Ci a ion: Muga a, A.; Gue e o, J.M.;
Mah ani, K.; Pla e o, C.A.
Synch onous Gene a o S abili y
Cha ac e iza ion o Gas Powe
Plan s Using Load Rejec ion Tes s.
Appl. Sci. 2023,13, 11168. h ps://
doi.o g/10.3390/app132011168
Recei ed: 20 Sep embe 2023
Re ised: 8 Oc obe 2023
Accep ed: 9 Oc obe 2023
Published: 11 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/).
applied
sciences
A icle
Synch onous Gene a o S abili y Cha ac e iza ion o Gas
Powe Plan s Using Load Rejec ion Tes s
Asie Muga a 1, JoséM. Gue e o 2, Kuma Mah ani 1and Ca los A. Pla e o 1,*
1
Au oma ics, Elec ical and Elec onical Enginee ing and Indus ial Compu ing Depa men , E.T.S. Ingenie os
Indus iales, Uni e sidad Poli écnica de Mad id, 28006 Mad id, Spain; [email p o ec ed] (A.M.);
kuma [email p o ec ed] (K.M.)
2Elec ic Enginee ing Depa men , School o Enginee ing o Bilbao, Uni e sidad del País Vasco,
48940 Leioa, Spain; josemanuel.gue e [email p o ec ed]
*Co espondence: ca losan onio.pla e [email p o ec ed]
Abs ac :
Fo powe g id ope a o s, knowing he ansien esponse o he synch onous gene a o s
(SGs) included in hei g ids is impo an in o de o simula e and moni o aul s and o he con in-
gencies. Howe e , he ime cons an o he au oma ic ol age egula o (AVR) and speed go e no s
o SGs a e no as enough o show hei ansien dynamics in he case o a aul in he g id. This
pape p esen s a ieldwo k ca ied ou in mo e han 60 gas powe plan s, whe e he esponse o hei
con olle s was s udied. These powe plan s a e unning and supplying elec ici y o he Spanish g id.
The s udy consis s o eco ding some SG esponses in di e en si ua ions, a ying he AVR o he
speed go e no se poin s while he gene a o is unning a no-load condi ions, and also pe o ming
load ejec ion es s, achie ing a eal aul emula ion. Once all he da a a e ga he ed, a i ing o
he SG pa ame e s is pe o med by compu e simula ions using GENSAL, GAST and SEXS models
eplica ing he pe o med ield es s. This wo k allows us o build an accu a e ne wo k model o
he whole powe sys em and check which plan s a e ha ing ouble in he case o con ingencies in
he g id.
Keywo ds:
au oma ic ol age egula o ; load ejec ion; aul ; speed go e no ; synch onous gene a o ;
pa ame e se poin
1. In oduc ion
Elec ical powe sys ems a e by a one o he g ea es achie emen s o enginee ing and,
a he hea o hem, elec ical gene a o s a e ound, which pump he elec ical powe in o
he ne wo k. Back in he old days, he powe sys em was small and weakly in e connec ed,
bu wi h he indus ial de elopmen and he inc ease in household consump ions, i has
had o become la ge and mo e in e connec ed.
The expansion o he powe sys em, such as he addi ion o new gene a o s o ansmis-
sion lines, can lead o inc eased s ess on he sys em. This s ess can esul in an inc eased
likelihood o inco ec ope a ion, such as powe ou ages o equipmen ailu es, which can
nega i ely impac he eliabili y o he powe sys em. As a esul , he p edic abili y o he
sys em’s ope a ion can be educed, making i mo e di icul o ope a o s o an icipa e
and espond o po en ial issues in a imely manne . The e o e, i is impo an o ca e ully
plan and manage he expansion o he powe sys em o ensu e ha i emains eliable and
p edic able e en unde inc eased s ess. Addi ionally, in e connec ions wi h neighbo ing
powe sys ems make he ne wo k s onge . Howe e , hey expose he sys em o mo e
in e e ences because o he la ge co e ed a ea. This ype o si ua ion jeopa dizes he
sys em, causing i o ace many dis u bances simul aneously o wi hin a sho in e al o
ime [1].
A de aul powe sys em is mean o sus ain N-l con ingencies, i.e., he powe sys em
should be able o con inue ope a ing wi hou one o he elemen s ha compose i . Howe e ,
Appl. Sci. 2023,13, 11168. h ps://doi.o g/10.3390/app132011168 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2023,13, 11168 2 o 13
i does no gua an ee ull secu i y o he powe sys em [
2
]. The main eason o he sys ems’
blackou s in a powe sys em is due o dynamic ins abili y and ol age ins abili y [3–6]. In
his ield, many ad ances in imp o ing he ne wo k in e connec ion s abili y and e o s
in es o ing he sys em a e majo dis u bances ha e been ca ied ou [
7
,
8
]. Ne e heless,
he e a e p oblems de ining and classi ying powe sys em s abili y p oblems as hey can be
ol age, equency o load angle s abili y p oblems. This is a ask ha aims o p o ide a
sys ema ic basis o he discussion on issues like powe sys em secu i y and eliabili y [9].
One impo an poin ha mus be ema ked is he p o ec ion sys em and i s ela ion-
ship wi h he sys em’s s abili y, which can cause a majo ou age in he powe sys em [
10
].
P o ec ion elays a e in ol ed in abou h ee ou o ou con ingencies in he elec ic sys-
em [
11
] due o w ong sys em coo dina ion o imp ope con olle s’ adjus men s a powe
plan s, which cause he cascade ipping o ups eam elays.
In o de o sol e his issue, powe sys em ope a o s (PSOs) equi e ansien echnical
pa ame e s om he di e en powe plan s in o de o be e i hei p o ec ions, pe o m
con ingencies simula ions and deeply s udy he ansien beha io o he g ids. Howe e ,
he es ima ion o hese pa ame e s is no a i ial ask. Fo example, in synch onous
gene a o s (SGs), he au oma ic ol age egula o (AVR) ol age a ia ion a es a e qui e
slow in pe o ming he emula ed ansien s equi ed o cha ac e ize he machines in
compliance wi h he equi emen s o he PSO.
In his pape , h ee eal cases o he s udy and cha ac e iza ion o eal gas powe
plan s a e exposed om mo e han 60 examined powe plan s, all coupled o he Spanish
powe g id, he p oduc o a p ojec ca ied ou o he Spanish PSO. A load es ejec ion is
p oposed o sol e he p oblem and p o oke a as ejec ion esponse simila o a eal aul
in o de o s udy he ansien beha io . Then, he ansien powe plan pa ame e s a e
i ed h ough simula ions o eplica e he eal load ejec ion esponse.
The model used in his pape o eplica e he powe plan gas u bine and speed
go e no is he GAST model, as i is one o he mos used o dynamic modeling [
12
–
14
].
The AVR model chosen was he simpli ied exci a ion sys em (SEXS) [
15
,
16
] and, o ep esen
he SG, he model used was GENSAL [
17
–
19
]. The ull models ha combine GAST, SEXS
and GENSAL a e al eady alida ed models ha can be ound in he li e a u e [
20
–
24
] and
hey a e widely used by PSOs in simula ion p og ams like PSS/E®.
Wi h he esea ch mo i a ions explained, he main con ibu ions o his s udy a e
summed up as ollows:
•
Pe o ming load ejec ion es s is p oposed in o de o s udy he powe plan ’s and
synch onous gene a o ’s ansien esponse. This es allows us o p o oke ealis ic
as ansien s emula ing eal aul s whe e he AVR and he speed go e no dynamics
a e no as enough.
•
Wi h he load ejec ion es s’ da a, well-known models a e i ed o sa is y he dynamic
esponse in o de o p o ide his in o ma ion o he co esponding PSO.
•
To co obo a e he dynamic ansien esponse cha ac e iza ion, load ejec ion es s
ha e been ca ied ou o e mo e han 60 eal powe plan s o he Spanish powe g id.
In his manusc ip , h ee o hem a e shown as examples.
The pape is s uc u ed as ollows: i s , Sec ion 2desc ibes he heo e ical model used
o he ansien s abili y pa ame e s acquisi ion and i ing. Secondly, Sec ion 3shows
he expe imen al es s ca ied ou in h ee eal gas powe plan s. A e wa ds, Sec ion 4is
ocused on he simula ion esul s o pa ame e s i ing. Finally, Sec ion 5concludes he
pape wi h he main ideas ob ained du ing he esea ch.
2. Theo e ical Models
As he au oma ic ol age egula o (AVR) esponse is no as enough o clea ly show
he ansien dynamics o a synch onous gene a o (SG) du ing a aul e en , a load ejec ion
es is p oposed o model he SG beha io . A load ejec ion es is a con olled and delibe a e
es whe e he SG is subjec ed o a sudden educ ion in load. This helps o simula e a aul
condi ion and p o ides aluable in o ma ion abou he SG’s ansien esponse.
Appl. Sci. 2023,13, 11168 3 o 13
Unde s anding he ansien dynamics o SGs du ing aul e en s is c ucial o powe
g id ope a o s as i allows hem o moni o and simula e aul s and o he con ingencies
in he powe sys em. This in o ma ion can be used o imp o e he o e all s abili y and
eliabili y o he powe sys em. The p oposed model in Figu e 1illus a es he SG’s beha io
du ing a load ejec ion es , whe e he main ci cui b eake (CB) is opened once he SG is
unning a a ed speed and powe , and he model can also be ob ained a educed powe .
Appl. Sci. 2023, 13, x FOR PEER REVIEW 3 o 13
2. Theo e ical Models
As he au oma ic ol age egula o (AVR) esponse is no as enough o clea ly show
he ansien dynamics o a synch onous gene a o (SG) du ing a aul e en , a load ejec-
ion es is p oposed o model he SG beha io . A load ejec ion es is a con olled and
delibe a e es whe e he SG is subjec ed o a sudden educ ion in load. This helps o sim-
ula e a aul condi ion and p o ides aluable in o ma ion abou he SG’s ansien esponse.
Unde s anding he ansien dynamics o SGs du ing aul e en s is c ucial o powe
g id ope a o s as i allows hem o moni o and simula e aul s and o he con ingencies in
he powe sys em. This in o ma ion can be used o imp o e he o e all s abili y and eli-
abili y o he powe sys em. The p oposed model in Figu e 1 illus a es he SG’s beha io
du ing a load ejec ion es , whe e he main ci cui b eake (CB) is opened once he SG is
unning a a ed speed and powe , and he model can also be ob ained a educed powe .
GAST
SEXS
Powe
Sys em
Powe
ans o me
CB
GENSAL
SG
Speed go e no
AVR
w
Pe
V
Pmec
Figu e 1. Elec ical scheme and simula ion model co ela ion o an SG connec ed o an in ini e
powe bus.
In Figu e 1, he models used in simula ions and hei co ela ion a e plo ed. The
heo e ical model consis s o he SG as GENSAL, which p oduces as ou pu s he elec ical
powe (Pe) and he o o speed (w ), he speed go e no as GAST, whose ou pu is me-
chanical powe (Pmec), and he AVR as SEXS, whose ou pu is he ield ol age (V ). Each o
he models is desc ibed in mo e de ail below.
Sa u a ion ac o a 1.2 pu ol age
S(1.2)
2.1. SG Model: GENSAL
The SG is shaped using he GENSAL model, which is included in Figu e 2. Table 1
shows all he pa ame e s ela ed o Figu e 2. Mos o hese pa ame e s a e gi en by he
manu ac u e .
Table 1. GENSAL model pa ame e s.
Desc ip ion
Pa ame e
Uni s
d-axis open ci cui ansien ime cons an
T′do
[s]
d-axis open ci cui sub- ansien ime cons an
T″do
[s]
q-axis open ci cui sub- ansien ime cons an
T″qo
[s]
Machine ine ia
H
[s]
Speed damping
D
[s]
d-axis synch onous eac ance
Xd
[pu]
q-axis synch onous eac ance
Xq
[pu]
d-axis ansien eac ance
X′d
[pu]
Sub- ansien eac ance
X″d
[pu]
Leakage eac ance
Xl
[pu]
Sa u a ion ac o a 1.0 pu ol age
S(1.0)
Figu e 1.
Elec ical scheme and simula ion model co ela ion o an SG connec ed o an in ini e
powe bus.
In Figu e 1, he models used in simula ions and hei co ela ion a e plo ed. The
heo e ical model consis s o he SG as GENSAL, which p oduces as ou pu s he elec ical
powe (P
e
) and he o o speed (w
), he speed go e no as GAST, whose ou pu is mechan-
ical powe (P
mec
), and he AVR as SEXS, whose ou pu is he ield ol age (V
). Each o he
models is desc ibed in mo e de ail below.
Sa u a ion ac o a 1.2 pu ol age S(1.2)
2.1. SG Model: GENSAL
The SG is shaped using he GENSAL model, which is included in Figu e 2. Table 1
shows all he pa ame e s ela ed o Figu e 2. Mos o hese pa ame e s a e gi en by he
manu ac u e .
Appl. Sci. 2023, 13, x FOR PEER REVIEW 4 o 13
∑
∑
∑
∑
∑
∑
Field cu en
o exci e
E d +
-
1
T’do·s
lad·i d
1
T’’do·s
X’’d-Xl
X’d-Xl
+
-
-
+E’’q+
+
ψ’d
IdIq
X’d-X’’d
(X’d-X’’l)2
Xd-X’d
+
++
+
+
X’d-XlXq-X’’q
1
T’’qo·s
- E’’d
Figu e 2. GENSAL model o he SG.
Howe e , h ee pa ame e s need o be calcula ed, which include wo e ms ela ed
o he sa u a ion ac o s and he ine ia o he powe plan . These ac o s a e encompassed
by he u bine and he al e na o .
On he one hand, he sa u a ion pa ame e s a e calcula ed acco ding o exp essions
(1) and (2) as:
𝑆(1.0) =𝐴10 −𝐵10
𝐵10
(1)
𝑆(1.2) =𝐴12 −𝐵12
𝐵12
(2)
The alues A10, B10, A12 and B12 a e pa ame e s ha a e equi ed o be calcula ed o
he modeling o a synch onous gene a o . These pa ame e s a e ob ained om he no-
load cha ac e is ic, which can be ound in he gene a o da ashee . Figu e 3 shows an ex-
ample o a ypical sa u a ion es plo ha is used o ob ain he no-load cha ac e is ic.
Figu e 3. SG no-load cha ac e is ic.
On he o he hand, du ing he load ejec ion es , he ine ia o he sys em can be
de e mined. The kine ic model o he sys em can be ep esen ed by exp ession (3):
𝜔𝑟(𝑡)=1
2𝐻∫𝑇𝑎(𝑡)𝑑𝑡= 1
2𝐻∫[𝑇𝑚𝑒𝑐(𝑡)−𝑇𝑒𝑙𝑒𝑐(𝑡)]𝑑𝑡
(3)
whe e ω ( ) is he o o speed, Tmec( ) is he sha o que due o he u bine, Telec( ) is he
elec ical o que due o he ne wo k load and H is he machine ine ia.
A he momen o load ejec ion, he elec ical o que becomes null (Telec( ) = 0) bu he
mechanical o que emains. The ine ia o he machine de e mines he equency a ia-
ion. The e o e, he alues o ∆ and ∆ used o de e mine he ine ia mus be calcula ed as
Figu e 2. GENSAL model o he SG.
Appl. Sci. 2023,13, 11168 4 o 13
Table 1. GENSAL model pa ame e s.
Desc ip ion Pa ame e Uni s
d-axis open ci cui ansien ime cons an T0
do [s]
d-axis open ci cui sub- ansien ime cons an T00
do [s]
q-axis open ci cui sub- ansien ime cons an T00 qo [s]
Machine ine ia H[s]
Speed damping D[s]
d-axis synch onous eac ance Xd[pu]
q-axis synch onous eac ance Xq[pu]
d-axis ansien eac ance X0
d[pu]
Sub- ansien eac ance X00
d[pu]
Leakage eac ance Xl[pu]
Sa u a ion ac o a 1.0 pu ol age S(1.0)
Howe e , h ee pa ame e s need o be calcula ed, which include wo e ms ela ed o
he sa u a ion ac o s and he ine ia o he powe plan . These ac o s a e encompassed by
he u bine and he al e na o .
On he one hand, he sa u a ion pa ame e s a e calcula ed acco ding o exp essions (1)
and (2) as:
S(1.0)=A10 −B10
B10
(1)
S(1.2)=A12 −B12
B12
(2)
The alues A
10
,B
10
,A
12
and B
12
a e pa ame e s ha a e equi ed o be calcula ed o
he modeling o a synch onous gene a o . These pa ame e s a e ob ained om he no-load
cha ac e is ic, which can be ound in he gene a o da ashee . Figu e 3shows an example
o a ypical sa u a ion es plo ha is used o ob ain he no-load cha ac e is ic.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 4 o 13
∑
∑
∑
∑
∑
∑
Field cu en
o exci e
E
d
+
-
1
T’
do
·s
l
ad
·i
d
1
T’’
do
·s
X’’
d
-X
l
X’
d
-X
l
+
-
-
+E’’
q
+
+
ψ’
d
I
d
I
q
X’
d
-X’’
d
(X’
d
-X’’
l
)
2
X
d
-X’
d
+
++
+
+
X’
d
-X
l
X
q
-X’’
q
1
T’’
qo
·s
- E’’
d
Figu e 2. GENSAL model o he SG.
Howe e , h ee pa ame e s need o be calcula ed, which include wo e ms ela ed
o he sa u a ion ac o s and he ine ia o he powe plan . These ac o s a e encompassed
by he u bine and he al e na o .
On he one hand, he sa u a ion pa ame e s a e calcula ed acco ding o exp essions
(1) and (2) as:
𝑆
.
𝐴
𝐵
𝐵
(1)
𝑆
.
𝐴
𝐵
𝐵
(2)
The alues A
10
, B
10
, A
12
and B
12
a e pa ame e s ha a e equi ed o be calcula ed o
he modeling o a synch onous gene a o . These pa ame e s a e ob ained om he no-
load cha ac e is ic, which can be ound in he gene a o da ashee . Figu e 3 shows an ex-
ample o a ypical sa u a ion es plo ha is used o ob ain he no-load cha ac e is ic.
Figu e 3. SG no-load cha ac e is ic.
On he o he hand, du ing he load ejec ion es , he ine ia o he sys em can be
de e mined. The kine ic model o he sys em can be ep esen ed by exp ession (3):
𝜔
𝑡1
2𝐻𝑇
𝑡𝑑𝑡 1
2𝐻𝑇
𝑡𝑇
𝑡𝑑𝑡
(3)
whe e ω
( ) is he o o speed, T
mec
( ) is he sha o que due o he u bine, T
elec
( ) is he
elec ical o que due o he ne wo k load and H is he machine ine ia.
A he momen o load ejec ion, he elec ical o que becomes null (T
elec
( ) = 0) bu he
mechanical o que emains. The ine ia o he machine de e mines he equency a ia-
ion. The e o e, he alues o ∆ and ∆ used o de e mine he ine ia mus be calcula ed as
Figu e 3. SG no-load cha ac e is ic.
On he o he hand, du ing he load ejec ion es , he ine ia o he sys em can be
de e mined. The kine ic model o he sys em can be ep esen ed by exp ession (3):
ω ( )=1
2HZTa( )d =1
2HZ[Tmec( )−Telec( )]d (3)
whe e
ω
( ) is he o o speed, T
mec
( ) is he sha o que due o he u bine, T
elec
( ) is he
elec ical o que due o he ne wo k load and His he machine ine ia.
A he momen o load ejec ion, he elec ical o que becomes null (T
elec
( ) = 0) bu he
mechanical o que emains. The ine ia o he machine de e mines he equency a ia ion.
The e o e, he alues o
∆
and
∆
used o de e mine he ine ia mus be calcula ed as he
di e ence be ween he s eady s a e and he i s sample ob ained a e opening he main
Appl. Sci. 2023,13, 11168 5 o 13
ci cui b eake . By pe o ming his, he in luence o he speed go e no on he equency
change is no aken in o conside a ion.
Using pe -uni alues o he machine, he machine ine ia, H, can be calcula ed h ough
(4). Also, a g aphical example is plo ed in Figu e 4.
H=Pmec[pu]·∆ [s]
2·∆ [pu](4)
Appl. Sci. 2023, 13, x FOR PEER REVIEW 5 o 13
he diffe ence be ween he s eady s a e and he i s sample ob ained a e opening he
main ci cui b eake . By pe o ming his, he in luence o he speed go e no on he e-
quency change is no aken in o conside a ion.
Using pe -uni alues o he machine, he machine ine ia, H, can be calcula ed
h ough (4). Also, a g aphical example is plo ed in Figu e 4.
𝐻𝑃
𝑝𝑢∆𝑡𝑠
2∆
𝑓
𝑝𝑢
(4)
Figu e 4. Case example: calcula ing SG ine ia on an ac ual gene a o .
The P
mec
pa ame e gi en in (4) is calcula ed as:
𝑃
𝑝𝑢𝑃
𝑆
(5)
whe e P
es
is he ac i e powe deli e ed o he g id be o e he load ejec ion, S
b
is he ma-
chine a ed powe , ∆ is he ime diffe ence be ween he s eady-s a e measu emen and
he load ejec ion measu emen and ∆ is he equency diffe ence be ween he s eady-
s a e measu emen and he load ejec ion measu emen .
2.2. AVR Model: SEXS
The model chosen o ep esen he beha iou o he powe plan s AVR is SEXS. Fig-
u e 5 shows he ol age egula ion con ol diag am o he AVR model. In he AVR-SEXS
model, he inpu ol age o he exci a ion sys em is deno ed by VS. This ol age is ob-
ained by adding wo signals—VPSS, which ep esen s he ol age eedback om he
powe sys em s abilize , and VOEL, which is he diffe ence be ween he e e ence ol age
se poin and he gene a o e minal ol age. Thus, he alue o VS is he summa ion o
hese wo signals and se es as he inpu o he exci a ion sys em. Addi ionally, he model
uses wo o he inpu s: V
e
, which is he e e ence ol age se poin , and V
C
, which is he
compensa ed e minal ol age, bo h exp essed in pe -uni alues.
∑
+
-1 + s·T
A
+
1 + s·T
B
K
1 + s·T
E
E
d
V
S
V
e
V
C
E
MIN
E
MAX
Figu e 5. Simpli ied exci a ion sys em (SEXS) model.
Figu e 4. Case example: calcula ing SG ine ia on an ac ual gene a o .
The Pmec pa ame e gi en in (4) is calcula ed as:
Pmec[pu]=P es
Sb
(5)
whe e P
es
is he ac i e powe deli e ed o he g id be o e he load ejec ion, S
b
is he
machine a ed powe ,
∆
is he ime di e ence be ween he s eady-s a e measu emen and
he load ejec ion measu emen and
∆
is he equency di e ence be ween he s eady-s a e
measu emen and he load ejec ion measu emen .
2.2. AVR Model: SEXS
The model chosen o ep esen he beha iou o he powe plan s AVR is SEXS. Figu e 5
shows he ol age egula ion con ol diag am o he AVR model. In he AVR-SEXS model,
he inpu ol age o he exci a ion sys em is deno ed by V
S
. This ol age is ob ained by
adding wo signals—VPSS, which ep esen s he ol age eedback om he powe sys em
s abilize , and VOEL, which is he di e ence be ween he e e ence ol age se poin and
he gene a o e minal ol age. Thus, he alue o V
S
is he summa ion o hese wo signals
and se es as he inpu o he exci a ion sys em. Addi ionally, he model uses wo o he
inpu s: V
e
, which is he e e ence ol age se poin , and V
C
, which is he compensa ed
e minal ol age, bo h exp essed in pe -uni alues.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 5 o 13
he di e ence be ween he s eady s a e and he i s sample ob ained a e opening he
main ci cui b eake . By pe o ming his, he in luence o he speed go e no on he e-
quency change is no aken in o conside a ion.
Using pe -uni alues o he machine, he machine ine ia, H, can be calcula ed
h ough (4). Also, a g aphical example is plo ed in Figu e 4.
𝐻=𝑃𝑚𝑒𝑐[𝑝𝑢]·∆𝑡[𝑠]
2·∆𝑓[𝑝𝑢]
(4)
Figu e 4. Case example: calcula ing SG ine ia on an ac ual gene a o .
The Pmec pa ame e gi en in (4) is calcula ed as:
𝑃𝑚𝑒𝑐[𝑝𝑢]=𝑃𝑡𝑒𝑠𝑡
𝑆𝑏
(5)
whe e P es is he ac i e powe deli e ed o he g id be o e he load ejec ion, Sb is he ma-
chine a ed powe , ∆ is he ime di e ence be ween he s eady-s a e measu emen and
he load ejec ion measu emen and ∆ is he equency di e ence be ween he s eady-
s a e measu emen and he load ejec ion measu emen .
2.2. AVR Model: SEXS
The model chosen o ep esen he beha iou o he powe plan s AVR is SEXS. Fig-
u e 5 shows he ol age egula ion con ol diag am o he AVR model. In he AVR-SEXS
model, he inpu ol age o he exci a ion sys em is deno ed by VS. This ol age is ob-
ained by adding wo signals—VPSS, which ep esen s he ol age eedback om he
powe sys em s abilize , and VOEL, which is he di e ence be ween he e e ence ol age
se poin and he gene a o e minal ol age. Thus, he alue o VS is he summa ion o
hese wo signals and se es as he inpu o he exci a ion sys em. Addi ionally, he model
uses wo o he inpu s: V e , which is he e e ence ol age se poin , and VC, which is he
compensa ed e minal ol age, bo h exp essed in pe -uni alues.
∑
+
-1 + s·TA
+
1 + s·TB
K
1 + s·TEE d
VS
V e
VC
EMIN
EMAX
Figu e 5. Simpli ied exci a ion sys em (SEXS) model.
Figu e 5. Simpli ied exci a ion sys em (SEXS) model.
Appl. Sci. 2023,13, 11168 6 o 13
Table 2displays he pa ame e s o he AVR model, which a e de e mined h ough
simula ion i ing based on es s. These es s include an indi idual es o he AVR con olle
ha a ies he ol age e e ence wi hou a load, as well as a load ejec ion es ha enables
he i ing o he ansien esponse. The ansien esponse allows o he i ing o he ime
cons an T
E
, as well as he i s block pa ame e s T
A
and T
B
. The emaining pa ame e s can
be i ed using he s eady-s a e a ying poin s obse ed du ing no-load condi ions.
Table 2. SEXS model pa ame e s.
Desc ip ion Pa ame e Uni s
Ra e o change in he exci a ion sys em nume a o TA[s]
Ra e o change in he exci a ion sys em denomina o TB[s]
Exci e gain K[pu]
Exci e ime cons an TE[s]
Maximum AVR ou pu EMIN [pu]
Minimum AVR ou pu EMAX [pu]
2.3. Speed Go e no Model: GAST
The model chosen o ep esen he beha io o he powe plan s speed go e no is
GAST. The model is plo ed in Figu e 6. Fu he mo e, Table 3collec s he pa ame e s
ela ed o he GAST model.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 6 o 13
Table 2 displays he pa ame e s o he AVR model, which a e de e mined h ough
simula ion i ing based on es s. These es s include an indi idual es o he AVR con ol-
le ha a ies he ol age e e ence wi hou a load, as well as a load ejec ion es ha
enables he i ing o he ansien esponse. The ansien esponse allows o he i ing
o he ime cons an TE, as well as he i s block pa ame e s TA and TB. The emaining
pa ame e s can be i ed using he s eady-s a e a ying poin s obse ed du ing no-load
condi ions.
Table 2. SEXS model pa ame e s.
Desc ip ion
Pa ame e
Uni s
Ra e o change in he exci a ion sys em nume a o
TA
[s]
Ra e o change in he exci a ion sys em denomina o
TB
[s]
Exci e gain
K
[pu]
Exci e ime cons an
TE
[s]
Maximum AVR ou pu
EMIN
[pu]
Minimum AVR ou pu
EMAX
[pu]
2.3. Speed Go e no Model: GAST
The model chosen o ep esen he beha io o he powe plan s speed go e no is
GAST. The model is plo ed in Figu e 6. Fu he mo e, Table 3 collec s he pa ame e s e-
la ed o he GAST model.
∑
Low
Value
Ga e
D u b
∑
∑∑
Vmin
Vmax
1
R
1
1 + s·T1
1
1 + s·T2
1
1 + s·T3
KT
Load
e e ence
Load limi
w
Pmec+-
+
+ +
-
+-
Figu e 6. Speed go e no model (GAST).
Table 3. GAST model pa ame e s.
Desc ip ion
Pa ame e
Uni s
Pe manen d oop
R
[pu]
Go e no mechanism ime cons an
T1
[s]
Tu bine powe ime cons an
T2
[s]
Tu bine exhaus empe a u e ime cons an
T3
[s]
Ambien empe a u e load limi
AT
[pu]
Tempe a u e limi e gain
KT
[pu]
Maximum u bine powe
Vmax
[pu]
Minimum u bine powe
Vmin
[pu]
Tu bine damping ac o
D u b
[pu]
Figu e 6. Speed go e no model (GAST).
Table 3. GAST model pa ame e s.
Desc ip ion Pa ame e Uni s
Pe manen d oop R[pu]
Go e no mechanism ime cons an T1[s]
Tu bine powe ime cons an T2[s]
Tu bine exhaus empe a u e ime cons an T3[s]
Ambien empe a u e load limi AT[pu]
Tempe a u e limi e gain KT[pu]
Maximum u bine powe Vmax [pu]
Minimum u bine powe Vmin [pu]
Tu bine damping ac o D u b [pu]
As o he p e ious AVR model, he speed go e no pa ame e s a e collec ed om
a gas injec ion se poin changing es and om a load ejec ion es . The damping ac o
and une cons an s a e i ed om he load es ejec ion; meanwhile, he uppe and lowe
ope a ion limi s and pe manen d oop a e i ed om he s eady-s a e se poin change es s.
Appl. Sci. 2023,13, 11168 7 o 13
The pa ame e s’ i ing om es s and simula ions is an i e a i e p ocess, and he e a e
some s anda ds pa ame e p oposed by [
25
,
26
]. Howe e , hose a e used jus o ini ialize
he simula ion i e a ion; i s , he indi idual con olle s mus be simula ed, because he
egula o s (SEXS and GAST) a e decoupled and i is easie o ge nea e o he inal solu ion.
A e ob aining he pa ame e s h ough he p e ious simula ions, he load ejec ion is
simula ed. The solu ion is hen checked, and i i is unsa is ac o y, he no-load se poin
simula ion mus be e un o ine- une he p e ious adjus men s. Subsequen ly, he load
ejec ion simula ion mus be pe o med again. This i e a i e p ocess should be epea ed
un il all he simula ions con e ge o a sa is ac o y adjus men .
Finally, a schema ic lowcha ha sums up he powe plan cha ac e iza ion me hod-
ology using load ejec ion es s is plo ed in Figu e 7. The i e a i e p ocess used o i
he pa ame e s o he GAST and SEXS models has been ca ied ou manually in o de
o adjus he i s ansien oscilla ion, which is he mos impo an o s abili y s udies.
Howe e , o he i ing ools such as e olu iona y algo i hms could be used o sol e he
p oblem [27–29].
Appl. Sci. 2023, 13, x FOR PEER REVIEW 7 o 13
As o he p e ious AVR model, he speed go e no pa ame e s a e collec ed om a
gas injec ion se poin changing es and om a load ejec ion es . The damping ac o
and une cons an s a e i ed om he load es ejec ion; meanwhile, he uppe and lowe
ope a ion limi s and pe manen d oop a e i ed om he s eady-s a e se poin change
es s.
The pa ame e s’ i ing om es s and simula ions is an i e a i e p ocess, and he e
a e some s anda ds pa ame e p oposed by [25,26]. Howe e , hose a e used jus o ini-
ialize he simula ion i e a ion; i s , he indi idual con olle s mus be simula ed, because
he egula o s (SEXS and GAST) a e decoupled and i is easie o ge nea e o he inal
solu ion.
A e ob aining he pa ame e s h ough he p e ious simula ions, he load ejec ion
is simula ed. The solu ion is hen checked, and i i is unsa is ac o y, he no-load se poin
simula ion mus be e un o ine- une he p e ious adjus men s. Subsequen ly, he load
ejec ion simula ion mus be pe o med again. This i e a i e p ocess should be epea ed
un il all he simula ions con e ge o a sa is ac o y adjus men .
Finally, a schema ic lowcha ha sums up he powe plan cha ac e iza ion me h-
odology using load ejec ion es s is plo ed in Figu e 7. The i e a i e p ocess used o i
he pa ame e s o he GAST and SEXS models has been ca ied ou manually in o de o
adjus he i s ansien oscilla ion, which is he mos impo an o s abili y s udies. How-
e e , o he i ing ools such as e olu iona y algo i hms could be used o sol e he p ob-
lem [27–29].
S a
Load ejec ion es
Measu e: PMec, V , w
GENSAL modelGAST model SEXS model
Calcula e ∆ and
∆
De ine R, T1, T2, T3,
AT, KT and D u b
De ine TA, TB and
TE
Calcula e H wi h
eq. (4)
V w
AVR da aSG da aGo e no da a
A e sim. simila
o es s?
A e sim. simila
o es s?
Expe imen al
da a
Expe imen al
da a
Expe imen al
da a
Simula ion
esul s
Simula ion
esul s
Powe plan
inal da a o
PSO
End
I e a i e p ocess
I e a i e p ocess
YesYesNo No
Figu e 7. Schema ic lowcha o he powe plan cha ac e iza ion ia load ejec ion es .
3. Expe imen al Tes s
The audi p ocess is composed o wo g oups o es s ha ha e o be ca ied ou in
o de o obse e he dynamic esponse o he gas powe plan . The AVR and speed go -
e no con olle s ha e o be i s ly es ed indi idually and hen oge he .
Figu e 7. Schema ic lowcha o he powe plan cha ac e iza ion ia load ejec ion es .
3. Expe imen al Tes s
The audi p ocess is composed o wo g oups o es s ha ha e o be ca ied ou
in o de o obse e he dynamic esponse o he gas powe plan . The AVR and speed
go e no con olle s ha e o be i s ly es ed indi idually and hen oge he .
Appl. Sci. 2023,13, 11168 8 o 13
3.1. Tes P ocedu e
The i s s ep in he audi p ocess was ob aining he p ojec dossie o he powe plan ,
i.e., he summa y desc ip ion o he en i e p ojec o he powe plan cons uc ion and i s
ou pu s. I con ains all he echnical in o ma ion and a desc ip ion o each componen o
he plan .
Nex , indi idual con olle es s we e pe o med, which can be classi ied in o wo
ypes: AVR se poin changes wi hou load and speed go e no se poin changes wi hou
load. To ca y ou hese es s, he powe plan ’s load was g adually educed un il he
gene a o becomes idle, a e which he se poin s o he AVR and speed go e no can
be changed (ei he au oma ically o manually h ough he con ol panel) o obse e how
he con olle s espond o ol age and equency a ia ions. This no-load es p o ides
in o ma ion abou how he con olle s beha e as sepa a e en i ies.
A second se o es s was conduc ed o obse e how he AVR and speed go e no
con olle s beha e when wo king oge he . Load ejec ion es s we e hen ca ied ou
o e alua e he ansien esponse o powe g id aul s. Fo hese es s, he load was
se o be ween 10% and 15% o he gene a o ’s a ed load o p e en o e s essing he
sys em, which could po en ially damage he plan . Once he load eached s eady-s a e
ope a ion, he main ci cui b eake was u ned o o isola e he gene a o and c ea e an
islanded condi ion.
3.2. Measu ing De ices and Con igu a ion
A se ies o eco ds o he es s we e ca ied ou on mo e han 60 gas powe plan s
o he Spanish powe g id. The s eady-s a e and ansien measu emen s we e egis e ed
using a 4-channel oscilloscope whe e he machine’s equency (CH1 = ), he AVR ou pu
ol age (CH2 = E
FD
) and he ou pu ac i e and eac i e powe (CH3 = P
S
, CH4 = Q
S
) we e
measu ed. The las wo a iables we e used o i 10–15% o he a ed powe condi ion and
o moni o he load ejec ion. The egis e s we e ca ied ou du ing 60 s, bu di e en ime
sp ead esponses we e ound a ending o he di e en powe plan s ine ias and o he
AVR and speed go e no se ings. The maximum, minimum and ime se ings o each
channel can be also obse ed in he oscilloscope egis e s shown in Figu es 8–10.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 8 o 13
3.1. Tes P ocedu e
The i s s ep in he audi p ocess was ob aining he p ojec dossie o he powe plan ,
i.e., he summa y desc ip ion o he en i e p ojec o he powe plan cons uc ion and i s
ou pu s. I con ains all he echnical in o ma ion and a desc ip ion o each componen o
he plan .
Nex , indi idual con olle es s we e pe o med, which can be classi ied in o wo
ypes: AVR se poin changes wi hou load and speed go e no se poin changes wi hou
load. To ca y ou hese es s, he powe plan ’s load was g adually educed un il he gen-
e a o becomes idle, a e which he se poin s o he AVR and speed go e no can be
changed (ei he au oma ically o manually h ough he con ol panel) o obse e how he
con olle s espond o ol age and equency a ia ions. This no-load es p o ides in o -
ma ion abou how he con olle s beha e as sepa a e en i ies.
A second se o es s was conduc ed o obse e how he AVR and speed go e no
con olle s beha e when wo king oge he . Load ejec ion es s we e hen ca ied ou o
e alua e he ansien esponse o powe g id aul s. Fo hese es s, he load was se o
be ween 10% and 15% o he gene a o ’s a ed load o p e en o e s essing he sys em,
which could po en ially damage he plan . Once he load eached s eady-s a e ope a ion,
he main ci cui b eake was u ned off o isola e he gene a o and c ea e an islanded
condi ion.
3.2. Measu ing De ices and Con igu a ion
A se ies o eco ds o he es s we e ca ied ou on mo e han 60 gas powe plan s o
he Spanish powe g id. The s eady-s a e and ansien measu emen s we e egis e ed us-
ing a 4-channel oscilloscope whe e he machine’s equency (CH1 = ), he AVR ou pu
ol age (CH2 = EFD) and he ou pu ac i e and eac i e powe (CH3 = Ps, CH4 = Qs) we e
measu ed. The las wo a iables we e used o i 10–15% o he a ed powe condi ion
and o moni o he load ejec ion. The egis e s we e ca ied ou du ing 60 s, bu diffe en
ime sp ead esponses we e ound a ending o he diffe en powe plan s ine ias and o
he AVR and speed go e no se ings. The maximum, minimum and ime se ings o each
channel can be also obse ed in he oscilloscope egis e s shown in Figu es 8–10.
(a) (b) (c)
Figu e 8. Plan 1 es s: (a) no-load ol age se poin changes; (b) no-load equency se poin changes;
(c) load ejec ion es a PS = 1.7 MW and QS = 1.4 MVA .
Figu e 8.
Plan 1 es s: (
a
) no-load ol age se poin changes; (
b
) no-load equency se poin changes;
(c) load ejec ion es a PS= 1.7 MW and QS= 1.4 MVA .
Appl. Sci. 2023,13, 11168 9 o 13
Appl. Sci. 2023, 13, x FOR PEER REVIEW 9 o 13
(a) (b) (c)
Figu e 9. Plan 2 es s: (a) no-load ol age se poin changes; (b) no-load equency se poin changes;
(c) load ejec ion es a PS = 5 MW and QS = 5 MVA .
(a) (b) (c)
Figu e 10. Plan 3 es s: (a) no-load ol age se poin changes; (b) no-load equency se poin
changes; (c) load ejec ion es a PS = 15 MW and QS = 10 MVA .
3.3. Cases o S udy
F om he es ed powe plan s, h ee o hem a e shown and analyzed in his sec ion.
Some in o ma ion abou he gene a o s is collec ed in Table 4.
Table 4. Gas powe plan s in o ma ion.
Powe
Plan SG Manu ac u e SG Model Ra ed Powe
[MVA]
Ra ed Vol age
[kV]
1 ABB HSG 6.5 6.3
2 ABB GBA 1250 22.5 11
3 HMA DG215ZL-04 47.7 11
Resul s o he no-load AVR a ia ions, speed go e no beha io and load ejec ion
es s a e plo ed in Figu e 7, Figu e 9 and Figu e 10 o plan s 1, 2 and 3 espec i ely. I can
be obse ed ha , a ending o he powe plan , as he pa ame e s and SGs a e diffe en ,
he esponses a y conside ably om one ano he .
Figu e 9.
Plan 2 es s: (
a
) no-load ol age se poin changes; (
b
) no-load equency se poin changes;
(c) load ejec ion es a PS= 5 MW and QS= 5 MVA .
Appl. Sci. 2023, 13, x FOR PEER REVIEW 9 o 13
(a) (b) (c)
Figu e 9. Plan 2 es s: (a) no-load ol age se poin changes; (b) no-load equency se poin changes;
(c) load ejec ion es a PS = 5 MW and QS = 5 MVA .
(a) (b) (c)
Figu e 10. Plan 3 es s: (a) no-load ol age se poin changes; (b) no-load equency se poin
changes; (c) load ejec ion es a PS = 15 MW and QS = 10 MVA .
3.3. Cases o S udy
F om he es ed powe plan s, h ee o hem a e shown and analyzed in his sec ion.
Some in o ma ion abou he gene a o s is collec ed in Table 4.
Table 4. Gas powe plan s in o ma ion.
Powe
Plan SG Manu ac u e SG Model Ra ed Powe
[MVA]
Ra ed Vol age
[kV]
1 ABB HSG 6.5 6.3
2 ABB GBA 1250 22.5 11
3 HMA DG215ZL-04 47.7 11
Resul s o he no-load AVR a ia ions, speed go e no beha io and load ejec ion
es s a e plo ed in Figu e 7, Figu e 9 and Figu e 10 o plan s 1, 2 and 3 espec i ely. I can
be obse ed ha , a ending o he powe plan , as he pa ame e s and SGs a e diffe en ,
he esponses a y conside ably om one ano he .
Figu e 10.
Plan 3 es s: (
a
) no-load ol age se poin changes; (
b
) no-load equency se poin changes;
(c) load ejec ion es a PS= 15 MW and QS= 10 MVA .
3.3. Cases o S udy
F om he es ed powe plan s, h ee o hem a e shown and analyzed in his sec ion.
Some in o ma ion abou he gene a o s is collec ed in Table 4.
Table 4. Gas powe plan s in o ma ion.
Powe Plan SG
Manu ac u e SG Model Ra ed Powe
[MVA]
Ra ed Vol age
[kV]
1 ABB HSG 6.5 6.3
2 ABB GBA 1250 22.5 11
3 HMA DG215ZL-04 47.7 11
Resul s o he no-load AVR a ia ions, speed go e no beha io and load ejec ion
es s a e plo ed in Figu es 7,9and 10 o plan s 1, 2 and 3 espec i ely. I can be obse ed
ha , a ending o he powe plan , as he pa ame e s and SGs a e di e en , he esponses
a y conside ably om one ano he .
