Predictive & Adaptive MPPT point tracking (MPPT) of ... · Predictive & Adaptive MPPT Perturb and Observe Method N. FEMIA, Member, IEEE D. GRANOZIO G. PETRONE G. SPAGNUOLO, Member,

Predictive & Adaptive MPPTPerturb and Observe Method

N. FEMIA, Member, IEEE

D. GRANOZIO

G. PETRONE

G. SPAGNUOLO, Member, IEEEUniversity of SalernoItaly

M. VITELLISecond University of NaplesItaly

The perturb and observe (P&O) best operation conditions are

investigated in order to identify the edge efficiency performances

of this most popular maximum power point tracking (MPPT)

technique for photovoltaic (PV) applications. It is shown that

P&O may guarantee top-level efficiency, provided that a proper

predictive (by means of a parabolic interpolation of the last

three operating points) and adaptive (based on the measure

of the actual power) hill climbing strategy is adopted. The

approach proposed is aimed at realizing, in addition to absolute

best tracking performances, high robustness and promptness

both in sunny and cloudy weather conditions. The power gain

with respect to standard P&O technique is proved by means of

simulation results and experimental measurements performed on

a low power system. Besides the performance improvements, it is

shown that the proposed approach allows possible reduction of

hardware costs of analog-to-digital (A/D) converters used in the

MPPT control circuitry.

Manuscript received October 4, 2005; revised February 15, 2006;released for publication September 15, 2006.

IEEE Log No. T-AES/43/3/908401.

Refereeing of this contribution was handled by M. Veerachary.

Authors’ current addresses: N. Femia, F. Petrone, G. Spagnuolo,DIIIE, University of Salerno, Via Ponte Don Mellilo, 84084Fisciano, Salerno, Italy, E-mail: ([email protected]); D. Granozio,National Semiconductor, Germany; M. Vitelli, Second University ofNaples, Naples, Italy.

0018-9251/07/$25.00 c° 2007 IEEE

I. INTRODUCTION

Many papers concerning the maximum powerpoint tracking (MPPT) of renewable energy sourceshave appeared in last ten years (see [1—10] andreferences cited therein). Most of them treat strategiesaimed at drawing the maximum power from aphotovoltaic (PV) field at the current environmentalconditions, in terms of irradiance and temperature,regardless of the actual PV field conditions, e.g. interms of aging. The greatest part of such methodsconverges into two strategies, that are well knownas perturb and observe (P&O) and incrementalconductance (IC) techniques. The former is often usedfor its simplicity, since it is essentially based on ahill climbing approach to the maximum power point(MPP) of the power-voltage characteristic of the PVfield. On the other hand, its main drawbacks are thewaste of energy in stationary conditions, when theworking point moves across the MPP, and the poordynamic performances exhibited when a steep changein solar irradiance occurs.

A. Stationary Irradiance Conditions

The first problem is due to the repeated climbingof the MPP. As often evidenced in literature, a largevariation of the control variable to be perturbed is themain reason for such a loss. Unfortunately, a smallperturbation apparently reduces such a detrimentaleffect, but it compromises the dynamic features ofthe MPPT strategy and may even lead to a significantwaste of power.Regardless of the entity of the applied

perturbation, the sequence of two voltage valuescorresponding to similar power levels in a standardP&O implementation leads to a stationary behaviorcharacterized by a four-points sequence, with twopoints for each branch of the power-voltage curve (seeFig. 1). Such a situation is essentially caused by theuse of analog-to-digital (A/D) converters resultingin discretized values of the perturbation. Fig. 1(a)shows an experimental case and a simulated one bymeans of a sequence of seven operating points ina row. Due to noise and/or a slightly varying sunirradiance, the operating point jumps back fromposition 5 to 6, instead of traveling newly throughpoint 2. This causes the return back to the initial point1´ 7, since the operating points sequence 4-5-6 givesa monotonically increasing power with a decreasingvoltage.A similar effect is introduced by the error

associated with the quantization. Fig. 1(b) comparesthe almost equal power levels of two possibleoperating points placed on both sides of the MPP,characterized by a very small difference in powerlevels ¢P, with the uncertainty u(¢P) on the powerlevels introduced by the A/D converters used to

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Fig. 1. (a) Experimental data showing four-points steady-statebehavior. (b) Simulated data illustrating four-points behavior

triggered by quantization error.

pick the values of both voltage and current at thePV array terminals. Such an error is given by thecombination of the uncertainties introduced by the twoA/D converters used to sample the electrical variablesat the PV field output.The position of the points 2, 3, 5, and 6 in

Fig. 1(a) confirms that a four-operating-pointssequence occurs in case more than one operatingpoint lies quite close to the MPP, at its left or rightsides. It would be better to have sequences of threeoperating points only, with the central one close tothe MPP and the other two at both sides of the MPP,both characterized by similar power levels, just belowthe lower limit of the uncertainty band introducedby the A/D converters and related to the centraloperating point (see Fig. 1(b)). The preference forsuch a three-points-based behavior is documented inliterature and is confirmed in Section II by a simpleestimation of the total power drawn from thePV field.To avoid the occurrence of such conditions, some

expedients have been presented in literature. Forexample, in [6] a first attempt of limiting to three thenumber of operation points is introduced. The authorsshow that the use of a memory buffer containingthe last three voltage-power couples of the PV fieldhelps in detecting the MPP and a rapid changingof the solar radiation. They also put in evidence theimportance of freezing the value of the converter’s

duty cycle d when the MPP is reached. This allowsto draw the maximum power in stationary conditions,without wasting any of it due to oscillations aroundMPP.In [8]—[9], and references cited therein, the authors

compare the basic P&O MPPT technique with itsimproved versions. Some of them suggest the useof a “waiting” function to freeze the duty cycleperturbation ¢d if its sign is reversed several timesin a row. This trick reduces the hill climbing of theoperating point across the MPP under stationaryirradiance conditions, but it deteriorates the system’sresponse under changing atmospheric conditions,thus emphasizing the P&O erratic behavior under therapidly changing irradiance level typical of windy andpartly cloudy days.Other approaches [9] do not use a fixed value of

the duty cycle perturbation, but they work on a realtime adjustment of ¢d to improve both steady-stateand dynamic P&O performances.

B. Varying Irradiance Conditions

The second limit of P&O is represented by thefact that it is usually slow in tracking rapid solarirradiation changes. The mechanism that leads toan erratic behavior, especially in cloudy and/orwindy days, is well described in [8]. Dynamic P&Operformances can be improved by means of variousstrategies presented in literature. A possible strategy[8] consists in comparing the value of the powerdelivered by the PV source at the same voltage intwo different sampling instants. The comparison mayallow to estimate the irradiance change and it may beuseful to decide the sign and the amplitude of the nextperturbation of the operating point. Nevertheless, thislogic increases the complexity of the MPPT technique,thus slowing down its response.Dynamic P&O performances have been also

improved by using a suitable interpolation of the PVfield characteristics. For example, in [7] a comparisonof simulated and experimental characteristics isdone in order to validate the theoretical model usedfor predicting the locus of the MPPs at differentirradiance levels. Unfortunately, as for all thosetechniques using an open-loop MPPT control, thefitting might not ensure good performances if thepanel characteristics sensibly change with temperature,aging, and so on.In [10] the authors suggest a criterion in order

to limit the negative effects associated with theabove drawbacks: a theoretical analysis leading tothe optimal choice of the P&O MPPT parameters,according to the total dynamic behavior of thespecific converter and of the adopted PV array, iscarried out. It has been shown that, if the parametersare properly optimized by using the systematic

FEMIA ET AL.: PREDICTIVE & ADAPTIVE MPPT PERTURB AND OBSERVE METHOD 935


Fig. 2. Simplified circuit of boost converter with MPPT control. Ci = 6:52 ¹F, RCi = 13:22 m−, L= 272:81 ¹H, RL = 233 m−,controlled switch ON resistance RS,ON = 13 m−, diode ON resistance RD,ON = 177 m−, diode threshold voltage VD,ON = 1:06 V,

Co = 13:22 ¹F, RCo = 6:21 m−.

approach proposed, rather than by means of expensivetrial and error tests, but the P&O MPPT techniqueis able to guarantee an efficiency which is equalto that obtainable by the IC method. In [10], thebenefits deriving from the optimization of both theperturbation amplitude ¢d and the sampling periodTa are shown, in terms of reduced steady-state lossescaused by the oscillation of the array operating pointaround the MPP and improved quickness duringirradiance transients.In synthesis, overall P&O performances need to be

improved in order to

1) ensure a three-points behavior across theMPP under a fixed irradiation level, with a centralpoint blocked on the MPP and the other twooperating points at its sides, at voltage values thatguarantee almost the same power level, just below theMPP;2) quickly detect the MPP movement in presence

of varying atmospheric conditions by increasing theperturbation ¢d so that the MPPT is guaranteedwithin few sampling periods Ta.

As shown in Sections II and III, both goals arepursued by means of a perturbation ¢d whoseamplitude is chosen as a function of the actual powerdrawn from the PV field together with the adoptionof a parabolic interpolation of the sequence of the lastthree acquired voltage-power couples correspondingto as many operating points. Simulation results willput in evidence that the proposed strategy ensuresthe balancing of the three operating points acrossthe MPP and guarantees an MPPT promptnessfaster than the one ensured by the classical P&Oapproach with constant duty cycle perturbation. Theproposed technique ensures that the power difference¢P between two consecutive operating points isalways higher than the power quantization error,thus making the three-points-based sequence morerobust and allowing to reduce the cost of the A/Dconverters, because a coarser resolution is needed todistinguish the two power levels. Section IV presentsexperimental results that demonstrate the effectiveness

and robustness of the approach. Conclusions end thepaper.

II. STEADY-STATE IRRADIANCE CONDITIONS

In [10] the nonlinear model of the PV field and thecontrol-to-PV array voltage transfer function of theswitching converter were used to demonstrate that, ifthe P&O perturbation ¢d is settled as greater than athreshold ¢dmin, the algorithm is able to reliably trackirradiances characterized by average rates of changeslower than a fixed threshold.The boost converter shown in Fig. 2 was

considered in [10] and is studied here for furtherconsiderations. Results obtained can be extended toany other converter topology as well.In [10] it has also been demonstrated that a

sampling period Ta greater than a fixed thresholdT" ensures that the P&O MPPT algorithm is notconfused by the transient behavior of the system andthe duty cycle oscillates assuming only three differentvalues: fdMPP¡¢d,dMPP,dMPP +¢dg, with dMPP theconverter’s duty cycle ensuring the maximum powertransfer.In [10] it has also been demonstrated that a

constant ¢d greater than the ¢dmin ensures a reliableMPPT, but this choice does not allow to overcomeproblems related to the imbalance of the operationpoints across the MPP under stationary irradianceconditions. Nevertheless, once the maximum value_S of the average irradiance rate of change that needsto be tracked is fixed, the value of ¢dmin depends onthe irradiance value [10].

A. Perturbation Proportional to the Actual PowerLevel

The behavior of ¢dmin versus S in the rangeS = [100,1000] W/m2 has been reported in Fig. 3,together with a linear interpolation of the two extremepoints obtained for the lowest irradiation level, S =100 W/m2, which gives the highest ¢dmin, and for thehighest one, S = 1000 W/m2, which gives the lowest¢dmin.



Fig. 3. Duty cycle perturbation versus irradiance in the rangeS = [100,1000] W/m2. Solid line represents ¢dmin as function ofS by using (6); the dashed line joins the two extreme values of¢dmin at lowest (100 W/m

2) and at highest (1000 W/m2)irradiation levels considered.

The plot of Fig. 3 has been obtained by referringto a 48 V battery charger fed by a PV sourceconsisting of two Kyocera KC 120 panels connectedin series and controlled by the boost converter ofFig. 2 working with a switching frequency fs =50 kHz. The plot has also been done by taking intoaccount the nominal performances of the hardwareused to perform the MPPT. In our case, it has beenpractically realized by means of a personal computerequipped with a National Instruments PCI S-61105 MS/s, 12-bit, 4 analog input simultaneous-samplingmultifunction DAQ. Such information allows to refinethe estimation of the minimum duty cycle perturbationreported in [10]; in fact, given the quantization errorsthat affect the measurements of PV field’s voltage andcurrent ¢qVMPP = 19 mV and ¢qIMPP = 4:9 mV, itresults that:

¢dmin =

1G0

vuuut (VMPP ¢K ¢ j _Sj ¢Ta) + (¢qIMPP ¢ IMPP +¢qVMPP ¢VMPP)μH ¢VMPP +

1RMPP

¶(1)

where H is a parameter which depends on the PVarray parameters [10], on the PV array MPP voltageand current VMPP and IMPP, respectively, on RMPP =VMPP=IMPP, on K =¢IS=¢S that is a PV panelsmaterial constant expressing the ratio between thevariations of the diode saturation current IS and thevariations of irradiation S [11], and on Ta, that is thesampling period between the kth and the (k+1)thsample.Since, at a fixed array voltage level, PV power

is proportional to the irradiance level [11], the trendhighlighted by the plot of Fig. 3 can also be read interms of ¢d versus P. Even if the curve of Fig. 3refers to a specific example, a general relationshipbetween the minimum duty cycle perturbation and the

Fig. 4. Time domain waveforms of PV power and voltage atS = f300,800,1000g W/m2. Thick line = adaptive ¢d =¢dlin, thin

line = constant perturbation ¢d =¢dmin =¢djSmin = 0:043.

current PV power expressed as

¢dlin¡¢djSmax¢djSmax ¡¢djSmin

=P¡PjSmax

PjSmax ¡PjSmin(2)

can be deduced and applied in general. Equation (2)gives the value of the duty cycle perturbation ¢dlinat a given power level P. It ensures that the operatingpoints are quite close to the MPP at high irradiancelevels, when the power versus voltage (p-v) curveis narrow, but allows to draw a high power even atlow S, because the operating points are spaced outdue to a high ¢d but they lie on a rather flat p-vcharacteristic.For our example, if the range S = [100,1000] W/m2

is considered, the constant values in (2) are equal to

¢djSmax = 0:015 PjSmax = 186 W¢djSmin = 0:043 PjSmin = 21 W

(3)

so that the dashed line representing ¢dlin reported inFig. 3 is obtained. It is worth noting that, in principle,the exact relationship between ¢d and P (the solidline in Fig. 3) can be used to settle a proper valueof ¢d according to the power level actually drawnfrom the PV field. Unfortunately, such a choiceshould require an expensive characterization of thesystem under more than the two extreme irradiancelevels. Consequently, it seems to be suitable to justtake into account the linear approximation (2) of thetrend of variation of ¢d versus P represented by thedashed line depicted in Fig. 3. Note that such a choiceensures that a ¢d greater than the ¢dmin given in [10]is settled. This margin allows to avoid some mistakesdue to the possible underestimation of the ¢dmin value[10].Time domain results obtained by simulating the

system of Fig. 2 under three different irradiance levelsS = f300,800,1000g W/m2 are shown in Fig. 4, wherethe comparison of the performances of P&O withadaptive (2) and fixed (1) ¢d =¢dmin =¢djSmin =0:043 perturbations, suggested by the approach



Fig. 5. Three points steady-state operation at (a) S = 300 W/m2,(b) S = 800 W/m2, (c) S = 1000 W/m2. Squares = fixed

¢d =¢dmin =¢djSmin = 0:043; dots = power adaptive perturbation¢d =¢dlin based on (5).

described in [10], are reported. In both cases ofconstant or adaptive perturbation a three-pointsbehavior of the MPPT has been achieved, but theadaptive perturbation according to (2) ensures areduced power step with respect to the use of a fixed¢d =¢dmin. Such a conclusion is more evident bylooking at the same results, reported in Fig. 5, butshown by means of the operating points placed on thep-v characteristic.The results presented above, and in particular

those presented in Fig. 5, show the usefulness ofthe relationship (2) and how it can further improve

Fig. 6. Second-order fitting of three possible operating points atS = f300,1000g W/m2. Black diamond represents current

operating point, grey diamond is the penultimate one, and whitediamond is last but two of the sequence.

the already good performances guaranteed by theapproach discussed in [10]. Fig. 5 also puts inevidence that, unfortunately, (1) is not always able toensure a three-points steady state with a central pointvery close to the MPP and the other two at its sides, atalmost the same power level, slightly below the MPP.

B. Parabolic Prediction of the Next Operating Point

In order to achieve this end, a geometricconsideration concerning the shape of the p-vcurve can be of great help. In [10] it has alreadybeen demonstrated that a parabola gives a goodapproximation of the PV power variation as a functionof voltage variation. In particular, it has been shownthat, if ¢P is the array output power variation (at aconstant irradiance level S) caused by the P&O drivenduty cycle variation and ¢V is the correspondingarray voltage variation, by means of a second-orderTaylor approximation around the MPP point, thefollowing relationship holds:

¢P ¼μIMPP¡

VMPPRMPP

¶¢V¡

μHVMPP +

1RMPP

¶¢V2

=¡μHVMPP +

1RMPP

¶¢V2: (4)

Such a model allows a more accurateapproximation of the p-v curve the closer to the MPPthe fitting is done. This is confirmed by the plotsof Fig. 6 that show the p-v curves at two differentirradiation levels, S = f300,1000g W/m2, togetherwith three possible operating points each. In bothcases, the operating points have been representedby means of a diamond: the black one is the currentoperating point, the grey diamond is the penultimateone, and the white diamond is the last but two of thesequence. The parabola that best fits each sequence ofoperating points is presented in Fig. 6.Fig. 6 clearly suggests that the parabolic

approximation of the p-v curve is useful the closer tothe MPP the three operating points are. Nevertheless,



a relevant contribution to an efficient MPPT can comefrom a parabolic approximation of the p-v curveeven if the current operating point is far from theMPP, provided that a downwards-turned parabola isconsidered

P = a ¢V2 + b ¢V+ c (5)

with a < 0 and the vertex Vpeak =¡b=(2 ¢ a)@Ppeak =c¡ b2=(4 ¢ a).A first-in-first-out array containing the current

operating point and the preceding two is usedto find the interpolating parabola. Once such anapproximation is obtained, the vertex of the parabolais used as a prediction of the new operating point. Theinterpolating parabola is considered as misleading inthe MPPT process if it exhibits an upwards-turnedconcavity, as in Fig. 7, or if it has a vertex at a voltagehigher than the open circuit voltage, as in Fig. 8. Insuch cases, as well as if it cannot be found by meansof the three points given (e.g. when two of them aresuperimposed), the perturbation used by the P&Oalgorithm is the one determined by means of (2), thatis to say ¢d =¢dlin.If no such cases occur, the interpolation of the

last three operating points is performed as in thecase examples of Figs. 6 and 9, the three coefficientsfa,b,cg of (5) are determined, and the vertex ofthe parabola Vpeak =¡b=(2 ¢ a) is considered as thecandidate for the new operating point.

Fig. 9. Three-points operation refreshment: solid line = interpolating parabola, dash-dotted line = p-v characteristic.

Fig. 7. Example of upward-turned interpolating parabola.

Fig. 8. Example of interpolating parabola with vertexcorresponding to voltage higher than PV open circuit voltage.



Fig. 10. Comparison of steady-state three-points-based operating conditions with (a) S = 300 W/m2, (b) S = 800 W/m2,(c) S = 1000 W/m2. Left column: dots=perturbation ¢dlin, diamonds = parabola-based operating point prediction.

Right column: thin line = perturbation ¢dlin, thick line = parabola-based operating point prediction.

Given the ideal input/output conversion ratio of theboost converter:

VinVout

= 1¡D (6)

where D is the converter’s duty cycle, the perturbation¢d can be expressed as

¢dparab =Vin¡VpeakVout

: (7)

The numerator is the difference between thecurrent PV voltage and the one corresponding tothe vertex of the interpolating parabola, while thedenominator is the converter’s output voltage that hasbeen fixed at 48 V in the case under test of a batterycharger. Note that (6) and, consequently, (7), hold foran ideal model of the converter, namely if losses areneglected. Consequently, prediction given by (7) can

be more inaccurate as losses increase. On the contrary,a more detailed model could lead to a more realisticrelationship between D, Vin, and Vout, but at the priceof a more burdensome computation.In any case, according to the guidelines given

in [10], the amplitude of the parabola-predictedperturbation j¢dparabj cannot fall below the minimumvalue prescribed by (1), so that the final duty cyclevariation that the P&O technique applies is

j¢dj=maxfj¢dparabj, j¢dlinjg (8)

with a sign chosen as usual for the basic P&Otechnique.

C. Simulation Results

Simulation results are presented in Fig. 10, withreference to the three steady-state PV power levels



Fig. 11. Power drops in three-points-based operation mode.

Fig. 12. P-v plane power drops in three-points-based operationmode.

S = f300,800,1000g W/m2. They have been obtainedby using the model of the boost converter reported inFig. 2, thus also taking into account passive and activecomponents losses.Comparisons among the simulation results

obtained by means of a constant perturbation ¢dmin(1), a perturbation ¢dlin adapted to the current powerlevel (2), and a duty cycle variation predicted bymeans of the parabolic interpolation of the last threeoperating points (8) clearly put in evidence that theproposed technique arranges the operating pointssymmetrically around the MPP, with the central oneplaced very close to the MPP and the other twoat almost the same power level, slightly below theMPP itself. The average power of the three-points setachieved by means of the parabolic prediction showsas much higher than the one drawn from the PV fieldif approaches given by (1) or (2) are used. Note thatthe power gain has been obtained by using a boostconverter model that includes passive componentsequivalent series resistances (ESRs) and ON stateswitch losses.Moreover, the two approaches presented above, if

compared with the classical P&O method operatingwith a constant ¢d, ensure a better balancing ofthe power levels associated with the two operatingpoints placed at the two sides of the MPP, with aspacing of at least 2 ¢¢dmin. This inherently reducesthe possibility that an inefficient four-points sequenceof operating points arises. On the basis of the

Fig. 13. Power drops in four-points-based operation mode.

Fig. 14. P-v plane power drops in three-points-based operationmode.

remarks and the equations reported above, it is nowpossible to give an estimation of the power lossesdue to a four-points behavior with respect to the onecharacterized by three points in a row. In both casesa symmetrical distribution of the operating pointsacross the MPP is supposed, the system’s intrinsicoscillations are neglected, and constant weatherconditions are assumed.If an operating point is placed on the MPP and

the other two are on its sides, the working period isTMPPT = 4 ¢Ta, as illustrated in Fig. 11.The energy loss occurs during one half of TMPP,

thus:¢E3 points = 2 ¢Ta ¢¢P (9)

where the power collapse ¢P can be evaluated bymeans of (4) and is depicted in Fig. 12.The resulting average energy loss obtained by

using (2) is

h¢P3 pointsiTMPPT =¢E3 pointsTMPPT

=¢P

2: (10)

If a four-points behavior occurs, the workingperiod is TMPPT = 6 ¢Ta, as illustrated in Fig. 13.The energy loss is evaluated as

¢E4 points = 4 ¢Ta ¢¢P1 +2 ¢Ta ¢¢P2 (11)

where the two power collapses ¢P1 and ¢P2 aregraphically shown in Fig. 14.



Fig. 15. Operating point transient due to sudden irradiance step from 300 W/m2 to 1000 W/m2. Circles = linear perturbationdetermined by (2), diamonds = parabolic prediction by (8). Black marker = current operating point, grey marker = penultimate operating

point, white marker = last but two operating point.

By using (4) it results:

¢P1 =¢Pj¢V=2 ¼¡μHVMPP +

1RMPP

¶¢μ¢V

2

¶2=¢P

4

¢P2 =¢Pj3¢V=2 ¼¡μHVMPP +

1RMPP

¶¢μ3 ¢¢V2

¶2=9 ¢¢P4

¢E4 points ¼ 4 ¢Ta ¢¢P

4+2 ¢Ta ¢

9 ¢¢P4

=112¢Ta ¢¢P

(12)and this means that the mean power loss is

h¢P4 pointsiTMPPT =¢E4 pointsTMPPT

¼ 1112¢P (13)

so that

h¢P4 pointsiTMPPT ¼116h¢P3 pointsiTMPPT

¼ 1:83 ¢ h¢P3 pointsiTMPPT : (14)

This means that a four-points behavior determinesa power loss 80% higher than the one associated witha three-points operation. Such a power gain assumes agreater significance if one considers that it has beenobtained at no additional cost with respect to theclassical P&O MPPT technique.Moreover, if a cheaper A/D converter is adopted,

u(¢P) increases and consequently the value of ¢Pthat allows to distinguish between the power levelsof two operating points in a row must be chosenas higher. This has a great impact on the MPPTefficiency, especially for low power/low cost systems.In fact, by using a robust three-points behavior in



Fig. 15. (Continued).

place of a four-points operation, the MPPT efficiencyimproves by almost a factor 0:83 ¢¢P=P.

III. DYNAMIC IRRADIANCE CONDITIONS

Once ascertained the steady-state performancesof the proposed duty cycle adjustment, the dynamicbehavior obtained by using both the duty cycleperturbation laws (2) and (8) has been investigated.The two approaches have been used separately

to reach a steady-state operation at S = 300 W/m2;afterwards, a steep sun irradiance variation up to S =1000 W/m2 has been imposed. Under such conditions,the two transients whose steps are shown in Figs. 15and 16 have been obtained. In both the sequences theblack, grey, and white markers stand for the currentoperating point, the penultimate, and the third lastoperating point, respectively. The parabola that fits thethree operating points in a row has been show onlyif the prediction it gives is used to determine the next

operating point. It has not been displayed if it gives a¢d <¢dmin, if it is concave, or if it has a vertex at avoltage level that exceeds the open circuit voltage.In the sequence reported in Fig. 15 the irradiation

level changes while the P&O procedure has detecteda power decrease at S = 300 W/m2, so that the nextoperating point is placed at a lower voltage, but closerto the new MPP at S = 1000 W/m2. In other words,the predicted ¢d correction has a sign that brings theoperating point near to the new MPP at the higherS. Such a situation can be deduced by comparingFig. 15(b) and Fig. 15(c).If the linear relationship (2) between PV power

and ¢d perturbation is adopted, about nine steps (dotsfrom (c) to (k) of Fig. 15) are needed to reach thethree-points-based operation across the new MPP atS = 1000 W/m2; the slow hill climbing is shown inFig. 15, from (d) to (j). The parabola-based predictionbased on (8), instead, quickly recovers the MPPright from four steps after the irradiation change (see



Fig. 16. Operating point transient due to sudden irradiance step from 300 W/m2 to 1000 W/m2. Circles = linear perturbationdetermined by (2), diamonds = parabolic prediction by (8). Black marker = current operating point, grey marker = penultimate operating

point, white marker = last but two operating point.

Fig. 15(f)). Afterwards, it works on the balancing ofthe three operating points with a decisive alignmentoccurring after seven steps (see Fig. 15(i)) and theirsettlement at the ninth step (see Fig. 15(k)).The example illustrated in the sequence of Fig. 16

shows the performances of the two strategies inpresence of an irradiance step from S = 300 W/m2

to S = 1000 W/m2 occurring when the P&O strategyis increasing the voltage, so that the operating point isdriven away from the new MPP at S = 1000 W/m2

(see Fig. 16(c)). In such penalizing conditions,the operating point hopping that characterizes theparabolic prediction (see Fig. 16(d)—(f)) is ableto ensure a quick recover of the MPP at the newirradiance level. In particular, up to the step shownin Fig. 16(d), the evolution of the two strategies isalmost similar. At that step, the parabolic interpolationof the current operating point and of the last two

ones allows to converge efficiently towards the newMPP by using both sides of the p-v characteristic,instead of beginning a climb that lasts ten steps(dots from Fig. 16(d) to Fig. 16(m)). Indeed, thestrategy that works with a duty cycle perturbationproportional to the available power requires aboutten steps to win the MPP at S = 1000 W/m2, andbegins a new three-points operation across it (seeFig. 16(m) and Fig. 16(n)). The parabola-basedoperating point prediction strategy, instead, endsthe approach to the new MPP after eight steps (seeFig. 16(i)). The steps that follow are needed tobalance the points across the MPP. By looking at thesequence of Fig. 16(d), Fig. 16(e), and Fig. 16(f), it isinteresting to note that the parabolic prediction allowsto climb the MPP and get close to it (Fig. 16(d)).The next ¢d is determined by means of the newinterpolating parabola (see Fig. 16(e)), but, as



Fig. 16. (Continued).

stated above, its sign is given by a standard P&Ostrategy. In fact, the sequence of operating points(see the white-grey-black sequence of diamondsof Fig. 16(e)) indicates a growing power for adecreasing voltage, so that the next operating pointis placed at the left of the current one, thus onthe opposite side with respect to the vertex of theinterpolating parabola, at a distance given by the

parabola-predicted ¢d. This causes a temporarydecrease of the power drawn from the p-v array(compare the power level of the black dot and of theblack diamond of Fig. 16(f)), but this temporarilycollapse is promptly made up in one step, as can bededuced by comparing the power level of the blackdiamond (close to the MPP) and of the black dot inFig. 16(g).



Fig. 17. Power tracking after sudden irradiance step from300 W/m2 to 1000 W/m2. Dashed line =¢dlin perturbation by(2), thin line =¢dmin perturbation by (1), thick line = parabolic

prediction by (8).

Fig. 18. Power tracking after sudden irradiance step from300 W/m2 to 1000 W/m2. Dashed line =¢dlin perturbation by(2), thin line =¢dmin perturbation by (1), thick line = parabolic

prediction by (8).

The choice of introducing the simulation resultsobtained under changing weather conditions in thep-v plane has been made to the aim of illustrating theway the operating point climbs the PV curve hill if theproposed P&O strategies are implemented. A differentrepresentation of the simulation results can be done bylooking at the PV power drawn along the time duringthe transient. Such an analysis is useful in order tofurther investigate the advantages of the techniques.Figs. 17 and 18 refer to the transients shown inFigs. 15 and 16, respectively. The first one shows that,during the transient, the performances of the strategiesadopting (2) and (8) are quite comparable with thoseexhibited by the classical P&O algorithm with aconstant perturbation ¢dmin. Fundamental differencesappear when the new steady state is reached. Indeed,the parabolic prediction of the perturbation as well asthe mere use of the linear relationship between ¢dand the delivered power result in a very small powerswing for the sequence of three operating points in arow. Such performances assume a great significanceif they are compared with the one given by the use ofthe constant ¢dmin.The same comments concerning steady-state

performances can be done by looking at Fig. 18.

Fig. 19. Experimental results obtained with constant perturbationP&O strategy under steady-state irradiation.

Nevertheless, in this case the transient looks moretroubled, with some power drops affecting all thestrategies. It is worth noting that, in the case undertest, during two time intervals the power drawn bythe parabola-prediction-based algorithm is below theone obtained by means of a constant ¢dmin. Suchan undesirable behavior is offset by a sequence ofmany time intervals during which the power level thatstrategy (8) is able to ensure is by far higher than theone given by a constant perturbation (1) ¢dmin. Thisconfirms the conclusions drawn by looking at Fig. 16and strengthens the effectiveness of the approach (8)which is able to guarantee a quick approach to thenew MPP due to the intrinsic ability of jumping overthe PV characteristic in a single step.

IV. EXPERIMENTAL RESULTS

To the aim of validating both the steady-stateand transient simulation results presented above, theexperimental setup of Fig. 2 has been realized.The system is composed of two series-connected

PV modules (KC120 made by Kyocera, rated power120 W), a boost converter with filter parameterschosen as reported in Fig. 2, with fs = 50 kHz, andwith an electronic load serving as a 48 V battery.The power system has been digitally controlled bya National Instruments PCI S-6110 5 MS/s, 12-bit,4 analog input simultaneous-sampling multifunctionDAQ.Many experiments have been done to put in

evidence features and drawbacks of the proposedstrategies. Nevertheless, the behavior of the classicalP&O approach with a constant ¢d =¢dmin = 0:043perturbation has been verified both under stationaryand varying irradiance conditions.Waveforms reported in Fig. 19 show that a strategy

based on a constant perturbation is not able to ensurea three-points behavior with balanced power levels.Power drawn from the PV field assumes a high valueplaced around the MPP and two lower and quiteunbalanced levels, with a power collapse every threeoperating points. The acquired waveforms in the



time window shown in Fig. 19 also put in evidencethe frequent occurrence of a further detrimentalfour-points behavior. The zoom shown in Fig. 19,indeed, shows four different power levels taking placebetween 3.76 s and 3.8 s. The A/D conversion ofthe PV field voltage and current does not allow todiscriminate the two close power levels and leads toa further increase of the duty cycle with a growingdeviation from the actual MPP. Such a behavior isbecause, in the presence of a power variation belowthe quantization error, the P&O algorithm imposes aduty cycle perturbation in the same direction of thelast one, thus leading to an operating point that goesfar away from the MPP. This choice has been madeto exalt the described deception effect, which in turnshould also occur if the sign of the perturbation ischanged after two operating points with almost thesame power.The noteworthy improvement obtained by means

of (8) is also proved by the plots of experimentalmeasurements of Fig. 20. The proposed techniqueensures a reduced power oscillation below the MPPand a real power gain that, in the case shown in thefigure, is just above 1%.Fig. 21 shows an example of the response of the

P&O technique with constant ¢d in the presence ofa sharp ramp varying irradiation level. As expected,the new duty cycle and PV voltage correspondingto the new environmental conditions are reachedslowly; furthermore, a rough three-points behavior,with a coarse power balancing among the operatingpoints, begins at the end of the transient. On the otherside, better experimental results have been obtainedby applying the strategies described in the previoussections.Waveforms of Fig. 22 show the effect of the

proper arrangement of the three operation points bymeans of the parabolic prediction of the duty cycle

Fig. 20. Comparison between results obtained by means of (a) the proposed technique (mean power = 110:59 W) and (b) classicalP&O MPPT approach (mean power = 109:33 W) under same irradiance levels. Upper waveforms = IPV (A/100), central

waveforms = VPV (V), lower waveforms = powers (W/100).

Fig. 21. Experimental waveforms obtained with constantperturbation P&O strategy under increasing irradiation level.

Fig. 22. Experimental waveforms obtained with proposed P&Ostrategy under stationary irradiation level.

perturbation. The system operates with a ¢d that isproportional to the power; when the ¢d predicted bythe parabolic interpolation is bigger than ¢dmin, thecorrection performs a balancing of the three operatingpoints. Indeed, on the left of the dashed line reportedin Fig. 22 the operating points exhibit quite differentpowers, while after the correction their power levels



Fig. 23. Experimental waveforms obtained with proposed P&Ostrategy under varying irradiation level.

Fig. 24. Experimental waveforms obtained with proposed P&Ostrategy under varying irradiation level. Dotted line evidencescorrection introduced by parabola-based prediction of duty cycle

perturbation.

are quite high and close. The bottom plot of Fig. 22shows the operating way at each time interval ofwidth Ta: mode = 1 stands for a perturbation varyinglinearly with the power (2), mode = 2 stands for aparabolic prediction of the next operating point (8).Waveforms depicted in Figs. 23 and 24 have been

obtained by testing the proposed procedure undervarying weather conditions. Plots of Fig. 23 allowto put in evidence that, even if in the selected timewindow the MPPT controller always uses a ¢d thatdecreases according to the increasing power drawnfrom the PV field (2), during a large part of thetransient the method ensures a three-points behavior.Finally, waveforms of Fig. 24 highlight the benefit

derived from the use of the parabolic prediction ofthe operating point also in the presence of varyingweather conditions. During such a variation, infact, the MPPT technique prevalently works with aperturbation given by (2). Nevertheless, when theparabolic prediction acts, the duty cycle is suddenlyvaried and the PV voltage undergoes a 20 V step thatpushes it toward its value corresponding to the newirradiance conditions. Such a sharp correction causesa temporary power drop (just before the time instantplaced at 15 s) that is suddenly recovered with a muchhigher power during the subsequent time intervals.

Such a jump would have required a high numberof time intervals of duration Ta if a classical P&Ostrategy with a constant ¢d were adopted, with anenergy loss globally higher than the one caused by thementioned power drop. The advantages and drawbacksof the jumping ability of the proposed techniqueshave been also evidenced in the preceding section bydiscussing the simulation results presented in Figs. 15and 16.

V. CONCLUSIONS

In this paper the problem of the optimizationof the P&O strategy for PV MPPT presented. Theclassical constant duty cycle perturbation has beenreplaced by a ¢d that linearly reduces with theincrease of the power drawn from the PV field. Thisallows to improve the constant-¢d P&O performancesunder stationary irradiance levels, especially in termsof power levels and stability of the sequence ofoperating points. Indeed, sequences of three points,one placed quite close to the MPP and the othertwo at its sides with an almost equal power level,are insensitive to quantization errors and noise. Afurther refinement of the technique, essentially basedon a parabolic prediction of the next operation pointbased on the last three, has also been introduced.The combined use of both the proposed strategiesimproves P&O performances under constant andvarying irradiation levels. The effectiveness of theproposed solutions, that can be implemented withoutany additional cost with respect to the classicalP&O strategy, has been demonstrated not only bymeans of simulations, but also through experimentalmeasurements.

ACKNOWLEDGMENTS

The authors wish to thank engineer FilippoDe Rosa and engineer Antonio Sirianni for theircooperation in developing the experimental part ofthis work.

REFERENCES

[1] Casadei, D., Grandi, G., and Rossi, C.Single-phase single-stage photovoltaic generation systembased on a ripple correlation control maximum powerpoint tracking.IEEE Transactions on Energy Conversion, 21, 2 (June2006), 562—568.

[2] Leyva, R., Alonso, C., Queinnec, I., Cid-Pastor, A.,Lagrange, D., and Martinez-Salamero, L.MPPT of photovoltaic systems using extremum–seekingcontrol.IEEE Transactions on Aerospace and Electronic Systems,42, 1 (Jan. 2006), 249—258.

[3] Kobayashi, K., Matsuo, H., and Sekine, Y.An excellent operating point tracker of the solar-cellpower supply system.IEEE Transactions on Industrial Electronics, 53, 2 (Apr.2006), 495—499.



[4] Veerachary, M.Power tracking for nonlinear PV sources with coupledinductor SEPIC converter.IEEE Transactions on Aerospace and Electronic Systems,41, 3 (July 2005), 1019—1029.

[5] Shmilovitz, D.On the control of photovoltaic maximum power pointtracker via output parameters.IEE Proceedings–Electric Power Applications, 152, 2(Mar. 2005), 239—248.

[6] Hsiao, Y.-T., and Chen, C.-H.Maximum power tracking for photovoltaic power system.In Industry Applications Conference Record (37thIEEE IAS Annual Meeting), vol. 2, Oct. 13—18, 2002,1035—1040.

[7] Mutoh, N., and Inoue, T.A controlling method for charging photovoltaicgeneration power obtained by a MPPT control methodto series connected ultraelectric double layer capacitors.In it Industry Applications Conference Record (39thIEEE IAS Annual Meeting), vol. 4, Oct. 3—7, 2004,2264—2271.

Nicola Femia (M’94) was born in Salerno, Italy, in 1963. He received the Doctordegree (honors) in engineering of industrial technologies (section electronics)from the University of Salerno, Italy, in 1988.From 1990 to 1998 he was an Assistant Professor, from 1998 to 2001 an

Associate Professor and since 2001 he is a Full Professor of Electrotechnics atthe Faculty of Engineering, the University of Salerno. His main scientific interestsare in the fields of circuit theory and applications and power electronics.Dr. Femia is coauthor of about 80 scientific papers published in the

proceedings of international symposia and in international journals. He wasassociate editor of IEEE Transactions on Power Electronics from 1995 to 2003.

Domenico Granozio was born in Salerno, Italy, in 1976. He received the“Laurea” degree in electronic engineering from the University of Salerno, Italy,in 2003.From June 2003 until June 2005, he collaborated with the Electrical

Engineering Department, University of Salerno as a contract researcher. Hismain research interests are in the analysis and design of switching converters forrenewable energy sources. Moreover his interests are in developing software tomonitor switching converters in photovoltaic applications. Since September 2005he is a product application engineer in National Semiconductor, Germany.

[8] Hohm, D. P., and Ropp, M. E.Comparative study of maximum power point trackingalgorithms.Progress in Photovoltaics: Research and Applications, 11, 1(2003), 47—62.

[9] Hohm, D. P., and Ropp, M. E.Comparative study of maximum power point trackingalgorithms using an experimental, programmable,maximum power point tracking test bed.In Record of the Twenty-Eighth IEEE PhotovoltaicSpecialists Conference, 2000, 1699—1702.

[10] Femia, N., Petrone, G., Spagnuolo, G., and Vitelli, M.Optimization of perturb and observe maximum powerpoint tracking method.IEEE Transactions on Power Electronics, 20, 4 (July2005), 963—973.

[11] Liu, S., and Dougal, R. A.Dynamic multiphysics model for solar array.IEEE Transactions on Energy Conversion, 17, 2 (June2002), 285—294.



Giovanni Petrone was born in Salerno in 1975. He received the “Laurea” degreein electronic engineering from the University of Salerno, Italy, in 2001 and thePh.D. in electrical engineering from the University of Napoli “Federico II,” Italy,in 2004.Since January 2005 he is assistant professor of electrotechnics at the

University of Salerno. His main research interests are in the analysis and designof switching converters for telecommunication applications, renewable energysources in distributed power systems, and tolerance analysis of electronic circuits.

Giovanni Spagnuolo (M’98) was born in Salerno, Italy, in 1967. He received the“Laurea” degree in electronic engineering from the University of Salerno, Italy,in 1993 and the Ph.D. in electrical engineering from the University of Napoli“Federico II,” Italy, in 1997.From November 1993 to October 1994 he worked as a researcher on

the design, building and tuning of a high voltage test-bed of a cryogenicsuperconducting cable. In 1993 he joined the Dipartimento di Ingegneriadell’Informazione ed Ingegneria Elettrica of the University of Salerno, Italy,where he was a Post-Doctoral Fellow (1998/1999), an assistant professor ofelectrotechnics (1999/2003) and, since January 2004, he is associate professor.His main research interests are in numerical methods for the analysis ofelectromagnetic fields, in the analysis and simulation of switching converters, andin tolerance analysis and design of electronic circuits.

Massimo Vitelli was born in Caserta, Italy, in 1967. He received the “Laurea”degree (honors) in electrical engineering from the University of Naples “FedericoII,” Italy, in 1992.In 1994 he joined the Department of Information Engineering of the Second

University of Naples as a researcher. In 2001 he was appointed associateprofessor in the Faculty of Engineering of the Second University of Napleswhere he teaches electrotechnics. His main research interests concern theelectromagnetic characterization of new insulating and semi-conducting materialsfor electrical applications, electromagnetic compatibility and the analysis andsimulation of power electronic circuits.Dr. Vitelli is an associate editor of IEEE Transactions on Power Electronics.



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