A Global Maximum Power Point Tracking Scheme Employing DIRECT Search Algorithm for Photo Voltaic Systems

8/3/2019 A Global Maximum Power Point Tracking Scheme Employing DIRECT Search Algorithm for Photo Voltaic Systems

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3456 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 10, OCTOBER 2010

A Global Maximum Power Point Tracking SchemeEmploying DIRECT Search Algorithm for

Photovoltaic SystemsTat Luat Nguyen and Kay-Soon Low, Senior Member, IEEE

AbstractThis paper presents a maximum power point track-ing approach for a photovoltaic system using the dividing rectan-gles algorithm. The new approach overcomes some weaknesses ofthe existing methods such as the perturb and observe method asit is capable of searching for global maximum. This is particularlyimportant fora system that is partially shaded. To validate the per-formance of the proposed scheme, experimental studies have beenconducted. The results have shown that the proposed approach isrobust and possesses a fast tracking speed.

Index TermsGlobal peak (GP), maximum power point track-ing (MPPT), partially shaded, photovoltaic (PV) systems, solarenergy.

I. INTRODUCTION

PHOTOVOLTAIC (PV) energy generation has become in-

creasingly important as a renewable source due to its

environmentally friendly nature and a practically unlimited

source. In some applications, particularly in space, PV energy

is also the primary power source available.

Until today, PV modules still have relatively low conversion

efficiency. Consequently, an approach to track its optimum

operating point (OP) is always an essential issue in a PVsystem. Over the past decades, many maximum power point

tracking (MPPT) techniques have been developed and imple-

mented. They vary in complexity, convergent speed, cost, and

range of effectiveness [1], [2] or hardware implementation

[3][6]. Among those techniques, the perturb and observe

(P&O) scheme [7][9] and the incremental conductance (INC)

scheme [10], [11] are the most common due to their ease of

implementation. The main drawback of these methods is that

they can only track a single maximum, which is absent when

the solar panels are partially shaded. The reason is that these

methods are based on the hill-climbing principle of moving

the next OP in the direction in which power increases. If the

PV (or PI) characteristic is not unimodal, these methodscould only successfully reach a local maximum.

In recent years, a few novel MPPT methods have been dis-

cussed to overcome this limitation [12][19]. Kobayashi et al.

[12] and Irisawa et al. [13] have proposed a two-stage method

to track the global peak (GP). In the first stage, the OP of the

Manuscript received December 31, 2008; revised April 20, 2009, August 6,2009, and October 29, 2009; accepted November 30, 2009. Date of publicationJanuary 19, 2010; date of current version September 10, 2010.

The authors are with the School of Electrical and Electronic Engineer-ing, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIE.2009.2039450

PV system moves into the vicinity of the real maximum power

point (MPP). Then, it converges to the real MPP in the second

stage. However, this method may not track the real MPP for

some nonuniform insolation conditions. Miyatake et al. [14]

employed a line search algorithm with improved Fibonacci

search to find the GP when the PV array is partially shaded.

This approach too cannot guarantee to find the GP under all

conditions [14]. In [15], a fractional open-circuit voltage(Voc)method that periodically sweeps the PV array voltage from

open circuit to short circuit is proposed. It updates the fraction

that gives the relationship between the MPP voltage (VMPP)and Voc to find the MPP. Consequently, this causes somepower losses. In [16], a voltage-based power compensation

method that deactivates shaded PV modules by forward biasing

corresponding bypass diodes according to the shaded level of

the PV module is proposed. This method is suitable for a system

that consists of multimodules in series and parallel. Moreover,

knowledge of the system is essential. In [17], an approach

for adaptive reconfiguration of solar PV arrays under shadow

conditions has been described. A switching matrix connects a

solar adaptive bank to a fixed part of the PV array accordingto a model-based control algorithm. The method would require

a large number of switches and sensors if the number of rows

in the PV array is large. Gules et al. [18] proposed a parallel-

connected MPPT system in which the PV modules are con-

nected in parallel. Each module is treated as one unit that tracks

its own MPP. When a module is shaded, the performance will

not propagate to other modules. However, the method incurs

extra hardware and cost. Moreover, a good MPPT should also

need to be implemented in each branch to track the MPP when

a module is shaded. Patel and Agarwal [19] also proposed a

two-stage method to track the GP. A global stage is used to find

the region of local MPPs, while the local stage employs P&Oto track the local MPPs. Initially, the method finds the nearest

local MPP. It then searches on the local MPPs left and later

on its right to find other local MPPs. The decision to search

in the same or reverse direction depends on the comparison of

local MPPs and other criteria, as described in [19]. The search

is terminated when the algorithm finds the highest local MPP.

Thus, the tracking speed is limited as almost all local MPPs

may be found and compared to find the GP.

In this paper, a new search algorithm that has the same ease

of implementation as the P&O and INC schemes is proposed.

The new approach shows a better performance and fast tracking

speed, particularly in the presence of multiple MPPs and sudden

0278-0046/$26.00 2010 IEEE


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NGUYEN AND LOW: GLOBAL MPPT SCHEME EMPLOYING DIRECT SEARCH ALGORITHM FOR PHOTOVOLTAIC SYSTEMS 3457

high level changing of insolation. The proposed approach is de-

veloped based on the dividing rectangles (DIRECT ) algorithm

that was developed in [20] for searching the global extreme of

a Lipschitz function in an interval. In this paper, it is shown that

the function describing the power/voltage relationship of PV

cells is a Lipschitz function. Therefore, the DIRECT algorithm

can be employed in tracking global maximum power of a PVsystem.

The organization of this paper is as follows. In

Section II, the fundamental characteristics of PV cells are

discussed. Section III introduces an overview of the DIRECT

algorithm. Section IV presents its implementation for PV

systems. Section V shows the experimental results and

evaluates the system performance on convergent speed as

well as its tracking efficiency. Finally, Section VI summarizes

the work.

II. FUNDAMENTAL CHARACTERISTICS OF PV CEL L

A. PV Array Characteristics

In [24][26], different models have been proposed to char-

acterize PV cells. As only a moderate model is needed for

control purposes in this paper, a single-diode PV model is

used [25]. For a group of solar cells (i.e., a module) under the

same environmental conditions that consists of ns solar cellsconnected in series and np solar strings connected in parallel,the currentvoltage output characteristics can be described as

i = npIph npIrs

exp

q

kTAns

v + i

nSnP

RS

1

v + inSnP RS

nSnP

RSH(1)

where Iph is the photocurrent generated by a PV cell, Irs isthe reversed saturation current of a diode, A is the ideal factorwith a value from one to two, k is the Boltzmanns constant,q is the electron charge, Rs and RSH are the series and shuntresistances, respectively, and i and v are the solar cell currentand voltage, respectively.

When the PV array is under a partially shaded condition, the

PV cells under the same insolation condition can be regrouped

to form new modules [27], [28]. Then, these modules can be

considered to be connected in series and/or parallel to form anew PV array according to the shading pattern. Assume that

the new configuration consists of Np branches in parallel anda maximum of Ns modules in series in a branch; the outputcurrent ia and voltage va can be described as

ia =

Npb=1

ib (2)

va =

NSj=1

vj (3)

where ib is the current in the bth branch and vj is the voltageacross the jth module in a branch.

B. Lipschitz Characteristics ofPV Function

Multiplying (2) by (3) yields the power pa, and then per-forming partial differentiation with respect to va yields thefollowing:

pa

va = ia + va

ia

va va [a, b](4)

where

iava

=

Npb=1

NSj=1

vjib

1

va [a, b]. (5)

Consider thejth module in the bth branch; it can be verified that

vjib

= 1 +q

kTAIRSRSe

K

vbj+ibj

nS_bjnP_bj RS

+ RS

RSH

qnP_bjkTAnS_bj IRSe

Kvbj+ibj nS_bjnP_bj RS + nP_bjnS_bjRSH

.

(6)

From (2)(6), Pa/Va exists and is bounded by a maximumvalue M. By the mean value theorem, for every v1, v2 [a, b],there exists c [v1, v2] such that

|p(v1) p(v2)||v1 v2| =

p

va

c

= p(c), c (v1, v2). (7)

As p(c) is bounded by M, (7) becomes

|p(v1) p(v2)| M|v1 v2| v1, v2 [a, b]. (8)Equation (8) is known as the Lipschitz condition [20]. Since

the function p(v) satisfies the condition, it is known as aLipschitz function with a Lipschitz constant M and is alsouniformly continuous and bounded on [a, b] [23].

Assume that v1 is a sampled point and that v is a variable.The Lipschitz inequality (8) gives both the upper and lower

bounds on the values of the function p(v) at other points as [23]

p(v1) M|v v1| p(v) maxv[a,b]

p(v) p(v1) + M|v v1|.(9)

Ifv1 is at the center of [a, b], it can be shown from (9) that

p(v) maxv[a,b]

p(v) p(v1) + Mb a2

. (10)

Thus, with just one sample, (9) and (10) give a bound on

how far the GP is deviated from the observed sample p(v1).Both M and (b a) might be large initially. However, bytaking further samples, we can effectively replace (b a) bythe length of smaller subintervals successively. In this manner,

one can develop an efficient algorithm to find a solution within a

prespecified tolerance of an optimal solution in a finite number

of iterations [21], [22]. The DIRECT search algorithm is one of

them and particularly effective where the Lipchitz constant Mis unknown or difficult to be estimated [20].


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Fig. 1. (a) Dividing strategy. (b) POIs.

III. OVERVIEW OF DIRECT ALGORITHM

In this section, two main ideas of the DIRECT algorithm,

namely, the area-dividing strategies and the potentially optimal

intervals (POIs), will be reviewed. Subsequently, its develop-

ment to track an MPP of PV arrays will be presented in the next

section.

A. Area-Dividing Strategies

Fig. 1(a) shows the area-dividing strategy of the DIRECT

algorithm when a sampling interval [a, b] has been specified.Assume that the algorithm has already taken a sample V1 at

the center of [a, b] in the previous step. This interval is thendivided into three parts, and samples V2 and V3 are taken atthe center points of the left and right intervals, respectively.

The sample V1 simply becomes the center of the new middleinterval. The algorithm then evaluates three samples to decide

the next sampling interval. With this strategy, DIRECT only

requires two new samples in each dividing cycle for evaluation.

Once an interval is chosen to be explored further, it will be

further triply divided, and two more samples [V32 and V33 inthe case shown in Fig. 1(a)] will be created. This results in five

samples at the end of the second dividing cycle, as shown in

Fig. 1(a).

B. POI

When an interval is to be divided for further sampling, the

interval is referred to as potentially optimal. Let > 0 be apositive constant and fmax be the current best function value.Interval J is said to be potentially optimal if there exists a rateof change constant K > 0 such that [20]

f(xj) +

K

(aj bj)2

f(xi) +

K

(ai bi)2

i (11)

f(cj) + K(aj bj)2

fmax + |fmax|. (12)

The inequality (11) expresses the decision only to choose in-

tervals that would promise the best improvement in the function

value. For intervals with the same length, it implies that only the

interval with the highest function value at its middle point is the

POI. The parameter in (12) ensures that the POIs would yieldbetter improvement than fmax by at least an amount |fmax|.As reported in [20], the algorithm becomes more local in its

searching when the value of gets smaller. For the PV systemunder investigation, a maximum percentage error of the mea-

sured power can be used as a guideline for the choice of . Inour design, the maximum errors of current and voltage sensors

are 1.5%. Thus, the maximum measurement error of power isless than 3%. When the proposed algorithm performs global

search, is chosen as 0.03. When the algorithm is doing thelocal search, is set to zero to allow the GP to be reached. Thedefinition of POI in the original algorithm is shown in Fig. 1(b),

which plots the functions values at the center of the sampled

intervals versus the intervals length. Among all the intervals,

only those that satisfy (11) and (12) are considered potentially

optimal [20]. The original DIRECT algorithm divides all POIs

to search for the GP globally and locally at the same time. For

the proposed algorithm, the dividing strategy is different, as

described in Section IV-C and D.

IV. IMPLEMENTATION FOR PV SYSTEM

A. Identification of Sampling Interval for PV System

In the following, the interval that the duty cycle always falls

within is termed as the absolute sampling interval. Theoret-

ically, VMMP falls between 0 V and Voc_max. In the case thata dc/dc converter is used to vary the OP of the PV system, the

duty cycle would be in the range of (0, 1). However, this range

[Dmin_abs, Dmax_abs], where Dmin_abs > 0 and Dmax_abs VD1) of the IV curve representing themiddle stair. In other words, IDi and VDi (i = 1, 2, 3) are wellseparated, which means that both (19) and (20) are satisfied

ID3,1ID3

=ID3 ID1

ID3 0.1 (19)

VD1,2VD2

= VD2 VD1VD2

0.2. (20)

The criterion values 0.1 and 0.2 are chosen based on the

observation that IMPP and VMPP are about 90% and 80% ofIsc and Voc of a single IV curve, respectively [12].

If the IV curve has more than three stairs, any two consec-utive stairs can always be considered as under one larger stair,

as shown in Fig. 4(b). Thus, (19) and (20) easily hold true in

those cases. Fig. 4(a) shows that (19) and (20) also hold true, in

general, for two-stair IV curve cases.In the case that only (19) or (20) is satisfied, DIRECT would

need to take further samples to identify the insolation condition.

Fig. 5(a) shows cases when (19) is not satisfied, which means

that ID3 is close to ID1. Since VD3 < VD1, PD3 < PD1. Thus,either sample at D1 or D2 is the maximum among the firstthree samples. Assume that a sample at Di (i is one or two) ismaximum; according to the definition of POIs, DIRECT would

divide interval Di into three subintervals and take two newsamples Di2 and Di3 at the new middle points, as shown inFig. 5(a). Again, with information given by D1, Di2 (or Di3),and D2, the insolation condition can be identified properly.Similar process is applied for cases when only (20) is not

satisfied.

In general, DIRECT has high chance to identify a partially

shaded condition if there is at least one of the first threesamples taken in a different stair from others. This condition


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Fig. 3. (a) OP movement. (b) First three samples illustration.

Fig. 4. Partially shaded condition identification in (a) two-stair IV curves and (b) more-than-three-stair IV curves.

Fig. 5. IV curve has two stairs.

always happens if the initial sampling interval is estimated large

enough. However, if the first three samples are taken in the

same stair, as shown in Fig. 5(b), DIRECT would identify the

condition as a uniform case and switch to the locally biased

strategy for faster tracking speed. Since the area under the stair

that the first three samples are taken in is always larger than

others if they present, DIRECT still can reach the GP.

C. Globally Biased Strategy of DIRECT Algorithm

When the PV arrays are under a partially shaded condition,

the globally biased form of the DIRECT algorithm that focuseson exploring a larger POI is implemented. In the second itera-

tion, DIRECT triply divides POI Dj [j = 1 in the case shownin Fig. 6(a)] and then samples power values at two new middle

points DJ3 and DJ2, marked by a cross sign in Fig. 6(a). Atthe end of the second iteration, DIRECT records the presence of

five intervals which can be categorized into two types of interval

length, one-third and one-ninth of the original interval length, as

shown in Fig. 6(b). In Fig. 6, the arrows illustrate the movement

ofDj when it changes from representing an old larger intervalthat has been triply divided to representing a smaller interval.

According to (11) and (12), both interval D2 and D12 are POIs.However, the globally biased DIRECT only chooses the one

with the largest interval length, i.e., D2, for further sampling inthe third iteration, as shown in Fig. 6(c). This results in six small


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Fig. 6. Iterations of DIRECT in global-biased form.

intervals and one larger interval, interval D3, whose length isone-third of the original length as shown in Fig. 6(d).

In the fourth iteration, there are two POIs theoretically.

However, DIRECT still divides the one with the larger length,

interval D3 as shown in Fig. 6(e). The dividing results in nineintervals whose lengths are all equal to one-ninth of the original

length. Depending on the known parameters available, when

estimated as described in Section IV-A, the initial sampling

intervals length ranges from 0.3 to 0.5. Then, the length of

those nine intervals ranges from 0.03 to 0.05. In most appli-

cations, this value is sufficiently small enough so that some

sampling points have a near approach to the GP. In other words,

the intervals that they represent contain the GP. Thus, if two

samples that have the highest powers are consecutive, D1,1 andD1,2 in Fig. 6(e), the GPs region is considered to be foundand falls in the POI. To reach the GP, DIRECT switches to

locally biased form. However, if those two sampling points are

not consecutive, this indicates that the system may have two

GPs or one local MPP whose value is closed to the GP. In this

case, globally biased DIRECT would continue for two more

cycles. This means that DIRECT will further divide and sample

the single POI, interval D1,2, in the fifth iteration. As a result,

there are two types of interval length again: 1/9 and 1/27 of theinitial sampling intervals length. In the sixth iteration, DIRECT

will further sample the POI that has the larger length (1/9 of

the initial sampling intervals length) to continue exploring the

searching range. Then, DIRECT changes to locally biased form

to focus on reaching the GP.

Generally, in the first three iterations, DIRECT takes a total

of nine samples to explore the searching region. To prevent

DIRECT from exploring unpromising regions, the number of

samples can be reduced if the first three sampling points

Di (i = 1, 2, 3) give the following information.

1) VD3 is less than Vmin (Vmin = 1/3Voc in our experi-ments), which means that D33 would fall in a region thatglobal MPP cannot appear. Then, sampling point D3,3 isnot taken.

2) ID2 < Imin (Imin = 1/3 Isc), or VD2 > Vmax (Vmax =0.9 Voc), which means that D22 would fall in a region thatglobal MPP cannot appear. Then, sampling point D2,2 isnot taken.

3) Inequality (19) is not satisfied, which means that D3 andD1 fall in the current region of the same peak. Then, D3,3and D3,2 are not taken.

4) Inequality (20) is not satisfied, which means that D2 and

D1 fall in the voltage region of the same peak. Then, D2,2and D2,3 are not taken.


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Fig. 7. PV characteristic curve under uniform insolation.

D. Locally Biased Strategy of DIRECT Algorithm

1) POI: When PV arrays operate under uniform insolation

condition, the IV curve has only a single step, and the PVcurve has a unique MPP, as shown in Fig. 7.In this case, the unique MPP always falls in or is very close to

the boundary of POI DJ, which has the maximum power PDJ.In Fig. 7(b), this is the center subinterval D1. This means thatDIRECT does not need to explore other intervals Di (i = j)in later iterations, even though they can be potentially optimal

if they satisfy (11) and (12). In summary, the locally biased

strategy always considers the interval with maximum sampling

power at its center being the only POI.

2) Stopping Criteria and Tracking Speed: The locally bi-

ased strategy of DIRECT reduces the sampling interval to

one-third after iteration if the stopping criterion has not met.

When the change in duty cycle dcr reaches a predefinedsufficiently small value, the search is terminated, and it is

assumed that the maximum point has been reached. The critical

value dcr should be chosen to be smaller than the duty cyclestep perturbation d in the P&O or INC algorithm, which canbe evaluated as proposed in [9].

Assume that n is the number of iterations when the search isterminated; s is the sampling time for the system, which canbe evaluated as proposed in [9]; we have

Dmax_abs Dmin_abs3n

dcr. (21)

Then, the maximum tracking speed of the algorithm can be

evaluated as

tabs = 3n S = 3ln 3

ln

Dmax_abs Dmin_absdcr

S .

(22)

Fig. 8 shows the simplified flowchart of the DIRECT al-

gorithm. To maintain the OP, the P&O method with small

duty cycle perturbation dcr is employed. This increases the

systems tracking efficiency in a slightly changing insolationenvironment.

Fig. 8. Flowchart of the DIRECT algorithm.

V. EXPERIMENTAL RESULTS

A. System Setup

The operation of the DIRECT algorithm has been evaluated

by experiments. A prototype of the MPPT system shown in

Fig. 9 has been implemented.

According to the comparative study of the converter topolo-

gies for MPPT in a PV system [3], the buckboost dc/dc

converter possesses the characteristics for it to follow the

PV arrays MPP at all times, regardless of the cell tempera-

ture, the solar global irradiation, and the connected load. For

this study, we use a buckboost converter with the following

specifications: C = 470 F, Co = 220 F, L = 1.5 mH, and20-kHz switching frequency. As the system should reach the

steady state before another MPPT cycle begins, the sampling

interval is chosen as 0.05 s. To evaluate the effectiveness ofthe proposed approach, its performance is compared with that


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Fig. 9. System block diagram of the PV system.

TABLE ISPECIFICATIONS OF THE 20-W PV PANEL

of the algorithm developed for a partially shaded condition as

proposed in [19]. The experiments were conducted using three

Agilent E4360B solar array simulators (SASs) connected in

parallel as a power source. The SAS is capable of simulating the

IV curves of different arrays under different environmentalconditions if these data points of the IV curve are availableand input to the SAS. The solar array which was used to collect

the actual IV curves is a parallel of three 20-W solar panels

with integrated bypass diodes. The key specifications of thesolar panels are shown in Table I. To prevent the systems

voltage drop caused by the shaded panels, blocking diodes were

also installed in each branch. When environmental conditions

were changed, the data points of the new IV curves werecollected so that these IV curves could be built back by theSAS later in the experiments. Thus, we can reproduce the same

changing scenarios in two experiments implemented with our

proposed algorithm and other algorithm.

Assume that the PV system is operating in the temperature

range of (10 C, 60 C) and insolation range of (0 W/m2,1000 W/m2). Moreover, it is assumed that the resistive load is

10 . Then, the absolute sampling interval (0.45, 0.85) can beestimated using (17) and (18).

B. Partially Shaded Condition Results

The experimental results in Fig. 10(a) and (b) show the track-

ing voltage, current, and power for DIRECT and the algorithm

in [19], respectively. The experiments were conducted with

three consecutive scenarios. In the first scenario, the SAS gen-

erates the IV curve of the PV array under uniform insolationcondition. This condition was maintained for 1.5 s before it

was changed to partially shaded condition. For partially shaded

condition 2, the IV curve was programmed to have two local

MPPs. After another 1.5 s, the partially shaded condition waschanged such that the IV curve is having three local MPPs.

Fig. 10. Tracking voltage, current, and power. (a) Proposed algorithm.(b) Algorithm developed in [19].

From the experimental data, the movement of the OP in the first

three samples for the last two scenarios is shown in Fig. 11(a)

and (b), together with the changing characteristic curves. In

Fig. 11, the thin lines represent the characteristic curves from

the previous scenario, while the bold lines represent the latest

characteristic curves.

The proposed algorithm first samples three points in the

sampling interval to identify the insolation state, as shown on

the top left in Fig. 10(a). From (19) and (20), the informationobtained from these samples is used to confirm the presence of


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Fig. 11. Illustration of the OP movement in the experiment. (a) Uniforminsolation to partially shaded condition 2. (b) Partially shaded condition 2 tocondition 3.

the uniform insolation condition. Subsequently, the proposed

algorithm switches to the locally biased mode in the fourth

sampling cycle, as indicated by the vertical arrow in Fig. 10(a).

In Fig. 10(b), the algorithm in [19] first tracks the nearest local

MPP. It then searches on the left of this local MPP to find others.

This is illustrated by the gradual increase and then decrease inthe tracking voltage (and power). Since the PV panels are under

uniform insolation, the tracking power drops when the tracking

voltage reduces. The algorithm in [19] detects the presence of

the uniform insolation when the power reduction is larger than

the critical value. Then, it considers the found local MPP as the

GP and set the OP at this local MPP.

In the second scenario, the IV curve changes shape asthe environment changes from uniform insolation to partially

shaded condition. Consequently, the OP shifts from 1 to 1,as shown in Fig. 11(a). The movement of the OP results in

a drop of the tracking power. This is indicated by the dotted

circle in Fig. 10(a). This drop in the tracking power activates the

proposed algorithm to take three new samples. The informationderived from the samples verifies the presence of the partially

TABLE II(a) TRACKING PERFORMANCE COMPARISON AT A RATE OF CHANGE

OF 1.5 s. (b) TRACKING PERFORMANCE COMPARISONAT A RATE OF CHANGE OF 3 s

shaded condition based on (19) and (20). Hence, the globally

biased mode is set to explore the GPs region. This exploration

results in the fluctuations of the tracking voltage and current

in Fig. 10(a). At the ninth sampling time, the system finds the

GPs region and switches to local-biased mode to track this GP.

As shown in the PV curve in Fig. 11(a), there is no otherlocal MPP on the left of the nearest found local MPP. Thus, the

algorithm in [19] keeps searching on the left until it reachesVmin, as shown in Fig. 10(b). Then, it searches on the rightto find other local MPPs. Since the second found local MPP

is higher than the first, the algorithm continues searching on

the right until it reaches Vmax. The algorithm then considersthe second local MPP as the GP and set it to be the OP. This

searching strategy is illustrated by the experimental results in

Fig. 10(b). In the other two-peak PV curve, the searchingscenario is the same. Thus, this strategy would result in longer

tracking time and larger power loss as compared to the proposed

algorithm.

In the third scenario, the partially shading patterns change

again. This results in the presence of the three local MPPs inthe PV curve, as shown in Fig. 11(b). The OP shifts from2 to 2. Similar to the second scenario, DIRECT focuses onexploring the new sampling interval until it finds the GPs

region at the eighth sampling cycle. Then, it switches to locally

biased mode to reach the GP, as shown in Fig. 10(a). In this

scenario, the algorithm in [19] has a favorable condition since

the first local MPP is also the GP. When searching on the left,

the algorithm finds the second local MPP, which is smaller

than the first, as shown in Fig. 11(b). It reverses the searching

direction and then finds the third local MPP. Since the third

local MPP is also smaller than the first, the algorithm stops

exploring and considers the first local MPP as the GP. Table II

shows the comparative results with different rate of change ofenvironmental conditions.


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Fig. 12. Test of the DIRECT algorithm with actual solar panels.

Fig. 13. Test of the algorithm in [19] with actual solar panels.

Fig. 14. Tracking characteristics of DIRECT.

Fig. 15. Tracking characteristics of the algorithm in [19].

In conclusion, the experiments show that both the algorithms

can successfully track the GP. However, the proposed algorithm

can track two times faster, and its tracking efficiency is 10%

higher than that of the existing algorithm during a rapidly

changing environment. In slowly changing environmental con-

ditions as shown in Table II(b), the tracking efficiency of both

the algorithms is more comparable since both can track the GP.

To further evaluate the effectiveness of the proposed algo-

rithm in an actual environment, some experiments have been

conducted with the actual solar arrays as the power source.

For the experiment, two branches of the solar arrays have beenconnected in parallel with each branch using two 20-W solar

panels connected in series. To reduce the effect of shading,

bypass diodes are used across each panel, and the blocking

diodes have been installed in each branch [27], [30]. To increase

the chance of partial shading, the solar panels are placed 5 m

apart along the same direction. The experimental data have been

collected continuously from 10 A.M. to 4 P.M. as that in [31]

and [32]. Figs. 12 and 13 show the typical experimental results

of the DIRECT algorithm and the algorithm in [19] carried up

on two different days. Figs. 14(a) and 15(a) show the details of

the experiments corresponding to the portion circled by dotted

lines in Figs. 12 and 13, respectively. They show the trackingability of the DIRECT algorithm and the algorithm in [19]


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when partial shading happened. Figs. 14(b) and 15(b) show

the corresponding IV curves of the two algorithms during thetracking time.

From Fig. 14(b), it is observed that DIRECT has a good

tracking performance since most of its tracking points gather

closely to the GP with only a few points spread through the

IV curve when searching for the GPs region. Furthermore,the algorithm follows the MPP well when the insolation level

reduced. On the other hand, the algorithm in [19] needs to scan

almost 80% of the IV curve to search for the MPP. The densityof the tracking points is distributed quite evenly in the IVcurve and only slightly higher at the GP, as shown in Fig. 15(b).

In this case, the reducing insolation did not happen during the

experiment. However, the tracking ability is expected to be

the same as the DIRECT algorithm since both algorithms use

the P&O method to maintain the OP.

VI. CONCLUSION

In this paper, a new approach for global maximum powertracking for a PV system has been proposed based on the

DIRECT algorithm. The proposed approach overcomes the

weaknesses of some of the existing methods as it is capable of

searching for global maximum. This is particularly important

for a system that is partially shaded. The experimental results

have shown that the proposed approach outperforms some

approaches in terms of tracking performance and robustness,

particularly in fast-changing environmental conditions. Further-

more, the algorithm can be implemented quite easily using a

low-cost microcontroller.

ACKNOWLEDGMENT

The authors would like to thank DSO National Laboratories

for the support of this research.

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Tat Luat Nguyen received the M. Eng. degree inelectrical and electronics engineering from NanyangTechnological University, Singapore, in 2010.

He is currently a Research and DevelopmentEngineer at Seagate Technology International,Singapore. His research interests include computer-aided simulation techniques and renewable energy,particularly photovoltaic energy.

Kay-Soon Low (M88SM00) received the B.Eng.degree in electrical engineering from the NationalUniversity of Singapore, Singapore, and the Ph.D.degree in electrical engineering from The Universityof New South Wales, Sydney, Australia.

In 1994, he joined the School of Electricaland Electronic Engineering, Nanyang Technologi-cal University, Singapore, as a Lecturer and subse-

quently became an Associate Professor, where he iscurrently the Director of the Satellite Research Cen-tre. He hasserved as a Consultant to many companies

and has a number of granted patents on nonlinear circuits and UWB systems.His funded projects are in the field of UWB medical imaging, wireless sensornetworks, motion control systems, pulse neural networks, and satellite systems.

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A Global Maximum Power Point Tracking Scheme Employing DIRECT Search Algorithm for Photo Voltaic Systems