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  • Research ArticleMaximum Power Point Tracking Based on Sliding Mode Control

    Nimrod Vzquez,1 Yuz Azaf,2 Ilse Cervantes,2 Esl Vzquez,3 and Claudia Hernndez1

    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; n.vazquez@ieee.org

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

    Academic Editor: Emilio Bueno

    Copyright 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 irradiation,temperature, 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 process.In 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 [119]. However,the MPP locus varies over a wide range, depending on PVarray, temperature, and irradiation intensity [13].

    A tracking of the maximum power point (MPPT) guar-antees the operation of the PV generator at the MPPunder changing atmospheric conditions.Although 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 perturb and observe (P&O) 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 state;however, 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[519], 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 P&Oalgorithm.The sliding surface is based on a voltage controller

    Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2015, Article ID 380684, 8 pageshttp://dx.doi.org/10.1155/2015/380684

  • 2 International Journal of Photoenergy

    for generating the input current reference. Since theseschemes employ P&Oalgorithm,which 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 found,where its scheme eliminates thesteady state variation and reduces the tradeoff engagementbetween precision and dynamic response.The sliding surfaceis based on the classic equation of P&O 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 modules.Therefore, a linear controller, which reduces the tradeoffengagement between precision and dynamic response, couldbe designed in order to operate the PV system near the MPP.An 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 temperature.TheMPP 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 P&O method is considered toguarantee a low error at steady state.

    This proposal let us have a fast dynamic response,simple 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 algorithm.The 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 modeling,operation, 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 MPPT:a fast and a slow loop. Figure 1 shows the block diagram.It 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.

    2.1. 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 15C. 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 30C, 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

    pv 2.54Vpv 0.455 + ref = 0, (1)

    where pv is the panel current, Vpv is the panel voltage, is theenvironmental temperature, and ref is a displacement term =93.63.

    This plane is considered as sliding surface for the pro-posed controller. According to the theory of sliding modes,the 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

    54.5

    43.5

    32.5

    21.5

    10.5

    i pv

    vpv

    T = 15C

    100% rad

    40% rad

    60% rad

    80% rad35.45V3.58A127.14W35.28V2.88A101.66W34.91V2.17A

    76.08 W

    50.60 W34.12V1.48A

    (a) At 15C

    54.5

    43.5

    32.5

    21.5

    10.5

    i pv

    0 45403530252015105vpv

    T = 30C

    100% rad

    40% rad

    60% rad

    80% rad33.16V3.58A119.07W32.98V2.89A

    32.61V2.19A

    31.84V1.50A

    71.50 W

    47.78 W

    95.34 W

    (b) At 30C

    Figure 2: PVG characteristics under different irradiance and temperature conditions.

    Voltagesense

    Currentsense

    PVLoad

    Gate driver

    A/D

    MicrocontrollerMPPT D/A

    Switchingfrequency

    limiter

    (ipv , pv , T)

    ipv bpv cT + sref

    S

    T

    Cin Cout

    ipvpv

    sref

    Figure 3: Power stage and proposed controller.

    2.2. 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 perturband observe MPPT was employed. The parameter ref isconsidered as the output in order to follow the MPP andreduce the error at steady state.

    2.3. Control Design and Implementation. The power stageconsidered in this paper is a traditional DC/DC 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

    = 2.54Vpv 0.455 + ref = 0,

    ={

    {

    {

    1, if < 0,

    0, if < 0,

    (2)

    where is the sliding surface and is the control law.

    OffOff

    New MPPT

    OnRadiationchange

    > 0 < 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 ref parameter,which 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 switch.These are when it is turned on andoff. A simplified model for the PV panel is also considered[19]:

    pv = sc ((Vpv/) 1) , (3)

    where is the ideality factor of the diode, is the Boltzmannconstant, is the electron charge, is the percentage ofirradiance (1 = 100%), sc is the short circuit current of thePV panel,

    is the saturation current of the diode, 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 on are

    =

    Vpv,

    V=

    V

    out,

    Vpv =

    pv

    in

    in,

    (4)

    where is the current of the inductor, V

    is the voltage of the

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

    The equations when the switch is off are

    =

    Vpv

    V

    ,

    V=

    out

    V

    out,

    Vpv =

    pv

    in

    in.

    (5)

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

    =

    Vpv

    V

    (1 ) ,

    V=

    out(1 )

    V

    out,

    Vpv =

    scin

    in((Vpv/) 1)

    in,

    (6)

    where is the control law.

    Existence of the Sliding Mode. Existence of sliding mode isdemonstrated by the next inequality, which must be satisfied[2125]:

    < 0. (7)

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

    =

    2.54

    Vpv. (8)

    Substituting (6) in (8) lets us obtain

    =

    Vpv

    V

    (1 )

    2.54 (scin

    in((Vpv/) 1)

    in) .

    (9)

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

    (a) If > 0 then < 0 and = 0. The followinginequality is obtained:

    Vpv

    V

    2.54 (

    scin

    in((Vpv/) 1)

    in) < 0.

    (10)

    (b) If < 0 then > 0 and = 1. The followinginequality is obtained:

    Vpv

    2.54 (scin

    in((Vpv/) 1)

    in) > 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 DC/DC boostconverter (V

    is 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:

    Vpv

    V

    (1 eq)

    2.54 (scin

    in((Vpv/) 1)

    in) = 0.

    (12)

    Developing the equivalent control from (12) is obtainedas

    eq = 1 VpvV

    +2.54

    V

    (scin

    in((Vpv/) 1)

    in) .

    (13)

    Substituting (13) in (6) is obtained:

    = 2.54 (

    scin

    in((Vpv/) 1)

    in) ,

    V=

    Vpv

    outV2.54

    outV

    (scin

    in((Vpv/) 1)

    in)

    V

    out,

    Vpv =

    scin

    in((Vpv/) 1)

    in.

    (14)

  • International Journal of Photoenergy 5

    Making the linearization around the operating point nextis obtained:

    =

    2.54

    in2.54

    in(Vpv/)Vpv,

    V= 1+ 2V+ 3Vpv,

    Vpv =

    1

    in

    in(pv/)Vpv,

    (15)

    where

    1= (

    pv

    out

    2.54

    out(scin

    in((pv/) 1))

    +2.54

    out(2

    in)) ,

    2=

    1

    pv

    out2

    +2.54

    out2

    (scin

    in((pv/) 1)

    in) ,

    3=

    out+

    2.54

    outin(pv/).

    (16)

    System (15) has the following eigenvalues:

    0= 0

    1= (

    127 + 50(pv/)

    50in) ,

    2= ((50in (

    2

    + pv)

    + 127 (2

    + ((pv/)

    sc)))

    (50inout2

    )1

    ) .

    (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

    (2

    + pv)

    +127

    50in(2

    + ((pv/)

    sc)) > 0.

    (18)

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

    Table 1: Parameters of the system.

    = 90 in = 220 F pv = 35.45 = 1.38 10

    23

    o = 220 F = 3.58 = 15C = 288.15K = 200 H

    = 61.75

    = 2.39 104

    = 30

    sc = 4.1A = 1.6 10

    19

    = 1 (1000W/m2)

    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 on or off, 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 200H, aninput capacitor of 220F, an output capacitor of 220F, andthe load resistance of 30.

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

    3.1. Simulation at Steady State. Figure 5 shows the simulationresults at steady state. Figure 5(a) illustrates the operation atsteady state when the temperature is 15C; the irradiance is = 1, which is equivalent to 1000W/m2, so that the MPP islocated at a power of 127.15W. 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 0.5 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 in.

    3.2. Simulation under Radiation Change. Figure 6(a) showssystem operation under a sudden irradiation change; initiallyirradiation value is 1000W/m2, and it changes to 600W/m2,this 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 iL Ppv

    10 15 20 25 30 35

    c

    (W)

    (V)

    (a)

    85.084.884.684.584.284.0

    0.5 1 1.5Time (s)

    pv 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 15C, 1000W/m2. (b) At steady state 15, 1000W/m2; ref changes every 0.5 s.

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

    Since each decision is made every 0.5 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.

    3.3. Simulation under Temperature Change. Figure 6(b)shows the system operation under a sudden temperaturechange; initially temperature value is 15C and it changesto 30C. This represents a huge variation on the PV panelconditions. It is easily seen that the system takes around 8msto track the newMPP.This 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.

    3.4. 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. Actually,this 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 600W/m2.From top to bottom, the PV panel voltage, the inductor current, and the drain-source voltage of themain switch are

    shown.This 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 PVpanel.Initially, the system was evaluated under a change from 40%to 60%of irradiation, which is illustrated in Figure 8(a). Fromtop to bottom, the PV panel voltage, the inductor current,and 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 current,and the drain-source voltage of the main switch are shown.The 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 method.Thisis 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 iL

    Ppv

    c

    100

    020406080

    120

    140

    (W)

    (V)

    0.1 0.15 0.2 0.25 0.3Time (s)

    (a)

    pv iL

    Ppv

    c

    100

    50

    0

    150

    (W)

    80

    60

    40

    20

    0

    100

    (V)

    0.1 0.15 0.2 0.25 0.3Time (s)

    (b)

    Figure 6: Simulation results. (a) Irradiation change: 1000W/m2 to 600W/m2. (b) Temperature change: 15C to 30C.

    50.0V150.0V4 2.00A 3

    2.21A592.0m40m131m

    Duty cycle- RMS

    45.85% 45.76 3.571 98.9643

    Value Mean Min Max Stand. dev.

    2.21 2.24

    440.0 s 25.0 MS/s10k pts. 49.0 VT 0.00000 s

    TT

    Tek

    1

    3

    4

    Figure 7: Experimental results at steady state condition.

    50.0V150.0V3 2.00A 4

    1.84ADuty cycle- RMS

    35.35%34

    Value Mean low resolution Min Max Stand. dev.

    1.84 1.84 1.84 0.00

    Tek

    1

    TT

    4

    3

    vpv

    i pv

    VDS

    4100 kS/s10k pts. 2.04 A

    10.0 ms0.00000 sT

    (a)

    50.0V150.0V3 2.00A 4

    2.10ADuty cycle- RMS

    49.64%34

    Value Mean low resolution Min Max Stand. dev.

    2.33 2.10 2.35 44.7 m

    410k pts. 1.64 A

    10.0 ms0.00000 s

    4

    1

    T

    T

    T

    vpv

    i pv

    VDS

    Tek

    3100 kS/s

    (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 perturb and observe method.

    Operation and analysis for the converter were given.Simulation and experimental results were also shown.

    Conflict of Interests

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

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