Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
A ailable online 10 Feb ua y 2024
0142-0615/© 2024 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/).
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In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems
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A g id o ming con olle wi h in eg a ed s a e o cha ge managemen o
V2G cha ge s
Ande O dono a,∗, F ancisco Ja ie Asensioa, Jose An onio Co aja enab, Inmaculada Zamo a c,
Mikel González-Pé ez a, Gaizka Saldaña c
aDepa men o Elec ical Enginee ing, Uni e si y o he Basque Coun y (UPV/EHU), A d. O aola, 29, Eiba , 20600, Spain
bDepa men o Elec onic Technology Enginee ing, Uni e si y o he Basque Coun y (UPV/EHU), A d. O aola, 29, Eiba , 20600, Spain
cDepa men o Elec ical Enginee ing, Uni e si y o he Basque Coun y (UPV/EHU), Alameda U quijo, s/n, Bilbao, 48013, Spain
ARTICLE INFO
Keywo ds:
Elec ic ehicle
F equency egula ion
G id o ming
V2G
ABSTRACT
Vehicle- o-g id (V2G) echnology o e s an inno a i e solu ion o p o ide g id se ices using elec ic ehicle
(EV) ba e ies. This wo k p oposes a no el g id o ming (GFM) con olle o V2G applica ions which can
ensu e he ol age sou ce beha iou and p o ide suppo o he g id, ega dless o he s a e o cha ge (SoC)
and he cha ging equi emen s o he ba e y. This is achie ed by in eg a ing a SoC con olle ha modi ies
he classical GFM algo i hm. The con olle only elies on he SoC and powe measu emen s, achie ing a
decen alized wi hou he need o communica ion. Wi h he p oposed app oach, he V2G cha ge will always
beha e as a ol age sou ce ha p o ides ine ial esponse and ol age suppo o he g id. The p ima y
equency egula ion, on he o he hand, will depend on he ba e y s a us and cha ging needs. F equency
egula ion could be enabled, disabled o i could be limi ed o some pe u ba ions (unde /o e equencies).
Mo eo e , he SoC con olle p o ides eedom o une he equency suppo o he de ice, limi ing i o
ine ial esponse o ex ending i s con ibu ion along he ime. The uning o he sys em pa ame e s is add essed
in de ail o ensu e a damped esponse unde all he ope a ion scena ios p o ided by he SoC con olle . I s
pe o mance and s abili y is e alua ed using small signal ans e unc ions. Finally, i is alida ed bo h in
simula ion and expe imen ally.
1. In oduc ion
In he ecen yea s, powe g ids a e in eg a ing inc easing amoun s
o non-dispa chable enewable ene gy sou ces (RES), shi ing owa ds
a mo e en i onmen ally iendly g id. Howe e , new challenges a ise
due o he pa adigm shi [1]. On he one hand, he g id managemen
complexi y inc eases due o he s ochas ic beha iou and he educed
powe ese es o RES [2]. On he o he hand, as he kine ic ene gy
s o ed in o a ing masses o con en ional plan s (ine ia) is eplaced
by in e e -based RES, he g id u ns weake and p one o bigge
and as e ol age and equency excu sions [3]. All in all, he g id
pa adigm shi leads o a mo e dynamic and complex g id powe
managemen [4].
In his scena io, g id ope a o s a e implemen ing s a egies o en-
su e g id s abili y and eliabili y. Ene gy S o age Sys ems (ESS), de-
mand managemen and RES cu ailmen a e among he mos ele an
app oaches o p o ide lexibili y [5]. Rela ed o ESS, Vehicle- o-G id
(V2G) has also a isen as a p omising solu ion [6]. V2G cha ge s enable
bidi ec ional ene gy low be ween elec ic ehicles (EVs) and he g id,
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (A. O dono).
allowing hem o no only consume, bu also p o ide ene gy back o he
g id when needed. By agg ega ing mul iple EV ba e ies, a signi ican
amoun o lexibili y can be p o ided o he g id, emo ing he need o
ESS sys ems and educing he in es men cos s [7].
Se e al se ices ha e been p oposed o V2G applica ions [8], being
he mos in e es ing hose which equi e as esponse and ha e a
low ba e y deg ada ion impac (low ene gy, high powe ). In his
con ex , he con ibu ion o EVs o he Load F equency Con ol has been
ex ensi ely s udied [9]. Se e al wo k ha e shown ha V2G sys ems can
con ibu e o keep he equency close o i s a ed alue while ensu ing
a p ope SoC managemen o he EVs [10–12]. Howe e , hese con-
olle s usually ely on a communica ion link o a cen alized con olle ,
inc easing he complexi y when he numbe o cha ge s is high o hey
a e geog aphically dispe sed. To p e en his issue, se ices which can
be p o ided based on local measu emen s ha e gained a en ion o
V2G applica ions (dis ibu ed app oach). Suppo ing he g id h ough
ine ia emula ion, p ima y equency egula ion and ol age suppo
s and ou .
h ps://doi.o g/10.1016/j.ijepes.2024.109862
Recei ed 18 Sep embe 2023; Recei ed in e ised o m 15 Janua y 2024; Accep ed 8 Feb ua y 2024
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
2
A. O dono e al.
As o he in e e -based esou ces, V2G cha ge s could suppo he
g id using wo con ol s a egies: g id ollowing (GFL) and g id o ming
(GFM) [13]. GFL is he mos ma u e and widesp ead s a egy o hese
applica ions. A synch oniza ion mechanism, usually a Phase-Locked
Loop (PLL), is used o de ec he g id phase. Based on his in o ma ion,
he exchanged cu en ampli ude and phase is egula ed o handle
he ac i e and eac i e powe ans e . F om g id pe spec i e, he
powe con e e beha es as a con olled cu en sou ce. GFL-based V2G
cha ge s ha e been ex ensi ely s udied in li e a u e, whe e he main
goal is o maximize he g id suppo while ensu ing a p ope SoC man-
agemen . Au ho s in [14] ha e p oposed a con ol s a egy in which
he cha ge could ope a e in 3 disc e e s a es (cha ge, discha ge o idle)
depending on local measu emen s. To p o ide a smoo he suppo , he
sma cha ging concep has also been p oposed by se e al au ho s [15–
17]. In hese, he cha ge powe se poin is modi ied h ough a d oop
con olle . Sma cha ging s a egies equi e he cha ge o ope a e
a below he a ed powe o p o ide up and down egula ion, which
has a nega i e impac on he e iciency o he powe elec onics. To
p o ide a symme ical suppo and op imize he cha ging e iciency o
he sys em, [18] di ides he EV cha ge ope a ion in o wo egions:
he equency suppo egion and he o ced-cha ge bounda y egion.
E en i he EV is cha ged e icien ly, he equency egula ion capabili y
is los du ing he o ced-cha ge bounda y. Adap i e d oops, in which
he d oop coe icien is modi ied using he s a e o cha ge (SoC) o he
ehicle ha e also been p o ed use ul o p o ide keep he SoC limi ed
o a ce ain ange o o p e en an excessi e ba e y deg ada ion.
Di e en ela ions be ween he d oop coe icien and he SoC ha e been
p oposed in li e a u e, depending on he goal [15,19]. Finally, V2G
cha ge s ope a ing as GFL ha e also been p oposed o p o ide some
syn he ic ine ia. This is usually achie ed by adding a de i a i e e m
o he d oop con olle [20,21]. [22] ha e me ged he ine ial esponse
and he adap i e d oop concep oge he in a hyb id sys em based on
a EV ba e y an ul a-capaci o s.
Despi e he popula i y o GFL s a egies in V2G cha ge s, hey
ace some limi a ions: hey do no ope a e p ope ly on weak g ids
no can p o ide wi hou an exis ing g id (s andalone). [23]. In his
scena io, GFM s a egies ha e eme ged as an al e na i e o ace he
issues ela ed o GFL and achie e a 100% IBR-based g id [24]. Despi e
sha ing he same ha dwa e, GFM de ices beha e as con olled ol age
sou ces which can mimic he beha iou o synch onous gene a o s
(SGs), p o iding accu a e ine ia, highe s abili y unde weak g ids and
s andalone ope a ion. V2G cha ge s ope a ing as GFM de ices could
be in e es ing o small scale g id applica ions o o ensu e he powe
supply unde blackou s. Au ho s in [25] ha e p oposed a communi y
o EVs ope a ing as Vi ual Synch onous Gene a o s (VSG) ha ensu es
he supply in case o powe ailu e. VSGs o low powe single-phase
EV cha ge s ha e also been p oposed in [26,27]. The o me e e ence
is ocused on he dynamic esponse o g id pe u ba ions, whe eas he
la e aims o op imize he cha ge pe o mance wi h a educed DC
link capaci ance. Au ho s in [28] ha e also sugges ed a V2G cha ge
based on a GFM d oop con olle , ocusing on ac i e/ eac i e powe
decoupling wi hou ine ia emula ion.
In all he p e ious GFM s a egies, he SoC limi s and he cha ging
equi emen s o he EV we e no conside ed. In ac , he GFM ope a ion
conside ing he EV ba e y has no been s udied in dep h in li e a u e.
A SoC managemen was desc ibed in [29], bu he esponse o he
con olle and i s s abili y unde he di e en scena ios was no ad-
d essed in de ail. Limi ing he con ibu ion o ine ial esponse has also
been sugges ed as a solu ion o p e en SoC d i s o cha ge s [30,31].
Howe e , his app oach migh lead o unde usage o he ba e y, as
he e a e scena ios in which he p ima y equency egula ion o EVs
could be ad an ageous bo h o he EV and he g id.
Conside ing all he men ioned abo e, his pape aims o de elop a
GFM con olle wi h an in eg a ed SoC managemen o V2G cha ge
applica ions. When he ba e y SoC is inside i s ope a ional limi s and
Fig. 1. One-line diag am o a 3-phase EV cha ge using a GFM s a egy.
no cha ging is equi ed, he V2G cha ge will beha e as a con en-
ional GFM de ice, p o iding ine ia emula ion, p ima y equency and
ol age suppo . Howe e , when he SoC limi s a e hi o cha ging is
equi ed, he SoC con olle will educe he p ima y equency suppo
depending on he pe u ba ion ype, limi ing i s con ibu ion o mee
he SoC equi emen s. The SoC con olle p o ides eedom o une he
ansien suppo o he de ice, limi ing i o ine ial esponse o p o id-
ing ime-ex ended con ibu ions. The impac o he SoC con olle on
he s abili y and esponse o he V2G is add essed in de ail, and pa am-
e e s a e uned o p o ide a damped esponse. The p oposed con olle
will only use he SoC and powe measu emen s o ope a e, achie ing a
decen alized app oach and no needing equency measu emen s.
This pape is o ganized as ollows. Sec ion 2desc ibes he o e all
s uc u e o he V2G cha ge , ocusing on he in e e side and i s in e -
ac ion wi h he AC g id. The GFM s a egy, he in e nal con ol loops
and he SoC con olle a e desc ibed in de ail, including he iden i ied
ope a ing modes, which depend on he SoC condi ions and cha ging
equi emen s. Sec ion 3e alua es he ans e unc ion o he sys em o
he p e iously iden i ied ope a ing modes. The pe o mance o he V2G
cha ge can be e alua ed by conside ing wo scena ios, which depend
on he s a us (enabled/disabled) o he SoC con olle . The con olle
is uned o p io i ize he damping o he esponse. The pe o mance
o he p oposed con ol s a egy unde di e en ope a ing modes is
alida ed in Sec ion 4, bo h using a simula ion and an expe imen al
se up. Finally, he main conclusions a e ga he ed in Sec ion 5.
2. Sys em desc ip ion
Fig. 1 shows he simpli ied diag am o a 3-phase bidi ec ional EV
cha ge . The EV cha ge is composed o a DC/DC and a DC/AC s age,
connec ed h ough an in e media e DC bus (𝑣𝑏𝑢𝑠). The DC/AC s age is
connec ed o he g id using a LCL il e , which is designed o mee
he ha monic dis o ion equi emen s o he g id [32]. The il e is
composed o an in e e -side induc o 𝐿𝑐, a g id-side induc o 𝐿𝑔and
a capaci o 𝐶𝑓. A damping esis o 𝑅𝑓can be connec ed in se ies o
he capaci o o a enua e he esonance peak o he il e . The g id
is ep esen ed using i s equi alen Thé enin ci cui , composed o a
ol age sou ce 𝑣𝑔and i s equi alen se ies impedance 𝑍𝐺. The g id
impedance includes induc i e 𝐿𝐺and esis i e 𝑅𝐺componen s.
When EV cha ge s ope a e in GFL mode, he DC/AC egula es he
in e media e ol age 𝑣𝑏𝑢𝑠 and he eac i e powe (o powe ac o )
exchanged wi h he g id, whe eas he DC/DC manages he ac i e powe
which is exchanged wi h he ba e y. In GFM, he con ol s uc u e
is modi ied: he DC/DC is used o egula e 𝑣𝑏𝑢𝑠, whe eas he DC/AC
manages he ac i e and eac i e powe exchanged wi h he g id. Fo
he sake o simplici y, his analysis will only ocus on he GFM s a egy
o he DC/AC s age. The dynamics o he DC/DC s age a e neglec ed,
conside ing a s i DC ol age sou ce.
2.1. GFM con ol s uc u e
The GFM con ol o he DC/AC s age o he V2G cha ge is shown
in Fig. 2. The con olle is implemen ed using he synch onous 𝑑𝑞
ame. All he pa ame e s and equa ions in he diag am a e based on
he pe uni sys em (pu), excep o he base angula equency 𝜔𝑏
and he in e nal angula posi ion 𝜃𝑟, which a e gi en in ad/s and ad
espec i ely. The GFM is composed o 4 main blocks:
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
3
A. O dono e al.
Fig. 2. G id o ming s a egy o he DC/AC s age o he V2G cha ge .
•Powe Synch oniza ion Loop (PSL)
•Reac i e Powe Con ol (RPC)
•Vi ual Admi ance
•Cu en Con olle
A b ie desc ip ion o each con ol block is gi en in he ollowing
subsec ions. The p oposed SoC con olle , ma ked in ed in he igu e,
will be desc ibed mo e in o de ail in Sec ion 2.2.
2.1.1. Powe synch oniza ion loop
The PSL gene a es he angula equency 𝜔𝑟and posi ion 𝜃𝑟o he
ou pu ol age o he GFM sys em. 𝜃𝑟is used o con e a iables o and
om 𝑑𝑞 sys em, as shown in Fig. 2. Compa ed o GFL in e e s, which
synch onize o he exis ing g id using g id ol age measu emen s and a
PLL, he GFM in e e s use an ac i e powe based synch oniza ion. This
allows hem o ope a e in s andalone condi ions, wi hou an exis ing
g id. The p oposed PSL is based on a VSG algo i hm, which emula es
he swing equa ion o SGs [33]:
𝑑𝜔𝑟
𝑑𝑡 =1
2𝐻(𝑃∗−𝑃+𝐷𝑝(𝜔∗
𝑟
′−𝜔𝑟) − 𝑃𝑑)(1)
In he p e ious equa ion, 𝑃∗is he ac i e powe command, 𝑃is
he measu ed ac i e powe , 𝜔𝑟is he ou pu angula equency o he
con olle , 𝐷𝑝is he s a ic damping e m and 𝐻is he i ual ine ia
e m. The e m 𝜔∗
𝑟
′is he angula equency command, which can be
modi ied by he SoC con ol algo i hm.
𝐻is selec ed o p o ide dynamic equency suppo o he g id. Fo
his analysis, an ine ia o 8 s is used. 𝐷𝑝, which is he in e se o he
d oop coe icien , de e mines he s eady-s a e ac i e powe alue unde
g id equency de ia ions (p ima y equency egula ion). The ypical
alues o 𝐷𝑝 anges be ween 20 o 50 pu, o ensu e a p ope powe
sha ing among he sou ces connec ed o he g id. Fo his analysis, a
𝐷𝑝o 50 pu is selec ed. This means ha a change in he g id equency
o 0.02 pu will lead o a change o 1 pu in he ac i e powe o he
sys em.
As 𝐻and 𝐷𝑝 e ms a e usually de ined by he sys em ope a o ,
he ac i e powe loop dynamics a e ixed [34]. The dynamic damping
powe e m, 𝑃𝑑, is added o he swing equa ion o imp o e he ansien
esponse o he ac i e powe loop. The dynamic damping e m will no
a ec he s eady-s a e esponse o he swing equa ion, so i is use ul
o decouple he ansien and s eady-s a e esponse. Among exis ing
dynamic damping s a egies, a powe de i a i e e m (2) is p oposed,
whe e 𝐷𝑑is he dynamic damping coe icien . The alue o he dynamic
damping e m 𝐷𝑑will be uned in Sec ion 3[35].
𝑃𝑑=𝐷𝑑𝑠
𝜏𝑑𝑠+ 1 (2)
The dynamic damping e m includes a low pass il e (LPF) wi h a
ime cons an 𝜏𝑑. The bandwi h o his il e is se o 20 Hz. This will
p o ide damping in he ange o he ac i e powe loop (1–3 Hz), bu
i will p e en he in e ac ions wi h synch onous oscilla ions (50 Hz)
ha could make he sys em uns able [36].
2.1.2. Reac i e powe con ol
The RPC gene a es he ol age se poin 𝐸o he GFM, emula ing
he eac i e powe d oop beha iou o SGs acco ding o:
𝐸=𝑣∗+𝑚𝑞(𝑄∗−𝑄
𝜏𝑞𝑠+ 1 )(3)
Whe e 𝑣∗and 𝑄∗a e he ol age and eac i e powe commands,
𝑚𝑞is he eac i e powe d oop, and 𝑄is he measu ed eac i e powe .
A i s o de low-pass il e (LPF) wi h a ime cons an 𝜏𝑞is used o
emo e high equency componen s and o adjus he dynamics o he
eac i e powe loop. The eac i e powe d oop is se o a ypical alue
o 0.1 pu. The il e ime cons an is se o 20 ms.
2.1.3. Vi ual admi ance
The i ual admi ance algo i hm emula es an impedance be ween
he RPC ol age se poin 𝐸and he measu ed capaci o ol age 𝑣𝑜.
The i ual admi ance beha iou is equi alen o a ol age con olle
wi h a i ual impedance, bu wi h he ad an age o emo ing he
ol age con olle . The i ual impedance is use ul o connec ing GFM
in e e s o s ong g ids, in which he line impedance is small compa ed
o he a ed powe o he con e e , which could be he case o a V2G
cha ge . By inc easing he induc i e e m o he i ual impedance,
he ac i e and eac i e powe can be decoupled ega dless o he g id
impedance, allowing a p ope ope a ion o he PSL and RPC con olle s.
Addi ionally, he i ual impedance can educe he ac i e and eac i e
powe loop dynamics, imp o ing he s abili y o he sys em [37].
The ollowing equa ion desc ibes he implemen a ion o he i ual
admi ance s a egy in he 𝑑𝑞 ame:
𝑑𝑖∗
𝑐𝑑𝑞
𝑑𝑡 =𝜔𝑏
𝐿𝑣(𝐸−𝑣𝑜𝑑𝑞 −𝑅𝑣𝑖∗
𝑐𝑑𝑞 +𝑗𝜔𝑟0𝐿𝑣𝑖∗
𝑐𝑑𝑞 )(4)
Whe e 𝑖∗
𝑐𝑑𝑞 is he con e e cu en ec o se poin , 𝑣𝑜𝑑𝑞 is he
capaci o ol age ec o eedback, and 𝑅𝑣and 𝐿𝑣a e he i ual esis-
ance and induc ance alues. By conside ing ha he angula equency
a ia ion o he GFM con e e will be small, he angula equency 𝜔𝑟0
in he coupling e ms can be conside ed cons an and equal o 1 pu.
The p oposed algo i hm uses a i ual induc ance and esis ance o
0.3 and 0.06 pu, espec i ely. The addi ion o a i ual impedance is
used o damp he synch onous oscilla ions, which a e ou o he scope
o his analysis [38].
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
4
A. O dono e al.
Fig. 3. G id o ming ope a ion modes based on SoC le el and cha ging ime.
2.1.4. Cu en con olle
The con e e cu en is egula ed using a PI con olle . To imp o e
he sys em esponse, i includes 𝑑𝑞 decoupling e ms and capaci o
ol age eed o wa d:
𝑣∗
𝑐𝑑𝑞 = (𝑖∗
𝑐𝑑𝑞 −𝑖𝑐𝑑𝑞 )(𝑘𝑝+𝑘𝑖𝑐 ∕𝑠) + 𝑗𝜔𝑟0𝐿𝑐𝑖𝑐𝑑𝑞 +𝑣𝑜𝑑𝑞 (5)
𝑣∗
𝑐𝑑𝑞 is he con e e ol age ec o se poin , 𝑖𝑐𝑑𝑞 is he con e e
cu en ec o eedback, 𝑘𝑝𝑐 is he p opo ional gain and 𝑘𝑖𝑐 is he in e-
g al gain. As in he i ual admi ance, he e m 𝜔𝑟0in he decoupling
e ms can be conside ed cons an . A modulus op imum uning app oach
is used o selec he PI gains [39].
The cu en con olle bandwid h is se 20 imes lowe han he
swi ching equency o he con e e (𝑓𝑠𝑤), which is 10 kHz. The
500 Hz bandwid h is high enough compa ed o he bandwid h o he
PSL and RPC loops, and hence, i dynamics can be neglec ed in he
analysis.
2.2. SoC con olle
V2G cha ge s, due o hei bidi ec ional capabili y, could ope a e as
GFM de ices. Howe e , he SoC o he ba e y mus be p ope ly man-
aged du ing ope a ion. The GFM con olle should mee he ollowing
condi ions:
•The ba e y SoC mus be limi ed o an ope a ional ange o
p e en ba e y deg ada ion. The lowe and uppe ope a ional
limi s a e de ined as 𝑆𝑜𝐶𝑂𝑃 𝑚𝑖𝑛 and 𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥, which a e mo e
es ic i e ha he absolu e ba e y limi s 𝑆𝑜𝐶𝑚𝑖𝑛 and 𝑆𝑜𝐶𝑚𝑎𝑥.
•When he EV is unplugged, i should ha e enough cha ge o mee
he mobili y equi emen s o he EV use .
2.2.1. GFM modes unde SoC con ol
Fig. 3 shows a SoC s ime diag am o a plugged EV. The ehicle
is plugged in o he V2G cha ge a ime 𝑡𝑖𝑛, wi h an ini ial cha ge
le el 𝑆𝑜𝐶𝑖𝑛 (%). The owne o he ehicle will unplug he ehicle om
he cha ging s a ion a ime 𝑡𝑜𝑢𝑡, expec ing a cha ge le el o a leas
𝑆𝑜𝐶𝑜𝑢𝑡 (%). I is assumed ha he plug ou - ime and expec ed cha ge a e
in oduced by he use o hey can be es ima ed using his o ical da a.
Mo eo e , he equi ed cha ge will always be lowe han 𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥. Ac-
co ding o he igu e, 4 ope a ion modes can be iden i ied: The B-GFM,
in which he EV cha ge ope a es as a con en ional GFM de ice. The
CL-GFM and DL-GFM, in which ansien equency suppo is p o ided,
bu he p ima y equency suppo is limi ed o p e en c ossing he
ope a ional limi s. Finally, he C-GFM, in which he p io i y is o mee
he cha ge le el o he EV and hence, only ansien suppo is p o ided.
A mo e de ailed explana ion o each mode is gi en in Table 1. In all he
cases, he ol age suppo is always a ailable, as i depends on eac i e
powe .
I should be no ed ha e en i he con ollable ol age sou ce
beha iou is kep in all he ope a ing modes, he s andalone ope a ion
Fig. 4. Implemen a ion o SoC con olle , including logic able.
capabili y is only a ailable in B-GFMI mode. In he emaining modes,
he EV cha ge will con ibu e o he s abili y o he g id by p o iding
ansien equency suppo , bu he s eady s a e con ibu ion o p i-
ma y equency suppo , which depends on he s a ic damping powe
is no gua an eed. The sys em should ely on o he GFL o GFM de ices
o ensu e he s able ope a ion. An addi ional eme gency mode could
also be de eloped, in which he SoC con olle could be deac i a ed
when he g id equency goes below o abo e a h eshold o p io i ize
he g id s abili y o e he ba e y condi ions. This analysis is ou o he
scope o his wo k.
2.2.2. Con olle implemen a ion
The p oposed SoC con olle implemen a ion is shown in Fig. 4.
I is based on an in eg al ac ion, which will emo e he equency
de ia ion e o (𝜔∗
𝑟−𝜔𝑟), ensu ing ha he powe se poin 𝑃∗is me
ega dless o he g id condi ions. A dynamic sa u a ion is used o
handle he con ibu ion o unde and o e - equencies independen ly.
Addi ionally, i can be used o disable he SoC con olle by se ing he
sa u a ion le els o 0.
A logic able is used o ob ain he in eg a o uppe and lowe
dynamic limi , 𝐿𝐻and 𝐿𝐿, and he cha ging se poin 𝑃∗. The logic
able uses h ee boolean inpu s (𝑆1, 𝑆2, 𝑆3) o de e mine i he SoC is
inside he ope a ional limi s and o check i cha ging is equi ed. These
boolean inpu s a e he ones de ined in he condi ions column o Table 1.
A hys e esis could be added o p e en con inuous igge ing o boolean
inpu s 𝑆1and 𝑆2, bu i is neglec ed o he sake o simplici y. The ‘‘M’’
column in Fig. 4 iden i ies he ope a ion mode de ined in Table 1.
3. T ans e unc ion & s abili y analysis
The p oposed con olle has a non-linea beha iou due o he
sa u a ion block in oduced by he SoC con olle . Howe e , i s pe -
o mance can be e alua ed conside ing wo independen scena ios:
1. SoC con olle disabled: The in eg al ac ion can be neglec ed
om he s udy. This con olle is disabled in he ollowing
modes:
•B-GFM
•DL-GFM unde o e - equencies
•CL-GFM unde unde - equencies
2. SoC con olle enabled: The in eg al ac ion modi ies he angula
equency command o he GFM algo i hm. The SoC con olle
is enabled in he ollowing modes:
•C-GFM
•DL-GFM unde unde - equencies
•CL-GFM unde o e - equencies
The linea ized model o he ac i e powe loop is shown in Fig. 5.
The e m 𝛥is added o all he signals o indica e ha hey a e small
signal a ia ions. The SoC con olle b anch is ma ked in ed, and i
mus be conside ed only when he SoC con olle is ac i e. The impac
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
5
A. O dono e al.
Table 1
Ope a ion modes desc ip ion.
Mode Desc ip ion Condi ion
B-GFM Basic ope a ion. The SoC con ol does no modi y 𝜔∗
𝑟. The sys em ope a es as a
con en ional g id o ming de ice. The cha ge p o ides ine ia emula ion and
p ima y equency egula ion capabili y.
𝑆𝑜𝐶 ∈ (𝑆𝑜𝐶𝑂𝑃 𝑚𝑖𝑛, 𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥 )
DL-GFM Discha ge-limi ed ope a ion. I p e en s an excessi e discha ge o he ba e y by
limi ing ac i e powe suppo o g id unde - equencies. The cha ge p o ides
ansien equency suppo , and p ima y equency egula ion unde
o e - equencies.
𝑆𝑜𝐶 ≤𝑆𝑜𝐶𝑂𝑃 𝑚𝑖𝑛
CL-GFM Cha ge-limi ed ope a ion. I p e en s an excessi e cha ge o he ba e y by limi ing
he ac i e powe suppo o g id o e - equencies. The cha ge p o ides ansien
equency suppo , and p ima y equency egula ion unde unde - equencies.
𝑆𝑜𝐶 ≥𝑆𝑜𝐶𝑂𝑃 𝑚𝑎𝑥
C-GFM Cha ging ope a ion. I ensu es ha EV cha ge le el is me be o e plug-ou ime.
Du ing his ime, he ac i e powe suppo o bo h unde and o e - equencies is
limi ed. The cha ge only p o ides ansien equency suppo .
This mode is ac i a ed when he emaining plug ou ime (𝑡𝑜𝑢𝑡 −𝑡) is equal o lowe
han he cha ging ime 𝛥𝑡𝑐ℎ. Time is gi en in hou s. 𝐶𝑒𝑣 is he ba e y capaci y in
kWh and 𝑃∗is he cha ging powe in kW. 𝑃∗should be smalle han cha ge
maximum powe o p e en o e loading condi ion
𝑡𝑜𝑢𝑡 −𝑡≤𝛥𝑡𝑐ℎ
𝛥𝑡𝑐ℎ =𝐶𝐸𝑉
100
𝑆𝑜𝐶𝑜𝑢𝑡 −𝑆𝑜𝐶
|𝑃∗|
Fig. 5. Small-signal model o he ac i e powe loop.
o he ol age and he eac i e powe a e neglec ed, conside ing an in-
duc i e line ha p o ides p ope decoupling o ac i e/ eac i e powe s.
Fo con enience, he LPF o he dynamic damping, de e mined by 𝜏𝑑,
is also neglec ed. This simpli ica ion is alid o analysing equency
componen s ha a e well below he bandwid h o he il e , which is
he case o he PSL loop. The e m 𝛥𝜔𝑔is he g id angula equency
a ia ion, which is conside ed as an ex e nal pe u ba ion o he plan .
𝜔𝑔0is he angula equency alue a he linea iza ion poin , in ad/s.
The simpli ied model o he g id plan is ob ained om he ac i e
powe ans e equa ion on induc i e lines (6), whe e 𝛿is he phase
shi be ween he GFM and he g id ol age, in ad/s. The i ual
eac ance (𝑋𝑣=𝐿𝑣in pu) is conside ed much highe han he g id
impedance, so ha he la e can be neglec ed in he analysis. This
would be he case o an EV cha ge connec ed o a u ili y g id o mic o-
g id, in which he o e all powe o he cha ge is small compa ed o
he a ed powe o he sys em.
𝑃=𝐸𝑉𝑔
𝑋𝑣
sin 𝛿(6)
The p e ious equa ion can be linea ized a ound he ope a ing angle
𝛿0. Assuming ha he ol ages a e close o he base alues, and ha he
ope a ing angle is small, he ela ion be ween he ac i e powe and he
angle is in e sely p opo ional o he i ual eac ance, o p opo ional
o he i ual suscep ance 𝑌𝑣:
𝑑𝑃
𝑑𝛿 =𝐸𝑉𝑔cos 𝛿0
2𝜋𝐿𝑣
𝛿≈1
𝑋𝑣
=𝑌𝑣(7)
Table 2 p o ides an o e iew o he ac i e powe open-loop
𝛥𝑃 ∕(𝛥𝑃 ∗−𝛥𝑃 )and closed-loop 𝛥𝑃 ∕𝛥𝑃 ∗ ans e unc ions, aking
in o accoun he SoC con olle s a e. The esponse o g id equency
pe u ba ions 𝛥𝑃 ∕𝛥𝜔𝑔is also included.
Table 2
Ac i e powe ans e unc ions wi h and wi hou SoC con olle .
SoC con ol enabled SoC con ol disabled
𝛥𝑃
𝛥𝑃 ∗−𝛥𝑃
𝑌𝑣𝜔𝑔0(𝐷𝑑𝑠+1)(𝑠+𝜔𝑖)
2𝐻𝑠3+(2𝐻𝜔𝑖+𝐷)𝑠2
𝑌𝑣𝜔𝑔0(𝐷𝑑𝑠+1)
2𝐻𝑠2+𝐷𝑠
𝛥𝑃
𝛥𝑃 ∗
𝑌𝑣𝜔𝑔0(𝑠+𝜔𝑖)
2𝐻𝑠3+(𝐷𝑝+2𝐻𝜔𝑖+𝑌𝑣𝜔𝑔0𝐷𝑑)𝑠2+𝑌𝑣𝜔𝑔0(1+𝐷𝑑𝜔𝑖)𝑠+𝑌𝑣𝜔𝑔0𝜔𝑖
𝑌𝑣𝜔𝑔0
2𝐻𝑠2+(𝐷𝑝+𝑌𝑣𝜔𝑔0𝐷𝑑)𝑠+𝑌𝑣𝜔𝑔0
𝛥𝑃
𝛥𝜔𝑔
−𝑌𝑣𝜔𝑔0(2𝐻𝑠2+(2𝐻𝜔𝑖+𝐷𝑝)𝑠)
2𝐻𝑠3+(𝐷𝑝+2𝐻𝜔𝑖+𝐷𝑑𝑌𝑣𝜔𝑔0)𝑠2+𝑌𝑣𝜔𝑔0(1+𝐷𝑑𝜔𝑖)𝑠+𝑌𝑣𝜔𝑔0𝜔𝑖
−𝑌𝑣𝜔𝑔0(2𝐻𝑠+𝐷𝑝)
2𝐻𝑠2+(𝐷𝑝+𝑌𝑣𝜔𝑔0𝐷𝑑)𝑠+𝑌𝑣𝜔𝑔0
3.1. SoC con ol disabled
When he SoC con olle is no enabled, he ac i e powe loop be-
ha es as a second o de sys em. Acco ding o he closed loop equa ion
in Table 2, he bandwid h o he ac i e powe esponse, 𝜔𝑐, depends
on he ine ia and i ual suscep ance (8), whe eas he damping 𝜉also
depends on he 𝐷𝑝and 𝐷𝑑 e ms (9). The e m 𝐷𝑑does no a ec he
s eady s a e esponse unde equency pe u ba ions, only depending
on 𝐷𝑝. This can be clea ly seen by applying he inal heo em o he
closed loop equa ion.
𝜔𝑐=√𝑌𝑣𝜔𝑔0
2𝐻(8)
𝜉=1
2𝜔𝑐
𝐷𝑝+𝑌𝑣𝜔𝑔0𝐷𝑑
2𝐻(9)
The impac o he dynamic damping 𝐷𝑑on he closed loop esponse
o he ac i e powe loop is shown in Fig. 6(a), whe eas he esponse
agains g id equency pe u ba ions is shown in Fig. 6(b). The closed
loop esponse p o ides a p ope powe con ol o equencies up o
1.2–2 Hz, consis en wi h expec ed bandwid h. Inc easing 𝐷𝑑allows he
a enua ion o he esonance peak in he ans e unc ion, albei wi h a
sligh educ ion in bandwid h. When 𝐷𝑑= 0, he damping o he sys em
is lowe han 0.3. By se ing 𝐷𝑑= 0.13 pu, he sys em is c i ically o e -
damped. The 𝛥𝑃 ∕𝛥𝜔𝑔 ans e unc ion p o ides a DC gain o 34 dB,
ega dless o he dynamic damping e m. This gain ma ches he s a ic
damping e m 𝐷𝑝.
The impac o he dynamic damping can also be assessed by analysing
he e olu ion o he poles, as depic ed in Fig. 7. In his igu e, he
eal pa o he pole 𝜎is ep esen ed in he 𝑥-axis and he imagina y
pa 𝜔is depic ed in he 𝑦-axis. As he 𝐷𝑑 e m inc eases, he poles
associa ed wi h he elec omechanical equa ion mo e owa ds he le
hal -plane, which enhancing he sys em damping. Lines ep esen ing
di e en 𝜉 alues ha e been added o he g aph. The e m 𝐷𝑑could be
selec ed using di e en app oaches. One me hod is o ind a sui able
comp omise be ween speed esponse and o e shoo by se ing 𝜉=
1∕√2. This co esponds o a 𝐷𝑑 alue o 0.1 pu.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
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Fig. 6. Sys em esponse when SoC con olle is disabled.
Fig. 7. CL pole e olu ion unde a 𝐷𝑑sweep. SoC con ol disabled.
Fig. 8. Small-signal model o he PSL.
3.2. SoC con ol enabled
When he SoC con ol is enabled, he in eg al ac ion o he SoC
con olle modi ies he s a ic damping e m 𝐷𝑝, adding a i s o de
high-pass il e (HPF) in se ies. In his scena io, he ela ion be ween
he angula equency de ia ion 𝛥𝜔𝑟and he ac i e powe 𝛥𝑃 can
be ew i en as (10). The in eg al gain 𝜔𝑖, in ad/s, de e mines he
bandwid h o he il e . The simpli ied small-signal diag am o he PSL
is shown in Fig. 8, whe e he ed block ep esen s he HPF in oduced
by he SoC con ol. Hence, he main e ec o he SoC con olle is o
emo e he con ibu ion o he s a ic damping powe , which is equi -
alen o he p ima y equency egula ion. The highe he bandwi h o
he il e , he as e he s a ic damping powe will be emo ed.
𝛥𝑃
𝛥𝜔𝑟
=𝐷𝑝
𝑠
𝑠+𝜔𝑖
(10)
When he SoC con olle is enabled, he dynamic damping e m
plays a key ole in he s abili y o he sys em, specially when he
in eg al gain is high. Unde hese condi ions, he con ibu ion o 𝐷𝑝
can be nea ly neglec ed, wi h damping p ima ily p o ided by 𝐷𝑑 e m.
Fig. 9. CL pole e olu ion unde a 𝜔𝑖sweep, wi hou dynamic damping.
Fig. 10. CL pole e olu ion unde a 𝐷𝑑sweep, wi h 𝜔𝑖= 5 ad∕s.
The in luence o 𝜔𝑖on he s abili y o he sys em becomes e iden
when analysing he pole displacemen unde a 𝜔𝑖sweep wi h a null
dynamic damping e m (Fig. 9). As he in eg al gain is inc eased,
he poles associa ed wi h he mechanical sys em p og essi ely shi
owa d he igh -hand plane, esul ing in a educ ion o damping and
a po en ial loss o s abili y in he sys em.
Fo his analysis, a 𝜔𝑖= 5 ad/s is p oposed. Wi h his bandwid h,
he s a ic damping e ec will be emo ed in a ound 0.8 s (4 ime
cons an s). The pole displacemen unde a 𝐷𝑑sweep is gi en in Fig. 10.
Fo a ce ain in eg al gain, inc easing 𝐷𝑑will inc ease he damping o
he elec omechanical poles o he sys em, as obse ed in he p e ious
analysis. Howe e , he damping inc ease is conside ably educed when
going abo e a ce ain c i ical 𝐷𝑑 alue. Beyond his alue, he impac
on he damping o he elec omechanical mode is conside ably educed,
and ins ead, he angula equency dec eases. As he a ge o his
con olle is o p o ide a damped esponse, a 𝐷𝑑= 0.08 pu is used
o simula ion and expe imen al es s. This is he alue in which he
damping o he elec omechanical poles changes i s end, iden i ied
g aphically in Fig. 10.
The bode esponses o he sys em wi h he SoC con olle enabled
and disabled a e compa ed in Fig. 11. The closed loop ac i e powe
esponse emains nea ly equal, indica ing ha he SoC con olle does
no impac i s pe o mance. Howe e , he esponse o he sys em unde
g id equency pe u ba ions is al e ed when he SoC con olle is
enabled. Wi h he SoC con olle enabled, he sys em exhibi s ze o gain
a DC alue, indica ing ha he ac i e powe will e u n o he desi ed
se poin a e a pe u ba ion. The magni ude o he low equency
componen s can be modi ied by a ying he in eg al gain o he SoC
con olle , 𝜔𝑖.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
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Fig. 11. Bode esponse when SoC con olle is enabled and disabled.
Fig. 12. Expe imen al se up.
4. Simula ion & expe imen al alida ion
The pe o mance o he p oposed con olle has been es ed bo h in
simula ion and expe imen ally. The pa ame e s which ha e been used
o alida ing he sys em a e summed up in Table A.3.
Fo he simula ion, a Simulink model based on Fig. 1 has been
de eloped. The g id is modelled using i s Thé enin equi alen ci cui .
The impac o he DC/DC s age is neglec ed by conside ing a s i
DC ol age sou ce, and an a e age DC/AC model is used o emo e
swi ching equency e ec s. These assump ions ha e been ex ensi ely
used in li e a u e when modelling g id-connec ed GFM de ices [40,41].
The expe imen al se up and i s main componen s a e shown in
Fig. 12. The DC/DC and DC/AC s ages a e based on INF-50 powe
in e e s om Du Elec onics. The bidi ec ional DC/DC is buil us-
ing wo o he in e e ’s hal b idges, ope a ing as an in e lea ed
buck/boos . The ba e y is emula ed using a BIC-2200-96 om Mean-
well, which p o ides a 96 Vdc bidi ec ional supply. Fo he 3-phase
g id, a Paci ic Powe 320-AMX supply is used. O - he-shel componen s
ha e been used o passi e and senso ing de ices. The con ol algo i hm
is implemen ed in a cRIO-9040, which includes a Kin ex-7 70T FPGA
and a Dual-Co e 1.30 GHz CPU. The cRIO de ice includes an acquisi ion
ask ha cap u es analog inpu s and con olle in e nal signals a
10 kHz. All he analog inpu s include a 3.3 kHz an ialiasing il e .
4.1. Response o ac i e powe se poin s ep
The heo e ical analysis om Sec ion 3concluded ha he ac i e
powe closed loop dynamics we e highly dependen on 𝐻,𝐷𝑝and 𝐷𝑑.
As he i s wo pa ame e s a e usually de ined by he sys em ope a o
o g id equi emen s, 𝐷𝑑can be used o manage he 𝜉o he ac i e
powe esponse.
Fig. 13 shows he e ec o he dynamic damping e m 𝐷𝑑on
he ac i e powe closed loop esponse. The igu e p esen s bo h he
Fig. 13. Ac i e powe unde a powe se poin o −0.1 pu using di e en 𝐷𝑑.
expe imen al and simula ed esponses o he GFM unde a powe
se poin s ep o −0.1 pu, using 𝐷𝑑 alues o 0 and 0.1 pu. Bo h
expe imen al and simula ion esul s a e o e lapped, showing iden ical
powe dynamics. The measu ed ac i e powe includes some ipple due
o he swi ching noise o he eal powe con e e , which does no
appea in he simula ed a e aged model. The bandwid h o he ac i e
powe con olle is nea ly cons an , a ound 1.8 Hz. When 𝐷𝑑is se o
0, he ac i e powe esponse has a 𝜉= 0.27. Howe e , when i is se o
0.1 pu, he damping is conside ably inc eased o 𝜉= 0.85.
The ac i e powe closed loop esponse is ba ely modi ied when
he SoC con olle is enabled and he in eg al ac ion is execu ed (see
Fig. 11(a)) Hence, he p e ious analysis is alid o all he ope a ion
modes de ined in Table 1.
4.2. Response o equency pe u ba ions
The ope a ion mode o he EV cha ge will de e mine he esponse
o he sys em o equency pe u ba ions. Simula ion and expe imen al
esul s a e ca ied ou o B-GFM, CL-GFM and C-GFM modes. Fo he
sake o simplici y, DL-GFM mode is no included because i s beha iou
is symme ical o he CL-GFM mode. The esul s, which will be dis-
cussed mo e in o de ail in he nex subsec ions, a e plo ed in Fig. 14.
The igu e includes he angula equency o he g id, he angula
equency o he GFM and bo h measu ed ac i e and eac i e powe s.
Expe imen al and simula ion esul s a e supe imposed, showing simila
esul s.
Fo all he ope a ion modes, he es ing sequence is he same.
The g id s a s a he a ed equency o 1 pu. A i s o e - equency
e en is gene a ed by inc easing he g id equency o 1.002 pu using
a s ep. A e some ime, he g id equency expe iences a equency
a ia ion o −0.004 pu, inishing in a s eady s a e alue o 0.998 pu. By
ansi ioning om an o e - equency o an unde - equency scena io,
he non-linea beha iou o he CL-GFM mode can be iden i ied.
The analysis in he ollowing subsec ions will be mainly ocused on
he ac i e powe esponse, as he p oposed algo i hm does no modi y
he pe o mance o he RPC. As i is expec ed in GFM con e e s, he e
is a coupling be ween he exchanged ac i e and eac i e powe . The
equency s eps sligh ly modi y he eac i e powe due o he esis i e
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
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Fig. 14. Ac i e and eac i e powe esponses unde di e en ope a ing modes. G id equency pe u ba ions o 0.002 and −0.004 pu a e applied.
e m o he impedance (impedance o esis ance a io o 5). How-
e e , he ac i e powe is p edominan du ing equency pe u ba ions,
showing a di ec ela ion be ween bo h. Expe imen al esul s show a
highe eac i e powe exchange, indica ing a highe coupling han he
ob ained in simula ion. This disc epancy seems o be ela ed o a highe
esis i i y in he expe imen al se up.
4.2.1. B-GFM
Fig. 14(a) shows he ope a ion o he EV cha ge in B-GFM mode.
In his mode, he SoC is inside he ope a ional ange and no cha ging
is equi ed, s a ing wi h an ac i e powe se poin 𝑃∗= 0 pu.
The V2G cha ge p o ides ansien suppo , in he o m o ine ia
simula ion, o bo h posi i e and nega i e g id equency s eps. Due o
he dynamic damping e m, he ac i e powe ansien esponse has a
highly damped beha iou , wi hou an excessi e o e shoo no inging.
In B-GFM, as he SoC con olle is disabled, he s a ic damping
powe con ibu ion o he con e e is no al e ed. The cha ge con-
ibu es o suppo he g id equency unde s eady-s a e condi ions. A
powe exchange o ±0.1pu is measu ed o a equency de ia ion o
±0.002 pu, co esponding o he 𝐷𝑝 e m o 50 pu.
4.2.2. CL-GFM
Fig. 14(b) shows he ope a ion o he EV cha ge in CL-GFM mode.
As in B-GFM, he EV is no being cha ged and he sys em s a s wi h
an ac i e powe se poin o 0 pu.
Unde he i s o e - equency e en , he CL-GFM con olle p o-
ides suppo du ing he ansien , bu i does no p o ide s eady-s a e
suppo . This occu s because he in eg al gain o he SoC con olle e-
mo es he con ibu ion o he s a ic damping e m 𝐷𝑝in app oxima ely
0.8 s, acco ding wi h he in eg al gain o 5 ad/s. The ac i e powe
exchanged du ing he o e - equency ansien is mainly associa ed
o he ine ial esponse o he sys em, bu i is ex ended o some
addi ional hund ed o milliseconds un il he s a ic damping powe
con ibu ion is comple ely emo ed by he SoC con olle . Once he
ansien is inished, he ac i e powe e u ns o he p e-e en alue
o 0 pu.
When he unde - equency e en occu s, he SoC con olle is dis-
abled and he CL-GFM p o ides bo h ansien and s eady-s a e suppo .
Due o he ansi ion om an o e - equency o an unde - equency
condi ion, he non-linea beha iou o he sys em can be iden i ied:
he CL-GFM suppo s he g id o a ansien o 0.004 pu, bu he
s eady-s a e suppo is only gi en o a de ia ion o 0.002 pu. This non-
linea i y leads o a esponse wi h a highe o e shoo . Once he ansien
is inished, he s eady s a e ac i e powe eaches 0.1 pu, which ma ches
he s a ic damping alue.
4.2.3. C-GFM
Fig. 14(c) shows he ope a ion o he EV cha ge in C-GFM mode.
The ac i e powe se poin s a s a −0.5 pu, assuming ha he ehicle
is being cha ged a hal o he cha ge a ed powe .
In C-GFM mode, he SoC con olle in eg al ac ion is always en-
abled, emo ing he s eady-s a e equency suppo and p o iding only
ansien suppo . The esponse o he o e - equency e en is he same
as in CL-GFM mode, and he concep s explained in p e ious subsec ion
a e alid. They could be applied o he unde - equency e en , whe e
only ansien suppo is also iden i ied. A e bo h unde - equency and
o e - equency ansien s, he ac i e powe se poin e u ns o he p e-
e en alue o −0.5 pu. One key di e ence be ween he C-GFM and
he CL-GFM o DL-GFM is ha he SoC con olle is always enabled, so
non-linea beha iou is no p esen anymo e.
Finally, Fig. 15 shows an scope cap u e o he g id cu en s and
capaci o ol ages. The V2G cha ge , ope a ed in C-GFM mode, is sub-
jec ed o a 0.004 pu o e - equency. The e olu ion o he g id cu en s
du ing he o e - equency e en a e shown in Fig. 15(a). Analogous o
he ac i e powe , he ampli ude o he g id cu en s inc ease du ing
he ansien , and hey e u n o he p e-e en ampli ude due o he
SoC con olle ac ion.
A zoom om he p e ious ansien is gi en in Fig. 15(b). The
g id cu en s ha e a low THD alue due o he LCL il e , which
emo es he high equency swi ching componen s o he in e e . On
he o he hand, i can be seen ha he capaci o ol age and he g id
cu en om he phase A ha e a phase-shi o 180◦, meaning ha
he cha ge is consuming mainly ac i e powe , wi h an small eac i e
powe exchange.
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 157 (2024) 109862
9
A. O dono e al.
Fig. 15. Capaci o ol age (g een — phase A) and cu en (yellow — phase A, pink
— phase B, blue — phase C) wa e o ms du ing GFM-C ope a ion. Vol age and cu en
scales a e 50 V/di and 2 A/di . Time scale is 200 ms/di o (a) and 10 ms/di o
(b).
4.3. E ec o SoC con olle in eg al gain
As i was demons a ed in Sec ion 3, he SoC con olle will in o-
duce a i s o de HPF in he s a ic damping powe when i is enabled.
As he bandwi h o he HPF (𝜔𝑖) is inc eased, he closed loop dynamics
o he ac i e powe will be de e io a ed, by educing he damping o he
elec omechanical modes. In his con ex , he dynamic damping e m
has been sugges ed as an al e na i e o keep a p ope ansien o he
sys em when he SoC con olle is enabled.
The p oposed analysis has used a bandwi h o 5 ad/s o he SoC
con olle . Howe e , smalle bandwid hs could also be used. The main
d awback o educing 𝜔𝑖is he ex a powe exchanged du ing g id
equency pe u ba ions. In his scena io, he con ibu ion o he s a ic
damping powe will be ex ended in ime, and i will no be limi ed
o ine ial esponse. The ansien esponse will be sligh ly imp o ed
due o he con ibu ion o he s a ic damping e m, bu he dynamic
damping e m is s ill equi ed.
Fig. 16 shows he esponse o he C-GFM mode o di e en 𝜔𝑖
alues. A g id equency s ep o 0.002 pu is applied in all he cases.
A𝜔𝑖o 5 ad/s will esul in a nea ly ine ial esponse, whe eas an
𝜔𝑖o 0.1 ad/s ex ends he s a ic damping powe o se e al seconds,
p o iding highe suppo a he cos o addi ional ene gy injec ion o
abso p ion.
5. Conclusions
This pape has p oposed a modi ied GFM con olle o V2G cha g-
e s, which includes an in eg a ed SoC managemen o he ba e y. The
p oposed con olle will ensu e he ol age sou ce beha iou and he
g id suppo , ega dless o he SoC le el and he cha ging equi emen s
Fig. 16. Ac i e powe esponse in C-GFM using di e en 𝜔𝑖 alues. Response o a g id
equency s ep o 0.002 pu.
o he EV owne . Mo eo e , i equi es mino modi ica ions o he
con en ional GFM algo i hms.
Wi h he p oposed s a egy, he V2G cha ge will always beha e
as a con olled ol age sou ce ha p o ides ine ial esponse and
ol age suppo o he g id. I will also con ibu e o p ima y equency
egula ion when he EV does no need cha ging and he SoC le els
a e inside ope a ional limi s. When he SoC is close o he ope a ional
limi s, i s p ima y equency egula ion will depend on he pe u ba ion
ype (o e o unde - equency). Wi h his s a egy, he EV will keep a
pa ial egula ion capabili y o balance i s SoC. Finally, when cha ging
is equi ed, he equency egula ion will be emo ed o ensu e ha
cha ging needs a e me .
The ans e unc ion and s abili y analysis o he ac i e powe loop
ha e shown ha he dynamic damping e m o GFM plays a key ole in
p o iding a damped ansien esponse, especially as he ac ion o he
SoC con olle inc eases. This pa ame e is uned o p o ide a damped
powe esponse (𝜉 > 0.7), ega dless o he ope a ion mode. Mo eo e ,
he ansien esponse o he V2G unde equency excu sions can be
easily modi ied h ough he in eg al gain o he SoC con olle . These
ansien con ibu ions can go om 1 s o 𝜔𝑖= 5 ad/s, up o ens
o seconds when 𝜔𝑖<0.1 ad/s. Smalle in eg al gains could educe
he dynamic damping e m needed, bu hey will esul in addi ional
ene gy exchange wi h he g id,
The pe o mance o he con olle has been alida ed h ough simu-
la ion and expe imen ally, showing ha an s able ope a ion is achie ed
unde all he ope a ion modes.
CRediT au ho ship con ibu ion s a emen
Ande O dono: Concep ualiza ion, Fo mal analysis, In es iga ion,
So wa e, Valida ion, Visualiza ion, W i ing – o iginal d a . F ancisco
Ja ie Asensio: Supe ision, W i ing – e iew & edi ing. Jose An o-
nio Co aja ena: Supe ision, Valida ion, W i ing – e iew & edi ing.
Inmaculada Zamo a: Supe ision, W i ing – e iew & edi ing. Mikel
González-Pé ez: W i ing – e iew & edi ing. Gaizka Saldaña: W i ing
– e iew & edi ing.
Decla a ion o compe ing in e es
The au ho s whose names a e lis ed immedia ely below ce i y ha
hey ha e NO a ilia ions wi h o in ol emen in any o ganiza ion o
en i y wi h any inancial in e es , o non- inancial in e es in he subjec
ma e o ma e ials discussed in his manusc ip .
Da a a ailabili y
Da a will be made a ailable on eques .
