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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)...