he RMS o QP spec a o he whole eco ding in
Fig. 15, does no e lec he impulsi e in e e ing emissions a all, as hey
a e hidden by he assessmen p ocess.
The eco ding ’Rec-2
′
also con ains PLC ansmissions in he
42–89 kHz ange (delimi a ed wi h wo black lines Fig. 16 and Fig. 17)
and se e al impulsi e dis o ions. A ound 130 kHz, 6 impulsi e emis-
sions in he o m o bu s s o simila du a ion can be app ecia ed (see
whi e ec angles in Fig. 16). The ampli ude cha ac e iza ion and he
ime- equency beha io o he eco dings a e shown in Fig. 17 and
Fig. 18, espec i ely, whe e black boxes ha e been included o highligh
he impulsi e dis o ions.
Resul s in Fig. 17 do no e lec i he emissions in 130 kHz a e
cons an o e he ime o no , as i s a ia ion o e he ime is los . On he
Fig. 11. Ampli ude cha ac e iza ion o he dis u bances and he me ics o
impulsi e dis o ions.
A. Galla e a e al.
