ContentslistsavailableatScienceDirect
Electric
Power
Systems
Research
jou rn a l h om ep a g e :w w w . e l s e v i e r . c o m / l oc a t e / e p s r
A
sliding-mode
voltage
regulator
for
salient
pole
synchronous
generator
R.L.A.
Ribeiro
∗,
C.M.S.
Neto,
F.B.
Costa,
T.O.A.
Rocha,
R.L.
Barreto
FederalUniversityofRioGrandedoNorte,CampusUnivesitárioLagoaNova,NatalRN,CEP:59.078-970,Brazila
r
t
i
c
l
e
i
n
f
o
Articlehistory: Received7May2015
Receivedinrevisedform25July2015 Accepted29July2015
Availableonline28August2015 Keywords:
Automaticvoltageregulator Powersystemstabilizer Synchronousgenerator Sliding-modecontrol
a
b
s
t
r
a
c
t
Thispaperpresentsasliding-modecontrolstrategyforvoltageregulationofsynchronousgenerators
connectedtothepowergridthatcombinesslidingmodeandlinearcontrollaws.Thishybridcontrol
schemecontributespreventingsysteminstability,bysuppressingthelow-frequencyoscillationsarising
frompowergridfaultdisturbances.Inaddition,thisstrategydoesnotrequiretheestimationofsystem
parameters.Thiscontrolstrategywasdesignedtobeintroducedeasilyinaconventionalautomatic
volt-ageregulator(AVR)algorithm.Experimentalresultsobtainedwithalaboratorytestset-up,consistingof
thesynchronousgeneratorconnectedtothegridandsubjectedtoseverepowertransients,wasemployed
tovalidatetheproposedcontrolapproach.Comparisonswithaconventionalaswellaswithtwohybrid
controlschemesdemonstratetheadvantagesoftheproposedcontrolstrategy.
©2015ElsevierB.V.Allrightsreserved.
1. Introduction
Despitethenumerousworksproposedinthepastdecade,AVR appliedtosynchronousgeneratorsisstillconsideredan interest-ingproblem.ThemainobjectiveofanAVRsystemistoregulate thegeneratorterminalvoltage,whichimprovesthetransient per-formanceand ensuresthestability of thepowersystematany occurrenceof externaldisturbances orparametricvariation [1]. Typically,proportional-integral-derivative(PID)controllerswith fixedor variableparameters are usedin theAVR [2]. Different approachessuchaspredictivecontrolschemes[3,4]orLyapunov directmethod[5]canbeused.Ingeneral,themodelingadopted inthesecontrolschemesincludesthelinearizedmodelofa syn-chronousgeneratorconnectedtoapowergrid.Predictiveschemes, withfixedparameters,presentagoodtransientstabilityand inher-entrobustnesstotheparametervariations[6].Recently,control schemesthatdonotdependonthesystemmodelsuchasfuzzy logiccontrol[7,8]orneuralnetworks[9–11]havebeenproposed. However,thesecontrollersdonotensurethesystemclosed-loop stability.Itispossibletodesignacontrolschemethatensures sys-temstabilityandgoodtransientperformancebyusingasystem modelingcombinedwithfeedbackcontroltheory,likelinear opti-malcontrol [12],H∞ feedbackcontrol[13]or nonlinearcontrol strategy[14].
∗ Correspondingauthor.Tel.:+558432153731. E-mailaddress:rlucio@ct.ufrn.br(R.L.A.Ribeiro).
AdaptivecontrolstrategieshavealsobeenproposedforAVRto ensuresystemstabilityandtosuppressthelow-frequency oscilla-tions.Intheself-tuningschemes,anadaptiveexternalloopisadded totheconventionalAVR,whichsystemparametersareestimated from the excitation command and generator voltage terminal
[12,15–17].Althoughthesetechniquesdifferontheirdesign pro-cedure,allofthemuseblack-boxdescriptioninthediscrete-time domainandhavecompleximplementations[18].Twosimplified approachesofadaptivestrategieshavebeenintroducedto over-comethis:AVRwithconstrainedleast-squaresalgorithm(CRLS)
[19]andasimpleadaptivecontrol(SAC)basedonthequadratic performanceindex.
Duetothelowsensitivitytoparametricvariationsand exter-naldisturbances,thesliding-modecontrol(SMC)[20,21]canbe alsoconsidered.Thesecontrollershavebeenproposedforsingle machineconnectedtoapowergrid[22]orformultimachine sys-tems[23].ThedrawbackoftheSMCreferstothechatteringdue totheunmodeledexciter dynamics[24].Anapproach basedon high-orderslidingmode(HOSM)algorithms[25] hasbeen pro-posedforreducingtheseeffects.Although,thisalgorithmstillhas asignificantcomplexityofimplementation.Hybridstructuresthat combineSMCandadaptivecontrolhavegainedconsiderable inter-est[26],becausetheyallytherobustnessofSMCtoparametric uncertaintiesandthegrowingofstabilitymarginduetothe adap-tivecontrol.Thisstructurehasbeenusedwithactivepowerfilter applications,implemented withtheassociation ofthe adaptive poleplacementcontrol(VS-APPC)[26]ormodelreferencescheme (VS-MRAC)[27].However,thesecontrolstructuresstillpresenta
http://dx.doi.org/10.1016/j.epsr.2015.07.016 0378-7796/©2015ElsevierB.V.Allrightsreserved.
Chopper
1
Chopper 2
r
s
l
s
r
s
l
s
r
l
l
l
v
t
123i
g
123i
fdi
a
e
fde
a
e
8
k
2 CPr
sc
k
1Fault Emulator
Synchronous
Generator
DC Motor
nPower Grid
Usb
Optical
DSP
Sensors
Fig.1.Blockdiagramoftheexperimentaltestset-up.
considerablecomplexityofimplementation. In ordertoachieve robustness,hybridstrategiesthatcombineSMCand proportional-integral(PI)controllershavealsobeenintroduced[28].Inthese structures,thediscontinuouscontrolisapproximatedbyan adap-tivePIcontrolstructure,employedforminimizingthechattering oftheSMC.Themaindrawbackofthesestrategiesreferstothe persistenceofthechattering.However,thesestrategieshavethe advantageofnotrequiringthesystemparameterestimation.
Inthesamedirection,thispaperproposesanAVRforasalient polesynchronousgeneratorbasedonahybridcontrolstructure, composedoftheintegrationofSMCapproachand PIcontroller (SM-PI).Differentlyfromthestrategiespresented previously,in theproposedscheme,theSMCdeterminesthePIcontrollergains fromasuitablesliding-surface.Thisslidingsurfaceisobtainedfrom theerrorofgeneratorterminalvoltage.Thechatteringduetothe SMCisminimizedbyPIcontroller bandwidth.Besidesthe sim-plicityofimplementation,theSM-PIexhibitsexcellentrobustness toparametricuncertaintiesandimmunitytounmodeled distur-bances.Experimentalresults,obtainedfromlaboratorytestsetup consistingofthesynchronousgeneratorconnectedtothemains andsubjectedtoseveretransientsinthepowersystem,validate theproposedcontrolapproach.
2. Systemdescriptionandmodeling
Fig. 1 presents the block diagram of the laboratory-based powersystem.It comprises an electromechanicalcomposedby asynchronousgeneratorpulledbyaDCmotor.Thisgeneratoris connectedtoapowergridemulatorthatiscomposedoftwo trans-missionlinesconnectedtothepointofcommoncoupling(PCC), whichisconnectedtoathree-phaseRLload,equippedwith con-trolledby-passswitchesandexternalresistorstoemulatefaults. BothDCmotorarmatureandsynchronousgeneratorfieldare feed-ingthroughH-bridgebuckconverter.Theproposedcontrolstrategy aswellasPWMschemeswereimplementedina floating-point digitalsignalprocessor(DSP).
3. Voltagegeneratorcontrolsystem
Thestandardsalientpolesynchronousgeneratormodelis rep-resentedby a stator composedof three stator windings, and a rotorconsistedofonefieldandtwodamperwindings.According to[29],thesmallsignalmodelformachineterminalvoltage devia-tions
v
t(s)canberelatedtothechangesofgeneratorfieldvoltageefd(s)andtheloadangleı(s)asfollows:
v
t(s)=Gvt(s)efd(s)+Gı(s)ı(s) (1)K
3K
61+ K
s
3 d0'(
)
1+
s
d0'(
a
')
1+
s
d0'(
')
a
SM-PI
e
fdG (s)
v
tv
t*+
+
+
-v
t’v
tSynchronous
Generator
with the Grid
ε
Fig.2. Blockdiagramoftheautomaticvoltageregulatorsystem.
with Gvt(s)= K3K6a(1+sd0 ) (1+sad0 )(1+sK3d0) (2) and Gı(s)=K5− K4d(1+scd0 ) (1+sad0 )(1+sK3d0 )+ K4qK6d (1+sbq0 ) (3)
ThetermsGvt(s)andGı(s)representedbyEq.(1)presentsa
sec-ondorderdynamicbehaviordeterminedbypoless1=−1/K3d0
ands2=−1/ad0 .Italsohasathirdorderdynamicbehavior
deter-mined by poles s1=−1/K3d0, s2=−1/ad0 and s3=−1/bq0 ,
respectively.Theblockdiagramoftheproposedcontrolsystemis presentedinFig.2.TheproposedSM-PIcontrolsthegenerator ter-minalvoltage,whichdeterminesthefieldvoltageefd(s)thatis synthesizedbyaPWMbuckconverter,omittedintheblock dia-gramofFig.2.Theeffectontheterminalvoltageduetotheload angledeviationGı(s)ı(s)isconsideredasadisturbancetobe
compensatedbytheSM-PIcontroller. 3.1. SM-PIcontroller
TheproposedcontrolschemeisarobustPIcontrollerinwhich itscontrollergainsarecalculatedbySMCstrategy.Theyare deter-minedbyswitchinglawsaccordingtoaslidingsurfaceobtained fromthecontrollooperroranditsderivative.Thecontroller sta-bility is verifiedby using theLyapunov stability theory. In the generatordynamicmodelofEq.(2),thezeroats=−1/d0
approx-imately cancels the pole at s=−1/ad0 , which adresses to a first-ordersystemgivenby[29]:
Gvt(s) ∼=
v
t(s) efd(s)=bv
where
v
t(s)=v
t(s)+v
tı(s), av=1/(K3d0 ), bv=aK6/(d0 )and
v
tı(s)=Gı(s)ı.ThetransferfunctionoftheproposedSM-PIcontrollerisgivenby: Gc(s)=
˜kps+ ˜ki
s (5)
where ˜kpand ˜kiarethecontrollergains.Theclosedloopdynamics
ofthegeneratorterminalvoltageisgivenby:
v
t(s)= Gc(s)Gvt(s) 1+Gc(s)Gvt(s)v
∗t(s)+ Gı(s) 1+Gc(s)Gvt(s) ı(s) (6)andtheerrorofgeneratorterminalvoltagecontrolloopis:
ε(s)=1 1
+Gc(s)Gvt(s)
v
∗t(s)− Gı(s)1+Gc(s)Gvt(s)
ı(s) (7)
AsGc(s)istype-oneandGvt(s)andGı(s)aretype-zerothetwo
parcelsofsystemdescribebyEq.(7)aretype-one,whichensures zerosteady-stateerrorforsmallstepvoltagereferenceandsmall steploadangledisturbance,whichisreasonableforthis applica-tion,andthestabilityofthegeneratorterminalvoltageisassured. Duringthetransientstate,thegain ˜kpswitchesbetweenkavp −
2k−p andkavp +2kp+.Uponreachingthesteadystate, ˜kpiskept
con-stantatkav
p .Asimilarstatementappliesto ˜ki.
Definingaslidingsurfacedescribedby
=cvε+ ˙ε (8)
whereε=
v
∗t−v
t, ˙ε isitsderivative,and cisapositivecon-stant.Thederivative ˙εiscomputedbyusingtheEulerapproach.To provethestabilityoftheproposedSM-PIattheorigin(=0),let theLyapunovcandidatebe:
V (ε)=12ε2 (9)
anditstimederivativethatcanbeexpressedas:
˙V(ε)=ε ˙ε=ε(−cvε)=−cvε2<0 (10)
Sincetheconstantcvispositive,theproposedcontrolis
asymp-toticallystable.Basedonthesestabilityrestrictions,thecontroller gainscanbedeterminedbyusingthefollowingswitchinglaws ˜kp=[(1+sgn())k+p −(1−sgn())k−p]+kavp (11)
˜ki=[(1+sgn())k+i −(1−sgn())k−i]+k av
i (12)
wherek+p,k−p,ki+,ki−,kpavandkavi arepositiveconstantsdetermined
asafunctionofthedesiredsystemperformance(thesegainscan beobtainedbyusingastandardPIdesignmethodologye.g.root locus).Themathematicalfunctionsgn()returnsthevalues1for >0or−1for<0.
3.2. DesigncriteriaoftheSM-PIcontroller
Thedesigncriteriaemployedinthisworkisbasedinthepole assignment,based onthesolutionoftheDiophantineequation. Thus,thetransferfunctionsofthesynchronousgenerator(Gvt(s))
andthevoltageregulatorSM-PI(Gc(s))canbewrittenintermsof
thefollowingpolynomials Gvt(s)= Z(s) R(s), Gc(s)= P(s) L(s), (13) where Z(s)=aK6/(d0 ), R(s)=s+1/(K3d0 ), P(s)= ˜kps+ ˜ki and
L(s)=s.Theclosed-looptransferfunctionofgeneratorterminal volt-agecanthenbegivenby
Tet(s)=
Z(s)P(s)
Z(s)P(s)+R(s)L(s) (14)
whosecharacteristicequationis
Z(s)P(s)+R(s)L(s)=0 (15)
ThedesignobjectiveistochoosesuitablepolynomialsP(s)andL(s) yielding
Z(s)P(s)+R(s)L(s)=A∗(s) (16)
where A*(s) is a desired monic Hurwitz polynomial and the
superscript ={fs(fast),av(average), sl(slow)} refersto the per-formancecriteriaemployedfordeterminingdesiredpolynomials. OncedefinedthesuitablepolynomialsA*(s),thevoltageregulator
parameterscanbeobtainedfromthesolutionoftheDiophantine equation.The polynomialsAsl*(s) and Afs*(s) shouldbe sized so
thatthecontrolsystemcompensatestheloadanglevariation dis-turbancequickly.Thedesigncriterionfirstlydeterminestheslow polynomial(Asl*(s))fromthenominalparametersofthecontrol
plant(Eq.(4)).Thus,consideringtheperformanceindexesof maxi-mumovershootanddampingcoefficient,thefollowingpolynomial canbeobtained Asl∗(s)=s2+2asl m+2(aslm) 2 (17) whereasl m=4/tslss(2%)andt sl ss(2%)=t nom
ss(2%)isthenominalsettlingtime
ofthesteady-state system.To determinetheamplitudes ofthe switching laws given by (11)and (12), two other polynomials (Aav*(s)andAfs*(s))arealsodefined,correspondingtothereduction
of42.85%and60%ofthenominalsteady-statetime(tss(2%)sl ).Taking intoaccountthethreepolynomialsandsolvingtheDiophantine equationsforeachcase,thefollowinggainscanbecalculated: kp= 2am−av bv , k i = 2(am)2 bv , (18) wherekp andk
i,with={fs,av,sl}refertothecontrollergains
obtainedfromthepolynomialsA*(s).Inaddition,thecoefficients
k+p,k−p,ki+,andk−i aredeterminedasfollows k+p =k fs p −kavp 2 , k + i = kfsi −kav i 2 (19) k−p =k av p −kslp 2 , k−i = kav i −ksli 2 (20)
ThevalueofthisconstantdetermineshowtheSM-PIactsduring thetransient.
4. ExperimentalevaluationoftheSM-PIvoltageregulator
The proposed SM-PI voltage regulator has been evaluated experimentallybyusingalaboratoryset-upwhosestructurewas presentedinFig.1,whichconsistsof5kVAthree-phasesalientpole synchronousgeneratorpulledbya7kWDCmotorandanelectrical energysubstationof45kVA–220/127V(rms),aspowergrid.The synchronousgeneratorisconnectedtoathree-phasepowergrid emulatorcomposedoftwotransmissionlinesegments(rs=0.1
andls=2mH).InthemiddleofthislinePCC,thereisabalanced
three-phaseRLload,star-connected(rl=20andll=60mH).Their
loadphasescanbeconnectedtoexternalresistorsbycontrolled switchesforemulatingsystemshort-circuitfaultsorsteady-state workingpointchanges.ThetorqueoftheDCmotorisregulated toensuretheoperationof thegeneration insynchronism with thepowergrid.Thefieldwindingofthesynchronousmachineis fedviaaH-BridgebuckconvertercommandedbyaPWM strat-egywhose referencevoltage isgenerated by theSM-PIvoltage regulator.Bothcontrolstrategiesforregulatingthetorqueofthe DCmotorandgeneratorterminalvoltagewereimplementedona DSP(TMS320F28335)platform.TheA/DconvertersoftheDSPcard wereconnectedtoameasurementunit,composedofhall-effect
Table1
Synchronousgeneratorparameters.
S=5kVA e∞=220/127V rf=1.2
lf=79mH lmd=117.62mH lmq=69.4mH
xd=50 xq=31.6 xd=16.5
fs=60Hz P=6poles H=0.09kgm2
rsc=5 a=1 xs=1.5
voltageandcurrentsensors.Thesignalstakenfromthesesensors
passthroughlow-passfilterswithacutofffrequencyoffc=2.5kHz.
Thecontrolalgorithmwasexecutedwithasamplingtimeof100
s.Theparametersofthesynchronousgeneratoremployedinthe
laboratoryprototypeareprovidedinTable1.
Theperformanceoftheproposedcontrolsystemwasassessed through experimental tests, according to the following steps: performance undervoltagereference variation, systemstability undershort-circuitfault,andvariationofthesteady-stateworking point.
4.1. Performanceundervoltagereferencevariation
Theperformanceofthevoltageregulator,wasaccomplishedby anexperimentaltestinwhichthereferencevoltageisincreased andreducedbystepsprofiles.Fig.3showstheexperimentalresults ofthegeneratorterminalvoltagewhenitsreferenceischanged. Inthisgraph,thereferencevoltageofthegeneratorisinitiallyin steady-state(
v
t=380V)andint=28.3sitisincreasedbythestepof
v
t=15V.andreducedint=31.25s,bynegativevoltagestepof
v
t=15V.Inbothstepchanges,thegeneratorterminalvoltagetakesapproximatelyt=0.5s,withoutovershoot,forreachingits reference,whichdemonstratesgoodperformanceunderreference voltagevariation.
4.2. Systemstabilityundershort-circuitfault
TheperformanceoftheSM-PIcontrollertoensurethesystem stabilityandtomaintainthesynchronizationofthegenerator dur-ingtheoccurrenceofseveredisturbancesinthepowersystemwas experimentallyevaluated.Inthisexperiment,asevereelectricload variationwasimposedonthesynchronousgeneratorbymeansof theshort-circuittransientcarriedonthepowergridemulator.At thePCC,resistorsof5wereinsertedinparallelwiththe three-phaseloadthroughcontrolledswitchesforincreasingthegenerator phasecurrent byaboutfivetimes.Theperformance ofthe pro-posedSM-PIwasalsoevaluatedincomparisonwiththreedifferent controlschemes:standardPID[2]andhybridstrategiesVS-APPC
[26]andVS-MRAC[27].Figs.4-8showtheexperimentalresults
28 28.5 29 29.5 30 30.5 31 31.5 32 32.5 33
Time (s)
375
V
o
ltage (
V)
380
385
390
395
400
v t
t( )
SM-PI
Reference
Fig.3. Experimentalresultoftheterminalvoltageofthegeneratorregulatedfrom aSM-PIcontrollerduringastepinthevoltagereference.
28 Rms current (A) 6 8 10 12 14 16 2 4 0 ig1( )t t1 t2
Fault clearing time Fault inception time
t1 t2
28.5 29 29.5 30 30.5
Time (s)
Fig.4.ExperimentalresultofthegeneratorphaseRMScurrent1.
28 28.5 29 29.5 30 30.5 31 31.5
V
o
ltage (V
)
0
10
20
30
40
50
60
70
80
Δe
t
( )
fdTime (s)
Fig.5. ExperimentalresultoftheSM-PIoutputduringtheshort-circuittest.
regardingtheshort-circuittest.Fig.4presentsthermsvalueofthe generatorphasecurrentig1duringtheshort-circuitonthepower
grid.Inthistest,att=28.3s,themachinephasecurrentisincreased from2Ato14A,withoutovershoot,duringt=0.5s.
Fig.5presentstheoutputcontrolsignaloftheSM-PIrequiredto obtainthedynamicperformanceofthesystemtransientcondition. Thedv/dtimposedbytheshort-circuittestdoesnotchangethe magnitudeofthechatteringinthecontrolsignalgeneratedbythe proposedcontrolscheme.Moreover,thischatteringeffectdoesnot increasetheoscillationofthegeneratorterminalvoltagebecause itissmoothbythePWMdc–dcbuckconverter.
Fig.6presentsthreedifferenttestsforthesynchronous gener-atorspeedωrundershort-circuit.Ineachexperiment,theSM-PI
iscomparedwiththreedifferentcontrolstrategiesforevaluating itsperformance. Inthesteady-stateoperation, thespeedof the synchronousgeneratorisωr=600rpm.Thefaultinceptiontimeis
t=28.3s.Fig.6ashowstheexperimentalresultsofthegenerator speedωrwhentheterminalvoltageisregulatedbytheSM-PIor
astandardPID.Inthistest,thestabilizationtimewhentheSM-PI isemployedistss=0.86s,boththeovershootandtheundershoot
areapproximately4.33%.WhenthePIDisused,thesettlingtimeis tss=0.96s,theovershootis3%andtheundershootis2%.Inthe
sec-ondtest,theSM-PIiscomparedwiththecontrolschemeVS-APPC aspresentedinFig.6b.Sincethetestsareperformedunderthe sameconditions,thestabilizationtimeofSM-PIremainsthesame. However,whentheVS-APPCisused,thesettlingtimebecomes tss=1.88s,theovershootis3.33%andtheundershootis3%.Finally, Fig.6cpresentsthesametestwiththeVS-MRAC.Inthiscase,the
r
t
rt
28 28.5 29 29.5 30 30.5 31 31.5
Time (s)
560
Speed
(R
P
M
)
570
580
590
600
610
620
630
640
28 28.5 29 29.5 30 30.5 31 31.5
Time (s)
560
Speed
(R
P
M
)
570
580
590
600
610
620
630
640
rSM-PI
PID
(a)
(b)
SM-PI
VS-APPC
SM-PI
VS-MRAC
28 28.5 29 29.5 30 30.5 31 31.5
Time (s)
560
Speed
(R
P
M
)
570
580
590
600
610
620
630
640
(c)
t
Fig.6.Experimentalresultofthegeneratorspeedduringtheshort-circuittest:(a) PIDandSM-PI;(b)VS-APPCandSM-PI;(c)VS-MRACandSM-PI.
stabilizationtimeistss=1.58s,theovershootis3.5%andthe
under-shootis3.33%.ThesetestsdemonstratethattheSM-PIprovidedthe bestperformance.
Fig.7showstheexperimentalresultsoftheAVRimplemented by the SM-PI and also by the control strategies PID, VS-APPC andVS-MRACforthesameoperationalcondition.Thecontrollers presentedthefollowingstabilizationtimes,overshootsand under-shoots:PID(tss=1.99s,theovershootis2.89%andtheundershoot
is6.97%,SM-PI(tss=0.75s,theovershootis3.55%andthe
under-shootis4.6%)VS-APPC(tss=1.39s,theovershootis3.68%andthe
undershootis6.84%)andVS-MRAC(tss=1.64s,theovershootis
3.55%andtheundershootis4.47%).
Basedontheseresults,theSM-PIpresentedsuperior perfor-mance.Theseexperimentalresultsdemonstrate thatthevoltage oscillationspresented in thegenerator terminal voltage,in the steady-state,arealmostthesameforallcontrollers.
v
t( )
t
v
t( )
t
28 28.5 29 29.5 30 30.5 31 31.5
Time (s)
350
V
o
ltage (V)
355
360
365
370
375
380
385
390
395
400
28 28.5 29 29.5 30 30.5 31 31.5
Time (s)
350
V
oltage (V
)
355
360
365
370
375
380
385
390
395
400
v
tt( )
t
SM-PI
PID
(a)
(b)
28 28.5 29 29.5 30 30.5 31 31.5
Time (s)
350
V
oltage (V
)
355
360
365
370
375
380
385
390
395
400
(c)
SM-PI
VS-APPC
SM-PI
VS-MRAC
Fig.7. Experimentalresultofterminalvoltagevectorvtofthegeneratorregulated bycontrollers:(a)SM-PIandPID;(b)SM-PIandVS-APPC;(c)SM-PIandVS-MRAC duringtheshort-circuittest.
Fig.8presentstheexperimentalresultsoftheSM-PIaverage gainskp(Fig.7a)andki(Fig.7b)duringtheshort-circuittest.The
controller gainskp and ki obtainedfromEqs.(11)–(12),filtered
byafirstorderlow-passfilterwithacutofffrequencyof100Hz. Thevariationofthecontrollergainkpaddressestotheovershoots
of64.29%andundershootsof46.43%.Aswellas,changesof con-trollerthecontrollergainskiresultsinovershootsof78.95%and
undershootsof47.37%. Thesegraphsshowthatcontrollergains varyregularlytoobtaintherequiredsystemdynamicperformance forthetransientcondition,whichdemonstratestheiradaptivefor systemdynamicchanges.
TheparametersofthecontrollersPID,SM-PI,VS-APPC,and VS-MRACarepresentedinTable2.
28 28.5 29 29.5 30 30.5 31 31.
5
Time (s)
0.05
0.1
0.15
0.2
0.25
k
p( )
t
( )
a
28 28.5 29 29.5 30 30.5 31 31.
5
Time (s)
2
4
6
8
10
12
14
16
18
k
i( )
t
( )
b
Fig.8.ExperimentalresultoftheSM-PIcontrollergainaveragevalue ¯kpand ¯ki duringtheoccurrenceofshort-circuitfault.
Table2
Controllersparameters.
PID VS-APPC VS-MRAC SM-PI
kc=0.054 ¯a=45 ¯ 1=0.02 kslp=0.028 ksli =2.679 i=0.012 ¯b =15 ¯ 2=0.15 kavp =0.128 kavi =8.202 d=0.009 bn=300 am=35 kfsp=0.229 kfsi =16.74
N=50 am=35 cv=30
4.3. PerformanceoftheproposedSM-PIundersteady-state
systemworkingpointvariation
TheperformanceoftheproposedSM-PIvoltageregulatorwas
evaluated when the generator wassubjected toa steady-state
workingpoint change.Inthis test, att=28.7s, thegeneratoris
subjectedtoaloadstepchangeofapproximately1.8kW.Thistest
demonstratesthatSM-PIcontrollerhasagoodperformancewhen
thesystemoperates underloadanglechangestransients.Fig.9
presentstheexperimentalresultsoftheactivepowergenerated bythemachineduringtheloadchangetest.Thegeneratoractive powerincreasedfrom2.3kWtoapproximately4.1kW, increment-ingthetorqueimposedbytheDCmotor.
Fig.10showstheexperimentalresultoftheterminalvoltage
v
t,regulatedbytheSM-PIcontroller,duringtheintervalinwhichthe steady-stateworkingpointwaschanged.Atthetimeinwhichthe loadvariationisintroduced,thereisadropinthegenerator termi-nalvoltage.However,theSM-PIchangeditsdynamicbehaviorfor convergingthegeneratorterminalvoltagetoitsreference,which takesapproximatelyt=0.2sandtheundershootis0.66%.
28 28.5 29 29.5 30 30.5 31 31.5
2
Active power (kW
)
2.5
3
3.5
4
4.5
P
0( )
t
Time (s)
Fig.9.Experimentalresultoftheactivepowerduringthesteady-sateoperating pointchange.
28 28.5 29 29.5 30 30.5 31 31.
5
v
t( )
t
350
V
oltage (V)
355
360
365
370
375
380
385
390
395
400
Time (s)
Fig.10.Experimentalresultoftheterminalvoltageofthegeneratorregulatedfrom aSM-PIcontrollerduringthesteady-sateoperatingpointchange.
5. Conclusion
Thispaperproposedasliding-modecontrolstrategyfor regulat-ingtheterminalvoltageofthesynchronousgeneratorconnected toapowergrid.Thiscontrolschemewasbasedonahybrid struc-turecomposedoftheintegrationoftheSMCandthestandardPI regulator,whichresultsintheSM-PIcontroller.Inthisapproach, thecontrollergainswereissuedfromaswitchinglawdefinedby theslidingsurfaceforthegeneratorterminalvoltage.
RegardingthecontrollerSM-PI,theproofofstability andthe designcriteriafordeterminingthecontrollergainswereprovided. The performance of proposed SM-PI wascompared withthree differentcontrollers(PID,VS-APPC,andVS-MRAC).TheSM-PI pre-sentedsuperiorperformanceforthesameoperationalcondition. Duetoitssimplicity,theSM-PIcanbeintroducedintothecontrol algorithmoftheconventionalAVRwithoutmuchcomputational effort.Theexperimentalresultsdemonstratedthatthecontrolleris efficientindampingthevoltageoscillationsofthegenerator termi-nalvoltageduetotheoccurrenceofseveretransientsinthepower system.
References
[1]F.P.Demello,C. Concordia,Conceptsofsynchronousmachinestability as affectedbyexcitationcontrol,IEEETrans.PowerApp.Syst.88(2011)316–329. [2]K.Kim,R.C.Schaefer,Understandingpower-systemstability,IEEETrans.Ind.
Appl.41(2005)485–492.
[3]M.Saidy,F.M.Hughes,Apredictiveintegratedvoltageregulatorandpower systemstabilizer,Elect.PowerEnergySyst.17(1995)101–111.
[4]M.S.Ghazizadeh,M.Saidy,F.M.Hughes,Predictiveanaloggeneratorexcitation controller,Proc.Inst.Elect.Eng.Gener.Transm.Distrib.144(1997)271–278. [5]J.Machowski,J.W.Bialek,S.Robak,J.R.Bumby,Excitationcontrolsystemfor
usewithsynchronousgenerators,Proc.Inst.Elect.Eng.Gener.Transm.Distrib. 145(1998)537–546.
[6]M.Saidy,Aunifiedapproachtovoltageregulatorpowersystemstabilizer designbasedonpredictivecontrolinanalogueform,Elect.PowerEnergySyst. 19(1997)103–109.
[7]T.Hiyama,Y.Ueki,H.Andou,Integratedfuzzylogicgeneratorcontrollerfor stabilityenhancement,IEEETrans.EnergyConvers.12(1997)400–406. [8]K.Vahid,S.Mohsen,S.Ghazanfar,Anintegratedapproachforoptimal
place-mentandtuningofpowersystemstabilizerinmulti-machinesystems,Int.J. Electr.PowerEnergySyst.63(2014)132–139.
[9]J.He,O.P.Malik,Anadaptivepowersystemstabilizerbasedonrecurrentneural networks,IEEETrans.EnergyConvers.12(1997)413–418.
[10]M.Farahani,Amulti-objectivepowersystemstabilizer,IEEETrans.PowerSyst. 28(2013)2700–2707.
[11]D.Molina,G.K.Venayagamoorthy,J.Liang,R.G.Harley,Intelligentlocalarea signalsbaseddampingofpowersystemoscillationsusingvirtualgenerators andapproximatedynamicprogramming,IEEETrans.SmartGrid4(2013) 498–508.
[12]O.P.Malik,G.S.Hope,Anadaptivegeneratorexcitationcontrollerbasedon linearoptimalcontrol,IEEETrans.EnergyConvers.4(1990)673–678. [13]Hardiansyah,S.Furuya,J.Irisawa,ArobustH∞powersystemstabilizerdesign
usingreduced-ordermodels,Int.J.Elect.PowerEnergySyst.28(2006)21–28. [14]A.Barakat,S.Tnani,G.Champenois,E.Mouni,Monovariableandmultivariable voltageregulatordesignforasynchronousgeneratormodeledwithfixedand variableloads,IEEETrans.EnergyConvers.26(2011)811–821.
[15]H.M.Hasanien,Designoptimizationofpidcontrollerinautomaticvoltage reg-ulatorsystemusingtaguchicombinedgeneticalgorithmmethod,IEEESyst.J. 7(2013)825–831.
[16]M.Farsi,K.J.Zachariah,J.W.Finch,Adaptivecontrolofturbogenerator excita-tion,Proc.Inst.Elect.Eng.Coll.Adapt.Controll.2(1996)1–5.
[17]D.Flynn,B.W.Hogg,E.Swidenbank,K.J.Zachariah,Aself-tuningautomatic voltageregulatordesignedforanindustrialenvironment,IEEETrans.Energy Convers.11(1996)429–434.
[18]G.Fusco,M.Russo,Adaptivevoltageregulatordesignforsynchronous genera-tor,IEEETrans.EnergyConvers.23(2008)946–956.
[19]S.Zhang,F.L.Luo,Animprovedsimpleadaptivecontrolappliedtopowersystem stabilizer,IEEETrans.PowerElectron.24(2009)369–375.
[20]V.I.Utkin,J.Guldner,J.Shi,SlidingModeControlinElectromechanicalSystem, TaylorandFrancis,1999.
[21]K.Abidi,A.Sabanovic,Sliding-modecontrolforhigh-precisionmotionof piezostage,IEEETrans.Ind.Electron.54(2007)629–637.
[22]A.G.Loukianov,J.M.Canedo,V.I.Utkin,J.Cabrera-Vazquez,Discontinuos con-trollerforpowersystem:sliding-modeblockcontrolapproach,IEEETrans.Ind. Electron.51(2004)340–353.
[23]H.Huerta,A.G.Loukianov,J.M.Canedo,Multimachinepowersystemcontrol: integral-smapproach,IEEETrans.Ind.Electron.56(2009)2229–2236. [24]I.Boiko,L.Fridman,A.Pisano,E.Usai,Analysisofchatteringinsystemswith
second-orderslidingmodes,IEEETrans.Autom.Control52(2007)2085–2102. [25]A.G.Loukianov,J.M.Canedo,L.M.Fridman,A.Soto-Cota,High-orderblock sliding-modecontrollerforasynchronousgeneratorwithexcitersystem,IEEE Trans.Ind.Electron.58(2011)337–347.
[26]R.L.A.Ribeiro,C.C.Azevedo,R.M.Souza,Arobustadaptivecontrolstrategyof activepowerfiltersforpower-factorcorrection,harmoniccompensation,and balancingofnonlinearloads,IEEETrans.PowerElectron.27(2012)718–730. [27]L.Hsu,Variablestructuremodel-referenceadaptivecontrol(VS-MRAC)using
onlyinputandoutputmeasurements:thegeneralcase,IEEETrans.Autom. Control35(1990)1238–1243.
[28]R.Shahnazi,H.M.Shanechi,N.Pariz,Positioncontrolofinductionanddc ser-vomotors:anoveladaptivefuzzypislidingmodecontrol,IEEETrans.Energy Convers.23(2008)138–147.
[29]M.Saidy,F.M.Hughes,Blockdiagramtransferfunctionmodelofa genera-torincludingdamperwindings,IEEProc.Gener.Transm.Distrib.141(1994) 599–608.