Maximum Power Point Tracking of Multiple Photovoltaic Arrays: A PSO Approach

Maximum Power Point

Tracking of Multiple

Photovoltaic Arrays: A PSO

Approach

MASAFUMI MIYATAKE, Member, IEEE

Sophia University

MUMMADI VEERACHARY, Senior Member, IEEE

Indian Institute of Technology Delhi

FUHITO TORIUMI

NOBUHIKO FUJII

Sophia University

HIDEYOSHI KO

Suzuka University of Medical Science

Multiple photovoltaic (PV) modules feeding a common load

is the most common form of power distribution used in solar

PV systems. In such systems, providing individual maximum

power point tracking (MPPT) schemes for each of the PV

modules increases the cost. Furthermore, its v-i characteristic

exhibits multiple local maximum power points (MPPs) during

partial shading, making it difficult to find the global MPP

using conventional single-stage (CSS) tracking. To overcome

this difficulty, the authors propose a novel MPPT algorithm by

introducing a particle swarm optimization (PSO) technique.

The proposed algorithm uses only one pair of sensors to control

multiple PV arrays, thereby resulting in lower cost, higher overall

efficiency, and simplicity with respect to its implementation.

The validity of the proposed algorithm is demonstrated through

experimental studies. In addition, a detailed performance

comparison with conventional fixed voltage, hill climbing, and

Fibonacci search MPPT schemes are presented. Algorithm

robustness was verified for several complicated partial shading

conditions, and in all cases this method took about 2 s to find the

global MPP.

Manuscript received February 24, 2008; revised March 27 and July

21, 2009; released for publication August 16, 2009.

IEEE Log No. T-AES/47/1/940035.

Refereeing of this contribution was handled by W. Polivka.

Authors’ addresses: M. Miyatake, F. Toriumi, and N. Fujii, Dept. of

Engineering and Applied Sciences, Sophia University, Kioicho 7-1,

Chiyoda-ku, Tokyo, Japan, E-mail: ([email protected]);

M. Veerachary, Dept. of Electrical Engineering, Indian Institute

of Technology Delhi, Hauz Khas, New Delhi, India; H. Ko, Dept.

of Clinical Engineering, Suzuka University of Medical Science,

Kishioka-cho 1001-1, Suzuka, Mie, Japan.

0018-9251/11/$26.00 c° 2011 IEEE

I. INTRODUCTION

Clean and renewable energy sources such asphotovoltaic (PV) power generation are expected tobecome essential for mitigating global warming. It ispossible to use PV power in distributed generation,transportation, and mobile applications, etc. SincePV sources exhibit nonlinear v-i characteristics,their power output mainly depends on the nature ofthe connected load. Hence, direct load connectionsto PV systems result in poor overall efficiency. Assolar panels are still expensive, minimizing the costof their life cycle has recently become an importantconsideration. To achieve some of these goals, directconnected PV systems are being replaced by PVsystems having an intermediate maximum power point(MPP) tracker.The power generated from a given PV module

mainly depends on solar irradiance and temperature.As these quantities vary with time, it is necessary todevelop a control logic that continuously monitorsthe terminal voltage and current and updates thecontrol signal accordingly. Furthermore, for optimaloperation of a PV module, its terminal voltage mustbe equal to the corresponding MPP value. To achievethese goals, various conventional single-stage (CSS)MPP tracking (MPPT) algorithms [1—18] have beenproposed and used to extract maximum power fromPV arrays under different operating conditions. AFibonacci search-based MPPT realization for PVsources has been reported [19—20]. It compares thevalues of measured power at two operating points andthen determines the operating point movement. It issimilar to the hill-climbing method with variable stepsize; the only difference here is that the step size isdetermined by the Fibonacci sequence. The MPPTsearch performance, however, is almost identical tothat of the conventional hill-climbing algorithm, andhence this scheme, Fibonacci based-search, also settlesto local MPP under certain operating conditions.If a PV array is partially shaded by a building,

a tree, and/or clouds, it becomes difficult forconventional MPPT schemes to extract maximumpower. If modules with different optimal currents,caused by uneven insolation, are connected inseries-parallel, MPPs often appear in the power versusvoltage characteristic. This is because the optimalcurrent of each PV module is nearly proportionalto the insolation on it. Under these conditions, theconventional MPPT controller mostly finds localMPP instead of finding the global MPP. Hence, thegenerated PV power, as well as the overall systemefficiency, is low.

CSS-MPPT techniques mostly rely on perturb and

observe steps and use the hill-climbing concept in

subsequent iterations. While doing so, these methods

constantly compare present and previous power

values, and when they reach the first local maximum,

the algorithm stops progressing in the forward

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011 367

direction. Additionally, these conventional methods

extract maximum power only when the global MPP is

the first peak power point. If the global MPP appears

after the local MPP during the search process, the

CSS methods hit the first peak of the local MPP

and then settle or oscillate around this point only.

Furthermore, these algorithms are not capable of

identifying the local and global MPPs. Nevertheless,

they are definitely able to capture at least one MPP,

either local or global, that depends on the shape of

the power versus voltage characteristic, which in

turn depends on the shape of partial shading and its

position on the PV module, the commencement of

shading, and the search direction of the algorithm.

Several research groups have made attempts

to realize global MPPTs by evolving different

algorithms [8]. Most of them use lengthy calculations,

online sensed data, or special circuit configurations.

Reference [21] introduces a typical two-stage MPPT

scheme that requires accurate information about

open-circuit voltage and short-circuit current. In

addition, its expansion to two- or more dimensional

control increases complexity. In this paper, the authors

have made an attempt to simplify the MPPT algorithm

as applied to multiple PV modules and to track

global MPP even under partial shading conditions.

In this context, the authors propose a particle swarm

optimization (PSO) [22—23] in order to realize the

above mentioned features and demonstrate the utility

of the PSO through experimental investigations.

II. PHOTOVOLTAIC SYSTEM

Connecting all the PV modules either in series or

in parallel alone is not recommended due to space

limitations for installation in addition to the load

voltage and current demands. Normally these are

connected in series and parallel fashion in order to

satisfy the required voltage and current demands.

Modular connection has several advantages both

from a physical layout as well as a load demand

point of view. These can be broadly classified into

two schemes from the MPPT point of view wherein

1) each modular PV system is provided with its

own MPPT controller, and 2) all the modular PV

systems are controlled by a single centralized MPPT

controller. These schemes are shown in Figs. 1 and

2, respectively. Each has its own advantages as well

as limitations. In these investigations, the authors

have made an attempt to realize centralized MPPT

control of the modular PV system. To demonstrate

the proposed methodology, a system having two PV

arrays with a centralized MPPT is discussed in this

paper.

A. Characteristics of Photovoltaic Array

A PV module is composed of several solar cells

connected in series-parallel and shielded with glass

Fig. 1. Multiple arrays controlled by multiple MPPT controllers.

Fig. 2. Multiple arrays controlled by single centralized MPPT

controller.

Fig. 3. I-V characteristics of solar cell.

to protect against environmental changes. Its v-i

characteristic is shown in Fig. 3 wherein the current

is almost proportional to solar insolation. Most PV

modules also have a bypass diode and a reverse

blocking diode. A typical PV generation system is

composed of several such modules to meet the load

power demand. Here a PV system consisting of two

modules, associated with bypass diodes, connected in

series is considered for global power point tracking

investigations. Let us assume that one module is

fully illuminated, while the second one is partially

shaded. Under this condition, the current flowing

through the two modules is the same as the modules

are connected in series, but the current generated

by the second module is less than that of the fully

illuminated module. Hence, the excess current must

flow through the bypass diode. The v-i characteristics

of an individual module as well as the total PV system

are shown in Fig. 4 where the existence of two MPPs,

i.e., the local and global MPPs, are indicated. If there

are more modules, the characteristics under uneven

368 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011

Fig. 4. Characteristics of PV modules connected in series.

Fig. 5. Movement of a PSO agent in search space.

insolation are complicated, and may exhibit two or

more MPPs. In such cases, it becomes difficult to

realize the MPPT using conventional methods. Even if

it is possible to identify the global MPP, each module

cannot be operated at the optimal condition, as their

optimal current is inherently different at different

insolations.

If the PV system is divided into submodules

and each such module is controlled with its MPPT

controller, the power loss due to partial shading can

be minimized. However, this scheme requires more

voltage and current sensors as shown in Fig. 1. In

order to reduce the cost as well as the problems

associated with the tracking scheme, the control

circuitry must be simple and easy to implement with a

minimum number of sensors. To this end, the authors

have proposed a new control scheme, shown in Fig. 2,

wherein a single pair of voltage and current sensors

is sufficient to realize the MPPT of the combined

system. A detailed MPPT control technique based

on this new scheme is discussed in the following

lines.

III. PARTICLE SWARM OPTIMIZATION APPLIEDTO MAXIMUM POWER POINT TRACKINGCONTROL

A. Particle Swarm Optimization

The authors have proposed a PSO [22] technique

to resolve some of the problems encountered in

CSS MPPT control, as discussed in the preceding

sections. The PSO method is a simple and effective

metaheuristic approach that can be applied to a

multivariable function optimization having many

local optimal points. Several cooperative agents are

used, and each agent shares or exchanges information

obtained in its respective search process. In this

method, each agent moves with a velocity vki in thesearch space, and this movement depends on two

factors: 1) its own previous best position and 2) the

previous best position attained among all the agents.

These points are expressed mathematically in two

equations which specify the velocity and position

update of the agent:

vk+1i = wvki + c1r1pbesti + c2r2gbest (1)

sk+1i = ski + vk+1i (2)

where w is the learning factor; c1 and c2 are positiveconstants; r1 and r2 are the normalized randomnumbers and their range is (0—1). The variable pbestiis used to store the best position that the ith agenthas found so far, and its position (3), is updated if

condition (4) is satisfied.

pbesti = ski (3)

f(ski )> f(pbesti ): (4)

Here f is the objective function that is maximized ineach iteration cycle. The variable gbest is used to storethe best position attained among the agents. During

this optimization process, the agents movement is

spread over the search space in different directions

and for illustration; the trajectory of various quantities

for one iteration cycle is drawn in Fig. 5.

B. Application of Particle Swarm Optimization toMaximum Power Point Tracking

The PSO algorithm described in the preceding

section is now applied to realize the MPPT control

of a PV system, wherein the P-V characteristic

exhibits multiple local MPP. When two PV modules

are connected in series and one of them is partially

shaded, the shaded module’s terminal voltage is

different from that of the unshaded module. Under

this condition, their terminal voltages are V1, V2; totalpower is P; and their variation, in 3-D, is shown inFig. 6. From this figure, it is clear that tracking to a

global maximum is nothing but a multidimensional

MPPT control problem, wherein both V1 and V2must be controlled simultaneously. In general, if

the PV array contains N number of modules, then

each individual module voltage (V1,V2, : : : ,VN) mustbe controlled. Here, the terminal voltages of the

individual PV modules are grouped together and

represented in the form of an N-dimensional row

MIYATAKE ET AL.: MPP TRACKING OF MULTIPLE PHOTOVOLTAIC ARRAYS: A PSO APPROACH 369

Fig. 6. Image of multidimensional function: PV power versus

voltages.

vector as (5)

sk = [Vk1 ,Vk2 , : : : ,V

ki , : : : ,V

kN ] (5)

where N is the size of the row vector, and it indicates

the number of PV modules in the system. The velocity

vector v can be written as

vk = [Vk1 ¡Vk¡11 ,Vk2 ¡Vk¡12 , : : : ,VkN ¡Vk¡1N ]: (6)

Here, the objective function f is the generated powerP, which is the summation of power generated byeach module. Assuming that there are M number of

agents involved in the search process, the terminal

voltage vector sk changes in the following order andalso computes the power P(sk) at each stage.

¢ ¢ ¢ ! sk1! sk2! ¢¢¢ ! skM

! sk+11 ! sk+12 ! ¢¢¢ ! sk+1M ! ¢¢ ¢ : (7)

This process is continued until the global optimum

is reached, and in each iteration the position and

velocities are updated as per the relationships defined

by (1) and (2). In a real-time operation, the objective

function f often changes due to environmental aswell as electrical loading conditions. In such cases,

the agents must be reinitialized to search for the

new MPP again. If the reinitialization process is not

implemented for the change in operating point due

to change in solar insolations or load variations, pbestand gbest cannot be updated automatically. As a result,the agents stop searching for new MPP. The authors

have modified the algorithm to resolve this problem,

and now two additional constraints are imposed:

1) agents convergence detection and 2) detection of

solar insolation change as defined by incremental

power. Accordingly, the PSO algorithm reinitializes

the agents whenever the following two conditions are

satisfied.

jvi+1j<¡¢V (8)

jP(si+1)¡P(si)jP(si)

>¢P: (9)

Equations (8) and (9) form the basis for

convergence detection of the agents and sudden

changes in insolation, respectively.

IV. DESCRIPTION OF EXPERIMENTAL DSP-BASEDREAL-TIME PROTOTYPE SYSTEM

Exhaustive investigations were made using

a test bed of real-time digital signal processing

(DSP)-based data acquisition integrated with the PV

system. The tested PV array configuration consists

of two PV arrays, PV1 and PV2, and each of the

individual arrays again consists of six PV modules,

(1Ax-1Ay-1Az) series string k (1Bx-1By-1Bz) seriesstring (Fuji Electric Co.; ELR-615-160Z) connected

in series-parallel, as shown in Fig. 9. Rated output

power and voltage of each PV array is about 300 W

and 50 V, respectively. A 3-phase intelligent power

module (IPM) consisting of a suitable driver, voltage

sensor, and current sensor are used for experimental

circuit realization. Only two insulated-gate bipolar

transistors (IGBTs) and diodes of IPM are used,

and these are connected to form two different

dc-dc boost converters, as shown in Fig. 10. DSP

(DSP-TMS320C32)-based data acquisition is used

to generate the pulsewidth modulated (PWM) gate

signals, PWM-1 and PWM-2, and to realize the

proposed MPPT control scheme. A voltage/current

sensor pair is inserted in the load circuit, and this

measures the total power generated by the two arrays

including losses in the converter. The proposed PSO

MPPT control program was developed in a C++

environment and is compiled and downloaded on to

the DSP platform. A programmable electronic load is

used to absorb the generated power, and it is set for

constant battery voltage of 200 V. A 60 mH inductor

is used as a boost inductor, and the converter is driven

at a 10 kHz switching frequency. The output voltage

vector sk is updated after every 0.05 s and follows thesequence of control as described in (7). PSO MPPT

real-time implementation is briefly described in the

flowchart shown in Fig. 7.

The PSO algorithm parameters used in this paper

are tabulated in Table I, which were obtained from

experiments conducted on the real-time system.

The proposed scheme is a kind of knowledge-based

technique, wherein depending on the type of system,

one needs to choose 1) the momentum factor (w),2) the agents’ speed-determining constants c1 andc2, and 3) the number of agents. Here w determinesthe inertia of agents. If it is too small, response is

slow, but the agent can quickly change the direction

of movement. If it is too large, response is also slow

because it causes overshoot. The searching speed of

each agent without the cooperation of other agents

is determined by c1. If it is too small, responseis slow. If it is too large, some of the agents may

converge at a local maximum point as the exchange of


Fig. 7. Flowchart of PSO algorithm experimental realization.

Fig. 8. PV power extraction rate with number of PSO algorithm

agent’s.

Fig. 9. Connection diagram of PV modules.

information among the agents decreases. The constant

c2 determines the searching speed of each agent withthe cooperation of other agents. If it is too small,

response is slow and the agents tend to converge

at different points. If it is too large, all agents may

converge quickly at the same point. Although it

restricts the range of the search region, in some cases

the agents may settle near the MPP location. More

agents can find the MPP more easily even under

complex shading conditions, but it takes more time

to converge with all of the agents at the MPP. In the

event that any one of the agents is far from the MPP,

TABLE I

Parameters of the PSO

M 3 N 2

w 0.4

c1 1.2 c2 1.6

¢V [V] 0.39 ¢P 0.15

TABLE II

Initial Position of Agents

Agent V1 [V] V2 [V]

1 0:2Vop 0:2Vop2 0:8Vop 0:5Vop3 0:5Vop 0:8Vop

Note: Vop: Open circuit voltage of PV array.

the PV operates at a suboptimal power point and thus

reduces the extracted energy. Hence, the main concern

here, in MPPT applications, is faster convergence with

a minimum number of agents. To demonstrate this

aspect, the simulation results of percentage of PV

extracted to the number of agents used is shown in

Fig. 8. These results suggest that for the present PV

array system, three agents is the optimal selection.

In an ideal case, the initial positions of the

agents can be assigned at random. However, random

selection of all the agents may converge at a local

maximum. Experimental observations revealed

that 30—40% of the agents’ initial positions may

be chosen at random, while the remaining agents’

initializations should be made judiciously depending

on the type of shadow expected. To maximize the

generated power of the PV system under all operating

conditions including partial shading cases, each one

of the system modules must be controlled in such

a way that their terminal voltages are equal to the

corresponding MPPT voltages and their magnitudes

vary between (0—Vop). Here the PSO algorithm uses

the agents’ help to identify each module optimal

terminal voltage and then to maximize the total power

output of the PV system. In the process of optimal

terminal voltage identification, at the beginning,

the PSO algorithm needs to initialize the agents’

position in the search space. Here since the search

region is known explicitly (0—Vp), the agents initialposition can be assigned to a fraction of open-circuit

voltage instead of having random locations during the

initialization. Although several different combinations

are possible for assigning these positions to the

agents, one such feasible case is listed in Table II

obtained from real-time experiments. Here, the three

initial positions were chosen to match the typical

position of MPP. Agents 1 and 2 are set near the

MPP voltages of PV1 and PV2, 0:8Vop and 0:5Vop,while agent 3 is at a distance apart from the MPP

in order to have better spread or movement among


Fig. 10. Block diagram of experimental PV system.

them. The MPPT performance is not going to vary

even if these values are reshuffled among the agents.

However, the tracking performance depends on 1) the

set of weights used for the agents, and 2) the relative

magnitudes of ¢V and ¢P used in the reinitializationconstraints. Selection of these parameters depends on

several factors, of which the most important factors

are 1) environmental factors, like solar radiation and

temperature; 2) the nature of PV modules and solar

insolation distribution on the given PV module; and 3)

the shading area and its variation with time. As most

of these quantities vary stochastically, generalizing

the magnitudes of the parameters ¢V and ¢P isa complex task. However, to guide the particles

effectively in the search space, the maximum drift

(or) velocity during any iteration must be between

the minimum and maximum velocity. To ensure

this while tracking the power, the PV array voltage

is constrained to 0:05Vop <Vi < 0:95Vop so that thealgorithm keeps track of the agents within the search

region. In the process, if any of the agents fall beyond

the range, the algorithm automatically fixes their

extreme positions.

For a given PV system, one can easily arrive at

final values of ¢V and ¢P based on experimentalobservations. The meaning of the higher ¢V is thatthe agents are moving actively at a higher speed, and

thus the system reaches the optimal point quickly.

Although the use of very large values for the ¢Vmakes the algorithm (8) more sensitive, reinitialization

of the agents takes place more frequently, which in

turn causes larger power oscillations. Hence there are

two issues in ¢V selection: 1) smaller values result inbetter MPPT stability but poor tracking response and

2) higher values amount to faster tracking response at

the expense of larger oscillations. Hence a balanced

value must be chosen. However when ¢P is large,

the second constraint (9) may not be satisfied on

account of smaller variations in actual power, and

thus the agents’ reinitialization rate is smaller. In

order to overcome these limitations and to achieve

better tracking performance, ¢V and ¢P must betuned simultaneously. The real-time experimental

investigations reveal that use of extreme values for

¢V and ¢P should be avoided to ensure MPPTstability.

Once the PV modules’ voltage information Vk(k = 1,2) given by (5) and (7) is known, the requiredduty ratios for the individual boost converter (Dk)can easily be computed from (10). As this expression

is based on the assumption of negligible drops due

to nonidealities, the experimentally computed duty

ratio will be slightly different from the one obtained

through computations.

Dk = 1¡VkV0: (10)

V. EXPERIMENTAL RESULTS AND DISCUSSIONS

To validate the proposed MPPT algorithm

discussed in the preceding sections, exhaustive

experimental studies were conducted on the actual PV

system shown in Fig. 11. Real-time test measurements

were presented for the following cases: 1) MPPT

dynamic response of the PV system under the

partial shading condition, 2) testing the algorithm

tracking capability for various shading patterns, and

3) comparisons of the proposed MPPT scheme

tracking capability with other MPPT methods.

A. Proposed MPPT Scheme Dynamic Response

The experimental power versus voltage profile

of the PV system was measured under fine weather


Fig. 11. Making artificial shade with sheets for observing

response.

conditions, and it is represented by curve PV1 in

Fig. 12. The shaded conditions are realized on

modules 2Az and 2Bz, and then the PV system’s

total power characteristics are measured as indicated

by PV2 in Fig. 12. From PV1 and PV2, one can

see that there are two optimal operating voltages for

the two PV arrays during partial shading, and both

exhibit two local MPPs. In view of this, the two boost

converters, which control the terminal voltages of

each PV array, must be controlled at different duty

ratios; failing to do so causes the PV system to track

to the local maximum, thereby reducing the overall

efficiency. In order to verify the effectiveness of the

proposed tracking scheme, dynamic performance

power characteristics were measured when the test

conditions changed from fully illuminated to shaded;

the measured results are shown in Fig. 13 for two

different shading cases, case A and case B listed in

Table III. These results indicate that the two individual

PV arrays are now being operated at different duty

ratios D1 and D2. The above experimental resultsshow that the global MPP can be tracked within 2 s

even under partially shaded conditions. This tracking

time includes the 0.05 s required to execute the

proposed algorithm and takes about 20 iterations to

reach the steady-state tracking point.

B. Power Tracking with Various Shading Patterns

The authors have also verified the control

effectiveness of the proposed MPPT for various

partial shading conditions (for identification of shaded

modules refer to Fig. 9) as given in Table III, and

in all these cases the tracking time was close to 2 s.

TABLE IV

PV Power and Operating Voltage for Different Shading Patterns

PV1 voltage (Volt) PV2 voltage (Volt) Power (Watts)

Case Vmexp Vmpso Vmexp Vmpso Pm Ppso P0

A 48 45 28 24 334 328 310

B 48 45 48 29 345 340 325

C 48 44 48 45 262 253 235

D 30 28 45 45 211 203 185

E 45 45 45 47 264 255 240

Fig. 12. Measured P-V curve of PV 1 and 2 under partial shade.

TABLE III

Tested Shading Patterns

Case Shaded Modules

A 2Az, 2Bz

B 2Bz

C 2Ay, 2Az, 2By, 2Bz

D 1Az, 1By, 1Bz, 2Bx, 2By, 2Bz

E 1By, 1Bz, 2By, 2Bz

For all these shading cases, dynamic power tracking

experiments were conducted (in the interest of limiting

paper length, dynamic response plots are not shown

here), and the corresponding MPPT voltages of PV1

and PV2 along with the total power injected into

the load are tabulated in Table IV. To verify these

MPPT voltages, various V-I/P-V characteristics were

obtained for identical shading conditions, as listed

in Table III, by connecting a variable resistance

across the PV system. In each case, the PV power

(Pm) and the respective MPPT voltages (Vmexp) wererecorded and tabulated in Table IV. It is clear from

this table that the measured voltages (Vmexp) and thevoltages obtained from the PSO algorithm (Vmpso)are in close agreement for both PV modules except

for case B wherein the PV2 power curve has 2 peak

power points that are almost identical in magnitude

but exhibit at two different voltages: 28 and 48 V.

In addition, from each of these measurements, the

power extracted from the PV (Ppso) and absorbed bythe load (P0) were also compiled and tabulated inTable IV for comparison. In all these observations,


Fig. 13. Transient response of power absorbed by load and duty ratios. (a) Shading case A. (b) Shading case B.

the discrepancy in the maximum power value is

less than 10 W. This slight discrepancy in power

is primarily attributed to 1) inaccurate control of

the individual array voltages, 2) slight mismatch

of operating test conditions, i.e., the few minutes’

time difference between the measurement of P-V

characteristics and the MPPT control experiments, and

3) slight mismatch of insolation levels.

The proposed scheme can also be extended for

PV systems consisting of more modules. However

the adoptability of the proposed algorithm depends

on several factors, of which the most important are

1) the nature of the PV modules employed for power

generation; 2) the algorithm execution speed, which

primarily depends on the type of partial shading and

the number of agents used for the search process; and

3) the number of independent PWM channels that

the given computational processing platform system

is capable of handling/processing in a control cycle.

From the algorithm point of view, a larger number of

agents results in truer MPPT even under complicated

shading patterns. However a large number of agents

leads to a slower convergence rate, so a balanced

number must be used, taking the above factors into

account, to ensure good tracking speed and accuracy

in maximum power tracking.

C. Proposed MPPT Scheme Comparison with OtherTracking Methods

It is difficult to analyze, through simulations,

the amount of energy obtainable with a PV system

while taking into account the influence of partial

shade. The difficulty lies in simulating the moving

shadow as well as its shape in such a way that the

simulation faithfully reflects the actual behavior

of a PV system. Hence, the most reliable way to

evaluate the merit of the proposed method is by

having real-time measurements of generated energy

for several hours. In the following list, performance


TABLE V

Weather and Solar Insolation Conditions used in the 4-different MPPT Testing Schemes

Measured Illuminance Solar Radiation Reported

Controller Date Status of Weather at Noon [lx] by JMA [MJ/m2]

FIX 2007/Jan/05 clear 102£ 103 7.03

HIL 2007/Jan/09 clear 110£ 103 7.40

FIB 2007/Jan/10 clear 106£ 103 6.90

PSO 2007/Jan/14 clear 110£ 103 7.65

of the proposed algorithm is compared with the three

established MPPT schemes: 1) fixed voltage MPPT,

2) the hill-climbing algorithm, and 3) MPPT based on

the Fibonacci search method.

FIX: Fixed voltage, no control. The array voltage is

not controlled but fixed at the MPP value at

10:00 A.M. The fixed voltage is optimal only

when there is no shadow on the PV module.

HIL: Hill-climbing method. This is the most widely

used MPPT scheme. The method involves

moving the operating voltage by one step and

then examining the change in generated power.

If the power increases, the operating point

moves in the same direction; otherwise it moves

in the opposite direction. Here the step size of

the change in voltage is set to 0.8 V, and the

required control cycle time is 0.1 s.

FIB: Fibonacci search MPPT. A line search technique

was proposed by the authors for the MPPT

control of PV. The searching range was

restricted and widened by using the Fibonacci

sequence. Detailed algorithm and controller

parameters are described in [19]—[20].

PSO: The proposed PSO-MPPT.

Because of the constraints on the number of the

experimental systems, only one MPPT scheme was

tested on a given day. Therefore, 4 different clear

days were chosen for conducting the experiments,

and the weather information for all these days is

listed in Table V. Additionally, the experiments were

carried out in the month of January as the weather

is clear and more stable in Tokyo, Japan, during this

period. The altitude of the sun was almost the same

during these 4 days because this January period is

near the winter solstice. The illuminance on these

4 days was also measured in order to ensure a fair

enough comparison. The measured temperature

and solar radiation in central Tokyo, reported by

the Japan Meteorological Agency (JMA) [24], is

plotted in Fig. 15. The weather data were measured

about 2 km east of the PV system location. This

figure demonstrates that for the 4 days chosen for

the experiment, the weather profile in Tokyo was

almost the same and hence the test conditions for the

4 days were almost similar. Furthermore the JMA

also reported the duration of sunshine information

Fig. 14. Moving artificial shade realization with stacked boxes.

on all these four days on an hourly basis, as shown

in Fig. 15, which indicates clear weather and almost

identical test conditions. Fig. 14 shows that artificial

shade was realized by using stacked boxes, which

emulated a shadow moving with time. In addition, the

stacked boxes were arranged such that the shadow

was always covering a portion of the PV module

throughout the experimentation time from 10 to

14 hrs.

The experimental measurements, obtained from

different MPPT schemes conducted on four different

days are tabulated in Table VI. The corrected energy,

given in Table VI, was computed using the ratio

of global solar radiation (GSR) on the measuring

day to that of GSR obtained on January 05, 2007.

The correction eliminates the influence of different


Fig. 15. Data of temperature and solar radiation in central Tokyo

reported by JMA [24].

TABLE VI

Generated Energy of the PV System with Different MPPT

Schemes

Measured Energy Corrected Energy

Controller [Wh] [Wh]

FIX 184.5 184.5

HIL 246.2 233.9

FIB 228.1 232.4

PSO 269.2 247.4

Note: Measured for 4 hrs duration.

solar radiations on the measured energy. The graph

of instantaneous voltage and power for each MPPT

scheme is also shown in Fig. 16. It should be noted

that there is a difference in energies extracted by the

different MPPT schemes. This is mainly due to the

nature of the corresponding MPPT algorithm. The

FIX, HIL, and FIB power tracking methods show

lower generated energies compared with that of the

proposed PSO algorithm.

The PV system was exposed to partial shading

from 10:00 A.M. onwards, shown in Fig. 16, and

the three conventional tracking algorithms were

unable to find the best operating point, i.e., the MPP,

until 11:20 A.M. From this time instant onward,

the three algorithms settled to a somewhat better

operating point, and hence the power extracted was

also somewhat higher than that of the preceding time

interval. However the proposed PSO algorithm was

capable of finding the optimal operating point quickly,

as evidenced from the experimental results and shown

in Fig. 16(d), even under complicated partial shading

conditions, and hence the amount of generated energy

in this case was comparatively higher than those of

the other tracking methods discussed above.

The FIX, HIL, and FIB tracking methods show

unwanted oscillations in their power and voltage

curves. These oscillations were mainly due to 1)

fluctuations of the operating point, 2) the algorithms’

shortcomings with respect to systems in which solar

insolation is not uniformly distributed, and 3) the

algorithms’ inability to identify the global optimum

point when the power curve exhibits multiple local

MPPs. In view of these reasons, the three power

tracking algorithms were unable to track the true MPP

when the PV array was covered with a slowly moving

shade. The above discussions clearly demonstrate

the proposed MPPT controller’s power extracting

feature, both in normal as well as in partial shading

conditions, and hence this PSO-based tracking scheme

provides a feasible alternative solution to real-time PV

systems.

VI. CONCLUSIONS

A novel MPPT algorithm using a PSO technique

was proposed to control several PV arrays with one

pair of voltage and current sensors. As the proposed

scheme is a multidimensional search-based technique,

it is able to find the global MPP even under complex

partial shading conditions. The developed algorithm

is simple and also reduces the cost of the data

acquisition system. Experimental comparison with

various tracking schemes demonstrated its novelty as

well as its validity. The PSO algorithm took about 1 to

2 s to find the global MPP. Additionally, this response

time was observed to be almost independent of the

search space dimensions and shape of the partial

shading.

REFERENCES

[1] Enslin, J. H. R., Wolf, M. S., Snyman, D. B., and

Swiegers, W.

Integrated photovoltaic maximum power point tracking

converter.

IEEE Transactions on Industrial Electronics, 44, 6 (1997),

769—773.

[2] Hua, C., Lin, J., and Shen, C.

Implementation of a DSP-controlled photovoltaic system

with peak power tracking.


99—107.

[3] Veerachary, M., Senjyu, T., and Uezato, K.

Neural-network—based maximum-power—point tracking of

coupled-inductor interleaved-boost-converter-supplied PV

system using fuzzy controller.


749—758.

[4] Al-Atrash, H., Batarseh, I., and Rustom, K.

Statistical modeling of DSP based hill-climbing

algorithms in noisy environments.

In Proceedings of Applied Power Electronics Conference

(APEC), 2005, 1773—1777.


Fig. 16. Measured power curve with different MPPT controllers. (a) Power tracking with FIX-MPPT controller. (b) Power tracking

with HIL-MPPT controller. (c) Power tracking with FIB-MPPT controller. (d) Power tracking with PSO-MPPT controller.


Voltage based maximum power point tracking control of

PV system.

IEEE Transactions on Aerospace and Electronic Systems,

38, 1 (2002), 262—270.


Feedforward maximum power point tracking of PV

System using fuzzy controller.


38, 3 (2002), 969—981.

[7] Kasa, N., Iida, T., and Chen, L.

Flyback inverter controlled by sensorless current MPPT

for photovoltaic power system.


1145—1152.

[8] Esram, T. and Chapman, P. L.

Comparison of photovoltaic array maximum power point

tracking techniques.

IEEE Transactions on Energy Conversion, 22, 2 (June

2007), 439—449.

[9] Sun, X., Wu, W., Li, X., and Zhao, Q.

A research on photovoltaic energy controlling system

with maximum power point tracking.

In Proceedings of PCC-OSAKA, vol. II, D6-3, 2002,

822—826.

[10] Kasa, N., Iida, T., and Majumdar, G.

Robust control for maximum power point tracking in

photovoltaic power system.

In Proceedings of PCC-OSAKA, vol. II, D6-4, 2002,

827—832.

[11] Shraif, M. F., Alons, C., and Martinez, A.

A simple and robust maximum power point control

(MPPC) for ground photovoltaic generators.

In Proceedings of IPEC-Tokyo, vol. 1, 2000, 158—163.

[12] Veerachary, M.

Power tracking for non-linear PV sources with coupled

inductor SEPIC converter.


41, 3 (2005), 1019—1029.


[13] Matsui, M., et al.

New MPPT control scheme utilizing power balance at DC

link instead of array power detection.

In Proceedings of IPEC-Tokyo, vol. 1, 2000, 164—169.

[14] Kuo, Y., et al.

Novel maximum-power-point-tracking controller for

photovoltaic energy conversion system.


594—601.

[15] Kobayashi, K., Matsuo, H., and Sekine, Y.

An excellent operating point tracker of the solar-cell

power supply system.


495—499.

[16] Kim, I-S., Kim, M-B., and Youn, M-J.

New maximum power point tracker using sliding-mode

observer for estimation of solar array current in the

grid-connected photovoltaic system.


1027—1035.

[17] Mutoh, N., Ohno, M., and Inoue, T.

A method for MPPT control while searching for

parameters corresponding to weather conditions for PV

generation systems.


1055—1065.

[18] Kajihara, A. and Harakawa, T.

On considerations of equivalent model about PV-cell

under partial shading.

In Proceedings of Japan Industry Applications Society

Conference, vol. 1, 71, 2005, I-289—292 (in Japanese).

Masafumi Miyatake (M’00) received the B.E., M.E., and Dr. Eng. degrees fromthe University of Tokyo, Japan, in 1994, 1996, and 1999, respectively.

Since April 1999, he joined the Tokyo University of Science as a research

associate. In April 2000, he joined Sophia University, Japan, where he is

currently an associate professor of the Department of Engineering and Applied

Sciences. His research interests include renewable energy, energy management

control, power electronics, and their applications to transportation systems. He is

a member of the IEEJ.

[19] Miyatake, M., Kouno, T., and Nakano, M.

A simple maximum power point tracking control

employing Fibonacci search algorithm for power

conditioners of photovoltaic generators.

In Proceedings of EPE-PEMC 2002, T6-003, Croatia,

2002.

[20] Miyatake, M., Inada, T., Hiratsuka, I., Zhao, H. Otsuka, H.,

and Nakano, M.

Control characteristics of a Fibonacci-search—based

maximum power point tracker when a photovoltaic array

is partially shaded.

In Proceedings of IPEMC 2004, 8.17, Xi’an China, 2004.

[21] Kobayashi, K., Takano, I., and Sawada, Y.

A study on a two stage maximum power point tracking

control of a photovoltaic system under partially shaded

insolation conditions.

In Proceedings of IEEE Power Engineering Society

General Meeting, 2003, 2612—2617.

[22] Kennedy, J. and Eberhart, R.

Particle swarm optimization.

In Proceedings of IEEE International Conference on

Neural Networks, vol. IV, Perth, Australia, 1995,

1942—1948.

[23] Kadirkamanathan, V., Selvarajah, K., and Fleming, P. J.

Stability analysis of the particle dynamics in particle

swarm optimizer.

IEEE Transactions on Evolutionary Computation, 10, 3

(2006), 245—255.

[24] Website of Japan Meteorological Agency,

http://www.jma.go.jp/.


Mummadi Veerachary (M’00–SM’04) was born in Survail, India, in 1968.He received the Bachelor’s degree from the College of Engineering, Anantapur,

Jawaharlal Nehru Technological University (JNTU), Hyderabad, India in 1992,

the Master of Technology degree from the Regional Engineering College,

Warangal, India in 1994, and the Dr. Eng. Degree from the University of the

Ryukyus, Okinawa, Japan in 2002.

From 1994 to 1999, he was an assistant professor with the Department of

Electrical Engineering, JNTU College of Engineering, Anatapur. From October

1999 to March 2002, he was a research scholar with the Department of Electrical

and Electronics Engineering, University of the Ryukyus. Since July 2002, he

has been with the Department of Electrical Engineering, Indian Institute of

Technology Delhi, New Delhi, India where he is currently an associate professor.

His fields of interest are power electronics and applications, modeling and

simulation of large power electronic systems, design of power supplies for

spacecraft systems, control theory application to power electronic systems, and

intelligent controller applications to power supplies.

Dr. Veerachary was the recipient of the IEEE Industrial Electronics Society

Travel Grant Award for the year 2001, Best Paper Award at the International

Conference on Electrical Engineering (ICEE-2000) held in Kitakyushu,

Japan, and Best Researcher Award for the year 2002 from the President of the

University of the Ryukyus. He is an editorial member of IET Proceedings on

Power Electronics, Institution of Engineering & Technology, UK, and the Journal

of Power Electronics. He is a member of the IEEE Industrial Electronics Society

and the Institution of Engineers India. He is currently serving as an Associate

Editor of the IEEE Transactions on Aerospace and Electronic Systems and the

IEEE Transactions on Industrial Electronics. He is listed in Who’s Who in Science

and Engineering 2003.

Fuhito Toriumi received the B.E. and M.E. degrees from Sophia University,

Japan in 2006 and 2008, respectively.

Nobuhiko Fujii received the B.E. and M.E. degrees from Sophia University,

Japan in 2005 and 2007, respectively.

He is now with Honda Motor Co., Ltd.


Hideyoshi Ko received the B.E., M.E. and Dr. Eng. degrees from Sophia

University, Japan in 2000, 2004, and 2007, respectively.

He joined Suzuka University of Medical Science, Japan, where he is currently

an assistant professor in the Department of Clinical Engineering. His research

interests include mathematical optimization, metaheuristics, and theri applications.

Dr. Ko is a member of the IEEJ.


Documents

Maximum Power Point Tracking of Multiple Photovoltaic Arrays: A PSO Approach