Ci a ion: Daboul, M.; O ságo á, J.;
Ju ák, V.; V al, M. Tes ing Rogowski
Coils wi h Me ging Uni s o Sma
G ids. Ene gies 2023,16, 7323.
h ps://doi.o g/10.3390/en16217323
Academic Edi o : Vaidyana han
K ishnamu hy
Recei ed: 2 Oc obe 2023
Re ised: 23 Oc obe 2023
Accep ed: 26 Oc obe 2023
Published: 28 Oc obe 2023
Copy igh : © 2023 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/).
ene gies
A icle
Tes ing Rogowski Coils wi h Me ging Uni s o Sma G ids
Mayada Daboul *, Ja osla a O ságo á, Vik o Ju ák and Ma ˇej V al
Depa men o Elec ical Powe Enginee ing, Facul y o Elec ical Enginee ing and Communica ion, B no
Uni e si y o Technology, CZ-61600 B no, Czech Republic; o sago a@ u b .cz (J.O.); [email p o ec ed] (M.V.)
*Co espondence: [email p o ec ed]
Abs ac :
As sma g ids inco po a e enewable ene gy sou ces and ad anced powe elec onics,
ensu ing accu a e measu emen sys ems becomes pa amoun due o he inc eased complexi y and
po en ial sou ces o dis u bances. This a icle ocuses on he labo a o y calib a ion o Rogowski coils
(RCs) and me ging uni s (MUs), which a e undamen al o measu ing, con olling, and moni o ing
digi al powe sys ems. A comp ehensi e digi al calib a ion sys em is in oduced, u ilizing p ecise,
comme cially a ailable componen s such as a luxga e cu en ansduce and a Na ional Ins umen .
The sys em assesses magni ude and phase displacemen e o s unde a ious ope a ing condi ions,
including abno mal scena ios. Addi ionally, he impac o unce ain y sou ces on he measu emen
chain analysis is discussed, wi h es esul s con o ming o es ablished s anda ds. This esea ch
con ibu es o enhancing he accu acy and eliabili y o measu emen sys ems in he con ex o
e ol ing sma g ids.
Keywo ds:
low-powe cu en ans o me ; Rogowski coil; me ging uni ; IEC 61850-9-2; p ecision
ime p o ocol; calib a ion p ocedu e
1. In oduc ion
Ad anced echnologies, including digi al sys ems and communica ion s anda ds, ha e
pa ed he way o he e olu ion o powe sys ems in o sma g ids. These sma g ids
play a c ucial ole in mode n aul de ec ion, measu emen , and con ol applica ions [
1
].
Ensu ing he eliabili y and sa e y o hese sys ems is now hea ily elian on he accu a e
and apid measu emen o elec ical pa ame e s such as cu en , ol age, and equency.
Sma g ids a e ans o ming he managemen and con ol o powe sys ems by imple-
men ing in eg a ed dis ibu ion con ol sys ems ha ely on sma senso s and elec onic
de ices. This ma ks a depa u e om adi ional app oaches, o e ing mo e e icien and
ad anced ways o moni o and egula e elec ical dis ibu ion [2].
Sma g id senso s p o ide eal- ime, accu a e, and eliable da a o measu ing, moni-
o ing, and sa egua ding he ne wo k. In Medium-Vol age (MV) sma subs a ions, hese
senso s con e high ol age and cu en in o a mo e manageable ange, emo ing he
necessi y o ol age di ide s o cu en shun s. This simpli ies measu emen sys ems and
enhances accu acy. Moni o ing ol age and cu en om hese senso s is undamen al o
assessing powe quali y [3].
Low-powe cu en ans o me s (LPCTs) a e being widely implemen ed in he MV
sma g id o ansmi digi al cu en da a di ec ly om cables o moni o ing, p o ec ion,
and managemen sys ems.
LPCTs a y acco ding o hei wo king p inciple, which includes bu is no limi ed o
RCs, luxga es, and shun esis o s.
This wo k places pa icula emphasis on RC cu en senso s, one o he mos p omi-
nen ypes o LPCTs. RCs ha e inc easingly supplan ed adi ional cu en ans o me s in
a ious applica ions, including powe sys em cu en measu emen o p o ec i e elay-
ing [4,5], aul loca ion de ec ion [6,7], and cap u ing as ansien s [8].
Ene gies 2023,16, 7323. h ps://doi.o g/10.3390/en16217323 h ps://www.mdpi.com/jou nal/ene gies
Ene gies 2023,16, 7323 2 o 13
The digi al subs a ion cu en ly uses an LPCT wi h a digi al ou pu ha has a commu-
nica ion in e ace o is inco po a ed wi h he MU. Low-Powe Ins umen T ans o me s
(LPITs) a e used in conjunc ion wi h MUs as a measu ing ool in upg aded MV ne wo k
moni o ing sys ems because o hei high lexibili y and low cos .
The MU implemen s IEC 61850 s anda ds a he p ocess le el. I digi alizes ol age and
cu en da a om ans o me s (LPVTs o LPCTs) in o sampled alues (SV), imes amps
hem, and sends hem o e an E he ne p ocess bus [9].
Despi e hei ad an ages, RC measu emen accu acy can be a ec ed by ac o s like
empe a u e, conduc o posi ion, and ex e nal dis u bances. Consequen ly, i is essen ial
o calib a e he RC o ma ch eal-wo ld measu emen condi ions. Calib a ion iden i ies
e o s like a ios and phase e o s, imp o ing senso pe o mance in measu emen s and
p o ec ion, educing isks, and a oiding ope a ional delays and imp ope ac ions. Mo e-
o e , calib a ing RCs wi h digi al ou pu in ol es assessing MU pe o mance speci ica ions,
as he accu acy o elec ical pa ame e measu emen s is closely ied o he iming p ecision
o SV measu emen s [9].
Fi s ly, he calib a ion o RCs is ypically able o de e mine he a io e o and phase
e o o he LPCT du ing he adi ional calib a ion p ocedu e by compa ing he ou pu o
he ans o me unde es wi h ha o he e e ence ans o me a e applica ion o he
same exci a ion cu en o he p ima ies o he wo ans o me s.
Simila ly, RCs wi h digi al ou pu s can be calib a ed wi h some necessa y modi ica-
ions. The digi al ou pu o he RC is ma hema ically compa ed wi h he ou pu o he
e e ence ans o me , which mus be digi ized. The ma hema ical compa ison is based
on he con e sion o he compa ed signals in o he equency domain by Fas Fou ie
T ans o m (FFT). The a io and displacemen e o s o he senso unde calib a ion a e
e alua ed o he undamen al equency o o he equencies.
Va ious calib a ion me hods o RCs a e a ailable and can be ound in he lis ed
e e ences. Fo ins ance, in e e ence [
10
], calib a ion o RCs is ca ied ou o assess he
in luence o empe a u e, humidi y, and posi ioning on powe quali y accu acy, bu hese
calib a ion me hods a e p ima ily designed o RCs wi h analogue ou pu .
Calib a ing RCs wi h digi al ou pu was in oduced in [
11
,
12
] using 16-bi digi al
ol me e s ins ead o highe esolu ion equipmen . This calib a ion p ocess is ela i ely
s aigh o wa d bu may no o e su icien accu acy and can be cos ly due o he equi e-
men o wo sampling ol me e s o digi izing compa a i e signals.
The widesp ead use o RCs alongside MUs in subs a ions o c ea e digi al in e aces
has made i c ucial o e alua e he pe o mance o his combina ion o compa ibili y
and unc ionali y. Su p isingly, he calib a ion o RCs wi h digi al ou pu using MUs has
ecei ed limi ed esea ch a en ion, e en hough many s udies ha e ocused on calib a ing
MUs independen ly.
Fo example, e e ences [
9
,
13
,
14
] p o ided a calib a ion me hod o MUs by compa -
ing each measu emen sample om he MU wi h hose om a e e ence digi ize . This
calib a ion p ocess necessi a es p ecise de ice synch oniza ion. Synch oniza ion is accom-
plished h ough he use o he Ne wo k Time P o ocol (NTP) and Pulses Pe Second (PPS)
p o ocols, which can p o ide accu acy in he o de o mic oseconds. Fu he imp o emen s
in iming accu acy can be achie ed by using o he p o ocols like he P ecision Time P o ocol
(PTP) [15], also known as IEEE 1588 [16].
In ligh o he p eceding in o ma ion, his pape in oduces a calib a ion app oach o
measu ing he RC + MU. This app oach is inspi ed by he li e a u e ha explo es calib a ing
he LPCT + MU [17–19].
The calib a ion p esen ed in [
17
] was achie ed using a b oad dynamic ange Da a
Acquisi ion (DAQ) sys em wi h a 24-bi analogue- o-digi al (A/D) con e e . Howe e , i
equi ed he addi ion o a signal con e e o adap he Re e ence T ans o me (RT) signal
o he DAQ ca d inpu ange, which may sligh ly educe he calib a ion sys em’s accu acy
due o he in oduc ion o addi ional de ices.
Ene gies 2023,16, 7323 3 o 13
Re e ence [
19
] imp o ed he compa a o me hod by eplacing a con en ional ans-
o me wi h a s anda d cu en senso in he e e ence channel. Ye , o coun e accu acy
issues ela ed o magne ic sa u a ion, hey added an addi ional clamp-shaped senso
wi hou a magne ic co e, inc easing design complexi y.
The key con ibu ion o his s udy lies in he assessmen o accu acy achie ed by
u ilizing a high-sensi i i y and high-p ecision e e ence senso , e en a high measu ed
cu en le els, as opposed o adi ional cu en ans o me s. Addi ionally, we del e
in o he necessa y implemen a ion p e equisi es, including compliance wi h he IEEE
1588 p o ocol o p ecise ime synch oniza ion. The calib a ion p ocess encompasses
bo h s eady-s a e and abno mal condi ions, ensu ing a comp ehensi e assessmen o he
sys em pe o mance.
Finally, i should be men ioned ha he accu acy o he calib a ion can be a ec ed by
sou ces o unce ain y ela ed o he equipmen used, i.e., he highe he accu acy o he
de ices included in he calib a ion sys em, he be e he accu acy class in he calib a ion
sys em. The unce ain y calcula ion can be pe o med using Mon e Ca lo simula ion [
20
]
o acco ding o he ISO guide e e ed o as GUM [
21
]. The Mon e Ca lo me hod is a
p obabilis ic modelling and simula ion echnique ha employs p obabili y dis ibu ions o
inpu a iables o es ima e unce ain y. I excels in handling complex and unce ain sys ems
by di ec ly simula ing he measu emen p ocess. In con as , GUM o e s a sys ema ic
app oach o es ima e and exp ess unce ain y in measu emen s, employing a combina ion
o analy ical and s a is ical me hods. I en ails iden i ying sou ces o unce ain y, assessing
hei impac s, and p opaga ing hese unce ain ies h ough ma hema ical models.
In his pape , we diligen ly assessed he po en ial con ibu ions o unce ain y and
hei implica ions on he calib a ion esul s, adhe ing o he GUM guidelines ins ead o
eso ing o he Mon e Ca lo simula ion [20].
2. Digi al LPCT in he MV Subs a ion
Subs a ion au oma ion sys ems ha e signi ican ly ad anced in ecen yea s due o
he o al digi aliza ion o all in o ma ion collec ed, communica ed, and p ocessed a
he subs a ion.
The digi al elec ical signal acquisi ion echnology based on an elec onic ans o me
is no longe eliable o su icien o sa is y he ansi ion needs o sma subs a ions o a
widesp ead powe sys em. Combining ans o me s and MUs is a p ac ical al e na i e o
sampling cu en s/ ol ages and sha ing hem wi hin he sma subs a ion.
The h ee-phase cu en o he dis ibu ion line in he MV subs a ion is now being
measu ed using LPCTs. The co e componen s o he digi al LPCT include an analogue
senso and a signal MU.
The choice o LPCT senso o MV cu en measu emen s is in luenced by wo key
ac o s: he accu acy class and he p ice. MV senso s ypically ha e an accu acy class limi o
1%, al hough he e a e ins ances whe e 0.5% o e en 0.2% accu acy is necessa y, especially
o a i me e ing applica ions. Among he a ailable op ions, Ins umen T ans o me s
(ITs), RCs, and shun esis o s eme ge as op choices o use in MV ne wo ks due o hei
balanced pe o mance in e ms o accu acy and cos conside a ions.
The non-linea i y o cu en ans o me s (CTs) and he cons ained ope a ing ange
imposed by he magne ic sa u a ion pose signi ican challenges when used in MV applica-
ions. Shun esis o s also ha e he d awback o no o e ing su icien and eliable gal anic
isola ion. RCs a e he p e e ed ype o LPCTs due o hei bene icial cha ac e is ics, includ-
ing simplici y o measu emen and he absence o he necessi y o open he MV connec ion
while adding o emo ing he senso . RCs a e an AC measu ing ansduce made up o
uni o mly wounded coils ha ing a nonmagne ic co e. The coil is used o measu e cu en
by w apping i a ound he conduc o ha holds he cu en .
The absence o an i on co e in he RC elimina es he sa u a ion e ec , esul ing in a
linea ela ionship be ween he measu ed p ima y cu en and he seconda y ol age. The
ou pu ol age is di ec ly p opo ional o he de i a i e o he p ima y cu en .
Ene gies 2023,16, 7323 4 o 13
Because he RC ou pu ol age is p opo ional o he u ns’ a ea, RC inaccu acy may
a ise o se e al easons, including:
•
Non-Uni o m Tu n Densi y: The wi e used o c ea e he coil is ex emely hin, leading
o a ia ions in he densi y o u ns.
•
Incomple e Closu e: The coil may no be en i ely closed, impac ing he de ec ion o
he ou pu ol age Us.
•
Tu n I egula i y: I egula i ies in he a angemen o u ns a e especially p onounced
nea he coil end and a e o en he p ima y sou ce o inaccu acy.
Due o all hese es ic ions, he RC sensi i i y is no independen o i s ela i e posi ion
and inclina ion. Mo eo e , pa asi ic capaci ances, including conduc o - o-coil, u n- o- u n,
and ou pu cable- o-g ound capaci ance, all ha e an impac on he equency esponse o
he RC. This in luence can limi he bandwid h o he RC senso . Hence, manu ac u e s
should calib a e hese senso s be o e eleasing hem o he ma ke o educe he possibili y
o inaccu acies.
In digi al subs a ions, he RC senso connec ed o he MV connec o measu es cu -
en s. These analogue cu en measu emen s a e subsequen ly ga he ed, digi ized, and
ansmi ed o me e ing o p o ec ion sys ems h ough an MU. The MU se es as a physical
in e ace ha links p ocess equipmen (e.g., ans o me s and senso s) o bay-le el de ices
(including moni o ing and p o ec ion sys ems). Acco ding o IEC 61850-2 [
22
], MU is mean
o cap u e cu en and ol age signals om ans o me s/senso s and con e hem in o
he s anda d digi al ou pu o ma . The me ging uni s can be equipped wi h analogue
inpu s o connec ion o con en ional CT/VT o wi h analogue inpu s plus bina y I/O o
connec ion o senso s.
IEC 61869-13 [
23
] de ines he a ed analogue inpu s as 1/5 A and 100–200 V o CTs
and VTs, espec i ely. Addi ionally, he s anda d de ines he a ed bina y inpu s as
22.5 mV,
150 mV, and 225 mV o LPCTs and 3.25 V o LPVTs.
IEC 61869-9 de ines sample a es as 4.8 kHz o measu ing and p o ec i e applica ions
and 14.4 kHz o quali y measu emen applica ions.
The MU suppo s he p ocess bus (IEC 61850-9-2 LE [
24
]) by ans e ing sampled
alues o measu ed cu en s/ ol ages in he o m o da a packe s o e he Local A ea
Ne wo k (LAN). This allows o he ins alla ion o me e ing sys ems in he con ol oom
and he use o he E he ne ne wo k o ad anced subs a ion da a ansmission.
MU con ains an inbuil eal- ime clock ha is used o imes amp he measu ed da a.
The eal- ime clock may be ee- unning o synced om an ex e nal signal such as PPS,
bu he bes is he PTP. Due o he imes amps embedded in each SV, he IED ecei e can
dis inguish and a ange all SV packe s a i ing om a single MU o e en mul iple MUs in
ch onological o de be o e p ocessing hem.
I should be no ed ha he digi al ou pu o en lags he inpu signal due o imes amp
delay. Addi ionally, encapsula ing he sampled alue in o E he ne da a may esul in a
delay known as MU p ocess delay ime. Thus, inco ec MU da a esul in inaccu a e sha ed
in o ma ion wi h simul aneous IEDs leading o inaccu a e elec ical powe measu emen
and he c i ical unc ion ailu e o he p o ec ion sys em.
The IEC 61850-5 [
25
] s anda d o sma g ids ou lined he ime p ecision c i e ia o
he ime ag o e en s and ime-synch onized measu emen s in i e ime pe o mance
classes, T1 o T5, anging om 1 ms o 1 µs as shown in Table 1.
Table 1. Time synch oniza ion classes.
Time Class Synch oniza ion Accu acy
T1 1 ms
T2 0.1 ms
T3 ±25 µs
T4 ±4µs
T5 ±1µs
Ene gies 2023,16, 7323 5 o 13
The a ia ions among IEDs s em om he synch oniza ion p o ocols used. These
p o ocols synch onize he IED clock wi h he ne wo k and main ain i s accu acy o a
speci ic p ecision.
Ne wo k-based synch oniza ion p o ocols, such as he Ne wo k Time P o ocol (NTP)
and he Simple Ne wo k Time P o ocol (SNTP), o e insu icien synch oniza ion accu acies
o 10−1ms, making hem unsui able o synch onizing all IED subs a ions.
The mos demanding subs a ion applica ions, such as he IEC 61850-9-2 p ocess bus,
can be me by he IEEE 1588 ne wo k-based ime synch oniza ion p o ocol ha has sub-
mic osecond accu acy.
The bene i o PTP synch oniza ion is ha i elimina es he equi emen o addi ional
wi es ha a e ypically equi ed wi h he IRIG-B o PPS and ins ead uses he E he ne
ne wo k o communica e wi h he synch oniza ion signal [
16
]. PTP is able o au oma ically
iden i y and co ec he dynamic ne wo k ime delays o each da a packe ha may ha e
ex a delay om ne wo k componen s such as swi ches. Due o he anspa en clock
in oduced by IEEE 1588, he ime equi ed o pass h ough he swi ch is measu ed, and
he clock ecei ing he PTP message is in o med o his ime.
Howe e , synch oniza ion inaccu acy can occu o a ew easons, such as he synch o-
niza ion signal being co up ed wi hin he MU o no being able o each he sou ce ( he
GPS ecei e ). Thus, he MU digi al ou pu may lag he inpu signal due o a imes amping
delay. Addi ionally, encapsula ing he sampled alue in o E he ne da a may esul in a
delay known as MU p ocess delay ime. When he ime o he MU da a is inco ec , i can
lead o inaccu a e sha ed in o ma ion wi h simul aneous IEDs and cause inco ec elec ical
powe measu emen . This, in u n, can lead o he c i ical unc ion ailu e o he p o ec ion
sys em. Hence, i is c ucial o pe o m MU calib a ion egula ly. This calib a ion helps
es ima e synch oniza ion pa ame e s and compensa es o any possible e o s, ensu ing
accu a e esul s.
3. Digi al LPCT Calib a ion
I is impo an o unde s and ha he eadings o a de ice o a ce ain quan i y can
a y o e ime due o se e al ac o s such as empe a u e, humidi y, powe supply ol age,
and elec omagne ic in e e ence. Also, sudden changes in he inpu quan i y can a ec he
ins umen pe o mance du ing and a e hose changes. The e o e, he measu ed cu en
may no be a pe ec sine wa e. Thus, i is c ucial o ha e a acking p ocess o he cu en
measu ing chain.
T aceabili y is de ined as a con inuous chain o pe missible compa isons ha bind he
measu ing de ice o na ional o in e na ional ins umen s anda ds.
In gene al, compa ing he LPCT wi h a s anda d cu en measu ing ins umen in
a labo a o y se ing is c i ical o ensu e he accu acy o he cu en measu emen . The
objec i e o ou ine LPCT accu acy calib a ion is o alida e he eliabili y o i s pe o mance
in e ms o accu acy and bandwid h a e a pe iod o ope a ion. The calcula ion o he a io
di e ence and phase di e ence is used o assess accu acy calib a ion.
The LPCT pe o mance can a y unde he in luence o di e en ypical ac o s. Cali-
b a ion becomes mo e challenging when he LPCT is subjec o he simul aneous in luence
o mul iple ac o s [10].
3.1. Calib a ion Me hod
The aim o his s udy is o enhance ou unde s anding o he accu acy and pe o mance
o RC when used in conjunc ion wi h an MU. To achie e his, he wo k p oposes a simple
calib a ion me hod o RCs wi h a digi al ou pu ha can be used in an academic o
indus ial en i onmen . An app op ia e calib a ion in as uc u e has been es ablished o
assess he accu acy o he digi al cu en a he nominal cu en as well as a alues abo e
and below he nominal cu en . I is no ewo hy ha , in he pu sui o p ecise ope a ing
condi ions, we made e o s o main ain consis en ambien empe a u e and humidi y
le els. Fu he mo e, o minimize he po en ial impac o elec omagne ic in e e ence on

Ene gies 2023,16, 7323 6 o 13
he RC pe o mance, we inc eased he dis ance be ween he RC and he e e ence senso
and implemen ed shielding measu es a ound nea by ex e nal conduc o s.
The calib a ion s uc u e diag am is shown in Figu e 1, and i comp ises he ollowing:
•
Cu en gene a o (Omic on CMC 356): I p o ides a sinusoidal analogue cu en
signal, which ep esen s he high cu en o be measu ed.
•
Calib a ion channel: I consis s o an RC and an MU. The comme cial RC is an
80/150 mV
(a 50 Hz) ansduce , used o MV measu emen pu poses wi h accu acy
class 0.5. The MU gene a es SVs a e ecei ing he analogue cu en measu ed by he
RC senso .
•
S anda d channel: I consis s o a Re e ence Cu en T ansduce (RCT) and a highly
accu a e e e ence digi ize 24-bi esolu ion ADC. The e e ence senso is a comme cial
luxga e ansduce ha has he ollowing ea u es: Nominal inpu cu en 600 A,
ans o ma ion a io 1500:1. The digi ize consis s o an NI PXI-4472 digi izing module
and an NI PXI-6682 iming boa d. The NI PXI-4472 ea u es a 24-bi a chi ec u e,
±10 V inpu , and a sampling a e o 102.4 kS/s.
•
The calib a ion pla o m: This is a se o compu e p og ams ha cap u e and analyze
digi al ou pu om channels, as well as an e o calcula ion algo i hm based on he
di e en ial me hod.
•
GPS synch oniza ion ecei e : I gene a es he ime synch oniza ion signal o accu a e
synch oniza ion be ween sampling equipmen by uning i s clock oscilla o ia PPS o
PTP p o ocols.
•
PTP ne wo k: This is a LAN con igu ed wi h PTP and is used as a synch oniza ion
sou ce as well as a sha ing ne wo k o ansmi he da a o he MU and PXI o he
calib a ion pla o m o e o calcula ion.
Ene gies 2023, 16, 7323 6 o 13
3.1. Calib a ion Me hod
The aim o his s udy is o enhance ou unde s anding o he accu acy and pe o -
mance o RC when used in conjunc ion wi h an MU. To achie e his, he wo k p oposes a
simple calib a ion me hod o RCs wi h a digi al ou pu ha can be used in an academic
o indus ial en i onmen . An app op ia e calib a ion in as uc u e has been es ablished
o assess he accu acy o he digi al cu en a he nominal cu en as well as a alues
abo e and below he nominal cu en . I is no ewo hy ha , in he pu sui o p ecise op-
e a ing condi ions, we made effo s o main ain consis en ambien empe a u e and hu-
midi y le els. Fu he mo e, o minimize he po en ial impac o elec omagne ic in e e -
ence on he RC pe o mance, we inc eased he dis ance be ween he RC and he e e ence
senso and implemen ed shielding measu es a ound nea by ex e nal conduc o s.
The calib a ion s uc u e diag am is shown in Figu e 1, and i comp ises he ollow-
ing:
• Cu en gene a o (Omic on CMC 356): I p o ides a sinusoidal analogue cu en
signal, which ep esen s he high cu en o be measu ed.
• Calib a ion channel: I consis s o an RC and an MU. The comme cial RC is an 80/150
mV (a 50 Hz) ansduce , used o MV measu emen pu poses wi h accu acy class
0.5. The MU gene a es SVs a e ecei ing he analogue cu en measu ed by he RC
senso .
• S anda d channel: I consis s o a Re e ence Cu en T ansduce (RCT) and a highly
accu a e e e ence digi ize 24-bi esolu ion ADC. The e e ence senso is a comme -
cial luxga e ansduce ha has he ollowing ea u es: Nominal inpu cu en 600
A, ans o ma ion a io 1500:1. The digi ize consis s o an NI PXI-4472 digi izing
module and an NI PXI-6682 iming boa d. The NI PXI-4472 ea u es a 24-bi a chi ec-
u e, ±10 V inpu , and a sampling a e o 102.4 kS/s.
• The calib a ion pla o m: This is a se o compu e p og ams ha cap u e and analyze
digi al ou pu om channels, as well as an e o calcula ion algo i hm based on he
diffe en ial me hod.
• GPS synch oniza ion ecei e : I gene a es he ime synch oniza ion signal o accu-
a e synch oniza ion be ween sampling equipmen by uning i s clock oscilla o ia
PPS o PTP p o ocols.
• PTP ne wo k: This is a LAN con igu ed wi h PTP and is used as a synch oniza ion
sou ce as well as a sha ing ne wo k o ansmi he da a o he MU and PXI o he
calib a ion pla o m o e o calcula ion.
Figu e 1. S uc u e o he measu emen bench o he calib a ion o he es se .
RC calib a ion is based on high cu en loop gene a ion employing a coaxial bus ba
wi h bo h an RC and RCT o educe unce ain ies caused by conduc o posi ion. The RC
Figu e 1. S uc u e o he measu emen bench o he calib a ion o he es se .
RC calib a ion is based on high cu en loop gene a ion employing a coaxial bus ba
wi h bo h an RC and RCT o educe unce ain ies caused by conduc o posi ion. The RC
ou pu is connec ed o an MU ha c ea es cu en SVs based on he IEC 61850-9-2 LE
s anda d a a a e o 80 samples/second. The MU sends cu en SVs o he PTP-LAN
ne wo k wi h imes amps a he ele an sampling ime. Simila ly, he RCT ou pu is
digi ized and acqui ed h ough he NI PXI-4472 Da a Acquisi ion Boa d (DAB). The NI PXI-
4472 ADC clock oscilla o is also d i en by PTP, allowing o imp o ed signal digi iza ion
and enhancing compa ison alidi y.
On he calib a ion pla o m, he e is a se o compu e so wa e ha cap u es cu en
samples o MU and DAB samples.
•
The Sampled Value Analyze (SVA 0.93) so wa e was c ea ed and de eloped a he
B no Uni e si y o Technology o he high-accu acy cap u e o SV packe s, decoding
and eco ding hem o a ile, and p o iding eal- ime wa e o ms o measu ed cu en .
Ene gies 2023,16, 7323 7 o 13
The eco ding ile con ains he SV ID, MAC des ina ion, MAC sou ce, and sample
imes amps. SVA can also show he s a us o da a loss.
•
The Lab View g aphical p og am can acqui e da a, eco d da a, and display he
wa e o m o he RCT cu en . LabView may addi ionally cap u e he MU signal
in synch onized mode. The eco ding ile con ains sample imes amps o he RCT
digi ized signal.
•
The MATLAB p og am is used o c ea e he essen ial analysis ool equi ed o execu e
he LPCT e o calcula ion algo i hm.
3.2. Calib a ion Algo i hm
The algo i hm o es ima e he composi e e o o an LPCT wi h a digi al ou pu is based
on he a ia ions be ween each measu emen sample o he synch onized MU and RC. The
composi e e o o he measu ing chain can be exp essed acco ding o IEC61869-9 [
26
] as:
εc%=
u
u
u
u
u
u
N
∑
n=1iX(n)−iR(n)2
N
∑
n=1iR(n)2·100 (1)
whe e iX(n) is he ac ual ins an aneous alue o he MU a he sampling ime;
iR(n) is he ac ual ins an aneous alue o he RC a he sampling ime;
Nis he nominal sample a e (samples pe second) di ided by he undamen al
equency (Hz).
Mo eo e , he ampli ude e o is simply calcula ed using he a io o he di e ence
be ween he oo mean squa e (RMS) o he cu en signal measu ed by he MU and
RC o he RMS o he cu en measu ed by he RC du ing each pe iod. Howe e , he
de e mina ion o he phase e o is sligh ly mo e complex. Thus, he Fas Fou ie T ans o m
(FFT) should be pe o med on MU and RC samples.
IEC61869-9 de ined he a io/phase e o o he measu ing chain using FFT on he
samples as:
→
ε(s) =
√2
N
N
∑
n=1iX(n)−iR(n)e−j2πn
Nk
sN−1
∑
n=1iR(n)2
(2)
whe e →
ε(s)is he a io e o and he phase e o o he measu ing chain;
kis he numbe o ha monics being measu ed (k= 1 o he undamen al).
The FFT algo i hm s a s by subdi iding he o iginal se o measu emen da a, which
consis s o da a ga he ed synch onously om he MU and RC a a sampling a e o
4 kHz,
in o nsubwindows wi h 97.5% o e lap con aining
80 samples
(each pe iod con-
ains
80 samples,
so ha each subsequen pe iod has an o e lap o 78 samples om he
p e ious pe iod).
The ampli ude/phase o he undamen al ha monic o each signal is ob ained by
pe o ming FFT analysis a each subwindow. The ampli ude/phase di e ences o each
pe iod a e de e mined using he di e en ia ion me hod be ween he wo alues ha a e
gi en by he FFT a he signal equency componen (50 Hz) o bo h he MU and RC.
A e calcula ing he di e ences o each pe iod in he measu emen windows, he
di e ences a e a e aged o e nwindows, which gi es he inal alues o he ampli ude/
phase e o s.
Ra ioE o =1
N
N
∑
n=1 I1 ms,X(n)−I1 ms,R(n)
I1 ms,R(n)!·100% (3)
Ene gies 2023,16, 7323 8 o 13
PhaseE o =1
N
N
∑
n=1
(ϕ1X(n)−ϕ1R(n))(4)
whe e I
1 ms,X(n)
and I
1 ms,R(n)
a e he RMSs o he i s ha monic o he cu en signal o he
MU and RC, espec i ely, a he n h sub-window;
ϕ1X(n)
and
ϕ1R(n)
a e he phases o he i s ha monic o he cu en signal o he MU
and RC, espec i ely, a he n h sub-window;
Nis he o al numbe o subwindows.
Simila ly, he algo i hm is also capable o es ima ing ype-A measu emen unce ain-
ies, because he mean and s anda d de ia ions o he ampli ude and phase e o s can also
be compu ed [14].
3.3. Ta ge Unce ain y o LPCT Calib a ion
The e o ep esen s he di e ence be ween he measu ed alue and he ue o
e e ence alue. Unce ain y exp esses he eliabili y o he measu ed alue. Unce ain y is
o en desc ibed as a ange o in e al wi h a co esponding con idence le el o p obabili y.
I indica es how ce ain i is ha he eal alue alls wi hin ha speci ied ange. The
unce ain y alue consis s o se e al elemen s ha a e es ima ed using a ious s a is ical
dis ibu ions o he measu emen da a. These elemen s include sys ema ic and andom
in luences on he measu emen s.
Acco ding o [
27
], he le el o unce ain y necessa y o he calib a ion o LPCT is
iden i ied by he accu acy class o he calib a ed ansduce i sel .
IEC 61869-6 de ined ha each accu acy class o he LPCT has limi s ha should no be
exceeded by he a io/phase e o , wi hou men ioning any a ge unce ain y o he e o
measu emen s [28].
Linea i y, empe a u e and empo al s abili y, s anda d calib a ion, and o he ac o s
ha ha e a signi ican impac on LPCT e o measu emen s mean ha he p obabili y dis-
ibu ion o he unce ain y ha impac s he calcula ed a io/phase e o can be conside ed
no mal [29].
The unce ain y sou ces o igina e om e e y de ice used o LPCT calib a ion, and he
e ec s o hese sou ces p opaga e h oughou he measu emen chain, causing inaccu acies
in he a io/phase e o assessmen . The ollowing sou ces o unce ain y a e he key
ac o s ha limi he accu acy o he measu emen in ou calib a ion se up.
•
Unce ain y induced by he RCT a io and phase e o : The RCT should ha e an
accu acy class ha is app op ia ely lowe han ha o he RC o be calib a ed. The
con ibu ion o RCT is he ampli ude e o o
±
0.05% and he phase e o o 0.35 m ad.
•
The unce ain y caused by he e e ence analogue- o-digi al con e e o PXI gain and
phase e o . The con ibu ion o PXI-4472 is he ampli ude e o
±
0.025% and he
phase e o 0.4 m ad.
•
The unce ain y caused by he digi al alue cap u e p og ams. The con ibu ion o
SVA is he ampli ude e o o 4.7 ×10−6and he phase e o o 0.1 m ad.
A ype-B e alua ion can be used o es ima e each o he abo e-men ioned elemen s.
3.4. Unce ain y Calcula ion
The unce ain y analysis in his wo k is calcula ed by linea e o p opaga ion acco d-
ing o he ollowing equa ions.
uc(y) =
u
u
N
∑
i=1
c2
i·u2(xi)(5)
wi h u
c
(y) being he s anda d unce ain y, c
i
a e he sensi i i y coe icien s, and u(x
i
)a e he
s anda d unce ain ies o he inpu quan i ies Xi.
Ene gies 2023,16, 7323 9 o 13
The e o e, he s anda d measu emen unce ain ies o he LPCT calib a ion uc o
measu emen s a nominal cu en and 50 Hz a e calcula ed by:
uc(y) = qu2(RCT) + u2(PXI) + u2(SVA)(6)
wi h u(RCT),u(PXI), and u(SVA) being he indi idual s anda d unce ain ies o unce ain y
sou ces.
The expanded unce ain y o he desi ed con idence le el can be calcula ed as
U=k·uc(y)(7)
wi h kbeing he co e age ac o ha can be k= 2 o he co e age p obabili y o 95.45% o
k= 3 o he co e age p obabili y o 99.73%.
4. Resul s
The linea i y measu emen o he LPCT made up o RC + MU was pe o med unde
no mal and abno mal ope a ing condi ions.
The desc ibed p ocedu e was used o calcula e he e o s o he measu ing chain a
he p ima y cu en s o 16 A, 40 A, 80 A, and 96 A wi h a equency o 50 Hz.
Du ing each es , whe e a single cu en alue is applied o bo h senso s simul ane-
ously, digi al samples o he measu ed cu en gene a ed by bo h channels a e eco ded o
a pe iod o no less han 6 s. Each measu emen consis s o 4000 samples o a
200 ms
win-
dow wi h a leas 300 epe i ions. Then, he MATLAB en i onmen was used o calcula e
he e o s be ween Fou ie - ans o med cu en signals.
The e o s be ween he samples o he wo cu en signals a e calcula ed acco ding o
Equa ions (3) and (4).
Following he applica ion o he FFT algo i hm and subsequen pa i ioning o he
measu emen da a in o subwindows, a minimum o 11,960 alues we e ob ained o each
measu ed cu en . Subsequen ly, 11,960 alues we e iden i ied o bo h phase e o and
angle e o .
Due o he signi ican olume o alues ep esen ing di e ences be ween he wo
cu en signals, i became impe a i e o u ilize s a is ical analysis o he calcula ion o
mean e o and s anda d de ia ion.
The ini ial esul s we e de i ed om es s conduc ed unde s eady-s a e condi ions,
whe e he measu ed cu en was main ained a he nominal le el (80 A) and he equency
a he nominal a e (50 Hz). Subsequen ly, he es ima ed P obabili y Densi y Func ion (PDF)
o he a io e o
ε
% can be obse ed in Figu e 2a, and he es ima ed PDF o he phase
e o
δ
is shown in Figu e 2b. The e o s o his measu ing chain a e a a io e o o
−
0.26%,
phase e o o 0.021 ad, and composi e e o o 2.2%.
Ene gies 2023, 16, 7323 10 o 13
(a) (b)
Figu e 2. His og am o he e o s a nominal cu en . (a) PDF o a io e o ; (b) PDF o he phase
e o .
In acco dance wi h he Cen al Limi Theo em, i can be in e ed om hese da a ha
he PDFs end o ollow a no mal dis ibu ion, assuming ha he measu emen p ocess is
linea .
I is essen ial o highligh ha he dis ibu ion o he phase e o appea s o be no -
mal, which is in con as o he assump ion o a uni o m dis ibu ion o en made when
employing he Mon e Ca lo me hod [29].
To p o ide a mo e comp ehensi e iew o he es esul s, he expe imen was dupli-
ca ed unde abno mal ope a ing condi ions. This in ol ed using cu en alues ha ex-
ceeded he nominal cu en by 120% and lowe cu en s, speci ically 5% and 50% below
he nominal cu en . Subsequen ly, he e o s o each measu emen we e calcula ed, and
he summa ized esul s can be ound in Table 2.
Table 2 indica es ha a cu en s diffe en om he nominal cu en , he e o is ela-
i ely g ea e compa ed o when he cu en is a he nominal alue.
I is wo h no ing ha he unce ain y men ioned in Table 2 indica es ha he o al
unce ain y is caused by he measu ing de ices and he measu emen chain (RC + MU).
Table 2. Resul s o measu emen chain e o s.
Cu en Quan i y Mean Value S anda d De ia ion
16 A
50 Hz
ε% −0.17 0.22
Δ [ ad] 0.022 0.0021
40 A
50 Hz
ε% −0.162 0.125
Δ [ ad] 0.0216 0.00122
80 A
50 Hz
ε% −0.16 0.12
Δ [ ad] 0.021 0.0012
96 A
50 Hz
ε% −0.18 0.08
Δ [ ad] 0.021 0.0008
Fo unce ain y calcula ion, he e o s ha could con ibu e o unce ain y, ob ained
om he manu ac u e ’s b ochu es o each de ice, we e conside ed.
The unce ain y in he measu emen p ocess was calcula ed acco ding o Equa ion
(6). The ex ended s anda d unce ain y o measu emen caused by measu emen equip-
men is calcula ed as:
222
() 2 ( ) ( ) ( )
333
RCT SVA
PXI
c
uy
εε
ε
=⋅ + + (8)
whe e εRCT, εPXI, and εSVA a e he maximum e o s o he RCT, PXI, and SVA, espec i ely.
Figu e 2.
His og am o he e o s a nominal cu en . (
a
) PDF o a io e o ; (
b
) PDF o he
phase e o .