Ci a ion: La ea, A.M.; De La Hoz,
M.; E xega ai, A.; Mazon, A.J.;
A anzabal, I. Design o an
An i-Co ona De ice o HVAC
Subs a ion Connec o s. Ene gies 2022,
15, 5781. h ps://doi.o g/
10.3390/en15165781
Academic Edi o s: Meng Huang,
Yunxiao Zhang and Chenyuan Teng
Recei ed: 18 July 2022
Accep ed: 4 Augus 2022
Published: 9 Augus 2022
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ene gies
A icle
Design o an An i-Co ona De ice o HVAC Subs a ion Connec o s
Ane Mi en La ea , Manuel De La Hoz , Agu zane E xega ai , Angel Ja ie Mazon * and I xaso A anzabal
Depa men o Elec ical Enginee ing, Facul y o Enginee ing o Bilbao, Uni e si y o he Basque Coun y
UPV/EHU, 48013 Bilbao, Spain
*Co espondence: ja ie [email p o ec ed]
Abs ac :
One o he aspec s o conside du ing high- ol age (HV) equipmen design is he educ ion
in he p obabili y o co ona e ec onse . Indeed, he co ona e ec is ela ed o high elec ic ield alues
beyond he equipmen ’s insula ion le els and insula ion s eng h, among o he ac o s. This issue
can be add essed du ing he design s ep, ei he by modi ying he geome y o he elec ical de ice
o by including addi ional elemen s in he equipmen s uc u e o smoo h ou he ol age g adien
along c i ical egions, such as an i-co ona de ices. The s udy o an i-co ona de ices o HV insula o s
is well documen ed, in con as o subs a ion connec o s. The e o e, he p esen s udy p oposed
he design o a no el an i-co ona de ice o HV subs a ion connec o s, including a me hod o he
selec ion o i s dimensions. This s udy shows ha he ela ionship be ween he dimensional design
a iables and he c i ical elec ical ield on he connec o is desc ibed by linea and a ional unc ions.
Thus, he design p ocess imes a e cu down due o a educ ion in he numbe o simula ions equi ed
o un he assessmen o he an i-co ona de ice a angemen impac .
Keywo ds: compu e -aided manu ac u ing; connec o ; co ona ing; elec ic ields; high ol age
1. In oduc ion
The appea ance o he co ona e ec is common in high- ol age (HV) o e head lines.
The phenomenon co esponds o a discha ge a he poin whe e he elec ic ield is g ea e
han he dis up i e s eng h o he insula ion ha su ounds he su ace o he conduc o
and has se e al physical aspec s, such as sound, luminance, and elec omagne ic pulse
wa es ha p oduce ene gy losses on he ansmission sys em [
1
]. In he wo s case, a co ona
e ec could de elop in o an a c ha causes he des uc ion o elec ic de ices ins alled in
o e head lines, such as insula o s o connec o s [2,3].
The s udy o he co ona e ec in ol es he calcula ion o he maximum elec ic ield
ha insula ion can wi hs and, which is a common s ep in he design o HV ins alla ions
(e.g., subs a ions) [
4
] and HV equipmen (e.g., swi chgea , insula o s, connec o s) [
5
]. The
ools used in powe sys em analysis s udies gene ally include app oxima ed modelling
ega ding he geome ies o he ansmission lines and owe s [
6
]. Howe e , in some
speci ic geome ies o insula o s and connec o s, a mo e de ailed analysis is equi ed [
7
,
8
].
In all cases, ini e elemen analysis (FEA) is a aluable ool o calcula ing he elec ic
ield dis ibu ion.
The elec ic ield ha is gene a ed a he su ace and a ound insula o s and line connec-
o s depends di ec ly on he applied ol age and he geome y o he elec ode. Howe e ,
i is necessa y o conside he en i onmen al and insula ion condi ions o unde s and
he co ona e ec comple ely [
7
]. Connec o s a e only subjec o he line ol age, whe eas
in he case o insula o s, one end is connec ed o he line ol age and he o he end is
g ounded. The la ge di e ence in he ol age suppo ed by he insula o s causes an elec ic
ield g adien [
9
]. In con as , o connec o s, i is due o he smalle cu a u e in hei
geome y [10] since he e is no ol age di e ence o e hem.
The ins alla ion o an i-co ona de ices o insula o s is well documen ed in he li -
e a u e. In he case o insula ing s ings, Ilhan and Ozdemi [
11
] conside ed he elec ic
Ene gies 2022,15, 5781. h ps://doi.o g/10.3390/en15165781 h ps://www.mdpi.com/jou nal/ene gies
Ene gies 2022,15, 5781 2 o 12
ield su ace o di e en poin s om he g ading ing and he insula o s ing. Then,
based on a sensi i i y analysis, possible solu ions we e es ed by conside ing he adio
in e e ence ol age p oduced by he con igu a ion. O he au ho s applied op imisa ion
me hods [
12
]. Howe e , hese wo ks did no show an e iden solu ion o he loca ion and
size o he co ona ings. P oposed op imisa ion algo i hms a e he ba lying algo i hm [
13
],
pa icle swa m op imisa ion [
14
,
15
], and su ace esponse [
16
]. Gene ally, some minimum
elec ical ield alue is conside ed as an objec i e a a pa icula ly c i ical poin (e.g., he
insula ion iple poin o an insula ing s ing [
17
]) o along a cha ac e is ic line leng h
(e.g., he pe iphe y line o he insula ing s ing [
18
]). Rega ding he co ona e ec onse a
subs a ion connec o s, Gui e as e al. [
19
] sugges ed ins alling shielding pa s a ound he
connec o s o o co e hem wi h a sphe ical cage unde he same ol age. This solu ion
educes he elec ic ield, and he e o e, i can be used on sys ems ope a ing unde highe
ol age. Ne e heless, o he speci ic p oblem condi ions, he au ho s concluded ha a
edesign o he geome y o he connec o is p e e ed. This app oach is only alid o
ce ain connec o s since i may no be easible o ce ain conduc o a angemen s. The
edesign o he connec o s also implies ano he kind o s udy o he connec o ( he mal,
mechanical, e c.), and he e o e, mo e indus ial es s o be ca ied ou .
Th ee essen ial equi emen s a e desi able in he design, manu ac u ing, and ins al-
la ion o co ona ings. Fi s , he ings mus be simple o build. Second, he ins alla ion o
he co ona ings on si e mus be s aigh o wa d, in ol ing a minimal numbe o s eps.
Consequen ly, in he p esen s udy, uncon en ional su aces we e no analysed, such as in
Pa anadech e al. [
20
] and Liao e al. [
21
]. Howe e , i could be a alid ype o op imisa ion
when applied o insula o s [
22
]. Thi d, he poin o a achmen o he o oid is also ele an .
I s posi ion in space mus be suppo ed by some objec o which i can be mechanically
linked using an adjus men o achie e ixa ion [
23
]. Fo connec o s, his means using hei
ci il wo k suppo , i hey ha e one, o ixing he ings on he conduc o s ha en e he
connec o . The las op ion was conside ed o his wo k.
O he ime minimisa ion echniques in he es de elopmen a e implemen ed in he
modelling o an i-co ona ings, such as he design o expe imen s (DOE) and analysis o
a iance (ANOVA) [
16
], in his case, o insula o s. The limi a ion o his me hod lies in he
ac ha he ela ionships be ween he mul iple ac o s conside ed mus be linea [24].
The p esen s udy p oposed he design o a no el an i-co ona de ice, i.e., an an i-
co ona ing, o HV subs a ion connec o s, including a me hod o ing dimension selec ion.
The co ona ing shape was mainly selec ed because i is easie o manu ac u e and main ain
compa ed wi h sphe ical cages o o he geome ies.
The applied me hod was ocused on conside ing whe he algo i hmic exp essions can
be de i ed o he sizing o co ona ings o educe he analysis ime in he design s age, as
well as applying i o usual cases on subs a ion connec o s. I educes he design p ocess
calcula ions by conside ing he ela ionship be ween he geome ic dimensions o he
co ona ings and he alue o he maximum su ace elec ic ield o he subs a ion connec o
nea he an i-co ona ing. The objec i e was o educe he numbe o ials o es ablish he
possible ela ionship be ween design pa ame e s, hus minimising he simula ion esou ces
equi ed o an i e a i e op imisa ion p ocess.
The o he ad an age comes om he simula ion o es ing condi ions using FEA.
Al hough we conside ed he elec ical ield only a he connec o su ace, he connec o
geome y is challenging o model and mus be done wi hou any dimensional simpli ica ion
( om a h ee-dimensional model o an axis-symme y one, o ins ance). Any educ ion in
he nume ical me hods equi ed speeds up he design p ocess and inc eases he possibili y
o educed es ing.
This pape is o ganised as ollows. In he i s pa , geome ical de ails o he subs a ion
connec o s, es ing se up, and he an i-co ona de ice a angemen a e in oduced. Thus,
a nume ical FEA model ha was used o simula e s anda d HV labo a o y condi ions
is p esen ed, and he loca ion o he maximum su ace elec ic ield is gi en. Based on
p e ious esul s, in he second pa , he speci ic posi ions o he co ona ings nea he
Ene gies 2022,15, 5781 3 o 12
subs a ion connec o s unde s udy ha educed he elec ic ield a e gi en. The esul s o
se e al simula ions o de e mine he e ec o he p oposed an i-co ona ing’s geome ical
ac o s on he elec ic ield a e p esen ed. The las pa o e s in o ma ion abou he
algeb aic ela ionship be ween a iables ha diminish he design ime, educe he numbe
o simula ions, and conside he su ace elec ic ield as an indica o . The me hod can also
be used on si e o imp o e he loca ion o he co ona ings o s anda d condi ions.
2. Desc ip ion o he Connec o s and he Tes ing Se up
2.1. Geome y o he Connec o s and he Tes ing Se up
The no el an i-co ona de ice p oposed in he p esen s udy was in es iga ed o i s
applica ion in speci ic aluminium connec o s used in HV elec ical subs a ions. Howe e ,
he a angemen is alid o any subs a ion connec o p o ided ha a co ona ing is
ins alled in each o he connec o s coupled h ough a subs a ion connec o ollowing he
design me hod in oduced in Sec ion 4.
The connec o s unde s udy a e shown in Figu e 1, whe e hei main dimensions a e
de ined, including hei leng h, wid h, heigh , and minimum adius. The dimensions o
each connec o a e shown in Table 1.
Ene gies 2022, 15, x FOR PEER REVIEW 3 o 12
This pape is o ganised as ollows. In he i s pa , geome ical de ails o he subs a-
ion connec o s, es ing se up, and he an i-co ona de ice a angemen a e in oduced.
Thus, a nume ical FEA model ha was used o simula e s anda d HV labo a o y condi-
ions is p esen ed, and he loca ion o he maximum su ace elec ic ield is gi en. Based
on p e ious esul s, in he second pa , he speci ic posi ions o he co ona ings nea he
subs a ion connec o s unde s udy ha educed he elec ic ield a e gi en. The esul s o
se e al simula ions o de e mine he e ec o he p oposed an i-co ona ing’s geome ical
ac o s on he elec ic ield a e p esen ed. The las pa o e s in o ma ion abou he alge-
b aic ela ionship be ween a iables ha diminish he design ime, educe he numbe o
simula ions, and conside he su ace elec ic ield as an indica o . The me hod can also
be used on si e o imp o e he loca ion o he co ona ings o s anda d condi ions.
2. Desc ip ion o he Connec o s and he Tes ing Se up
2.1. Geome y o he Connec o s and he Tes ing Se up
The no el an i-co ona de ice p oposed in he p esen s udy was in es iga ed o i s
applica ion in speci ic aluminium connec o s used in HV elec ical subs a ions. Howe e ,
he a angemen is alid o any subs a ion connec o p o ided ha a co ona ing is in-
s alled in each o he connec o s coupled h ough a subs a ion connec o ollowing he
design me hod in oduced in Sec ion 4.
The connec o s unde s udy a e shown in Figu e 1, whe e hei main dimensions a e
de ined, including hei leng h, wid h, heigh , and minimum adius. The dimensions o
each connec o a e shown in Table 1.
Figu e 1. Geome y o connec o s.
Table 1. Geome ical dimensions o connec o s.
Connec o Leng h (mm) Wid h (mm) Heigh (mm) Radius Min. (mm)
Connec o 1 470 470 100 6
Connec o 2 585 270 95 3
Connec o 3 240 120 230 4
In he p esen s udy, he in es iga ion o he elec ic ield a ound he connec o s was
based on he ec ea ion o a labo a o y es ing se up, as shown in Figu e 2. In he es ing
a angemen , se e al ubes allowed he connec o o be suspended in he model, e lec ing
i s possible ins alla ion in he subs a ion, which would be he con en ional assembly o be
es ed in he labo a o y. Thei diame e s a e he same as hose used unde s anda d in-
s alla ion equi emen s.
One o he simples and mos e ec i e solu ions o educing he elec ical s ess gen-
e a ed a he ends o he conduc o s in he es bench is o use co ona-shielding sys ems
(sphe es and ings) a hei ends [25] o p e en he elec ic ield om inc easing d ama -
ically. Gene ally, hese me al pa s ha e a ing, sphe ical, o bowl shape [8]. No e ha
Figu e 1. Geome y o connec o s.
Table 1. Geome ical dimensions o connec o s.
Connec o Leng h (mm) Wid h (mm) Heigh (mm) Radius Min. (mm)
Connec o 1 470 470 100 6
Connec o 2 585 270 95 3
Connec o 3 240 120 230 4
In he p esen s udy, he in es iga ion o he elec ic ield a ound he connec o s was
based on he ec ea ion o a labo a o y es ing se up, as shown in Figu e 2. In he es ing
a angemen , se e al ubes allowed he connec o o be suspended in he model, e lec ing
i s possible ins alla ion in he subs a ion, which would be he con en ional assembly o
be es ed in he labo a o y. Thei diame e s a e he same as hose used unde s anda d
ins alla ion equi emen s.
One o he simples and mos e ec i e solu ions o educing he elec ical s ess gen-
e a ed a he ends o he conduc o s in he es bench is o use co ona-shielding sys ems
(sphe es and ings) a hei ends [
25
] o p e en he elec ic ield om inc easing d ama i-
cally. Gene ally, hese me al pa s ha e a ing, sphe ical, o bowl shape [
8
]. No e ha hese
elemen s a e independen o he co ona ings. The es ing enclosu e consis ed o a box wi h
dimensions 15 m
×
15 m
×
10 m and he a angemen was loca ed a he cen e, as shown
in Figu e 2.
Ene gies 2022,15, 5781 4 o 12
Ene gies 2022, 15, x FOR PEER REVIEW 4 o 12
hese elemen s a e independen o he co ona ings. The es ing enclosu e consis ed o a
box wi h dimensions 15 m × 15 m × 10 m and he a angemen was loca ed a he cen e,
as shown in Figu e 2.
Figu e 2. Modelled se up o he connec o s. The box ep esen s he es ing oom.
2.2. Con igu a ion o he Simula ion Tool
The elec ic ield o he connec o was calcula ed wi h FEA. The assump ions consid-
e ed we e as ollows. Fi s , he FEA model simula ion was ca ied ou unde HV labo a-
o y condi ions, acco ding o no mal p essu e, empe a u e, and humidi y, as es ablished
in s anda d IEC 61284 [26]. The FEA so wa e ool o p e e ence o his wo k was COM-
SOL Mul iphysics.
Second, when simula ing a piece ha is connec ed o conduc o s, i s ends a e ex-
posed. Tha is, an in ini e conduc o canno be de ined. Howe e , his had no impac when
e alua ing he piece, p o ided i s leng h is conside ably longe han he connec o unde
analysis. E en so, a sphe e co e ed he ends o a oid he maximum elec ic ield o he
whole assembly being ound a he ends o he conduc o , gi en i s sha p geome y.
The es ing se up in Figu e 2 was modelled in he FEA so wa e. Then, he elec ic
ield was only analysed a i s mos c i ical poin , i.e., he maximum alues a each poin
o he connec o su ace we e iden i ied, omi ing he ac ha he ol age a ied o e ime
( he maximum alue is a he peak o he sinusoidal wa e).
The simula ion enclosu e was g ounded o de ine an app op ia e en i onmen . The
es o he pieces we e connec ed o a line ol age o 450 kV
peak
as he e e ence.
The cha ac e is ics o he mesh a e a key ac o when ca ying ou an analysis by
means o FEA. To ob ain p ecise esul s, he “ e y ine mesh” op ion in he meshing s age
on COMSOL Mul iphysics was selec ed. O he impo an cha ac e is ics ela ed o he
ype o mesh used a e desc ibed in Annex I.
A e de ining meshing cha ac e is ics, a s a iona y s udy was ca ied ou . Once he
elec ic ield on he connec o was calcula ed, he poin wi h he highes elec ic ield alue
was ob ained.
3. Geome y and Design o he An i-Co ona De ice
3.1. Geome y o he An i-Co ona De ice
The elec ic ield depends di ec ly on he geome y o a powe sys em elemen unde
ol age. The e o e, i he geome y o he elemen is a ied, i has an impac on i s elec ic
ield. To educe he elec ic ield o subs a ion connec o s, he p esen s udy p oposed o
include a ing a ound each conduc o (Figu e 3). In his way, i was possible o al e he
geome y o he whole assembly (connec o , ings, and conduc o s) and, in u n, he elec-
ic ield. By a aching he ings o he conduc o s, a s able hold was allowed. Thus, a dis-
ance was kep be ween he ing and he connec o , as de ined by he designe . The ing
Figu e 2. Modelled se up o he connec o s. The box ep esen s he es ing oom.
2.2. Con igu a ion o he Simula ion Tool
The elec ic ield o he connec o was calcula ed wi h FEA. The assump ions con-
side ed we e as ollows. Fi s , he FEA model simula ion was ca ied ou unde HV
labo a o y condi ions, acco ding o no mal p essu e, empe a u e, and humidi y, as es ab-
lished in s anda d IEC 61284 [
26
]. The FEA so wa e ool o p e e ence o his wo k was
COMSOL Mul iphysics.
Second, when simula ing a piece ha is connec ed o conduc o s, i s ends a e exposed.
Tha is, an in ini e conduc o canno be de ined. Howe e , his had no impac when
e alua ing he piece, p o ided i s leng h is conside ably longe han he connec o unde
analysis. E en so, a sphe e co e ed he ends o a oid he maximum elec ic ield o he
whole assembly being ound a he ends o he conduc o , gi en i s sha p geome y.
The es ing se up in Figu e 2was modelled in he FEA so wa e. Then, he elec ic
ield was only analysed a i s mos c i ical poin , i.e., he maximum alues a each poin o
he connec o su ace we e iden i ied, omi ing he ac ha he ol age a ied o e ime
( he maximum alue is a he peak o he sinusoidal wa e).
The simula ion enclosu e was g ounded o de ine an app op ia e en i onmen . The
es o he pieces we e connec ed o a line ol age o 450 kVpeak as he e e ence.
The cha ac e is ics o he mesh a e a key ac o when ca ying ou an analysis by
means o FEA. To ob ain p ecise esul s, he “ e y ine mesh” op ion in he meshing s age
on COMSOL Mul iphysics was selec ed. O he impo an cha ac e is ics ela ed o he ype
o mesh used a e desc ibed in Annex I.
A e de ining meshing cha ac e is ics, a s a iona y s udy was ca ied ou . Once he
elec ic ield on he connec o was calcula ed, he poin wi h he highes elec ic ield alue
was ob ained.
3. Geome y and Design o he An i-Co ona De ice
3.1. Geome y o he An i-Co ona De ice
The elec ic ield depends di ec ly on he geome y o a powe sys em elemen unde
ol age. The e o e, i he geome y o he elemen is a ied, i has an impac on i s elec ic
ield. To educe he elec ic ield o subs a ion connec o s, he p esen s udy p oposed
o include a ing a ound each conduc o (Figu e 3). In his way, i was possible o al e
he geome y o he whole assembly (connec o , ings, and conduc o s) and, in u n, he
elec ic ield. By a aching he ings o he conduc o s, a s able hold was allowed. Thus,
a dis ance was kep be ween he ing and he connec o , as de ined by he designe . The
ing a angemen p esen ed in his wo k allowed o a s aigh o wa d eplacemen o
he ings i necessa y and a pe ec as ening a a dis ance om he piece as de e mined
by he designe . In his way, he same connec o could be used unde di e en ope a ion
condi ions by changing he geome y o dis ance o he ings ins ead o changing o
Ene gies 2022,15, 5781 5 o 12
edesigning he connec o . In addi ion, compa ed wi h sphe ical cages, ings a e easie o
manu ac u e and main ain.
Ene gies 2022, 15, x FOR PEER REVIEW 5 o 12
a angemen p esen ed in his wo k allowed o a s aigh o wa d eplacemen o he
ings i necessa y and a pe ec as ening a a dis ance om he piece as de e mined by he
designe . In his way, he same connec o could be used unde di e en ope a ion condi-
ions by changing he geome y o dis ance o he ings ins ead o changing o edesigning
he connec o . In addi ion, compa ed wi h sphe ical cages, ings a e easie o manu ac u e
and main ain.
The design o he an i-co ona de ice was classi ied acco ding o he ollowing pa am-
e e s: hickness o he ings (A), inne diame e o he ings (Din ), and dis ance be ween
he ing and he connec o (dis ), as iden i ied in Figu e 4.
Figu e 3. Connec o wi h ings ins alled a ound he conduc o s.
Figu e 4. Design o indi idual ings ins alled a ound he conduc o s.
3.2. Modelling and Simula ion o he Se up wi h he An i-Co ona De ice
The elec ic ield o he connec o was calcula ed wi h FEA again, bu now o se e al
cases ha conside ed di e en pa ame e alues. Fi s , he es ing se up in Figu e 2 wi h
he an i-co ona de ice was modelled in he FEA so wa e again. Then, he maximum elec-
ic ield in he posi ion ound in Sec ion 2.2 has been eco ded. Two o he pa ame e s
we e always cons an and he las one was modi ied in o de o ind ou he dependency
wi h he maximum elec ic ield on he connec o su ace.
The simula ion enclosu e was g ounded o de ine an app op ia e en i onmen . The
es o he pieces we e connec ed o a line ol age o 450 kV
peak
as a e e ence, including
he an i-co ona de ice, since i was ixed o he cables o he se up.
4. Simula ion Resul s
4.1. Simula ion Resul s wi hou he An i-Co ona De ice
The elec ic ield a he su ace o he connec o s unde s udy wi hou any an i-co ona
de ice ins alled is shown in Figu e 5. I can be obse ed ha he maximum elec ic ield
alue mos ly occu ed in he zone wi h he highes cu a u e. Howe e , he no mal ec o
om hese c i ical su aces was no always in he same di ec ion as he axis o he ubes,
as shown o connec o 3 in Figu e 5.
Figu e 3. Connec o wi h ings ins alled a ound he conduc o s.
The design o he an i-co ona de ice was classi ied acco ding o he ollowing pa ame-
e s: hickness o he ings (A), inne diame e o he ings (Din ), and dis ance be ween he
ing and he connec o (dis ), as iden i ied in Figu e 4.
Ene gies 2022, 15, x FOR PEER REVIEW 5 o 12
a angemen p esen ed in his wo k allowed o a s aigh o wa d eplacemen o he
ings i necessa y and a pe ec as ening a a dis ance om he piece as de e mined by he
designe . In his way, he same connec o could be used unde di e en ope a ion condi-
ions by changing he geome y o dis ance o he ings ins ead o changing o edesigning
he connec o . In addi ion, compa ed wi h sphe ical cages, ings a e easie o manu ac u e
and main ain.
The design o he an i-co ona de ice was classi ied acco ding o he ollowing pa am-
e e s: hickness o he ings (A), inne diame e o he ings (Din ), and dis ance be ween
he ing and he connec o (dis ), as iden i ied in Figu e 4.
Figu e 3. Connec o wi h ings ins alled a ound he conduc o s.
Figu e 4. Design o indi idual ings ins alled a ound he conduc o s.
3.2. Modelling and Simula ion o he Se up wi h he An i-Co ona De ice
The elec ic ield o he connec o was calcula ed wi h FEA again, bu now o se e al
cases ha conside ed di e en pa ame e alues. Fi s , he es ing se up in Figu e 2 wi h
he an i-co ona de ice was modelled in he FEA so wa e again. Then, he maximum elec-
ic ield in he posi ion ound in Sec ion 2.2 has been eco ded. Two o he pa ame e s
we e always cons an and he las one was modi ied in o de o ind ou he dependency
wi h he maximum elec ic ield on he connec o su ace.
The simula ion enclosu e was g ounded o de ine an app op ia e en i onmen . The
es o he pieces we e connec ed o a line ol age o 450 kV
peak
as a e e ence, including
he an i-co ona de ice, since i was ixed o he cables o he se up.
4. Simula ion Resul s
4.1. Simula ion Resul s wi hou he An i-Co ona De ice
The elec ic ield a he su ace o he connec o s unde s udy wi hou any an i-co ona
de ice ins alled is shown in Figu e 5. I can be obse ed ha he maximum elec ic ield
alue mos ly occu ed in he zone wi h he highes cu a u e. Howe e , he no mal ec o
om hese c i ical su aces was no always in he same di ec ion as he axis o he ubes,
as shown o connec o 3 in Figu e 5.
Figu e 4. Design o indi idual ings ins alled a ound he conduc o s.
3.2. Modelling and Simula ion o he Se up wi h he An i-Co ona De ice
The elec ic ield o he connec o was calcula ed wi h FEA again, bu now o se e al
cases ha conside ed di e en pa ame e alues. Fi s , he es ing se up in Figu e 2wi h he
an i-co ona de ice was modelled in he FEA so wa e again. Then, he maximum elec ic
ield in he posi ion ound in Sec ion 2.2 has been eco ded. Two o he pa ame e s we e
always cons an and he las one was modi ied in o de o ind ou he dependency wi h
he maximum elec ic ield on he connec o su ace.
The simula ion enclosu e was g ounded o de ine an app op ia e en i onmen . The
es o he pieces we e connec ed o a line ol age o 450 kV
peak
as a e e ence, including
he an i-co ona de ice, since i was ixed o he cables o he se up.
4. Simula ion Resul s
4.1. Simula ion Resul s wi hou he An i-Co ona De ice
The elec ic ield a he su ace o he connec o s unde s udy wi hou any an i-co ona
de ice ins alled is shown in Figu e 5. I can be obse ed ha he maximum elec ic ield
alue mos ly occu ed in he zone wi h he highes cu a u e. Howe e , he no mal ec o
om hese c i ical su aces was no always in he same di ec ion as he axis o he ubes, as
shown o connec o 3 in Figu e 5.
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Figu e 5. Elec ic ield (kV/cm) a he connec o su ace.
The maximum ield alues a he su ace o he connec o s wi hou any ing we e
45.2 kV/cm (connec o 1), 46.5 kV/cm (connec o 2), and 65.3 kV/cm (connec o 3).
The poin o e alua ion o he elec ic ield o he simula ions in Sec ion 4.2 is indi-
ca ed in Figu e 5 by E
bc
. I coincided wi h he loca ion o he maximum elec ic ield E
max
,
excep in he s udy o connec o 2. The p oposed solu ion educed he elec ic ield mag-
ni ude in he closes poin s o he ings and he elec ic ield ec o mus be almos pa allel
o he ing axis. The e o e, o connec o 2, he poin selec ed o analyse E
bc
was a poin
nea he plane o he an i-co ona de ice ins alla ion wi h an elec ic ield alue o 20.0
kV/cm.
4.2. Simula ion Resul s wi h an An i-Co ona De ice
Fo he di e en con igu a ions in Figu e 3, se e al simula ions we e ca ied ou by
changing he ing pa ame e s: hickness (A), inne diame e (Din ), and dis ance be ween
he ing and he connec o (dis ). Figu e 6 desc ibes he maximum elec ic ield alue
ound a he connec o su ace unde each speci ic pa ame e while keeping he o he s
cons an . I can be no ed ha o any con igu a ion wi h an i-co ona de ices, he elec ic
ield was weake han wi hou he an i-co ona de ices, as indica ed in Sec ion 4.1, and he
co ona incep ion ol age was also educed.
(a)
5
10
15
20
25
30
35
40
45
15 35 55 75 95
E [kV/cm]
A [mm]
RING THICKNESS (A)
Connec o 1 Connec o 2 Connec o 3
Din 1= 100 mm
dis 1= 200 mm
Din 2= 100 mm
dis 2= 250 mm
Din 3=80mm
dis 3= 250 mm
Figu e 5. Elec ic ield (kV/cm) a he connec o su ace.
The maximum ield alues a he su ace o he connec o s wi hou any ing we e
45.2 kV/cm (connec o 1), 46.5 kV/cm (connec o 2), and 65.3 kV/cm (connec o 3).
The poin o e alua ion o he elec ic ield o he simula ions in Sec ion 4.2 is indica ed
in Figu e 5by E
bc
. I coincided wi h he loca ion o he maximum elec ic ield E
max
, excep
in he s udy o connec o 2. The p oposed solu ion educed he elec ic ield magni ude in
he closes poin s o he ings and he elec ic ield ec o mus be almos pa allel o he
ing axis. The e o e, o connec o 2, he poin selec ed o analyse E
bc
was a poin nea he
plane o he an i-co ona de ice ins alla ion wi h an elec ic ield alue o 20.0 kV/cm.
4.2. Simula ion Resul s wi h an An i-Co ona De ice
Fo he di e en con igu a ions in Figu e 3, se e al simula ions we e ca ied ou by
changing he ing pa ame e s: hickness (A), inne diame e (Din ), and dis ance be ween
he ing and he connec o (dis ). Figu e 6desc ibes he maximum elec ic ield alue ound
a he connec o su ace unde each speci ic pa ame e while keeping he o he s cons an .
I can be no ed ha o any con igu a ion wi h an i-co ona de ices, he elec ic ield was
weake han wi hou he an i-co ona de ices, as indica ed in Sec ion 4.1, and he co ona
incep ion ol age was also educed.
Figu e 6. Con .
Ene gies 2022,15, 5781 7 o 12
Figu e 6.
Elec ic ield on he connec o ’s su ace as a unc ion o he ing dimensions: (
a
) ing
hickness, (b) in e nal diame e , and (c) ing–connec o dis ance.
E en i he sweep ange was modi ied o he di e en s udy cases, he endency was
simila o each pa ame e s udy. Depending on he elec ic ield p esen a he ins alla ion
poin o he an i-co ona de ice, he esul s o Figu e 6allowed o deciding he dimensional
cha ac e is ics o he an i-co ona de ice as a i s app oxima ion.
As obse ed in Figu e 6a, he change in hickness o he ing (keeping i s in e nal
diame e cons an ) ollowed a downwa d linea end. Analogously o he hickness, he
inc ease in he in e nal diame e o he ing (Figu e 6b) ollowed he same end. Thus,
he la ge he in e nal diame e o he ings (keeping he es o he pa ame e s cons an ),
he smalle he elec ic ield. Finally, he a ia ion o he dis ance be ween he ing and
he connec o in Figu e 6c did no ollow a linea end, bu a mo e complex end. I was
e i ied ha he a he he ings we e om he connec o , he less in luence hey had on
he elec ic ield.
Ene gies 2022,15, 5781 8 o 12
Fo a mo e accu a e design, h ee i ing equa ions we e ex apola ed om Figu e 6
based on he pa ame e s analysed and he maximum elec ic ield alue.
Equa ions (1)–(3)
a e in ended o he selec ion o he co ona ing dimensions. Equa ions (1) and (2) co e-
spond o he ela ionships be ween he elec ic ield E (kV/cm) and ing hickness
A (mm)
and be ween he elec ic ield E (kV/cm) and he in e nal diame e o he ing
Din (mm)
.
Equa ion (3) ela es he elec ic ield E (kV/cm) and he dis ance be ween ings and connec-
o s dis (mm). The alue o R
2
o all he i ings was abo e 0.92. The cons an alues C1
o C6 acco ding o he connec o and equa ion a e shown in Table 2.
Emax =C1×A+C2 (1)
Emax =C3×Din +C4 (2)
Emax =C5
√dis
+C6 (3)
Table 2. Cons an alues o Equa ions (1) o (3) o each connec o .
Connec o C1 C2 C3 C4 C5 C6
Connec o 1 −0.161 32.1 −0.103 37.3 −212 41.3
Connec o 2 −0.138 16.8 −0.082 20.8 −376 36.9
Connec o 3 −0.103 42.1 −0.074 47.3 −106 46.78
In Equa ions (1)–(3), he o he pa ame e s a e kep cons an , as speci ied in Table 2. A
single i ed Equa ion (4) was deduced o he mos gene al case, whe e all he pa ame e s
a e desc ibed oge he . The cons an alues L1 o L4 o each connec o a e shown in
Table 3.
Emax =L1 +L2 ×A+L3 ×Din +L4
√dis (4)
Table 3. Cons an alues o Equa ion (4) o each connec o .
Connec o L1 L2 L3 L4
Connec o 1 56.8 −0.161 −0.103 −212
Connec o 2 46.8 −0.138 −0.082 −376
Connec o 3 56.2 −0.103 −0.074 −106
Equa ion (4) is use ul o de e mining he elec ic ield in a combina ion o he pa-
ame e s ha a e no included in he s udied cases, as long as he case conside ed is
an in e pola ion.
The dis ance be ween he ings and he connec o (dis ) is a key ac o when s udying
he adequacy o an an i-co ona de ice. I physical es ic ions a e dis ega ded, he close
he ings a e o he piece, he smalle he elec ic ield. In case he elec ic ield alue is no
su icien ly low, he ings would ha e o be eplaced by o he ings o g ea e hickness o
g ea e in e nal diame e .
5. Discussion
Based on he con igu a ion o a speci ic connec o , i is possible o a oid he appea ance
o he co ona e ec by dec easing he alue o he elec ic ield a i s su ace. Fo his
pu pose, he p esen s udy p oposed ins alling co ona ings a ound each conduc o linked
by he connec o . Unde hese condi ions, he incep ion ol age inc eased, allowing o use
o his equipmen in applica ions wi h a highe elec ical ol age. The geome y o he ings
was de ined by h ee pa ame e s: hickness (A), in e nal diame e (Din ), and dis ance (dis ),
which can be calcula ed sepa a ely using Equa ions (1)–(3) o he connec o s in es iga ed
in his s udy (Figu e 1). The equa ions we e e i ied o he connec o s unde s udy, which
we e subjec ed o a line ol age o 450 kV
peak
AC. The p ocedu e can be gene alised, and
Ene gies 2022,15, 5781 9 o 12
hus, i can be applied o o he connec o designs a any ol age le el. The gene alised
design me hodology is in oduced in he p esen pape .
The pape p esen s o he con ibu ions, oo. Fi s , he maximum elec ic ield unde
some condi ions (e.g., connec o 2) was no loca ed in a a ou able posi ion o he an i-
co ona ing o educe i s magni ude by a conside able pe cen age. The elec ic ield
educ ion was s ongly in luenced by he sepa a ion be ween he an i-co ona ing and he
connec o poin unde s udy. Hence, o e y long connec o s, he solu ion in oduced in
he p esen wo k could be imp ac ical. Al e na i ely, he an i-co ona ing can ci cumsc ibe
he poin whe e he elec ic ield needs o be a enua ed. Howe e , he ixa ion o he ing
should be u he s udied.
Mo eo e , he design o he co ona ings sugges s he possibili y o op imisa ion.
Equa ion (4) gi es a en a i e objec i e unc ion, whe e bo h economic and echnical aspec s
should be conside ed. In any case, a sweep o e each o he s udy cases is use ul o analyse
he beha iou o all he a iables oge he , as shown in Figu e 7. In each axis o Figu e 7,
one o he pa ame e s in ol ed in Equa ion (4) is ep esen ed. The elec ic ield o each
squa e has a colou ha ep esen s i s alue and co esponds o he case wi h he midpoin
combina ion alues. The hype su ace does no allow o in e ing he beha iou o he
design pa ame e s analy ically, bu i does o e a global idea o he co ona ing designs
ha should be conside ed by he designe . Fo ins ance, we could quickly es ablish a eas
wi h a limi alue (e.g., 30 kV/cm) and disca d hose designs on he hype su ace.
Ene gies 2022, 15, x FOR PEER REVIEW 9 o 12
linked by he connec o . Unde hese condi ions, he incep ion ol age inc eased, allowing
o use o his equipmen in applica ions wi h a highe elec ical ol age. The geome y o
he ings was de ined by h ee pa ame e s: hickness (A), in e nal diame e (Din ), and
dis ance (dis ), which can be calcula ed sepa a ely using Equa ions (1)–(3) o he connec -
o s in es iga ed in his s udy (Figu e 1). The equa ions we e e i ied o he connec o s
unde s udy, which we e subjec ed o a line ol age o 450 kVpeak AC. The p ocedu e can
be gene alised, and hus, i can be applied o o he connec o designs a any ol age le el.
The gene alised design me hodology is in oduced in he p esen pape .
The pape p esen s o he con ibu ions, oo. Fi s , he maximum elec ic ield unde
some condi ions (e.g., connec o 2) was no loca ed in a a ou able posi ion o he an i-
co ona ing o educe i s magni ude by a conside able pe cen age. The elec ic ield educ-
ion was s ongly in luenced by he sepa a ion be ween he an i-co ona ing and he con-
nec o poin unde s udy. Hence, o e y long connec o s, he solu ion in oduced in he
p esen wo k could be imp ac ical. Al e na i ely, he an i-co ona ing can ci cumsc ibe
he poin whe e he elec ic ield needs o be a enua ed. Howe e , he ixa ion o he ing
should be u he s udied.
Mo eo e , he design o he co ona ings sugges s he possibili y o op imisa ion.
Equa ion (4) gi es a en a i e objec i e unc ion, whe e bo h economic and echnical as-
pec s should be conside ed. In any case, a sweep o e each o he s udy cases is use ul o
analyse he beha iou o all he a iables oge he , as shown in Figu e 7. In each axis o
Figu e 7, one o he pa ame e s in ol ed in Equa ion (4) is ep esen ed. The elec ic ield
o each squa e has a colou ha ep esen s i s alue and co esponds o he case wi h he
midpoin combina ion alues. The hype su ace does no allow o in e ing he beha -
iou o he design pa ame e s analy ically, bu i does o e a global idea o he co ona ing
designs ha should be conside ed by he designe . Fo ins ance, we could quickly es ab-
lish a eas wi h a limi alue (e.g., 30 kV/cm) and disca d hose designs on he hype su -
ace.
Figu e 7. Elec ic ield on connec o 1 as a unc ion o he ing dimensions: hickness (A), in e nal
diame e (Din ), and ing–connec o dis ance (dis ), ep esen ed simul aneously.
6. Conclusions
The ins alla ion o co ona ings a ound a de ice o p o ec i , e.g., HV subs a ion con-
nec o s, is a simple and e ec i e way o a oid he appea ance o he co ona e ec . The
ings dec ease he elec ic ield a he c i ical poin s, and consequen ly, he p obabili y o
Figu e 7.
Elec ic ield on connec o 1 as a unc ion o he ing dimensions: hickness (A), in e nal
diame e (Din ), and ing–connec o dis ance (dis ), ep esen ed simul aneously.
6. Conclusions
The ins alla ion o co ona ings a ound a de ice o p o ec i , e.g., HV subs a ion
connec o s, is a simple and e ec i e way o a oid he appea ance o he co ona e ec . The
ings dec ease he elec ic ield a he c i ical poin s, and consequen ly, he p obabili y
o he co ona e ec occu ing. The p esen s udy p oposed a no el an i-co ona de ice
a angemen consis ing o he ins alla ion o a co ona ing pe conduc o coupled h ough
subs a ion connec o s. This an i-co ona de ice gua an eed a co ec ixa ion and he co ona
e ec onse was educed. The design was s udied o speci ic connec o s used o he
connec ion o ou conduc o s unde a line ol age o 450 kVpeak AC.
The design o co ona de ices is a key ac o when e alua ing he elec ic ield a a
subs a ion connec o o in he case o subs a ion epowe ing. The e o e, se e al simula ions
we e ca ied ou in he p esen wo k in o de o de e mine he mos adequa e an i-co ona
