Sliding mode control of an active power filter with photovoltaic maximum power tracking

Nomencla u e
di ec andquad a u eaxesexp essedin hes a iona y e e ence ame
di ec andquad a u eaxesexp essedin hesynch onous o a ing e e ence ame
Lg
g id il e induc ance
Rg
g id il e  esis ance
Slidingmodecon olo anac i epowe  il e wi hpho o ol aicmaximumpowe  acking
JoséAn onioCo aja enaa,⁎
josean.co aja [email protected]
Osca Ba ambonesb
Pa xiAlko aa
JonCo aja enac
aEnginee ingSchoolo Gipuzkoa(Eiba ),Uni e si yo  heBasqueCoun y,O aola29,20600Eiba ,Spain
bEnginee ingSchoolo Vi o ia,Uni e si yo  heBasqueCoun y,Nie esCano12,01006Vi o ia,Spain
cEnginee ingSchoolo Gipuzkoa,Uni e si yo  heBasqueCoun y,Eu opaPlaza,1,20018Donos ia,Spain
⁎Co espondingau ho .
Abs ac
Nowadays, heinc easeinsola ene gyins alla ionsasasou ceo ene gyisg owingconside ably.Theconnec ion o heg ido  heseins alla ionsgene allyinjec sall hepowe ob ained om hepanelasac i epowe ,
makingze o he eac i epowe .Thesamepowe injec ionsys emcanbeused oachie eauni powe  ac o i  heac i e il e  ea u eisin eg a edini .In hispape ,anac i epowe  il e (APF) ha cancon olbo h, he
MPP (maximum powe  poin ) o  a pho o ol aic sys em (PV) and he powe  ac o  o  a nonlinea  load connec ed o he g id using a h ee phase DC/AC powe  in e e  wi h new sliding mode con olle s is p esen ed.
Pe u ba ion–obse a ion(P&O)is heusedMPPTalgo i hmand h eeSlidingModeCon olle s(SMC)a eused o egula e heDC ol ageo  hePVand hecu en dandqcomponen so  heac i e il e using hePQ
heo y.Wi haSMC,noexac knowledgeo  hemodelpa ame e sis equi edandi o e sgoodbeha io agains unmodeleddynamics,insensi i i y opa ame e  a ia ionsandgood ejec iono ex e naldis u bances.The
space ec o pulsewidemodula ion(SVPWM)o 7and5segmen sisimplemen edino de  ocheck hee iciencyandg idcu en  ipple.Se e alexpe imen al es sha ebeenca iedindi e en condi ions,concluding ha
hep esen edsys emp o idesane icien maximumpowe  ackingandagoodpowe  il e cha ac e is ic.
Keywo ds:Ac i epowe  il e ;Slidingmodecon olle ;MPPTcon ol;PQ heo y;E iciency
α
,
β
d
,
q
This is he accep ed manusc ip o he a icle ha appea ed in inal o m in
In e na ional Jou nal o Elec ical Powe and Ene gy Sys ems 110 : 747-758
(2019), which has been published in inal o m a h ps://doi.o g/10.1016/
j.ijepes.2019.03.070. © 2019 Else ie unde CC BY-NC-ND license (h p://
c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
g id ol age ec o angle
g id ol age equency
ig
g idcu en
iPV
sola panelcu en
iF
in e e ou pu cu en
iF_MPPT
in e e ou pu cu en due o heMPPT
iF_APF
in e e ou pu cu en due o heAPF
iin _DC
DC/ACin e e a e ageinpu cu en
g
g id ol age
C
in e e capaci o  ol age
PV
sola panel ol age
in
DC/ACin e e  ol agemainha monic
P
ac i epowe
Q
eac i epowe
θe
ωe
PWM
in e e commu a ion equency
VOC
PVopenci cui  ol age
ISC
PVsho ci cui cu en
VMP
PVmaximumpowe poin  ol age
IMP
PVmaximumpowe poin cu en
PMP
PVmaximumpowe poin powe
d( )
SMCunce ain y e ms
S( )
SMCsliding a iable
β
SMCswi chinggain
λ
ol agecon olle SMCcons an gain
KSMC
cu en con olle SMCcons an gain
V
Lyapuno  unc ion
1In oduc ion
Themos abundan pe manen ene gy esou ceonea hissola ene gyandi sa ailabili yin he o mo  adia ionishighinmanypa so  hewo ld.
TheGe manAd iso yCouncilonGlobalChange(WBGU)conduc edananalysiso ene gyneedsand esou cesin he u u eun il he2050sand2100s.Thiss udyhighligh s heimpo an con ibu iono sola ene gy o he
long- e mglobalene gyneeds.Thisscena ioisbasedon he ecogni ion ha i isessen ial omo eene gysys ems owa dssus ainabili y h oughou  hewo ld.Thead ancemen o  echnologyand esea chin hede elopmen o
sys emsbasedonpho o ol aicpanels,mo eeconomicalandwi hbe e cha ac e is ics,p edic saninc easeinins alla ionswo ldwidein hecomingyea s[1].
Theene gygene a edbypho o ol aicpanelsismainlydependen on hele elo sola  adia ion ha a ec s hepho o ol aicpanelsand hei  empe a u e.The e o e,when a ia ionso  hesepa ame e soccu , hesys emmus
loca e hemaximumpowe wo kingpoin .Ino de  odo his,oneo  hesea ch echniques o  hemaximumpowe poin o  hepho o ol aicpanelmus beused[2,3].
Mos g id-connec edpho o ol aicsys emschemesusea wo-s ageene gycon e sion opology[4–6].The i s s ageisaBoos con e e  o aise hepanel ol ageabo e heg idpeak ol age.Thiscon e e implemen s he
MPPTalgo i hm.Theobjec i eo  hesecondcon e e ,DC/AC,is oinjec  heene gysuppliedby hep e iouscon e e in o heelec icalg id.
Anexpe imen als udyisp esen edinAQuan i a i eCompa isono Cen alIn e e sandS ingIn e e sinU ili y-ScaleSola Sys emsinNo hAme ica[7].
By using a highe  DC ol age le el, he DC/DC s age can be elimina ed. Some o  he bene i s o  inc ease he DC/AC inpu  ol age a e he componen s educ ion, including o e cu en  p o ec ion de ices, combine s,
disconnec s,e c.;lowe labo cos s;lesscoppe in heDCcollec ionsys em;lessexpensi ein e e s(lesscoppe ,lowe cu en  alues o componen s);andlowe  o alcos pe wa .Theconclusionsa e ha  hecen alin e e is1%
mo ee icien  han hes ingin e e ssolu ion.
Thus,inacco dancewi h he endency oinc ease hein e e 'sinpu  ol age[8], hese ies-pa allelo cen alized opologywillbeusedin hep esen edapplica ion,asshowninFig.1.
Thelocalloadso  hepho o ol aicsys emcanbeespeciallynonlinea ,suchas he ec i ie - il e s ageso  hepowe supplieso mos householdappliances[9].Theseloadswo sen hepowe  ac o byinc easinglossesin
ans o me sandcables undamen allyandleads opowe quali yp oblems ha maya ec o he loadsconnec eda  hesamepoin o commoncoupling[10].Shun ac i epowe  il e sha ebeens udiedandde elopedasane ec i e
solu ion o hisp oblem[11–13].
Thecon olo  heMPPTinpho o ol aicsys emsand heac i epowe  il e cha ac e is iccanbecombinedinonesys em.In[14] hein e e DC ol ageis ixed o  hePVpanelbu noMPPTisimplemen edand hecu en is
con olledwi hhys e esiscon olle s,changing heswi ching equencyand he e o e he ippleo  hecu en andinc easing hecomplexi yo inpu  il e s.In[15] hePVMPPTisob ainedand hePIa e heusedcu en con olle s.
Thesecon olle sha e obeadjus edwi hahighbandwid hino de  o ackco ec ly hechanging e e enceand hiscanmake hesys emuns able.In[16] heMPPTisimplemen edbu  hecu en is egula edwi hahys e esis
con olle wi h hedisad an ageo p o idinganoncons an swi ching equencyand he e o eachangingcu en  ipple.In[17]aDC/DC i s s ageisincludedbe o e heDC/ACcon e e  educing heo e alle iciencyandPI
con olle swi h as dynamica eused o egula e hecu en .In[18]whe eonlyp esen ssimula ion esul s, heMPPTisimplemen edand heusedcon olle isahys e esiscon olle .Thehys e esisbandismodula easa unc iono
Vdc, heslopeo  e e encecu en and he il e induc ance alue.E o sin hepa ame e sp oduce a ia ionin hehys e esisbandand he e o ein heswi ching equency.In[19] heg idcu en sa e egula edusinghys e esis
cu en con olle s ogene a e hein e e ga ingpulseschanging heswi ching equencyand he e o e he ippleo  hecu en .
In hispape , hedesign,implemen a ionandpe o manceanalysiso a h eephasesac i epowe  il e wi hPVMPPTcha ac e is icsisp esen ed.Thep oposednewcon olschemecan egula eno only hemaximumpowe
o aPVbu also hepowe  ac o o anonlinea loadcouldbe egula ed,usually oauni ypowe  ac o .I shouldbeno ed ha achie ingauni ypowe  ac o  helossesin heelec iclinesa e educed.
Themainha dwa e ea u ecompa ed oo he sys emsis heelimina iono  he ol ageboos ings ageand hus heBoos con e e s ageisno necessa y,anddi ec ly hein e e inpu  ol ageis egula edwi haslidingmode
con olle  oge  om hePV hemaximumpowe .Theimplemen edMPPTalgo i hmis hepe u ba ionandobse e(P&O)and oa oid hemeasu emen o  hePVpanelcu en  hein e e ou pu powe ismeasu edandusedin he
MPPTalgo i hm.
Fig.1Ac i epowe  il e  opology,measu edsignalsandSMCcon olle s.
Some me hods o  adjus men  o  con en ional con olle s such as PI (p opo ional-in eg al) o  PR (p opo ional- esonan ) equi e accu a e in o ma ion o  he plan  model o ensu e s abili y [20]. In his con ex , he mos
app op ia eop ionis oconside some ypeo  obus con olschemesuchas heslidemodecon olini iallyde elopedbyU kin[21]andsuccess ullyapplied o a ious ypeso con ols uc u es[22–24].In[25]ano el e minal
slidingmodecon olme hod o maximumpowe  ackingo pho o ol aicpowe sys emsisp esen edbu only o aBoos con e e wi ha esis i eload.In[26]aslidingmodecon oldi ec powe con olle basedac i eand eac i e
powe con olle  o  h ee-phaseg id- iedpho o ol aicsys emwi haBoos s ageisp oposed.In[27]asys emconnec ed oaPVpanelconsis ingo  wocascadeddc–dcboos con e e sunde sliding-modecon ola es udiedinaDC
g id.In[28]ano elunce ain yanddis u bancees ima o basedslidingmodecon olapp oachisapplied oDC–DCpowe con e e sandin[29]anadap i eslidingmodecon olalgo i hmisde eloped o g idsynch oniza iono a
pho o ol aicsys em.
A e  heex e nalloop esponsible o  egula ing hepanel ol age, wonewin e nalSMC egula o sa e esponsible o  egula ing heac i epowe  il e cu en bycon olling hecu en dandqcomponen s.Thep oposed
cu en dandq e e enceso  heac i e il e pa a egene a edusing hePQ heo y.
The s abili y demons a ion o  he p oposed con olle s will be ca ied ou  using he Lyapuno  s abili y heo y showing ha  he p esen ed SMC con olle s can o e come he sys em unce ain ies, like g id induc ance,
measu emen smalle o sandnoise,andg id ol age ole ances.So, hepe o manceand obus nesso  hep oposednewSMCsis alida einsimula ionandina ealpla o minsui ableandad e secondi ions.TheSMCisalso
compa edexpe imen allywi hacon en ionalPIcon olle ino de  oshow hepe o manceo  hep oposedcon olscheme.
Finally, wospace ec o pulsewidemodula ion(SVPWM) echniquesa e es ed, he7and5segmen sSVPWM,ino de  ocheck hee iciencyo  hesys emand hecu en  ipple.
All heexpe imen sa ede elopedona ealpla o m.
2Sys emmodel
Theg id oin e e equa ion ha de ined hesys emo Fig.1in hes a iona y e e encesys emis,
Thesys emwillbecon olledin hed-qsynch onous o a ing e e ence ameso heequa ionsob ained om(1)a eas ollows:
Theac i eand eac i epowe sa ede e minedin hes a iona y e e encesys emas,
2.1In e e DC ol agecon ol
The MPPT algo i hm adjus s he in e e  DC ol age acco ding o he pe u ba ion and obse e me hod. Howe e , he MPP ol age le el mus  be highe  han he minimum in e e  DC ol age equi ed o main ain he
egula ion, ha  is, he in e e  inpu  ol age should be highe  han he g id peak ol age plus he ol age d op in he induc ances. I  he PV panel is unable o each his ol age le el due o educed i adiance o  inc eased
empe a u e, heac i epowe  il e willge  heene gy om heg id okeep he ol agele el o he ixedminimum,wo kingin hiswayasacon en ionalac i epowe  il e .Thiswillbedemons a edin hesec iononexpe imen al
esul s.
Makingapowe balancea e conside ing heDC/ACin e e and he il e induc anceasidealand he o a ing e e ence amelinked o heg id ol age(
gq
= 0), hein e e capaci o cu en isexp essedas,
F omEq.(5)i isob ained:
(1)
(2)
(3)
(4)
(5)

whe e
gd
is heg id ol agepeak alueandis heo e icallycons an .Eq.(6)canbe ew i ena e conside ingsys emunce ain iesas:
whe e he e m
d( )
 ep esen s hesys emunce ain ies,likecapaci o  ole ances,measu emen smalle o s,andg id ol age ole ances.
Le usde ine he ol age ackinge o as ollows:
Taking hede i a i eo  hep e iousequa ionwi h espec  o imeyields:
Whe ei isconside ed ha  he e e ence ol ageisaquasi-cons an signalbecausewi h heMPPTalgo i hm hechangeisslow o  hecon olpe iod.
Tocompensa e hesys emunce ain iesanSMCschemeisp oposedwi h hesliding a iable
S( )
de inedas:
Then, heslidingsu aceisde inedas:
Theslidingsu ace(11)isselec edwi hanin eg al e mino de  oa oid he imede i a i eo  hee o signalbecause hisde i a i ewillinc ease henoisesignal a io ina ealimplemen a ion.
Finally, heslidingmode ol agecon olle isdesignedas:
Thep oposedcon olsignal(12)p esen s h ee e msandino de  oob ainagood ackingo  he ol age ajec o y, hegain
λ
mus bechoses ic lyposi i eand heswi chinggain
β
mus bechose
β≥|d( )|
 o all ime.The
s abili ydemons a iono  hep oposedcon olle isca iedou using heLyapuno s abili y heo yandcanbe oundin[30].
2.2In e e ac i epowe  il e con ol
Theins an aneous eac i epowe (IRP)p–q heo yis heusedalgo i hm ogene a e hecu en  e e encesignalsin hecon olo  hein e e asac i epowe  il e .Thisalgo i hm,unde  hecondi ion ha  heloadissupplied
wi hasinusoidalsymme ical ol age,shows ha  he e e encesignalsgene a ionwi h heIRPp–q heo yalgo i hmp o idesco ec  esul sand heins an aneous alueso ac i eand eac i epowe a e[31],
is hea e agepa o  heac i epowe abso bedby heloadandmus besuppliedby heg idand/o by hePVpanels. is hea e agepa o  he eac i epowe abso bedby heloadandmus besuppliedby heac i e
powe  il e ino de  oge auni ypowe  ac o in heg id. and a e heal e na ingcomponen o  heac i eand eac i epowe s espec i ely obesuppliedby heac i epowe  il e .
Using(4)and akinginconside a ion hecu en senseo  hein e e , hein e e cu en componen s e e ences ela edwi h heloadins an aneousac i eand eac i epowe sa eob ainedas,
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
   
   
(14)
Wi h hePa k ans o ma ion he e e encesin he o a ingsynch onous e e encesys ema ede e mined,
2.3Cu en SMCs
Thecomponen so  he e e encecu en a e he e o e,
Once hecu en  e e encesa eob ained, hecon olle s o egula e hecu en dandqcomponen swillbedesigned.SlidingModeCon olle sa eused o ack he e e encecu en co ec lyandp o ide obus nesswhen
he ealpa ame e sdi e sligh ly om hemodeland he ea esys emunce ain ies.
Conside ingEqs.(2)and(3), hede i a i eso  hecomponen so  hecu en a e,
whe e he e ms and ep esen  hesys emunce ain ieslike il e  ole ances,measu emen smalle o s,andg id ol age ole ances.
Thecu en componen s ackinge o sa ede inedas,
Taking hede i a i eo  hep e iousequa ionwi h espec  o ime,
Tocompensa e hesys emunce ain ies hep oposedSMCschemewi h hesliding a iable and a e,
Finally, heslidingmodecu en componen scon olle sa edesignedas:
Now, hes abili ydemons a iono  hep oposedcon olle willbeca iedou using heLyapuno s abili y heo y.Le usde ine he ollowingLyapuno  unc ion:
(15)
(16)
(17)
(18)
(19)

dd
(
)
dq
(
)
(20)
(21)
(22)

Sd
(
)
Sq
(
)
(23)
(24)
(25)
(26)
(27)
Taking he imede i a i eo  heLyapuno  unc ion,andusingEqs.(21),(23)and(25)i isob ained:
whe e isde inedas,
The e o e,
Using heLyapuno 'sdi ec me hod,since isclea lyposi i e-de ini e, isnega i ede ini eand ends oin ini yas ends oin ini y, hen heequilib iuma  heo igin isgloballyasymp o icallys able.
The e o e, ends oze oas he ime ends oin ini yandalso ens oze o.Mo eo e ,all ajec o iess a ingo  heslidingsu ace mus  eachi in ini e imeand henwill emainon hissu ace.So,
Sol ing hep e iousequa ion,i canbeconcluded ha  he ackinge o  con e ges oze oexponen ially.
Fo  heqcu en componen , hesameanalysiscanbedoneusing henex Lyapuno  unc ion,
3Ac i epowe  il e con ols uc u e
Fig.2showsinadeepe way hes uc u eo  heg id- ied h ee-phasein e e o Fig.1wo kingasac i epowe  il e wi h hePVmaximumpowe poin  ackingcha ac e is ic.Themainpa ame e s alueso  hesys ema e
showninTable1.
Table1Pa ame e so  hesys em.
Pa ame e Value
G id ol age, 380 V
G id equency, 2π50 ad/s

Dd
(
)
(29)
(30)

Vd
(
)  
Vd
(
)
Sd
(
)
Sd
(
)=0

Sd
(
)  
Sd
(
)=0
(31)

ed
(
)
(32)
Fig.2Con ols uc u eo  he h ee-phaseg id- iedin e e o Fig.1.

g

ωg
=
ωe
G id il e  esis ance, 0.2 Ω
G id il e induc ance, 2mH
In e e capaci ance, 1500μF(±20%)
In e e modula ion equency, 20 kHz
PVopenci cui  ol age,
VOC
(25°C,1000W/m2)670 V
PVso ci cui cu en ,
ISC
(25°C,1000W/m2)4.9A
PVmaximumpowe poin  ol age,
VMP
(25°C,1000W/m2)595 V
PVmaximumpowe poin cu en ,
IMP
(25°C,1000W/m2)4.4A
PVmaximumpowe ,
PMP
(25°C,1000W/m2)2618 W
Loadinduc ance, 1mH
Load esis ance, 98 Ω
Loadcapaci ance, 2000μF(±20%)
Asynch onous e e ence amephase-lockedloop(SRF-PLL)isused o ex ac iono g id ol agephase, equency,andampli udeasshowninFig.1.ThePLLPIcon olle gainsa eadjus edasindica edin[32]wi hana u al
equencyo 628  ad/sandadamping ac o o 1[33].
Theimplemen edmaximumpowe poin  ackingalgo i hmis hepe u ba ion-obse a ion(P&O).Thepowe  o  heP&Oiscalcula edusingEq.(4)wi h hemeasu edg id ol ageand hein e e cu en ,a oiding heuseo
aDCcu en senso in heou pu o  hePVa ay.Theg idsupplies heloada e agepowe and heins an aneousha monicpowe shouldbesuppliedby heac i epowe  il e .The e o e, hea e agepowe shouldbe il e edusinga
lowpass il e .Takingin oaccoun  ha  heg id equencyis50 Hz(and hepowe ha monicswillbee enhighe ),agoodcu o  equency o  helowpass il e couldbe1/5o  heg id equency.Also heexpe imen al esul sshown
ha  heusedcu o  equencyisadequa e.The ol agepe u ba ionisas epo 2 Vandis ealizede e y300 ms.Thepa ame e so  heSMCin e e DC ol agecon olle a eadjus ed akingin oaccoun Sec ion2.1andi sou pu ,
,is henecessa ycu en componen  omake hePVwo ka  hemaximumpowe poin .Howe e , heMPPTalgo i hmse s heminimum ol agele el, husope a ingou side heMPPpoin ,ensu inga ol agele elon he
DCbuswi hou losing egula ionand huskeeping heac i e il e cha ac e is icwo kingp ope ly.
Theac i epowe  il e  e e enceisob ainedasexplainedinSec ion2.2andwi h hecalcula ed and cu en  e e ences, hein e e  o al e e enceisde e minedasshownin he igu eandindica edinEqs.(16)
and(17).
The o aldandqcu en componen sa e egula edusing woSMC,gene a ing hein e e dandq ol age e e ences.Bo hSMCsha ebeenadjus edwi h hec i e iaexplainedinSec ion2.3.
TheemployedPVisanemula eda aywi h hecha ac e is icsshowninTable1.The ol agepowe cha ac e is iccu eso  hea ay o  wo empe a u esand h eele elso i adiancea eshowninFig.3.Theshadeda ea
shows hepossibleope a ingzone o  hein e e .Tha is, hezonewhe e hein e e inpu  ol ageishighe  han heg idpeak ol ageplus he ol aged opin heinduc ance.

Rg

Lg

C

PWM

LL

RL

CL

   
The eisasligh deg ada iono  heg idcu en ,THDis9%,bu  he egula ionisgoodenoughdespi e henoisele el,whichshows he obus beha io o  heslidemodecon olle .Theinjec edpowe  o heg idwhen heDC
ol ageis600 Vis2200 W.
Thecon ols uc u ewi h hePIcon olle sisshowninFig.16whe e heSMCcon olle sha ebeen eplaced o PIcon olle s.ThePI ol agecon olle hasbeen unedexpe imen allyob ainingKp = 0.2andKi = 10. The
cu en PIcon olle sha ebeenadjus edusingZiegle -Nichols echnique, hus heKp = 0.5and heKi = 140.Howe e ,due o henoise hePIgainsha e obe educedino de  oensu e hes abili y.The esul ob ainedcanbeseen
inFig.17,whe einc eases hese ling imeand hecu en dis o ionge swo se,THDisnow11%.Inc easing hebandwid hon hePI egula o sb ings hesys emclose  oins abili y.
Fig.15APFDC ol ageandcu en wi hnoisyin heDC ol ageo ±20 V o150 Hz.Vol ageSMCcon olle .
Fig.16Con ols uc u ewi h hePIcon olle sins eado  heSMCcon olle s.

Table2shows hesumma yo  hepe o mancecha ac e is icso cu en and ol agecon olle sbe weenSMCandPIcon olle squan i a i ely.Basedon heda a abula edinTable2,SMChas he as es se ling imeand he
lowes o e shoo inboo hcon olle s.Acco ding o hes eadys a ee o ,bo ho  hecon olle shadshown e yexcellencepe o mancebygi ingze oe o .In e mo  he ise ime, heSMCand hePIcon olle sha easimila
beha iou .
Table2Cu en and ol ageSMCandPIcompa ison.
Pa ame e SMC(cu en ) PI(cu en ) SMC( ol age) PI( ol age)
Rise ime 1.1 ms 1.2 ms 46 ms 48 ms
S eadys a ee o 0 0 0 0
Se ling ime 2.1 ms 2.4 ms 152 ms 162 ms
Maximumo e shoo 3% 6% 1% 3%
Ino de  oanalyze he obus nessagains LgandRg,somesimula ionsa eca iedou .Fig.18shows hebeha io  o  wononlinea load alueswhen he eal alueo Lgisused,2mH.Up o0.4 s he esis i eloadRLis196
Ohmand om ha momen  heloadbecomesRL = 98Ω.Thenonlinea loadcu en , heac i e il e cu en , heg idcu en and hedcomponen  e e enceand ealcu en a ep esen ed.Asexpec ed, heg idcu en issinusoidal
and he egula iono  hedcu en componen wi h heSMCis e ygood.Howe e ,nomen ionablechangesin hesignalsa ep oducedin hesimula ionswhen a ia ionsonRgo ±50%a e es ed.
When he ea e a ia ionsin he alueo Lg, he ea ealso a ia ionsin hepe o manceo  hesys em.The e o e, a ia ionsinLgby±40%and±25%ha ebeensimula ed.Thus,Fig.19shows hecu en ob ainedin heg id
o di e en  alueso Lg.The u he away om henominal alue hemo edeg ada ion hecu en su e s,howe e  hesys em emainss ableinspi eo  hese a ia ionsshowing he obus nessle elo  heSMCused.
Fig.17APFDC ol ageandcu en wi hnoisein heDC ol ageo ±20 V o150 Hz.Vol agePIcon olle .
Fig.18Dynamicands a icbeha iou  o aloads epin  = 0.4 swhen he eisno misma chinLgandRg.
Thespikesobse edin heg idcu en a edue o heinc eased alueo Lgand helow alueo  heDC ol ageasindica edinEq.(33).
5.4O e alle iciency
TwoSVPWM echniquesa e es ed omeasu e hesys eme iciencyandcu en THD.Bo hha e hePVpanelwo king o hesamepowe ,2600 W.When he7segmen sSVPWMis heselec edmodula ion, heob ainedTHDis
4.7%and hemeasu ede iciencyis86%asi isshowninFig.20.Howe e , he5segmen sSVPWMimp o essligh ly hee iciencydue olowe swi chinglosses,87.2%bu THDge swo se8.2%.Wi h he7segmen sSVPWM he
ob ainedcu en THDislowe  han he aluelimi edby heIEEE-519(cu en THD < 5%)(IEEES d519–2014).
Thee iciencyo  hepowe in e e canbeimp o edby educing heswi ching equency.Howe e , hiswould esul inaninc easein hecu en  ipple,wo sening hecu en THD.
6Conclusions
In hispape , heac i epowe  il e  ea u eisadded o hein e e usedin hePVMPPcon ol.Thedesignedcon olloops, o  heDCbus ol ageaswellas o  hecu en a emadewi hslidingmodecon olle s.These
con olle swe e i s adjus edbymeanso se e alsimula ionsand inally e ouchedin he ealsys em.Thes abili yo  heSMCsisdemons a edusing hewell-knownLyapuno  heo y.TheusedMPPTme hodis hepe u band
obse eme hodwi h hemodi ica iono  hepowe measu emen a  heACsideo  hein e e ino de  oa oid heuseo  heDCsidecu en senso .Theac i epowe  il e cha ac e is ichasbeenimplemen edusing hePQ heo y.
Thegoods a icanddynamicbeha io o  hemaximumpowe poin aswellas hecha ac e is ico  heac i e il e ha ebeendemons a edexpe imen ally.The obus nesso  hesys emagains dis u bancessuchasnoisein
hemeasu emen sandg idinduc anceisalsosa is ac o ily es ed.Inaddi ion, hesys eme iciencyandcu en quali ya eshown o  wo ypeso modula ion, hese en-segmen and i e-segmen  ec o modula ion.Fo all hese
easonsi canbeconcluded ha  hep esen edsys emp o idesane icien maximumpowe  ackingandagoodpowe  il e cha ac e is icwi h hep esen edslidingmodecon olle s.
Acknowledgmen
Fig.19Beha iou  o aloads epin  = 0.4 swhen he eismisma chinLg.Lgchanges om+40% o−40%.
Fig.20SVPWMdu ycycle,g idcu en ,PV ol ageandcu en andg idcu en FFT o SVPWMo 7and5segmen s.
Theau ho sa e e yg a e ul o heUPV/EHUbyi ssuppo  h ough hep ojec PPGA18/04, o heBasqueGo e nmen byi ssuppo  h ough hep ojec ETORTEKKK-2017/00033and o heGipuzkoako
Fo uAldundiabyi ssuppo  h ough hep ojec E o kizunaE aikiz2019.
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Que iesandAnswe s
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con ac s. enki eswa an@else ie .comimmedia elyp io  o e u ningyou co ec ions.
Answe :Yes
Que y:Theau ho namesha ebeen aggedasgi ennamesandsu names(su namesa ehighligh edin ealcolo ).Pleasecon i mi  heyha ebeeniden i iedco ec ly.
Answe :Yes
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Highligh s
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•TheSlidingModeCon olle sshowedgooddynamicbeha iou anddis u bance ejec ion.
•PVwasdi ec lyconnec ed oa h ee-phaseg id iedin e e wi h heac i epowe  il e cha ac e is icin eg a ed.
•Expe imen al alida iono  heSMCcon olle sshowed heexpec ed obus ness.