Resea ch A icle
An E alua ion o a Me aheu is ic A i icial Immune Sys em o
Household Ene gy Op imiza ion
Ma ia Na a o-Cace es ,
1
P amod He a h,
2
Gab iel Villa ubia ,
1
F ancisco P ie o-Cas illo ,
1,2
and G. Kuma Venyagamoo hy
3,4
1
Uni e si y o Salamanca, s/n. Salamanca, 37003 Espejo, Spain
2
Media Lab, Massachuse s Ins i u e o Technology, 20 Amhe s S , Camb idge, MA, USA
3
Holcombe Depa men o Elec ical and Compu e Enginee ing, Real-Time Powe and In elligen Sys ems Labo a o y and Clemson
Uni e si y, Clemson, SC 29634, USA
4
School o Enginee ing, Uni e si y o KwaZulu-Na al, Du ban, Sou h A ica
Co espondence should be add essed o Ma ia Na a o-Cace es; [email p o ec ed]
Recei ed 25 Oc obe 2017; Accep ed 4 Ma ch 2018; Published 2 July 2018
Academic Edi o : Hugo Mo ais
Copy igh © 2018 Ma ia Na a o-Cace es e al. This is an open access a icle dis ibu ed unde he C ea i e Commons
A ibu ion License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal
wo k is p ope ly ci ed.
De ices in a sma home should be connec ed in an op imal way; his helps sa e ene gy and money. Among nume ous op imiza ion
models ha can be ound in he li e a u e, we would like o highligh a ificial immune sys ems, which use special bioinspi ed
algo i hms o sol e op imiza ion p oblems effec i ely. The aim o his wo k is o p esen he applica ion o an a ificial immune
sys em in he con ex o diffe en ene gy op imiza ion p oblems. Likewise, a case s udy is pe o med in which an a ificial
immune sys em is inco po a ed in o de o sol e an ene gy managemen p oblem in a domes ic en i onmen . A ho ough
analysis o he diffe en s a egies is ca ied ou o demons a e he abili y o an a ificial immune sys em o find a success ul
op ima which sa isfies he p oblem cons ain s.
1. In oduc ion
A Home Ene gy Managemen Sys em (HEMS) is a key ele-
men in a domes ic en i onmen ha imp o es household
economy h ough au oma ed echnologies.
In he ecen yea s, diffe en domes ic buildings equipped
wi h communica ion channels (sma houses) ha e ac i ely
pa icipa ed in elec ical ne wo ks [1] as building blocks in
sma g ids (SGs). The e o e, hey play an impo an ole in
op imizing he scheduling o elec ic powe [1, 2].
The e a e a numbe o s a egies ha employ diffe en
echniques o op imize he scheduling o ene gy use in he
home. Among many o he s a egies, s a is ical models a e
one example o hem. We can see how hey a e le e aged in
he wo k o [3], which models con ollable loads using a
Ma ko ian app oach. These loads depend on wea he condi-
ions. In [4], a demand- esponse p og am is au oma ically
applied om classical me hods o con ol he de ices
connec ed o he ne wo k unde he unce ain y o he ou -
side empe a u e and he p ice o elec ici y. In [5], h ee
p oblems ela ed o HEMS ha e been sol ed by applying an
obse able Ma ko ian decision p ocess. This wo k made i
possible o educe domes ic ene gy cos s in he elec ici y
p ice ma ke .
Classical app oaches had some limi a ions [6]; hus, new
pa adigms ha e been applied o sol e HEMS. One success-
ully de eloped pa adigm is ha which uses bioinspi ed algo-
i hms o sol e op imiza ion p oblems. These algo i hms y
o mimic he beha io o some biological en i ies o find solu-
ions which, applying classical compu a ion, would be oo
cos ly o e en implausible in e ms o ime and esou ces.
Some widely used and no ewo hy algo i hms a e a ificial
neu al ne wo ks (ANN), gene ic algo i hms (GA), o swa m
in elligence [7]. Some bioinspi ed algo i hms wo k in diffe -
en con ex s, and hey ende good esul s. One o hese algo-
i hms is he a ificial immune sys em (AIS) which ollows
Hindawi
Complexi y
Volume 2018, A icle ID 9597158, 11 pages
h ps://doi.o g/10.1155/2018/9597158
he p inciples o he e eb ae immune sys em o find solu-
ions in an op imiza ion p oblem. The AIS algo i hm can be
designed in a a ie y o ways. F om he diffe en a ian s, in
his wo k, i is decided o use Op -aiNe [8], which has been
used success ully o he op imiza ion o unc ions in diffe en
con ex s [8]. Op -aiNe allows finding se e al solu ions in
pa allel. By using ope a ions such as mu a ion, cloning, and
supp ession, each solu ion co esponds o diffe en op ima
(maxima o minima) poin s in he op imiza ion unc ion.
In he a ea o in elligen ne wo k op imiza ion, se e al
wo ks ha ollow he bioinspi ed pa adigm ha e been p o-
posed. These include [9], who p opose an ene ge ic se ices
modeling me hod based on he pa icle swa m op imiza ion
(PSO) algo i hm. Soa es e al. [10] p opose a mul iobjec i e
gene ic app oach o scheduling domes ic cha ge in an
ene gy managemen sys em. Yuce e al. [11] p esen a neu al
ne wo k wi h a gene ic algo i hm (ANN-GA) o op imize
ene gy managemen in he domes ic sec o . Howe e , o
he au ho s’knowledge, AIS has only been implica ed in
some p elimina y achie emen s in powe managemen , such
as sol ing powe supply p oblems, o elec ical econfigu a-
ions. Fo example, in [12], an AIS is used o con ol he mal
uni s in esiden ial buildings, and in [13], he au ho s op i-
mize a wind ene gy-gene a ing sys em also wi h an AIS.
In his pape , an in-dep h e iew o he AIS concep and
i s applica ion o diffe en elec ical p oblems is made. F om
he esul s o his e iew, a case s udy on a p oblem o home
ene gy managemen op imiza ion is desc ibed and sol ed
using his algo i hm. We aim o demons a e ha AIS can
be success ully applied o elec ical managemen p oblems
in domes ic se ings. Pa o ou objec i e has been o adap
he Op -aiNe algo i hm o include complex cons ain s on
he op imiza ion p oblem and o wo k efficien ly wi h a la ge
numbe o a iables.
This pape p esen s a simple elec ic con ex wi h
diffe en de ices, namely, a pho o ol aic panel (PV), a
ba e y sys em, a space hea e o hea e , a wa e hea e , and
mus - un se ices. All o hem a e connec ed in a sma
home, wi hin an elec ical sys em. I is aimed a op imizing
he scheduling o he nex 24 hou s so ha he elec ical
benefi is maximized be ween he ene gy ha is sold and
he ene gy ha is bough .
Two s a egies a e designed in ou case s udy o ep e-
sen wo diffe en elec ical si ua ions. In s a egy 1, he
HEMS manages he elec ic powe wi h he elec ici y g id
wi hou conside ing any in e nal es ic ion. In o he
wo ds, we do no conside any a iable ela ed o he
main enance o he domes ic elec ic cha ge h ough he
elec ical ene gy p oduced by he PV sys em. The e o e,
his s a egy only seeks o op imize ene gy benefi s. How-
e e , s a egy 2 is aimed a supplying he elec ici y
demand au onomously whene e possible. The e o e, he
su plus gene a ed by he PV is s o ed in he ba e y.
HEMS will sell elec ici y o he g id when he ba e y is
ully cha ged. Also, he ba e y is discha ged when he
elec ical demand is g ea e han he powe gene a ed by
he PV. I he ba e y canno supply all he elec ical
cha ge, hen he HEMS mus buy elec ici y om he
powe g id. Based on hese wo s a egies, h ee diffe en
expe imen s we e de eloped. Fi s ly, a compa ison o AIS
wi h wo diffe en bioinspi ed algo i hms is made, namely,
he classical gene ic algo i hm (GA) and he pa icle
swa m op imiza ion (PSO). Secondly, bo h s a egies a e
compa ed o analyze he influence o he ba e y in he
home ne wo k. Finally, a deep analysis is ca ied ou wi h
diffe en si ua ions o he ba e y cha ge in he home ne -
wo k. The esul s ob ained in all si ua ions a e expec ed o
alida e he AIS as an app op ia e algo i hm o he op i-
miza ion o HEMS.
This documen is s uc u ed as ollows. Sec ion 2
p o ides an o e iew o he design o AIS and a e iew
abou i s in ol emen in elec ical p oblems. Sec ion 3
desc ibes he echnical de ails o he add essed elec ical
p oblem. Sec ion 4 p esen s he configu a ion o AIS and i s
applica ion o he elec ical p oblem. In Sec ion 5, he
esul s ob ained in he h ee case s udies a e ou lined and
discussed. Finally, Sec ion 6 p esen s he conclusions o ou
esea ch and u u e wo k.
2. A i icial Immune Sys ems
The o ganisms o many species ha e de eloped immune
sys ems o p o ec hem om ex e nal agen s. Abo e all,
e eb a e immune sys ems consis o diffe en molecules,
cells, and o gans ha a e dis ibu ed h oughou he body
and a e no con olled by any cen al en i y. F om an
immunological poin o iew, any elemen p esen in he
immune sys em is called an an igen. I his an igen belongs
o he in e nal o ganism o p o ec he body, i is called
sel -an igen o an ibody. O he wise, he an igens om he
ex e nal en i onmen a e called non-sel -an igens and can
p o oke diffe en diseases. The e o e, immune sys ems a e
aimed a dis inguishing be ween sel -an igens and non-sel -
an igens h ough a pa e n ecogni ion p ocess, a acking
only hose ha a e ha m ul o he body [14].
D awing on he concep o he immune sys em, [15]
de eloped he CLONALG algo i hm, a clonal selec ion p oce-
du e ha allows mu a ing some an ibodies acco ding o hei
affini y o an ex e nal an igen; he e o e, in o de o pe o m
pa e n ecogni ion, i gene a es copies o he an ibodies
acco ding o hei affini y wi h he an igen. The copies a e
mu a ed ollowing a a e δin e sely p opo ional o hei
affini y wi h he an igen (1).
δ=e i
β,1
whe e βis a cons an ob ained empi ically o no malize he
effec o he fi ness alue
i
o each cell. These new indi iduals
a e added o he gene al popula ion and ee alua ed o be
ep oduced and mu a ed again.
In o de o gi e a new solu ion o he op imiza ion o
unc ions, [8] de eloped Op -aiNe , an a ificial immune sys-
em (AIS) based on he CLONALG beha io . The in o ma-
ion is encoded as an igens which should be ecognized by
he an ibodies o ou immune sys em. Then, he fi ness alue
o an an igen is defined as he affini y be ween he an igen
and he an ibody and can be compa ed wi h a dis ance
2 Complexi y
me ic. Hence o h, small dis ances be ween an an igen and
an an ibody ep esen high affini y, whe eas longe dis ances
ep esen lowe affini y.
The Op -aiNe algo i hm ollows he gene al desc ip ion
o an a ificial immune sys em. Fi s ly, an ibodies, which ep-
esen he diffe en da a o op imize, a e andomly gene a ed.
Then, hey a e p esen ed o he an igens, which encode he
objec i e unc ion, in o de o calcula e he affini y be ween
hem when he da a a e applied o he unc ion. I one an i-
body ob ains a good a ing in he objec i e unc ion, ha
means i has high affini y and he e o e is selec ed. These
chosen an ibodies a e ep oduced and mu a ed based on
hei fi ness alue acco ding o he CLONALG algo i hm
and he βpa ame e . In o de o p ese e di e si y, an ibod-
ies whose affini y is lowe han a gi en h eshold
s
a e
emo ed om he popula ion.
A ificial immune sys ems, in pa icula Op -aiNe , a e
able o find se e al op ima o he objec i e unc ion in pa al-
lel. This means ha AIS can find a se o good candida es o
he solu ion o op imiza ion p oblems ha a e diffe en om
one ano he . Addi ionally, AIS can p ese e hose indi iduals
ha a e good enough o be ep oduced and mu a ed in con-
secu i e i e a ions.
2.1. AIS Applica ions in Ene gy Con ex s. The concep o a
nex -gene a ion powe sys em such as sma g id, efficien
ene gy managemen , and be e powe sys em planning
canno be achie ed wi hou elec ical load o ecas ing
[16]. Consequen ly, mul iple ime ho izons which a e asso-
cia ed wi h he egula ion, dispa ching, scheduling, and
uni commi men o he powe g id a e analyzed and
sol ed using diffe en me hods. A ificial in elligence (AI)
is widely applied o a a ie y o applica ions, as i can han-
dle he complexi y de i ed om such elec ical p oblems.
In pa icula , bioinspi ed algo i hms, such as a ificial neu-
al ne wo ks o swa m in elligence, a e especially effec i e
in sol ing his kind o p oblems. In his sec ion, a b ie
bu comp ehensi e li e a u e e iew o a special bioin-
spi ed algo i hm, he a ificial immune sys ems, is p o-
ided. AIS was applied in diffe en con ex s wi h posi i e
esul s: when sol ing combina o ial p oblems [17, 18], o
de ec in usions in wi eless senso ne wo ks [19], o e en
o gene a e cho d p og essions [20]. The majo goal o his
sec ion is o e iew, iden i y, e alua e, and analyze he pe -
o mance o AIS in powe sys ems and model esea ch.
Rega ding he elec ical con ex , he e a e plen y o p o-
posals ocusing on di e se fields. One o hem is ela ed o
he con ol o a iables and configu a ion o an elec ical
sys em. de Mello Hono io e al. [21] model an op imal
powe flow (OPF), which is a nonlinea , noncon ex, and
la ge-scale p oblem wi h bo h con inuous and disc e e con-
ol a iables, using a modified a ificial immune sys em
(AIS). The AIS makes use o hype mu a ion, which is
esponsible o local sea ch, and ecep o edi ion, which
explo es diffe en a eas in he solu ion space. The p oposed
AIS is combined wi h a g adien ec o o imp o e he final
esul s. This combina ion is also aimed a collec ing aluable
in o ma ion du ing he hype mu a ion p ocess, dec easing
he numbe o gene a ions and clones, and, consequen ly,
speeding up he con e gence p ocess while educing he
compu a ional ime. Belkacemi and Feliachi [22] use a mul-
iagen sys em (MAS) which ollows he human immune
sys em beha io o p opose a new echnique o powe sys-
em econfigu a ion and es o a ion, applied o a model o
Sou he n Cali o nia Edison’s Ci cui o he Fu u e. Each ele-
men o he MAS ep esen s a na u al immunological ele-
men ha in e ac s wi h he o he elemen s o heal he
body. Simila ly, he MAS is able o de ec and isola e aul s
and es o e powe o he affec ed loads aking in o conside -
a ion line capaci y, ol age p ofile, and powe losses [22]. de
Oli ei a e al. [23] p esen a me hodology o he econfigu-
a ion o adial elec ical dis ibu ion sys ems o minimize
ene gy losses making use o he bioinspi ed me aheu is ic
a ificial immune sys em. The AISs ha e o plan he sys em
ope a ion conside ing bo h adiali y and connec i i y con-
s ain s and diffe en load le els. Consequen ly, he AIS
algo i hm is adap ed o accommoda e he ea u es o he
p oblem be e and o imp o e he sea ch p ocess. The algo-
i hm de eloped is es ed in well-known dis ibu ion sys-
ems, wi h e y success ul esul s. Souza e al. [24] sol e
he econfigu a ion p oblem o elec ical dis ibu ion sys-
ems (EDSs) wi h a iable demand, using he a ificial
immune algo i hm. As he econfigu a ion p oblem wi h
a iable demand is a complex p oblem o a combina o ial
na u e, Cop -aiNe (a ificial immune ne wo k o combina-
o ial op imiza ion), which is a combina o ial e sion o he
algo i hm Op -aiNe , is applied o iden i y he bes adial
opology o an EDS in o de o minimize he cos o ene gy
losses in a gi en ope a ion pe iod. A specialized sweep load
flow o adial sys ems was used o e alua e he easibili y
o he opology wi h espec o he ope a ional cons ain s
o he EDS and o calcula e he ac i e powe losses o each
demand le el. The ob ained esul s we e compa ed wi h
hose in he li e a u e in o de o alida e and p o e he effi-
ciency o he p oposed algo i hm. Souza e al. [25] also aim
o sol e he econfigu a ion p oblem o EDS by compa ing
he esul s o he Cop -aiNe (a ificial immune ne wo k
o combina o ial op imiza ion) and he Op -aiNe (a ificial
immune ne wo k o op imiza ion) algo i hms. A specialized
o wa d/backwa d adial powe flow was used o e alua e
each o he p oposed solu ions in o de o de e mine i s
powe losses and i s easibili y ega ding he ope a ional
cons ain s o he EDS. To alida e he use o an AIS, he
final esul s we e compa ed wi h o he solu ions ob ained
wi h o he algo i hms in he li e a u e.
O he impo an field o applica ion is he o ecas ing o
elec ical a iables (loads and powe gene a ion o consump-
ion). Abdul Hamid and Abdul Rahman [26] p opose an a i-
ficial neu al ne (ANN) ained ollowing he beha io o an
a ificial immune sys em (AIS) o gene a e a sho - e m load
o ecas ing model. Two se s o elec ical ene gy demand da a
we e used o es he capabili y o he p oposed algo i hm.
The esul s p esen ed in he manusc ip show ha he p o-
posed AIS lea ning algo i hm is capable o p o iding a o e-
cas compa able o ha o an a ificial neu al ne wo k wi h
an in eg a ed back p opaga ion (BP) algo i hm. Conse-
quen ly, he AIS is an al e na i e lea ning algo i hm o an
a ificial neu al ne wo k. The wo k p oposed by [27] is one
3Complexi y
o he fi s s udies using an in eg a ed AIS simula ion o
imp o ed o ecas ing o elec ici y consump ion wi h an-
dom a ia ions. They de elop a new sys em wi h diffe en
algo i hms, namely, AIS, gene ic algo i hm (GA), and pa i-
cle swa m op imiza ion (PSO), o simula e annual elec ici y
consump ions in selec ed coun ies. The mean absolu e pe -
cen age e o (MAPE) is applied o e alua e he esul s and
selec he bes o ecas ing model. A case s udy wi h da a o
he annual elec ici y consump ions o 16 coun ies om
1980 o 2006 is analyzed. Fo he selec ed coun ies, he AIS
me hod wi h he clonal selec ion algo i hm (CLONALG)
shows sa is ac o y esul s when applied wi h simula ed da a
and has been selec ed as he p e e ed me hod. He nandez
e al. [28] model a hyb id a ificial immune sys em (AIS)
combining he back p opaga ion me hod wi h he a ificial
immune sys em, o achie e highe accu acy, lesse inpu load
da a equi emen , and as e con e gence. The hyb id
app oach is implemen ed, and i s esul s a e compa ed wi h
a GA and a PSO. This analysis e eals ha AIS sol es he
p oblem in a mo e efficien way han do GA and PSO.
Dudek [29] p oposes a sho - e m load o ecas model
based on an AIS o p edic he hou ly load demand o a week.
In his p oposed echnique, each an igen o AIS, which con-
ains he ime se ies load sequences (some pa is a o ecas
sequence), is compa ed wi h his o ical load pa e ns. MAPE
is also used o e alua e he pe o mance o he p oposed o e-
cas model. The sys em achie es a minimum MAPE o
1.77%, which means he AIS ob ains e y success ul esul s.
AISs a e also applied o economic op imiza ion in an elec i-
cal en i onmen . Dynamic economic dispa ch de e mines
he op imal scheduling o online gene a o ou pu s wi h p e-
dic ed load demands o e a ce ain pe iod o ime aking in o
conside a ion he amp a e limi s o he gene a o s [30].
Basu [31] p esen s an a ificial immune sys em algo i hm
ha sol es a hea and powe economic op imiza ion p ob-
lem. The AIS is adap ed o his p oblem, adding new ope a-
ions such as hype mu a ion and ou namen , and is hen
used in a p elimina y es sys em.
Basu [30] implemen s adap i e cloning, hype mu a ion,
aging ope a ion, and ou namen selec ion. In o de o al-
ida e he new AIS, nume ical esul s o a en-uni sys em
wi h uel cos unc ion ha e been de eloped. The esul s
ob ained om he p oposed algo i hm a e compa ed wi h
hose ob ained om pa icle swa m op imiza ion and e o-
lu iona y p og amming. F om nume ical esul s, i is
shown ha he p oposed AIS p o ides a mo e efficien
solu ion han do pa icle swa m op imiza ion and e olu-
iona y p og amming in e ms o minimum cos and com-
pu a ion ime. A agón e al. [32] p esen an AIS-inspi ed
algo i hm, called IA EDP, which ies o sol e an eco-
nomic dispa ch p oblem. I makes use o wo e sions o
a edis ibu ion powe ope a o which ies o keep he
solu ions ha i finds. The p oposal is applied o eigh
p oblems aken om he li e a u e. The esul s a e com-
pa ed wi h hose de i ed om se e al o he app oaches
o de e mine he ad an ages o he IA EDP agains classi-
cal e olu iona y compu ing.
This b ie backg ound leads us o he conclusion ha
AIS can be applied o a a ie y o elec ical con ex s wi h
e y success ul esul s. This ac encou ages us o wo k
wi h a specific AIS, called Op -aiNe , also le e aged in di -
e en pape s [24, 25] and o adjus i specifically o ou
case s udy. The classical Op -aiNe usually wo ks wi h a
low numbe o a iables (each indi idual con ains abou
6 a iables a mos ) and wi hou cons ain s encoded as
ma hema ical unc ions. In he p esen wo k, his algo-
i hm is adjus ed o admi up o 336 a iables and 25 lin-
ea cons ain s (inequali ies and equa ions).
3. Home Ene gy Managemen P oblem
In he designed case s udy, we conside a home elec ical
sys em ha has some household appliance connec ed o
i (Figu e 1).
The con ex can be hough as a domes ic g id wi h a
gene a ion pa and a consump ion pa , connec ed o he
powe g id. As shown in Figu e 1, he gene a ion sys em
o he PV sys em includes he PV gene a o and he ba -
e y. The consump ion pa s a e he elec ic loads which
con ain he ollowing appliances: a space hea e , a s o age
wa e hea e , and mus - un se ices. To balance he p ofi
o ene gy se ices be ween he PV sys em and he loads,
he schedule is connec ed o he g id. The schedule aims
a maximizing he p ofi o ene gy se ices p o ided in a
Space hea e
Powe g id
Ba e y PV panel
Schedule
Wa e s o age
hea e
Mus - un
se ices
Figu e 1: Schema ic image o domes ic elec ical sys em.
4 Complexi y
domes ic ene gy managemen sys em h ough (2) OF,
which is he objec i e unc ion o op imize.
OF = 〠
λsoldPsold −λbough Pbough
−〠
j∈ELs
VOLLjLj shed −Vs
p 2
OF is a linea combina ion o ou elec ical ac o s.
λsold,λbough , VOLLjand Vp a e cons an s ha p o ide he
p ices pe uni o ene gy load and a e gi en by he ma ke .
The fi s e m λsoldPsold ep esen s he income om he
sale o ene gy p oduced by he PV panel o he elec ici y
g id. The second ac o is he o al cos o elec ical ene gy
ha is bough om he ne wo k, λbough Pbough . The alue
o elec ical ene gy is no se ed, meaning he lo is encoded
in he hi d pa ,∑j∈ELsVOLLjLj shed. Finally, he spillage
cos s o PV panels, Vs
p Sp , a e ep esen ed in he las e m
o he equa ion.
We need o balance he loads be ween he ene gy gene -
a ed ( he PV sys em Pp , he ene gy p o ided by he ba -
e y Pb,ou , and he ene gy bough om he powe g id
Pbough ) and he ene gy consumed, meaning he elec ical
loads o he diffe en se ices Lj −Lj shed (hea e , s o age
wa e hea e , and mus ung se ices) and he ba e y cha ge
Pb,in (3). Addi ionally, he powe flow limi a ion h ough
he dis ibu ion line is s a ed in (4), whe e max is a cons an
se o 6 acco ding o [33].
Pbough +Pp +Pb,ou =〠
j∈ELs
Lj −Lshed
j +Pb,in ,
3
− max ≤Pbough −Psold ≤ max 4
The specificdefini ions o all domes ic appliances a e
desc ibed in he ollowing subsec ions.
3.1. PV Sys em. The PV sys em can gene a e he powe ou -
pu Pp o he g id, which can be modelled h ough
Equa ion 5.
Pp =Pp ,p −Sp , 5
whe e S e e s o he spillage cos s o he PV sys em and
P
p ,p
( ) is he po en ial powe gene a ion o he PV sys em.
P
p ,p
( ) is limi ed o maximum and minimum bands due o
he p edic ion o he PV powe gene a ion, ollowing (6).
σdown
p and σ
p
up
a e down and up p edic ion a iances o
he PV sys em, espec i ely, and a e calcula ed ollowing
[34]. Pp ed
p is he p edic ed powe gene a ed by he PV sys-
em. This amoun is posi i e o equal o ze o and is limi ed o
he ac ual powe gene a ion o he PV, P
p ,p
( ), as ep esen ed
in (7). In o he wo ds, he PV sys em can po en ially gene a e
his powe bu HEMS canno ope a e i because o economic
and echnical cons ain s.
Pp ed
p −σdown
p ≤Pp ,p ≤Pp ed
p −σup
p ,6
0≤Sp ≤Pp ,p 7
3.2. Elec ical Loads. Elec ical loads include loads ha can
be con ollable and/o shi able. In his case s udy, h ee
ypes o loads a e modelled: space hea e , L
sh
( ), which is
a con ollable load, s o age wa e hea e , L
swh
( ), which is
a shi able load, and mus - un se ices, L
m s
( ), which a e
noncon ollable-shi able loads. Equa ions 8 and 9 define
he o al elec ical load and o al load shedding o ou
domes ic g id, espec i ely. These loads a e desc ibed in
he ollowing subsec ions.
〠
j∈ELs
Lj =Lsh +Lswh +Lm s ,8
〠
j∈ELs
Lshed
j =Lshed
sh +Lshed
swh +Lshed
m s 9
3.2.1. Space Hea e . The space hea e p o ides he desi ed
indoo empe a u e. Equa ion 10 ep esen s he pe o mance
o he space hea e based on he ela ionship be ween he
indoo empe a u e and i s elec ical load. In (10), θ
0
is he
ini ial indoo empe a u e in ime = 1, which is assumed o
be equal o he desi ed empe a u e. Ris he he mal esis-
ance, and Cis he he mal capaci y o
θin +1 =θin e−1/RC +Lsh R 1−e−1/RC
+θp ed
ou 1−e−1/RC ,
≥2θin =θ0=θdes,  =1
10
Equa ion 11 ep esen s he limi a ion o he indoo
empe a u e. In ou case s udy, his limi a ion is se o
1
°
C mo e o less han he desi ed empe a u e. Finally,
due o physical ac o s, he loads and he load sheddings
a e bo h limi ed by hei maximum and minimum con-
s ain s (12) and (13).
−1≤θin −θdes ≤1, 11
Lmin
sh ≤Lsh ≤Lmax
sh ,12
0≤Lsshed
sh ≤Lsh 13
3.2.2. S o age Wa e Hea e . The s o age wa e hea e is
esponsible o p ese ing he hea in he wa e anks. The
maximum and minimum limi a ions o he s o age wa e
hea e ’s load a e s a ed in (14). The maximum ene gy con-
sump ion o he s o age wa e hea e should be less han
he maximum capaci y o he ank U
swh
, acco ding o (15).
Finally, he maximum o he load shedding o he s o age
wa e hea e is always less han he ene gy consump ion o
he appliance (16).
Lmin
swh ≤Lswh ≤Lmax
swh ,14
〠
N
=1
Lswh =Uswh,15
5Complexi y

0≤Lshed
swh ≤Lswh 16
3.2.3. Mus -Run Se ices. Mus - un se ices consis o loads
ha should be p o ided quickly, and he e o e, i is no
easy o p edic hem, o example, ligh ing and en e ain-
men . Fo he pu poses o his pape , i is assumed ha
he e is no unce ain y in p edic ing he elec ical loads
o mus - un se ices (17). As in he s o age wa e hea e ,
he maximum o he load shedding Lshed
m s mus always
be less han he ene gy consumed L
m s
( ) (18).
Also, he load shedding cons ain is s a ed in (18).
Lm s =Lp ed
m s ,17
o≤Lshed
m s ≤Lm s 18
3.3. Ba e y Sys em. The ba e y sys em can be used o apply
he cha ge and discha ge s a egies in he HEMS. A flowcha
(Figu e 2) is designed o ope a e wi h he ba e y in he
domes ic en i onmen . The sys em aims a p o iding he
equi ed elec ical demand, maximizing i s benefi s. When
he e is a su plus P
b,in
( ) o he ene gy gene a ed (i.e., he
PV panel gene a es mo e ene gy P
p
( ) han he o al load
TL( ) demands), i is s o ed in he ba e y (C
b
( )). I he ba -
e y is ully cha ged Cb >Cmax
b, hen i is sold o he g id
P
sold
( ). On he con a y, he sys em makes use o he ene gy
s o ed in he ba e y P
b,ou
( ) when he elec ical demand is
highe han he powe gene a ion o he PV panel. Addi ion-
ally, i he ba e y canno p o ide he ene gy needed (i.e., is
una ailable o comple ely discha ged, Cb >Cmin
b), he sys-
em will buy he elec ici y P
bough
( ) om he powe g id.
4. Expe imen al Se ing
To assess he pe o mance o he p oposed HEMS, some
pa ame e s ha e been se o op imize he sys em. The maxi-
mum powe p oduced by he PV sys em is 2kW. The ba e y
can s o e be ween Cb
min 48 and Cb
max 2.4 kWh. The maximum
hea ing powe o he space hea e (SH) Lmax
sh equals 2 kW
o main ain he empe a u e o he house wi hin ±1 o he
desi ed empe a u e (θ
des
23
°
C). The he mal esis ance, R,
o he building shell is equal o 18
°
C/kW, and he capaci y
Cequals 0.525 kWh/
°
C. The ene gy capaci y o he s o age
wa e hea e (U
swh
) is 10.46 kWh (180 L) which has 2 kW as
maximum o hea ing elemen s Lmax
swh . Table 1 displays he p e-
dic ed da a ha has been used in [33]. Table 2 gi es he p ice
da a o he sys em. VOLL and spillage cos s o PV powe
gene a ion a e shown in Table 3.
These da a a e used in ou HEMS o op imize he unc ion
(2). The objec i e unc ion is in eg a ed in o Op -aiNe o ge
an op imized schedule o 24 hou s in a domes ic en i onmen .
Following he Op -aiNe p ocedu e, he ini ial popula ion an-
domly gene a ed, whe e each indi idual is a se o elec ical
alues o 24 hou s, mus comply wi h he cons ain s modelled
in he elec ical managemen p oblem. Fo his pu pose, each
da um o he indi idual is conside ed as an elec ical pa ame e
o op imize o 24 hou s. Ini ially, he pa ame e s which only
depend on some fixed bounda ies (6), (7), (12), (14), and (17)
a e gene a ed. Then, hese pa ame e s a e used as new
bounda ies o hose elec ical pa ame e s ha depend on hem
( he es o heequa ionsa egi enin hemodelo Sec ion3).
This me hodology is ecu si ely applied un il all he pa ame e s
needed o each indi idual a e gene a ed. Finally, o ob ain he
pa ame e s ela ed o he ba e y load, he pa ame e s p e i-
ously calcula ed and he flowcha o Figu e 2 a e applied o
gene a e he new ones.
Wi h he indi iduals gene a ed, Op -aiNe wo k ollows
hese s eps:
(1) Ini ia e Npopula ion ollowing he me hod abo e, o
espec he linea cons ain s and he flowcha i i is
he case.
(2) E alua e each indi idual acco ding o he op imiza-
ion unc ion gi en in (2).
(3) C ea e N
c
clones o each indi idual. The elemen s o
each clone should be sligh ly changed acco ding o
he mu a ion equa ion (1).
(4) Fo each cell o an ibody, selec he bes clone wi h
he highes objec i e alue.
(5) I he mean objec i e o he las i e a ion and he
p esen one a e below a limi , hen simila indi iduals
a e supp essed acco ding o he simila i y h eshold
s
ha measu es dis ances be ween wo an ibodies.
(6) I some indi iduals a e supp essed, hen i is needed
o add a new andom popula ion. These new solu-
ions a e gene a ed ollowing he me hod gi en abo e
o espec he cons ain s and he flowcha i ha is
he case.
(7) This wo k flow is epea ed un il he con e gence c i-
e ion (maximum numbe o i e a ions gen). The
esul is one o mo e indi iduals wi h an op imum
objec i e alue.
As we can see, AIS con ains fi e pa ame e s, namely,
numbe o indi iduals N, numbe o clones N
c
, simila i y
h eshold
s
, maximum numbe o gene a ions gen, and
he mu a ion pa ame e β. Depending on he p oblem,
hey can ake se e al alues and a e essen ial o a co ec
ope a ion. AIS needs some pa ame e s o be se be o e-
hand in o de o op imize a p oblem co ec ly. These
pa ame e s a e ela ed o he cloning and mu a ion p o-
cess, he supp ession algo i hm, and he con e gence
c i e ion. Fo each i e a ion, a numbe o clones N
c
is gen-
e a ed pe cell. This numbe N
c
is se empi ically and can
influence he final esul s. Gene ally, i N
c
is se wi h a e y
low alue, he con e gence c i e ion can be delayed, as we
a e no able o find enough di e si y o selec be e indi-
iduals o each cell. O he wise, i oo many clones a e
gene a ed, he ime upon con e gence migh be longe
han expec ed.
We empi ically se he AIS pa ame e s acco ding o
Table 4, which ga e he op imal pe o mance in e ms o
fi ness and ime.
The nex sec ion will desc ibe he simula ions and esul s
wi h Op -aiNe configu ed o he p esen ed HEMS.
6 Complexi y
5. Simula ion Resul s
The e alua ion is wo old. Fi s ly, i is expec ed ha Op -
aiNe ob ains posi i e esul s in sol ing op imiza ion
p oblems in he c ea ed se ing and compa ing hem wi h
o he classical bioinspi ed app oaches. Consequen ly, a
compa a i e analysis was ca ied ou be ween a classical
gene ic algo i hm (GA) and a pa icle swa m op imiza-
ion (PSO). Addi ionally, we analyzed he impac o he
flowcha (Figu e 2) on ou sys em, when he ba e y
was in ol ed. The e o e, wo s a egies ha ep esen
wo elec ical si ua ions a e designed. In he fi s s a egy
(s a egy 1), he domes ic en i onmen does no conside
any a iable ela ed o he main enance o he domes ic
elec ic cha ge h ough he elec ical ene gy p oduced by
he PV sys em. This s a egy only aims a op imizing i s
ene gy benefi s. In he second s a egy (s a egy 2), he
home en i onmen aims a supplying he elec ici y
demand au onomously. The e o e, he su plus gene a ed
by he PV is s o ed in he ba e y. In his s a egy, he
elec ici y could be sold o he g id i he ba e y is
comple ely cha ged. On he con a y, i he ba e y can-
no supply all he elec ical cha ge, hen he HEMS mus
buy elec ici y om he powe g id.
S a
Ini
Pp ( ) >
TL( )
Pp ( ) =
TL ( )
Pb,in ( ) = Pp ( )−TL( )
Pbough ( ) = 0
Cb ( ) = Cb ( −1) + Pb,in ( )−Pb,ou ( )
Cb ( ) = Cb ( −1) + Pb,in ( )−Pb,ou ( )
Cb ( ) = Cbmin
Cb ( ) = Cbmax
Pb,in ( ) = Cbmax−Cb ( −1) +Pb,ou ( )
Psold ( ) = Pp ( )−TL( )−Pb,ou ( )
Pb,ou ( ) = TL( ) -Pp ( )
Pb,ou ( ) = Cb ( −1)− Cbmin +Pb,in ( )
Pbough ( ) = TL ( )− Pp ( )−Pb,ou ( )
Cb ( ) >
Cbmax
Cb ( ) >
Cbmin
Psold ( ) = 0
Psold ( ) = 0
Pb,in ( ) = 0
Psold ( ) = 0
Pbough ( ) = 0
Pb,ou ( ) = 0
Pb,in ( ) = 0
Pb,ou ( ) = 0
Yes
No
Yes Fin
Yes
Yes
No
No
End
End
No
Pbough ( ) = 0
Figu e 2: Flowcha modelling he ba e y pa ame e s.
7Complexi y
Based on hese wo main goals, h ee diffe en expe i-
men s a e conside ed:
(i) Expe imen I: compa a i e s udy be ween GA, PSO,
and AIS
(ii) Expe imen II: compa ison be ween s a egy 1 and
s a egy 2
(iii) Expe imen III: analysis o s a egy 2 when he ba -
e y is disconnec ed o connec ed
Expe imen I makes a compa ison be ween GA, PSO, and
AIS. Expe imen II op imizes he pa ame e s ela ed o he
PV sys em, he space hea e , he wa e hea e , and he
mus - un se ices; he e o e, he pa ame e s ela ed o he
ba e y cha ge a e no conside ed (s a egy I). The esul s
ob ained om he op imiza ion p ocess a e compa ed wi h
he esul s ha a e e ie ed when he pa ame e s o he ba -
e y a e included in he sys em, al hough all a e se o 0. Tha
means he ba e y is disconnec ed om he home en i on-
men bu he AIS ollows he flowcha o op imize he
sys em.
Finally, expe imen III pe o med wo diffe en analyses:
when he ba e y was disconnec ed and when he ba e y was
connec ed, o s udy he impac o his de ice on he sys em.
5.1. Compa ison be ween GA, PSO, and AIS. In his sec ion,
we aim o compa e he esul s ob ained wi h h ee diffe en
bioinspi ed algo i hms: gene ic algo i hm, pa icle swa m
op imiza ion, and a ificial immune sys em. The gene ic
algo i hm (GA) is widely used in op imiza ion p oblems wi h
many configu a ions. In his pape , a classical app oach o
GA is applied so ha he mu a ion and c osso e as well as
he numbe o gene a ions a e empi ically se o 0.3, 0.8,
and 2000, espec i ely. Addi ionally, he selec ion unc ion
chosen was he oule e algo i hm.
The pa icle swa m op imiza ion (PSO) was fi s in o-
duced by Ebe ha and Kennedy [35] and consis s o a
popula ion-based op imiza ion algo i hm which is deemed
o be a na u e-inspi ed op imiza ion me hodology. PSO
employs a se o pa icles which would mo e h ough
he sea ch space a e e y i e a ion and would calcula e
he fi ness alue a each poin . A e a e mina ion condi-
ion is me , he bes op imized alue is selec ed by choos-
ing he bes alue ound in he his o y o pa icles. The
success o PSO lies in i s “ eloci y equa ion”; his equa ion
decides on he nex poin in space ha each pa icle would
mo e o. The eloci y equa ion can be shown as
Vid,k+1 =wVid,k+c1× and1×Xpbes id,k−Xid,k
+c2× and2×Xgbes d,k−Xid,k
19
He e, V
id,k+1
is he eloci y o he d h dimension o he
i h pa icle in he nex i e a ion (k + 1s ), wis he ine ia
o he pa icle, V
id,k
is he eloci y o he d h dimension
o he i h pa icle in he cu en i e a ion (k h i e a ion),
c
1
is he cogni i e accele a ion cons an , c
2
is he social
accele a ion cons an , X
pbes id,k
is he posi ion o he pa i-
cle in he d h dimension a which he bes solu ion was
Table 4: Op ima alues se o N,N
c
,gen,
s
, and βin bo h s a egies.
NN
c
gen s β
S a egy I 250 12 250 10 100
S a egy II 250 18 300 3 10
Table 1: P edic ed da a o unce ain a iables.
P
p
p ed( )σ
p
up
σ
p
down θou p ed( )Lp ed
m s
( )
1 0 0.03 0.01 5.5 0.3
2 0 0.03 0.01 5.5 0.3
3 0 0.03 0.01 5.2 0.3
4 0 0.03 0.01 5.2 0.3
5 0 0.03 0.01 4.8 0.4
6 0 0.03 0.01 5.5 0.6
7 0.25 0.03 0.01 6.5 0.8
8 0.75 0.03 0.01 7.5 0.8
9 1.25 0.03 0.01 9.8 0.7
10 1.75 0.03 0.01 10.1 0.55
11 1.9 0.03 0.01 11.5 0.5
12 1.9 0.03 0.01 12 0.5
13 1.9 0.03 0.01 12.5 0.5
14 1.75 0.03 0.01 12 0.5
15 1.25 0.03 0.01 11.5 0.6
16 0.75 0.03 0.01 10 0.8
17 0.25 0.03 0.01 9 1.5
18 0 0.03 0.01 8.5 1.8
19 0 0.03 0.01 8 1.7
20 0 0.03 0.01 7.5 1.1
21 0 0.03 0.01 7 0.9
22 0 0.03 0.01 6.5 0.7
23 0 0.03 0.01 6.2 0.6
24 0 0.03 0.01 6 0.4
Table 2: P ice da a o he sys em.
P ice ($/MW)
Time (hou ) λ
i
λne
23–7 2.2 0.0814
8–14 2.2 0.1408
15–20 2.2 0.3564
21-22 2.2 0.1408
Table 3: VOLL and spillage cos s.
VOLL ($/MW) Spillage cos ($/MW)
Time (hou ) SH SWH MRS PV
22–7 1 1 2.2 4
8–21 1 1 2.2 4
8 Complexi y
ound so a by he i h pa icle, X
gbes d,k
is he alue o he
d h dimension a which he bes solu ion so a was ound
by he whole sys em, X
id,k
is he cu en posi ion o he i h
pa icle in he d h dimension, and c
1
and c
2
a e andom
numbe s. Using he eloci y calcula ed, he nex posi ion
o be e alua ed is calcula ed as
Xid,k+1 =Xid,k+Vid,k20
The abo e eloci y equa ion wo ks well when he sys em
is unde no cons ain s. Howe e , when he e a e cons ain s,
some o he pa icles migh all off he easible egion. In his
case, he pa icles should no upda e hei pe sonal bes when
a pa icle is ou side he easible egion. Nei he should he
global bes be upda ed in case o a pa icle being ou side he
easible bounda y, ha ing a be e alue han he cu en
global bes . In case a pa icle has no ound a pe sonal bes
ha alls in he easible egion, he pa icle should ely only
on global bes o guide i s mo emen . In his case, he calcu-
la ion o eloci y would change o
Vid,k+1 =wVid,k+c1+c2× and × Xgbes d,k−Xid,k21
Howe e , equali y cons ain sa is ac ion is mo e difficul
han he inequali y cons ain sa is ac ion. To sol e his p ob-
lem, a mending p ocedu e is ca ied ou a e e y i e a ion o
make su e all pa icles sa is y he equali y cons ain . The
mending p ocedu e calcula es he o e shoo o each o he
pa icle and adds a co ec ion alue o co ec he e o .
The co ec ion is equally added o each o he in e als o
he pa icle.
In o de o demons a e he efficiency o he a ificial
immune sys em in he ene gy managemen op imiza ion
p oblem, we pe o med a compa a i e es wi h a e sion o
cons ained PSO adop ed om [36] and an app oach o he
gene ic algo i hm. The goal was o p edic he op imum
alues o each a iable du ing 24 hou s, ollowing s a egy
1 and s a egy 2. The linea cons ain s p oposed in he elec-
ical model a e applied, and subsequen ly, he objec i e
unc ion o he op imized a iables is measu ed.
Table 5 shows he esul s ob ained when he objec i e
unc ion and he ene gy a e bough and consumed when
AIS, GA, and PSO a e applied wi h an op imal se ing.
As Table 5 shows, AIS ob ains sligh ly be e esul s in he
objec i e unc ion o bo h s a egies when bo h se ings a e
op imal o sol e his p oblem. Tha means AIS is a be e
configu a ion o he elec ical pa ame e s o op imize he
p oblem s a ed. Likewise, AIS is able o find lowe alues
o he amoun o ene gy bough , which means he algo i hm
allows sa ing ene gy and money o he cus ome . The esul s
o he AIS o he ene gy sold a e lesse han in PSO and in
GA. Tha could be explained because in PSO and in GA,
he mean amoun s o ene gy ha a e managed a e g ea e
han in AIS. Howe e , PSO also ob ained posi i e esul s
(a leas , be e han wi h he classical app oach o GA);
he e o e, we p opose o make a deepe compa ison wi h
mo e complex p oblems o alida e bo h algo i hms and
s udy he limi a ions o each one.
5.2. Analysis o he Ene gy Managemen S a egy. In his sec-
ion, he wo s a egies desc ibed below a e deeply analyzed
and compa ed. The fi s s a egy looks o maximizing he
domes ic ene gy p ofi . Howe e , he second s a egy aims
a maximizing ene gy p ofi and ac ing as an au onomous
ene gy sys em. I is expec ed ha s a egy II ob ains be e
esul s, as his s a egy pu sues he au onomous managemen
o ene gy, sa ing mo e money han in s a egy I.
Op -aiNe wo ked wi h indi iduals o ec o o 264
elemen s wi h equali y and inequali y cons ain s, as each
indi idual con ains all he a iables o 24 hou s. Each
alue co esponds o he diffe en elec ic loads and pow-
e s desc ibed in Sec ion 3 o he PV panel, he s o age
wa e hea e , he space hea e , and he mus - un se ices.
We un he algo i hm wi h wo diffe en configu a ions,
one wi h s a egy 1, excluding all he cons ain s ela ed
o ba e y managemen , and one wi h s a egy 2, including
all he cons ain s ela ed o ba e y managemen , bu wi h
he ba e y a iables se o 0. Table 6 shows he esul s
acco ding o he fi ness alue o he objec i e unc ion
OF and he pa ame e s o sold and bough ene gy.
As we can see, he alue o he objec i e unc ion in s a -
egy 1 is highe han ha o s a egy 2. Howe e , he ans-
ac ed ene gy be ween home and powe g id is lesse in
s a egy 1, which means ha S a egy 2 allows o he au on-
omous managemen o ene gy a home.
5.3. Impac o he Ba e y. In his analysis, s a egy 2 is
applied o s udy he influence o he ba e y in he domes ic
en i onmen . In his case pa icula ly, indi iduals in he
AIS ha e 336 elemen s because he pa ame e s co espond-
ing o he ba e y cha ge and load a e se as elemen s o op i-
miza ion. Each indi idual is cons uc ed ollowing he linea
cons ain s and he flowcha be o e being inse ed in o he
popula ion. Two diffe en execu ions a e made, fi s ly, wi h
all he a iables ela ed o he ba e y managemen se o
0. In he second execu ion, he a iables o he ba e y
could change acco ding o he co esponding equa ions
and flowcha (Figu e 2). The esul s ob ained a e shown
in Table 7.
F om he da a in Table 7, we can see ha he ba e y sys-
em can imp o e he alue o he objec i e unc ion. Table 7
also conside s a si ua ion in which he ba e y inc eases he
amoun o elec ical ene gy sold om he sma home o
he g id, and i dec eases he amoun o elec ical ene gy ha
a home buys om he ne wo k.
Table 5: Resul s o he objec i e unc ion and he ene gy bough and
consumed when AIS and PSO a e applied wi h an op imal se ing.
Objec i e alue Ene gy bough Ene gy sold
S a egy 1 PSO 23.52 46.61 14.12
GA 22.48 46.94 14.09
AIS 23.86 45.66 14.22
S a egy 2 PSO 4.86 37.60 5.40
GA 4.92 32.66 5.22
AIS 5.11 26.53 4.64
9Complexi y