POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 4 |2018 |DECEMBER
PSO Op imized PID Regula o o a Va iable
F equency B ushless Synch onous Gene a o
Hassen SMAIL1, Mos a a Kamel SMAIL2, Che i FETHA1, Taha BAHI 3
1Elec ical Enginee ing Depa emen , Facul y o Technology, Uni e si y o Ba na 2,
Rou e de Cons an ine 53, Fesdis, 05078 Ba na, Alge ia
2Ins i u Poly echnique des Sciences A ancees (IPSA), Boule a d de B andebou g 63,
94200 I y-su -Seine, F ance
3Elec ical Enginee ing Depa emen , Facul y o Enginee ing Sciences,
Badji Mokh a - Annaba Uni e si y, BP 12, 23000 Annaba, Alge ia
[email p o ec ed], mos a a-k[email p o ec ed], c[email p o ec ed], [email p o ec ed]
DOI: 10.15598/aeee. 16i4.2344
Abs ac . The aim o his pape is o desc ibe de elop-
men o a new con ol s uc u e o Au oma ic Vol age
Regula o sys em. This app oach is based on he op i-
miza ion o he con ol ol age magni ude o a b ushless
exci a ion synch onous al e na o machine ope a ing a
a iable speed. The choice o he machine ype is jus-
i ied by i s a ac i eness in se e al a eas such as he
ai c a domain due o i s au onomy and obus ness.
The conside ed con ol echnique is based on he simul-
aneous op imiza ion o wo egula o s in oduced in he
loop con ol. The pa ame e s o he P opo ional In e-
g al De i a i es (PID) egula o ha e been op imized
using he Pa icle Swa m Op imiza ion (PSO), which
is conside ed as an a ac i e me hod conside ing he
wide ope a ing speed ange, and he load a ia ions
compa ed wi h he classical me hods such as Ziegle
Nichols. Many obus ness es s a e ca ied ou by con-
side ing he pa ame e s a ia ions as well as he pe -
u ba ion connec ion and disconnec ion o he load a
low and high speeds.
Keywo ds
Op imiza ion, PID, PSO, Synch onous Gene a-
o wi h B ushless Exci e , a iable speed, ol -
age ampli ude con ol.
1. In oduc ion
The p oduc ion o he elec ical ene gy wi h a iable
speed al e na o s seems o be he bes solu ion in e ms
o pe o mance and eliabili y [1]. This sys em is based
on a combina ion o a gene a o ha ope a es a a i-
able speed and a aining mo o . A s a ic con e e
is associa e a he ou pu o he gene a o in o de o
s abilize he sui able equency [2].
The choice o a a iable equency gene a ion is
based on he machine ype and ield o applica ion ha
allows he educ ion o he mechanical losses, he gea -
box cos s and he size o he assembly.
The p oduc ion o embedded elec ical ene gy is
cha ac e ized by a wide aining speed o he al e na o
ha is used in se e al applica ions including ai c a
ield [3]. Howe e , he wide aining speed in oduces
cons ain s in ol ages and cu en s in he load. In his
ega d, se e al s udies ha e been published and allowed
choosing he al e na o and i s sui able con ol s a -
egy [4] and [5].
The ad ances in powe elec onics allow us a new
challenge in he a ea o elec ical p oduc ion. F om
a mechanical sou ce o a iable speed, a ixed equency
and a egula ed cons an ol age can be ob ained ia
a s a ic con e e . Which has he ad an ages o educ-
ing he gene a o size and weigh , since he mechanical
egula ion sys em o speed is emo ed, as in he new
ai c a supply sys em [4].
The a iable speed ope a ion allows an op imiza ion
in he ene gy cap u ed by a u bine, bu i equi es he
implemen a ion o a con e e and i s con ol. Which
leads o an addi ional cos in compa ison o a ixed
speed ope a ion [4] and [6].
In case o hyb id ehicles, all he s udies conduc ed
on he a iable speed gene a o s ha e shown ha diesel
consump ion is op imized and educed compa a i ely
o hei ope a ing a a ixed speed [5], [6] and [7].
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A wide ange o speed a ia ion, in d i ing he
B ushless Exci a ion Synch onous Gene a o (BESG)
engine, penalizes he s abili y o he ou pu ol age
con ol o he main gene a o . To emedy his, se e al
s udies ha e been ini ia ed o imp o e and de elop new
con ol echniques [8].
The schema ic mechanism o BESG is illus a ed in
Fig. 1. The gene a o is assumed equi alen o h ee
sepa a ed machines placed in cascade, such as Pe -
manen Magne Gene a o (PMG), synch onous ma-
chine and al e na o . The PMG machine allows he
gene a o a comple ely au onomous ope a ion. The
supply ol age o his machine is adjus ed o eed
a connec ed choppe o he second synch onous ma-
chine. The h ee-phases a e powe ed h ough a con-
e e . The mono-phase induc o is placed in he s a-
o side while he h ee-phase a ma u e is placed in he
o o .
The ob ained ol ages a e used o eed he induc o
o he main gene a o , and hese ol ages a e adjus ed
om he o o h ough six o a ing diodes. This con-
igu a ion is a con en ional synch onous machine wi h
a con en ional wound induc o connec ed o he ne -
wo k o load. I ’s no iced o his con igu a ion, he ab-
sence o b ushes which causes he inc ease he cos and
he eal complexi y o he gene a o . The equency
o he ob ained ol ages is in unc ion o he o a ion
speed [9].
Vexc
Ω
I
Exci e
Rec i ie
Main Gene a o
PMG
Iexc
Ro o
Ro o
Load
Vol age
Con ol
V
Vdc
Choppe
V e : Ampli ude ol age e e ence
~
N
S
Rec i ie
V
exc
I
exc
Vs
PMG
I
s
PMG
Fig. 1: Schema ic mechanism o b ushless exci a ion syn-
ch onous gene a o .
In he li e a u e, he con ol o he main gene a-
o ol age egula ion is based on h ee ac ions. The
i s one is he inne eedback loop ha con ols he
exci a ion cu en o he exci e . The second ac ion
is he ou e eedback loop o di ec ou pu ol age
egula ion o he main gene a o . And he hi d one
is he dis u bance- ejec ion loop ha compensa es he
changes in he ou pu ol ages caused by he gene a o
load (i.e., s a o ) cu en . The global loop is in oduced
o he ol age con ol o he machine [8].
This echnique o e s s abili y o he o al ol age o
he al e na o and ejec s all dis u bances ega dless
o he a ia ion o he o a ion speed o load. Bu he
p oposed con ol echnique is e y di icul o be imple-
men ed in p ac ice, due o he complexi y o he block
diag am and hey depend on he machine pa ame e s
ha a ec he s abili y o he sys em.
In o de o s abilize and simpli y he con ol, a new
echnique is de eloped in he p esen wo k. This ech-
nique consis s o calcula ing he ol age exci a ion o
he p incipal exci e -gene a o ha co esponds o he
nominal ol age ou pu o he main gene a o . The
ol age exci a ion is in e sely p opo ional o he o a-
ion speed.
This exci a ion is he e e ence o he egula o o he
machine wi h pe manen magne s. Thus, he p oposed
con ol echnique comp ises wo P opo ional-In eg al-
De i a i e (PID) con olle s; he i s one o he egu-
la ion o he ou pu ol age o he PMG and he second
one o he egula ion o he main gene a o e minal
ol age. In o de o op imize he PID con olle pa-
ame e s, he Pa icle Swa m Op imiza ion (PSO) has
been used.
The PID con ol is he mos e icien and widely
used eedback con ol s a egy, due o i s simplici y
and sa is ac o y con ol pe o mance. The wide use o
PID con ol has sus ained esea ch on inding he key
me hodology o PID uning o ob ain he bes possible
pe o mance ou o he PID con ol. Op imal con ol
pe o mance can only be achie ed a e iden i ying he
ines se o P opo ional gain (Kp), In eg al gain (Ki)
and De i a i e gain (Kd).
A i icial in elligence me hods, such as neu al ne -
wo k, uzzy sys em, and neu al- uzzy logic ha e been
widely applied o op imize he PID con olle pa am-
e e s. Many i e a i e echniques, such as Gene ic Al-
go i hm (GA), Simula ed Annealing (SA) and Chao ic
Algo i hm (CA) ha e ecen ly ecei ed much a en ion
o achie ing high e iciency and sea ching global op i-
mal solu ion in p oblem space [10], [11] and [12].
Pa icle Swa m Op imiza ion (PSO) as one o he
mode n heu is ic algo i hms, was de eloped h ough
simula ion o a simpli ied social sys em and has been
ound o be obus in sol ing con inuous nonlinea op-
imiza ion p oblems. The PSO echnique can gene -
a e a high-quali y solu ion wi hin sho e calcula ion
ime and s able con e gence cha ac e is ic han o he
s ochas ic me hods [11].
The adop ed con ol echnique is composed o wo
loops and wo egula o s. The i s loop is o he ou -
pu ol age o PMG con olle , induce an o e ol age
p o ec ion o he sys em, while he second loop is o
he o al ol age egula ion. The e o e, i is ound o
be simple compa ed o he h ee-loop echnique and
he sys em ejec ed all dis u bances (Fig. 1).
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Since he machine wo ks in a wide speed ange, ind-
ing he egula o pa ame e s (Kp,Kiand Kd) alues
is e y di icul . Mo eo e , he de e mina ion o hese
pa ame e s by di ec con en ional me hods like Ziegle
Nichols (ZN) and In e nal Model Con ol (IMC) is
somewha complica ed. The e o e, he Pa icle Swa m
Op imiza ion (PSO) me hod is used o ind op imal
alues o hese pa ame e s. PSO is an i e a i e op-
imiza ion me hod ha can handle complex sys ems
ha a e composed o se e al blocks.
In ou applica ion, he PSO ends o minimize bo h
esponse imes, o e shoo and di e ence be ween he
e e ence ol age and he ac ual inal ol age o he
main gene a o [13].
The ad an age o using wo egula o s is he limi a-
ion o he ol age gene a ed by PMG which p oduced
a high speed. This p o ec ion allows he sys em o
ope a e in a wide ange o speed [14].
In his pape , a machine d i e is conside ed as
a speed sou ce, i.e. he al e na o ou pu is low com-
pa ed o mechanical powe d i e: a case o he ene gy
p oduc ion embedded [4].
This pape is o ganized as ollows. Fi s ly, he p e-
sen a ion and moduliza ion o BEGS will be p esen ed
in Sec. 2. Then he o mula ion o he op imiza ion
echnique will be ea ed in Sec. 3. Finally, he sim-
ula ion esul s and obus ness s udy will be p esen ed
in he las sec ion in o de o illus a e he e iciency
o he p oposed con ol echnique.
2. P esen a ion o BESG
The synch onous BESG machine, o nomina ed he
Va iable F equency Gene a o , is shown in Fig. 1. I
is composed o h ee sepa a e synch onous gene a o s
linked in cascade, om he le o igh . The i s ma-
chine con ains a PMG, which allows he BESG o be
ully au onomous in e ms o exci a ion. The second
machine is an in e se synch onous machine s uc u e
(o exci e ). The ou pu ol age o he PMG will sup-
ply he Choppe a e ec i ica ion. The ou pu ol -
age o he choppe will egula e he second s age o
he BESG. The ou pu o he second s age ha comes
om he a ma u e ( o o ) will be ec i ied, by a diode
b idge ec i ie , o supply he induc o main gene a o ,
which ep esen s he las s age. And a he end, he
ou pu o he main gene a o will supply he load.
The main ea u e o he synch onous BESG ma-
chine is he absence o he mechanical ic ion which
inc eases he cos and he complexi y o he gene a o .
The ou pu ol age equency o he BESG machine
is ela ed o he common o a ional speed o he h ee
machines. The adop ed BESG machine s uc u e can
be ound in se e al applica ions, whe e he powe could
be p oduced in a a iable speed d i e, o example in
some indus ial applica ions, ene gy p oduc ion, em-
bedded o enewable ene gy [15].
2.1. Modelling and Block Diag am
o he Main Gene a o
In p ac ice, he machines a e known by hei wind-
ings and hei designs. In o de o analyse and ake
in o accoun hei exac con igu a ions, we shall de-
elop, o each ype o machine, a model ha can be
close o he eal model o be igo ously con olled. The
BESG machine consis s o h ee synch onous machines
(PMG, in e se synch onous machine and main gene -
a o ) whose models a e e y simila o he PMG wi h
sligh di e ences. In o de o modelize he main gen-
e a o , he Pa k T ans o ma ion is used o w i e he
synch onous machine model. In ou applica ion, he
o a ion speed and he ol age exci a ion will be he
inpu o he model. The ou pu o he main gene a o
model is ol age. By neglec ing he e ec s o shocks,
ega ding he small alues o he ime cons an s, he
model will be desc ibed by he ollowing equa ions:
Vol age equa ions:





d=Rsid+dΦd
d −ωφq,
q=Rsiq+dΦq
d −ωφd,
=R i +dΦ
d ,
(1)
whe e d, q,idand iqa e ol ages and cu en s in
dq ame (di ec and ans e se axe); and i a e
ol age and cu en o he main ield winding; Rsis
s a o esis ance; R is main ield esis ance, Φd,Φq
a e lux in dq ame, ωis he elec ical angula speed o
he BESG. The mechanical speed is supposed a iable,
i ’s e y impo an in ou p oposed con ol s a egy.
Flux equa ions:



φd=Ldid+M di ,
φq=Lqiq,
φ =L i +M did,
(2)
whe e Ldand Lqa e he di ec and ans e se s a-
o main induc ances; L is he main ield induc ance.
M d is he mu ual induc ance be ween di ec s a o
winding and main ield.
Subs i u ing he lux Eq. (2) in o he ol ages Eq. (1)
leads o w i e he model o he s a o ol age (induced)
in he ma ix o m as ollows:
[Vs] = [Zs]·[Is] + M d ·ω·0
1i .(3)
Wi h
[Vs] =  d q ,[Is] = idiq ,(4)
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[Zs] = Rs+S·Ld−ω·Lq
ω·LdRs+S·Lq,(5)
whe e Sis he Laplace ope a o (S=d/d ),Vs,Isand
Zsa e he Vol age, Cu en and he Impedance o he
main gene a o , espec i ely.
The subs i u ion o he lux Eq. (3) in ol ages
Eq. (1), o he induc o , allows deducing he ollow-
ing ope a ing equa ions:
i =1
R +S·L
U ,(6)
wi h
=i (R +S·L ) + S·M d ·id,(7)
whe e
U =i (R +S·L ), e d =S·M d ·id.(8)
Thus
=U +e d,(9)
whe e e d is he compensa ion ac o .
A linea con ol o he synch onous machine exci a-
ion ci cui , which co esponds o he cu en , i wi h
he ol age , equi es he compensa ion o he ans-
e e d ha ep esen s he EMF (null con inuous).
In oducing Eq. (6) in o equa ion Eq. (4) leads o
w i ing he model o he synch onous machine o an
al e na o by in e sing he sign o he s a o ol age
on he load le el, as ollows:
[Vs]=[Zs]·[Is] + M d ·ω
R +S·L ·0
1·( −e d).(10)
The ma ix Eq. (10) can be o mula ed as ollows:
[Vs] = [Zs]·[IS] + 0
1·M d
R +S·L −S·M2
d
R +S·L id.(11)
I he al e na o is equi ed o debi on he load, in
2D pa k componen s, he di ec and quad a u e com-
ponen s o he load ol age a e gi en by:
− d=Rl·id+Lldid
d −ω·Lliq,
− q=Rl·iq+Ll
diq
d −ω·Llid.(12)
Equa ion (11) can be exp essed by:
[−Vs]=[Zl]·[Il],(13)
wi h
[Zl] = Rl+S·Ll−ω·Ll
ω·LlRl+S·Ll,(14)
whe e Rl,Lland Zla e he esis ance, he induc ance
and he impedance o he load connec ed o he main
gene a o .
Wi h he ma ix Eq. (10) and Eq. (11), he block
diag am o he gene a o supplying a load is illus a ed
in Fig. 2.
Fig. 2: Block o a main gene a o supplying an induc i e load.
2.2. Modelling and Func ional
Diag am o he Exci e and
Rec i ie
The exci e ep esen s he exci a ion sys em ha sup-
plies he induc o o he main gene a o . The exci e
is a h ee-phase synch onous machine wi h ixed exci-
a ion (s a o ) and wi hou dampe whose phases a e
ca ied by he o o wi h a six-diode b idge connec ed
o i s e minals. The six diodes a e moun ed on he o-
o in o de o eed he induc o o he main gene a o
wi h DC (Fig. 1).
The exci e ci cui is modelled by he same app oach
as used o he main gene a o . The exci a ion ol age
o he exci e sys em will be conside ed as he powe
sou ce o he exci a ion o he main gene a o h ough
a ec i ie diode (Fig. 1).
Fo he exci e model, he same equa ions o he
main gene a o model will be used, whe e all he a i-
ables will be w i en om he o o side o he exci e ,
as shown in Fig. 3.
Fig. 3: AC o DC con e sion using o a ing diode b idge.
The e ec i e ec i ied ol age is gi en by:
Va exc =q 2
dexc + 2
dexc
√2.(15)
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The a e age alue o he ou pu ol age o a ec i ie
o qphase’s numbe is:
Vdc =2q
πsin π
q·Va exc .(16)
To calcula e he new alues o he load exci e a e
eco e y, an equali y o powe s be ween he inpu and
he ou pu o he con e e is conside ed as ollows:
PAC = 3Va exc ·Ia exc ·cos(ϕexc) = Vdc·Idc =Pdc.(17)
Thus, he al e na ing side can be obse ed, which is
seen con inuous, in e ms o ac i e powe , i he losses
in he diodes a e neglec ed:
PAC =3V2
e exc
Rlexc
=V2
dc
R
=Pdc.(18)
F om he knowledge o powe elec onics, he DC
ol age (a e age ec i ied) o qnumbe phases can be
w i en:
Vdc =2q
πsin π
q·Ve exc .(19)
Fo he h ee-phase case:
q= 3 →Vdc =3√3
πVe exc .(20)
DC es a ed o qphases:
Idc = q
2Ie exc .(21)
Fo he h ee-phase case:
q= 3 →Idc = 3
2Ie exc .(22)
Powe s equali y AC & DC allows w i ing:
PAC =Pdc.(23)
In e ms o ac i e powe , i he losses in he diodes
a e neglec :
Rlexc =π2
9R .(24)
This gi es, a e calcula ing AC side:
Llexc ·ω=Rlexc · an(ϕexc) =
=Rlexc q1
cos2(ϕexc )−1.(25)
The alue o an ϕob ained by Eq. (24) is eplaced
in Eq. (16), he exp ession o Llexc is ob ained by:
Llexc =1
ωRlexc · an(ϕexc) =
=1
3ωRlexc √2π2−9.
(26)
Thus, Llexc is ela i ely low.
Equa ion (24) and Eq. (25) a e in eg a ed in o he
o e all simula ion model, which is e y close o he eal
sys em.
2.3. Modelling and Func ional
Diag am o PMG
The PMG p o ides he powe o he con ol sys em
o he exci a ion o he exci e . The applica ion o
Pa k T ans o ma ion o he PMG model co esponds
o ans o m he h ee coils (s a o ) wo equi alen
coils. Wi h he same app oach used o he main gen-
e a o , we assume ha he o o o he PMG machine
is la , and he magne ic ci cui is no sa u a ed. The
equa ions a e de ined as ollow:
[Vspmg ]=[Zspmg ]·[Ispmg ] + φpmg ·ω·0
1.(27)
Wi h:
[Vspmg ] = [Vdpmg Vqpmg ] .(28)
[Ispmg ]=[Idpmg Iqpmg ] .(29)
[Zspmg ] = Rspmg +S·Ldpmg −ω·Lqpmg
ω·Ldpmg Rspmg +S·Lqpmg .(30)
The symbols o he las equa ions a e he same as
hose desc ibed p e iously. The mechanical speed o
he PMG machine is conside ed a iable.
When he PMG is loaded, he di ec and quad a u e
componen s o he ol ages a e gi en by:















− dpmg =Rlpmg ·idpmg +Llpmg
didpmg
d −
ω·Llpmg ·iqpmg ,
− qpmg =Rlpmg ·iqpmg +Llpmg
diqpmg
d −
ω·Llpmg ·idpmg .
(31)
Equa ion (27) and Eq. (31) in ma ix and ope a-
ional o m a e w i en as:
[−Vspmg ]=[Zlpmg ]·[Ispmg ].(32)
Wi h:
[Zlpmg ] = Rlpmg +S·Llpmg −ω·Llpmg
ω·Llpmg Rlpmg +S·Llpmg .(33)
Wi h he ma ix Eq. (27) and Eq. (32), he block
diag am o a gene a o supplying a load is illus a ed
by Fig. 4.
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0
p
ϕ0
p
ϕ
d
q
pmg
pmg
zspmg
zlpmg
-1
d
q
pmg
pmg
i
i
d
q
pmg
pmg
spmg
ppmg
qpmg
22
+
Fig. 4: Block diag am o pe manen magne al e na o supply
he induc i e load.
2.4. Fo mula ion o he Op imiza ion
P oblem
In his p oblem, he e e ence ol age, he esponse
ime, and he o e shoo a e egula ed by op imizing he
PID con olle pa ame e s. PSO is used o minimize
he objec i e unc ion Fgi en in [15], whe e Osh is he
maximum o e shoo o change in e minal ol age, s
is he se ling ime o change in e minal ol age (s)
and max_d is he maximum de i a i e o cha ge in
e minal ol age.
F= (Osh ·1000) + 2
s +0.001
max_d 2.(34)
3. Pa icle Swa m
Op imiza ion
The PSO is an e olu iona y algo i hm o he solu ion
o op imiza ion p oblems. I belongs o he ield o
Swa m In elligence and Collec i e In elligence and is
a sub- ield o Compu a ional In elligence [16]. I was
de eloped by Ebe ha and Kennedy and inspi ed by
social beha iou o bi d locking o ish schooling [17].
The PSO me hod is ega ded as a popula ion-based
me hod, whe e he popula ion is e e ed o as a swa m
[18]. The swa m consis s o n indi iduals called pa -
icles, each o which ep esen s a candida e solu ion
[19]. Each pa icle iin he swa m holds he ollowing
in o ma ion:
•i occupies he posi ion xi,
•i mo es wi h a eloci y i,
• he bes posi ion, he one associa ed wi h he bes
i ness alue pa icle has achie ed so a pbes i,
• he global bes posi ion, he one associa ed wi h
he bes i ness alue ound among all o he pa -
icles gbes .
In ou applica ion, he posi ions o pa icles xi ep-
esen he pa ame e s o PID con olle (Kd,Kiand
Kp).
G(S) = Kp+Ki
S+S·Kd.(35)
G(S)is he ans e unc ion o he PID con olle .
The i ness o a pa icle is de e mined om i s posi-
ion. The i ness is de ined in such a way ha a pa i-
cle close o he solu ion has highe i ness alue han
a pa icle ha is a away. In each i e a ion, eloci ies
and posi ions o all pa icles a e upda ed o pe suade
hem o achie e be e i ness acco ding o he ollow-
ing equa ions:
+1
ij =
ij +c1· and
1j·(pbes
ij −x
ij)
+c2· and
2j·(pbes
ij +x
ij),(36)
x +1
ij =x
ij + +1
ij ,(37)
o j= 1, ..., d whe e dis he numbe o dimensions,
i= 1, ..., n whe e nis he numbe o pa icles, is he
i e a ion numbe , wis he ine ia weigh , and1and
and2a e wo andom numbe s uni o mly dis ibu ed
in he ange [0,1], c1and c2 he accele a ion ac o s.
The c1is he cogni i e accele a ion cons an . This
componen p opels he pa icle owa ds he posi ion
whe e i had he highes i ness. The c2is he social
accele a ion cons an . This componen s ee s he pa -
icle owa ds he pa icle ha cu en ly has he highes
i ness.
The ine ia weigh wa ec s he con ibu ion o
ij
o he new eloci y ( +1)
ij . I wis la ge, i makes a la ge
s ep in one i e a ion (explo ing he sea ch space), while
i w is small, i makes a small s ep in one i e a ion,
he e o e ending o s ay in a local egion [20].
Typically, he eloci y o a pa icle is bounded be-
ween p ope ly chosen limi s min < id < max (in
mos cases min =− max). Likewise, he posi ion o
a pa icle is bounded as ollows: xmin < xid < xmax.
A e wa ds, each pa icle upda es i s pe sonal bes
posi ion using he ollowing equa ion:
pbes +1
i=(pbes
i,i (pbes
i)< (x +1
i),
x +1
i,i (pbes
i)> (x +1
i).(38)
Finally, he global bes o he swa m is upda ed using
he ollowing equa ion:
gbes +1 =a gmin · (pbes +1
i),(39)
whe e is a unc ion ha e alua es he i ness alue
o a gi en posi ion.
The PSO p ocess is epea ed i e a i ely un il one
o he ollowing e mina ion c i e ia occu s [21] i he
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maximum numbe o i e a ions has been eached, an
accep able solu ion should be ound, o no imp o e-
men is obse ed o e a numbe o i e a ions.
The PSO con ol pa ame e s used in his s udy a e;
he popula ion size is 60, maximum gene a ion 100, he
accele a ion ac o s (c1= 0.5and c2= 1.25) and he
ine ia weigh (w= 0.6). I is no ewo hy o men ion
ha all he de eloped p og ams a e unde he comme -
cial so wa e Ma lab-Simulink.
4. Applica ion
4.1. Simula ion o he Sys em
Beha iou
The simula ion o he sys em beha iou e eals an im-
po an p oblem in he con ol. When he aining
speed is a iable, he ol ages and he cu en s o he
exci e and he main gene a o a y in o de o main-
ain he ol age a nominal alue.
The p oblems men ioned be o e can be p esen ed as
ollows:
In he case, whe e he aining speed is high, he
heo e ical exci a ion ol age o he exci e and main
gene a o ha p o ides a nominal ol age ( he ol age
o he main gene a o ) is low, due o he exci a ion
ol age ha is in e sely p opo ional o he aining
speed. The di e ence be ween he ol age deli e ed
by he PMG machine and he heo e ical exci a ion
ol age o he main gene a o and exci e is e y im-
po an , which makes he con ol sys em, in his case,
e y complica ed.
In he case o low speed, he ol age deli e ed by
PMG machine can be insu icien o exci e he main
gene a o exci e g oup, because he exci a ion ield o
he PMG machine is cons an .
Choosing PMG machine depends on speci ica ions,
i.e. expe ise, knowledge and ield o use. To o e come
his p oblem ( he insu iciency o PMG machine), he
PMG machine wi h low speed (high numbe o poles)
is used. This p oduces enough ol age o exci e he
g oup main gene a o -exci e . In o de o con ol he
ou pu ol age o he BESG, he exci a ion ol age o
he main exci e -gene a o g oup is calcula ed om he
load and he speed.
The exci a ion ol age alue co esponds o he a ed
ol age (220 V) which is conside ed as a e e ence o
he ol age egula o o he MSAP (Fig. 5). A e -
e y momen and o a gi en speed, he exci a ion ol -
ages o he main exci e and gene a o a e calcula ed.
Which will be a e e ence o he egula o ol age o
he PMG, i.e. dec ease he di e ence be ween he ol -
age deli e ed by PMG machine and exci a ion ol age
o he main gene a o -exci e g oup. This ensu es s a-
bili y when he machine wo ks a high speed. Fo each
a ia ion in speed o load, ou sys em adap s i s sel o
hese changes.
Fig. 5: Schema ic diag am o b ushless exci a ion synch onous
gene a o con ol using PID-PSO con olle .
4.2. Compa ison Be ween PSO and
Ziegle Nichols
In ou case, Ziegle Nichols uning is based on he open-
loop s ep esponse o he sys em which is cha ac e ized
by he ollowing pa ame e s; he p ocess ime cons an
Lz, he delay ime and he ime cons an Tz.
These pa ame e s a e used o de e mine he con-
olle ’s uning pa ame e s (see Tab. 1).
We no e ha he esponse o ou sys em is a i s
o de equa ion. The de e mina ion o con olle pa-
ame e s by he con en ional me hods such as Ziegle
Nichols, o a gi en speed, is a o dable. Howe e , o
he alues o egula o s pa ame e s, ha a e adap ed
o he speed and load a ia ions, a e di icul o de e -
mine, and especially o he second con olle , because
he Ziegle Nichols me hod calcula es he pa ame e s
o a single egula o (Fig. 5).
Thus, he pa ame e s o he second con olle a e
e y di icul o be calcula ed, since i elies on he
ial and e o me hod as illus a e Fig. 5. The ob-
ained simula ion esul s o he PID con olle using
ZN me hod gi e he pa ame e s:
Kop = [Kp1, Ki1, Kd1, Kp2, Ki2, Kd2] =
= [2.08,0.1664,0.0486,0.12,1.22,3.04].(40)
The pa ame e s Kp1,Kil and Kd1a e de e mined
by Ziegle Nichols me hod (Tab. 1) while Kp2,Ki2and
Kd2a e de e mined by ial and e o .
The simula ion esul s a e illus a ed in Fig. 6. They
e eal he beha iou o he ol age V o he main gen-
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e a o o an induc i e load o cos(ϕ) = 0.8. The e-
sponse ime o he main gene a o becomes as e and
akes less han 0.2 s, and i s ope a ion is s able as
shown in he zoom o Fig. 6.
In Fig. 6, he dis up ions in high-speed egion a e
due o inco ec alues o he second egula o pa am-
e e s. The de e mina ion o he pa ame e s o se e al
egula o s using PSO echnique is e y use ul.
Tab. 1: Ziegle -Nichols o open-loop uning pa ame e s.
Con olle Kp1Ti1=Kp1
Ki1Td1=Kd1
Kp
PTz
Lz- 0
PI 0.9( Tz
Lz)Lz
0.30
PID 1.2( Tz
Lz) 2Lz0.5Lz
Time(s)
0 5 10 15 20 25 30
V ( )
0
50
100
150
200
250
300
350
Connex ion
High speed
Low speed
Disconnex ion
Connex ion
O e speed Disconnex ion
Fig. 6: Va ia ion o he main gene a o ol age o induc i e
load: cos(ϕ)=0.8using Ziegle Nichols me hod.
Time (s)
0 5 10 15 20 25 30
V (V)
0
50
100
150
200
250
300
Time (s)
0 0.5
V (V)
0
100
200
300
Time (s)
19.820 20.2
V (V)
220
240
260
280
Time (s)
9 9.5
V (V)
214
216
218
220
222
Passage O e speed Connex ion
Disconnex ion
Connex ion
Disconnex ion
Time(s)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
V ( )
0
50
100
150
200
250
Low speed
Fig. 7: Zoom o Fig. 6 be ween 0 and 0.5 s.
The PSO me hod is used o op imize he pa ame e s
o he egula o s o -line, howe e , in on-line con ol,
he egula o pa ame e s mus be calcula ed by PSO,
when he speed a y.
4.3. Simula ion Resul s and
Discussion
In o de o op imize he pa ame e s o he PID con-
olle , he PSO is implemen ed in Ma lab-Simulink
en i onmen . The esul s ob ained when he main gen-
e a o unning a ull load wi h a powe o 7 kVA.
The simula ion esul s a e illus a ed in Fig. 8. They
illus a e he beha iou o he ol age V o he main
gene a o o an induc i e load o cos(ϕ)=0.8.
When he aining speed eaches 314 ad·s−1 o
induc i e load (cos(ϕ)=0.8), he esponse ime o
he main gene a o becomes as e and akes less han
0.2 s, and i s ope a ion is s able as shown in zoom o
Fig. 8(a). When a load is applied a he e minals o
he main gene a o , he ol age ampli ude ollows he
e e ence in bo h cases co esponding o he connec-
ion and he disconnec ion o he a ed load, as shown
in zoom o igu e Fig. 8(b). One can no e ha he e -
ec o he load a ia ion is pe ec ly damped, and he
sys em, in his case, ejec s all dis u bances.
In he same con igu a ion, when he aining speed
eaches 3140 ad·s−1, a ol age peak a he 15 h second
is obse ed. When speed a ies om 314 ad·s−1 o
3140 ad·s−1, as illus a ed in he zoom o Fig. 8(c),
he peak du a ion is less han 0.2 s and he ol age is
s able and has ampli ude less han 20 % o he nominal
one.
A high speed o 3140 ad·s−1, illus a ed in he
zoom o Fig. 8(c), when a load is applied a he e -
minals o he main gene a o . In hese cases o con-
nec ion and disconnec ion, he ol age ampli ude ol-
lows he e e ence and he a ia ion e ec o he load is
pe ec ly damped, Fig. 9. In high-speed case, he am-
pli ude o he ol age peak, a 20 h and 25 h seconds,
is mo e impo an bu accep able (in he no ms; less
han 20 %) and he s abili y ime is also accep able
ha jus i y he obus ness o he con ol echnique.
Table 2 shows he PSO pa ame e s ha a e used o
e i ying he pe o mance o he PSO-PID con olle
o sea ching he PID con olle pa ame e s. Ine ia
weigh ac o is se by:
ω=ωmax −((ωmax −ωmin)
i e max
)i e , (41)
whe e ωmax = 0.9, ωmin = 0.4, i e max is he maximum
numbe o i e a ions, and i e is he cu en numbe
o i e a ions. Fo hese se ings, he simula ion esul
ha shows he bes solu ion co esponds o he PID
pa ame e s gi en:
Kop = [Kp1, Ki1, Kd1, Kp2, Ki2, Kd2] =
= [99.96,1.956,2.407,100,0.201,63.86].(42)
Tab. 2: The PSO pa ame e s used in simula ion.
Pa ame e s Value
α10
β4
Popula ion size :n50
c12
c22
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Time(s)
0 5 10 15 20 25 30
V (V)
0
50
100
150
200
250
300
Low speed High speed
Disconnexion
Passege O e speed
Connexion
Disconnexion
Connexion
(a) V Vol age a ia ion o he main gene a o wi h induc i e
load: cos(ϕ)=0.8.
Times(s)
0 0.05 0.1 0.15 0.2 0.25 0.3
V (V)
0
50
100
150
200
250
(b) Zoomed be ween 0 and 0.5 s.
Time(s)
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5
V (V)
212
214
216
218
220
222
224
226
228
Disconnexion
Connexion
Low speed
(c) Zoomed be ween 4.5 and 10 s.
Time(s)
14 15 16 17 18 19 20 21 22 23 24 25
V (V)
160
180
200
220
240
260
280
Passege O e speed Connexion
Disconnexion
High speed
Low speed
(d) Zoomed be ween 14 and 25 s.
Fig. 8: V Vol age a ia ion o he main gene a o wi h induc i e load: cos(ϕ)=0.8wi h zoomed a eas.
Time(s)
0 5 10 15 20 25 30
Speed ( ad ·s-1)
0
500
1000
1500
2000
2500
3000
3500
O e speed
Low spped High spped
Fig. 9: D i e speed a ia ion o b ushless exci a ion syn-
ch onous gene a o .
4.4. Robus ness S udy
The obus ness con ol is s udded h ough pa ame e s
a ia ion. I is jus i ied when he machine ope a es a
high speed due o he Foucaul cou an and he em-
pe a u e e ec s which a e conside able impo an .
In o de o illus a e he obus ness o he p oposed
con ol, he e ec o he a ia ion o main gene a o
pa ame e s on he pe o mances o he ol age se ing
is s udied.
The a ia ion in oduced in he es e e s in p ac ice
o he eal condi ion as o e hea ing, sa u a ion o he
magne ic ci cui and he ope a ing condi ions such as
he a ia ion o he speed and he load.
Th ee cases a e conside ed:
•Va ia ion in he s a o esis ance o 50 %.
•Va ia ion in he o o esis ance o 50 %.
•S a ing wi h low speed o 100 ad·s−1.
To illus a e he pe o mances o se ing, he a ia-
ion o s a o and o o esis ance o 50 % compa ed
o he a ed alues, wi h a ol age s ep o 220 V has
been simula ed. Figu e 10 and Fig. 11 illus a e he
es esul s which illus a e ha he p oposed ech-
nique is insensi i e o he machine o o o s a o esis-
ances a ia ions. Hence, wi h e en poo ly de e mined
pa ame e s, he adop ed con ol echnique wi hs ands
and s ays s able.
Fo he hi d simula ed case, a a low speed
(100 ad·s−1) wi h applica ion o a a ed load, he sys-
em is always insensi i e o his speed, as shown in
Fig. 12. The con ol sys em ensu es he dis u bances
ejec ion in h ee cases conside ed ( he ime cons an s
o he sys em a e g ea e han hose o he machine).
The p oposed con ol echnique p esen ed in his pape
is obus , simple and has he ad an age o being easily
implemen ed.
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