Variable Perturbation Size Adaptive P&O MPPT Algorithm for Sudden Changes in Irradiance

Variable Perturbation Size Adaptive P&O MPPTAlgorithm for Sudden Changes in Irradiance

Sathish Kumar Kollimalla, Student Member, IEEE, and Mahesh Kumar Mishra, Senior Member, IEEE

AbstractIn this paper, a variable perturbation size adaptiveperturb and observe (P&O) maximum power point tracking(MPPT) algorithm is proposed to track the maximum power undersudden changes in irradiance. The proposed method consists ofthree algorithms, namely current perturbation algorithm (CPA),adaptive control algorithm (ACA), and variable perturbation algo-rithm (VPA). CPA always tries to operate the photovoltaic (PV)panel at maximum power point (MPP). ACA sets the operatingpoint closer to MPP, only if the operating limits are violated. Theseoperating limits are expressed in terms of the operating currentrange of the PV panel and the sudden changes in irradiance. VPAdynamically reduces the perturbation size based on polarity ofchange in power. Two-stage variable size perturbation is proposedin this paper. The proposed algorithm is realized using a boostconverter. The effectiveness of proposed algorithm in terms ofdynamic performance and improved stability is validated bydetailed simulation and experimental studies.

Index TermsAdaptive control algorithm (ACA), adaptive P&OMPPTalgorithm, current perturbation algorithm (CPA), fractionalshort circuit current (FSCC) method, maximum power pointtracking (MPPT), perturb and observe (P&O) method, variableperturbation algorithm (VPA).

I. INTRODUCTION

T HEMAIN objective of the maximum power point (MPP)tracking (MPPT) algorithms is to achieve fast and accuratetracking performance and minimize oscillations due to varyingweather conditions. A comparative study on MPPT techniquesfor photovoltaic (PV) power systems is reported in [1] and [2].Among different MPPT algorithms, much focus has been onperturb and observe (P&O) [3], hill climbing [4], and incrementalconductance (INC) methods [5]. In [3], a survey of P&O tech-niques has been presented. It has been shown that the existingtechniques suffer from oscillations, complexity, designer depen-dency, and more computational effort. In the P&O method, theoperating point oscillates around the MPP giving rise to thewastage of some amount of available energy. These oscillationscan be minimized by reducing the xed perturbation size, but ittakes relatively more time to reach MPP. The solution to thisconicting situation is to have a variable step size as suggested in[6]. Although the implementation of these methods are simple, it

is not very accurate and rapid, since the effects of temperature andirradiation are not taken into consideration. Patel andAgarwal [7]proposed a variable perturb by adopting four power ranges. Ineach range, a specic perturb value is used; hence, the method isnot fully adaptive. Several methods are proposed to address theseissues by considering adaptive perturbation [8], [9].An INC method is given in [5], [10], and [11], which is based

on the fact that the slope of the PV array power curve is zero atMPP, negative on the right, and positive on the left of the MPP.The INCmethod inherits the same problems as P&O, namely thetradeoff between the speed and oscillations. In [4], the authorclaims that the INC method is prone to failure in case of largechanges in irradiance.In another method, the MPP current IMPP (or MPP voltage

VMPP) is continuously monitored with respect to the short circuitcurrent ISC (or open circuit voltage VOC) [12][14]. This methodis well known as the fractional short circuit current [(FSCC) orfractional open circuit voltage] method. Since this methodapproximates a constant ratio, its accuracy cannot be guaranteedunder varying weather conditions.To overcome the above-mentioned drawbacks, several meth-

ods have been proposed using articial intelligence (AI)-basedalgorithms such as neural network (NN) [15] and fuzzy logiccontroller (FLC) [16]. But these methods also have drawbackssuch as the requirement of large data storage and extensivecomputation. For instance, NN requires a large amount of datafor training, which is the major constraint. Similarly, FLCrequires extensive computation to deal various stages. Since thenonlinear characteristics of the solar module should be wellascertained to create the control rules, the versatility of thesemethods is limited. Furthermore, low-cost hardware processorscannot be used for these applications because the MPP continu-ously changes with atmospheric conditions in real time.In this paper, a variable perturbation size adaptive P&OMPPT

algorithm is proposed in order to overcome the drawbacks in theconventional P&O method. The proposed method consists ofthree algorithms namely, current perturbation, adaptive control,and variable perturbation. The adaptive control algorithm(ACA) moves the operating point closer to the MPP by multi-plying the short circuit current with optimal proportionalityconstant. The ACA gets activated only if there is sudden changein irradiance or sudden change in PV current. In the proposedmethod, the short circuit current is estimated instead of measur-ing, which reduces the losses and saves the additional componentcost required. Further, the proposed algorithm features the tuningof variable perturbation size in two stages, namely coarse andne tuning. In the coarse tuning, the perturbation size is deter-mined based on irradiance level. In the ne tuning, the

Manuscript received August 19, 2013; revised November 22, 2013;accepted January 08, 2014. Date of publication February 05, 2014; date ofcurrent version June 17, 2014. Thisworkwas supported in part by theDepartmentof Science and Technology (DST), India, under the project Grant DST/TM/SERI/2k10/47(G).

The authors arewith theDepartment of Electrical Engineering, Indian Instituteof Technology Madras, Chennai 600036, Tamil Nadu, India (e-mail:[email protected]; [email protected]).

Color versions of one ormore of the gures in this paper are available online athttp://ieeexplore.ieee.org.

Digital Object Identier 10.1109/TSTE.2014.2300162

718 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 3, JULY 2014

1949-3029 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

perturbation size is determined based on operating point oscilla-tions around MPP.

II. VARIABLE PERTURBATION SIZE ADAPTIVE P&O MPPTALGORITHM

The objective of the MPPT algorithm is to track the currentIMPP and voltage VMPP of PV array, where maximum outputpower PMPP is obtained under a specic irradiance andtemperature. In this paper, a variable perturbation size adaptiveP&OMPPT algorithm is proposed using conventional P&O andFSCC methods. The proposed method is divided into threealgorithms:1) Current Perturbation Algorithm (CPA): This algorithm

uses the concept of a conventional P&O algorithm, but itconsiders current perturbation instead of voltage perturba-tion to speed up the tracking performance. CPA is ex-plained using a owchart as shown in Fig. 1.

2) Adaptive Control Algorithm (ACA): This algorithm usesthe concept of FSCC. It determines the new operating pointcloser to MPP. It was carried out by multiplying the shortcircuit current with an optimal proportionality constant.Further, ACA sets the perturbation size to coarse pertur-bation size (IC), which varies with irradiance. Thisalgorithm gets activated only if there is sudden change inirradiance or sudden change in PV current.

3) Variable Perturbation Algorithm (VPA): This algorithmreduces the perturbation size dynamically whenever theoperating point crosses the MPP to minimize the oscilla-tions around MPP. It provides the ne tuning of perturba-tion size.

A. Current Perturbation Algorithm

In Fig. 1, Ipvk, Vpvk, and Ppvk are current, voltage, andpower of PV module at kth iteration, respectively. The general-ized equation is derived for the proposed MPPT algorithm asgiven

Iref Ipvk signIpvk Ipvk 1 signPpv Ik(1)

where the function sign: gives either 1 or 1 depending onpositive or negative value inside the function, respectively.The idea behind considering current perturbation is explained

as follows. At a given temperature and irradiance, the outputcurrent of PV module in the voltage region, 0 to VMPP, i.e., left-hand side (LHS) of MPP, is almost constant as shown in Fig. 2.On the other hand, the current is drastically changing on the right-hand side (RHS). Therefore, when the operating point lies in theLHS of MPP, the PV system reaches MPP faster with reducedoscillations with relatively small perturbation in current ascompared to voltage. If the operating point lies in the RHS of

Fig. 1. Flowchart of the proposed MPPT algorithm.

KOLLIMALLA AND MISHRA: VARIABLE PERTURBATION SIZE ADAPTIVE P&O MPPT ALGORITHM 719

MPP and operating current Ipvk is less than IMPP ISCIMPP, then the current perturbation gives slower response.To avoid this situation, an ACA is proposed. Therefore, theoperating range for which the current perturbation alone givessatisfactory response is given as

2IMPP ISC Ipvk ISC: (2)

B. Adaptive Control Algorithm

ACA always tries to keep the operating point within theoperating range as given in (2). Once MPP is reached, thenVMPP and IMPP oscillate around MPP depending on the pertur-bation size. If the operating point violates (2) due to suddenchange in irradiance, then Ipv is to be controlled such that theoperating point satises (2). This can be performed by obtainingthe short circuit current. Different methods are available forobtaining the short circuit current as mentioned in the FSCCmethod. But these methods will give power losses and increaseadditional component cost. To avoid these, a generalized ex-pression is derived in this paper to estimate the short circuitcurrent for changes in irradiance and temperature.The variation in short circuit current with irradiance and

temperature given in [4] is modied as follows:

ISC KT SSnom

ISCSnom; TnomKA (3)

where

KT 1 ISCT Tnom (4)

ISC is current temperature coefcient, KA is correction factoraccounting for ambient temperature and PV panel aging. Theterms Snom, Tnom, and ISCSnom; Tnom are irradiance, tempera-ture, and short circuit current of PV panel at standard testconditions (STCs), respectively. The term S is variable irradi-ance, and T is variable temperature. The variation in short circuitcurrent with temperature is much less as compared to irradiance[3]. Thus,KT in (4) can be approximated to unity. This approxi-mationwill save thememory, computation time, and temperaturesensor cost. Therefore, the short circuit current is approximatedas given

ISC SSnom

ISCSnom; TnomKA mS (5)

where m ISCSnom; TnomKASnom .

1)Determination of ReferenceCurrent:Once ISC is estimated,then the new operating point is calculated using FSCC.According to FSCC, IMPP is approximately linearly related toISC as given in [1]

IMPP kscISC (6)

where ksc is a proportionality constant. It is assumed that thevalue of ksc lies between ksc low and ksc up for given range ofirradiance and temperature.The value of ksc is chosen such that i) the operating point lies

within the limits of (2) and ii) all the currents, ksc lowISC toksc upISC, of (6) are considered while calculating operatingcurrent. Based on these two conditions, optimal proportionalityconstant (ksc opt) is determined by equating the lower currentlimit of (2) and lower MPP current of (6) as given

2IMPP ISC ksc lowISC: (7)

Substituting (6) and ksc ksc opt in (7) gives

ksc opt 1 ksc low2

: (8)

Therefore, the reference current is given as

Iref ksc optISC 1 ksc low2

mS: (9)

2) Determination of Operating Current Limits: From (2) and(5), the upper operating current limit for a given irradiance S isdened as

Iup ISC mS: (10)

Similarly, from (2), the lower operating current limit for a givenirradiance S is dened as

Ilow 2IMPP ISC: (11)

Substituting (5), (6), and ksc ksc opt in (11) givesIlow ksc lowmS: (12)

3) Determination of S: Let us consider that S1; S0,and S2 are three irradiance levels with S1 > S0 > S2. Thecorresponding operating ranges for which the currentperturbation alone gives satisfactory response are dened as

2IMPP1 ISC1 Ipvk ISC1 (13)2IMPP0 ISC0 Ipvk ISC0 (14)2IMPP2 ISC2 Ipvk ISC2: (15)

Let us assume that the PV panel is operating at S0. Suddenly theirradiance is increased to S1 such that the lower limit of (13) isequal to the upper limit of (14) as given

2IMPP1 ISC1 ISC0: (16)

Fig. 2. Characteristics of PV array.


Solving (16) using (5), (6), and ksc ksc opt gives S1 1

2ksc opt1S0. Therefore, the incremental limit ofS is dened as

SINC S1 S0 21 ksc opt2ksc opt 1 S0: (17)

Similarly, assume that irradiance is suddenly decreased from S0toS2 such that the lower limit of (14) is equal to the upper limit of(15) as given

2IMPP0 ISC0 ISC2: (18)

Solving (18) using (5), (6), and ksc ksc opt gives S2 2ksc opt 1S0. Therefore, the decremental limit of S isdened as

SDEC S2 S0 2ksc opt 1S0: (19)

4) Determination of IC: The threshold current range ITHfor a given irradiance S is dened as

ITH Iup Ilow: (20)

Substituting (10) and (12) in (20) gives

ITH 1 ksc lowmS: (21)Assuming N as the maximum number of iterations required todetermineMPP in theITH range from any extreme limit of (2),the coarse perturbation size IC is dened as

IC ITHN

1 ksc lowN

mS: (22)

From the above equation, it is clear thatIC varies linearly withirradiance. This value sets the coarse tuning of variableperturbation size.

C. Variable Perturbation Algorithm

The ne perturbation size (IF) is dened as

IF m1 m2 jMj2

Ik (23)

where m1 is the reduction factor of perturbation size andm2 1m1. The variable M accounts for oscillations ofoperating point around MPP and dened as

M signPpv1 signPpv0 (24)

where

Ppv1 Ppvk Ppvk 1 (25)Ppv0 Ppvk Ppvk 1: (26)

If the operating point is moving away from the MPP, thensignPpv1 or signPpv0 in (24) is equal to1, otherwise1.

Depending on the movement of operating point as shown inFig. 3, the variableM assumes2 or 0 or2 as explained below.Case 1) If the operating point is moving toward MPP for two

consecutive iterations, then signPpv1 andsignPpv0 are equal to 1 and M 2.

Case 2) If the operating point crosses theMPP fromLHS toRHSor vice versa, then signPpv1 and signPpv0 willhave opposite polarity and M 0.

Case 3) If the operating point is moving away from MPP and inthe next iteration if it moves toward MPP, thensignPpv1 and signPpv0 will have opposite po-larity and M 0.

Case 4) If the operating point is moving away fromMPP for twoconsecutive iterations, then signPpv1 andsignPpv0 are equal to 1 and M 2.

Therefore, whenever the power oscillations occur, the pertur-bation size is reduced by factor m1 as shown in Table I.After repeated oscillations around MPP, IF 0 and hencethe oscillations become negligible. If m1 1, then VPA isabsent; similarly, if m1 0, then IF 0. Therefore, theoperating range for m1 is given as

0

It is assumed that the boost converter is operating in continu-ous current mode (CCM). According to the state space averagingmethod [17], the system dynamics are described by the followingequations:

dipvdt

1 dL

vo vpvL

(28)

dvodt

1 dC

ipv 1RC

vo (29)

where ipv, vpv, and vo are input current, input voltage, and outputvoltage of boost converter, respectively, and d is duty ratio.

A. Design of Current Control Loop

Fig. 4 shows that vpv and ipv are given to the MPPT controllerthat generates the reference inductor current Iref . This referencecurrent is given to the current control loop. The transfer functionof control to inductor current is given as [18]

Gids ~ipv~d VoCs 2

VoR

LCs2 LR s 1D2(30)

where ~vpv; ~ipv; ~vo, and ~d are small perturbations in vpv; ipv; vo,and d, respectively.The transfer function of proportional integral (PI) controller

is given by

Gcs Kp Kis: (31)

The open-loop transfer function of current loop is given by

GOLs GidsGcs: (32)

The parameters of boost converter considered for experimentalstudy are given in Table II. The nominal switching frequency ofthe boost converter considered is 20 kHz. Fig. 5(a) shows theBode plot of the open-loop transfer function GOLs for thesenominal values. It shows that the open-loop transfer functionwithout compensator has a phase margin of 89:6 at 12.9 krad/s.The MPPT algorithm is executed at every 50 cycles of the

switching frequency. Therefore, the PI controller is designed to

achieve a phase margin of 60 at 2.51 krad/s. The parameterscalculated areKp 0:169 andKi 226:6. Fig. 5(b) shows theroot locus diagram of compensated and uncompensated system.The root locus shows that the closed-loop poles for designedphase margin occur at p1 177 ( 1, !n 177 krad/s)and p2;3 1:05e3 j1:38e3 ( 0:607, !n 1:74 krad/s)ensuring the system stability.

IV. SIMULATION STUDIES

The proposed MPPT algorithm is veried for sudden changesin irradiance through digital simulations. The PV module con-sidered for simulation is HHV Solar 240 Watt multicrystallinePVpanel. The specications of the PVpanel are given inTable III.

Fig. 4. Circuit diagram of PV system with MPPT controller.

TABLE IINOMINAL PARAMETERS OF BOOST CONVERTER

Fig. 5. (a) Bode plot and (b) root locus of current control loop.

TABLE IIISPECIFICATIONS OF PV PANEL AT STC


A PV array is formed by connecting seven modules in series andtwo modules in parallel. The PV array is simulated to determineksc, in the range of S 10 to 1000 W=m2 and T 10 C to100 C. From the simulation results, it was found thatksc low 0:78 and ksc up 0:95. Substituting ksc low in (8) givesksc opt 0:89.The proposed algorithm is compared with two algorithms,

namely conventional P&O [19] and adaptive P&O [20]. Thevoltage perturbation size (V ) is chosen such that the conven-tional P&O algorithm and proposed algorithm withN 10 andm1 1 give the same dynamic performance in terms of oscilla-tions at STC. The parameters considered in this study arem 0:0166, N 10, m1 0:9, and V 2:5 V.In this study, the PV array is simulated for sudden changes in

irradiance assuming a constant temperature of 25 C. Initially,the PV array is simulated at S 800 W/m2. At the 50thiteration, the irradiance is suddenly decreased to 400 W/m2.At the 100th iteration, the irradiance is suddenly increased to800 W/m2. Fig. 6(a) and (b) shows the comparison of theproposed algorithm with conventional P&O and adaptiveP&O algorithms, respectively. To observe the performance ofthe proposed algorithm, the simulation results are zoomed in theiterations of (5185) and (101135). From the simulation results,it is observed that the proposed algorithm is taking feweriterations to reachMPPwhen compared with the two algorithms.It is further observed that the oscillations are reduced signi-cantly when compared with the two algorithms. Fig. 6(c) showsthe variation in I, corresponding to the sudden changes inirradiance and power oscillations determined using (22) and (23),respectively, as shown in Fig. 6(a) and (b).From the above simulation study, it is observed that the

proposed MPPT algorithm effectively reduces the sustainedoscillations and tracks the MPP faster, irrespective of increaseor decrease in irradiance.

V. EXPERIMENTAL STUDIES

The realization of the proposedMPPT algorithm is carried outby dSPACE real-time control. The laboratory prototype used to

verify the performance of the proposed MPPT algorithm isshown in Fig. 7. Data acquisition and the control systemare implemented by using dSPACE 1104 software with a digitalsignal processor module in the PCI slot of the host PC.The specications of the boost converter are given in Table II.The Semikron SKM75GB128D is used as a control switch in theboost converter circuit. In this experiment, HHV Solar 240Wattmulticrystalline PV panel is used. The specications of the PVpanel are given in Table III. Currents and voltages are measuredby LEM transducers.

A. Determination of m, KA, IC, and Operating Limits

The short circuit current is estimated using (5) for differentvalues of KA and S as shown in Fig. 8(a). Similarly, ISC ismeasured for different values of S by shorting the PV panel.Thesemeasured currents are superimposed on estimated currentsas shown in Fig. 8(a). From the graph, it was observed that forKA 0:5542, the measured ISC and estimated ISC are approxi-mately equal. Therefore, using KA 0:5542, it was found thatm 0:0046 A/W/m2 in (5).As S increases, the maximum power will also increase

accordingly. In order to track MPP faster, perturbation size hasto be changed according toS. Fig. 8(b) shows the variation in theperturbation size calculated using (22). From the results, it is

Fig. 6. Comparison of proposed algorithm with (a) conventional P&O, (b) adaptive P&O, and (c) variable perturbation size.

Fig. 7. Experimental setup.


observed that as S is increased, the perturbation size is alsoincreased in proportion. Further, the perturbation size is alsocustomized by choosing N .The variations in upper and lower current limits for different

values of S are calculated using (10) and (12), respectively, asshown in Fig. 8(c). If the PV current is not lying between thesecurves, then ACA gets activated. Similarly, the variations inincremental and decremental limits of S are calculated using(17) and (19), respectively, as shown in Fig. 8(d). If the change inirradiance is not lying between these curves, then ACA getsactivated.

B. Effect of m1 on Proposed Algorithm

In this study, the effect of m1 on the proposed algorithm isstudied. Fig. 9(a) shows the current, power, and voltages of thePV system. Initially, the boost converter switch is OFF, so that thePV panel is directly connected to load resistance of 25 . At t1,t3, and t5 instants, the proposed algorithm is activated withm1 0:95, 0.9, and 0.85, respectively, at constant N 2. Theproposed algorithm is deactivated at t2 and t4 instants, so that thePV panel is directly connected to the load. The irradiancemeasured is varying around 500 W/m2. To analyze the effectofm1, the powers are zoomed at t1, t3, and t5 instants, as shownin Fig. 9(b). From the results, it is observed that the steady-stateresponse time to reach MPP, tss 0:3, 0.08, and 0.04 s form1 0:95, 0.9, and 0.85, respectively. Therefore, as m1 isdecreasing, the oscillations around MPP are also reducingrapidly, and hence the PV panel reaches steady state rapidly.Fig. 9(c) shows the variation inI, corresponding to changes inm1 determined by (22) and (23).

C. Effect of N on Proposed Algorithm

In this study, the effect of N on the proposed algorithm isstudied. Fig. 10(a) shows the current, power, and voltages of thePV system. Initially, the boost converter switch is OFF, so that thePV panel is directly connected to load resistance of 25 . At t1,t3, and t5 instants, the proposed algorithm is activated withN 1, 3, and 10, respectively, at constantm1 1 (i.e., VPA isabsent). The proposed algorithm is deactivated at t2 and t4instants, so that the PV panel is directly connected to the load.

The irradiance measured is varying around 490 W/m2. Theperturbation sizes corresponding to N 1, 3, and 10 are deter-mined using (22); these values are I 0:496, 0.165, and0.049 A, respectively. To analyze the effect of N , the powersare zoomed at t1, t3, and t5 instants, as shown in Fig. 10(b). Fromthe results, it is observed that for N 1, the PV panel reachesMPP faster with signicant oscillations around MPP, whencomparedwithN 3 and 10. ForN 10, the PV panel reachesMPP relatively slowly with reduced oscillations. The magnitudeof oscillations around MPP (Pmag osc) is 14, 4, and 0.5 W forN 1, 3, and 10, respectively. Therefore, asN is increasing, thePV panel reaches MPP relatively slowly with reduction inmagnitude of oscillations.

VI. COMPARISON OF MPPT ALGORITHMS

The proposed algorithm is evaluated for 1) operating currentlimit violation, 2) sudden decrease in irradiance, and 3) suddenincrease in irradiance. In this study, sudden changes in irradianceare articially created by shading the PV panel. The parametersconsidered are m1 0:9 and N 10. In this study, the lowerlimit of I is kept at 0.01 A.The proposed algorithm is compared with three algorithms

namely 1) voltage-based P&O (algorithm 1) [19], 2) current-

Fig. 8. Variation in current and operating limits with irradiance.

Fig. 9. Experimental results for m1 0:95, 0.9, and 0.85 at N 2: (a) outputvoltage, PV power, voltage, and current; (b) powers; and (c) variable perturbationsize.


based P&O (algorithm 2) [21], and 3) duty ratio-based INC(algorithm 3) [22].There is a tradeoff between response speed and oscillations

around MPP in the conventional MPPT algorithms. To comparethe algorithms, voltage perturbation (VP&O), current perturba-tion (IP&O), and duty ratio perturbation (DINC) of algorithms1, 2, and 3 are determined, respectively, by xing the oscillationsaround MPP approximately equal to the oscillations obtained byproposed algorithm. Therefore, the performance is evaluatedbased on response speed to reach MPP, for the same amount ofoscillations.Figs. 11(a), 12(a), and 13(a) show the variation in irradiance

pattern considered in this study. It shows that the irradiance issuddenly decreased at t2 and t6 instants and suddenly increased att3 and t7 instants. Figs. 11(b), 12(b), and 13(b) show the voltage(vpv), current (ipv), and power (ppv) of PV panel and outputvoltage (vo) of boost converter. Figs. 11(c)(e), 12(c)(e), and13(c)(e) show the zoomed powers of the proposed and conven-tional algorithms at (t1, t5), (t2, t6), and (t3, t7) instants corre-sponding to operating current limit violation, sudden decrease inirradiance, and sudden increase in irradiance, respectively.To demonstrate the performance of the proposed algorithm,

the boost converter is operated in three modes: 1) inactive mode,2) proposed algorithm mode (t1 t4), and 3) conventional algo-rithmmode (t5 t8). In inactivemode, the control switch is OFF sothat the PV panel is directly connected to the load. The operatingpoint of PV panel is decided by the load resistance. In the proposedand conventional algorithm modes, switching pulses are given tothe control switch according to the individual control logic.

A. Comparison of Proposed Algorithm With Voltage-BasedP&O Algorithm (Algorithm 1) [19]

Initially, the boost converter is operated in inactive mode.Therefore, the PV panel is directly connected to the load resis-tance of 25 . The corresponding PV panel operating voltageand current are 27.5 V and 1.1 A, respectively.At t1 instant, the proposed algorithm is activated. The irradi-

ance measured at this instant is 535 W/m2. According to (12),Ilow 1:91 A for S 535 W/m2. But ipv 1:1 A, which isless than Ilow. Therefore, ACA gets activated and sets Irefto 2.19 A and I to 0.0541 A using (9) and (22), respectively.The current perturbation algorithm takes these values as inputsand drives the operating point to MPP, as shown in Fig. 11(b).

Fig. 11. Experimental results of proposed algorithm and algorithm 1:(a) irradiance; (b) output voltage, PV power, voltage, and current; and(c)(e) powers.

Fig. 10. Experimental results forN 1, 3, and 10 atm1 1: (a) output voltage,PV power, voltage, and current, and (b) powers.


As the operating point oscillates around MPP, VPA gets acti-vated and continuously reduces the I using (23). The CPAdrives the operating point toMPP in less than 60 ms, as shown inFig. 11(c).At t2 instant, the irradiance is suddenly decreased from 535 to

410 W/m2. According to (19),SDEC 117 W/m2. But theirradiance is decreased by125 410 535 W/m2, which isless thanSDEC. Therefore, ACA gets activated and sets the Irefto 1.678 A andI to 0.0415 A using (9) and (22), respectively.The CPA drives the operating point toMPP in less than 40ms, asshown in Fig. 11(d).At t3 instant, the irradiance is suddenly increased from 412

to 537 W/m2. According to (17), SINC 116 W/m2. Butthe irradiance is increased by 125 537 412 W/m2,which is greater than SINC. Therefore, ACA gets activatedand sets the Iref to 2.198 A and I to 0.0543 A using (9) and(22), respectively. The CPA drives the operating point to MPPin less than 70 ms as shown in Fig. 11(e).At t4 instant, the boost converter is brought back to inactive

mode. Therefore, the PV panel is directly connected to the load.At t5 instant, algorithm 1 is activated with VP&O 0:1 V. Att6 instant, the irradiance is suddenly decreased to 418 W/m

2. Att7 instant, the irradiance is suddenly increased to 515 W/m

2.The results are shown in Fig. 11(b).From Fig. 11(c)(e), it is observed that the steady-state

response time to reach MPP (tss) for proposed algorithm is60, 40, and 70 ms, respectively, whereas for algorithm 1 is 350,180, and 160 ms, respectively.

B. Comparison of Proposed Algorithm With Current BasedP&O Algorithm (Algorithm 2) [21]

Initially, the boost converter is operated in inactive mode.At t1 instant, the proposed algorithm is activated. At thisinstant, vpv, ipv, S, and Ilow are 25 V, 1 A, 525 W=m2, and1.88 A, respectively. As ipv is less than Ilow, ACA getsactivated and sets Iref to 2.14 A and I to 0.0531 A. Thecurrent perturbation algorithm takes these values as inputsand drives the operating point to MPP, as shown inFig. 12(b).At t2 instant, the irradiance is suddenly decreased from 525 to

374 W/m2. According to (19),SDEC 115 W/m2. But theirradiance is decreased by151 374 525 W/m2, which isless thanSDEC. Therefore, ACA gets activated and sets the Irefto 1.531 A and I to 0.0378 A.At t3 instant, the irradiance is suddenly increased from 374 to

523 W/m2. According to (17), SINC 105 W/m2. But theirradiance is increased by 149 523 374 W/m2, which isgreater than SINC. Therefore, ACA gets activated and sets theIref to 2.141 A and I to 0.0529 A.At t4 instant, the boost converter is brought back to inactive

mode. At t5 instant, algorithm 2 is activated with IP&O 0:01 A. At t6 instant, the irradiance is suddenly decreased to375 W/m2. At t7 instant, the irradiance is suddenly increasedto 535 W/m2.From Fig. 12(c)(e), it is observed that tss for proposed

algorithm is 80, 60, and 70 ms, respectively, whereas for algo-rithm 2 is 750, 190, and 340 ms, respectively.

C. Comparison of Proposed Algorithm With Duty Ratio-BasedINC Algorithm (Algorithm 3) [22]

Initially, the boost converter is operated in inactivemode.At t1instant, the proposed algorithm is activated. At this instant, vpv,ipv, S, and Ilow are 22.5 V, 0.9 A, 508 W/m

2, and 1.82 A,respectively. As ipv is less than Ilow, ACA gets activated and setsIref to 2.079 A and I to 0.0514 A. The current perturbationalgorithm takes these values as inputs and drives the operatingpoint to MPP, as shown in Fig. 13(b).At t2 instant, the irradiance is suddenly decreased from 510 to

364 W/m2. According to (19),SDEC 112 W/m2. But theirradiance is decreased by146 364 510 W/m2, which isless thanSDEC. Therefore, ACA gets activated and sets the Irefto 1.49 A and I to 0.0368.

Fig. 12. Experimental results of proposed algorithm and algorithm 2: (a) irradi-ance; (b) output voltage, PV power, voltage, and current; and (c)(e) powers.


At t3 instant, the irradiance is suddenly increased from 366 to516 W/m2. According to (17), SINC 103 W/m2. But theirradiance is increased by 150 516 366 W/m2, which isgreater than SINC. Therefore, ACA gets activated and sets theIref to 2.112 A and I to 0.0522 A.At t4 instant, the boost converter is brought back to inactive

mode. At t5 instant, algorithm 3 is activated with DINC 0:005. At t6 instant, the irradiance is suddenly decreased to370 W/m2. At t7 instant, the irradiance is suddenly increased to537 W/m2. The results are shown in Fig. 13(b).From Fig. 13(c)(e), it is observed that tss for the proposed

algorithm is 60, 40, and 40 ms, respectively, whereas for algo-rithm 3 is 290, 120, and 160 ms, respectively.From the above results, it is observed that the proposed

algorithm reaches MPP relatively faster when compared withalgorithms 1, 2, and 3. Therefore, the proposedMPPT algorithm

effectivelyworks for operating current limit violation and suddenchanges in irradiance.

VII. CONCLUSION

In this paper, a two-stage variable perturbation size algorithmwas proposed for sudden changes in irradiance and PV currentlimit violation. The proposed method has the following threefeatures: 1) steadily tracks the MPP under normal conditions,2) speeds up the dynamic performance under sudden operatinglimits violation, and 3) provides variable perturbation to reducethe oscillations around MPP. These three features are accom-plished using three algorithms namely CPA, ACA, and VPA,respectively. Unlike the conventional P&O, the proposed algo-rithm has faster response with reduced oscillations around MPP.The computational efforts caused due to the derivatives asexplained in INC method are absent. It tracks true maximumpower, unlike the fractional open circuit voltage and FSCCmethods. Also, it does not require a large amount of data(storage) for training and extensive computation to deal variousstages, as required by FLC and NN. The simulation and experi-mental studies show that the proposed algorithm gives fasterresponse than the conventional algorithms.

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Fig. 13. Experimental results of proposed algorithm and algorithm 3: (a) irradi-ance; (b) output voltage, PV power, voltage, and current; and (c)(e) powers.


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Sathish Kumar Kollimalla (S12) received theBachelor degree from VITAM College of Engineer-ing, Visakhapatnam, Andhra Pradesh, India, in 2003,and the Master of Engineering degree from AndhraUniversity, Visakhapatnam, Andhra Pradesh, India,in 2006. Currently, he is pursuing the Ph.D. degreefrom the Indian Institute of Technology Madras,Chennai, Tamil Nadu, India.His research interests include power electronics

applications in power systems, microgrid, renewableenergy systems, and power quality.

Mahesh Kumar Mishra (S00M02SM10) re-ceived the B.Tech. degree from the College of Tech-nology, Pantnagar, Uttarakhand, India, in 1991,the M.E. degree from the University of Roorkee,Roorkee, Uttarakhand, India, in 1993, and the Ph.D. degree in electrical engineering from the IndianInstitute of Technology Kanpur, Kanpur, UttarPradesh, India, in 2002.He has teaching and research experience of about

20 years. For about 10years, hewaswith theElectricalEngineering Department, Visvesvaraya National In-

stitute of Technology, Nagpur, India. Currently, he is a Professor with theElectrical Engineering Department, Indian Institute of Technology Madras,Chennai, Tamil Nadu, India. His interests are in the areas of power distributionsystems, power electronic applications in microgrid, and renewable energysystems.Dr. Mahesh is a life member of the Indian Society of Technical Education

(ISTE).


Variable Perturbation Size Adaptive P&O MPPT Algorithm for Sudden Changes in Irradiance

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