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Solar Energy 85 (2011) 2965–2976

A hybrid maximum power point tracking methodfor photovoltaic systems

Mohammad H. Moradi ⇑, Ali Reza Reisi

Department of Electrical Engineering, Faculty of Engineering, Bu Ali Sina University, Hamedan, Iran

Received 23 May 2011; received in revised form 21 August 2011; accepted 25 August 2011Available online 14 September 2011

Communicated by: Associate Editor Nicola Romeo

Abstract

Solar panels exhibit non-linear current–voltage characteristics producing maximum power at only one particular operating point. The max-imum power point changes with temperature and light intensity variations. Different methods have been introduced for tracking the maximumpower point based on offline and online methods. In this paper a new method is presented to improve the performance of maximum powerpoint tracking in solar panels. The proposed algorithm is a combination of two loops, set point calculation and fine tuning loops. First the setpoint loop approximates the maximum power using offline calculation of the open circuit voltage. The exact amount of the maximum powerwill, then, be tracked by the fine tuning loop which is based on perturbation and observation (P&O) method. The proposed method is sim-ulated in Matlab/Simulink environment and experimentally verified using a laboratory prototype. In maximum power point tracking, theeffects of frequency variation and disturbance amplitude on dynamic response and steady state performance are examined. Simulation andexperimental results are compared with other methods and the effectiveness of the proposed method is evaluated.� 2011 Elsevier Ltd. All rights reserved.

Keywords: MPPT; Photovoltaic; Perturbation and observation; Open circuit voltage

1. Introduction

In the recent decade there has been a major increase inthe use of renewable sources of energy due to the drastic risein the price of fossil fuels and the environmental pollutionassociated with the use of atomic and fossil fuels (Wuet al., 1998; De Broe et al., 1999). Among renewable sourcesof energy, solar energy is a suitable choice for a variety ofapplications mainly due to its capability to be directly con-verted to electrical energy using solar cells. The outputpower of solar cells depends on the ambient temperatureand the radiation intensity. There is a single maximumpower operating point the tracking of which is very

0038-092X/$ - see front matter � 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2011.08.036

⇑ Corresponding author. Tel.: +98 811 8220954; fax: +98 811 2511176.E-mail addresses: Mh_moradi@yahoo.co.uk (M.H. Moradi), reisi.

alireza@gmail.com (A.R. Reisi).

important in order to ensure the efficient operation of thesolar cell array (Fig. 1).

Maximum power point tracking (MPPT) is one of themost important issues in solar cell systems. There havebeen numerous methods proposed for tackling this issue(Esram and Chapman, 2007). These methods differ in termsof complexity, speed of response, amount of investment,the number and types of sensors required and the hardwareimplementation.

Different MPPT methods can be categorized as offlinemethods, which are dependent on solar cell models, andonline methods which are model-free. In (Esram andChapman, 2007) different offline and online methods havebeen reviewed.

Offline methods generally use the open circuit voltage,and short circuit current of the solar panel as initial param-eters as well as the ambient parameters such as temperatureand radiation intensity to determine the control signal

Fig. 1. I–V and P–V characteristics of solar cell.

Fig. 2. Perturbation and observation algorithm.

2966 M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976

necessary to drive the solar cell to its MPP. During opera-tion, this control signal is constant if ambient parameterscan be regarded as fixed and there are no attempts to reg-ulate the amount of output power of the solar cell.

The open circuit method (Schoeman and Van Wyk,1982; Enslin et al., 1997) is one of the simplest offline meth-ods, which uses an approximately linear relationshipbetween the open circuit voltage (Voc) and the maximumpower point voltage (VMPP) under different environmentalconditions as described by the following equation:

V MPP � kV oc ð1Þ

where K is a constant usually between 0.7 and 0.8 which de-pends on the solar cell characteristics. This constant isempirically derived based on measurement of the Voc andVMPP under different environmental circumstances. Basedon Eq. (1), in the open circuit method VMPP is approxi-mated by measuring the Voc. In order to measure the Voc,however, the load seen by the solar cell has to be shed.In spite of the relative ease in implementation and lowcosts, this method suffers from two major disadvantages.First, the MPP may not be achieved accurately. Second,measurement Voc requires periodic shedding of the load,which may interfere with circuit operation.

The other offline method is the short circuit currentmethod (Noguchi et al., 2002) which is relatively similarto the open circuit voltage method. There is also anapproximately linear relationship between the short circuitcurrent of the solar panel (Isc) and the maximum powerpoint current (IMPP), which can be described by the follow-ing equation:

IMPP � KIsc ð2Þ

where K is a coefficient between 0.8 and 0.9. Similar to theopen circuit voltage method, the load should be shed inorder to determine the Isc. While the short circuit currentmethod is more accurate and efficient than the open circuitvoltage method (Noguchi et al., 2002), due to practical is-sues associated with measuring the Isc, its implementationcosts are higher.

Using Artificial Neural Networks (ANN) Hiyama et al.(1995a,b) have proposed an offline method. In this method,Voc serves as the only input to the ANN originating from

the solar panel. The output of the ANN is a signal whichcan be compared with the instantaneous voltage in orderto generate the control signal needed to drive the solarpanel to MPP using a PI controller.

In online methods, usually the instantaneous variables(voltage and current) are used to generate control signals.Hence, unlike offline methods, the control signal is not con-stant and even under steady state conditions the outputoscillates around the optimum value. The perturbationand observation (P&O) method (Hua et al., 1998; Chenet al., 2004) the Ripple Correlation Control (RCC) (Huynhand Cho, 1996) and Incremental Conductance (Husseinet al., 1995) are amongst online MPPT methods.

As one of the simplest online methods, the P&O methodcan be implemented by applying a disturbance to the refer-ence voltage (Hua et al., 1998) or the reference current sig-nal (Esram et al., 2006) of the solar panel. This method usesan algorithm known as “hill climbing”, which is depicted inFig. 2 where X is the reference signal. In this algorithm, bysetting X = V, the instantaneous voltage of the solar panelfollows the maximum power point voltage according to apredetermined voltage and power values. The solar panelvoltage is changed by applying small and constant changes(C) as disturbance thereby changing the system operatingpoint. In this case the voltage variation (DV) follows C,but the power variations (DP) can either follow or opposeC. That is DP can be either positive or negative. If DP ispositive, power will approach MPP, so that the applied var-iation in current must be in the same direction in the follow-ing stage. A negative DP, on the other hand, indicates thatpower has moved away from MPP, so the variations mustbe applied in the reverse direction as compared with the pre-vious stage in order for power to approach MPP. In thisalgorithm the amplitude of the disturbances applied to thesystem, is the main factor determining the amplitude ofoscillations and hence the convergence rate to the final

M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976 2967

response. The larger the disturbance the faster thealgorithm will find the maximum value. Nevertheless a lar-ger disturbance will lead to a higher value of oscillationamplitude. In other words, in this algorithm there is atrade-off between the rate of response and the amount of

oscillations (stability?) under steady state conditions. Toovercome this trade-off, disturbances of varying amplitudecan be applied. The disturbance amplitude can be deter-mined according to power variations based on the previ-ously applied disturbance. Therefore, small disturbanceamplitude is selected when power is close to MPP and largeramplitude is selected when power is far from MMP. Themagnitude of the disturbance is given by the slope of thepower–current curve (Chen et al., 2004) as indicated inthe following equation:

I ½k þ 1� ¼ I ½k� þMDP k

DIkð3Þ

where DP k and DIk denote power and current variationsrespectively, M is an adjustment factor, and I[k] andI[k + 1] represent values of current before and after theapplication of the kth disturbance. The slope of thepower–current curve takes on a value of zero at the maxi-mum power point but increases as power departs from theMPP.

As indicated in Eq. (4), a similar relationship holds, ifthe reference signal is chosen as the solar panel voltage,

V ½k þ 1� ¼ V ½k� þMDP k

DV kð4Þ

In this case, the amount of disturbance is selected pro-portional to the slope of power–voltage curve.

The use of variable disturbance amplitude overcomesthe trade-off between the response speed and the steadystate oscillations, but if the system operating point changesquickly, the algorithm will be prone to errors (Zhi-danet al., 2008; Hua, 2003). To address this problem, differentmethods have been presented. For example a new condi-tion has been added to P&O method in Hua and Lin(2003), Yu et al. (2004) and the P&O method have beencombined with the open circuit voltage method in Taftichtet al. (2008).

In this paper, a hybrid approach (offline–online) is pre-sented to track the maximum power point, MPP, and it isshown that this method is able to track the maximumpower very effectively in spite of its simplicity. This articleconsists of following sections. The solar panel model is pro-vided in Section 2, and in Section 3, the photovoltaic sys-tem for tracking maximum power is introduced. InSection 4 our method for tracking the maximum power ispresented and finally in Section 5 simulation results arediscussed.

2. Solar panel model

The physical structure of a solar cell is similar to that of adiode in which the p–n junction is subjected to sun

exposure. The basic semi-conductor theory is captured inthe following equations:I ¼ Ipv;cell � Id ð5Þ

Id ¼ Io;cell expqV

aKT

� �� 1

� �ð6Þ

where Ipv,cell is current produced by the incident light, Id is thediode current modeled by the equation for a Shockley diode,I o,cell represents the saturated reverse current or leakagecurrent, q is the charge of an electron, K is the Boltzmannconstant, and T represents the absolute temperature of p–njunction and “a” is a constant known as the diode idealityfactor.

Eq. (5) can be modified to obtain the current–voltagecharacteristics of a photovoltaic cell employed in the solarpanel by adding some parameters as given in Eq. (7)(Villalva et al., 2009).

I ¼ Ipv � Io expV þ RsI

aV t

� �� 1

� �� V þ RsI

Rpð7Þ

where Ipv is the photovoltaic current, Io is the saturatedreverse current, V t ¼ NsKT

q represents the thermal voltagewith Ns indicating the number of series cells, and Rs andRp are the series and parallel equivalent resistances associ-ated with the solar panel respectively. Ipv exhibits a linearrelationship with light intensity and also varies with temper-ature. Io is also temperature-dependent. The equivalentcircuit of a solar panel is shown in Fig. 4. Values of Ipv andIo are given by the following equations:

Ipv ¼ ðIpv;n þ KIDT Þ GGn

ð8Þ

Io ¼ Io;nTT n

� �3

expqEg

aK1

T n� 1

T

� �� �ð9Þ

where Io,n is the saturated reverse current, Ipv,n is the photo-voltaic current under standard conditions (Tn = 25 �C andGn = 1000 W/m2), KI is the temperature coefficient of theshort-circuit current, DT ¼ T � T n is the deviation fromstandard temperature, G represents the light intensity andEg is the band gap energy of the semiconductor in units ofelectron-volts. The saturated reverse current, Io,n, is givenby the following equation:

Io;n ¼Isc;n

exp V oc;n

aV t

� � ð10Þ

in which Isc,n and Voc,n, are the short circuit current and opencircuit voltage under standard conditions respectively, “a” isa constant between 1 and 1/5 is dependent on the otherparameters of model (Carrero et al., 2007). Appropriateselection of “a” increases the accuracy of the model. Insteadof Eq. (8), the following equation can be used in order to in-crease the accuracy of the solar panel model(Villalva et al., 2009).

Io ¼Isc;n þ KIDT

expðV oc;n þ KvDT Þ=aV t � 1ð11Þ

2968 M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976

where Kv is the temperature coefficient of the open circuitvoltage. The open circuit voltage and short circuit currentare important parameters associated with the I–V charac-teristics of the solar panel. These parameters are subjectto variations in the atmospheric conditions. The short cir-cuit current and open circuit voltage can be calculated un-der different atmospheric conditions using the followingequations which are derived from Eqs. (8) and (9) describ-ing the solar panel model.

Isc ¼ ðI sc;n þ KIDT Þ GGn

ð12Þ

V oc ¼ V oc;n þ KvDT ð13Þ

Fig. 3 shows the I–V and P–V characteristics for differ-ent values of light intensity and temperature. As shown inFig. 3a the short circuit current has a direct relation withlight intensity, therefore the maximum power, which isitself proportional to the short circuit current, increaseswith increasing light intensity. On the other hand, the opencircuit voltage exhibits an inverse relation with temperature(Fig. 3b). That is, the open circuit voltage and, hence, themaximum power decrease when temperature increasingtemperature.

In this work, Eqs. (7), (8), and (11) are used for solarpanel modeling and simulation.

3. Photovoltaic system

Photovoltaic systems consist of a solar panels, DC–DCvoltage converters, controllers and batteries. DC–DC volt-age converters are used for matching the characteristics of

Fig. 3. The effects of ambient temperature and ir

the load with that of the solar panels (Tasi-Fu and Yu-Kai,1998). DC–DC voltage converters are classified into threecategories boost converters, buck converters and buck-boost converters. Selection of the type of DC–DC voltageconverter depends on the level of voltage variations. Theuse of the battery allows the photovoltaic system to behaveas a real source to the feeder so that it may exhibits con-stant voltage level for different power (load) levels. The bat-tery is also required for saving power and temporarycompensation of power variation. Fig. 4 shows the photo-voltaic systems implemented in this work. The boost volt-age converter has been used for matching the load to thesolar panel and the battery keeps the output voltage ofboost converter constant. Using the equation for the boostDC–DC voltage converter, we can write:

V L

V pv¼ 1

1� D! V pv ¼ ð1� DÞV L ð14Þ

where VL and Vpv represent the load voltage and solar celloutput voltage respectively and D is the duty cycle of theconverter. Eq. (14) indicates that the operating point ofthe solar panel can be changed by changing the value ofthe duty cycle. Considering the uniqueness of VMPP, thereexists a single value of DMPP for which maximum powerpoint, MPP is attained. That is

if : V pv ¼ V MPP ! D ¼ DMPP ð15Þ

The photovoltaic system exhibits maximum efficiencywhen the instantaneous power produced by the solar panelis maximized which occurs at the MPP. By changing theduty cycle (D), the characteristic of load seen by solar panel

radiation variations on P–V and I–V curves.

Fig. 4. Photovoltaic system.

Fig. 5. (a) P – duty cycle characteristics (b) I–V specification of operatingpoint for different duty cycle.

M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976 2969

will change from zero to infinity. The variation of the out-put power of the solar panel as a function of the duty cycleD is shown in Fig. 5.

4. Proposed method

The general algorithm employed in the proposedmethod is shown in Fig. 6. As indicated, the algorithm iscomposed of two loops whose operation can be describedas follows:

First, the initial values of the adjustable parameters arereceived and then the input variables related to offlinemethods such as temperature, light intensity as well as sys-

tem variables related to the online methods such as thevoltage and current of the solar panel are measured. Inthe next stage the input variables are compared with theirprevious values and based on the result of this comparison,one of two loops, namely either a set point loop or a finetuning loop are implemented. The following descriptionexplains each of the blocks in Fig. 6.

4.1. Initial values

The initial values of the photovoltaic system parametersare divided into two categories. The first group concernsthe solar panel data which is provided by the manufacturerwhich include the voltage at maximum power (VMPP), thecurrent at maximum power (IMPP), and the maximum powerpoint, MPP, the open circuit voltage (Voc), and the short cir-cuit current (Isc) under standard atmospheric conditions(temperature of 25 �C and light intensity of 1000 W/m2),temperature coefficients of the short-circuit current (KI),and the temperature coefficients of the open circuit voltage(Kv). The second group consists of the parameters used fortracking the maximum power point (MPPT), which mustbe evaluated by the operator, such as the ratio of voltageat maximum power to the open circuit voltage (K) and ratioof current of maximum power to short circuit current. Thevalues Voc,n and Kv from the first group and the K from sec-ond group must be determined as initial values.

4.2. Measured variables

These variables include input variables related to the off-line methods such as the temperature, the light intensity,the open circuit voltage and the system variables relatedto the online methods such as the instantaneous current,voltage and power. The proposed method employs themeasured values of the temperature and power variables.

4.3. Loop selection

Loop selection depends on loop performance and thesystem conditions. In the proposed algorithm, the set pointcalculation loop will be performed when the temperature

(b)(a)Fig. 6. Proposed method algorithm a: general and b: used in this paper.

2970 M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976

variations are greater than a certain value. Otherwise thefine tuning loop will be performed.

4.4. Set point calculation loop

Approximate values of VMPP, IMPP, and MPP for thesolar panel are calculated in this loop. The calculationsare performed based on offline methods with the operatingpoint calculation done using the open circuit voltage. Theopen circuit voltage, Voc, and the voltage at the maximumpower point, VMPP are calculated using the followingequations:

V oc ¼ V oc;n þ KvDT ð16Þ

V MPP ¼ KV oc ¼ KV oc;n þ KKvðT � T nÞ ð17Þ

It should be noted that Voc and VMPP change when thetemperature varies but exhibit little changes with variationsin intensity changes. Therefore, the set point calculationloop will be performed only in response to temperaturechanges in order to attain the new operating point.

4.5. Fine tuning loop

In this loop, the approximate value of VMPP and, hence,MPP which are obtained from the set-point loop are used toarrive at a more accurate value for MPP. Tracking of amore accurate value for MPP will be achieved based ononline methods. In particular, the classical P&O methodhas been used in the proposed algorithm. The P&O methoduses the measured value of the instantaneous power, toadjust the initial value of K such that the approximate valueof VMPP determined based on Eq. (17) approaches a moreaccurate value. This allows attainment of a more accuratevalue for MPP. Because the initial amount of the VMPP

has been estimated based on the set point loop calculations,convergence to a more accurate value of MPP is fast.

Therefore, the amplitude of the disturbance applied understeady state conditions can be small.

4.6. Control signal calculation (DMPP)

The photovoltaic system used in this work uses a boostvoltage converter whose output is connected to the battery.Therefore (VL) is constant. The control circuit comparesVMPP with the instantaneous voltage of the solar panel,Vpv, to generate an error signal, which can be applied tothe PI controller to produce a control signal. This controlsignal is, in turn, applied to the boost converter to adjustits duty cycle such that Vpv approaches VMPP. This forcesD to approach DMPP as given by the Eqs. (14) and (15).

In the proposed method uses the set point loop toapproximate value of the MPP voltage based on Eq. (1)and the value of the open circuit voltage. As opposed tothe conventional MPPT methods which involve sheddingthe load in order to measure the open circuit voltage, ourmethod simply approximates the open circuit voltage usingEq. (16) and the measured value of the temperature. There-fore, there is a trade-off between accuracy and the complex-ity associated with the value of open circuit voltage. Inorder to compensate for the resulting inaccuracy in thevalue of MPP voltage the fine tuning loop has beenemployed to arrive at a new K value in Eq. (17) based onthe classical P&O method (Fig. 8). The method is simpleand the combination of the two loops do not need to shed-ding the solar panel from load to calculate the open circuitvoltage and the accuracy of proposed method Indepen-dence accuracy of temperature.

The algorithm used in Tafticht et al. (2008), also consistsof two loops. In the first loop Voc is measured intermittentlyby shedding the load from the solar panel and a non-linearequation is used to calculate VMPP using the measured valueVoc. Then, in the second loop the P&O method is used toarrive at a more accurate value of MPP.

Table 2Model parameters of solar module.

Variable Value

Io,n 9.825 � 10�8 AIpv 2.662 AVt 26 mVRp 400 XRs .3 Xa 1.3

3 Proposed method 1 Classic P&O

Method of [19] 2 Improved P&O4

1

M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976 2971

5. Simulation and results

The photovoltaic system shown in Fig. 4 consists of a 60-Watt solar panel whose specifications are given in Tables 1and 2, a boost voltage converter, a 36 V lead-acid batterywith maximum current rating of 5 A. The system issimulated using the Matlab/Simulink software. The pro-posed method is implemented in the software environmentas a controller to study the various aspects of the system andcompare them to those obtained by other methods.

5.1. Efficiency

In this section the efficiency of the proposed method, theimproved P&O method, the method given in Tafticht et al.(2008), and the classical P&O method are compared witheach other. The efficiency is calculated from the followingequation (Tafticht et al., 2008).

gT ¼1

n

Xn

i¼0

P i

P max;i¼ 1

n

Xn

i¼0

1� P l

P max;ið18Þ

where Pi is the solar panel power, Pmax,i maximum solarpanel power, Pl (= Pmax,i � Pi) the wasted power and n isthe number samples.

In Eq. (18), maximum Power (Pmax) is proportional tolight intensity. The steady state loss (Pl) is proportionalto the disturbance amplitude which is applied to the con-trol signal. As the disturbance amplitude increases the lossincreases and consequently the efficiency decreases. In theclassical P&O method the disturbance amplitude is con-stant leading to power oscillations in steady state, therebydecreasing the efficiency.

In the method given in paper (Tafticht et al., 2008) theefficiency is dependent on the accuracy of the non-linearequation as well as the disturbance amplitude of the P&Omethod. In the fine tuning loop of our proposed method,the classical P&O algorithm is used, which causes steadystate oscillations. But given the fact that the disturbanceamplitude employed in our method is relatively small, theamount of power oscillations under steady state conditionsis also small. Finally, in the improved P&O method, sincethe disturbance amplitude under steady state conditionsapproaches zero thereby is reducing the amount of poweroscillations. As a result, a higher efficiency is attainable.

Table 1Solar module characteristics. (The ariasolar array at 25 �C, 1000 w/m2).

Variable Value

Imp 2.5 AVmp 23.1 VPmax,m 60 WIsc 2.66 AVoc 30 VKv �.356 V/KKI .024 A/KNs 48

The efficiency associated with the different methods is shownin Fig. 7 as a function of light intensity. Curve 1 correspondsto the classical P&O method in which the power oscillationsare constant due to constant application of constant distur-bance amplitude under steady state conditions. Therefore,the power losses (Pl) will be constant. The efficiency of thismethod is low for low light intensities, because the amountof the maximum power is low but the losses are constantand vice versa. Curve 2 corresponds to the method of paper(Tafticht et al., 2008) in which the efficiency depends on theaccuracy of the non-linear equation, the disturbance ampli-tude of P&O, and period of shedding the solar panel fromthe load. The amount of losses in this method is less thanthat of the classical P&O method but non-zero becausethe classical P&O method with a low disturbance amplitudehas been used in this method for fine tuning MPP. In addi-tion, in this method there are additional losses related toshedding of the load from the solar panel during Voc mea-surements. Curve 3 corresponds to our proposed methodwhose efficiency is dependent on the accuracy of the linearrelationship between Voc and VMPP as well as the distur-bance amplitude of the P&O used in the fine tuning loop.The efficiency of this method is higher than those of the clas-sical P&O method and the method of paper (Tafticht et al.,2008). Because, on the one hand, it uses a smaller distur-bance amplitude leading to smaller oscillations and powerlosses. On the other hand there is as opposed to the methodof paper (Tafticht et al., 2008) there is no need to shed the

200 400 600 800 1000

0.4

0.6

0.8

irradiation

effic

ienc

y

Fig. 7. Efficiency of different methods of maximum power tracking.

0.06 0.07 0.08 0.09 0.1 0.1125.2

25.4

25.6

25.8

time (s)

0.06 0.07 0.08 0.09 0.1 0.1160.5

60.52

60.54

60.56

60.58

time (s)

Pow

er (w

)Vo

ltage

(V)

3 f=200, C=.00125 1 f=200, C=.005

f=200, C=.0025 2

Fig. 9. Steady state of power and voltage for the proposed method withdisturbance frequency, 200 and different disturbances amplitudes.

0 0.01 0.02 0.03 0.04 0.05

600

800

1000

irrad

iatio

n

2972 M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976

load. Curve 4 corresponds to the improved P&O method inwhich the disturbance amplitude approaches zero understeady state conditions. The power losses are, therefore, zerothereby maximizing the efficiency.

5.1.1. The effects of the amplitude and frequency of

disturbances on efficiency

Figs. 8 and 9 show the effects of the variations of fre-quency and amplitude disturbances on output power andvoltage for the proposed method under steady stateconditions.

Simulation results in Fig. 8 shows that the frequencyvariation does not affect the efficiency of the proposedmethod under steady state conditions. In other words theaverage voltage of maximum power and the area underthe power curve are constant for different frequencies.Reducing the disturbance amplitude, however, leads to areduction in voltage oscillations, thereby increasing thearea under the power curve, which improves the efficiencyof the system as shown in Fig. 9.

5.2. Dynamic response

Variation of maximum power point in startup time andatmosphere changes means the dynamic response forphotovoltaic systems. System response is evaluated duringthe startup time and rapid variations of operating pointfor the proposed method and the results are compared withthose obtained for the P&O method.

5.2.1. Dynamic response to light intensity variations

Fig. 11 compares the effects of the light intensity on thedynamic response of the proposed method, the offline sec-

0.08 0.085 0.09 0.095 0.160.5

60.52

60.54

60.56

60.58

time (s)

pow

er (W

)

0.08 0.085 0.09 0.095 0.125

25.2

25.4

25.6

25.8

26

time (s)

Volta

ge (V

)

3 f=200, C=.005 1 f=1000, C=.005

f=500, C=.005 2

Fig. 8. Steady state of power and voltage for the proposed method withdisturbance amplitude 0.005 and different disturbances frequency.

time (s)

Fig. 10. Variations of light intensity.

tion of the proposed method, and the improved P&Omethod during startup and rapid variations in light inten-sity (operating point) at constant temperature. In this sec-tion, light intensity has increased linearly from 500 W/m2

to 1000 W/m2 in 20 ms as depicted in Fig. 10. Also, theMPP variations are depicted by curve 1 of Fig. 11.

According to Fig. 11, the offline part of the proposedmethod (curve 2) approximates the MPP very well but isunable to track the exact amount of MPP. The proposedmethod (curve 3) is follows the MPP closely at startup time,but the method exhibits errors during rapid changes in lightintensity. If the disturbance amplitude and frequency arereduced, the deviation from MPP during rapid variationsin light intensity will decrease. The improved P&O method(curve 4), on the other hand, is unable to follow the MPPneither during start-up time nor during rapid changes inthe light intensity.

5.2.2. Effects of the amplitude and frequency of disturbances

on power output and voltageThe effects of the amplitude and frequency of distur-

bances on the power output during startup time and rapid

4 P&O

0 0.01 0.02 0.03 0.04 0.050

10

20

30

40

50

60

time (s)

P (W

)

2 Set point loop 1 MPP 3 Proposed method

Fig. 11. Comparison of proposed method with P&O method for linearvariation of light intensity.

f=1000, C=.0025 2

3 f=1000, C=.005 1 f=1000, C=.00125 (a)

M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976 2973

variations in the operating point as a result of variations inlight intensity have been shown in Fig. 12.

In Fig. 12 curve (1) represents the proposed method withthe amplitude and frequency of disturbances chosen similarto the classical P&O method. This selection leads to rapidtracking of the MPP during startup time, but leads toerrors during rapid variations of light intensity. Curves 2and 3 correspond to reductions in the disturbance ampli-tude and frequency respectively. Although, these reduc-tions decrease the speed of MPPT during startup, butimprove MPPT during fast variations in light intensity.Curve 4 corresponds to the improved P&O method, whichexhibits the most undesirable responses during bothstartup time and rapid variations of light intensity.

Figs. 13a and 14a depict the performance of the pro-posed method in response to variations in amplitude and

0.03 0.035 0.04 0.045 0.05

30

40

50

60

time (s)

P (W

)

(b)

0 0.005 0.01 0.015

56

58

60

62

time (s)

P (W

)

(a)f=2000, C=.0025 2

1 f=2000, C=.005 3 f=1000, C=.005

P&O4

Fig. 12. Comparison of proposed method with P&O in (a) during start upand (b) fast irradiation changes for different frequency and amplitude ofdisturbances.

frequency of the disturbance respectively. As indicated,reductions in amplitude and frequency improve thedynamic response of the proposed. Figs. 13b and 14bdepict the power–voltage characteristics as a function ofvariations in the disturbance amplitude. Considering thatthe proposed method follows VMPP and given that VMPP

shows little variation with light intensity, the P–V charac-teristics of the proposed method has the best performancein terms of tracking MPP under constant voltage condi-tions. Curve 1 in Figs. 13b and 14b indicate that the lowerthe amplitude and frequency of the disturbance, the higherthe performance in terms of MPPT will be.

5.2.3. Dynamic response to temperature variations

Fig. 16 compares the simulation results for the proposedmethods (curve 2) with improved P&O method (curve 3)based on Eq. (4) in response to variations in temperatureas depicted in Fig. 15.

From Fig. 16 it is clear that the proposed method (curve2) tracks the MPP quite well in response to temperaturechanges and the resulting changes in MPP represented bycurve l. The improved P&O method (curve 3), on the otherhand, exhibits tracking errors in response to temperaturechanges.

5.3. Practical test results

To assess the practical impact of disturbance amplitudeon the proposed method, the system shown in Fig. 4 was

0.02 0.03 0.04 0.05 0.06

30

40

50

60

time (s)

Pow

er (w

)

0 5 10 15 20 25 300

10

20

30

40

50

60

time(s)

Pow

er (w

)

Voltage (V)

(b)

Fig. 13. The P–V characteristics and power performance of proposedmethod for disturbance amplitude variations.

0.04 0.045 0.05 0.055 0.06 0.065 0.07

30

354045

5055

60

time (s)

P (w

)

f=1000, C=.005 2

3 f=200, C=.0051 f=500, C=.005

0 5 10 15 20 25 300

10

20

30

40

50

60

P (w

)

Voltage (V)

(b)

(a)

Fig. 14. The P–V characteristics and power performance of proposedmethod for disturbance frequency variation.

0.03 0.035 0.04 0.045 0.05 0.055 0.06

54

56

58

60

time (s)

Pow

er (w

)

f=1000, C=.0025 2 3 Improved P&O 1 MPP

Fig. 16. Comparison of proposed method with P&O method fortemperature changes.

Fig. 17. Practical circuit.

2974 M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976

implemented using a 60 W solar panel (manufactured byAria solar) whose specifications are given in Table 1. Thealgorithm was implemented using the (At mega 32 AVR)microcontroller and the LM35 sensor was used to measuretemperature. The control signal was connected to the boostconverter which operated at a frequency 16 kHz using aninput inductance of 820 microHenry, the power buttonIRFZ44n (n-channel MOSFET) and a capacitor of100 microfarad. The input of the converter was connectedto the solar panel and the output was connected to a seriesof three 12-V batteries (sealed lead acid battery) as shownin Fig. 17.

The boost converter is designed so as to minimize thesolar panel voltage and the current ripple. If the inductorvalue is reduced below the designed value, the current ripplewill be increased, thereby limiting the performance of theproposed method for small perturbations. On the otherhand, increases in the value of the input inductor abovethe designed value, will lead to an increase in the systemresponse time.

0.03 0.035 0.04 0.045 0.05 0.055 0.06

20

25

30

35

40

time (s)

tem

pera

ture

Fig. 15. Temperature changes.

The experimental results further indicate that if the dutycycle of the boost converter is increased above 50%, thecurrent ripple will be increased intensified. In addition tothe appropriate design of the boost converter design, theabove effects can be overcome through appropriate selec-tion of the perturbation amplitude and frequency of theP&O method.

The measured solar panel output power is shown inFig. 18 during startup state for disturbances whoseamplitude are 8%, 4% and 2% of the maximum value of Kas determined by Eq. (17) for K = 0.7. The performance ofthe set-point loop and the tuning loop for MPPT is shownin Fig. 18. Solar panel voltage and power are shown inFig. 19 for the given values of the disturbances under steadystate conditions.

Figs. 18 and 19 show that decreasing the amplitude ofthe disturbance has led to a reduction in the tracking speed,but efficiency increases due to reduction of oscillationsunder steady state conditions. These results are in agree-ment with the simulation results given in Figs. 9 and 12.

(a)

P

2

1

P

2

1

(b)

P

2

1

1. Set Point Loop2. Fine Tuning Loop

(c)

1. Set Point Loop2. Fine Tuning Loop

1. Set Point Loop2. Fine Tuning Loop1. Set Point Loop2. Fine Tuning Loop

Fig. 18. Solar panel output power during startup for the differentdisturbances amplitudes. (a) 0.005, (b) 0.0025 and (c) 0.00125 (divisionof horizontal axis 15 ms and vertical axis 16.4 W).

V

P

V

P

V

P

(c)

(b)

(a)

Fig. 19. Variations of solar panel power and voltage in steady stateconditions for different disturbances amplitudes. (a) 0.005, (b) 0.0025 and(c) 0.00125 (division of horizontal axis 5 ms and vertical axis for power4 W and for voltage 0.4 V).

M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976 2975

6. Discussion

6.1. Efficiency

Factors which increase the losses and reduce efficiency,are the amplitude of the oscillations and shedding of theload during open circuit voltage measurements.

Since variable disturbance amplitude is used in theimproved P&O which approaches zero under steady stateconditions, this method exhibits the highest efficiency. Theproposed method, which uses the classical P&O method withsmall disturbance amplitude and approximates the opencircuit voltage using Eq. (16), has the next highest efficiency.The method of paper (Tafticht et al., 2008) exhibits addi-tional losses due to shedding of the load during the opencircuit voltage measurements ranks lower in terms ofefficiency and finally the classical P&O method exhibits thelowest efficiency among the four methods.

6.2. Dynamic response

The proposed method approximates the MPP duringstartup time and also tracks the MPP in response to rapidchanges in atmospheric conditions quite well. The dynamicresponse of the improved P&O method ranks lower thanthe proposed method, since it exhibits a delay during

startup and produces tracking errors under rapid changesin atmospheric conditions.

6.3. Stability issue

The set point loop is run when the changes in tempera-ture are large, but the tuning loop is run under the followingcases: (1) immediately following the set-point loop (2) whenthe temperature changes are small (3) when intensitychanges have occurred. In the latter two cases the opera-tions of the two loops do not interfere with one another.If each of the two loops is stable, stability of the entire algo-rithm is guaranteed. On the other hand, in presence of largetemperature changes when the set point loop is running,there will be no discernable oscillations as the set-point loopconverges quickly by positioning the search directly on theMPP. Furthermore, since our approach is based on the clas-sical P&O method employing a small perturbation ampli-tude and low frequency, there will be minimal interferencebetween the two loops and stability is not of major concern.

2976 M.H. Moradi, A.R. Reisi / Solar Energy 85 (2011) 2965–2976

6.4. Simplicity

The proposed method is quite simple. First a linear rela-tionship is used to estimate VMPP as given by Eq. (18) andthe MPP can be easily estimated using the known solarpanel characteristics. Second, the simple classical P&Omethod is used to track MPP relatively accurately.

7. Conclusion

In this paper, a method was proposed to improve themaximum power point tracking. The proposed algorithmis composed of two loops, namely the set point calculationand the fine tuning loops. In The set point calculation usesthe open circuit voltage method to approximate the maxi-mum power point, MPP, and then the fine tuning looptracks the exact amount MPP based on the classical P&Omethod. The proposed method was simulated in the Mat-lab/Simulink environment was experimentally verifiedbased on implementation of a laboratory prototype. Theproposed method exhibits acceptable efficiency and excel-lent performance during startup time and in response torapid changes in atmospheric conditions. Simplicity, lim-ited hardware requirements and low implementation costsare among the advantages of the proposed algorithm. Also,the experimental results demonstrated the good perfor-mance and the effectiveness of the proposed method, andwere in good agreement with the simulation results.

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