Research ArticleMaximum Power Point Tracking Based on Sliding Mode Control

Nimrod Vaacutezquez1 Yuz Azaf2 Ilse Cervantes2 Esliacute Vaacutezquez3 and Claudia Hernaacutendez1

1Electronics Engineering Department Technological Institute of Celaya 38010 Celaya GTO Mexico2Applied Mathematics Division Potosino Institute of Scientific and Technological Research 78216 San Luis Potosi SLP Mexico3Engineering Faculty Veracruz University 94294 Boca del Rio VER Mexico

Correspondence should be addressed to Nimrod Vazquez nvazquezieeeorg

Received 19 November 2014 Revised 27 January 2015 Accepted 27 January 2015

Academic Editor Emilio Bueno

Copyright copy 2015 Nimrod Vazquez et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Solar panels which have become a good choice are used to generate and supply electricity in commercial and residentialapplications This generated power starts with the solar cells which have a complex relationship between solar irradiationtemperature and output power For this reason a tracking of the maximum power point is required Traditionally this has beenmade by considering just current and voltage conditions at the photovoltaic panel however temperature also influences the processIn this paper the voltage current and temperature in the PV system are considered to be a part of a sliding surface for the proposedmaximum power point tracking this means a slidingmode controller is applied Obtained results gave a good dynamic response asa difference from traditional schemes which are only based on computational algorithms A traditional algorithm based onMPPTwas added in order to assure a low steady state error

1 Introduction

Energy availability in photovoltaic (PV) panel [1] dependson temperature and solar irradiation The PV panel suppliesmaximum power at a particular point of operation condi-tions which is known as the maximum power point (MPP)Unlike conventional power sources it is desirable to operatePV systems at this specific point the MPP [1ndash19] Howeverthe MPP locus varies over a wide range depending on PVarray temperature and irradiation intensity [1ndash3]

A tracking of the maximum power point (MPPT) guar-antees the operation of the PV generator at the MPPunder changing atmospheric conditionsAlthough theMPPTpower stage is typically implemented by means of a DC-DCconverter and a computational algorithm some other typesof converters and controllers may also be considered

The ldquoperturb and observerdquo (PampO) algorithm is proba-bly the most widely MPPT used The algorithm operationprinciple is simple the power is calculated from voltage andcurrent at the PV system and then the MPP is trackediteratively This algorithm implies a tradeoff of choosing theincrement value of the controlled parameter (such as dutycycle or reference voltage) and the period of time that this

adjustment is made On one hand small increment values ofthe controlled parameter decrease the error at steady statehowever the dynamic response is deteriorated On the otherhand the time interval between algorithm iterations not onlyshould be short to allow faster tracking but also must be longenough to assure a reliable signal measurement due to thesettling time of the PV current and voltage

TheMPPT should include a self-tuningmechanism [3 4]which rules the power stage and drives the system to operateat the MPPT Many MPPT algorithms have been proposed[5ndash19] some with faster positioning at the MPP and someothers more precisely A good dynamic behavior is usefulin situations with quickly changing irradiation conditions orload characteristics [8 9]

MPPT efficiency depends on the employed algorithmcomplexity however sophisticated algorithms show twomain drawbacks These not only may require expensivehardware but also may have a slow dynamic response Theperiod of time in algorithm iterations is always a special issueto evaluate when algorithms are considered

There exist papers in literature [10 11] based on slidingmode control these proposals include a traditional PampOalgorithmThe sliding surface is based on a voltage controller

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2015 Article ID 380684 8 pageshttpdxdoiorg1011552015380684

2 International Journal of Photoenergy

for generating the input current reference Since theseschemes employ PampOalgorithmwhich establish the trackingfor the MPP it becomes a disadvantage and therefore thetechnique still does a tradeoff engagement between precisionand dynamic response

In literature [12] a proposal for MPPT based in slidingmode controller is also foundwhere its scheme eliminates thesteady state variation and reduces the tradeoff engagementbetween precision and dynamic responseThe sliding surfaceis based on the classic equation of PampO algorithm andits implementation for this proposal implies derivative anddivision between variables which become a drawback sinceit requires expensive hardware

TheMPP locus may be approximated by a linear relation-ship [13 14] based on the characteristics from PV modulesTherefore a linear controller which reduces the tradeoffengagement between precision and dynamic response couldbe designed in order to operate the PV system near the MPPAn implementation for a system on this condition may offera much faster MPPT as it is suggested in literature [18]where this linear approximation just considers the voltageand current

All these previous schemes do not consider the tempera-ture in the tracking however the PV panel also depends onthis variable

In this paper a MPPT based on a linear approximation isproposedwhich considers not only the voltage and current onthe PV panel but also temperatureTheMPP locus is trackedat all times A linear approximation is used to establish thesliding surface for the sliding mode controller where a fasttracking response is obtained Additionally a slow controlloop based on traditional PampO method is considered toguarantee a low error at steady state

This proposal let us have a fast dynamic responsesimple implementation (no expensive hardware) and smallvariation at steady state The tradeoff between precision anddynamic response is reduced since the MPPT is performedby the sliding controller and not by the iterative algorithmThe best features of several different methods published inliterature have been gathered in this proposal

This work is organized as described next MPPT proposalis discussed in Section 2 which includes system modelingoperation and analysis Section 3 is addressed for simulationand experimental results And some final conclusions aregiven at the end

2 Proposed Maximum Power Point Tracking

Two control loops have been implemented for the MPPTa fast and a slow loop Figure 1 shows the block diagramIt is easily seen how voltage current and temperature areconsidered simultaneously these three variables are used intothe sliding surface which are provided for the fast loop andthe first two variables are employed for the slow loop in orderto guarantee a low error at steady state

The fast loop allows us to reach very closely the MPPvicinity with a good dynamic response while the slowloop allows us to decrease the steady state error by using

Powerstage Load

MPPT

Controller

Slowloop

Fastloop

sref

T

u

Figure 1 Block diagram of the proposed dual loop MPPT

a small step increment in the MPPT algorithm This tech-nique becomes a good tracking method Since trackingmostly is carried out by the fast loop the slow loop requiresfew iterations The two control loops are explained next

21 Fast Loop A sliding mode controller is considered forthis loop where the sliding surface is established by the PVpanel characteristics this may easily be obtained not onlyexperimentally but also by using a model

A switching surface is established by a linear combinationof voltage current and temperature in the PV generator(PVG) which contain the different MPP (or at least closeto the vicinity) at different operating conditions The slidingmode controller leads the system to the sliding surface and itis maintained in it so that the controller will reach the MPPvicinity

A typical graph of a PV panel is shown in Figure 2(a)where it is shown solar irradiation changes at a fixed tem-perature of 15∘C It is easily seen that the MPP in each graphis located at the knee of the curve and it suffers changesdepending on the radiation These points may almost beconnected by a line actually a linear approximation may bedone by using least squares

Figure 2(b) shows a similar PV panel graph as before ata fixed temperature of 30∘C where the points may also beadjusted by a linear approximation Actually these two linesmay be used to generate a plane which contains the MPPvicinities at different temperature and irradiation conditions

Through linear approximation analysis the plane isobtained which contains the MPP vicinities as

119894pv minus 254Vpv minus 0455119879 + 119904ref = 0 (1)

where 119894pv is the panel current Vpv is the panel voltage 119879 is theenvironmental temperature and 119904ref is a displacement term =9363

This plane is considered as sliding surface for the pro-posed controller According to the theory of sliding modesthe system is forced to be directed into the surface so thatthe system will reach the MPP vicinity with a fast dynamicresponse

International Journal of Photoenergy 3

0 45403530252015105

545

435

325

215

105

i pv

vpv

T = 15∘C

100 rad

40 rad

60 rad

80 rad3545V358A12714W3528V288A10166W3491V217A

7608 W

5060 W3412V148A

(a) At 15∘C

545

435

325

215

105

i pv

0 45403530252015105vpv

T = 30∘C

100 rad

40 rad

60 rad

80 rad3316V358A11907W3298V289A

3261V219A

3184V150A

7150 W

4778 W

9534 W

(b) At 30∘C

Figure 2 PVG characteristics under different irradiance and temperature conditions

Voltagesense

Currentsense

PVLoad

Gate driver

AD

MicrocontrollerMPPT DA

Switchingfrequency

limiter

120590(ipv pv T)

ipv minus bpv minus cT + sref

S

T

Cin Cout

ipvpv

sref

Figure 3 Power stage and proposed controller

22 Slow Loop The MPP vicinity is reached by the systemdue to the fast loop and then a small variation should bemade in order to adjust the system and reduce the steady stateerror with the aid of the slow loop A traditional ldquoperturband observerdquo MPPT was employed The parameter ldquo119904refrdquo isconsidered as the output in order to follow the MPP andreduce the error at steady state

23 Control Design and Implementation The power stageconsidered in this paper is a traditional DCDC boost con-verter as illustrated in Figure 3 where the load is a constantresistance Then the output voltage is adjusted according tothe power available at the PV panel

The sliding surface and control law employed are

120590 = 119894119871minus 254Vpv minus 0455119879 + 119904ref = 0

119906 =

1 if 120590 lt 0

0 if 120590 lt 0

(2)

where 120590 is the sliding surface and 119906 is the control law

OffOff

New MPPT

OnRadiationchange

120590 gt 0 120590 lt 0

i

v

Figure 4 Conceptual trajectory under a sudden change of irradia-tion

Operational amplifiers and comparators were consideredas analog devices for implementing the sliding surface andcontrol law A microcontroller generates the ldquo119904refrdquo parameterwhich is considered constant at steady state

The switching frequency is considered to be bounded bythe aid of a limiter The operation for this proposed system isgraphically shown in Figure 4 It should be noticed that theMPP is tracked when irradiance changes

A model was developed for verifying the functionality ofthis proposed system not only the existence of a slidingmodewas verified but also the stability analysis under one operatingpoint was made

Model of the System The system model considers two posi-tions for themain switchThese are when it is turned ldquoonrdquo andldquooffrdquo A simplified model for the PV panel is also considered[19]

119894pv = 120582119868sc minus 120582119868119904(119890(119902Vpv119860119870119879) minus 1) (3)

where119860 is the ideality factor of the diode119870 is the Boltzmannconstant 119902 is the electron charge 120582 is the percentage ofirradiance (1 = 100) 119868sc is the short circuit current of thePV panel 119868

119904is the saturation current of the diode 119879 is the

temperature of the ambient in ∘K and Vpv is the voltage of PVpanel or input capacitor

4 International Journal of Photoenergy

The equations when the switch is ldquoonrdquo are

119889

119889119905119894119871=

Vpv119871

119889

119889119905V119888= minus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(4)

where 119894119871is the current of the inductor V

119888is the voltage of the

output capacitor Vpv is the voltage of input capacitor and 119894pvis the current of the PV panel

The equations when the switch is ldquooffrdquo are

119889

119889119905119894119871=

Vpv119871

minusV119888

119871

119889

119889119905V119888=

119894119871

119862outminus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(5)

Then substituting (3) in (4) and (5) and after somealgebraic manipulations the complete model of the system isobtained as

119889

119889119905119894119871=

Vpv119871

minusV119888

119871(1 minus 119906)

119889

119889119905V119888=

119894119871

119862out(1 minus 119906) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(6)

where 119906 is the control law

Existence of the Sliding Mode Existence of sliding mode isdemonstrated by the next inequality which must be satisfied[21ndash25]

120590119889120590

119889119905lt 0 (7)

Considering at this point the negligible temperature varia-tion the derivative of the sliding surface is obtained as

119889120590

119889119905=

119889

119889119905119894119871minus 254

119889

119889119905Vpv (8)

Substituting (6) in (8) lets us obtain

119889120590

119889119905=

Vpv119871

minusV119888

119871(1 minus 119906)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(9)

The existence for the two possible cases of (7) is analyzednext

(a) If 120590 gt 0 then 1205901015840

lt 0 and 119906 = 0 The followinginequality is obtained

Vpv119871

minusV119888

119871minus 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) lt 0

(10)

(b) If 120590 lt 0 then 1205901015840

gt 0 and 119906 = 1 The followinginequality is obtained

Vpv119871

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) gt 0 (11)

Inequalities (10) and (11) must be satisfied in order toguarantee the existence of the sliding mode Inequality (10)is satisfied because the analyzed converter is a DCDC boostconverter (V

119888is always higher than Vpv) Therefore (10) is

negative if the voltage algebraic addition is more dominantthan the other term Same thing happens with inequality (11)since the PV panel voltage is always positive the inequality issatisfied only if the term is more significant than the secondone

Stability Analysis An equivalent control is obtained [24 25]in order to verify the system stability This control law issubstituted in the system model

The equivalent control is obtained from expression (9)which is made equal to zero and the control law is finallywritten as follows

Vpv119871

minusV119888

119871(1 minus 119906eq)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) = 0

(12)

Developing the equivalent control from (12) is obtainedas

119906eq = 1 minus

VpvV119888

+254119871

V119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(13)

Substituting (13) in (6) is obtained

119889

119889119905119894119871= 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

119889

119889119905V119888=

119894119871Vpv

119862outV119888minus254119871119894

119871

119862outV119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(14)

International Journal of Photoenergy 5

Making the linearization around the operating point nextis obtained

119889

119889119905119871= minus

254

119862in119871minus254120582119868

119904119902

119860119870119879119862in119890(119902Vpv119860119870119879)Vpv

119889

119889119905V119888= 1198601119871+ 1198602V119888+ 1198603Vpv

119889

119889119905Vpv = minus

1

119862in119871minus

120582119868119904119902

119860119870119879119862in119890(119902119881pv119860119870119879)Vpv

(15)

where

1198601= (

119881pv

119862out119881119888minus

254119871

119862out119881119888(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1))

+254119871

119862out119881119888(2119868119871

119862in))

1198602= minus

1

119877119862minus

119868119871119881pv

119862out1198812

119888

+254119868119871119871

119862out1198812

119888

(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1) minus

119868119871

119862in)

1198603=

119868119871

119862out119881119888+

254119871119868119871120582119868119904119902

119860119870119879119862out119862in119881119888119890(119902119881pv119860119870119879)

(16)

System (15) has the following eigenvalues

1198980= 0

1198981= minus (

127119860119870119879 + 50120582119868119904119902119890(119902119881pv119860119870119879)

50119860119870119879119862in)

1198982= minus ((50119862in (119881

2

119888

+ 119868119871119877119881pv)

+ 127119871119877 (1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)))

sdot (50119862in119862out1198771198812

119888

)minus1

)

(17)

Only two eigenvalues determine the stability establishedinto the sliding surface One eigenvalue is zero due to theproperty of the sliding mode controller which reduces theorder of the system [24 25] This is explained because thesystem is maintained into the sliding surface and thereforethemovement is restricted into the plane (the sliding surface)These two eigenvalues must have a negative real part toguarantee stability into the sliding surface Evaluating (17) itis obtained that the system is stable if

(1198812

119888

+ 119868119871119877119881pv)

+127119871119877

50119862in(1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)) gt 0

(18)

This inequality is satisfied for the parameters of theimplemented system Table 1 shows the system parameters

Table 1 Parameters of the system

119860 = 90 119862in = 220 120583F 119881pv = 3545

119870 = 138 times 10minus23

119862o = 220 120583F 119868119871

= 358

119879 = 15∘C = 28815∘K 119871 = 200 120583H 119881119888

= 6175

119868119904

= 239 times 10minus4

119877 = 30Ω

119868sc = 41A119902 = 16 times 10

minus19

120582 = 1 (1000Wm2)

Bounding the Switching Frequency An ideal sliding modecontroller implies an infinite switching frequency and thenin a practical implementation this switching frequency mustbe bounded

There are different techniques to limit the switchingfrequency [20 26] hysteresis delay and holding at a constanttime the switch in ldquoonrdquo or ldquooffrdquo and finally also the use ofPWMmay be considered

This paper considers the employedmethod in [20] whichallows operating at a fixed switching frequency even underlarge variations

3 Simulation and Experimental Results

System functionality was evaluated not only numerically butalso experimentally so that the proposed idea was validated

The boost converter consists of an inductor of 200120583H aninput capacitor of 220120583F an output capacitor of 220120583F andthe load resistance of 30Ω

The system was evaluated under different operating con-ditions Initially the simulations are addressed and later onthe experimental results

31 Simulation at Steady State Figure 5 shows the simulationresults at steady state Figure 5(a) illustrates the operation atsteady state when the temperature is 15∘C the irradiance is120582 = 1 which is equivalent to 1000Wm2 so that the MPP islocated at a power of 12715W It is easily seen that the systemreaches that PV panel power

Figure 5(b) illustrates the slow loop behavior which isalways oscillating when theMPP is tracked It is also seen thatthe variation at the output is small so that this variation isalmost negligible at the PV panel power at steady state

The slow loop has a 05 s as the time interval betweenalgorithm iterations

It is important to notice that in Figure 5 (and alsoFigure 6) the inductor current for illustrating the powerdemanded for the PV panel is considered this was done forhaving a better appreciation in the figure However the actualpower of the PV panel does not have this ripple due to theinput capacitor 119862in

32 Simulation under Radiation Change Figure 6(a) showssystem operation under a sudden irradiation change initiallyirradiation value is 1000Wm2 and it changes to 600Wm2this represents a huge variation on the PV panel conditions

6 International Journal of Photoenergy

100

50

0

80

60

40

20

0

Time (ms)

150

100

pv lowast iL Ppv

10 15 20 25 30 35

c

(W)

(V)

(a)

850848846845842840

05 1 15Time (s)

pv lowast iL

Ppv

c

s ref

100

50

0

150

(W)

80604020

0

100

(V)

s ref

(b)

Figure 5 Simulation results (a) At steady state 15∘C 1000Wm2 (b) At steady state 15 1000Wm2 119904ref changes every 05 s

It is easily seen that the system takes around 36ms to trackthe new MPP

Since each decision is made every 05 s it would take amuch longer time if only a slow loop was considered Theproposed system offers a faster response than this obtainedwith iterative methods based on just algorithms

33 Simulation under Temperature Change Figure 6(b)shows the system operation under a sudden temperaturechange initially temperature value is 15∘C and it changesto 30∘C This represents a huge variation on the PV panelconditions It is easily seen that the system takes around 8msto track the newMPPThis is mainly due to the considerationof the temperature in the sliding surface

Again it would take a much longer time if only a slowloop was considered The proposed system offers a fasterresponse than this obtained with iterative methods based onjust algorithms

34 Experimental Results This proposal was examined atsteady state and under renewable source variation in orderto carry out a reliable validation Therefore this proposalof power point tracker algorithm was evaluated Actuallythis proposed sliding mode MPPT was connected to a PVemulator which allows changing its condition in a dynamicmanner

Results for the system at steady state are shown inFigure 7 where the operating conditions are 600Wm2From top to bottom the PV panel voltage the inductor119871 current and the drain-source voltage of themain switch are

shownThis last voltage not only illustrates the commutationof the main switch but also allows seeing the value of theoutput voltage at the high voltage level

Figure 8 shows changes to the conditions on the PVpanelInitially the system was evaluated under a change from 40to 60of irradiation which is illustrated in Figure 8(a) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shown Itis easily seen that the system takes around 8ms to track thenew MPP of the PV It is also seen how the output voltageincreases for demanding more power according to the newMPP condition

Finally the systemwas also evaluated under changes from80 to 40 of irradiation as illustrated in Figure 8(b) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shownThe system takes around 25ms to track the new MPP forthe PV It is easily seen that the output voltage decreases fordemanding less power according to the new MPP condition

4 Conclusion

This proposal introduces a new sliding mode based MPPTmethod It offers an accelerated convergence to themaximumpower point as a difference from the traditional methodThisis accomplished by choosing the switching surface whichconsiders voltage current and temperature simultaneouslyof the PV panel

Fast loop implementation which includes a sliding sur-face generated based on the PV panel characteristics offersa fast tracking response in spite of changes on weather

International Journal of Photoenergy 7

65

60

55

50

45

pv lowast iL

Ppv

c

100

020406080

120

140

(W)

(V)

01 015 02 025 03Time (s)

(a)

pv lowast iL

Ppv

c

100

50

0

150

(W)

80

60

40

20

0

100

(V)

01 015 02 025 03Time (s)

(b)

Figure 6 Simulation results (a) Irradiation change 1000Wm2 to 600Wm2 (b) Temperature change 15∘C to 30∘C

500V1500V4 200A Ω3

221A5920m40m131m

Duty cycle- RMS

4585 4576 3571 989643

Value Mean Min Max Stand dev

221 224

4400 120583s 250 MSs10k pts 490 VT 000000 s

TT

Tek

1

3

4

Figure 7 Experimental results at steady state condition

500V1500V3 200A Ω4

184ADuty cycle- RMS

353534

Value Mean low resolution Min Max Stand dev

184 184 184 000

Tek

1

TT

4

3

vpv

i pv

VDS

4100 kSs10k pts 204 A

100 ms000000 sT

(a)

500V1500V3 200A Ω4

210ADuty cycle- RMS

496434

Value Mean low resolution Min Max Stand dev

233 210 235 447 m

410k pts 164 A

100 ms000000 s

4

1

T

T

T

vpv

i pv

VDS

Tek

3100 kSs

(b)

Figure 8 Experimental results under variations (a) Positive step (b) Negative step

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal ofPhotoenergy

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CatalystsJournal of

2 International Journal of Photoenergy

for generating the input current reference Since theseschemes employ PampOalgorithmwhich establish the trackingfor the MPP it becomes a disadvantage and therefore thetechnique still does a tradeoff engagement between precisionand dynamic response

In literature [12] a proposal for MPPT based in slidingmode controller is also foundwhere its scheme eliminates thesteady state variation and reduces the tradeoff engagementbetween precision and dynamic responseThe sliding surfaceis based on the classic equation of PampO algorithm andits implementation for this proposal implies derivative anddivision between variables which become a drawback sinceit requires expensive hardware

TheMPP locus may be approximated by a linear relation-ship [13 14] based on the characteristics from PV modulesTherefore a linear controller which reduces the tradeoffengagement between precision and dynamic response couldbe designed in order to operate the PV system near the MPPAn implementation for a system on this condition may offera much faster MPPT as it is suggested in literature [18]where this linear approximation just considers the voltageand current

All these previous schemes do not consider the tempera-ture in the tracking however the PV panel also depends onthis variable

In this paper a MPPT based on a linear approximation isproposedwhich considers not only the voltage and current onthe PV panel but also temperatureTheMPP locus is trackedat all times A linear approximation is used to establish thesliding surface for the sliding mode controller where a fasttracking response is obtained Additionally a slow controlloop based on traditional PampO method is considered toguarantee a low error at steady state

This proposal let us have a fast dynamic responsesimple implementation (no expensive hardware) and smallvariation at steady state The tradeoff between precision anddynamic response is reduced since the MPPT is performedby the sliding controller and not by the iterative algorithmThe best features of several different methods published inliterature have been gathered in this proposal

This work is organized as described next MPPT proposalis discussed in Section 2 which includes system modelingoperation and analysis Section 3 is addressed for simulationand experimental results And some final conclusions aregiven at the end

2 Proposed Maximum Power Point Tracking

Two control loops have been implemented for the MPPTa fast and a slow loop Figure 1 shows the block diagramIt is easily seen how voltage current and temperature areconsidered simultaneously these three variables are used intothe sliding surface which are provided for the fast loop andthe first two variables are employed for the slow loop in orderto guarantee a low error at steady state

The fast loop allows us to reach very closely the MPPvicinity with a good dynamic response while the slowloop allows us to decrease the steady state error by using

Powerstage Load

MPPT

Controller

Slowloop

Fastloop

sref

T

u

Figure 1 Block diagram of the proposed dual loop MPPT

a small step increment in the MPPT algorithm This tech-nique becomes a good tracking method Since trackingmostly is carried out by the fast loop the slow loop requiresfew iterations The two control loops are explained next

21 Fast Loop A sliding mode controller is considered forthis loop where the sliding surface is established by the PVpanel characteristics this may easily be obtained not onlyexperimentally but also by using a model

A switching surface is established by a linear combinationof voltage current and temperature in the PV generator(PVG) which contain the different MPP (or at least closeto the vicinity) at different operating conditions The slidingmode controller leads the system to the sliding surface and itis maintained in it so that the controller will reach the MPPvicinity

A typical graph of a PV panel is shown in Figure 2(a)where it is shown solar irradiation changes at a fixed tem-perature of 15∘C It is easily seen that the MPP in each graphis located at the knee of the curve and it suffers changesdepending on the radiation These points may almost beconnected by a line actually a linear approximation may bedone by using least squares

Figure 2(b) shows a similar PV panel graph as before ata fixed temperature of 30∘C where the points may also beadjusted by a linear approximation Actually these two linesmay be used to generate a plane which contains the MPPvicinities at different temperature and irradiation conditions

Through linear approximation analysis the plane isobtained which contains the MPP vicinities as

119894pv minus 254Vpv minus 0455119879 + 119904ref = 0 (1)

where 119894pv is the panel current Vpv is the panel voltage 119879 is theenvironmental temperature and 119904ref is a displacement term =9363

This plane is considered as sliding surface for the pro-posed controller According to the theory of sliding modesthe system is forced to be directed into the surface so thatthe system will reach the MPP vicinity with a fast dynamicresponse

International Journal of Photoenergy 3

0 45403530252015105

545

435

325

215

105

i pv

vpv

T = 15∘C

100 rad

40 rad

60 rad

80 rad3545V358A12714W3528V288A10166W3491V217A

7608 W

5060 W3412V148A

(a) At 15∘C

545

435

325

215

105

i pv

0 45403530252015105vpv

T = 30∘C

100 rad

40 rad

60 rad

80 rad3316V358A11907W3298V289A

3261V219A

3184V150A

7150 W

4778 W

9534 W

(b) At 30∘C

Figure 2 PVG characteristics under different irradiance and temperature conditions

Voltagesense

Currentsense

PVLoad

Gate driver

AD

MicrocontrollerMPPT DA

Switchingfrequency

limiter

120590(ipv pv T)

ipv minus bpv minus cT + sref

S

T

Cin Cout

ipvpv

sref

Figure 3 Power stage and proposed controller

22 Slow Loop The MPP vicinity is reached by the systemdue to the fast loop and then a small variation should bemade in order to adjust the system and reduce the steady stateerror with the aid of the slow loop A traditional ldquoperturband observerdquo MPPT was employed The parameter ldquo119904refrdquo isconsidered as the output in order to follow the MPP andreduce the error at steady state

23 Control Design and Implementation The power stageconsidered in this paper is a traditional DCDC boost con-verter as illustrated in Figure 3 where the load is a constantresistance Then the output voltage is adjusted according tothe power available at the PV panel

The sliding surface and control law employed are

120590 = 119894119871minus 254Vpv minus 0455119879 + 119904ref = 0

119906 =

1 if 120590 lt 0

0 if 120590 lt 0

(2)

where 120590 is the sliding surface and 119906 is the control law

OffOff

New MPPT

OnRadiationchange

120590 gt 0 120590 lt 0

i

v

Figure 4 Conceptual trajectory under a sudden change of irradia-tion

Operational amplifiers and comparators were consideredas analog devices for implementing the sliding surface andcontrol law A microcontroller generates the ldquo119904refrdquo parameterwhich is considered constant at steady state

The switching frequency is considered to be bounded bythe aid of a limiter The operation for this proposed system isgraphically shown in Figure 4 It should be noticed that theMPP is tracked when irradiance changes

A model was developed for verifying the functionality ofthis proposed system not only the existence of a slidingmodewas verified but also the stability analysis under one operatingpoint was made

Model of the System The system model considers two posi-tions for themain switchThese are when it is turned ldquoonrdquo andldquooffrdquo A simplified model for the PV panel is also considered[19]

119894pv = 120582119868sc minus 120582119868119904(119890(119902Vpv119860119870119879) minus 1) (3)

where119860 is the ideality factor of the diode119870 is the Boltzmannconstant 119902 is the electron charge 120582 is the percentage ofirradiance (1 = 100) 119868sc is the short circuit current of thePV panel 119868

119904is the saturation current of the diode 119879 is the

temperature of the ambient in ∘K and Vpv is the voltage of PVpanel or input capacitor

4 International Journal of Photoenergy

The equations when the switch is ldquoonrdquo are

119889

119889119905119894119871=

Vpv119871

119889

119889119905V119888= minus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(4)

where 119894119871is the current of the inductor V

119888is the voltage of the

output capacitor Vpv is the voltage of input capacitor and 119894pvis the current of the PV panel

The equations when the switch is ldquooffrdquo are

119889

119889119905119894119871=

Vpv119871

minusV119888

119871

119889

119889119905V119888=

119894119871

119862outminus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(5)

Then substituting (3) in (4) and (5) and after somealgebraic manipulations the complete model of the system isobtained as

119889

119889119905119894119871=

Vpv119871

minusV119888

119871(1 minus 119906)

119889

119889119905V119888=

119894119871

119862out(1 minus 119906) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(6)

where 119906 is the control law

Existence of the Sliding Mode Existence of sliding mode isdemonstrated by the next inequality which must be satisfied[21ndash25]

120590119889120590

119889119905lt 0 (7)

Considering at this point the negligible temperature varia-tion the derivative of the sliding surface is obtained as

119889120590

119889119905=

119889

119889119905119894119871minus 254

119889

119889119905Vpv (8)

Substituting (6) in (8) lets us obtain

119889120590

119889119905=

Vpv119871

minusV119888

119871(1 minus 119906)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(9)

The existence for the two possible cases of (7) is analyzednext

(a) If 120590 gt 0 then 1205901015840

lt 0 and 119906 = 0 The followinginequality is obtained

Vpv119871

minusV119888

119871minus 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) lt 0

(10)

(b) If 120590 lt 0 then 1205901015840

gt 0 and 119906 = 1 The followinginequality is obtained

Vpv119871

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) gt 0 (11)

Inequalities (10) and (11) must be satisfied in order toguarantee the existence of the sliding mode Inequality (10)is satisfied because the analyzed converter is a DCDC boostconverter (V

119888is always higher than Vpv) Therefore (10) is

negative if the voltage algebraic addition is more dominantthan the other term Same thing happens with inequality (11)since the PV panel voltage is always positive the inequality issatisfied only if the term is more significant than the secondone

Stability Analysis An equivalent control is obtained [24 25]in order to verify the system stability This control law issubstituted in the system model

The equivalent control is obtained from expression (9)which is made equal to zero and the control law is finallywritten as follows

Vpv119871

minusV119888

119871(1 minus 119906eq)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) = 0

(12)

Developing the equivalent control from (12) is obtainedas

119906eq = 1 minus

VpvV119888

+254119871

V119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(13)

Substituting (13) in (6) is obtained

119889

119889119905119894119871= 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

119889

119889119905V119888=

119894119871Vpv

119862outV119888minus254119871119894

119871

119862outV119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(14)

International Journal of Photoenergy 5

Making the linearization around the operating point nextis obtained

119889

119889119905119871= minus

254

119862in119871minus254120582119868

119904119902

119860119870119879119862in119890(119902Vpv119860119870119879)Vpv

119889

119889119905V119888= 1198601119871+ 1198602V119888+ 1198603Vpv

119889

119889119905Vpv = minus

1

119862in119871minus

120582119868119904119902

119860119870119879119862in119890(119902119881pv119860119870119879)Vpv

(15)

where

1198601= (

119881pv

119862out119881119888minus

254119871

119862out119881119888(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1))

+254119871

119862out119881119888(2119868119871

119862in))

1198602= minus

1

119877119862minus

119868119871119881pv

119862out1198812

119888

+254119868119871119871

119862out1198812

119888

(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1) minus

119868119871

119862in)

1198603=

119868119871

119862out119881119888+

254119871119868119871120582119868119904119902

119860119870119879119862out119862in119881119888119890(119902119881pv119860119870119879)

(16)

System (15) has the following eigenvalues

1198980= 0

1198981= minus (

127119860119870119879 + 50120582119868119904119902119890(119902119881pv119860119870119879)

50119860119870119879119862in)

1198982= minus ((50119862in (119881

2

119888

+ 119868119871119877119881pv)

+ 127119871119877 (1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)))

sdot (50119862in119862out1198771198812

119888

)minus1

)

(17)

Only two eigenvalues determine the stability establishedinto the sliding surface One eigenvalue is zero due to theproperty of the sliding mode controller which reduces theorder of the system [24 25] This is explained because thesystem is maintained into the sliding surface and thereforethemovement is restricted into the plane (the sliding surface)These two eigenvalues must have a negative real part toguarantee stability into the sliding surface Evaluating (17) itis obtained that the system is stable if

(1198812

119888

+ 119868119871119877119881pv)

+127119871119877

50119862in(1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)) gt 0

(18)

This inequality is satisfied for the parameters of theimplemented system Table 1 shows the system parameters

Table 1 Parameters of the system

119860 = 90 119862in = 220 120583F 119881pv = 3545

119870 = 138 times 10minus23

119862o = 220 120583F 119868119871

= 358

119879 = 15∘C = 28815∘K 119871 = 200 120583H 119881119888

= 6175

119868119904

= 239 times 10minus4

119877 = 30Ω

119868sc = 41A119902 = 16 times 10

minus19

120582 = 1 (1000Wm2)

Bounding the Switching Frequency An ideal sliding modecontroller implies an infinite switching frequency and thenin a practical implementation this switching frequency mustbe bounded

There are different techniques to limit the switchingfrequency [20 26] hysteresis delay and holding at a constanttime the switch in ldquoonrdquo or ldquooffrdquo and finally also the use ofPWMmay be considered

This paper considers the employedmethod in [20] whichallows operating at a fixed switching frequency even underlarge variations

3 Simulation and Experimental Results

System functionality was evaluated not only numerically butalso experimentally so that the proposed idea was validated

The boost converter consists of an inductor of 200120583H aninput capacitor of 220120583F an output capacitor of 220120583F andthe load resistance of 30Ω

The system was evaluated under different operating con-ditions Initially the simulations are addressed and later onthe experimental results

31 Simulation at Steady State Figure 5 shows the simulationresults at steady state Figure 5(a) illustrates the operation atsteady state when the temperature is 15∘C the irradiance is120582 = 1 which is equivalent to 1000Wm2 so that the MPP islocated at a power of 12715W It is easily seen that the systemreaches that PV panel power

Figure 5(b) illustrates the slow loop behavior which isalways oscillating when theMPP is tracked It is also seen thatthe variation at the output is small so that this variation isalmost negligible at the PV panel power at steady state

The slow loop has a 05 s as the time interval betweenalgorithm iterations

It is important to notice that in Figure 5 (and alsoFigure 6) the inductor current for illustrating the powerdemanded for the PV panel is considered this was done forhaving a better appreciation in the figure However the actualpower of the PV panel does not have this ripple due to theinput capacitor 119862in

32 Simulation under Radiation Change Figure 6(a) showssystem operation under a sudden irradiation change initiallyirradiation value is 1000Wm2 and it changes to 600Wm2this represents a huge variation on the PV panel conditions

6 International Journal of Photoenergy

100

50

0

80

60

40

20

0

Time (ms)

150

100

pv lowast iL Ppv

10 15 20 25 30 35

c

(W)

(V)

(a)

850848846845842840

05 1 15Time (s)

pv lowast iL

Ppv

c

s ref

100

50

0

150

(W)

80604020

0

100

(V)

s ref

(b)

Figure 5 Simulation results (a) At steady state 15∘C 1000Wm2 (b) At steady state 15 1000Wm2 119904ref changes every 05 s

It is easily seen that the system takes around 36ms to trackthe new MPP

Since each decision is made every 05 s it would take amuch longer time if only a slow loop was considered Theproposed system offers a faster response than this obtainedwith iterative methods based on just algorithms

33 Simulation under Temperature Change Figure 6(b)shows the system operation under a sudden temperaturechange initially temperature value is 15∘C and it changesto 30∘C This represents a huge variation on the PV panelconditions It is easily seen that the system takes around 8msto track the newMPPThis is mainly due to the considerationof the temperature in the sliding surface

Again it would take a much longer time if only a slowloop was considered The proposed system offers a fasterresponse than this obtained with iterative methods based onjust algorithms

34 Experimental Results This proposal was examined atsteady state and under renewable source variation in orderto carry out a reliable validation Therefore this proposalof power point tracker algorithm was evaluated Actuallythis proposed sliding mode MPPT was connected to a PVemulator which allows changing its condition in a dynamicmanner

Results for the system at steady state are shown inFigure 7 where the operating conditions are 600Wm2From top to bottom the PV panel voltage the inductor119871 current and the drain-source voltage of themain switch are

shownThis last voltage not only illustrates the commutationof the main switch but also allows seeing the value of theoutput voltage at the high voltage level

Figure 8 shows changes to the conditions on the PVpanelInitially the system was evaluated under a change from 40to 60of irradiation which is illustrated in Figure 8(a) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shown Itis easily seen that the system takes around 8ms to track thenew MPP of the PV It is also seen how the output voltageincreases for demanding more power according to the newMPP condition

Finally the systemwas also evaluated under changes from80 to 40 of irradiation as illustrated in Figure 8(b) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shownThe system takes around 25ms to track the new MPP forthe PV It is easily seen that the output voltage decreases fordemanding less power according to the new MPP condition

4 Conclusion

This proposal introduces a new sliding mode based MPPTmethod It offers an accelerated convergence to themaximumpower point as a difference from the traditional methodThisis accomplished by choosing the switching surface whichconsiders voltage current and temperature simultaneouslyof the PV panel

Fast loop implementation which includes a sliding sur-face generated based on the PV panel characteristics offersa fast tracking response in spite of changes on weather

International Journal of Photoenergy 7

65

60

55

50

45

pv lowast iL

Ppv

c

100

020406080

120

140

(W)

(V)

01 015 02 025 03Time (s)

(a)

pv lowast iL

Ppv

c

100

50

0

150

(W)

80

60

40

20

0

100

(V)

01 015 02 025 03Time (s)

(b)

Figure 6 Simulation results (a) Irradiation change 1000Wm2 to 600Wm2 (b) Temperature change 15∘C to 30∘C

500V1500V4 200A Ω3

221A5920m40m131m

Duty cycle- RMS

4585 4576 3571 989643

Value Mean Min Max Stand dev

221 224

4400 120583s 250 MSs10k pts 490 VT 000000 s

TT

Tek

1

3

4

Figure 7 Experimental results at steady state condition

500V1500V3 200A Ω4

184ADuty cycle- RMS

353534

Value Mean low resolution Min Max Stand dev

184 184 184 000

Tek

1

TT

4

3

vpv

i pv

VDS

4100 kSs10k pts 204 A

100 ms000000 sT

(a)

500V1500V3 200A Ω4

210ADuty cycle- RMS

496434

Value Mean low resolution Min Max Stand dev

233 210 235 447 m

410k pts 164 A

100 ms000000 s

4

1

T

T

T

vpv

i pv

VDS

Tek

3100 kSs

(b)

Figure 8 Experimental results under variations (a) Positive step (b) Negative step

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

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Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

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Journal of

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Analytical ChemistryInternational Journal of

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Quantum Chemistry

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Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

International Journal of Photoenergy 3

0 45403530252015105

545

435

325

215

105

i pv

vpv

T = 15∘C

100 rad

40 rad

60 rad

80 rad3545V358A12714W3528V288A10166W3491V217A

7608 W

5060 W3412V148A

(a) At 15∘C

545

435

325

215

105

i pv

0 45403530252015105vpv

T = 30∘C

100 rad

40 rad

60 rad

80 rad3316V358A11907W3298V289A

3261V219A

3184V150A

7150 W

4778 W

9534 W

(b) At 30∘C

Figure 2 PVG characteristics under different irradiance and temperature conditions

Voltagesense

Currentsense

PVLoad

Gate driver

AD

MicrocontrollerMPPT DA

Switchingfrequency

limiter

120590(ipv pv T)

ipv minus bpv minus cT + sref

S

T

Cin Cout

ipvpv

sref

Figure 3 Power stage and proposed controller

22 Slow Loop The MPP vicinity is reached by the systemdue to the fast loop and then a small variation should bemade in order to adjust the system and reduce the steady stateerror with the aid of the slow loop A traditional ldquoperturband observerdquo MPPT was employed The parameter ldquo119904refrdquo isconsidered as the output in order to follow the MPP andreduce the error at steady state

23 Control Design and Implementation The power stageconsidered in this paper is a traditional DCDC boost con-verter as illustrated in Figure 3 where the load is a constantresistance Then the output voltage is adjusted according tothe power available at the PV panel

The sliding surface and control law employed are

120590 = 119894119871minus 254Vpv minus 0455119879 + 119904ref = 0

119906 =

1 if 120590 lt 0

0 if 120590 lt 0

(2)

where 120590 is the sliding surface and 119906 is the control law

OffOff

New MPPT

OnRadiationchange

120590 gt 0 120590 lt 0

i

v

Figure 4 Conceptual trajectory under a sudden change of irradia-tion

Operational amplifiers and comparators were consideredas analog devices for implementing the sliding surface andcontrol law A microcontroller generates the ldquo119904refrdquo parameterwhich is considered constant at steady state

The switching frequency is considered to be bounded bythe aid of a limiter The operation for this proposed system isgraphically shown in Figure 4 It should be noticed that theMPP is tracked when irradiance changes

A model was developed for verifying the functionality ofthis proposed system not only the existence of a slidingmodewas verified but also the stability analysis under one operatingpoint was made

Model of the System The system model considers two posi-tions for themain switchThese are when it is turned ldquoonrdquo andldquooffrdquo A simplified model for the PV panel is also considered[19]

119894pv = 120582119868sc minus 120582119868119904(119890(119902Vpv119860119870119879) minus 1) (3)

where119860 is the ideality factor of the diode119870 is the Boltzmannconstant 119902 is the electron charge 120582 is the percentage ofirradiance (1 = 100) 119868sc is the short circuit current of thePV panel 119868

119904is the saturation current of the diode 119879 is the

temperature of the ambient in ∘K and Vpv is the voltage of PVpanel or input capacitor

4 International Journal of Photoenergy

The equations when the switch is ldquoonrdquo are

119889

119889119905119894119871=

Vpv119871

119889

119889119905V119888= minus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(4)

where 119894119871is the current of the inductor V

119888is the voltage of the

output capacitor Vpv is the voltage of input capacitor and 119894pvis the current of the PV panel

The equations when the switch is ldquooffrdquo are

119889

119889119905119894119871=

Vpv119871

minusV119888

119871

119889

119889119905V119888=

119894119871

119862outminus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(5)

Then substituting (3) in (4) and (5) and after somealgebraic manipulations the complete model of the system isobtained as

119889

119889119905119894119871=

Vpv119871

minusV119888

119871(1 minus 119906)

119889

119889119905V119888=

119894119871

119862out(1 minus 119906) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(6)

where 119906 is the control law

Existence of the Sliding Mode Existence of sliding mode isdemonstrated by the next inequality which must be satisfied[21ndash25]

120590119889120590

119889119905lt 0 (7)

Considering at this point the negligible temperature varia-tion the derivative of the sliding surface is obtained as

119889120590

119889119905=

119889

119889119905119894119871minus 254

119889

119889119905Vpv (8)

Substituting (6) in (8) lets us obtain

119889120590

119889119905=

Vpv119871

minusV119888

119871(1 minus 119906)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(9)

The existence for the two possible cases of (7) is analyzednext

(a) If 120590 gt 0 then 1205901015840

lt 0 and 119906 = 0 The followinginequality is obtained

Vpv119871

minusV119888

119871minus 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) lt 0

(10)

(b) If 120590 lt 0 then 1205901015840

gt 0 and 119906 = 1 The followinginequality is obtained

Vpv119871

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) gt 0 (11)

Inequalities (10) and (11) must be satisfied in order toguarantee the existence of the sliding mode Inequality (10)is satisfied because the analyzed converter is a DCDC boostconverter (V

119888is always higher than Vpv) Therefore (10) is

negative if the voltage algebraic addition is more dominantthan the other term Same thing happens with inequality (11)since the PV panel voltage is always positive the inequality issatisfied only if the term is more significant than the secondone

Stability Analysis An equivalent control is obtained [24 25]in order to verify the system stability This control law issubstituted in the system model

The equivalent control is obtained from expression (9)which is made equal to zero and the control law is finallywritten as follows

Vpv119871

minusV119888

119871(1 minus 119906eq)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) = 0

(12)

Developing the equivalent control from (12) is obtainedas

119906eq = 1 minus

VpvV119888

+254119871

V119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(13)

Substituting (13) in (6) is obtained

119889

119889119905119894119871= 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

119889

119889119905V119888=

119894119871Vpv

119862outV119888minus254119871119894

119871

119862outV119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(14)

International Journal of Photoenergy 5

Making the linearization around the operating point nextis obtained

119889

119889119905119871= minus

254

119862in119871minus254120582119868

119904119902

119860119870119879119862in119890(119902Vpv119860119870119879)Vpv

119889

119889119905V119888= 1198601119871+ 1198602V119888+ 1198603Vpv

119889

119889119905Vpv = minus

1

119862in119871minus

120582119868119904119902

119860119870119879119862in119890(119902119881pv119860119870119879)Vpv

(15)

where

1198601= (

119881pv

119862out119881119888minus

254119871

119862out119881119888(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1))

+254119871

119862out119881119888(2119868119871

119862in))

1198602= minus

1

119877119862minus

119868119871119881pv

119862out1198812

119888

+254119868119871119871

119862out1198812

119888

(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1) minus

119868119871

119862in)

1198603=

119868119871

119862out119881119888+

254119871119868119871120582119868119904119902

119860119870119879119862out119862in119881119888119890(119902119881pv119860119870119879)

(16)

System (15) has the following eigenvalues

1198980= 0

1198981= minus (

127119860119870119879 + 50120582119868119904119902119890(119902119881pv119860119870119879)

50119860119870119879119862in)

1198982= minus ((50119862in (119881

2

119888

+ 119868119871119877119881pv)

+ 127119871119877 (1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)))

sdot (50119862in119862out1198771198812

119888

)minus1

)

(17)

Only two eigenvalues determine the stability establishedinto the sliding surface One eigenvalue is zero due to theproperty of the sliding mode controller which reduces theorder of the system [24 25] This is explained because thesystem is maintained into the sliding surface and thereforethemovement is restricted into the plane (the sliding surface)These two eigenvalues must have a negative real part toguarantee stability into the sliding surface Evaluating (17) itis obtained that the system is stable if

(1198812

119888

+ 119868119871119877119881pv)

+127119871119877

50119862in(1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)) gt 0

(18)

This inequality is satisfied for the parameters of theimplemented system Table 1 shows the system parameters

Table 1 Parameters of the system

119860 = 90 119862in = 220 120583F 119881pv = 3545

119870 = 138 times 10minus23

119862o = 220 120583F 119868119871

= 358

119879 = 15∘C = 28815∘K 119871 = 200 120583H 119881119888

= 6175

119868119904

= 239 times 10minus4

119877 = 30Ω

119868sc = 41A119902 = 16 times 10

minus19

120582 = 1 (1000Wm2)

Bounding the Switching Frequency An ideal sliding modecontroller implies an infinite switching frequency and thenin a practical implementation this switching frequency mustbe bounded

There are different techniques to limit the switchingfrequency [20 26] hysteresis delay and holding at a constanttime the switch in ldquoonrdquo or ldquooffrdquo and finally also the use ofPWMmay be considered

This paper considers the employedmethod in [20] whichallows operating at a fixed switching frequency even underlarge variations

3 Simulation and Experimental Results

System functionality was evaluated not only numerically butalso experimentally so that the proposed idea was validated

The boost converter consists of an inductor of 200120583H aninput capacitor of 220120583F an output capacitor of 220120583F andthe load resistance of 30Ω

The system was evaluated under different operating con-ditions Initially the simulations are addressed and later onthe experimental results

31 Simulation at Steady State Figure 5 shows the simulationresults at steady state Figure 5(a) illustrates the operation atsteady state when the temperature is 15∘C the irradiance is120582 = 1 which is equivalent to 1000Wm2 so that the MPP islocated at a power of 12715W It is easily seen that the systemreaches that PV panel power

Figure 5(b) illustrates the slow loop behavior which isalways oscillating when theMPP is tracked It is also seen thatthe variation at the output is small so that this variation isalmost negligible at the PV panel power at steady state

The slow loop has a 05 s as the time interval betweenalgorithm iterations

It is important to notice that in Figure 5 (and alsoFigure 6) the inductor current for illustrating the powerdemanded for the PV panel is considered this was done forhaving a better appreciation in the figure However the actualpower of the PV panel does not have this ripple due to theinput capacitor 119862in

32 Simulation under Radiation Change Figure 6(a) showssystem operation under a sudden irradiation change initiallyirradiation value is 1000Wm2 and it changes to 600Wm2this represents a huge variation on the PV panel conditions

6 International Journal of Photoenergy

100

50

0

80

60

40

20

0

Time (ms)

150

100

pv lowast iL Ppv

10 15 20 25 30 35

c

(W)

(V)

(a)

850848846845842840

05 1 15Time (s)

pv lowast iL

Ppv

c

s ref

100

50

0

150

(W)

80604020

0

100

(V)

s ref

(b)

Figure 5 Simulation results (a) At steady state 15∘C 1000Wm2 (b) At steady state 15 1000Wm2 119904ref changes every 05 s

It is easily seen that the system takes around 36ms to trackthe new MPP

Since each decision is made every 05 s it would take amuch longer time if only a slow loop was considered Theproposed system offers a faster response than this obtainedwith iterative methods based on just algorithms

33 Simulation under Temperature Change Figure 6(b)shows the system operation under a sudden temperaturechange initially temperature value is 15∘C and it changesto 30∘C This represents a huge variation on the PV panelconditions It is easily seen that the system takes around 8msto track the newMPPThis is mainly due to the considerationof the temperature in the sliding surface

Again it would take a much longer time if only a slowloop was considered The proposed system offers a fasterresponse than this obtained with iterative methods based onjust algorithms

34 Experimental Results This proposal was examined atsteady state and under renewable source variation in orderto carry out a reliable validation Therefore this proposalof power point tracker algorithm was evaluated Actuallythis proposed sliding mode MPPT was connected to a PVemulator which allows changing its condition in a dynamicmanner

Results for the system at steady state are shown inFigure 7 where the operating conditions are 600Wm2From top to bottom the PV panel voltage the inductor119871 current and the drain-source voltage of themain switch are

shownThis last voltage not only illustrates the commutationof the main switch but also allows seeing the value of theoutput voltage at the high voltage level

Figure 8 shows changes to the conditions on the PVpanelInitially the system was evaluated under a change from 40to 60of irradiation which is illustrated in Figure 8(a) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shown Itis easily seen that the system takes around 8ms to track thenew MPP of the PV It is also seen how the output voltageincreases for demanding more power according to the newMPP condition

Finally the systemwas also evaluated under changes from80 to 40 of irradiation as illustrated in Figure 8(b) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shownThe system takes around 25ms to track the new MPP forthe PV It is easily seen that the output voltage decreases fordemanding less power according to the new MPP condition

4 Conclusion

This proposal introduces a new sliding mode based MPPTmethod It offers an accelerated convergence to themaximumpower point as a difference from the traditional methodThisis accomplished by choosing the switching surface whichconsiders voltage current and temperature simultaneouslyof the PV panel

Fast loop implementation which includes a sliding sur-face generated based on the PV panel characteristics offersa fast tracking response in spite of changes on weather

International Journal of Photoenergy 7

65

60

55

50

45

pv lowast iL

Ppv

c

100

020406080

120

140

(W)

(V)

01 015 02 025 03Time (s)

(a)

pv lowast iL

Ppv

c

100

50

0

150

(W)

80

60

40

20

0

100

(V)

01 015 02 025 03Time (s)

(b)

Figure 6 Simulation results (a) Irradiation change 1000Wm2 to 600Wm2 (b) Temperature change 15∘C to 30∘C

500V1500V4 200A Ω3

221A5920m40m131m

Duty cycle- RMS

4585 4576 3571 989643

Value Mean Min Max Stand dev

221 224

4400 120583s 250 MSs10k pts 490 VT 000000 s

TT

Tek

1

3

4

Figure 7 Experimental results at steady state condition

500V1500V3 200A Ω4

184ADuty cycle- RMS

353534

Value Mean low resolution Min Max Stand dev

184 184 184 000

Tek

1

TT

4

3

vpv

i pv

VDS

4100 kSs10k pts 204 A

100 ms000000 sT

(a)

500V1500V3 200A Ω4

210ADuty cycle- RMS

496434

Value Mean low resolution Min Max Stand dev

233 210 235 447 m

410k pts 164 A

100 ms000000 s

4

1

T

T

T

vpv

i pv

VDS

Tek

3100 kSs

(b)

Figure 8 Experimental results under variations (a) Positive step (b) Negative step

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

4 International Journal of Photoenergy

The equations when the switch is ldquoonrdquo are

119889

119889119905119894119871=

Vpv119871

119889

119889119905V119888= minus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(4)

where 119894119871is the current of the inductor V

119888is the voltage of the

output capacitor Vpv is the voltage of input capacitor and 119894pvis the current of the PV panel

The equations when the switch is ldquooffrdquo are

119889

119889119905119894119871=

Vpv119871

minusV119888

119871

119889

119889119905V119888=

119894119871

119862outminus

V119888

119877119862out

119889

119889119905Vpv =

119894pv

119862inminus

119894119871

119862in

(5)

Then substituting (3) in (4) and (5) and after somealgebraic manipulations the complete model of the system isobtained as

119889

119889119905119894119871=

Vpv119871

minusV119888

119871(1 minus 119906)

119889

119889119905V119888=

119894119871

119862out(1 minus 119906) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(6)

where 119906 is the control law

Existence of the Sliding Mode Existence of sliding mode isdemonstrated by the next inequality which must be satisfied[21ndash25]

120590119889120590

119889119905lt 0 (7)

Considering at this point the negligible temperature varia-tion the derivative of the sliding surface is obtained as

119889120590

119889119905=

119889

119889119905119894119871minus 254

119889

119889119905Vpv (8)

Substituting (6) in (8) lets us obtain

119889120590

119889119905=

Vpv119871

minusV119888

119871(1 minus 119906)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(9)

The existence for the two possible cases of (7) is analyzednext

(a) If 120590 gt 0 then 1205901015840

lt 0 and 119906 = 0 The followinginequality is obtained

Vpv119871

minusV119888

119871minus 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) lt 0

(10)

(b) If 120590 lt 0 then 1205901015840

gt 0 and 119906 = 1 The followinginequality is obtained

Vpv119871

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) gt 0 (11)

Inequalities (10) and (11) must be satisfied in order toguarantee the existence of the sliding mode Inequality (10)is satisfied because the analyzed converter is a DCDC boostconverter (V

119888is always higher than Vpv) Therefore (10) is

negative if the voltage algebraic addition is more dominantthan the other term Same thing happens with inequality (11)since the PV panel voltage is always positive the inequality issatisfied only if the term is more significant than the secondone

Stability Analysis An equivalent control is obtained [24 25]in order to verify the system stability This control law issubstituted in the system model

The equivalent control is obtained from expression (9)which is made equal to zero and the control law is finallywritten as follows

Vpv119871

minusV119888

119871(1 minus 119906eq)

minus 254 (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) = 0

(12)

Developing the equivalent control from (12) is obtainedas

119906eq = 1 minus

VpvV119888

+254119871

V119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

(13)

Substituting (13) in (6) is obtained

119889

119889119905119894119871= 254 (

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in)

119889

119889119905V119888=

119894119871Vpv

119862outV119888minus254119871119894

119871

119862outV119888

sdot (120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in) minus

V119888

119877119862out

119889

119889119905Vpv =

120582119868sc119862in

minus120582119868119904

119862in(119890(119902Vpv119860119870119879) minus 1) minus

119894119871

119862in

(14)

International Journal of Photoenergy 5

Making the linearization around the operating point nextis obtained

119889

119889119905119871= minus

254

119862in119871minus254120582119868

119904119902

119860119870119879119862in119890(119902Vpv119860119870119879)Vpv

119889

119889119905V119888= 1198601119871+ 1198602V119888+ 1198603Vpv

119889

119889119905Vpv = minus

1

119862in119871minus

120582119868119904119902

119860119870119879119862in119890(119902119881pv119860119870119879)Vpv

(15)

where

1198601= (

119881pv

119862out119881119888minus

254119871

119862out119881119888(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1))

+254119871

119862out119881119888(2119868119871

119862in))

1198602= minus

1

119877119862minus

119868119871119881pv

119862out1198812

119888

+254119868119871119871

119862out1198812

119888

(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1) minus

119868119871

119862in)

1198603=

119868119871

119862out119881119888+

254119871119868119871120582119868119904119902

119860119870119879119862out119862in119881119888119890(119902119881pv119860119870119879)

(16)

System (15) has the following eigenvalues

1198980= 0

1198981= minus (

127119860119870119879 + 50120582119868119904119902119890(119902119881pv119860119870119879)

50119860119870119879119862in)

1198982= minus ((50119862in (119881

2

119888

+ 119868119871119877119881pv)

+ 127119871119877 (1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)))

sdot (50119862in119862out1198771198812

119888

)minus1

)

(17)

Only two eigenvalues determine the stability establishedinto the sliding surface One eigenvalue is zero due to theproperty of the sliding mode controller which reduces theorder of the system [24 25] This is explained because thesystem is maintained into the sliding surface and thereforethemovement is restricted into the plane (the sliding surface)These two eigenvalues must have a negative real part toguarantee stability into the sliding surface Evaluating (17) itis obtained that the system is stable if

(1198812

119888

+ 119868119871119877119881pv)

+127119871119877

50119862in(1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)) gt 0

(18)

This inequality is satisfied for the parameters of theimplemented system Table 1 shows the system parameters

Table 1 Parameters of the system

119860 = 90 119862in = 220 120583F 119881pv = 3545

119870 = 138 times 10minus23

119862o = 220 120583F 119868119871

= 358

119879 = 15∘C = 28815∘K 119871 = 200 120583H 119881119888

= 6175

119868119904

= 239 times 10minus4

119877 = 30Ω

119868sc = 41A119902 = 16 times 10

minus19

120582 = 1 (1000Wm2)

Bounding the Switching Frequency An ideal sliding modecontroller implies an infinite switching frequency and thenin a practical implementation this switching frequency mustbe bounded

There are different techniques to limit the switchingfrequency [20 26] hysteresis delay and holding at a constanttime the switch in ldquoonrdquo or ldquooffrdquo and finally also the use ofPWMmay be considered

This paper considers the employedmethod in [20] whichallows operating at a fixed switching frequency even underlarge variations

3 Simulation and Experimental Results

System functionality was evaluated not only numerically butalso experimentally so that the proposed idea was validated

The boost converter consists of an inductor of 200120583H aninput capacitor of 220120583F an output capacitor of 220120583F andthe load resistance of 30Ω

The system was evaluated under different operating con-ditions Initially the simulations are addressed and later onthe experimental results

31 Simulation at Steady State Figure 5 shows the simulationresults at steady state Figure 5(a) illustrates the operation atsteady state when the temperature is 15∘C the irradiance is120582 = 1 which is equivalent to 1000Wm2 so that the MPP islocated at a power of 12715W It is easily seen that the systemreaches that PV panel power

Figure 5(b) illustrates the slow loop behavior which isalways oscillating when theMPP is tracked It is also seen thatthe variation at the output is small so that this variation isalmost negligible at the PV panel power at steady state

The slow loop has a 05 s as the time interval betweenalgorithm iterations

It is important to notice that in Figure 5 (and alsoFigure 6) the inductor current for illustrating the powerdemanded for the PV panel is considered this was done forhaving a better appreciation in the figure However the actualpower of the PV panel does not have this ripple due to theinput capacitor 119862in

32 Simulation under Radiation Change Figure 6(a) showssystem operation under a sudden irradiation change initiallyirradiation value is 1000Wm2 and it changes to 600Wm2this represents a huge variation on the PV panel conditions

6 International Journal of Photoenergy

100

50

0

80

60

40

20

0

Time (ms)

150

100

pv lowast iL Ppv

10 15 20 25 30 35

c

(W)

(V)

(a)

850848846845842840

05 1 15Time (s)

pv lowast iL

Ppv

c

s ref

100

50

0

150

(W)

80604020

0

100

(V)

s ref

(b)

Figure 5 Simulation results (a) At steady state 15∘C 1000Wm2 (b) At steady state 15 1000Wm2 119904ref changes every 05 s

It is easily seen that the system takes around 36ms to trackthe new MPP

Since each decision is made every 05 s it would take amuch longer time if only a slow loop was considered Theproposed system offers a faster response than this obtainedwith iterative methods based on just algorithms

33 Simulation under Temperature Change Figure 6(b)shows the system operation under a sudden temperaturechange initially temperature value is 15∘C and it changesto 30∘C This represents a huge variation on the PV panelconditions It is easily seen that the system takes around 8msto track the newMPPThis is mainly due to the considerationof the temperature in the sliding surface

Again it would take a much longer time if only a slowloop was considered The proposed system offers a fasterresponse than this obtained with iterative methods based onjust algorithms

34 Experimental Results This proposal was examined atsteady state and under renewable source variation in orderto carry out a reliable validation Therefore this proposalof power point tracker algorithm was evaluated Actuallythis proposed sliding mode MPPT was connected to a PVemulator which allows changing its condition in a dynamicmanner

Results for the system at steady state are shown inFigure 7 where the operating conditions are 600Wm2From top to bottom the PV panel voltage the inductor119871 current and the drain-source voltage of themain switch are

shownThis last voltage not only illustrates the commutationof the main switch but also allows seeing the value of theoutput voltage at the high voltage level

Figure 8 shows changes to the conditions on the PVpanelInitially the system was evaluated under a change from 40to 60of irradiation which is illustrated in Figure 8(a) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shown Itis easily seen that the system takes around 8ms to track thenew MPP of the PV It is also seen how the output voltageincreases for demanding more power according to the newMPP condition

Finally the systemwas also evaluated under changes from80 to 40 of irradiation as illustrated in Figure 8(b) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shownThe system takes around 25ms to track the new MPP forthe PV It is easily seen that the output voltage decreases fordemanding less power according to the new MPP condition

4 Conclusion

This proposal introduces a new sliding mode based MPPTmethod It offers an accelerated convergence to themaximumpower point as a difference from the traditional methodThisis accomplished by choosing the switching surface whichconsiders voltage current and temperature simultaneouslyof the PV panel

Fast loop implementation which includes a sliding sur-face generated based on the PV panel characteristics offersa fast tracking response in spite of changes on weather

International Journal of Photoenergy 7

65

60

55

50

45

pv lowast iL

Ppv

c

100

020406080

120

140

(W)

(V)

01 015 02 025 03Time (s)

(a)

pv lowast iL

Ppv

c

100

50

0

150

(W)

80

60

40

20

0

100

(V)

01 015 02 025 03Time (s)

(b)

Figure 6 Simulation results (a) Irradiation change 1000Wm2 to 600Wm2 (b) Temperature change 15∘C to 30∘C

500V1500V4 200A Ω3

221A5920m40m131m

Duty cycle- RMS

4585 4576 3571 989643

Value Mean Min Max Stand dev

221 224

4400 120583s 250 MSs10k pts 490 VT 000000 s

TT

Tek

1

3

4

Figure 7 Experimental results at steady state condition

500V1500V3 200A Ω4

184ADuty cycle- RMS

353534

Value Mean low resolution Min Max Stand dev

184 184 184 000

Tek

1

TT

4

3

vpv

i pv

VDS

4100 kSs10k pts 204 A

100 ms000000 sT

(a)

500V1500V3 200A Ω4

210ADuty cycle- RMS

496434

Value Mean low resolution Min Max Stand dev

233 210 235 447 m

410k pts 164 A

100 ms000000 s

4

1

T

T

T

vpv

i pv

VDS

Tek

3100 kSs

(b)

Figure 8 Experimental results under variations (a) Positive step (b) Negative step

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

International Journal of Photoenergy 5

Making the linearization around the operating point nextis obtained

119889

119889119905119871= minus

254

119862in119871minus254120582119868

119904119902

119860119870119879119862in119890(119902Vpv119860119870119879)Vpv

119889

119889119905V119888= 1198601119871+ 1198602V119888+ 1198603Vpv

119889

119889119905Vpv = minus

1

119862in119871minus

120582119868119904119902

119860119870119879119862in119890(119902119881pv119860119870119879)Vpv

(15)

where

1198601= (

119881pv

119862out119881119888minus

254119871

119862out119881119888(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1))

+254119871

119862out119881119888(2119868119871

119862in))

1198602= minus

1

119877119862minus

119868119871119881pv

119862out1198812

119888

+254119868119871119871

119862out1198812

119888

(120582119868sc119862in

minus120582119868119904

119862in(119890(119902119881pv119860119870119879) minus 1) minus

119868119871

119862in)

1198603=

119868119871

119862out119881119888+

254119871119868119871120582119868119904119902

119860119870119879119862out119862in119881119888119890(119902119881pv119860119870119879)

(16)

System (15) has the following eigenvalues

1198980= 0

1198981= minus (

127119860119870119879 + 50120582119868119904119902119890(119902119881pv119860119870119879)

50119860119870119879119862in)

1198982= minus ((50119862in (119881

2

119888

+ 119868119871119877119881pv)

+ 127119871119877 (1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)))

sdot (50119862in119862out1198771198812

119888

)minus1

)

(17)

Only two eigenvalues determine the stability establishedinto the sliding surface One eigenvalue is zero due to theproperty of the sliding mode controller which reduces theorder of the system [24 25] This is explained because thesystem is maintained into the sliding surface and thereforethemovement is restricted into the plane (the sliding surface)These two eigenvalues must have a negative real part toguarantee stability into the sliding surface Evaluating (17) itis obtained that the system is stable if

(1198812

119888

+ 119868119871119877119881pv)

+127119871119877

50119862in(1198682

119871

+ 119868119871120582 (119890(119902119881pv119860119870119879)119868

119904minus 119868119904minus 119868sc)) gt 0

(18)

This inequality is satisfied for the parameters of theimplemented system Table 1 shows the system parameters

Table 1 Parameters of the system

119860 = 90 119862in = 220 120583F 119881pv = 3545

119870 = 138 times 10minus23

119862o = 220 120583F 119868119871

= 358

119879 = 15∘C = 28815∘K 119871 = 200 120583H 119881119888

= 6175

119868119904

= 239 times 10minus4

119877 = 30Ω

119868sc = 41A119902 = 16 times 10

minus19

120582 = 1 (1000Wm2)

Bounding the Switching Frequency An ideal sliding modecontroller implies an infinite switching frequency and thenin a practical implementation this switching frequency mustbe bounded

There are different techniques to limit the switchingfrequency [20 26] hysteresis delay and holding at a constanttime the switch in ldquoonrdquo or ldquooffrdquo and finally also the use ofPWMmay be considered

This paper considers the employedmethod in [20] whichallows operating at a fixed switching frequency even underlarge variations

3 Simulation and Experimental Results

System functionality was evaluated not only numerically butalso experimentally so that the proposed idea was validated

The boost converter consists of an inductor of 200120583H aninput capacitor of 220120583F an output capacitor of 220120583F andthe load resistance of 30Ω

The system was evaluated under different operating con-ditions Initially the simulations are addressed and later onthe experimental results

31 Simulation at Steady State Figure 5 shows the simulationresults at steady state Figure 5(a) illustrates the operation atsteady state when the temperature is 15∘C the irradiance is120582 = 1 which is equivalent to 1000Wm2 so that the MPP islocated at a power of 12715W It is easily seen that the systemreaches that PV panel power

Figure 5(b) illustrates the slow loop behavior which isalways oscillating when theMPP is tracked It is also seen thatthe variation at the output is small so that this variation isalmost negligible at the PV panel power at steady state

The slow loop has a 05 s as the time interval betweenalgorithm iterations

It is important to notice that in Figure 5 (and alsoFigure 6) the inductor current for illustrating the powerdemanded for the PV panel is considered this was done forhaving a better appreciation in the figure However the actualpower of the PV panel does not have this ripple due to theinput capacitor 119862in

32 Simulation under Radiation Change Figure 6(a) showssystem operation under a sudden irradiation change initiallyirradiation value is 1000Wm2 and it changes to 600Wm2this represents a huge variation on the PV panel conditions

6 International Journal of Photoenergy

100

50

0

80

60

40

20

0

Time (ms)

150

100

pv lowast iL Ppv

10 15 20 25 30 35

c

(W)

(V)

(a)

850848846845842840

05 1 15Time (s)

pv lowast iL

Ppv

c

s ref

100

50

0

150

(W)

80604020

0

100

(V)

s ref

(b)

Figure 5 Simulation results (a) At steady state 15∘C 1000Wm2 (b) At steady state 15 1000Wm2 119904ref changes every 05 s

It is easily seen that the system takes around 36ms to trackthe new MPP

Since each decision is made every 05 s it would take amuch longer time if only a slow loop was considered Theproposed system offers a faster response than this obtainedwith iterative methods based on just algorithms

33 Simulation under Temperature Change Figure 6(b)shows the system operation under a sudden temperaturechange initially temperature value is 15∘C and it changesto 30∘C This represents a huge variation on the PV panelconditions It is easily seen that the system takes around 8msto track the newMPPThis is mainly due to the considerationof the temperature in the sliding surface

Again it would take a much longer time if only a slowloop was considered The proposed system offers a fasterresponse than this obtained with iterative methods based onjust algorithms

34 Experimental Results This proposal was examined atsteady state and under renewable source variation in orderto carry out a reliable validation Therefore this proposalof power point tracker algorithm was evaluated Actuallythis proposed sliding mode MPPT was connected to a PVemulator which allows changing its condition in a dynamicmanner

Results for the system at steady state are shown inFigure 7 where the operating conditions are 600Wm2From top to bottom the PV panel voltage the inductor119871 current and the drain-source voltage of themain switch are

shownThis last voltage not only illustrates the commutationof the main switch but also allows seeing the value of theoutput voltage at the high voltage level

Figure 8 shows changes to the conditions on the PVpanelInitially the system was evaluated under a change from 40to 60of irradiation which is illustrated in Figure 8(a) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shown Itis easily seen that the system takes around 8ms to track thenew MPP of the PV It is also seen how the output voltageincreases for demanding more power according to the newMPP condition

Finally the systemwas also evaluated under changes from80 to 40 of irradiation as illustrated in Figure 8(b) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shownThe system takes around 25ms to track the new MPP forthe PV It is easily seen that the output voltage decreases fordemanding less power according to the new MPP condition

4 Conclusion

This proposal introduces a new sliding mode based MPPTmethod It offers an accelerated convergence to themaximumpower point as a difference from the traditional methodThisis accomplished by choosing the switching surface whichconsiders voltage current and temperature simultaneouslyof the PV panel

Fast loop implementation which includes a sliding sur-face generated based on the PV panel characteristics offersa fast tracking response in spite of changes on weather

International Journal of Photoenergy 7

65

60

55

50

45

pv lowast iL

Ppv

c

100

020406080

120

140

(W)

(V)

01 015 02 025 03Time (s)

(a)

pv lowast iL

Ppv

c

100

50

0

150

(W)

80

60

40

20

0

100

(V)

01 015 02 025 03Time (s)

(b)

Figure 6 Simulation results (a) Irradiation change 1000Wm2 to 600Wm2 (b) Temperature change 15∘C to 30∘C

500V1500V4 200A Ω3

221A5920m40m131m

Duty cycle- RMS

4585 4576 3571 989643

Value Mean Min Max Stand dev

221 224

4400 120583s 250 MSs10k pts 490 VT 000000 s

TT

Tek

1

3

4

Figure 7 Experimental results at steady state condition

500V1500V3 200A Ω4

184ADuty cycle- RMS

353534

Value Mean low resolution Min Max Stand dev

184 184 184 000

Tek

1

TT

4

3

vpv

i pv

VDS

4100 kSs10k pts 204 A

100 ms000000 sT

(a)

500V1500V3 200A Ω4

210ADuty cycle- RMS

496434

Value Mean low resolution Min Max Stand dev

233 210 235 447 m

410k pts 164 A

100 ms000000 s

4

1

T

T

T

vpv

i pv

VDS

Tek

3100 kSs

(b)

Figure 8 Experimental results under variations (a) Positive step (b) Negative step

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

6 International Journal of Photoenergy

100

50

0

80

60

40

20

0

Time (ms)

150

100

pv lowast iL Ppv

10 15 20 25 30 35

c

(W)

(V)

(a)

850848846845842840

05 1 15Time (s)

pv lowast iL

Ppv

c

s ref

100

50

0

150

(W)

80604020

0

100

(V)

s ref

(b)

Figure 5 Simulation results (a) At steady state 15∘C 1000Wm2 (b) At steady state 15 1000Wm2 119904ref changes every 05 s

It is easily seen that the system takes around 36ms to trackthe new MPP

Since each decision is made every 05 s it would take amuch longer time if only a slow loop was considered Theproposed system offers a faster response than this obtainedwith iterative methods based on just algorithms

33 Simulation under Temperature Change Figure 6(b)shows the system operation under a sudden temperaturechange initially temperature value is 15∘C and it changesto 30∘C This represents a huge variation on the PV panelconditions It is easily seen that the system takes around 8msto track the newMPPThis is mainly due to the considerationof the temperature in the sliding surface

Again it would take a much longer time if only a slowloop was considered The proposed system offers a fasterresponse than this obtained with iterative methods based onjust algorithms

34 Experimental Results This proposal was examined atsteady state and under renewable source variation in orderto carry out a reliable validation Therefore this proposalof power point tracker algorithm was evaluated Actuallythis proposed sliding mode MPPT was connected to a PVemulator which allows changing its condition in a dynamicmanner

Results for the system at steady state are shown inFigure 7 where the operating conditions are 600Wm2From top to bottom the PV panel voltage the inductor119871 current and the drain-source voltage of themain switch are

shownThis last voltage not only illustrates the commutationof the main switch but also allows seeing the value of theoutput voltage at the high voltage level

Figure 8 shows changes to the conditions on the PVpanelInitially the system was evaluated under a change from 40to 60of irradiation which is illustrated in Figure 8(a) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shown Itis easily seen that the system takes around 8ms to track thenew MPP of the PV It is also seen how the output voltageincreases for demanding more power according to the newMPP condition

Finally the systemwas also evaluated under changes from80 to 40 of irradiation as illustrated in Figure 8(b) Fromtop to bottom the PV panel voltage the inductor 119871 currentand the drain-source voltage of the main switch are shownThe system takes around 25ms to track the new MPP forthe PV It is easily seen that the output voltage decreases fordemanding less power according to the new MPP condition

4 Conclusion

This proposal introduces a new sliding mode based MPPTmethod It offers an accelerated convergence to themaximumpower point as a difference from the traditional methodThisis accomplished by choosing the switching surface whichconsiders voltage current and temperature simultaneouslyof the PV panel

Fast loop implementation which includes a sliding sur-face generated based on the PV panel characteristics offersa fast tracking response in spite of changes on weather

International Journal of Photoenergy 7

65

60

55

50

45

pv lowast iL

Ppv

c

100

020406080

120

140

(W)

(V)

01 015 02 025 03Time (s)

(a)

pv lowast iL

Ppv

c

100

50

0

150

(W)

80

60

40

20

0

100

(V)

01 015 02 025 03Time (s)

(b)

Figure 6 Simulation results (a) Irradiation change 1000Wm2 to 600Wm2 (b) Temperature change 15∘C to 30∘C

500V1500V4 200A Ω3

221A5920m40m131m

Duty cycle- RMS

4585 4576 3571 989643

Value Mean Min Max Stand dev

221 224

4400 120583s 250 MSs10k pts 490 VT 000000 s

TT

Tek

1

3

4

Figure 7 Experimental results at steady state condition

500V1500V3 200A Ω4

184ADuty cycle- RMS

353534

Value Mean low resolution Min Max Stand dev

184 184 184 000

Tek

1

TT

4

3

vpv

i pv

VDS

4100 kSs10k pts 204 A

100 ms000000 sT

(a)

500V1500V3 200A Ω4

210ADuty cycle- RMS

496434

Value Mean low resolution Min Max Stand dev

233 210 235 447 m

410k pts 164 A

100 ms000000 s

4

1

T

T

T

vpv

i pv

VDS

Tek

3100 kSs

(b)

Figure 8 Experimental results under variations (a) Positive step (b) Negative step

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

International Journal of Photoenergy 7

65

60

55

50

45

pv lowast iL

Ppv

c

100

020406080

120

140

(W)

(V)

01 015 02 025 03Time (s)

(a)

pv lowast iL

Ppv

c

100

50

0

150

(W)

80

60

40

20

0

100

(V)

01 015 02 025 03Time (s)

(b)

Figure 6 Simulation results (a) Irradiation change 1000Wm2 to 600Wm2 (b) Temperature change 15∘C to 30∘C

500V1500V4 200A Ω3

221A5920m40m131m

Duty cycle- RMS

4585 4576 3571 989643

Value Mean Min Max Stand dev

221 224

4400 120583s 250 MSs10k pts 490 VT 000000 s

TT

Tek

1

3

4

Figure 7 Experimental results at steady state condition

500V1500V3 200A Ω4

184ADuty cycle- RMS

353534

Value Mean low resolution Min Max Stand dev

184 184 184 000

Tek

1

TT

4

3

vpv

i pv

VDS

4100 kSs10k pts 204 A

100 ms000000 sT

(a)

500V1500V3 200A Ω4

210ADuty cycle- RMS

496434

Value Mean low resolution Min Max Stand dev

233 210 235 447 m

410k pts 164 A

100 ms000000 s

4

1

T

T

T

vpv

i pv

VDS

Tek

3100 kSs

(b)

Figure 8 Experimental results under variations (a) Positive step (b) Negative step

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

8 International Journal of Photoenergy

conditions A good steady state performance is also obtaineddue to slow loop implementation which is based on atraditional ldquoperturb and observerdquo method

Operation and analysis for the converter were givenSimulation and experimental results were also shown

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Maffezzoni and D DrsquoAmore ldquoCompact electrothermalmacromodeling of photovoltaicmodulesrdquo IEEETransactions onCircuits and Systems II Express Briefs vol 56 no 2 pp 162ndash1662009

[2] H R Muhammad and L Char ldquoSolar power conversionrdquo inPower Electronics Handbook vol 26 chapter 26 pp 661ndash672Academic Press 2nd edition 2007

[3] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings GenerationTransmission and Distribution vol 142 no 1 pp 59ndash64 1995

[4] Z Zinger and A Braunstein ldquoDynamic matching of a Solar-Electrical (photovoltaic) system an estimation of the minimumrequirements on the matching systemrdquo IEEE transactions onpower apparatus and systems vol 100 no 3 pp 1189ndash1192 1981

[5] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[6] C-X Liu and L-Q Liu ldquoResearch into maximum powerpoint tracking method of photovoltaic generate systemrdquo inProceedings of the International Workshop on Intelligent Systemsand Applications (ISA rsquo09) May 2009

[7] D Shmilovitz ldquoOn the control of photovoltaic maximumpower point tracker via output parametersrdquo Electric PowerApplications IEE Proceedings vol 152 no 2 pp 239ndash248 2005

[8] S Jain and V Agarwal ldquoA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systemsrdquoIEEE Power Electronics Letters vol 2 no 1 pp 16ndash19 2004

[9] L Gao R A Dougal S Liu and A P Iotova ldquoParallel-connected solar PV system to address partial and rapidlyfluctuating shadow conditionsrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1548ndash1556 2009

[10] E Bianconi J Calvente R Giral et al ldquoA fast current-based MPPT technique employing sliding mode controlrdquo IEEETransactions on Industrial Electronics vol 60 no 3 pp 1168ndash1178 2013

[11] I-S Kim ldquoRobust maximum power point tracker using slidingmode controller for the three-phase grid-connected photo-voltaic systemrdquo Solar Energy vol 81 no 3 pp 405ndash414 2007

[12] C-C Chu and C-L Chen ldquoRobust maximum power pointtracking method for photovoltaic cells a sliding mode controlapproachrdquo Solar Energy vol 83 no 8 pp 1370ndash1378 2009

[13] V V R Scarpa G Spiazzi and S Buso ldquoLow complexity MPPTtechnique exploiting the effect of the PV cell series resistancerdquoIEEE Transactions on Industrial Electronics vol 56 no 5 pp1531ndash1538 2008

[14] M Sokolov and D Shmilovitz ldquoA modified MPPT schemefor accelerated convergencerdquo IEEE Transactions on EnergyConversion vol 23 no 4 pp 1105ndash1107 2008

[15] N Kasa T Iida and L Chen ldquoFlyback inverter controlled bysensorless current MPPT for photovoltaic power systemrdquo IEEETransactions on Industrial Electronics vol 52 no 4 pp 1145ndash1152 2005

[16] J Li and H Wang ldquoMaximum power point tracking of photo-voltaic generation based on the optimal gradient methodrdquo inProceedings of the Asia-Pacific Power and Energy EngineeringConference (APPEEC rsquo09) pp 1ndash4 Wuhan China March 2009

[17] V Mummadi ldquoImproved maximum power point trackingalgorithm for photovoltaic sourcesrdquo in Proceedings of the IEEEInternational Conference on Sustainable Energy Technologies(ICSET rsquo08) pp 301ndash305 Singapore November 2008

[18] Y Levron and D Shmilovitz ldquoMaximum power point trackingemploying sliding mode controlrdquo IEEE Transactions on Circuitsand Systems vol 60 no 3 pp 724ndash732 2013

[19] G Liu P Wang W Wang and Q Wang ldquoMPPT algorithmunder partial shading conditionsrdquo in Electrical InformationEngineering and Mechatronics vol 138 of Lecture Notes inComputer Science pp 91ndash98 Springer Berlin Germany 2011

[20] T Siew-Chon Y M Lai C K Tse and M K H CheungldquoA fixed-frequency pulsewidthmodulation based quasi-sliding-mode controller for buck convertersrdquo IEEE Transactions onPower Electronics vol 20 no 6 pp 1379ndash1392 2005

[21] G Spiazzi P Mattavelli L Rossetto and L Malesani ldquoApplica-tion of sliding mode control to switched mode power suppliesrdquoJournal of Circuits Systems and Computers (JCSC) vol 5 no 3pp 337ndash354 1995

[22] L Martinez-Salamero A Cid-Pastor R Giral J Calvente andV Utkin ldquoWhy is sliding mode control methodology neededfor power convertersrdquo in Proceedings of the 14th InternationalPower Electronics and Motion Control Conference (EPE-PEMCrsquo10) pp S9-25ndashS9-31 September 2010

[23] R A DeCarlo S H Zak and G P Matthews ldquoVariablestructure control of nonlinear multivariable systems a tutorialrdquoProceedings of the IEEE vol 76 no 3 pp 212ndash232 1988

[24] J Y HungWGao and J CHung ldquoVariable structure control asurveyrdquo IEEE Transactions on Industrial Electronics vol 40 no1 pp 2ndash22 1993

[25] V I Utkin Sliding Modes and Their Application in VariableStructure Systems MIR Publishers Moscow Russia 1974

[26] B J Cardoso A F Moreira B R Menezes and P C CortizoldquoAnalysis of switching frequency reduction methods applied tosliding mode controlled DC-DC convertersrdquo in Proceedings ofthe 7th Annual Applied Power Electronics Conference and Expo-sition (APEC rsquo92) pp 403ndash410 Boston Mass USA February1992

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of