6512 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 60, NO. 4, JULY/AUGUST 2024
Con ol o Agg ega ed Vi ual Synch onous
Gene a o s o PV Plan s Conside ing
Communica ion Delays
Daniel del Ri e o , G adua e S uden Membe , IEEE, Pablo Ga cía , Senio Membe , IEEE,
C is ian Blanco , Senio Membe , IEEE, and Ángel Na a o-Rod íguez , Membe , IEEE
Abs ac —In his pape , a new me hod o he delay compensa-
ion when using an agg ega ion o i ual synch onous gene a o s
is p oposed. Lack o ine ia in powe con e e s can po en ially
p o oke s abili y issues ha can be mi iga ed by he use o i ual
ine ia echniques. Among hose, he Vi ual Synch onous Gene a-
o (VSG)concep has ecei eds ongimpulsein helas yea s.This
pape is ocused on he idea o using he dis ibu ed VSG concep
in a enewable powe plan , in which a single Synch onous Cen al
Angle Con olle (SCAC) is used o he powe con ol exchange a
he Poin o Connec ion (PoC), while dis ibu ion con ol uni s a e
employed o he localin e e con ol.This idea, al eadydiscussed
in he li e a u e, is in he e ex ended o conside he implemen a ion
on indus ial s ing-le el comme cial powe con e e s, ecalling
heimpo anceo accessiblemeasu emen sandcommunica ionde-
lays.In o de o alida e he p oposal, i s ly communica iondelays
a e measu ed and modelled. Following, simula ions wi h di e en
SCAC ope a ing modes a e conduc ed, and inally expe imen al
esul s alida ion o di e en ope a ion modes wi h comme cial
con e e s a e p esen ed.
Index Te ms—Communica ion delay, eal- ime simula ion,
smi h p edic o , i ual synch onous gene a o .
I. INTRODUCTION
THE wo ld’s powe gene a ion is cu en ly mo ing owa d a
mo e sus ainable and en i onmen ally iendly app oach.
This is due o he usage o Dis ibu ed Ene gy Gene a ion
(DEG) acili ies based on Renewable Ene gy Sou ces (RES) has
eplaced ossil uels because o hei signi ican en i onmen al
Manusc ip ecei ed 12 Sep embe 2023; e ised 25 Janua y 2024; ac-
cep ed 26 Feb ua y 2024. Da e o publica ion 13 Ma ch 2024; da e o
cu en e sion 22 July 2024. Pape 2023-SECSC-1316.R1, p esen ed a
he 2022 IEEE Ene gy Con e sion Cong ess and Exposi ion, De oi , MI,
USA, Oc . 09–13, and app o ed o publica ion in he IEEE TRANSAC-
TIONS ON INDUSTRY APPLICATIONS by he Renewable and Sus ainable Ene gy
Con e sion Sys ems Commi ee o he IEEE Indus y Applica ions Socie y
[DOI:10.1109/ECCE50734.2022.9947466]. This wo k was suppo ed in pa
by Eu opean Union’s H2020 Resea ch and Inno a ion P og am unde G an
864459 (UE-19- TALENT-864459), in pa by he Spanish Minis y o Inno-
a ion and Science unde G an CI-MCINN-23-PID2022-139479OB-C22 and
G an MCINN-22- TED2021-129796B-C21, and in pa by he P incipali y o
As u ias, FICYT, FEDER Funds unde G an SV-PA-21-AYUD/2021/57546.
(Co esponding au ho : Daniel del Ri e o.)
The au ho s a e wi h he Depa men Elec ical Enginee ing, Uni e si y
o O iedo, 33203 Gijón, Spain (e-mail: i e odaniel@unio i.es; ga cia pablo
@unio i.es; blancoc is ian@unio i.es; na [email p o ec ed]).
Colo e sions o one o mo e igu es in his a icle a e a ailable a
h ps://doi.o g/10.1109/TIA.2024.3377169.
Digi al Objec Iden i ie 10.1109/TIA.2024.3377169
cos (g eenhouse emissions, lack o sou ce ma e ial, e c.). Addi-
ionally, he mos widely used RES, like pho o ol aic (PV) and
wind powe , a e becoming mo e a o dable, o e ing imp o ed
Le elized Cos o Elec ici y (LCOE) indices [1].
Howe e , he inclusion o his kind o gene a ion sys ems
p o okesa weake powe sys em due o he ine ia educ ion cu -
en ly p o ided by synch onous gene a o s wi h o a ing mass,
o a powe con e e -based sys em wi h li le o no ine ia [1],
[2],[3].
Since powe con e e s lack bo h ine ia and damping, his
p oblem could a ec he powe g id’s s abili y. I is cu en ly
unde s ood ha g id- o ming and g id-suppo ing se ices mus
be aken in o accoun in he design when signi ican pene a ion
o DEG, wi h agg ega ed sizes compa able o adi ional powe
plan s [4],[5],[6]. This is whe e he Vi ual Synch onous Gen-
e a o (VSG) app oach a ises. Fo he powe elec onics-based
DEG/RES uni s, his con ol me hod enables he emula ion o
he dynamic cha ac e is ics o a eal o a bi a y Synch onous
Gene a o (SG) [2],[3].
Using Ene gy S o age Sys ems (ESS), powe con e e s, and
an app op ia e con ol mechanism, he i ual ine ia concep
is applied o p o ide a speci ic amoun o ine ia o supplied
(usually in he ange o ms o a ew dozen seconds). In his way,
VSG es ablishes he amewo k o la e widesp ead applica ion
in RES sys ems wi hou jeopa dizing sys em s abili y. Se e al
VSG app oaches ha e been explo ed and implemen ed [1],
[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]. Two al e na i e
implemen a ions exis . A i s app oach e e s o hose me hods
oo ed in ma hema ical equa ions (e.g., synch on e e s [8],[9],
Kawasaki Hea y Indus ies [10], VISMA and IEPE opolo-
gies [9]). A second g oup elies on swing equa ions (e.g., Ise
Lab’s opology [11], he Synch onous Powe Con olle [5],
[12], Vi ual Oscilla o Con ol [9]). The Synch onous Powe
Con olle (SPC) is a p e alen opology o i ual ine ia
implemen a ion, syn hesizing he elec omechanical and elec-
ical cha ac e is ics o a SG. This app oach egula es in e e
equency by employing i ual ine ia and damping ac o s o
coun e ac g id equency dis u bances.
SPC ope a es wi h inne cu en and ou e ol age con ol
loops, using a i ual admi ance o es ablish a cascaded con-
ol loop. SPC is ypically in eg a ed in o he local con ol o
each in e e , o e ing equency and ol age suppo a local
PV collec o connec ion poin s [5]. Howe e , o PV plan s,
© 2024 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see
h ps://c ea i ecommons.o g/licenses/by/4.0/
RIVERO e al.: CONTROL OF AGGREGATED VIRTUAL SYNCHRONOUS GENERATORS FOR PV PLANTS CONSIDERING COMMUNICATION DELAYS 6513
Fig. 1. (a) SCAC scheme o n-con e e s. (b) Simpli ied Local con ol scheme. The ligh g een con ol loop is implemen ed in he cen al con olle . The o ange
con ol loop is implemen ed in he local con olle [13]. (c) Added AVG Con ol o g id o ming capabili ies [2].
g id suppo is ideally expec ed a he Poin o Connec ion
(PoC). Wi h ha mo i a ion, a modi ica ion o he SPC designed
o p o ide g id suppo a he PoC has been p oposed, he
Synch onous Cen al Angle Con olle (SCAC) [4].
The SCAC echnique sugges s simul aneously d i ing se e al
con e e s, emula ing a unique SG in he PoC, gi ing ise o
an agg ega ed VSG. This concep p esen s he idea o a single
i ual o o , emula ed a he PoC, whe e he elec omechanical
model o he SG is conside ed (cen al con ol a chi ec u e).
Hence, he SG ine ia and damping esponse a e emula ed a he
PoC. Rega dless o he dis ances be ween he local con e e s,
his con ol s uc u e enables he sys em ope a o a he PoC
o con ol he exchange o powe (bo h ac i e and eac i e),
allowing each con e e o dis ibu e he ene gy o be deli e ed
unde di e en ope a ing modes (powe and equency suppo )
on hei own. A mo e de ailed explana ion can be ound in
he li e a u e, whe e bo h, cen al and local con ol sys ems a e
de ailed [7].
A concep o a s uc u e wi h Ncon e e s is shown in
Fig. 1, whe e a cen al con olle handles he local con olle
e e ences o each con e e . In his sys em, i is possible o
independen ly con ol he exchanged ac i e and eac i e powe ,
asindica ed in he dynamic model and con olloops. InFig. 1(a),
a comp ehensi e connec ion diag am illus a es he in e con-
nec ion o a ious con e e s. In Fig. 1(b), he con ol block
diag am is depic ed, wi h he global con olle in g een and he
local con olle o each powe con e e in o ange. Each powe
con e e equi es a eplica ed local con olle ailo ed o i s
speci ic cha ac e is ics. Fu he explana ions o hese blocks
a e p o ided below. The key con ol sys em is implemen ed in
he cen al con olle , whe e he ine ia is emula ed by he swing
equa ion o a i ual synch onous gene a o (see (1) and (2)).
dδsm
d =Δω (1)
JdΔω
d =Pm−Pe
ωB|−DΔω =ΔP
ωB
−DΔω (2)
whe e δsm is he powe angle, Δω is he angula speed
de ia ion o he o o , Jis he SG ine ia, Pmis he mechanical
powe , Peis he elec ical powe , Dis he damping cons an and
ωBis he base equency. In [5], he elec omechanical con ol
has been s udied, and a equency analysis has been aken in o
accoun o ob ain he powe loop con ol HM(3).kp,ki, and KD
ha e been designed, acco ding o he equi ed ine ia cons an
and equency d oop slope, espec i ely.
HM=Δω
ΔP
=kp+kis
s+kD
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
kp=ω2
n
Pmax
kD=ω2
nD
Pmax
ki=2Pmax ξωn−ω2
nD
P2
max
wn=Pmax ωB
2HSN
H=Jω2
B
2SN
(3)
In (3),His he ine ia cons an , Pmax is he maximum ac i e
powe o he con e e , SNis he nominal powe , ωnis he na u-
al equency and ξis he damping ac o . In his con ol sys em,
he dynamic esponse is mainly suppo ed by he ine ia, while
he equency d oop suppo s he s eady s a e beha io . Based
on he analysis p esen ed in [4],[5],(4) shows he ela ionship
be ween ΔPoand he equency change Δωg.
ΔPo
Δωg
=SN
ωBDP
(4)
The in e nal ime-domain a iables and con ol loops (cu -
en / ol age) o he con e e a e p esumed o be accessible by
his con ol sys em, hough. Howe e only ac i e and eac i e
6514 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 60, NO. 4, JULY/AUGUST 2024
powe se -poin s a e no mally ex e nally accessible o com-
me cial con e e s ha ha e al eady been ins alled, ypically
ia a communica ions link. So, a modi ica ion o his con ol is
equi ed o a wide applicabili y. Due o i s wide adop ion as
he go- o solu ion in powe plan s, MODBUS TCP is p oposed
as he communica ion sys em [14].
In he ollowing sec ions, he con ol sys em a chi ec u e
is modi ied in acco dance wi h he p io mo i a ion using a
communica ion-based implemen a ion. In o de o pe o m ha
implemen a ion, he sys em communica ion delay is measu ed,
he in eg a ion o he Smi h p edic o (SP) in he sys em is
explained, and also a small s abili y analysis is pe o med. Fo
alida ing he model, se e al wo king ope a ions will be es ed
in local simula ion and in eal- ime ope a ion wi h comme cial
con e e s. Those wo king modes a e: I) Ac i e and eac i e
injec ion. II) Powe suppo ope a ion, aking in o accoun g id
ope a o eques s. III) F equency suppo ope a ion by powe
managemen depending on equency a ia ions. IV) Phase-
jump in he g id ol age pe o mance. V) Island ope a ion.
Fi s , a local simula ion is used o e alua e he con ol sys em,
and ollowing a eal- ime ha dwa e con olle wi h comme cial
con e e s is employed o he i s h ee cases. The main a -
icle con ibu ion is he p oposal o using a dis ibu ed i ual
synch onous gene a o in an indus ial en i onmen conside ing
communica ion delays and hei compensa ion.
This pape is based on he pape in [13] by he same au ho s,
wi h ex ended analysis and esul s. The added con en includes
a s abili y analysis o he sys em conside ing he delay impac .
Rega ding he esul s, a a ie y o di e en ope a ing condi-
ions is included, conside ing Ha dwa e-In- he-Loop (HIL) and
Powe -Ha dwa e-In- he-Loop (PHIL) alida ion schemes.
II. PROPOSED CONTROL SYSTEM
Mos o he VSG echniques in eg a e hei con olle s in o
each con e e ’s i mwa e as an add-on. Howe e , as i was
al eady indica ed, he SCAC echnique equi es ha ing access o
di e en con ol ac ions and senso eadings (cu en , ol ages).
This pape p oposes a new con ol s uc u e ha can be applied
o al eady-exis ing comme cial con e e s, ha only equi es ac-
cess o ac i e and eac i e powe s se -poin s and measu emen s
ob ained by MODBUS TCP communica ions and he dic iona y
a iables included in he SunSpec DER speci ica ion [15].The
me hod does no equi e any addi ional measu ing elemen s,
such as ex a ol age and cu en senso s, which would make im-
plemen a ion mo e complica ed and expensi e. Ins ead, i elies
on he RMS ol age, equency, and ac i e and eac i e powe
communica ion-based eadings om each con e e . The e o e,
his app oach is an appealing solu ion o he s anda diza ion
o he VSG concep o a massi e implemen a ion in u u e and
exis ing DEG’s. Howe e , i is impo an o acknowledge ce ain
limi a ions when compa ing he ex e nal implemen a ion o he
VSG concep in powe con e e s o i s in e nal coun e pa .
The ex e nal implemen a ion ocuses solely on he undamen al
componen o signal econs uc ion in he ime domain. Addi-
ionally, achie ing a apid esponse is cons ained by communi-
ca ion delays and he necessa y ime o econs uc ion, which
Fig. 2. (a) MODBUS TCP equency and RMS ol age. (b) Ins an aneous
alues om he RMS ol age, equency, and clock signal ob ained by a VCO
(Vol age Con olle Oscilla o ) [16]. (c) Ac i e and eac i e e e ence powe
calcula ion [13].
en ails one undamen al cycle, aking in o accoun RMS alues,
and i is easible only wi hin he in e nal con ol o he powe
con e e .
Fo he applica ion o his concep , ins an aneous ol age
signals o each con e e and PoC a e buil om he RMS
alues as shown in Fig. 2(a) and (b). These signals a e employed
in he con ol sys em’s eedback a iables (as a eplacemen
o bold and ci cled a iables in he o iginal scheme shown
in Fig. 1(b). A he same ime, as i was al eady indica ed,
comme cial con e e s ypically accep powe (ac i e/ eac i e)
se poin s. Howe e , o he implemen a ion o he VSG concep ,
cu en commandscompu ed om he con ol sys ema eneeded
ins ead. This p oposal de i es he powe e e ences om he
cu en e e ences and he econs uc ed ol age signals, as
shown in Fig. 2in he α−β e e ence ame.
III. DELAY COMPENSATION
Each con e e con ol uni communica es wi h he cen al
con olle in he p oposed enewable ene gy plan applica ion
using MODBUS TCP. The communica ion be ween he cen al
con olle and each o he dis ibu ed uni s may expe ience
some delay since MODBUS TCP is no a eal- ime p o ocol,
he delay depending on he numbe o componen s in he bus
and he dis ance. The e ec i eness o he closed-loop sys em is
comp omised by hese delays, which ha e a di ec impac on he
con ol ins uc ions ansmi ed om he cen al con olle and
he p o ided eedback in o ma ion.
Conside ing ha MODBUS TCP is no a eal- ime p o ocol,
i is expec ed a a iable delay dis ibu ion. Acco dingly, he
delay s a is ical dis ibu ion is modeled in his sec ion and a
compensa ing mechanism is discussed.
A. Delay Modelling
In he li e a u e, he e a e se e al p oposals o model andom
delays. One o hem uses he Ma ko chain [17],[18] as i s
ounda ion. A s ochas ic model called a Ma ko chain disc e ely
ep esen s ce ain po en ial s a es o e en s (in his case delays).
RIVERO e al.: CONTROL OF AGGREGATED VIRTUAL SYNCHRONOUS GENERATORS FOR PV PLANTS CONSIDERING COMMUNICATION DELAYS 6515
Fig. 3. Se up o HIL and PIL expe imen al es s. The con ol design is made on Ma lab and execu ed in he eal- ime Speedgoa a ge . The con e e s a e
con olled by w i ing/ eading published MODBUS/TCP a iables [13].
The p obabili y o hose po en ial ou comes is solely dependen
on he ou come o he p io e en . Fo his pape , o model he
communica ion la ency in he local ne wo k whe e he es s a e
going o be pe o med, he communica ion delays in a link using
MODBUS TCP p o ocol a e measu ed. A 30 kW bidi ec ional
dc/dc con e e (CNG) om Cine gia SL, simila o he one in
Fig. 3, was employed as he PHIL sys em. This powe supply
ea u es di e en emula ion uni s, including ba e ies and sola
panels, and may wo k as a ol age, cu en , and powe sou ce.
Two o hese powe sou ces will be used in Sec ion IV o
he expe imen al alida ion. Fo pe o ming he measu emen s,
a HIL sys em (Speedgoa a ge machine) is used o ac as a
communica ion ga eway be ween he con e e s and he con ol
sys em in a eal- ime simula ion. These componen s a e also
displayed in Fig. 3.
The delay measu emen p ocedu e is as ollows: a digi al
squa e e e ence signal o 0.25 Hz has been supplied simul-
aneously o he cu en con e e se -poin , so i can be used as
a igge signal in an ex e nal scope ha also cap u es he ou pu
cu en esponse. Bo h signals can be obse ed in Fig. 4(a).The
delay dis ibu ion a ies be ween a much wide ange, as i can
be seen in Fig. 4(b), wi h a mean alue o a ound 68 ms and
a mode o 45 ms. In Fig. 4(c), he ime a ia ion o he delay
du ing all he expe imen s can be easily app ecia ed. The ime
a ia ion o he delay h oughou he en i e expe imen is seen
in Fig. 4(c). Fo he delay modelling, a Poisson dis ibu ion wi h
he o m (5) is chosen, as p oposed in queuing heo y delay
models o communica ion ne wo ks [19],[20]. The Poisson
dis ibu ion is ob ained wi h he delay e olu ion om Fig. 4(b),
wi h 795 numbe o e en s (k) and he mean (λ) alue o 68 ms.
Tha dis ibu ion is used as delay es ima ion o compensa ing
he delays in he SP loop. Fo he eal communica ion delay, he
measu ed da a is used.
(k,λ)=P (X=k)=λke−λ
k!;λ>0;k=0,1,2... (5)
By using he Poisson dis ibu ion, he dis ibu ion om Fig. 4(d)
is ob ained.
B. Delay Compensa ion. The Smi h P edic o
Va ious me hods o delay compensa ion ha e been explo ed,
including he s udy o he Smi h p edic o (SP) and i s modi i-
ca ions [21],[22], he in es iga ion o he Sca e ing ans o -
ma ion [23],[24], he examina ion o he linea p edic o [25],
Fig. 4. (a) Ins an aneous delay measu emen in he lab (PWM is he sen
e e ence signal and I is he ac ual cu en he con e e de elops). (b) Time
a ia ion o delay. (c) Delay his og am om expe imen al es s. (d) P obabili y
densi y unc ion o he measu ed communica ion delay (M.D) in compa ison o
Poisson dis ibu ion (P.D) wi h λo 68 ms.
[26], and he conside a ion o p edic i e con ol [27],[28],
among o he s a egies. The Sca e ing ans o ma ion se es as
ame hod opassi a e hecon olsys em,mi iga ingdelaye ec s
and con ibu ing o s abiliza ion. Simila ly, he linea p edic o ,
acommonly usedmodel- ee scheme, employs he linea ex ap-
ola ion concep o p edic u u e con ol a iables. Howe e , o
he pu poses o his pape , he SP has been chosen due o i s
simplici y and eliable ope a ion [21]. Ongoing esea ch in his
ield aims o iden i y al e na i e delay compensa ion me hods
mo e sui able o he s ochas ic na u e o communica ion-based
delays. The SP achie es he emo al o he delay componen
om he sys em’s con ol loop by inco po a ing a model o he
6516 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 60, NO. 4, JULY/AUGUST 2024
Fig. 5. (a) Global SP a chi ec u e o n-con e e s (ligh g een block o global con ol and o ange o local con ol) [17]. (b) Local model o each con e e
(blue blocks) emula ed in he global con olle . (c) Basic Smi h p edic o s uc u e.
delay s uc u e, along wi h a ela i ely p ecise modeling o he
sys em plan [22].
In he SCAC sys em, he delay is p esen ed in he con ol
ac ions sen o he local con e e s. The SP compensa es o
he plan delay, h ough a plan model (
Gp) and an es ima ed
delay (
e ps). The plan model shall be he one be ween he
con ol ac ions (δm,ΔE) and he ou pu (Pou ,Qou )(see
Fig. 5(a). Un o una ely, inding he ans e model o he p o-
posed communica ions-based con ol sys em is no an easy ask.
The sugges ed app oach is o un a eplica o he local con ol o
each con e e in he cen al con olle . As many eplicas o he
local con ol will be used as he e a e SCAC con e e s. I should
also be cla i ied ha he local con ol s uc u e o each o he
con e e s is he same in all o hem, simply changing he alue
o he ins an aneous alues o each con e e . Fig. 5(c) shows
he simula ed plan o SP which is conside ed as he a ec ed
plan by he delay. Besides, δmand eiou pu s o he emula ed
local model a e used o compu ing he ou pu powe using he
powe (6). Finally, he e o be ween he p edic ed ac i e and
eac i e powe and he alues gi en by he local con ol uni s is
used o compensa e o he delay (see Fig. 5).
Pi=EiVi
Xi
sin(δm);Qi=Vi
Xi
(Ecos(δm)−Vg)(6)
In o de o demons a e and alida e he ope a ion o he SP,
he limi s abili y cons an delay is i s ly conside ed while he
compensa ion me hod is applied. The sys em used o applying
he delay wi h SP is he one shown in Fig. 5, and wi hou
compensa ion he one shown in Fig. 1.
To cla i y his poin , Fig. 6shows he di e ence in beha io
whenusingo no heSPunde helimi s abili ydelaycondi ion.
As i can be seen, by se ing he limi delay (75 ms), he esponse
wi h (dLSP ) and wi hou SP (dLNSP ) a e clea ly di e en ,
whe e he addi ional o e sho c ea ed by he delay is mos ly
emo ed by applying he SP.
I is also included a la ge delay (d=80 ms) o illus a e
he ins abili y condi ion abo e a ce ain delay le el. In his
case he uns able case is scaled o ep esen a ion pu poses. In
he nex subsec ion, a concise s abili y analysis is unde aken
Fig. 6. Sys em s ep esponse wi h a cons an communica ion delay o d3=
75 ms (which is he s able limi ega ding he delay), wi h (dLSP ) and wi hou
delay compensa ion (dLNSP ). Also, he uns able case (dUNS) is ep esen ed
o a case o d2=80 ms. Fo ep esen a ion, he uns able powe is co ec ed by
a ac o o 0.005. Ris he e e ence signal.
o complemen he explana ion and alida e he impo ance o
implemen ing a delay compensa ion me hod.
C. S abili y Analysis
In his sec ion, a compa a i e s abili y s udy is conduc ed,
conside ing bo h he sys em wi hou conside ing communica-
ion delays and hose ha include hem, leading o he sys em
ins abili y. This analysis is isually p esen ed in Fig. 7, illus a -
ing Bode diag ams o he di e en enume a ed cases.
The s abili y esponse will be compa ed in wo di e en sce-
na ios:onewhe e hesys emisope a edwi hou communica ion
delays (d1=0 ms) and ano he whe e communica ion delay is
in oduced a he s abili y bounda y (d2=75 ms). Those scena -
ios a e in oduced in Fig. 7, whe e Bode diag ams a e depic ed.
Ini ially, he Bode diag am wi hou communica ion delays was
app oxima ed using he F equency Response Func ion (FRF)
me hod, a equency-based measu emen unc ion. I consis s
in a equency-based measu emen unc ion ha exp esses he
equency domain ela ionship be ween an inpu and ou pu o a
sys em [29]. In he Fig. 7, jus he case wi hou delay is included
wi h his me hod. Howe e , conside ing ha he esponse a
low equencies closely esembles he ans e unc ion ob ained
om he sys em in Fig. 8(due o he ine ia con ol sys em being
slow and he es being as a low equencies), he la e has
been employed o he subsequen s abili y es s. The h ee i s
cases we e analysed in he Bode by using he sys em om Fig. 8.

RIVERO e al.: CONTROL OF AGGREGATED VIRTUAL SYNCHRONOUS GENERATORS FOR PV PLANTS CONSIDERING COMMUNICATION DELAYS 6517
TABLE I
STABILITY VALUES FOR THE DIFFERENT CASES FROM FIG.9
Fig. 7. Bode diag am o he SCAC sys em conside ing no delay (d1=0ms),
he limi delay which makes uns able he sys em (d2=75 ms), and he same
delaybu compensa edwi h heSPme hod(SP).Fu he mo e he Bodediag am
ex ac ed by FRF me hod is also p esen ed (jus o non delay case). (a) The
ampli ude Bode is p esen ed. (b) Shows he phase e olu ion o he di e en
cases, including he PMs. No ice he low- equency anges o he sys em (x-axis)
due o he emula ed sys em ine ia (10 s). Table Ishows he s abili y alues o
hese cases.
Fig. 8. Simpli ied model o SCAC wi h one con e e .
As obse ed in he Bode diag am o Fig. 7and he da a
p esen ed in Table I, sys em s abili y is e iden in he absence o
communica ion delays, wi h a Phase Ma gin (PM) o 143.44
and an in ini e Gain Ma gin (GM). When he limi ing delay (d2)
is in oduced, he sys em is posi ioned a he s abili y bounda y,
ea u ing a GM o 1.001 and a PM o 0.0038. Addi ionally,
upon he in oduc ion o he SP, he sys em egains i s s abili y
ma gin, displaying a GM o 6.86 and a PM o 97.7.
Taking ad an age o he s abili y analysis conduc ed in he
baseline case, a b ie assessmen o he sys em’s s abili y sen-
si i i y has been ca ied ou . C i ical pa ame e s such as ine ia
(H), damping (τ), and d oop slope (Kp) we e a ied ac oss
h ee di e en scena ios: A) wi hou delay, B) wi h a limi ing
delay, and C)limi ing delay bu employingSPas acompensa ion
me hod. These a ia ions a e e lec ed in Fig. 9. Fu he mo e,
he aim o his analysis is o emphasize he signi icance o
ce ain elemen s in he con ol sys em, demons a ing how hey
in luence he a ia ion o s abili y ma gins.
Le e aging Fig. 9and Table I, i can be obse ed ha , in
he case A) wi hou delays, he modi ica ion o H alues a)
causes he sys em o become mo e unde damped bu as e as
i s alue dec eases. Inc easing he alue o τb) esul s in a
mo e o e damped and slowe sys em, while he a ia ion o Kp
c) mainly a ec o he posi ion o he ze os, mo ing he oo
locus o he igh , as Kpis inc easing. In case B), he sys em
beha es simila ly, bu wi h eigen alues shi ed o he igh . I
is e en no iceable ha , by inc easing Hand dec easing τ, he
dominan poles can lead he sys em o he s abili y ma gin, as
de ailed in Table I. In case C), a e delay compensa ion wi h
SP, he signi ican eigen alues e u n o he nega i e semi-axis,
ensu ing sys em s abili y.
IV. RESULTS
In his sec ion some esul s a e p esen ed o alida e he
p oposed compensa ion me hod, p esen ing di e en wo king
modes o he sys em. Those ope a ions a e es ed in bo h local
Simulinksimula ions and eal- ime expe imen alp oo s h ough
Speedgoa emula o . Real- ime es s a e based on Fig. 3, whe e
wo 30 kW bidi ec ional dc/dc con e e s (CNG) om Cine gia
S.L a e used. In his case, CNG-2 has h ee s ings wo king as
powe sou ces o emula e he powe demand om he con ol
sys em, which will ecei e he commands om he simula ion
(P e 1,Q e 1,P e 2,Q e 2). Those se poin s a e sen and w i -
en in CNG-2 h ough MODBUS TCP. The ene gy compu ed by
he con ol sys em will be ob ained om CNG-1, which wo ks
as a ba e y emula o in each s ing, which is unning in ba e y
emula ion mode o eplica e he SCAC idea. As i was s a ed in
Sec ion III, a HIL sys em is used o eal- ime simula ion.
Fo he case o communica ion delays be ween he cen al
con olle and he local uni s, he same a iable ime delay used
in he local simula ions (compu ed in Sec ion III) a e used o
expe imen al es s.Howe e ,due o heCNGcon e e ’sin e nal
delay in he p ocessing o he powe e e ences and in eg a ion
windows used o he calcula ion o he ac i e and eac i e
powe , addi ional delays a e added o he con ol sys em (20 ms
o ac i e powe and 400 ms o eac i e powe ). These delays
a e also included in he model used by he Smi h p edic o o
achie e be e esul s.
This is a c i ical s ep, as he Smi h p edic o will also ackle
he addi ional delays p esen in a eal implemen a ion.
Fo hese es s, g id, and VSG models a e aken om [4],
whe e he SCAC idea was i s published. In his case, he
model includes h ee DEGs connec ed o a g id and conside s
a ba e y locally connec ed pe con e e , which is he elemen
ha p o ides/abso bs ene gy o equency suppo . In his case,
6518 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 60, NO. 4, JULY/AUGUST 2024
Fig. 9. Roo locus o con ol sys em. Base case pa ame e s shown in Table II. (a) Z-P map wi hou delay. (b) Z-P map wi h delay. (c) Z-P map wi h SP compensa ion
delay. In he i s ow o he igu e (a), he ine ia (H) is a ied. In (b) he damping (τ), and in (c) he d oop slope (Kp). In Table I he imp o ed alues a e bold.
TABLE II
SCAC PARAMETERS AND SET-POINTS FOR THE SIMULATION
eede impedance is conside ed, demons a ing ha he sys em
could wo k in a eal implemen a ion wi h eal eede s.
Fig. 10 shows an o e iew o he di e en es s ha a e
going o be e alua ed, showing se e al ope a ion modes o be
alida ed. Going om a simple ac i e and eac i e powe e e -
ence acking o a powe suppo ope a ion mode, depending on
he g id ope a o equi emen s modi ying he powe exchange
wi h he g id. Besides equency suppo capabili y, by injec -
ing/abso bing ene gy h ough an ESS, alida ing he dis u bance
ejec ion capabili y, which is one o he main pu poses o he
sys em. Also he phase-jump eac ion o he sys em and he
islanding mode ope a ion a e analysed in his pape , o show
o he ex a ope a ions o he sys em. The cases I, II and III
can be seen in Fig. 11, bu in e ms o powe signals in he
o m o a comple e simula ion. Fig. 11(a) shows I, II, and III
wo king modes in e ms o ac i e powe . Fig. 11(b) depic s
he beha io in Case I, injec ing he equi ed powe by he
global con olle . Fig. 11(c), depic s Case II, o ac i e powe
managemen . Besides, Fig. 11(d) and (e) show Case III, which
is he injec ed powe when a equency d op appea s in he
g id, ying o educe he equency a ia ion. These wo king
ope a ions will be explained in mo e de ail in he ollowing
subsec ions. Wo h no ing ha powe is oddly sha ed among
he h ee con e e s in he nex sec ion, p o iding a dis ibu ion
showninFig.12, o eachDEG.Simula ionpa ame e s a egi en
in Table II.
P e ious simula ion is pe o med by using an ideal g id.
Howe e , in o de o alida e and demons a e how he SCAC
sys em wo ks, he ollowing simula ions will be pe o med by
using a weak g id o med by a simple synch onous gene a o
(wi h eal equency a ia ions), wi h a limi ed powe (300 kW)
and ine ia (0.116 kgm2). In hese simula ions, he i e cases
om Fig. 10 a e alida ed: I) ac i e and eac i e powe injec ion,
II) suppo ing equency changes, III) g id ope a o ac i e powe
e e ence acking, IV) phase angle jump and V) islanding
ope a ion.
A. Case I
Conside ing wha is accoun ed in Figs. 10(b) and 11, ac i e
and eac i e powe se poin s a e es ablished in o de o con ol
he powe exchange wi h he g id. This p inciple is he basis
o he o he wo wo king modes, showing how he SCAC
can manage he equi ed powe by he global con olle . This
ope a ion is es ed by a simple local simula ion, and also by a
eal- ime simula ion. Besides, hese powe injec ions a e a ied
by adjus ing he i ual admi ance in con ol as Fig. 12 shows,
whe e he uni admi ance is di ided in 3, and i a ies du ing
ime.
1) Local Simula ion: As i can be seen in Fig. 13(a), he
powe se poin is eached, sha ing he ene gy among he DEGs,
ega ding he powe dis ibu ion be ween he DEGs shown in
Fig. 12. The same happens wi h he eac i e powe in b).
2) Real-Time Expe imen al Tes : As i was a o emen ioned,
he con ol sys em is es ed in eal- ime by using he Speedgoa
simula o and CNG con e e s. The expe imen al esul s a e
p esen ed in Fig. 14. As i can be seen ac i e and eac i e powe
a e acked pe ec ly, qui e simila o local esul s. I is impo an
o no e ha he e is a di e en delay be ween ac i e and eac i e
powe , which has o do wi h he in eg a ion window om each
a iable in he powe con e e used in he HIL sys em [13].In
case o c), he di e en s eps ha appea in he ead powe a e
di ec ly he delay o he in eg a ion window o ac i e powe .
Ne e heless, hose delays a e ackled by he Smi h p edic o
making he sys em con ollable and s able. The di e ence in he
ipple be ween he local simula ion and he eal- ime is because
RIVERO e al.: CONTROL OF AGGREGATED VIRTUAL SYNCHRONOUS GENERATORS FOR PV PLANTS CONSIDERING COMMUNICATION DELAYS 6519
Fig. 10. (a) Powe sys em scheme wi h h ee DEGs, showing global and local
con olle s, ba e y (SCAC) and PV panels. (b) Wo king mode I: Ac i e and
eac i e powe se poin s by each DEG, con olled by he SCAC. (c) Wo king
mode II: Powe suppo ope a ion, aking in o accoun g id ope a o eques s.
(d) Wo king mode III: F equency suppo ope a ion by powe managemen
depending on equency a ia ions. (e) Wo king mode IV: Vol age angle s ep-
change. ( ) Wo king mode V: Islanding mode.
he signals ead by MODBUS TCP do no ha e he ipple da a.
Al hough he powe wi h ipple is sen , he con e e used o
he expe imen al es s il e s he componen .
B. Case II
This case aims o demons a e he main ope a ion mode o
he SCAC sys em. As i was abo e-men ioned, SCAC sys em
Fig. 11. (a) Ac i e powe managemen o all wo king modes in each DEG,
aking in o accoun he powe -sha ing be ween hem. Legend G1is he i s
powe con e e , G2is he second powe con e e , G3is he hi d powe
con e e , DEG is he o al powe injec ed by he powe plan and Ris he
powe e e ence. Case I shows he Ac i e and eac i e powe se poin s by each
gene a o , con olled by he SCAC. Case II shows he powe suppo ope a ion.
Case III shows he equency o suppo ope a ion. (b) Zoom o case I o
ac i e powe injec ion. (c) Zoom o Case II o ac i e powe managemen .
(d) G id equency a ia ion. (e) Zoom o Case III o Ba e y powe injec ion
o compensa ing equency change.
Fig. 12. Vi ual admi ance a ia ion o Case I and Case II om his sec ion,
in o de o modi y he ou pu powe o each con e e . G1,G2and G3is he
designa ion o each powe con e e , as in Fig. 10.
adds i ual ine ia capabili ies, helping o educe any equency
dis u bancein he g id.Two equency a ia ions(see Fig.15(a))
a e induced by o cing some ab up load changes (8.5 kW a 12
and−12 kW 18s) oobse e hedynamicbeha io o he con ol
sys em.
1) Local Simula ion: In Fig. 15, he esponse o he sys em
is demons a ed, when a equency a ia ion is o ced due o
6520 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 60, NO. 4, JULY/AUGUST 2024
Fig. 13. Simula ion alida ion: (a) Ac i e powe e e ence acking injec ed
o he g id, aking in o accoun he powe -sha ing be ween DEGs. (b) Re-
ac i e powe e e ence acking injec ed o he g id, aking in o accoun he
powe -sha ing be ween DEGs. G1,G2and G3is he designa ion o each powe
con e e . DEG is he powe de eloped by he powe plan , as Fig. 10 shows.
Ris he e e ence powe .
Fig. 14. Expe imen al alida ion: (a) Ac i e powe command, o al powe
injec ed o g idandpowe injec edbyeachcon e e .(b) Reac i epowe injec ed
o he g id, showing he command and he ac ual eac i e powe . The same
legends as Fig. 13 a e used in his plo . (c) and (d) Zoomed ac i e and eac i e
powe alues and sen e e ences. Ac ual is he powe ead by MODBUS TCP.
Sen is he powe sen by MODBUS TCP o he con e e .
a load-s ep change. Fig. 15(a) shows he equency a ia ion
by using he SCAC sys em connec ed o he g id (showing he
equency wi h and wi hou SCAC sys em). Wi h SCAC sys em,
he equencies ha appea s a e o wo di e en a ed powe o
he SCAC sys em. So equency is o ced o change a 12 s. In
case o using he SCAC sys em, he ESS will injec ac i e powe
(Fig. 13(a)) o he sys em in o de o help he g id o inc ease
i s equency, as i can be seen in b). On he o he hand, i a
suddenly equency inc ease appea s, as i can be seen a 18 s,
he ESS-SCAC will abso b powe om he sys em o dec ease
he equency. The e o e, he powe injec ion/abso p ion by he
Fig. 15. Simula ion: (a) F equency a ia ion o a weak g id due o a powe
change demand (wi h and wi hou SCAC), modi ying he ins alled powe in he
powe plan . The highe powe he lowe equency a ia ion ( 0is o he case
wi hou SCAC, 1is o he case wi h SCAC and Sn=6kVA,and 2is o
he case wi h SCAC and Sn=10 kVA. (b) Powe injec ed by each DEG, o
mi iga e he equency a ia ion om he case 1o b). G1,G2and G3a e he
designa ions o each powe con e e and DEG is he powe o he o al powe
plan , as Fig. 10 shows.
SCAC sys em will depend on he ine ia emula ed and also he
powe ins alled in hei ESS. I can be concluded om [13],
he mo e powe ins alled in he sys em, he lowe he equency
a ia ion will be.
2) Real-Time Expe imen al Tes : In hecaseo eal- imesim-
ula ion, heSCACsys emhasbeenemula edbyusing heba e y
module om CNG. Those esul s a e p esen ed in Fig. 16.Asi
can be seen i wo ks as he local simula ion, when a equency
dip appea s (Fig. 18(a)), DEGs injec powe ying o educe
he equency a ia ion, espec ing he powe -sha ing be ween
con e e s (Fig. 18(b)).In his case, as a ba e yemula o is used,
he SOC s a e o each ba e y is p esen ed in c), showing how
he ba e y is cha ged o discha ged.
C. Case III
This ope a ion mode is con olled by he DEG ope a o
(cen al con olle ), in o de o educe o inc ease he powe
injec ed by he powe plan , depending on he g id equi emen s,
as long as he a ings o he powe plan a e no exceeded.
This means ha i a powe change is eques ed by he g id
ope a o , he powe injec ed will a y, aking in o accoun ha
he RES a e wo king no mally a hei maximum powe poin
(MPP), and he excess o lack o powe ega ding he new powe
command will be managed by he SCAC-ESS. Once he g id
ope a o ’s se poin e u ns o no mal s a e, he s o age sys em
would s op abso bing ene gy, e u ning o ze o powe i he e
a e no equency changes. Ano he possible scena io is ha
he s o age sys em eaches i s maximum capaci y and i canno
abso b mo e ene gy. This would mean ha he PV s ing has o
be aken ou o i s maximum powe poin o comply wi h he
condi ions o he g id ope a o .
1) Local Simula ion: The a o emen ioned e ec can be ob-
se ed in Fig. 17, whe e a =40 s, g id ope a o ac i e powe
e e ence a ies (PDEG, as shown in Fig. 15(a), o cing o injec
less powe om he DEG sys em. In his si ua ion, ei he an