energies

Article
Efficient Photovoltaic System Maximum Power Point
Tracking Using a New Technique
Mehdi Seyedmahmoudian 1, *, Ben Horan 1 , Rasoul Rahmani 2 , Aman Maung Than Oo 1 and
Alex Stojcevski 3
1 School of Engineering, Deakin University, Waurn Ponds, VIC 3216, Australia;
ben.horan@deakin.edu.au (B.H.); aman.m@deakin.edu.au (A.M.T.O.)
2 School of Software and Electrical Engineering, Swinburne University of Technology, Hawthorn,
VIC 3122, Australia; rrahmani@swin.edu.au
3 Centre of Technology, RMIT University, Ho Chi Minh 70000, Vietnam; alex.stojcevski@rmit.edu.vn
* Correspondence: mseyedma@deakin.edu.au; Tel.: +61-3-5227-2907

Academic Editor: Tapas Mallick

Received: 9 October 2015; Accepted: 4 February 2016; Published: 2 March 2016

Abstract: Partial shading is an unavoidable condition which significantly reduces the efficiency and
stability of a photovoltaic (PV) system. When partial shading occurs the system has multiple-peak
output power characteristics. In order to track the global maximum power point (GMPP) within an
appropriate period a reliable technique is required. Conventional techniques such as hill climbing and
perturbation and observation (P&O) are inadequate in tracking the GMPP subject to this condition
resulting in a dramatic reduction in the efficiency of the PV system. Recent artificial intelligence
methods have been proposed, however they have a higher computational cost, slower processing
time and increased oscillations which results in further instability at the output of the PV system.
This paper proposes a fast and efficient technique based on Radial Movement Optimization (RMO)
for detecting the GMPP under partial shading conditions. The paper begins with a brief description
of the behavior of PV systems under partial shading conditions followed by the introduction of the
new RMO-based technique for GMPP tracking. Finally, results are presented to demonstration the
performance of the proposed technique under different partial shading conditions. The results are
compared with those of the PSO method, one of the most widely used methods in the literature. Four
factors, namely convergence speed, efficiency (power loss reduction), stability (oscillation reduction)
and computational cost, are considered in the comparison with the PSO technique.

Keywords: photovoltaic systems; maximum power point tracking; partial shading conditions; soft
computing methods; energy efficiency; stability; computational cost

1. Introduction
Despite advances in PV systems such as reduction in cost and improved cell efficiency, low energy
conversion efficiency remains a significant barrier to widespread utilization. Additionally the amount
of energy generated depends significantly on environmental factors such as ambient temperature and
solar irradiance. Given this, in order to achieve the maximum power from the output of the PV array
the control unit needs to have an appropriate strategy for maximum power point tracking (MPPT)
so as to be able to provide the appropriate duty cycle to the DC-DC converter. Considering the costs
associated with different aspects of a PV system such as material efficiency, integration and structural
configuration, improving MPPT capability is the most economical way to improve the efficiency of the
PV system.
PV systems often comprise many PV modules connected in series and/or parallel to achieve
the required output voltage and current. Because of this, when some of the modules of a PV system

Energies 2016, 9, 147; doi:10.3390/en9030147 www.mdpi.com/journal/energies

Energies 2016, 9, 147 2 of 18

receive lower solar irradiance due to occlusion of the sun by objects such as clouds, trees and buildings,
a condition known as partial shading, the output of the PV system is affected. The impact to the
output power depends on factors such as shading scheme, system architecture, or even the number of
integrated bypass diodes. A common approach to increase efficiency of PV arrays subject to partial
shading is to include bypass diodes, however this can result in multi-peak voltage-power characteristics.
In this situation most of the conventional MPPT methods will detect the local maximum power point
(MPP) rather than the global MPP. Herein, local MPP refers to a point in which the power is maximum
for a portion of the search space, while global MPP represents a point that the power is greater than all
points for the whole search space.
A number of studies have investigated GMPP tracking strategies subject to non-uniform irradiance
levels [120]. The work [13] discusses a two-stage approach for GMPP tracking. The first stage of the
approach recognizes the neighboring areas of the MPP, and the second tracks the actual GMPP. This
method is not however able to track the actual GMPP for all partial shading conditions, such as when
the load intersecting the output curve lies on the right hand side of the GMPP. In [12] a new approach
for MPPT which works subject partial shading conditions is introduced. The method depends on the
voltage values for each MPP being previously evaluated and therefore is system dependent. In [11,16]
the authors proposed a Fibonacci sequence-based approach to tracking the GMPP. In a manner similar
to perturbation and observation (P&O), the measured power of two points is used to determine
movement to the next operating point. The difference with the P&O method is that the Fibonacci
sequence is used to determine the step size resulting in improved tracking speed. Despite this however,
the drawback of the conventional P&O method still remains where GMPP tracking is not guaranteed
for all partial shading conditions.
Another two-staged approach to finding the actual GMPP is proposed in [3]. All of the local
MPPs are monitored in the first stage and then in the second stage the GMPP is tracked using the P&O
method. Although the method has relatively high efficiency, for some partial shading conditions the
algorithm needs to scan almost all ranges of the search space resulting in a slow process. Another
two-stage approach uses the dividing rectangle search method to find the region of the GMPP. Once the
region is found, i.e., the condition for stopping is met, the GMPP is found using P&O. The results prove
the reliability of the approach for certain partial shading conditions. The method is however complex
and considerably increases the computational burden. The extremum seeking control approach is
introduced in [10] and uses the segmental search concept for modelling the PV array characteristic in
the tracking process. The approach was evaluated for different partial shading conditions and found
to be quite efficient however is system-dependent and produces initial steady-state errors.
Soft computing techniques, such as artificial neural networks (ANNs) and fuzzy logic control
(FLC) have been popular among researchers [2124]. In [24] the authors proposed reliable and efficient
fuzzy logic control for tracking the MPP under partial shading conditions. In [21] FLC is used to
improve the performance of the Hill climbing method, through scanning and storing the MPP during
the P&O procedures. FLC combined with an ANN is employed in [22], to track the GMPP where
the cell temperature and irradiance level are used to train the ANN for finding the MPP. The above
mentioned approaches are able to achieve satisfactory performance for finding the GMPP under
normal and certain partial shading conditions however are computationally heavy in the fuzzification,
rule base, and defuzzification processes.
Evolution-based methods, such as genetic algorithms, ant colony, differential evolution, and
particle swarm optimization (PSO), have been employed to find the best fitness for the MPP objective
function, as presented in [2532]. Owing to its capability for stochastic objective functions, the PSO
technique has been used prevalently in the literature. For example, in [25,26], the authors employed the
standard PSO technique to track the global MPP at the output of the partially shaded PV system. The
reliability of this technique under partial shading conditions was verified in these studies. However,
these techniques involved certain drawbacks that are associated with the standard PSO method.
Among these drawbacks are fixed velocity values, large dependency on random coefficients, relatively
 Energies2016,9,147 3of18

Energies 2016, 9, 147 3 of 18

method.Amongthesedrawbacksarefixedvelocityvalues,largedependencyonrandomcoefficients,
relatively slow convergence, and high computational cost, which are due to the use of a
microcontrollerwithlargememorytorecordtheparticlemovementsinallpreviousiterations.Many
slow convergence, and high computational cost, which are due to the use of a microcontroller with large
researchershaveattemptedtosolvetheseproblemsintheirstudies,mostofwhichhavesuccessfully
memory to record the particle movements in all previous iterations. Many researchers have attempted
modifiedtheperformanceofthestandardPSOtoacertainextent.However,theseproblemshave
to solve these problems in their studies, most of which have successfully modified the performance of
either
the not been
standard PSOfully addressed
to a certain extent.or other
However, drawbacks have appeared
these problems in the
have either notmodified
been fullyversions.
addressed For
orinstance,in[33],theauthorsusedadeterministicPSOmethodwithremovedrandomcoefficientsto
other drawbacks have appeared in the modified versions. For instance, in [33], the authors used a
reducethemetaheuristicaspectoftheseevolutionaryalgorithms.Inotherstudies[3436],PSOhas
deterministic PSO method with removed random coefficients to reduce the metaheuristic aspect of
beencombinedwithothermethodsintheformofhybridtechniquestoboosttheaccuracyandreduce
these evolutionary algorithms. In other studies [3436], PSO has been combined with other methods in
the
the effects
form of random
of hybrid coefficients
techniques to boost inthe
the PSO technique.
accuracy and reduceThese combinations
the effects of random however resulted
coefficients in thein
longerprocessingtimeorhighercomplexity.
PSO technique. These combinations however resulted in longer processing time or higher complexity.
This
This paper
paper aims
aims to to introduce
introduce a newa new simple
simple andevolutionary
and fast fast evolutionary
techniquetechnique for tracking
for tracking the
the global
globalMPPattheoutputofphotovoltaicsystemsunderanypartialshadingcondition.Thetechnique
MPP at the output of photovoltaic systems under any partial shading condition. The technique is
iscalledradialmovementoptimizationandhasbeenprovenhighlyefficientforglobaloptimization
called radial movement optimization and has been proven highly efficient for global optimization
ininacontinuoussearchspace.Unlikeconventionalmethods,thismethodiscapableoftrackingthe
a continuous search space. Unlike conventional methods, this method is capable of tracking the
globalMPP
global MPPunderany
under any partialpartialshadingcondition.
shading condition. The Themain
mainadvantages
advantages of ofthis
thismethod
methodoveroverother
other
evolutionarymethods
evolutionary methods are areefficiency
efficiency under underpartial
partialshading
shadingconditions,
conditions,highhighspeed,
speed,simplicity,
simplicity,and
and
stabilityduringtrackingandsteadystateperiods.ComparedwiththePSOmethodwhichhasbeen
stability during tracking and steady state periods. Compared with the PSO method which has been
extensivelypresented
extensively presentedininthe theliterature,
literature,the theproposed
proposedmethod
methodisisfaster,
faster,less
lessdependent
dependenton onrandom
random
coefficients,
coefficients, and
and needs
needs lessless memory
memory for processing.
for processing. Therefore,
Therefore, a lowcost
a low-cost controller controller
can becan
usedbe used
easily.
easily.Moreover,unlikemodifiedPSOorhybridmethods,theproposedmethodissimple,fast,and
Moreover, unlike modified PSO or hybrid methods, the proposed method is simple, fast, and has less
haslesscomputationalburdenduringtheprocessingtime.Thispaperrepresentsthefirsttimethat
computational burden during the processing time. This paper represents the first time that the RMO
theRMOmethodhasbeenusedforMPPtracking.Thespeed,efficiency,andstabilityofthemethod
method has been used for MPP tracking. The speed, efficiency, and stability of the method is verified
inisthis
verified
paperin this different
under paper under
partial different
shadingpartial shading
conditions, andconditions,
the results areandcompared
the results are compared
against those of
againstthoseofthePSOtechnique.
the PSO technique.
ToTounderstandthebehaviorofPVsystemsandperceivetheseveredetrimentaleffectsofpartial
understand the behavior of PV systems and perceive the severe detrimental effects of partial
shadingproblems,
shading problems,the theoutput
outputcharacteristics
characteristicsofofthe
thePV
PVsystem
systemunder
undernormal
normaland andpartial
partialshading
shading
conditionsaresummarizedinthefollowingsection.Then,abriefintroductionoftheRMOtechnique
conditions are summarized in the following section. Then, a brief introduction of the RMO technique
isisfollowedbytheimplementationoftheproposedmethodforMPPtracking.Then,differentpartial
followed by the implementation of the proposed method for MPP tracking. Then, different partial
shadingconditions,whichareusedastestbenchforevaluatingtheproposedmethod,aresimulated.
shading conditions, which are used as test bench for evaluating the proposed method, are simulated.
Finally,theperformanceresultsoftheproposedtechniquearecomparedwiththeresultsofthePSO
Finally, the performance results of the proposed technique are compared with the results of the PSO
MPPTforthesamethesimulatedconditions.
MPPT for the same the simulated conditions.

2.2.CharacteristicsofPhotovoltaicSystems
Characteristics of Photovoltaic Systems
Figure 1 depicts
Figure thethe
1 depicts circuit topology
circuit of a typical
topology PV cell.
of a typical Temperature
PV and solar
cell. Temperature irradiance
and directly
solar irradiance
alter the output characteristics of PV arrays and, as such, to determine the MPP, these values need to
directlyaltertheoutputcharacteristicsofPVarraysand,assuch,todeterminetheMPP,thesevalues
be accurately updated. In addition, the PVs mathematical model varies with the open circuit voltage
needtobeaccuratelyupdated.Inaddition,thePVsmathematicalmodelvarieswiththeopencircuit
(V oc ) and short
voltage(V circuit current (Isc ) as obtained
oc)andshortcircuitcurrent(I from the manufacturers data sheet.
sc)asobtainedfromthemanufacturersdatasheet.

Rs

+
Ipv
Iph Io Rp Vpv

Figure1.PVcellequivalentcircuit.
Figure 1. PV cell equivalent circuit.

Given that the power rating of one solar cell is relatively small and insufficient to provide
Giventhatthepowerratingofonesolarcellisrelativelysmallandinsufficienttoprovidethe
the required power
required power for
for majorityofofapplications,
majority applications,these
theseunits
unitsshould
should be
be arranged
arranged in
inseries
seriesor
orparallel
parallel
arrangements to form a module where Ns number
arrangementstoformamodulewhereN of cells all contribute to the output power. The output
snumberofcellsallcontributetotheoutputpower.The

current of the module can be determined by the following equation:

outputcurrentofthemodulecanbedeterminedbythefollowingequation:
Energies 2016, 9, 147 4 of 18

qpVpv ` I pv Rs q pVpv ` I pv Rs Ns q
I pva
Energies2016,9,147 I ph Io1 exp 1 0 4of18 (1)
Ns AKTk R p Ns

where I pv and V pv are qand

(V pv voltage
I pv Rs ) respectively,
(V pv I I pvis
R N s ) diode saturation level, q
I pvathe
Ioutput current
ph I o1 exp 1 o1 s the 0 (1)
has a value of 1.602 10 19

C and represents N selectron
AKTk constant,
charge Rp NA s and K are the diode ideality

factor and Boltzmann constant respectively, Tk is the operating temperature which in this paper is
where Ipvand Vpv are the output current andvoltagerespectively,Io1 is the diode saturation level,
considered to be the reference temperature (25 C), and I ph is the current generated from solar energy
qhasavalueof1.6021019Candrepresentselectronchargeconstant,AandKarethediodeideality
given as follows:
factorandBoltzmannconstantrespectively,Tkistheoperatingtemperaturewhichinthispaperis
consideredtobethereferencetemperature(25C),andI Gphisthecurrentgeneratedfromsolarenergy
I ph pIscr q (2)
givenasfollows: Gr
G
The value of the parallel resistance, R p ,I in
ph=Equation
(I scr ) (1), is typically very high. In the modeling
(2)
Gr
of the PV module R p is sometimes assumed as have negligible impact and of infinite resistance.
Thevalueoftheparallelresistance,Rp,inEquation(1),istypicallyveryhigh.Inthemodelingof
In contrast, RS needs to be considered because of its significant to the output power. The electrical
the PV module Rp is sometimes assumed as have negligible impact and of infinite resistance. In
parameters of the KC85T PV module are listed in Table 1.
contrast, RS needs to be considered because of its significant to the output power. The electrical
parametersoftheKC85TPVmodulearelistedinTable1.
Table 1. Specifications for the KC85T PV Module.

Table1.SpecificationsfortheKC85TPVModule.
Electrical Characteristics KC85T
ElectricalCharacteristics KC85T
Open circuit voltage 21.7 V
Opencircuitvoltage
Short circuit current 5.34 A 21.7V
Shortcircuitcurrent
Maximum power voltage 17.4 V 5.34A
Maximumpowervoltage
Maximum power current 5.02 A 17.4V
Maximumpowercurrent
Maximum power 87 W 5.02A
Maximumpower
ISC temperature coefficient 2.12 103 A/ 87W
C
SCtemperaturecoefficient
VIOC 2.1210 3A/C
temperature coefficient 8.21 10 V/ C
2
VOCtemperaturecoefficient 8.21102V/C

Figure 2 shows the KC85T PV modules output for varying levels of irradiance.
Figure2showstheKC85TPVmodulesoutputforvaryinglevelsofirradiance.

(a)

(b)

Figure 2. Output characteristic curves for the KC85T PV module for noshading conditions
Figure 2. Output characteristic curves for the KC85T PV module for no-shading conditions
(a)CurrentVoltagecorrelationcurvesand(b)PowerVoltagecorrelationcurves[36].
(a) CurrentVoltage correlation curves and (b) PowerVoltage correlation curves [36].
Energies 2016, 9, 147 5 of 18

Energies2016,9,147 5of18

It is possible that outdoor PV systems or part thereof may be subject to non-uniform insolation
ItispossiblethatoutdoorPVsystemsorpartthereofmaybesubjecttononuniforminsolation
conditions due to shading by passing clouds and trees. In this situation, i.e., partial shading, the PV
conditionsduetoshadingbypassingcloudsandtrees.Inthissituation,i.e.,partialshading,thePV
modules
modules receiving similar
receiving irradiance
similar willwill
irradiance continue operating
continue at optimal
operating efficiency.
at optimal However,
efficiency. as shown
However, as
in showninFigure3,duetotheseriesconfigurationofcellinthemodule,cellssubjecttoshading,have
Figure 3, due to the series configuration of cell in the module, cells subject to shading, have to
operate in the reverse bias voltage region in order to provide the current equal to that flowing in the
tooperateinthereversebiasvoltageregioninordertoprovidethecurrentequaltothatflowingin
unshaded cells. Operating in such conditions has an inverse impact on the efficiency of entire module
theunshadedcells.Operatinginsuchconditionshasaninverseimpactontheefficiencyofentire
and may cause
module and mayhotspots in solar cells,
cause hotspots inresulting in resulting
solar cells, an open circuit condition
in an open across
circuit the whole
condition module.
across the
This problem is normally solved through insertion of bypass diodes to a specified number of cells in
wholemodule.Thisproblemisnormallysolvedthroughinsertionofbypassdiodestoaspecified
thenumberofcellsintheseriesconfiguration.
series configuration.

Current
Operation of shaded cell in
reverse bias region
Isc
Break Down

Isc Operating
Bias Voltage
Voltage

point

Voltage

Voc
Voc

Figure3.CurrentVoltagecorrelationofaPVcellinthereversebiasregion.
Figure 3. Current-Voltage correlation of a PV cell in the reverse bias region.

Figure
Figure 4 shows
4 shows thethe location
location of bypass
of bypass diodes
diodes in a
in a PV PV array
array comprising
comprising k serieskconnected
series connected
modules.
modules.BypassdiodeschangethebehaviorofPVsystemsunderanyshadingcondition.Giventhe
Bypass diodes change the behavior of PV systems under any shading condition. Given the alternate
alternatecurrentpathsprovidedbythebypassdiodes,whensubjecttopartialshadingconditions,the
current paths provided by the bypass diodes, when subject to partial shading conditions, the modules
domodulesdonothavethesamecurrentvaluesandcreatemultiplemaximaattheoutputofthePVarray.
not have the same current values and create multiple maxima at the output of the PV array.

Rs IpvA

+ +
Ipvm(1)
Iph(G1) Io Rp Vpvm(1) Dby1

Rs IpvA

+
Ipvm(i)
Iph(Gi) Io Rp Vpvm(i) Dbyi

Rs IpvA

+
Ipvm(n)
Iph(Gn) Io Rp Vpvm(n) Dbyn

IpvA

Figure4.ArrayofkPVmodulesconnectedinseries[36].
Figure 4. Array of k PV modules connected in series [36].
Energies 2016, 9, 147 6 of 18
Energies2016,9,147 6of18

Figure5showshowbypassdiodescanincreasetheextractablemaximumpowerattheoutput
Figure 5 shows how bypass diodes can increase the extractable maximum power at the output
of PV
of PV arrays.
arrays. They
They do
do however
however create
create the
the multiple
multiple maxima
maxima at the output
at the output of
of the
thearray.
array. In
In such
such
conditions,mostofthecommonMPPTtechniquesareineffectiveastheycannotdifferentiatelocal
conditions, most of the common MPPT techniques are ineffective as they cannot differentiate local and
andglobalmaxima.
global maxima.

Characteristic of PV
with Bypass Diode

Characteristic of PV without
bypass diode
Power (Pa)

Voltage (V)
Figure5.PowerVoltagecurveofaPVarraysubjecttopartialshading.
Figure 5. Power-Voltage curve of a PV array subject to partial shading.

TheconsequenceofpartialshadingconditionsonPVsystemshasbeenextensivelystudiedin
The consequence of partial shading conditions on PV systems has been extensively studied in
therecentstudies[37,38].TheemergenceofmultiplepeaksontheoutputcharacteristiccurveofPV
the recent studies [37,38]. The emergence of multiple peaks on the output characteristic curve of PV
systemsadverselyaffectsthefunctionalityofcommonMPPTapproaches.Themainreasonforthis
systems adversely affects the functionality of common MPPT approaches. The main reason for this
ineffectivenessisusuallythatthesetechniquesoperateonhillclimbingprinciples,wherethenext
ineffectiveness is usually that these techniques operate on hill-climbing principles, where the next
operatingpoint
operating pointisis shifted
shifted in in
thethe direction
direction where
where the output
the output power power is optimized.
is optimized. These These strategies
strategies obtain
obtainonlyalocalMPPbecausetheP_Vcurveismultimodal.
only a local MPP because the P_V curve is multimodal.

3. Radial Movement Optimization

3.RadialMovementOptimization

3.1. Theory
3.1.Theory
RMO is a swarm-based stochastic optimization technique [39]. It has several similarities with
RMOisaswarmbasedstochasticoptimizationtechnique[39].Ithasseveralsimilaritieswith
other evolutionary techniques such as differential evolution and PSO. The RMO technique starts by
otherevolutionarytechniquessuchasdifferentialevolutionandPSO.TheRMOtechniquestartsby
initializing the particles inside the problem search space, where each particle proposes a solution to
initializingtheparticlesinsidetheproblemsearchspace,whereeachparticleproposesasolutionto
the problem. The evaluation function is called the objective function and calculates the fitness value
theproblem.Theevaluationfunctioniscalledtheobjectivefunctionandcalculatesthefitnessvalue
of all particles at each step. The generation of a resultant movement vector depends on the two best
ofallparticlesateachstep.Thegenerationofaresultantmovementvectordependsonthetwobest
values and on a random vector for the particles.
valuesandonarandomvectorfortheparticles.
Similar to PSO and differential evolution techniques, the particle location in the search space is
SimilartoPSOanddifferentialevolutiontechniques,theparticlelocationinthesearchspaceis
demonstrated with a nop nop matrix, where nop indicates the number of particles, and nod is the
demonstratedwithanopnopmatrix,wherenopindicatesthenumberofparticles,andnodisthe
number of dimensions. The number of particles is elective and depends on the user; however, the
numberofdimensions.Thenumberofparticlesiselectiveanddependsontheuser;however,the
number of dimensions depends of the number of variables which need to be optimized. The location
numberofdimensionsdependsofthenumberofvariableswhichneedtobeoptimized.Thelocation
of particles is determined in the matrix given in Equation (3):
ofparticlesisdeterminedinthematrixgiveninEquation(3):

X 1,1 X1,2X 1, 2 X1,nod

X 1, nod
fi
X1,1
X X 2 ,1 . . . ... ffi i i1
ffi #
ffi ,2,1,
3,..., nop
2, 3, ..., nop
Xi,j X i, j
2,1 where
where (3)
(3)
.. .. . . .. ffi ffi j j1
,2,1,
3,..., nod

. . . . fl 2, 3, ..., nod
X nop , 2 X nop , nod

Xnop,1 X nopX
,1
nop,2 Xnop,nod
Energies 2016, 9, 147 7 of 18
Energies2016,9,147 7of18

The nop and nod are constant values during each trial and cannot vary. The different parts of the
Thenopandnodareconstantvaluesduringeachtrialandcannotvary.Thedifferentpartsofthe
RMO technique are explained below.
RMOtechniqueareexplainedbelow.

3.1.1. Initialization
3.1.1.Initialization
First, the initial locations in the search space are randomly assigned to the particle. These
First,theinitiallocationsinthesearchspacearerandomlyassignedtotheparticle.Theseinitial
initial
locations shouldshould
locations be assigned in accordance
be assignedinaccordance with the boundaries
with theboundaries of dimensional search
ofdimensionalsearch space.
space. The
The random assignment must cover all possible locations in the dimensional
randomassignmentmustcoverallpossiblelocationsinthedimensionalsearchspace.Asampleis search space. A sample is
shown as follows:
shownasfollows: #
i 1, 2, 3, ..., nop
i 1, 2,3,..., nop

X i , j X min j rand 0,1 X max j X min j
Xi,j Xminp jq ` rand p0, 1q Xmax p j q X minp j q where
where j 1, 2, 3, ..., nod
(4)
(4)
j 1, 2,3,..., nod

whereX
where Xmax andXXmin(j)
pjqand
max(j) jq represent
minprepresent the
the constraintsofofthe
constraints jthdimension,
thejth dimension,defined
definedat
atthe
the start
start of
of the
the
programming. The rand (0,1) is taken from a normal distribution, like a Gaussian distribution
programming. The rand (0,1) is taken from a normal distribution, like a Gaussian distributionbetween
0between0and1.
and 1.

3.1.2. Movement Vectors

3.1.2.MovementVectors
The particles from the centre are spread along the radii. The particles escape in straight lines from
Theparticlesfromthecentrearespreadalongtheradii.Theparticlesescapeinstraightlines
the centre based on the Vi,j vector which is obtained through Equation (5):
fromthecentrebasedontheVi,jvectorwhichisobtainedthroughEquation(5):
$
Xmaxp jq Xminp jq
Vmaxp jq X max( j ) X min( j )


&
Vi , j rand
Vi,j randp0, (0V ) Vp jmax( V k
1q ,1max q j ) where max( j )
where k (5)
(5)
i i 1,21,
%
,...,2,nop ; j 1j,
..., nop; 1, 2,
2,..., nod ..., nod

Thecoefficient
The coefficientkkmust
must
bebe
anan integer
integer number.
number. TheThe
trialstrials on different
on different cases cases
show show that
that the bestthe best
values
valuesforthekarewithintherangeof2to5.However,thesevaluesstilldependonotherparameters.
for the k are within the range of 2 to 5. However, these values still depend on other parameters. For the
Forthetestcases,kisconsideredequal5.Normally,insuchmethodswhereparticlesareemployed
test cases, k is considered equal 5. Normally, in such methods where particles are employed to search
tosearchthesolutionspace,aninertiaweightisdefinedtoconsidertheconvergenceissue.Theinertia
the solution space, an inertia weight is defined to consider the convergence issue. The inertia weight in
weightinRMOisshownwithWandisreducedbasedonthenumberofgeneration.Equation(6)
RMO is shown with W and is reduced based on the number of generation. Equation (6) demonstrates
demonstratestherelationshipbetweenW,generation,andthemodifiedversionofEquation(5):
the relationship between W, generation, and the modified version of Equation (5):
Wmin W
Wmax W
k i , j Wk rand (0,1) Vmax( j ) Wk WWmax Generation
k
VV where max min (6)
i,j W k randp0, 1q Vmaxp jq where k W max
Generation Generation
k
k (6)
Generation
max max

Inthisstudy,W
In maxisequalto1,andW
this study, W max is equal to 1, and Wminto0.Figure6illustrateshowtheparticlesescapefrom
min to 0. Figure 6 illustrates how the particles escape from
thecentre.Thecentreisshownasred,andtheparticlesarescatteredalongthecentreinblackcolor.
the centre. The centre is shown as red, and the particles are scattered along the centre in black color.
ThedashedcircledemonstratestheboundariesofV
The dashed circle demonstrates the boundaries of V max max..

Figure6.Scatteringoftheparticlesalongtheradii[39].
Figure 6. Scattering of the particles along the radii [39].

UnlikePSOandDE,inRMOparticlesdonotflyoverthesolutionspace.Assuchsavingthe
current location of the particles for the next step is unnecessary. After scattering, the objective
Energies 2016, 9, 147 8 of 18

Unlike PSO and DE, in RMO particles do not fly over the solution space. As such saving the
current location of the particles for the next step is unnecessary. After scattering, the objective8of18
Energies2016,9,147 function
is used to score the fitness of the particles and define the radial best (Rbest) which is a particle with the
functionisusedtoscorethefitnessoftheparticlesanddefinetheradialbest(Rbest)whichisaparticle
best fitness value. This location along with its fitness value are saved in this step. Another best value is
withthebestfitnessvalue.Thislocationalongwithitsfitnessvaluearesavedinthisstep.Another
the global best (Gbest). These two parameters update the centre step by step based on Equation (7):
bestvalueistheglobalbest(Gbest).Thesetwoparametersupdatethecentrestepbystepbasedon
Equation(7):
Centrenew new
Centreold `oldC1 Gbest Centreold old
C 2 Rbest Centre
` C2 Rbest Centre (7)
Centre Centre C1 Gbest Centre
old old
(7)
where C1 and C2 are the coefficient factors to be set for the optimizer before running the program. After
whereC1andC2arethecoefficientfactorstobesetfortheoptimizerbeforerunningtheprogram.
updating the centre point, the scattering of the particles begins again from the new centre. The value of
Afterupdatingthecentrepoint,thescatteringoftheparticlesbeginsagainfromthenewcentre.The
the Gbest must be compared with that of Rbest. If Rbest proposes a better solution than Gbest, then the
valueoftheGbestmustbecomparedwiththatofRbest.IfRbestproposesabettersolutionthanGbest,
location
then Gbest
ofthe must be
location swapped
of Gbest with
must that of Rbest.
be swapped withThe
thatprocess continues
of Rbest. Gbest reaches
untilcontinues
The process untilaGbest
specified
defined value or once the generation number reaches its maximum value. Figure 7 shows a preview of
reachesaspecifieddefinedvalueoroncethegenerationnumberreachesitsmaximumvalue.Figure7
showsapreviewofthetwotandemgenerations.Theupdatevectorupdatesthelocationofthecentre
the two tandem generations. The update vector updates the location of the centre based on the equation
shown basedontheequationshownbelow.
below.

Figure7.Updatingthecentrepointusinganupdatevector[39].
Figure 7. Updating the centre point using an update vector [39].

3.2.RMOBasedMPPT
3.2. RMO Based MPPT
In the RMObased MPPTthe search space refers toa vector consists terminalvoltages at the
In the RMO-based MPPT the search space refers to a vector consists terminal voltages at the
outputofPVsystem.A1NvectorpresentedinEquation(8)showsthelocationvectoroftheMPPT
output of PV system. A 1 N vector presented in Equation (8) shows the location vector of the MPPT
problem.InthisequationNdenotesthenumberofparticipatingparticlesandeachlocationrefersto
problem. In this equation N denotes the number of participating particles and each location refers to a
avoltagevaluethatisapotentialsolutiontotheMPPTobjectivefunction.Thefitnessoftheseparticles
isevaluatedaccordingtotheoutputgeneratedpowerofPVsystemrespecttoeachterminalvoltage:
voltage value that is a potential solution to the MPPT objective function. The fitness of these particles
is evaluated according to theXoutput k generated power
, X ik ,of,.......,
PV system X Nk 1 , respect
X Nk to each terminal (8)
voltage:
i X1 ,
k
X 2k , ... ...

Xik X1k , X2k , ... ... , Xik , , ......., X N k
1 , X N
k
Inpractice,duringpartialshading,instantaneousvariationsintheinsolationlevelcausesharp (8)
fluctuations in the generated power. Therefore, the condition presented in Equation (9) must be
In practice, during partial shading, instantaneous variations in the insolation level cause sharp
satisfiedtoinitializethealgorithm.Theconditionindicatestheminimumallowedvariationinthe
fluctuations in the generated power. Therefore, the condition presented in Equation (9) must be
outputpowertorunthealgorithmandtofindthenewMPP,whichisgivenbyP:
satisfied to initialize the algorithm. The condition indicates the minimum allowed variation in the
output power to run the algorithm and to F (find Fnew
X i 1 )the ( X i )MPP, which is given by P:
P (9)
F ( Xi )
FpXi`1 q FpXi q
P
whereF(Xi)returnstheoutputpowerofthePVpanel,respectivetothelocationofithparticleinthe
(9)
FpXi q
searchspace.Giventhatpartialshadingisanenvironmentalphenomenon,itisstochasticinnature
andthereforethereareinnumerablepartialshadingconditionspossible.Herein,threechallenging
where F(Xi ) returns the output power of the PV panel, respective to the location of ith particle in the
partialshadingconditionsareselectedforthepurposeofevaluatingtheproposedMPPTtechnique.
search space. Given that partial shading is an environmental phenomenon, it is stochastic in nature and
The first condition considered is common one where two peaks appear on the systems output
therefore there are innumerable partial shading conditions possible. Herein, three challenging partial
shading conditions are selected for the purpose of evaluating the proposed MPPT technique. The first
Energies 2016, 9, 147 9 of 18

condition considered is common one where two peaks appear on the systems output Power-Voltage
curve.Energies2016,9,147
The second condition refers to where partial shading causes multiple peaks with similar 9of18
output
power values making it challenging to determine the global MPP. This condition is used to evaluate
PowerVoltagecurve.Thesecondconditionreferstowherepartialshadingcausesmultiplepeaks
the accuracy of the proposed MPPT technique. The third condition is where the global MPP is amongst
withsimilaroutputpowervaluesmakingitchallengingtodeterminetheglobalMPP.Thiscondition
multiple local maxima. These three conditions were chosen on the assumption that they cover a large
isusedtoevaluatetheaccuracyoftheproposedMPPTtechnique.Thethirdconditioniswherethe
proportion of partial shading conditions, and therefore provide a solid foundation for evaluating the
globalMPPisamongstmultiplelocalmaxima.Thesethreeconditionswerechosenontheassumption
proposed MPPT
that they technique.
cover a large proportion of partial shading conditions, and therefore provide a solid
foundationforevaluatingtheproposedMPPTtechnique.
4. Circuit Topology and Operation of the DC-DC Converter in the PV System
4.CircuitTopologyandOperationoftheDCDCConverterinthePVSystem
Figure 8 shows the topology of the proposed PV system. As shown, the DC-DC converter connects
the solar Figure 8 shows
PV modules tothe
thetopology of the
load. The proposed
measured PV system.
system output Aspower
shown,isthe
theDCDC converter
point where the PV
connectsthesolarPVmodulestotheload.Themeasuredsystemoutputpoweristhepointwhere
systems I_V curve and the load line intersect. The location of this point is not only affected by solar
thePVsystemsI_Vcurveandtheloadlineintersect.Thelocationofthispointisnotonlyaffected
irradiance and temperature, but also by output load. The load line represents the characteristics of the
by solar irradiance and temperature, but also by output load. The load line represents the
load as seen from the output of the PV arrays or the input of the converter. The MPPT controller varies
characteristicsoftheloadasseenfromtheoutputofthePVarraysortheinputoftheconverter.The
the point of intersection between the load line and I_V curve by varying the duty cycle to achieve an
MPPTcontrollervariesthepointofintersectionbetweentheloadlineandI_Vcurvebyvaryingthe
intersection point where maximum power transfer to the load is achieved.
dutycycletoachieveanintersectionpointwheremaximumpowertransfertotheloadisachieved.

CUK Converter
Cs
L1 L2
+
PV arrays

Load
Vpv IGBT D
(KC85T) C1 C2
_
(Duty Cycle)
Vpv & Ipv

PWM

MPPT
Controller

Figure8.TopologyoftheproposedPVsystem.
Figure 8. Topology of the proposed PV system.

Due to its popularity, a DCDC uk converter is used in the presented topology. uk and
Due to its converters
buckboost popularity,both
a DC-DC ability
provideCuk
the converter is used
to output in the
voltages presented
lower topology.
or higher
Cuk
than the input and
buckboost converters both provide the ability to output voltages lower or higher than the input
voltage.Despitethebuckboostconfigurationtypicallybeinglowercostthanukconverters,ithas
disadvantages
voltage. Despite thesuch as discontinuous
buckboost input current,
configuration highbeing
typically peak currents
lower costflowing
than through
Cuk power
converters, it
components,andpoortransientresponsewhichcanmakeitlessefficient.Theukconverterhaslow
has disadvantages such as discontinuous input current, high peak currents flowing through power
switchinglossesandthehighestefficiencyofnonisolatedDCDCconverters.ukconverterscan
components, and poor transient response which can make it less efficient. The Cuk converter has
also provide a better outputcurrent characteristic due to the inductor in the outputstage [40].
low switching losses and the highest efficiency of non-isolated DCDC converters. Cuk converters
Theinput/outputrelationoftheukconverterisgivenbyEquations(10)and(11):
can also provide a better output-current characteristic due to the inductor in the output stage [40].
The input/output relation of the Cuk converter 1 D by Equations (10) and (11):
Vin is( given )Vout (10)
D
1D
Vin p D qVout (10)
I in ( D ) I out (11)
1 D
D
Equations(10)and(11),canberewrittenasEquation(12).Thisequationshowsthattheoutput
Iin p qIout (11)
1 D
voltageandcurrentofthesystemdependsdirectlyonthedutycycleoftheconverterandthatany
changeindutycyclewillleadtoachangeintheintersectionpointofI_Vcurveandloadline.The
Equations (10) and (11), can be re-written as Equation (12). This equation shows that the output
proposedMPPTcontrollersearchestheentirevoltagesearchspacetodeterminethedutycyclewhere
voltage and current of the system depends directly on the duty cycle of the converter and that
theoutputpowerismaximized.Inthecaseofdynamicshadingpatterns,environmentalconditions
any change in duty cycle will lead to a change in the intersection point of I_V curve and load line.
or load values, through Equation (9), these changes will be considered and the algorithm will
The proposed MPPT controller searches the entire voltage search space to determine the duty cycle
determinethenewdutycycletobesetfortheconverter.TheparametersoftheDCDCconverterare
where the output power is maximized. In the case of dynamic shading patterns, environmental
inspiredfrom[40]andarelistedinTable2.
conditions or load values, through Equation (9), these changes will be considered and the algorithm
will determine the new duty cycle to be set for the converter. The parameters of the DC-DC converter
are inspired from [40] and are listed in Table 2.
Energies2016,9,147
Energies 2016, 9, 147 10of18
10 of 18

1 D
Z (1 D )22 Z out (12)
Zinin p D q Zout (12)
D

Table 2. Parameters of the selected DC-DC converter components.

Table2.ParametersoftheselectedDCDCconvertercomponents.

Components
Components Values
Values
InductorL1 5mH
Inductor L1 5 mH
InductorL2
Inductor L2 5 mH5mH
CapacitorC1
Capacitor C1 47f
47 f
CapacitorC2
Capacitor C2 1 f1f
SwitchingFrequency
Switching Frequency 20kHz
20 kHz

5.ResultsandDiscussion
5. Results and Discussion
TheperformanceoftheproposedMPPTcontrollerbasedontheRMOmethodwasevaluated
The performance of the proposed MPPT controller based on the RMO method was evaluated
under the
under thethree
threedifferent
differentpartial
partialshading
shadingconditions.
conditions. Accuracy, speed, reliability,
Accuracy, speed, power loss,
reliability, power loss,and
and
oscillationduringthetrackingperiodarethemainfactorsmonitoredintheevaluationandvalidation
oscillation during the tracking period are the main factors monitored in the evaluation and validation
processes.Itisworthnotingthattheproposedmethodisnotcomparedwithanyoftheconventional
processes. It is worth noting that the proposed method is not compared with any of the conventional
methodsbecause
methods becausethe
the method
method is an
is an evolutionary
evolutionary optimization
optimization technique
technique capablecapable of detecting
of detecting the
the global
globalcandidatesolutioninthesearchspace.Assuch,thepurposeofthisstudyistonotonlyevaluate
candidate solution in the search space. As such, the purpose of this study is to not only evaluate the
thereliabilityofthismethodunderpartialshadingconditionsbuttoalsoassessthequalityoftracking
reliability of this method under partial shading conditions but to also assess the quality of tracking
achieved. The
achieved. The results
results of
of the
the proposed
proposed method
method are
are compared
compared with
with those
those of the widely
of the widely used
used PSO
PSO
technique.InordertoevaluatetheperformanceoftheMPPTmethodaccordingtotherealcondition
technique. In order to evaluate the performance of the MPPT method according to the real condition
limitations,andtoensuretheconverterreachessteadystatepriortoanotherMPPTcyclebeginning,
limitations, and to ensure the converter reaches steady state prior to another MPPT cycle beginning,
thesamplingtimeof50mswaschosenandtheparametersofactualPVmoduleofKC85Thavebeen
the sampling time of 50 ms was chosen and the parameters of actual PV module of KC85T have been
consideredinthesimulationresults.
considered in the simulation results.

5.1.TestingConditions
5.1. Testing Conditions
Since the
Since thepartial
partialshading
shadingcondition
conditionis
isaastochastic
stochasticphenomenon,
phenomenon,innumerable
innumerableconditions
conditions and
and
scenariosmayoccur.However,toevaluatetheperformanceoftheproposedalgorithm,threedifferent
scenarios may occur. However, to evaluate the performance of the proposed algorithm, three different
caseswithvaryingdegreesofpartialshadingarerepresented,coveringarangeofinsolationlevelsfrom
cases with varying degrees of partial shading are represented, covering a range of insolation levels
moderatetoacute.Figure9showsthecircuittopologyofthePVarray,includingtwoPVmodules.
from
moderate to acute. Figure 9 shows the circuit topology of the PV array, including two PV modules.

Ipva
+
Sub-module 1
G1
Ip h(G1)
Dbyp ass1
Module 1

G2 Ip h(G2)
Dbyp ass2

Sub-module 2

Vpva
Sub-module 3
G3 Ip h(G3)
Dbyp ass1
Module 2

G4 Ip h(G4)
Dbyp ass2

Sub-module 4

_

Figure9.CircuitrydiagramoftheselectedPVarray[36].
Figure 9. Circuitry diagram of the selected PV array [36].
Energies 2016, 9, 147 11 of 18
Energies2016,9,147 11of18

Given
Given thethe doublebypass
double-bypass diode diode in each
in each module,
module, three possible
three possible scenariosscenarios
that have that have
been been
considered
in considered
this study in arethis study are(i)asthe
as follows: follows:
entire(i) the entire
module onemodule
receivesone
an receives
irradiancean level
irradiance level
of 1000 W/mof 2
(G11000 W/m (G1and
= G2 = entire
1000) and the entire module antwo receiveslevel
an irradiance level of 350 W/m
2 2 (G3 2
= G2 = 1000) the module two receives irradiance of 350 W/m = G4 = 350);
(ii)(G3=G4=350);(ii)theentiremoduleonereceivesanirradiancelevelof1000W/m
2(G1=G2=1000)
the entire module one receives an irradiance level of 1000 W/m2 (G1 = G2 = 1000) and module two
andmoduletworeceivesirradiancelevelsof700W/m 2and500W/m2(G3=700,G4=500);(iii)module
receives irradiance levels of 700 W/m2 and 500 W/m2 (G3 = 700, G4 = 500); (iii) module one receives
onereceivesirradiancelevelsof(G1=1200,G2=700)andmoduletworeceivesirradiancelevelsof
irradiance levels of (G1 = 1200, G2 = 700) and module two receives irradiance levels of 700 W/m2 and
700W/m 2
2and500W/m2(G3=500,G4=300).TheRMOtechniqueisappliedtoalloftheseconditions
500 W/m (G3 = 500, G4 = 300). The RMO technique is applied to all of these conditions to evaluate
toevaluatethequalityoftracking,andtheresultsarecomparedwiththoseofthePSOmethod.
the quality of tracking, and the results are compared with those of the PSO method.
5.1.1.FirstScenario
5.1.1. First Scenario
Figure10showstheoutputcharacteristicofthePVsystemalongwiththeperformanceofthe
Figure 10 shows the output characteristic of the PV system along with the performance of the
proposedmethodandthePSOmethodunderthefirstpartialshadingscenario.TheglobalMPPin
proposed method and the PSO method under the first partial shading scenario. The global MPP in this
thisconditioncanbetrackednotonlybythesoftcomputingmethodsbutalsobytheconventional
condition can be tracked not only by the soft computing methods but also by the conventional methods
methodsthatusehillclimbingapproachintheirtrackingsystem.However,mostofthesemethods
that use hill-climbing approach in their tracking system. However, most of these methods suffer from
sufferfromslowconvergencetimeorlowefficiency.Asshown,theproposedRMOalgorithmtracks
slow convergence time or low efficiency. As shown, the proposed RMO algorithm tracks the actual MPP
theactualMPPwithinaroundhalfthetrackingtimeofthePSOalgorithm.Thetrajectoryofthepower
within around half the tracking time of the PSO algorithm. The trajectory of the power shows that unlike
showsthatunliketheconventionalmethods,thetrackingprocessstartsfromrandomlocationsinthe
thesearchspace.
conventional methods, the tracking process starts from random locations in the search space.

Figure10.TheoutputresultsoftheproposedmethodandPSOmethodundershadingconditionfor
Figure 10. The output results of the proposed method and PSO method under shading condition for
thefirstscenario.
the first scenario.

5.1.2.SecondScenario
5.1.2. Second Scenario
FurtherverificationoftheRMOmethodispresentedinFigure11.Thisconditionreferstothe
Further verification of the RMO method is presented in Figure 11. This condition refers to the
secondscenariowheretheoutputcharacteristicsofthePVsystemcontainthreepeakswithminor
second scenario where the output characteristics of the PV system contain three peaks with minor
differences among their respective power values.The middlepeaks power value isaround 150.5
differences among their respective power values. The middle peaks power value is around 150.5 (W),
(W),whiletheotherpeaksontheleftandrightsideoftheactualGMPP,havethepowervaluesof149.3
while the other peaks on the left and right side of the actual GMPP, have the power values of 149.3 (W)
(W) and 148.2 (W), respectively. Therefore, this scenario creates a shading condition in which the
and 148.2 (W),
difference respectively.
between GMPPTherefore,
and localthis scenario
MPPs is lesscreates a shading
than 1.5%. condition
The purpose in which
of testing the
the difference
proposed
between GMPP and local MPPs is less than 1.5%. The purpose of testing the proposed method
methodunderthisconditionistocheckifitisabletotracktheglobalMPPwhilethefitnessvalues under
this condition is to check if it is able to track the global MPP while the fitness values of local solutions
oflocalsolutionsareveryclosetothefitnessvalueoftheglobalsolution.Thefigureshowsthatboth
aretheproposedalgorithmandPSOaccuratelytrackedtheactualMPPattheoutputofthePVsystem.
very close to the fitness value of the global solution. The figure shows that both the proposed
algorithm and PSO accurately tracked the actual MPP at the output of the PV system. The proposed
TheproposedRMOtechniquehowevertrackedtheGMPPinamuchshortertimeandwithfewer
RMO technique however tracked the GMPP in a much shorter time and with fewer oscillations during
oscillationsduringthetrackingperiod.
the tracking period.
Energies 2016, 9, 147 12 of 18
Energies2016,9,147 12of18
Energies2016,9,147 12of18

Figure11.TheoutputresultsoftheproposedmethodandPSOmethodundershadingconditionfor
Figure 11. The output results of the proposed method and PSO method under shading condition for
thethesecondscenario.
Figure11.TheoutputresultsoftheproposedmethodandPSOmethodundershadingconditionfor
second scenario.
thesecondscenario.
5.1.3.ThirdScenario
5.1.3. Third Scenario
5.1.3.ThirdScenario
To evaluate the performance of the proposed technique under extreme partial shading
To To
evaluate the performance
evaluate of theof
the performance proposed technique
the proposed under extreme
technique partial shading
under extreme partial conditions,
shading
conditions,theRMObasedMPPThasbeentestedunderthethirdscenario.Inthisscenario,theglobal
themaximumoccursamongmultiplelocalmaxima.MostoftheconventionalMPPTtechniquesareable
RMO-based MPPT has been tested under the third scenario. In this scenario, the global maximum
conditions,theRMObasedMPPThasbeentestedunderthethirdscenario.Inthisscenario,theglobal
occurs among multiple local maxima. Most of the conventional MPPT techniques are able to track
maximumoccursamongmultiplelocalmaxima.MostoftheconventionalMPPTtechniquesareable
totracktheactualMPPifitoccurspriortothelocalMPP.However,allofthesetechniquesbecome
thestuckinthelocalMPPiftheglobalMPPoccursafterthem.Figure12showshowtheproposedRMO
actual MPP if it occurs prior to the local MPP. However, all of these techniques become stuck in
totracktheactualMPPifitoccurspriortothelocalMPP.However,allofthesetechniquesbecome
themethodaccuratelytrackstheactualglobalMPPregardlessofthepositionsoflocalMPPs.
local MPP if the global MPP occurs after them. Figure 12 shows how the proposed RMO method
stuckinthelocalMPPiftheglobalMPPoccursafterthem.Figure12showshowtheproposedRMO
accurately tracks the actual global MPP regardless of the positions of local MPPs.
methodaccuratelytrackstheactualglobalMPPregardlessofthepositionsoflocalMPPs.

Figure12.TheoutputresultsoftheproposedmethodandPSOmethodundershadingconditionin
thirdscenario.
Figure12.TheoutputresultsoftheproposedmethodandPSOmethodundershadingconditionin
Figure 12. The output results of the proposed method and PSO method under shading condition in
thirdscenario.
third scenario.
5.2.ConvergenceSpeed,PowerLoss,andComputationalCost
5.2.5.2.ConvergenceSpeed,PowerLoss,andComputationalCost
Convergence Speed, Power Loss, and Computational Cost
Incomparingsoftcomputingmethods,theirreliabilityunderpartialshadingconditionsisnot
Incomparingsoftcomputingmethods,theirreliabilityunderpartialshadingconditionsisnot
normallyamaincomparisoncriteria.Otherfactorshoweversuchasconvergencespeed,simplicity,
In comparing soft computing methods, their reliability under partial shading conditions is not
normallyamaincomparisoncriteria.Otherfactorshoweversuchasconvergencespeed,simplicity,
output stability and computational burden are evaluated. One of the distinct advantages of the
normally a main comparison criteria. Other factors however such as convergence speed, simplicity,
output stability and computational burden are evaluated. One of the distinct advantages of the
proposedRMOmethodishigherspeedbecausetheparticlesscatteraroundacenterwitharadiance
output stability and computational burden are evaluated. One of the distinct advantages of the
proposedRMOmethodishigherspeedbecausetheparticlesscatteraroundacenterwitharadiance
of Rbest, which is updated during each iteration. This procedure does not let particles search the
proposed RMO method is higher speed because the particles scatter around a center with a radiance
of Rbest, which
unnecessary partisof
updated during
the search each
space oriteration. This the
diverge from procedure
search does not
space. Inlet particles
fact, duringsearch the
the early
Rbest, whichpart
of unnecessary is updated during
of the search eachor
space iteration. This procedure
diverge from does not
the search space. let particles
In fact, search
during the the
early
iterationswhentheradianceofthesphereislarger,theareaoftheglobalMPPisdetermined,andin
unnecessary part of the search space or diverge from the search space. In fact, during
iterationswhentheradianceofthesphereislarger,theareaoftheglobalMPPisdetermined,andin
thefinaliterations,theexactglobalMPPistracked.Figure13showstheconvergenceoftheproposed the early
iterations when the radiance of the sphere is larger, the area of the global MPP is determined, and in
thefinaliterations,theexactglobalMPPistracked.Figure13showstheconvergenceoftheproposed
RMOtechniqueandPSOtechniqueforallthreescenarios.
RMOtechniqueandPSOtechniqueforallthreescenarios.
Energies 2016, 9, 147 13 of 18

the final iterations, the exact global MPP is tracked. Figure 13 shows the convergence of the proposed
RMO technique and PSO technique for all three scenarios.
Energies2016,9,147 13of18

Figure 13. Convergence of the proposed RMO method versus PSO technique for three
Figure13.ConvergenceoftheproposedRMOmethodversusPSOtechniqueforthreeshadingconditions.
shading conditions.

AnotherimportantoutcomeresultingfromtheapplicationoftheRMOtechniqueforMPPTis
Another important outcome resulting from the application of the RMO technique for MPPT is the
the reduction in power loss during both the tracking and steadystate periods. Many of the
reduction in power loss during both the tracking and steady-state periods. Many of the conventional
conventionalorhybridmethodsresultinrelativelyhighpowerlosses.Themainreasonforthisis
or hybrid methods result in relatively high power losses. The main reason for this is that most of these
thatmostofthesemethodsarebasedonincrementalconductanceorhillclimbingtheories,thereby
methods are based on incremental conductance or hill climbing theories, thereby resulting in constant
resultinginconstantoscillationsattheoutputofthePVsystemevenwhentheareaoftheglobalMPP
oscillations at the output of the PV system even when the area of the global MPP is successfully
issuccessfullyidentified.SincetheefficiencyofthePVsystemisacriticalfactor,theseoscillations
identified. Since the efficiency of the PV system is a critical factor, these oscillations around the MPP
aroundtheMPPcancausesignificantpowerloss,whichcanfurtherreducetheefficiencyoftheentire
can cause significant power loss, which can further reduce the efficiency of the entire PV system.
PVsystem.Anothereffectoftheseoscillationsisvoltageinstabilitycausedbyconstantchangesin
Another effect of these oscillations is voltage instability caused by constant changes in duty cycles.
dutycycles.Accordingtotheinput/outputcorrelationoftheDC/DCconverters,anyslightchangein
According to the input/output correlation of the DC/DC converters, any slight change in the duty
thedutycyclechangestheoutputvoltageleveloftheconverterregardlessofthetypeofconverter
cycle changes the output voltage level of the converter regardless of the type of converter used in
usedinthesystem.
the system.
Even methods based on artificial intelligence approaches have large oscillations during the
Even methods based on artificial intelligence approaches have large oscillations during the
trackingperiod.Thereasonforthisisthatinmanyswarmbasedmethods,particlesexploreallparts
tracking period. The reason for this is that in many swarm-based methods, particles explore all parts
ofthesearchspaceduringtherunningtimeuntiltheglobalmaximumpowerpoint(GMPP)isfound;
of the search space during the running time until the global maximum power point (GMPP) is found;
andinevolutionbasedoptimization,theevolutionprocesslastsuntilthefinalgenerationstofind
and in evolution-based optimization, the evolution process lasts until the final generations to find and
andtracktheGMPP.Manyresearchershaveattemptedtoovercomethisproblembyeitherreducing
track the GMPP. Many researchers have attempted to overcome this problem by either reducing the
the random coefficient values or by setting the initial locations for the particles. However, these
random coefficient values or by setting the initial locations for the particles. However, these measures
measuresonlyhaveminoreffectontheoscillationsoftheoutputpowerandreducethereliabilityof
only have minor effect on the oscillations of the output power and reduce the reliability of the control
thecontrolstrategywhenintensivepartialshadinghappens.Therefore,ifthePVsystemissubjectto
strategy when intensive partial shading happens. Therefore, if the PV system is subject to rapidly
rapidly varying partial shading conditions, which is very common in residential microgrids, a
varying partial shading conditions, which is very common in residential microgrids, a considerable
considerableamountofpowerlossaswellaspoorvoltagestabilitywilloccur.
amount of power loss as well as poor voltage stability will occur.
InRMObasedMPPT,theseproblemshavebeenaddressed.Oneofthemainreasonsisthatin
In RMO-based MPPT, these problems have been addressed. One of the main reasons is that in the
theprocedureofthismethod,particlesscatterinthesphericalsearchspacealongtheradiiofRbest,
procedure of this method, particles scatter in the spherical search space along the radii of Rbest, which
whichisupdatedthroughouttheiterationprocess.Figures1012showthedifferencebetweenthe
is updated throughout the iteration process. Figures 1012 show the difference between the PSO- and
PSOandRMObasedMPPTmethodsintermsofconvergencespeedandoutputpoweroscillations
RMO-based MPPT methods in terms of convergence speed and output power oscillations while the
while the PV system is operating under the three scenarios. As these Figures show, the GMPP is
PV system is operating under the three scenarios. As these Figures show, the GMPP is tracked in less
trackedinlessthanhalfofthetimethanPSOcantrackthispoint.Inaddition,inPSObasedMPPT,
than half of the time than PSO can track this point. In addition, in PSO-based MPPT, because of the
becauseoftheroleofrandomcoefficients,particlesmaymoveoutofthesearchspace,asshownin
role of random coefficients, particles may move out of the search space, as shown in Figures 1012.
Figures1012.
Notably, the PSO algorithm applied in this study for the purpose of comparison has been
adjustedsuchthatthevelocityandtheparticlemovementarelimited;therefore,theconvergenceand
oscillationsarelessthanthoseofthestandardPSO.
Energies 2016, 9, 147 14 of 18

Notably, the PSO algorithm applied in this study for the purpose of comparison has been adjusted
such that the velocity and the particle movement are limited; therefore, the convergence and oscillations
Energies2016,9,147 14of18
are less than those of the standard PSO.
Figure 14 shows the voltage variation during the tracking and steady-state periods at the output
Figure14showsthevoltagevariationduringthetrackingandsteadystateperiodsattheoutput
of
of the PV system for
the PV system for the
thethree
threescenarios
scenariosfor
forboth
boththe
theRMO-
RMOand
andPSO-based
PSObasedMPPTs. Clearly, both
MPPTs. Clearly, both
methods have no oscillation around the MPP during the steady-state period. However, the graph
methodshavenooscillationaroundtheMPPduringthesteadystateperiod.However,thegraph
shows that, compared with the PSO method, the RMO technique reduces the voltage variation during
showsthat,comparedwiththePSOmethod,theRMOtechniquereducesthevoltagevariationduring
the tracking period. In order to evaluate the dynamic performance of the proposed method, it was also
thetrackingperiod.Inordertoevaluatethedynamicperformanceoftheproposedmethod,itwas
tested under varying load and shading conditions.
alsotestedundervaryingloadandshadingconditions.

Figure14.TheoutputvoltagefluctuationofthePVsystemcontrolledbytheRMOmethodversus
Figure 14. The output voltage fluctuation of the PV system controlled by the RMO method versus PSO
PSOtechniqueforthreeshadingconditions.
technique for three shading conditions.

AsshowninFigure15a,oncethesystemhasstabilizedaftertrackingtheGMPP,theshading
As
conditionshown in Figure
abruptly 15a,from
changes oncethe
the third
systemtohas
thestabilized after tracking
second scenario where the
the GMPP, the between
difference shading
condition abruptly changes from the third to the second scenario where the difference between GMPP
GMPP and local MPPs is less than 1.5%. The objective of this is to represent varying shading
and local MPPs is less than 1.5%. The objective of this is to represent varying shading conditions.
conditions.Intheothertest,showninFigure15b,aftertheGMPPhasbeentracked,theloadishalved, In
the other test, shown in Figure 15b, after the GMPP has been tracked, the load is halved, reducing
reducingfromR=20toR=10att=7.8s.TheloadisagainchangedtoR=20att=15.4sto
from R = 20 to R = 10 at t = 7.8 s. The load is again changed to R = 20 at t = 15.4 s to represent
representloadvariation.Inbothsituations,thecontrollerdetectsthechangesusingEquation(9)and
load variation. In both situations, the controller detects the changes using Equation (9) and starts
startstrackingtheGMPPunderthenewconditions.AsshowninFigures15a,bbothmethodsare
tracking the GMPP under the new conditions. As shown in Figure 15a,b both methods are capable of
capableofdynamicallytrackingtheGMPPundervaryingloadandshadingconditionshoweverthe
dynamically tracking the GMPP under varying load and shading conditions however the introduced
introducedDESPOmethodismuchfastercomparedthanthePSOmethod,resultinginasmoother
DESPO method is much faster compared than the PSO method, resulting in a smoother and more
andmorestableoutputpowersubjecttochangingconditions.
stable output power subject to changing conditions.
The comparison of the proposed RMO method with conventional methods, which are less efficient
and unreliable under partial shading conditions, has not been discussed. Rather, the comparison with
the modified PSO method has been presented in this paper.
In addition to the fast convergence speed and reduced oscillation during the tracking period,
less memory is needed for the proposed RMO technique to find the global solution in the search
space. Amongst the common criticisms of soft computation-based MPPT and particularly the PSO
method is high computational burden and the need to use a large amount of memory. The reason
for this is that the best position of each particle and the best global position of all particles should be
remembered. In the proposed RMO technique, however, the system only needs remember the global
Energies 2016, 9, 147 15 of 18

best position of all particles thereby requiring far less memory and allow the system to be implemented
Energies2016,9,147 15of18
on a lower-cost microcontroller.

(a)

(b)

Figure15.Dynamicperformanceofproposedmethodvs.PSO:(a)duringshadingconditionchanges;
Figure 15. Dynamic performance of proposed method vs. PSO: (a) during shading condition changes;
(b)(b)duringloadchanges.
during load changes.

The comparison
6. Conclusions of the
and Future proposed RMO method with conventional methods, which are less
Works
efficient and unreliable under partial shading conditions, has not been discussed. Rather, the
This study aimed to propose a fast, reliable, and system-independent technique for tracking the
comparisonwiththemodifiedPSOmethodhasbeenpresentedinthispaper.
MPP ofInadditiontothefastconvergencespeedandreducedoscillationduringthetrackingperiod,
the PV system under partial shading conditions. A new fast, simple, and efficient method
called RMO is used
less memory to track
is needed the
for actual
the MPP RMO
proposed at the technique
output of the PV system.
to find A sequential
the global solution inmathematical
the search
modeling procedure is applied to the model to simulate the behavior of the PV system under partial
space.AmongstthecommoncriticismsofsoftcomputationbasedMPPTandparticularlythePSO
methodishighcomputationalburdenandtheneedtousealargeamountofmemory.Thereasonfor
shading conditions. The proposed MPPT method is verified by testing the technique under three
thisisthatthebestpositionofeachparticleandthebestglobalpositionofallparticlesshouldbe
partial shading conditions. These predefined conditions are designed to verify the stability, speed,
andremembered.IntheproposedRMOtechnique,however,thesystemonlyneedsremembertheglobal
accuracy of the system. The proposed RMO technique can differentiate the GMPP from local
bestduring
MPPs position of all particles
mismatching thereby The
conditions. requiring
main far less memory
advantages of theand allow the
proposed systemover
technique to be
the
implementedonalowercostmicrocontroller.
other evolutionary methods are higher efficiency under partial shading conditions, higher speed,
simplicity, lower computational cost, and higher output stability. Compared with the PSO method,
Energies 2016, 9, 147 16 of 18

which has been extensively presented in the literature, the proposed method is faster, less dependent
on random coefficients, and needs less memory for processing. As such, the computational burden of
the algorithm is reduced, and the technique can be easily implemented on a low-cost microcontroller.
This paper represents the first application of RMO for MPPT and we are currently working on the
experimental set up in order to extend this research from simulation study to implementation on the
physical system.

Author Contributions: Mehdi Seyedmahmoudian, Ben Horan and Rasoul Rahmani conceived and designed
the approach to maximum power point tracking. Mehdi seyedmahmoudian, Aman Maung Than Oo and
Alex Stojscevski analysed the results. In terms of writing the paper all authors contributed jointly to preparing
this manuscript and all have read and approved the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.

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