Research ArticleMetaheuristic Optimization of Fractional Order IncrementalConductance (FO-INC) Maximum Power Point Tracking (MPPT)

Hossam Hassan Ammar12 Ahmad Taher Azar 34 Raafat Shalaby 15

and M I Mahmoud5

1School of Engineering and Applied Science Nile University Giza Egypt2Smart Engineering Systems Research Center (SESC) Nile University 12588 Shaikh Zayed City Giza Egypt3Robotics and Internet-of-ings Lab (RIOTU) Prince Sultan University Riyadh 12435 Saudi Arabia4Faculty of Computers and Articial Intelligence Benha University Banha Egypt5Faculty of Electronic Engineering Menoa University Menoa Egypt

Correspondence should be addressed to Ahmad Taher Azar ahmad_t_azarieeeorg

Received 25 July 2019 Revised 7 October 2019 Accepted 18 October 2019 Published 28 November 2019

Guest Editor Jianwu Zeng

Copyright copy 2019 Hossam Hassan Ammar et al shyis is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

shyis paper seeks to improve the photovoltaic (PV) system eciency using metaheuristic optimized fractional order incrementalconductance (FO-INC) control shye proposed FO-INC controls the output voltage of the PV arrays to obtain maximum power pointtracking (MPPT) Due to its simplicity and eciency the incremental conductance MPPT (INC-MPPT) is one of the most popularalgorithms used in the PV scheme However owing to the nonlinearity and fractional order (FO) nature of both PV and DC-DCconverters the conventional INC algorithm provides a trade-o betweenmonitoring velocity and tracking precision Fractional calculusis used to provide an enhanced dynamical model of the PV system to describe nonlinear characteristics Moreover three metaheuristicoptimization techniques are applied Particle Swarm Optimization (PSO) Ant Colony Optimization (ACO) and AntLion Optimizer(ALO) are used for tuning the FO parameters of the proposed INC-MPPT A MATLAB-Simulink-based model of the PV andoptimization have been developed and simulated for dierent INC-MPPTtechniques Dierent techniques aim to control the boostDC-DC converter towards the MPPshye proposed optimization algorithms are also developed and implemented in MATLAB to tune thetarget parameters Four performance indices are also introduced in this research to show the reliability of the comparative analysis of theproposed FO-INC with metaheuristic optimization and the conventional INC-MPPT algorithms when applied to a dynamical PVsystem under rapidly changingweather conditionsshye simulation results show the eective performance of the proposedmetaheuristicoptimized FO-INC as a MPPT control for dierent climatic conditions with disturbance rejection and robustness analysis

1 Introduction

Green energy sources are the primary research goalnowadays as they are viable ecological and cost-eectiveenergy sources Solar wind tidal and biomass energy havepenetrated the electric power production market in recentyears due to the diverse methods and their renewablenatureshye benets of developing renewable power includereducing fossil fuel usage mitigating the greenhouse im-pact and reducing air pollution [1] In addition controlapproaches and optimization have shown that the per-formance of photovoltaic devices depends upon climate

conditions (sunlight and temperature) and load impedance[2] However its low energy conversion eectiveness(especially in low radiation and temperatures) is the pri-mary disadvantage of PV systems shye MPPT needs to beoperated for ideal eciency and operation as mentioned[3] One of the pioneering challenges of the PV devices istheir nonlinear current-voltage I-V relationship dynamicwhich generates a distinctive MPP in the power-voltageP-V relationship as noted [4] Because of the P-V re-lationship with climate and load circumstances the MPPTmethod becomes complex MPPT methods do not onlyenhance the power performance of PV and energy

HindawiComplexityVolume 2019 Article ID 7687891 13 pageshttpsdoiorg10115520197687891

delivered to the load but they also increase the operatinglife of the PV system [5] Previous studies have suggestedseveral MPPT methods most MPPT techniques demon-strate higher efficiency under stable weather [6] MPPTalgorithms are usually used as electronic power conversiondevices and the control signal is a duty cycle for peak loadenergy [7] A wide variety of methods for solving the MPPTissue have been implemented such as the perturb andobserve (PampO) method incremental conductance (INC)algorithm and artificial intelligence includes fuzzy logicneural networks and metaheuristic techniques -e PampOand INC are the most common algorithms used for PV-MPPT systems [8] -e PampO technique is frugal and veryeasy to execute its operation is based on the iterativemeasurement of the voltage and current of the PV system toobtain the duty cycle and consequently the MPP Its maindisadvantage however is that it provides an oscillatorypower around the MPP and is also unable to manipulate PVpower variations due to climatic effects or inherent dis-turbances of the MPPT -e INC approach is based on thebehavior of PV given that a MPP is reached by zero in apitch of the PV curve positive to the left and negative to theright of the PV curve On the basis of this the techniquecalculates the DC-DC converter duty cycle by relating it-erative conductivity to the incremental conductivity -eprimary drawback in the INC technique is that the systemrsquosreaction to the MPP may be slow under some conditionsHowever the INC technique exhibits less oscillatory be-havior around the MPP compared to the PampO method [9]Fractional calculus introduces the nonintegral orderfractional of derivatives and integrals Many of the realsystems show a nonlinear and fractional order dynamicalbehavior such as heat conduction in solids electrical be-havior in R-L transportation lines mass diffusion andelectromagnetic waves [10] -e nonlinear characteristicsof the current-voltage of a PV cell occur because the PVcells are manufactured from semiconducting materials(crystalline silicon c-Si) -e power of PV cell depends onthe inherent voltage drop across the p-n junction (energyband) which produces a photoelectric current (currentsource)-e light and ambient temperature interaction alsoshows anomalous diffusion which can be described asfractional order diffusion [11] -erefore GrunwaldndashLetnikov fractional approximation [12] is introduced tocontrol the fractional order differentiation for current andvoltage nonlinear dynamical behavior To improve dy-namic performance FO-INC based on the nonlinear andfractional order changes of the PV voltage and current hasbeen proposed to track the maximum output power [13] Itis very important to select the proper converter [14] toenhance the MPPT performance -e MPPT techniqueshave been compared using MATLAB and Simulink toolscreated by MathWorks considering all the design andimplementation specs [15] -erefore metaheuristic op-timization techniquesrsquo robustness and ability to find theoptimal solution in different nonlinear systems havedemonstrated itself in numerous past research studiesMetaheuristic abilities are powerful techniques of resolvingoptimization problems for nonlinear and fractional order

systems [15] In power systems different optimization tech-niques have been utilized Considering the different constraintsin PV systems and difference in the nature of DC-DC convertersystem the ACO algorithm has been used [16] It has beenproved to be very robust consistent and performs better thanconventional optimization techniques (eg PSO and GA) [16]-e experiments show computational effectiveness and timedecrease in monitoring for a small PV Systems -e AntLionoptimizer (ALO) is a recent metaheuristic algorithm thatreplicates the hunting scheme of antlions in catching ants [17]ALO also gives a good performance results in PV-MPPTsystems [18]-is research aims to extract maximum powerfrom PV systems by using FO-INC and metaheuristic opti-mization technique -is enhanced system efficiency in dif-ferent climatic conditions using fixed and variable-step FO-INC with PSO ACO and ALO optimization techniques -ispaper is organized as follows Section 2 addresses the modelingof the complete PV system and Section 3 describes the MPPTalgorithm design and operation Section 4 gives the operationof metaheuristic optimization algorithms Sections 5 and 6illustrate the experimental results and conclusions to show theefficiency of the proposed technique

2 Photovoltaic (PV) System Modelingand Simulation

-e proposed PV system is constituted by a PV module theBuckndashBoost converter as a DC-DC converter between thePV panel and the DC load and the MPPT controller toachieve maximum power point of the PV panels -e modelof the solar panels used in the proposed system will be il-lustrated and the PV system is introduced [19] -e inputsto MPPT are the PV voltage and current which are used tocalculate and deliver the control signal (duty cycle) to theBuckndashBoost converter as shown in Figure 1 -e mainfunction of the MPPTalgorithm is to automatically track thevoltagecurrent change of the PV panel and feed theBuckndashBoost converter with the appropriate duty cycle to getthe MPP under specific climatic conditions

21 Modeling of PV Panel -e nonlinear equations ofthe PV system which describe the relationships between thedifferent PV model parameters are developed and solved viaMATLAB and Simulink tools where the PV cell electriccircuit model is shown in Figure 2 -e PV output currentIPV can be obtained using equation (1) where Np and Ns arethe number of parallel and series cells respectively

IPV Np times IG minus ID minus Ish( 1113857 (1)

-e nonlinear equation of I-V characteristics of one-diode PV model was expressed by Milici et al [9] as follows

IPV Np times IG minus Ns times Io eqηkTk( )times VPVNs( )+ IPVNp( )Rs( )minus 1( )1113876 1113877

minusNp

Rshtimes

VPV

Ns+

IPVRs

Np1113888 1113889

(2)

2 Complexity

where VPV and IPV are the PV terminal voltage and currentrespectively Rs and Rsh are the series and shunt resistancerespectively η is the ideality factor the Boltzmannrsquos constantis k q is the electron charge Tk is the temperature degree inKelvin IG is photo-generated current and the diode satu-ration current is Io -e PV panel parameters are shown inTable 1

-e I-V and P-V nonlinear characteristic curves of thePV array simulated using MATLAB at different climaticconditions (temperature and irradiance) are shown inFigure 3

22 DC-DC Converter Simulink and Simscape tools havebeen selected as platforms for modeling implementa-tion and testing the BuckndashBoost converter -e statespace modeling is primarily represented by equation (3)where A B C and D are the system matrices x is the statevariable vector xprime is the state variable derivative vectorwith respect to time u is the input and y is the output[14]

xprime Ax + Bu

y Cx + Du(3)

Figure 4 shows the BuckndashBoost model using Simscapewhich is simulated at different duty cycles and fixed load

according to the state space model represented in equation(4) where x1 IL x2 VCout and d duty cycle -e simu-lation results at different duty cycles are shown in Figure 5

MPPT

VPV

[IPV_T]

Inputs of the cell from MATLAB

BuckndashBoost converter

Load voltage

Load current

RL value from MATLAB

To workspace of Matlab

V_PV

IRR

Temp

A

ndashTndash

ndashTndash

VPV

IPV

ndashTndash

VPV1

IPV1

VL

IL

ndashTndash

ndashTndash

ndashTndash

ndashTndash

ndashTndash

ndashTndashX

ndashTndash

ndashTndash

V+

ndash

+

++

+

f (x) = 0

I_PV

D P [D]

[D]

gt

gt

A

V

PWM

In+

Inndash

Out+

Outndash

PS+

ndash

+

V

[IL]

[VL]

RL

Data

ndash

ndash

A+

Cell 1 IPV

Cell 1 IPV

I_PV

I_PV1

V_PV1

Resistive load

RL

Wm cell1

T cell1

Cell 01

PV cell 18V 72 A

P_Cell

Scope for results display

ndashgt

Figure 1 Complete PV system model using MATLAB and Simscape

IG

Rs

ID

Ipv

Vpv

Ish

Rsh

+

ndash

Figure 2 PV cell equivalent electric circuit model

Table 1 PV panel parameters

Parameter value ValueMax power Pmax 73572WOpen circuit voltage Voc 659VShort circuit current Ish 1521 ATemperature coefficient of VOC ndash123times10eminus 1 VCTemperature coefficient of Ish 318times10eminus 3 AC

PV at fixed T = 25degC

200 Wm2

400 Wm2

600 Wm2

800 Wm2

1000 Wm2

PV at fixed G = 1000 Wm2

25degC40degC

55degC70degC

0

5

10

15

PV cu

rren

t

7020 30 40 50 60100PV voltage

0

200

400

600

800

PV p

ower

0

5

10

15

PV cu

rren

t

10 20 30 40 50 600 70PV voltage

0

200

400

600

800

PV p

ower

Figure 3 P-V and I-V characteristic curves at different climaticconditions

Complexity 3

x1prime

x2prime

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

01 minus d

L

minus (1 minus d)

C

minus 1RC

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

x1

x2

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦ +

d

L

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦u1

y1

y2

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

1 0

0 1

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

IL

VCout

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦ +

0

0

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦u1

(4)

-e proposed BuckndashBoost has been designed and sim-ulated using the parameters illustrated in Table 2

3 Design and Implementation of MPPT

-e primary feature of the PV system is the total energymonitoring in which the power of the PV modules can beextracted in a certain climatic situation As shown in theliterature the most commonly usedMPPTalgorithm is INC-e INC algorithm is based on the reality that the PV outputenergy derivative for the output voltage at the MPP is zero(dPdV 0) positive on the left side of MPP (dPdVgt 0)and negative on the right side of MPP (dPdVlt 0) [5]

31 Fixed-step INC Method -e INC algorithm is used todetect the condition of MPP via the conductance (dIdV)behavior of the PV system -e INC-MPPT can be executedthrough the following sequence [20]

(1) -e voltage and current of the PV module are sensedby the MPPT controller

(2) If (dIdV lt minus IV) is satisfied the duty cycle of theconverter needs to be decreased and vice versa

(3) No change in the duty cycle occurs if I + V(dIdv)

0 is satisfied

-e duty cycle (PV reference voltage (Vref )) increasing ordecreasing occurs with fixed step

32 Variable-Step INC Method -e INC variable step sizealgorithm proposed by Motahhir et al [5] can improve theMPPT controllerrsquos tracking effectiveness -e algorithm

Input voltage = 12V

PWM generatorDuty cycle 0-1

C_in C_out

f (x) = 0

D2D1

Output voltageV_O

Output current

Current sensor

Voltage sensor

Resistive load

I_OR_L

+ndash

+

ndash

ndash

ndash

+

+ ndash

ndashndash

ndash

ndash

+

+

+

++

D P3D_C

V_in1

1

I

Vgt

A

2

2

PS

Figure 4 BuckndashBoost Simscape model

BuckndashBoost response with different duty andinput = 65v and RL = 100ohm

D = 01D = 02D = 03D = 04

D = 07D = 08

D = 05D = 06

0

50

100

150

200

250

V-o

ut (V

)

07 0803 04 05 0601 020Time (sec)

Figure 5 BuckndashBoost output voltage at different duty cycles

Table 2 BuckndashBoost design parameters

Parameter value ValueLoad resistance 45ΩFilter inductance 1mHOutput filter capacitance 4700 μFInput filter capacitance 47 μFSwitching frequency 25000Hz

4 Complexity

sequences are mostly comparable to the standard in-crements the only distinction is the calculation of the stepsize Step Nlowast abs(dPdV) is used in the variable step sizealgorithm to change the duty cycle step size where N is thescaling factor

33 Fractional Order INC Method (FO-INC) Many com-putational requests for fractional order derivatives accordingto the definition have been suggested by RiemannndashLiouvilleand GrunwaldndashLetnikov [9] -e general form of fractionalorder differentiator can be expressed by Kamal and Ibrahim[21] supposed that fm(t) tm and m 1 2 3 isdemonstrated at

Dtαt

m asympΓ(m + 1)

Γ((m + 1) minus α)t(mminus α)

(5)

where Γ(middot) represents Eularrsquos gamma function and α is theorder number of derivative when its value is 0lt αlt 1representing physical phenomenon of fractional order [9]-e FO-INC MPPT main criteria can be expressed byequations (7) and (8)

dαI(V)

dVα limΔV⟶0

I(V) minus α(V minus ΔV)

ΔVα (6)

dαI

dVα asympI minus αI0

V minus V0( 1113857α (7)

dα

dVαminus I0

V01113888 1113889

minus 1V

1113874 1113875Γ(2)

Γ(2 minus α)1113888 1113889 I0( 1113857

1minus αminus I0Γ(0)

Γ(minus α)V

1minus α0

(8)

-e control procedure of the FO-INC algorithm can beexpressed by the flowchart depicted in Figure 6 -e pro-cedure starts with measuring the PVrsquos voltage and current todetermine the MPPT action according to the followingconditions

Condition 1 If (ΔVα ne 0amp(dαIdVα) (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔI 0) keep the current dutycycle fix the duty cycleCondition 2 If (ΔVα ne 0amp(dαIdVα)gt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIgt 0) decrease the dutycycle of the BuckndashBoost converter (increase Vref as inequation (9))Condition 3 If (ΔVα ne 0amp(dαIdVα)lt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIlt 0) increase the duty cycleof the BuckndashBoost converter (decrease Vref as inequation (9))Condition 4 Calculate Po Vo times Io and P V times I IfPgtPo⟶ terminate otherwise update the voltageVo V current Io I and power Po P

-e duty cycle of the BuckndashBoost converter can becalculated based on the output of the FO-INC controllerVref as in

VL D

1 minus Dtimes VPV then

D VL

V0 plusmn ΔVα( 1113857 + VL

(9)

where VL is the resistive load voltage VPV Vref and D isthe duty cycle

Both fixed- and variable-step FO-INC MPPT have beenimplemented to improve the performance of the MPPtracking of the nonlinear PV system with BuckndashBoostconverter and resistive load In case of fixed step the ef-fective parameter of MPPT performance is alpha α Forvariable step both alpha (α) and step size S are affecting theMPPT performance as shown in Figure 6

4 Metaheuristic Optimization Algorithms

Genetic algorithms Particle Swarm Optimization and AntColony Optimization are among the most frequent algo-rithms in this field However these algorithms can solvemanyreal and difficult problems As one of the recent algorithmsthe AntLion Optimizer Optimizer will be introduced alongwith its basic working principle updated criteria and pseudoalgorithms According to Pradhan et al [20] the searchingtechniques of different optimizers are as follows

(1) Initialize solution randomly(2) Specify the search direction(3) Specify the update criteria(4) Specify the stopping criteria

41 Particle Swarm Optimization (PSO) -e inspiration ofthe particle swarm algorithm is to simulate the navigation andforaging of swarm of birds or school of fishes PSO was de-veloped by James Kennedy and Russel Eberhart in 1995 whilestudying the social behaviors of animals working in swarms[22] -e PSO is seeking high-quality optimization by refiningiteratively a candidate solution -e pseudo code of the PSOalgorithm is illustrated in detail with the steps inAlgorithm1InAlgorithm 1 N is the number of particles C1 and C2 are theacceleration coefficients andWmin andWmax are the ranges ofweight of particles PSO uses fewer resources than the otheroptimization techniques Usually it does not require theproblem to be differentiable as the gradient of the problem isnot taken into consideration As a result there might bechances that PSO does not converge to optimal solution

42 Ant Colony Optimization (ACO) Ant Colony Optimi-zation (ACO) introduces an artificial algorithm motivatingactual ant colonies that solve discrete optimization problemIt was first presented by Marco Dorigo in 1992 as a majoraspect of his PhD thesis and called it the ant system [12]While further improvements were carried out to ant colonyby Gambardella Dorigo in 1997 [23] Pseudo code for antcolony optimization is implemented with the steps asAlgorithm 2

Complexity 5

In Algorithm 2 τij(t) represents the intensity of trailon connection (i j) at time t L(ant) is the cost functionresult at each ant and λ is pheromone decay coefficientbetween time (t and t + 1) (ie 0lt λlt 1) Evaporationoccurs in real trails but it is too slow to play an importantrole For continuous improvements it allows the searchroutine to forget errors and poor quality solution in favorof better ones

43 AntLion Optimizer Optimization (ALO) -e primarymotive of ALO is the running behavior of larvae of antlions

ALO is suggested based on the Emary and Zawbaa [24]mathematical model -e ALO algorithm simulates theinteraction between the traps-e ants must move across thesearch area in order to model such interactions and theantlions are permitted to chase and fit the traps Given thatants move randomly to find food in actual life a randomwalk algorithm is selected as shown in Heidari et al [25] tomodel the antsrsquo motion

In Algorithm 3 I is a ratio ct is the minimum of allvariables at tth iteration and dt indicates the vector in-cluding the maximum of all variables at tth iterationI 10w(Tt) where t is the current iteration T is the

Measure the PV voltage and Current I amp V

Calculate the fractional derivative I and VdαI = I ndash αIo = ΔI

dαV = (V ndash Vo)α = ΔVα

Start

Calculate the output Power of PV (P = I times V)

End

Yes

Yes

Yes

Yes

Yes

No

No

No No

No

ΔVα = 0

ΔI = 0

ΔI = 0

Equation (7) = equation (8)

Equation (7) = equation (8)

Vref = Vo + ΔVα Vref = Vo + ΔVαVref = Vo ndash ΔVα Vref = Vo ndash ΔVα

Vo = VIo = IPo = P

P gt Po

Figure 6 Fractional order INC MPPT flowchart

6 Complexity

maximum number of iterations and w is a constant definedbased on the current iteration X(t) is antrsquo movementcumsum calculates the cumulative sum n is the maximumnumber of iteration t shows the step of random walk andr(t) is a stochastic function Also ai is the minimum ofrandom walk and bi is the maximum of random walk inith variable Rt

A is the random walk around the antlionselected by the roulette wheel at tth iteration and Rt

E is therandom walk around the elite at tth iteration -e pseudocode of ALO for MPPT developed as mentioned inAlgorithm 3

5 Modeling and Simulation Results

-e proposed system has been modeled and simulatedusing MATLAB and Simscape software environments inorder to study the system behavior and MPPTperformance

with different metaheuristic optimization algorithms -eblock diagram describing the total PV system with MPPTand optimizer is shown in Figure 7 where the MPPT al-gorithm is changed between conventional INC methodsand FO-INC (fixed and variable step) -e MPPT is op-timized by one of the metaheuristic techniques (PSO ACOand ALO)

-e operation sequence of PV with MPPT and opti-mization process is a closed loop as shown in Figure 8 and itstarts with measuring the irradiance (G) and temperature(T) applied to the PV system to get the reference maximumpower point from PV characteristics curves (PMPP) A closedloop of PV withMPPTand BuckndashBoost converter is runningin Simscape environment for two seconds to measure the PVoutput power -e mean squared-error (MSE) betweenthe MPP (PMPP) and output power of the PV system (PPV) isthe cost function of the metaheuristic optimizer calculated

Result MPPT parameter to achieve MPPInitialize the PSO parameters (N C1 C2 Wmin Wmax Vmax)while the termination criteria not achieved (MPP) doFor (each Particle i)

Simulate and calculate the MPP and the cost function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update the velocity (V) Vt+1

i Vti + C1r1(Pi minus Xt

i ) + C2r2(Pg minus Xti )

where Vti is inertia C1r1(Pi minus Xt

i ) is cognitive component and C2r2(Pg minus Xti ) is social component

(b) Update the position of particles Xt+1i Xt+1

i + Vti

end

ALGORITHM 1 PSO-MPPT

Result MPPT parameter to achieve MPPInitialize the ACO parameterswhile the termination criteria not achieved (MPP) doFor (each ant i)Simulate and calculate the MPP and the cost Functionif CostFunction(i)ltObjective(MPP) then

-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update pheromone for each ant τij(t + 1) Δτij(t) 1113936

antsant1Δτantij (t)

(i) Calculate the solution Δτantij (t) (1Lbest)⟶ if ant(t) travels on edge(i j)

0⟶ otherwise1113896

(b) Apply evaporation and globally update the ants position according to the optimum solutions calculated earlierend

ALGORITHM 2 ACO-MPPT

Complexity 7

Result MPPT parameter to achieve MPPInitialize the first population of ants and antlions randomlywhile the termination criteria not achieved (MPP) doFor (each antlion (i))Select an antlion using Roulette wheel algorithm [16]Simulate and calculate the MPP and the cost Function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e elite (i)-e -e Best Solution (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e elite (i)-e Best Solution (i minus 1)

end(a) Update c and d using equations Ct (CtI) and dt (dtI)

(b) Create a random walk and normalize it using X(t) [0 cumsum(2r(tn) minus 1)] where n 1 2 3 n andXt

i ((Xti minus ai) times (di minus ct

i )(dti minus ai)) + ci

(c) Update the position of antlions using antti (RtA + Rt

E)2(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

end

ALGORITHM 3 ALO-MPPT

Cost function mean square error MSE (Pmpp Ppv)

Metaheuristic optimization algorithm (PSO ACO and ALO)

Initialize the model and measure G and T

From PV model get the value of MPP fromP-V characteristics curve Figure 3

Pmpp = MPP (T G)

Measure PV current I and voltage V and calucalte Ppv = I lowast V

MPPT algorithm (fixed INC variable INCfixed FO-INC and variable FO-INC)

DC-DC converter and the load

MPPT optimal parameters

Pmpp

Ppv

Control signal duty cycle

MPPT number and range of parameters

Figure 8 -e proposed system implementation flowchart

MPPT

Temperature degC Irradiance Wm2

+

ndash I_PV

V_PV

PWM

+

ndashPV panel

DC-DC converter DC load

Optimizer

Figure 7 -e proposed PV system with metaheuristic optimization

8 Complexity

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

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Applied MathematicsJournal of

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Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom

where VPV and IPV are the PV terminal voltage and currentrespectively Rs and Rsh are the series and shunt resistancerespectively η is the ideality factor the Boltzmannrsquos constantis k q is the electron charge Tk is the temperature degree inKelvin IG is photo-generated current and the diode satu-ration current is Io -e PV panel parameters are shown inTable 1

-e I-V and P-V nonlinear characteristic curves of thePV array simulated using MATLAB at different climaticconditions (temperature and irradiance) are shown inFigure 3

22 DC-DC Converter Simulink and Simscape tools havebeen selected as platforms for modeling implementa-tion and testing the BuckndashBoost converter -e statespace modeling is primarily represented by equation (3)where A B C and D are the system matrices x is the statevariable vector xprime is the state variable derivative vectorwith respect to time u is the input and y is the output[14]

xprime Ax + Bu

y Cx + Du(3)

Figure 4 shows the BuckndashBoost model using Simscapewhich is simulated at different duty cycles and fixed load

according to the state space model represented in equation(4) where x1 IL x2 VCout and d duty cycle -e simu-lation results at different duty cycles are shown in Figure 5

MPPT

VPV

[IPV_T]

Inputs of the cell from MATLAB

BuckndashBoost converter

Load voltage

Load current

RL value from MATLAB

To workspace of Matlab

V_PV

IRR

Temp

A

ndashTndash

ndashTndash

VPV

IPV

ndashTndash

VPV1

IPV1

VL

IL

ndashTndash

ndashTndash

ndashTndash

ndashTndash

ndashTndash

ndashTndashX

ndashTndash

ndashTndash

V+

ndash

+

++

+

f (x) = 0

I_PV

D P [D]

[D]

gt

gt

A

V

PWM

In+

Inndash

Out+

Outndash

PS+

ndash

+

V

[IL]

[VL]

RL

Data

ndash

ndash

A+

Cell 1 IPV

Cell 1 IPV

I_PV

I_PV1

V_PV1

Resistive load

RL

Wm cell1

T cell1

Cell 01

PV cell 18V 72 A

P_Cell

Scope for results display

ndashgt

Figure 1 Complete PV system model using MATLAB and Simscape

IG

Rs

ID

Ipv

Vpv

Ish

Rsh

+

ndash

Figure 2 PV cell equivalent electric circuit model

Table 1 PV panel parameters

Parameter value ValueMax power Pmax 73572WOpen circuit voltage Voc 659VShort circuit current Ish 1521 ATemperature coefficient of VOC ndash123times10eminus 1 VCTemperature coefficient of Ish 318times10eminus 3 AC

PV at fixed T = 25degC

200 Wm2

400 Wm2

600 Wm2

800 Wm2

1000 Wm2

PV at fixed G = 1000 Wm2

25degC40degC

55degC70degC

0

5

10

15

PV cu

rren

t

7020 30 40 50 60100PV voltage

0

200

400

600

800

PV p

ower

0

5

10

15

PV cu

rren

t

10 20 30 40 50 600 70PV voltage

0

200

400

600

800

PV p

ower

Figure 3 P-V and I-V characteristic curves at different climaticconditions

Complexity 3

x1prime

x2prime

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

01 minus d

L

minus (1 minus d)

C

minus 1RC

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

x1

x2

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦ +

d

L

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦u1

y1

y2

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

1 0

0 1

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

IL

VCout

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦ +

0

0

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦u1

(4)

-e proposed BuckndashBoost has been designed and sim-ulated using the parameters illustrated in Table 2

3 Design and Implementation of MPPT

-e primary feature of the PV system is the total energymonitoring in which the power of the PV modules can beextracted in a certain climatic situation As shown in theliterature the most commonly usedMPPTalgorithm is INC-e INC algorithm is based on the reality that the PV outputenergy derivative for the output voltage at the MPP is zero(dPdV 0) positive on the left side of MPP (dPdVgt 0)and negative on the right side of MPP (dPdVlt 0) [5]

31 Fixed-step INC Method -e INC algorithm is used todetect the condition of MPP via the conductance (dIdV)behavior of the PV system -e INC-MPPT can be executedthrough the following sequence [20]

(1) -e voltage and current of the PV module are sensedby the MPPT controller

(2) If (dIdV lt minus IV) is satisfied the duty cycle of theconverter needs to be decreased and vice versa

(3) No change in the duty cycle occurs if I + V(dIdv)

0 is satisfied

-e duty cycle (PV reference voltage (Vref )) increasing ordecreasing occurs with fixed step

32 Variable-Step INC Method -e INC variable step sizealgorithm proposed by Motahhir et al [5] can improve theMPPT controllerrsquos tracking effectiveness -e algorithm

Input voltage = 12V

PWM generatorDuty cycle 0-1

C_in C_out

f (x) = 0

D2D1

Output voltageV_O

Output current

Current sensor

Voltage sensor

Resistive load

I_OR_L

+ndash

+

ndash

ndash

ndash

+

+ ndash

ndashndash

ndash

ndash

+

+

+

++

D P3D_C

V_in1

1

I

Vgt

A

2

2

PS

Figure 4 BuckndashBoost Simscape model

BuckndashBoost response with different duty andinput = 65v and RL = 100ohm

D = 01D = 02D = 03D = 04

D = 07D = 08

D = 05D = 06

0

50

100

150

200

250

V-o

ut (V

)

07 0803 04 05 0601 020Time (sec)

Figure 5 BuckndashBoost output voltage at different duty cycles

Table 2 BuckndashBoost design parameters

Parameter value ValueLoad resistance 45ΩFilter inductance 1mHOutput filter capacitance 4700 μFInput filter capacitance 47 μFSwitching frequency 25000Hz

4 Complexity

sequences are mostly comparable to the standard in-crements the only distinction is the calculation of the stepsize Step Nlowast abs(dPdV) is used in the variable step sizealgorithm to change the duty cycle step size where N is thescaling factor

33 Fractional Order INC Method (FO-INC) Many com-putational requests for fractional order derivatives accordingto the definition have been suggested by RiemannndashLiouvilleand GrunwaldndashLetnikov [9] -e general form of fractionalorder differentiator can be expressed by Kamal and Ibrahim[21] supposed that fm(t) tm and m 1 2 3 isdemonstrated at

Dtαt

m asympΓ(m + 1)

Γ((m + 1) minus α)t(mminus α)

(5)

where Γ(middot) represents Eularrsquos gamma function and α is theorder number of derivative when its value is 0lt αlt 1representing physical phenomenon of fractional order [9]-e FO-INC MPPT main criteria can be expressed byequations (7) and (8)

dαI(V)

dVα limΔV⟶0

I(V) minus α(V minus ΔV)

ΔVα (6)

dαI

dVα asympI minus αI0

V minus V0( 1113857α (7)

dα

dVαminus I0

V01113888 1113889

minus 1V

1113874 1113875Γ(2)

Γ(2 minus α)1113888 1113889 I0( 1113857

1minus αminus I0Γ(0)

Γ(minus α)V

1minus α0

(8)

-e control procedure of the FO-INC algorithm can beexpressed by the flowchart depicted in Figure 6 -e pro-cedure starts with measuring the PVrsquos voltage and current todetermine the MPPT action according to the followingconditions

Condition 1 If (ΔVα ne 0amp(dαIdVα) (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔI 0) keep the current dutycycle fix the duty cycleCondition 2 If (ΔVα ne 0amp(dαIdVα)gt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIgt 0) decrease the dutycycle of the BuckndashBoost converter (increase Vref as inequation (9))Condition 3 If (ΔVα ne 0amp(dαIdVα)lt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIlt 0) increase the duty cycleof the BuckndashBoost converter (decrease Vref as inequation (9))Condition 4 Calculate Po Vo times Io and P V times I IfPgtPo⟶ terminate otherwise update the voltageVo V current Io I and power Po P

-e duty cycle of the BuckndashBoost converter can becalculated based on the output of the FO-INC controllerVref as in

VL D

1 minus Dtimes VPV then

D VL

V0 plusmn ΔVα( 1113857 + VL

(9)

where VL is the resistive load voltage VPV Vref and D isthe duty cycle

Both fixed- and variable-step FO-INC MPPT have beenimplemented to improve the performance of the MPPtracking of the nonlinear PV system with BuckndashBoostconverter and resistive load In case of fixed step the ef-fective parameter of MPPT performance is alpha α Forvariable step both alpha (α) and step size S are affecting theMPPT performance as shown in Figure 6

4 Metaheuristic Optimization Algorithms

Genetic algorithms Particle Swarm Optimization and AntColony Optimization are among the most frequent algo-rithms in this field However these algorithms can solvemanyreal and difficult problems As one of the recent algorithmsthe AntLion Optimizer Optimizer will be introduced alongwith its basic working principle updated criteria and pseudoalgorithms According to Pradhan et al [20] the searchingtechniques of different optimizers are as follows

(1) Initialize solution randomly(2) Specify the search direction(3) Specify the update criteria(4) Specify the stopping criteria

41 Particle Swarm Optimization (PSO) -e inspiration ofthe particle swarm algorithm is to simulate the navigation andforaging of swarm of birds or school of fishes PSO was de-veloped by James Kennedy and Russel Eberhart in 1995 whilestudying the social behaviors of animals working in swarms[22] -e PSO is seeking high-quality optimization by refiningiteratively a candidate solution -e pseudo code of the PSOalgorithm is illustrated in detail with the steps inAlgorithm1InAlgorithm 1 N is the number of particles C1 and C2 are theacceleration coefficients andWmin andWmax are the ranges ofweight of particles PSO uses fewer resources than the otheroptimization techniques Usually it does not require theproblem to be differentiable as the gradient of the problem isnot taken into consideration As a result there might bechances that PSO does not converge to optimal solution

42 Ant Colony Optimization (ACO) Ant Colony Optimi-zation (ACO) introduces an artificial algorithm motivatingactual ant colonies that solve discrete optimization problemIt was first presented by Marco Dorigo in 1992 as a majoraspect of his PhD thesis and called it the ant system [12]While further improvements were carried out to ant colonyby Gambardella Dorigo in 1997 [23] Pseudo code for antcolony optimization is implemented with the steps asAlgorithm 2

Complexity 5

In Algorithm 2 τij(t) represents the intensity of trailon connection (i j) at time t L(ant) is the cost functionresult at each ant and λ is pheromone decay coefficientbetween time (t and t + 1) (ie 0lt λlt 1) Evaporationoccurs in real trails but it is too slow to play an importantrole For continuous improvements it allows the searchroutine to forget errors and poor quality solution in favorof better ones

43 AntLion Optimizer Optimization (ALO) -e primarymotive of ALO is the running behavior of larvae of antlions

ALO is suggested based on the Emary and Zawbaa [24]mathematical model -e ALO algorithm simulates theinteraction between the traps-e ants must move across thesearch area in order to model such interactions and theantlions are permitted to chase and fit the traps Given thatants move randomly to find food in actual life a randomwalk algorithm is selected as shown in Heidari et al [25] tomodel the antsrsquo motion

In Algorithm 3 I is a ratio ct is the minimum of allvariables at tth iteration and dt indicates the vector in-cluding the maximum of all variables at tth iterationI 10w(Tt) where t is the current iteration T is the

Measure the PV voltage and Current I amp V

Calculate the fractional derivative I and VdαI = I ndash αIo = ΔI

dαV = (V ndash Vo)α = ΔVα

Start

Calculate the output Power of PV (P = I times V)

End

Yes

Yes

Yes

Yes

Yes

No

No

No No

No

ΔVα = 0

ΔI = 0

ΔI = 0

Equation (7) = equation (8)

Equation (7) = equation (8)

Vref = Vo + ΔVα Vref = Vo + ΔVαVref = Vo ndash ΔVα Vref = Vo ndash ΔVα

Vo = VIo = IPo = P

P gt Po

Figure 6 Fractional order INC MPPT flowchart

6 Complexity

maximum number of iterations and w is a constant definedbased on the current iteration X(t) is antrsquo movementcumsum calculates the cumulative sum n is the maximumnumber of iteration t shows the step of random walk andr(t) is a stochastic function Also ai is the minimum ofrandom walk and bi is the maximum of random walk inith variable Rt

A is the random walk around the antlionselected by the roulette wheel at tth iteration and Rt

E is therandom walk around the elite at tth iteration -e pseudocode of ALO for MPPT developed as mentioned inAlgorithm 3

5 Modeling and Simulation Results

-e proposed system has been modeled and simulatedusing MATLAB and Simscape software environments inorder to study the system behavior and MPPTperformance

with different metaheuristic optimization algorithms -eblock diagram describing the total PV system with MPPTand optimizer is shown in Figure 7 where the MPPT al-gorithm is changed between conventional INC methodsand FO-INC (fixed and variable step) -e MPPT is op-timized by one of the metaheuristic techniques (PSO ACOand ALO)

-e operation sequence of PV with MPPT and opti-mization process is a closed loop as shown in Figure 8 and itstarts with measuring the irradiance (G) and temperature(T) applied to the PV system to get the reference maximumpower point from PV characteristics curves (PMPP) A closedloop of PV withMPPTand BuckndashBoost converter is runningin Simscape environment for two seconds to measure the PVoutput power -e mean squared-error (MSE) betweenthe MPP (PMPP) and output power of the PV system (PPV) isthe cost function of the metaheuristic optimizer calculated

Result MPPT parameter to achieve MPPInitialize the PSO parameters (N C1 C2 Wmin Wmax Vmax)while the termination criteria not achieved (MPP) doFor (each Particle i)

Simulate and calculate the MPP and the cost function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update the velocity (V) Vt+1

i Vti + C1r1(Pi minus Xt

i ) + C2r2(Pg minus Xti )

where Vti is inertia C1r1(Pi minus Xt

i ) is cognitive component and C2r2(Pg minus Xti ) is social component

(b) Update the position of particles Xt+1i Xt+1

i + Vti

end

ALGORITHM 1 PSO-MPPT

Result MPPT parameter to achieve MPPInitialize the ACO parameterswhile the termination criteria not achieved (MPP) doFor (each ant i)Simulate and calculate the MPP and the cost Functionif CostFunction(i)ltObjective(MPP) then

-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update pheromone for each ant τij(t + 1) Δτij(t) 1113936

antsant1Δτantij (t)

(i) Calculate the solution Δτantij (t) (1Lbest)⟶ if ant(t) travels on edge(i j)

0⟶ otherwise1113896

(b) Apply evaporation and globally update the ants position according to the optimum solutions calculated earlierend

ALGORITHM 2 ACO-MPPT

Complexity 7

Result MPPT parameter to achieve MPPInitialize the first population of ants and antlions randomlywhile the termination criteria not achieved (MPP) doFor (each antlion (i))Select an antlion using Roulette wheel algorithm [16]Simulate and calculate the MPP and the cost Function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e elite (i)-e -e Best Solution (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e elite (i)-e Best Solution (i minus 1)

end(a) Update c and d using equations Ct (CtI) and dt (dtI)

(b) Create a random walk and normalize it using X(t) [0 cumsum(2r(tn) minus 1)] where n 1 2 3 n andXt

i ((Xti minus ai) times (di minus ct

i )(dti minus ai)) + ci

(c) Update the position of antlions using antti (RtA + Rt

E)2(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

end

ALGORITHM 3 ALO-MPPT

Cost function mean square error MSE (Pmpp Ppv)

Metaheuristic optimization algorithm (PSO ACO and ALO)

Initialize the model and measure G and T

From PV model get the value of MPP fromP-V characteristics curve Figure 3

Pmpp = MPP (T G)

Measure PV current I and voltage V and calucalte Ppv = I lowast V

MPPT algorithm (fixed INC variable INCfixed FO-INC and variable FO-INC)

DC-DC converter and the load

MPPT optimal parameters

Pmpp

Ppv

Control signal duty cycle

MPPT number and range of parameters

Figure 8 -e proposed system implementation flowchart

MPPT

Temperature degC Irradiance Wm2

+

ndash I_PV

V_PV

PWM

+

ndashPV panel

DC-DC converter DC load

Optimizer

Figure 7 -e proposed PV system with metaheuristic optimization

8 Complexity

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

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x1prime

x2prime

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

01 minus d

L

minus (1 minus d)

C

minus 1RC

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

x1

x2

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦ +

d

L

0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦u1

y1

y2

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

1 0

0 1

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

IL

VCout

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦ +

0

0

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦u1

(4)

-e proposed BuckndashBoost has been designed and sim-ulated using the parameters illustrated in Table 2

3 Design and Implementation of MPPT

-e primary feature of the PV system is the total energymonitoring in which the power of the PV modules can beextracted in a certain climatic situation As shown in theliterature the most commonly usedMPPTalgorithm is INC-e INC algorithm is based on the reality that the PV outputenergy derivative for the output voltage at the MPP is zero(dPdV 0) positive on the left side of MPP (dPdVgt 0)and negative on the right side of MPP (dPdVlt 0) [5]

31 Fixed-step INC Method -e INC algorithm is used todetect the condition of MPP via the conductance (dIdV)behavior of the PV system -e INC-MPPT can be executedthrough the following sequence [20]

(1) -e voltage and current of the PV module are sensedby the MPPT controller

(2) If (dIdV lt minus IV) is satisfied the duty cycle of theconverter needs to be decreased and vice versa

(3) No change in the duty cycle occurs if I + V(dIdv)

0 is satisfied

-e duty cycle (PV reference voltage (Vref )) increasing ordecreasing occurs with fixed step

32 Variable-Step INC Method -e INC variable step sizealgorithm proposed by Motahhir et al [5] can improve theMPPT controllerrsquos tracking effectiveness -e algorithm

Input voltage = 12V

PWM generatorDuty cycle 0-1

C_in C_out

f (x) = 0

D2D1

Output voltageV_O

Output current

Current sensor

Voltage sensor

Resistive load

I_OR_L

+ndash

+

ndash

ndash

ndash

+

+ ndash

ndashndash

ndash

ndash

+

+

+

++

D P3D_C

V_in1

1

I

Vgt

A

2

2

PS

Figure 4 BuckndashBoost Simscape model

BuckndashBoost response with different duty andinput = 65v and RL = 100ohm

D = 01D = 02D = 03D = 04

D = 07D = 08

D = 05D = 06

0

50

100

150

200

250

V-o

ut (V

)

07 0803 04 05 0601 020Time (sec)

Figure 5 BuckndashBoost output voltage at different duty cycles

Table 2 BuckndashBoost design parameters

Parameter value ValueLoad resistance 45ΩFilter inductance 1mHOutput filter capacitance 4700 μFInput filter capacitance 47 μFSwitching frequency 25000Hz

4 Complexity

sequences are mostly comparable to the standard in-crements the only distinction is the calculation of the stepsize Step Nlowast abs(dPdV) is used in the variable step sizealgorithm to change the duty cycle step size where N is thescaling factor

33 Fractional Order INC Method (FO-INC) Many com-putational requests for fractional order derivatives accordingto the definition have been suggested by RiemannndashLiouvilleand GrunwaldndashLetnikov [9] -e general form of fractionalorder differentiator can be expressed by Kamal and Ibrahim[21] supposed that fm(t) tm and m 1 2 3 isdemonstrated at

Dtαt

m asympΓ(m + 1)

Γ((m + 1) minus α)t(mminus α)

(5)

where Γ(middot) represents Eularrsquos gamma function and α is theorder number of derivative when its value is 0lt αlt 1representing physical phenomenon of fractional order [9]-e FO-INC MPPT main criteria can be expressed byequations (7) and (8)

dαI(V)

dVα limΔV⟶0

I(V) minus α(V minus ΔV)

ΔVα (6)

dαI

dVα asympI minus αI0

V minus V0( 1113857α (7)

dα

dVαminus I0

V01113888 1113889

minus 1V

1113874 1113875Γ(2)

Γ(2 minus α)1113888 1113889 I0( 1113857

1minus αminus I0Γ(0)

Γ(minus α)V

1minus α0

(8)

-e control procedure of the FO-INC algorithm can beexpressed by the flowchart depicted in Figure 6 -e pro-cedure starts with measuring the PVrsquos voltage and current todetermine the MPPT action according to the followingconditions

Condition 1 If (ΔVα ne 0amp(dαIdVα) (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔI 0) keep the current dutycycle fix the duty cycleCondition 2 If (ΔVα ne 0amp(dαIdVα)gt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIgt 0) decrease the dutycycle of the BuckndashBoost converter (increase Vref as inequation (9))Condition 3 If (ΔVα ne 0amp(dαIdVα)lt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIlt 0) increase the duty cycleof the BuckndashBoost converter (decrease Vref as inequation (9))Condition 4 Calculate Po Vo times Io and P V times I IfPgtPo⟶ terminate otherwise update the voltageVo V current Io I and power Po P

-e duty cycle of the BuckndashBoost converter can becalculated based on the output of the FO-INC controllerVref as in

VL D

1 minus Dtimes VPV then

D VL

V0 plusmn ΔVα( 1113857 + VL

(9)

where VL is the resistive load voltage VPV Vref and D isthe duty cycle

Both fixed- and variable-step FO-INC MPPT have beenimplemented to improve the performance of the MPPtracking of the nonlinear PV system with BuckndashBoostconverter and resistive load In case of fixed step the ef-fective parameter of MPPT performance is alpha α Forvariable step both alpha (α) and step size S are affecting theMPPT performance as shown in Figure 6

4 Metaheuristic Optimization Algorithms

Genetic algorithms Particle Swarm Optimization and AntColony Optimization are among the most frequent algo-rithms in this field However these algorithms can solvemanyreal and difficult problems As one of the recent algorithmsthe AntLion Optimizer Optimizer will be introduced alongwith its basic working principle updated criteria and pseudoalgorithms According to Pradhan et al [20] the searchingtechniques of different optimizers are as follows

(1) Initialize solution randomly(2) Specify the search direction(3) Specify the update criteria(4) Specify the stopping criteria

41 Particle Swarm Optimization (PSO) -e inspiration ofthe particle swarm algorithm is to simulate the navigation andforaging of swarm of birds or school of fishes PSO was de-veloped by James Kennedy and Russel Eberhart in 1995 whilestudying the social behaviors of animals working in swarms[22] -e PSO is seeking high-quality optimization by refiningiteratively a candidate solution -e pseudo code of the PSOalgorithm is illustrated in detail with the steps inAlgorithm1InAlgorithm 1 N is the number of particles C1 and C2 are theacceleration coefficients andWmin andWmax are the ranges ofweight of particles PSO uses fewer resources than the otheroptimization techniques Usually it does not require theproblem to be differentiable as the gradient of the problem isnot taken into consideration As a result there might bechances that PSO does not converge to optimal solution

42 Ant Colony Optimization (ACO) Ant Colony Optimi-zation (ACO) introduces an artificial algorithm motivatingactual ant colonies that solve discrete optimization problemIt was first presented by Marco Dorigo in 1992 as a majoraspect of his PhD thesis and called it the ant system [12]While further improvements were carried out to ant colonyby Gambardella Dorigo in 1997 [23] Pseudo code for antcolony optimization is implemented with the steps asAlgorithm 2

Complexity 5

In Algorithm 2 τij(t) represents the intensity of trailon connection (i j) at time t L(ant) is the cost functionresult at each ant and λ is pheromone decay coefficientbetween time (t and t + 1) (ie 0lt λlt 1) Evaporationoccurs in real trails but it is too slow to play an importantrole For continuous improvements it allows the searchroutine to forget errors and poor quality solution in favorof better ones

43 AntLion Optimizer Optimization (ALO) -e primarymotive of ALO is the running behavior of larvae of antlions

ALO is suggested based on the Emary and Zawbaa [24]mathematical model -e ALO algorithm simulates theinteraction between the traps-e ants must move across thesearch area in order to model such interactions and theantlions are permitted to chase and fit the traps Given thatants move randomly to find food in actual life a randomwalk algorithm is selected as shown in Heidari et al [25] tomodel the antsrsquo motion

In Algorithm 3 I is a ratio ct is the minimum of allvariables at tth iteration and dt indicates the vector in-cluding the maximum of all variables at tth iterationI 10w(Tt) where t is the current iteration T is the

Measure the PV voltage and Current I amp V

Calculate the fractional derivative I and VdαI = I ndash αIo = ΔI

dαV = (V ndash Vo)α = ΔVα

Start

Calculate the output Power of PV (P = I times V)

End

Yes

Yes

Yes

Yes

Yes

No

No

No No

No

ΔVα = 0

ΔI = 0

ΔI = 0

Equation (7) = equation (8)

Equation (7) = equation (8)

Vref = Vo + ΔVα Vref = Vo + ΔVαVref = Vo ndash ΔVα Vref = Vo ndash ΔVα

Vo = VIo = IPo = P

P gt Po

Figure 6 Fractional order INC MPPT flowchart

6 Complexity

maximum number of iterations and w is a constant definedbased on the current iteration X(t) is antrsquo movementcumsum calculates the cumulative sum n is the maximumnumber of iteration t shows the step of random walk andr(t) is a stochastic function Also ai is the minimum ofrandom walk and bi is the maximum of random walk inith variable Rt

A is the random walk around the antlionselected by the roulette wheel at tth iteration and Rt

E is therandom walk around the elite at tth iteration -e pseudocode of ALO for MPPT developed as mentioned inAlgorithm 3

5 Modeling and Simulation Results

-e proposed system has been modeled and simulatedusing MATLAB and Simscape software environments inorder to study the system behavior and MPPTperformance

with different metaheuristic optimization algorithms -eblock diagram describing the total PV system with MPPTand optimizer is shown in Figure 7 where the MPPT al-gorithm is changed between conventional INC methodsand FO-INC (fixed and variable step) -e MPPT is op-timized by one of the metaheuristic techniques (PSO ACOand ALO)

-e operation sequence of PV with MPPT and opti-mization process is a closed loop as shown in Figure 8 and itstarts with measuring the irradiance (G) and temperature(T) applied to the PV system to get the reference maximumpower point from PV characteristics curves (PMPP) A closedloop of PV withMPPTand BuckndashBoost converter is runningin Simscape environment for two seconds to measure the PVoutput power -e mean squared-error (MSE) betweenthe MPP (PMPP) and output power of the PV system (PPV) isthe cost function of the metaheuristic optimizer calculated

Result MPPT parameter to achieve MPPInitialize the PSO parameters (N C1 C2 Wmin Wmax Vmax)while the termination criteria not achieved (MPP) doFor (each Particle i)

Simulate and calculate the MPP and the cost function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update the velocity (V) Vt+1

i Vti + C1r1(Pi minus Xt

i ) + C2r2(Pg minus Xti )

where Vti is inertia C1r1(Pi minus Xt

i ) is cognitive component and C2r2(Pg minus Xti ) is social component

(b) Update the position of particles Xt+1i Xt+1

i + Vti

end

ALGORITHM 1 PSO-MPPT

Result MPPT parameter to achieve MPPInitialize the ACO parameterswhile the termination criteria not achieved (MPP) doFor (each ant i)Simulate and calculate the MPP and the cost Functionif CostFunction(i)ltObjective(MPP) then

-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update pheromone for each ant τij(t + 1) Δτij(t) 1113936

antsant1Δτantij (t)

(i) Calculate the solution Δτantij (t) (1Lbest)⟶ if ant(t) travels on edge(i j)

0⟶ otherwise1113896

(b) Apply evaporation and globally update the ants position according to the optimum solutions calculated earlierend

ALGORITHM 2 ACO-MPPT

Complexity 7

Result MPPT parameter to achieve MPPInitialize the first population of ants and antlions randomlywhile the termination criteria not achieved (MPP) doFor (each antlion (i))Select an antlion using Roulette wheel algorithm [16]Simulate and calculate the MPP and the cost Function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e elite (i)-e -e Best Solution (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e elite (i)-e Best Solution (i minus 1)

end(a) Update c and d using equations Ct (CtI) and dt (dtI)

(b) Create a random walk and normalize it using X(t) [0 cumsum(2r(tn) minus 1)] where n 1 2 3 n andXt

i ((Xti minus ai) times (di minus ct

i )(dti minus ai)) + ci

(c) Update the position of antlions using antti (RtA + Rt

E)2(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

end

ALGORITHM 3 ALO-MPPT

Cost function mean square error MSE (Pmpp Ppv)

Metaheuristic optimization algorithm (PSO ACO and ALO)

Initialize the model and measure G and T

From PV model get the value of MPP fromP-V characteristics curve Figure 3

Pmpp = MPP (T G)

Measure PV current I and voltage V and calucalte Ppv = I lowast V

MPPT algorithm (fixed INC variable INCfixed FO-INC and variable FO-INC)

DC-DC converter and the load

MPPT optimal parameters

Pmpp

Ppv

Control signal duty cycle

MPPT number and range of parameters

Figure 8 -e proposed system implementation flowchart

MPPT

Temperature degC Irradiance Wm2

+

ndash I_PV

V_PV

PWM

+

ndashPV panel

DC-DC converter DC load

Optimizer

Figure 7 -e proposed PV system with metaheuristic optimization

8 Complexity

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

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sequences are mostly comparable to the standard in-crements the only distinction is the calculation of the stepsize Step Nlowast abs(dPdV) is used in the variable step sizealgorithm to change the duty cycle step size where N is thescaling factor

33 Fractional Order INC Method (FO-INC) Many com-putational requests for fractional order derivatives accordingto the definition have been suggested by RiemannndashLiouvilleand GrunwaldndashLetnikov [9] -e general form of fractionalorder differentiator can be expressed by Kamal and Ibrahim[21] supposed that fm(t) tm and m 1 2 3 isdemonstrated at

Dtαt

m asympΓ(m + 1)

Γ((m + 1) minus α)t(mminus α)

(5)

where Γ(middot) represents Eularrsquos gamma function and α is theorder number of derivative when its value is 0lt αlt 1representing physical phenomenon of fractional order [9]-e FO-INC MPPT main criteria can be expressed byequations (7) and (8)

dαI(V)

dVα limΔV⟶0

I(V) minus α(V minus ΔV)

ΔVα (6)

dαI

dVα asympI minus αI0

V minus V0( 1113857α (7)

dα

dVαminus I0

V01113888 1113889

minus 1V

1113874 1113875Γ(2)

Γ(2 minus α)1113888 1113889 I0( 1113857

1minus αminus I0Γ(0)

Γ(minus α)V

1minus α0

(8)

-e control procedure of the FO-INC algorithm can beexpressed by the flowchart depicted in Figure 6 -e pro-cedure starts with measuring the PVrsquos voltage and current todetermine the MPPT action according to the followingconditions

Condition 1 If (ΔVα ne 0amp(dαIdVα) (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔI 0) keep the current dutycycle fix the duty cycleCondition 2 If (ΔVα ne 0amp(dαIdVα)gt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIgt 0) decrease the dutycycle of the BuckndashBoost converter (increase Vref as inequation (9))Condition 3 If (ΔVα ne 0amp(dαIdVα)lt (dαdVα)

(minus I0V0)) or (ΔVα 0ampΔIlt 0) increase the duty cycleof the BuckndashBoost converter (decrease Vref as inequation (9))Condition 4 Calculate Po Vo times Io and P V times I IfPgtPo⟶ terminate otherwise update the voltageVo V current Io I and power Po P

-e duty cycle of the BuckndashBoost converter can becalculated based on the output of the FO-INC controllerVref as in

VL D

1 minus Dtimes VPV then

D VL

V0 plusmn ΔVα( 1113857 + VL

(9)

where VL is the resistive load voltage VPV Vref and D isthe duty cycle

Both fixed- and variable-step FO-INC MPPT have beenimplemented to improve the performance of the MPPtracking of the nonlinear PV system with BuckndashBoostconverter and resistive load In case of fixed step the ef-fective parameter of MPPT performance is alpha α Forvariable step both alpha (α) and step size S are affecting theMPPT performance as shown in Figure 6

4 Metaheuristic Optimization Algorithms

Genetic algorithms Particle Swarm Optimization and AntColony Optimization are among the most frequent algo-rithms in this field However these algorithms can solvemanyreal and difficult problems As one of the recent algorithmsthe AntLion Optimizer Optimizer will be introduced alongwith its basic working principle updated criteria and pseudoalgorithms According to Pradhan et al [20] the searchingtechniques of different optimizers are as follows

(1) Initialize solution randomly(2) Specify the search direction(3) Specify the update criteria(4) Specify the stopping criteria

41 Particle Swarm Optimization (PSO) -e inspiration ofthe particle swarm algorithm is to simulate the navigation andforaging of swarm of birds or school of fishes PSO was de-veloped by James Kennedy and Russel Eberhart in 1995 whilestudying the social behaviors of animals working in swarms[22] -e PSO is seeking high-quality optimization by refiningiteratively a candidate solution -e pseudo code of the PSOalgorithm is illustrated in detail with the steps inAlgorithm1InAlgorithm 1 N is the number of particles C1 and C2 are theacceleration coefficients andWmin andWmax are the ranges ofweight of particles PSO uses fewer resources than the otheroptimization techniques Usually it does not require theproblem to be differentiable as the gradient of the problem isnot taken into consideration As a result there might bechances that PSO does not converge to optimal solution

42 Ant Colony Optimization (ACO) Ant Colony Optimi-zation (ACO) introduces an artificial algorithm motivatingactual ant colonies that solve discrete optimization problemIt was first presented by Marco Dorigo in 1992 as a majoraspect of his PhD thesis and called it the ant system [12]While further improvements were carried out to ant colonyby Gambardella Dorigo in 1997 [23] Pseudo code for antcolony optimization is implemented with the steps asAlgorithm 2

Complexity 5

In Algorithm 2 τij(t) represents the intensity of trailon connection (i j) at time t L(ant) is the cost functionresult at each ant and λ is pheromone decay coefficientbetween time (t and t + 1) (ie 0lt λlt 1) Evaporationoccurs in real trails but it is too slow to play an importantrole For continuous improvements it allows the searchroutine to forget errors and poor quality solution in favorof better ones

43 AntLion Optimizer Optimization (ALO) -e primarymotive of ALO is the running behavior of larvae of antlions

ALO is suggested based on the Emary and Zawbaa [24]mathematical model -e ALO algorithm simulates theinteraction between the traps-e ants must move across thesearch area in order to model such interactions and theantlions are permitted to chase and fit the traps Given thatants move randomly to find food in actual life a randomwalk algorithm is selected as shown in Heidari et al [25] tomodel the antsrsquo motion

In Algorithm 3 I is a ratio ct is the minimum of allvariables at tth iteration and dt indicates the vector in-cluding the maximum of all variables at tth iterationI 10w(Tt) where t is the current iteration T is the

Measure the PV voltage and Current I amp V

Calculate the fractional derivative I and VdαI = I ndash αIo = ΔI

dαV = (V ndash Vo)α = ΔVα

Start

Calculate the output Power of PV (P = I times V)

End

Yes

Yes

Yes

Yes

Yes

No

No

No No

No

ΔVα = 0

ΔI = 0

ΔI = 0

Equation (7) = equation (8)

Equation (7) = equation (8)

Vref = Vo + ΔVα Vref = Vo + ΔVαVref = Vo ndash ΔVα Vref = Vo ndash ΔVα

Vo = VIo = IPo = P

P gt Po

Figure 6 Fractional order INC MPPT flowchart

6 Complexity

maximum number of iterations and w is a constant definedbased on the current iteration X(t) is antrsquo movementcumsum calculates the cumulative sum n is the maximumnumber of iteration t shows the step of random walk andr(t) is a stochastic function Also ai is the minimum ofrandom walk and bi is the maximum of random walk inith variable Rt

A is the random walk around the antlionselected by the roulette wheel at tth iteration and Rt

E is therandom walk around the elite at tth iteration -e pseudocode of ALO for MPPT developed as mentioned inAlgorithm 3

5 Modeling and Simulation Results

-e proposed system has been modeled and simulatedusing MATLAB and Simscape software environments inorder to study the system behavior and MPPTperformance

with different metaheuristic optimization algorithms -eblock diagram describing the total PV system with MPPTand optimizer is shown in Figure 7 where the MPPT al-gorithm is changed between conventional INC methodsand FO-INC (fixed and variable step) -e MPPT is op-timized by one of the metaheuristic techniques (PSO ACOand ALO)

-e operation sequence of PV with MPPT and opti-mization process is a closed loop as shown in Figure 8 and itstarts with measuring the irradiance (G) and temperature(T) applied to the PV system to get the reference maximumpower point from PV characteristics curves (PMPP) A closedloop of PV withMPPTand BuckndashBoost converter is runningin Simscape environment for two seconds to measure the PVoutput power -e mean squared-error (MSE) betweenthe MPP (PMPP) and output power of the PV system (PPV) isthe cost function of the metaheuristic optimizer calculated

Result MPPT parameter to achieve MPPInitialize the PSO parameters (N C1 C2 Wmin Wmax Vmax)while the termination criteria not achieved (MPP) doFor (each Particle i)

Simulate and calculate the MPP and the cost function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update the velocity (V) Vt+1

i Vti + C1r1(Pi minus Xt

i ) + C2r2(Pg minus Xti )

where Vti is inertia C1r1(Pi minus Xt

i ) is cognitive component and C2r2(Pg minus Xti ) is social component

(b) Update the position of particles Xt+1i Xt+1

i + Vti

end

ALGORITHM 1 PSO-MPPT

Result MPPT parameter to achieve MPPInitialize the ACO parameterswhile the termination criteria not achieved (MPP) doFor (each ant i)Simulate and calculate the MPP and the cost Functionif CostFunction(i)ltObjective(MPP) then

-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update pheromone for each ant τij(t + 1) Δτij(t) 1113936

antsant1Δτantij (t)

(i) Calculate the solution Δτantij (t) (1Lbest)⟶ if ant(t) travels on edge(i j)

0⟶ otherwise1113896

(b) Apply evaporation and globally update the ants position according to the optimum solutions calculated earlierend

ALGORITHM 2 ACO-MPPT

Complexity 7

Result MPPT parameter to achieve MPPInitialize the first population of ants and antlions randomlywhile the termination criteria not achieved (MPP) doFor (each antlion (i))Select an antlion using Roulette wheel algorithm [16]Simulate and calculate the MPP and the cost Function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e elite (i)-e -e Best Solution (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e elite (i)-e Best Solution (i minus 1)

end(a) Update c and d using equations Ct (CtI) and dt (dtI)

(b) Create a random walk and normalize it using X(t) [0 cumsum(2r(tn) minus 1)] where n 1 2 3 n andXt

i ((Xti minus ai) times (di minus ct

i )(dti minus ai)) + ci

(c) Update the position of antlions using antti (RtA + Rt

E)2(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

end

ALGORITHM 3 ALO-MPPT

Cost function mean square error MSE (Pmpp Ppv)

Metaheuristic optimization algorithm (PSO ACO and ALO)

Initialize the model and measure G and T

From PV model get the value of MPP fromP-V characteristics curve Figure 3

Pmpp = MPP (T G)

Measure PV current I and voltage V and calucalte Ppv = I lowast V

MPPT algorithm (fixed INC variable INCfixed FO-INC and variable FO-INC)

DC-DC converter and the load

MPPT optimal parameters

Pmpp

Ppv

Control signal duty cycle

MPPT number and range of parameters

Figure 8 -e proposed system implementation flowchart

MPPT

Temperature degC Irradiance Wm2

+

ndash I_PV

V_PV

PWM

+

ndashPV panel

DC-DC converter DC load

Optimizer

Figure 7 -e proposed PV system with metaheuristic optimization

8 Complexity

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

In Algorithm 2 τij(t) represents the intensity of trailon connection (i j) at time t L(ant) is the cost functionresult at each ant and λ is pheromone decay coefficientbetween time (t and t + 1) (ie 0lt λlt 1) Evaporationoccurs in real trails but it is too slow to play an importantrole For continuous improvements it allows the searchroutine to forget errors and poor quality solution in favorof better ones

43 AntLion Optimizer Optimization (ALO) -e primarymotive of ALO is the running behavior of larvae of antlions

ALO is suggested based on the Emary and Zawbaa [24]mathematical model -e ALO algorithm simulates theinteraction between the traps-e ants must move across thesearch area in order to model such interactions and theantlions are permitted to chase and fit the traps Given thatants move randomly to find food in actual life a randomwalk algorithm is selected as shown in Heidari et al [25] tomodel the antsrsquo motion

In Algorithm 3 I is a ratio ct is the minimum of allvariables at tth iteration and dt indicates the vector in-cluding the maximum of all variables at tth iterationI 10w(Tt) where t is the current iteration T is the

Measure the PV voltage and Current I amp V

Calculate the fractional derivative I and VdαI = I ndash αIo = ΔI

dαV = (V ndash Vo)α = ΔVα

Start

Calculate the output Power of PV (P = I times V)

End

Yes

Yes

Yes

Yes

Yes

No

No

No No

No

ΔVα = 0

ΔI = 0

ΔI = 0

Equation (7) = equation (8)

Equation (7) = equation (8)

Vref = Vo + ΔVα Vref = Vo + ΔVαVref = Vo ndash ΔVα Vref = Vo ndash ΔVα

Vo = VIo = IPo = P

P gt Po

Figure 6 Fractional order INC MPPT flowchart

6 Complexity

maximum number of iterations and w is a constant definedbased on the current iteration X(t) is antrsquo movementcumsum calculates the cumulative sum n is the maximumnumber of iteration t shows the step of random walk andr(t) is a stochastic function Also ai is the minimum ofrandom walk and bi is the maximum of random walk inith variable Rt

A is the random walk around the antlionselected by the roulette wheel at tth iteration and Rt

E is therandom walk around the elite at tth iteration -e pseudocode of ALO for MPPT developed as mentioned inAlgorithm 3

5 Modeling and Simulation Results

-e proposed system has been modeled and simulatedusing MATLAB and Simscape software environments inorder to study the system behavior and MPPTperformance

with different metaheuristic optimization algorithms -eblock diagram describing the total PV system with MPPTand optimizer is shown in Figure 7 where the MPPT al-gorithm is changed between conventional INC methodsand FO-INC (fixed and variable step) -e MPPT is op-timized by one of the metaheuristic techniques (PSO ACOand ALO)

-e operation sequence of PV with MPPT and opti-mization process is a closed loop as shown in Figure 8 and itstarts with measuring the irradiance (G) and temperature(T) applied to the PV system to get the reference maximumpower point from PV characteristics curves (PMPP) A closedloop of PV withMPPTand BuckndashBoost converter is runningin Simscape environment for two seconds to measure the PVoutput power -e mean squared-error (MSE) betweenthe MPP (PMPP) and output power of the PV system (PPV) isthe cost function of the metaheuristic optimizer calculated

Result MPPT parameter to achieve MPPInitialize the PSO parameters (N C1 C2 Wmin Wmax Vmax)while the termination criteria not achieved (MPP) doFor (each Particle i)

Simulate and calculate the MPP and the cost function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update the velocity (V) Vt+1

i Vti + C1r1(Pi minus Xt

i ) + C2r2(Pg minus Xti )

where Vti is inertia C1r1(Pi minus Xt

i ) is cognitive component and C2r2(Pg minus Xti ) is social component

(b) Update the position of particles Xt+1i Xt+1

i + Vti

end

ALGORITHM 1 PSO-MPPT

Result MPPT parameter to achieve MPPInitialize the ACO parameterswhile the termination criteria not achieved (MPP) doFor (each ant i)Simulate and calculate the MPP and the cost Functionif CostFunction(i)ltObjective(MPP) then

-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update pheromone for each ant τij(t + 1) Δτij(t) 1113936

antsant1Δτantij (t)

(i) Calculate the solution Δτantij (t) (1Lbest)⟶ if ant(t) travels on edge(i j)

0⟶ otherwise1113896

(b) Apply evaporation and globally update the ants position according to the optimum solutions calculated earlierend

ALGORITHM 2 ACO-MPPT

Complexity 7

Result MPPT parameter to achieve MPPInitialize the first population of ants and antlions randomlywhile the termination criteria not achieved (MPP) doFor (each antlion (i))Select an antlion using Roulette wheel algorithm [16]Simulate and calculate the MPP and the cost Function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e elite (i)-e -e Best Solution (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e elite (i)-e Best Solution (i minus 1)

end(a) Update c and d using equations Ct (CtI) and dt (dtI)

(b) Create a random walk and normalize it using X(t) [0 cumsum(2r(tn) minus 1)] where n 1 2 3 n andXt

i ((Xti minus ai) times (di minus ct

i )(dti minus ai)) + ci

(c) Update the position of antlions using antti (RtA + Rt

E)2(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

end

ALGORITHM 3 ALO-MPPT

Cost function mean square error MSE (Pmpp Ppv)

Metaheuristic optimization algorithm (PSO ACO and ALO)

Initialize the model and measure G and T

From PV model get the value of MPP fromP-V characteristics curve Figure 3

Pmpp = MPP (T G)

Measure PV current I and voltage V and calucalte Ppv = I lowast V

MPPT algorithm (fixed INC variable INCfixed FO-INC and variable FO-INC)

DC-DC converter and the load

MPPT optimal parameters

Pmpp

Ppv

Control signal duty cycle

MPPT number and range of parameters

Figure 8 -e proposed system implementation flowchart

MPPT

Temperature degC Irradiance Wm2

+

ndash I_PV

V_PV

PWM

+

ndashPV panel

DC-DC converter DC load

Optimizer

Figure 7 -e proposed PV system with metaheuristic optimization

8 Complexity

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

maximum number of iterations and w is a constant definedbased on the current iteration X(t) is antrsquo movementcumsum calculates the cumulative sum n is the maximumnumber of iteration t shows the step of random walk andr(t) is a stochastic function Also ai is the minimum ofrandom walk and bi is the maximum of random walk inith variable Rt

A is the random walk around the antlionselected by the roulette wheel at tth iteration and Rt

E is therandom walk around the elite at tth iteration -e pseudocode of ALO for MPPT developed as mentioned inAlgorithm 3

5 Modeling and Simulation Results

-e proposed system has been modeled and simulatedusing MATLAB and Simscape software environments inorder to study the system behavior and MPPTperformance

with different metaheuristic optimization algorithms -eblock diagram describing the total PV system with MPPTand optimizer is shown in Figure 7 where the MPPT al-gorithm is changed between conventional INC methodsand FO-INC (fixed and variable step) -e MPPT is op-timized by one of the metaheuristic techniques (PSO ACOand ALO)

-e operation sequence of PV with MPPT and opti-mization process is a closed loop as shown in Figure 8 and itstarts with measuring the irradiance (G) and temperature(T) applied to the PV system to get the reference maximumpower point from PV characteristics curves (PMPP) A closedloop of PV withMPPTand BuckndashBoost converter is runningin Simscape environment for two seconds to measure the PVoutput power -e mean squared-error (MSE) betweenthe MPP (PMPP) and output power of the PV system (PPV) isthe cost function of the metaheuristic optimizer calculated

Result MPPT parameter to achieve MPPInitialize the PSO parameters (N C1 C2 Wmin Wmax Vmax)while the termination criteria not achieved (MPP) doFor (each Particle i)

Simulate and calculate the MPP and the cost function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update the velocity (V) Vt+1

i Vti + C1r1(Pi minus Xt

i ) + C2r2(Pg minus Xti )

where Vti is inertia C1r1(Pi minus Xt

i ) is cognitive component and C2r2(Pg minus Xti ) is social component

(b) Update the position of particles Xt+1i Xt+1

i + Vti

end

ALGORITHM 1 PSO-MPPT

Result MPPT parameter to achieve MPPInitialize the ACO parameterswhile the termination criteria not achieved (MPP) doFor (each ant i)Simulate and calculate the MPP and the cost Functionif CostFunction(i)ltObjective(MPP) then

-e Best Cost (i)Cost Function (i)-e Best Solution (i)-e particle (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e Best Solution (i)-e Best Solution (i minus 1)

end(a) Update pheromone for each ant τij(t + 1) Δτij(t) 1113936

antsant1Δτantij (t)

(i) Calculate the solution Δτantij (t) (1Lbest)⟶ if ant(t) travels on edge(i j)

0⟶ otherwise1113896

(b) Apply evaporation and globally update the ants position according to the optimum solutions calculated earlierend

ALGORITHM 2 ACO-MPPT

Complexity 7

Result MPPT parameter to achieve MPPInitialize the first population of ants and antlions randomlywhile the termination criteria not achieved (MPP) doFor (each antlion (i))Select an antlion using Roulette wheel algorithm [16]Simulate and calculate the MPP and the cost Function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e elite (i)-e -e Best Solution (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e elite (i)-e Best Solution (i minus 1)

end(a) Update c and d using equations Ct (CtI) and dt (dtI)

(b) Create a random walk and normalize it using X(t) [0 cumsum(2r(tn) minus 1)] where n 1 2 3 n andXt

i ((Xti minus ai) times (di minus ct

i )(dti minus ai)) + ci

(c) Update the position of antlions using antti (RtA + Rt

E)2(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

end

ALGORITHM 3 ALO-MPPT

Cost function mean square error MSE (Pmpp Ppv)

Metaheuristic optimization algorithm (PSO ACO and ALO)

Initialize the model and measure G and T

From PV model get the value of MPP fromP-V characteristics curve Figure 3

Pmpp = MPP (T G)

Measure PV current I and voltage V and calucalte Ppv = I lowast V

MPPT algorithm (fixed INC variable INCfixed FO-INC and variable FO-INC)

DC-DC converter and the load

MPPT optimal parameters

Pmpp

Ppv

Control signal duty cycle

MPPT number and range of parameters

Figure 8 -e proposed system implementation flowchart

MPPT

Temperature degC Irradiance Wm2

+

ndash I_PV

V_PV

PWM

+

ndashPV panel

DC-DC converter DC load

Optimizer

Figure 7 -e proposed PV system with metaheuristic optimization

8 Complexity

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

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Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Volume 2018

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Submit your manuscripts atwwwhindawicom

Result MPPT parameter to achieve MPPInitialize the first population of ants and antlions randomlywhile the termination criteria not achieved (MPP) doFor (each antlion (i))Select an antlion using Roulette wheel algorithm [16]Simulate and calculate the MPP and the cost Function if CostFunction(i)ltObjective(MPP)

then-e Best Cost (i)Cost Function (i)-e elite (i)-e -e Best Solution (i)

else-e Best Cost (i)-e Best Cost (i minus 1)-e elite (i)-e Best Solution (i minus 1)

end(a) Update c and d using equations Ct (CtI) and dt (dtI)

(b) Create a random walk and normalize it using X(t) [0 cumsum(2r(tn) minus 1)] where n 1 2 3 n andXt

i ((Xti minus ai) times (di minus ct

i )(dti minus ai)) + ci

(c) Update the position of antlions using antti (RtA + Rt

E)2(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

end

ALGORITHM 3 ALO-MPPT

Cost function mean square error MSE (Pmpp Ppv)

Metaheuristic optimization algorithm (PSO ACO and ALO)

Initialize the model and measure G and T

From PV model get the value of MPP fromP-V characteristics curve Figure 3

Pmpp = MPP (T G)

Measure PV current I and voltage V and calucalte Ppv = I lowast V

MPPT algorithm (fixed INC variable INCfixed FO-INC and variable FO-INC)

DC-DC converter and the load

MPPT optimal parameters

Pmpp

Ppv

Control signal duty cycle

MPPT number and range of parameters

Figure 8 -e proposed system implementation flowchart

MPPT

Temperature degC Irradiance Wm2

+

ndash I_PV

V_PV

PWM

+

ndashPV panel

DC-DC converter DC load

Optimizer

Figure 7 -e proposed PV system with metaheuristic optimization

8 Complexity

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

in MATLAB environment to get the optimal MPPT pa-rameters -e optimal parameters are applied to the chosenMPPT technique in Simscape Performance index is cal-culated in MATLAB through a dynamical data exchangebetween MATLAB and Simscape

-e proposed MPPT contribution is generated bymeasuring the output energy of the PV system underdifferent solar irradiances Simulation was conductedwhen solar radiation and cell temperature change with atransient method of approximately 2 sec with 001 secsampling-e characteristics of the PV array will be alteredwhen the natural radiation and cell temperature alterwhich causes the I-V curves of the PV array to change Inaddition the particular irradiance ranges from 400 to1000Wm2 and the cell temperature ranges from 20degC to40degC which makes it more realistic as shown in Tables 3and 4

Figure 9 shows the I-V and P-V curves of fixed-step INCunder different temperature and radiation with small stepwhich in return gives it better results and less oscillationhowever it takes more time to get maximum power -evariable-step INC curves shown in Figure 10 give betterresults than the fixed INC However in variable-step INCimproper selection of the initial step size may require largenumber of steps to reach the MPP Also improper selectionof the scaling factor may lead to oscillations

-e objective of PSO ACO and ALO is to select the bestvalue of α for the fixed-step FO-INC and the best values of αand S for variable step to get the maximum PV power Fixed-step FO-INC MPPT results optimized by PSO ACO andALO are shown in Figure 11 Fixed-step FO-INC-PSO givesbetter results than conventional INC methods less numberof MPPT steps to maximum power value and less oscilla-tion yet PSO optimization needs more iterations to get the

Table 3 Comparative results between MPPT algorithms at 800Wm2

Climatic condition

MPPT800Wm2 and 25degC 800Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 32184 137 587 mdash 31973 131 492 mdashVariable-step INC 32463 125 489 mdash 31990 127 417 mdashFO-INC fixedstep + PSO 42028 121 428 100 40001 127 434 100

FO-INC fixedstep +ACO 47062 115 4067 100 46224 121 3089 100

FO-INC fixedstep +ALO 48722 118 3067 100 47424 125 3089 100

FO-INC variablestep + PSO 49028 128 328 100 48001 132 334 100

FO-INC variablestep +ACO 51062 115 3067 100 49024 121 3089 100

FO-INC variablestep +ALO 51552 120 3269 100 51026 127 3802 100

Table 4 Comparative results between MPPT algorithms at 1000Wm2

Climatic condition

MPPT1000Wm2 and 25degC 1000Wm2 and 35degC

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Max power(Watt)

MPPsteps

Oscillation avg(Watt)

No ofiterations

Fixed-step INC 42884 145 487 mdash 41973 153 592 mdashVariable-step INC 42073 155 587 mdash 41990 139 517 mdashFO-INC fixedstep + PSO 43688 120 488 100 41051 121 484 100

FO-INC fixedstep +ACO 65082 101 2067 100 63224 112 2089 100

FO-INC fixedstep +ALO 66732 118 387 100 66424 120 3889 100

FO-INC variablestep + PSO 59028 86 228 100 58023 92 234 100

FO-INC variablestep +ACO 72062 65 2067 100 70524 71 2079 100

FO-INC variablestep +ALO 72532 80 2369 100 71063 96 2802 100

Complexity 9

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

optimal MPPT parameter Fixed-step FO-INC-ACO givesless number of MPPT steps than PSO and ALO howevernot the optimum parameter that can be obtained by ALOwith fewer number of MPPT steps shye output power andvoltage of the PV system generated using the optimization ofxed-step FO-INC-ACO gives less oscillation yet not asmuch maximum power as given by ALO as shown inFigure 12 Variable-step FO-INC gives better results thanconventional INC and xed-step FO-INC methods lessnumber of MPPT steps to maximum power value and lessoscillation PSO needs more number of iterations than ACOand ALO to get the optimal MPPT parameters ALO givesthe optimum parameters for the maximum power withlarger number of MPPT steps and vice-versa with ACO asshown in Figures 13 and 14

shyeMPPTperformance η can bemonitored as in equation(10) for all the abovementioned MPPT techniques Irradiancetemperature power and maximum power time waveform ofthe system using the proposedMPPTmethods have been used

Fixed-step INC PampI-V curve

V

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

G = 400 wm2 T = 25degC

G = 800 wm2 T = 25degC

G = 1000 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

0

100

200

300

400

500

600

700

800

3020 50 6010 40 700PV voltage

Figure 9 Fixed-step INC I-V and P-V curves

Variable step INC PampI-V curve

G = 800 wm2

T = 25degC

G = 1000 wm2 T = 25degC

G = 400 wm2 T = 25degC

0

5

10

15

PV cu

rren

t

10 20 30 40 50 60 700PV voltage

0

100

200

300

400

500

600

700

800

Ideal PampI-VMPPT steps

Max-P MPPTMax-P ideal

Figure 10 Variable-step INC I-V and P-V curves

PSO fixed-step FO-INC PampI-V MPPT curve

ACO fixed-step FO-INC PampI-V MPPT curve

ALO fixed-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

0200400600800

PV p

ower

(W)

0200400600800

PV p

ower

(W)

Figure 11 Optimization of xed-step FO-INC I-V and P-V curves

PV output voltage

PV output power

01020304050607080

PV v

olta

ge (V

)

20 40 60 80 100 120 140 160 180 2000Time samples

20 40 60 80 100 120 140 160 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

PSO-FS FO-INCACO-FS FO-INCALO-FS FO-INC

Figure 12 Optimization of xed FO-INC output response

10 Complexity

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

to get η -e irradiance and temperature variation mean thatoutput power follows the highest maximumpower profile veryclosely and the higher performance is obtained in case ofvariable-step FO-INC with ALO (981) as noted from Table 5

η 1113938PPV(t) dt

PMPP (10)

6 Conclusion and Future Work

-e output power of the PV system will be changed byirradiance and temperature according to the simulationresults of the system with different climatic conditions asillustrated in Tables 3 and 4 -e proposed incrementalfractional order FO-INC demonstrates better results thantraditional INC under environmental changing processesand improves the efficiency of MPPT as FO-INC is able toprovide a dynamical mathematical model for describing thenonlinear and fractional properties -e incrementalchange in the fractional order as a dynamic variable is usedto adjust the MPPT service cycle Using metaheuristicoptimization enhances the performance of FO-INC and

PSO variable-step FO-INC PampI-V MPPT curve

ACO variable-step FO-INC PampI-V MPPT curve

ALO variable-step FO-INC PampI-V MPPT curve

0

5

10

15

PV cu

rren

t (A

)

10 20 30 40 50 60 700PV voltage (V)

0200400600800

PV p

ower

(W)

0

5

10

15PV

curr

ent (

A)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

0

5

10

15

PV cu

rren

t (A

)

0200400600800

PV p

ower

(W)

10 20 30 40 50 60 700PV voltage (V)

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Ideal I-VMPPT steps

Max-P MPPTMax-P ideal

Figure 13 Optimization of variable-step FO-INC I-V and P-V curves

PV output voltage

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PSO-VS FO-INCACO-VS FO-INCALO-VS FO-INC

PV output power

01020304050607080

PV v

olta

ge (V

)

6040 140 160100 12020 80 180 2000Time samples

0100200300400500600700800

PV p

ower

(W)

20 40 60 80 100 120 140 160 180 2000Time samples

Figure 14 Optimization of variable FO-INC output response

Table 5 MPPT algorithms efficiency

MPPT method Efficiency (η)Fixed-step INC 759Variable-step INC 821Fixed-step FO-INC+PSO 902Fixed-step FO-INC+ACO 923Fixed-step FO-INC+ALO 932Variable-step FO-INC+PSO 947Variable-step FO-INC+ACO 975Variable-step FO-INC+ALO 981

Complexity 11

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

provides another dynamical variable to the MPPT controlCompared to ACO and ALO the PSO uses less number ofvariables and shorter calculation time for the same numberof iterations However sometimes it cannot achieve theoptimal solution -e ALO uses larger number of variablesand takes the longest calculation time yet it gives moreoptimal solution compared to ACO and PSO -is workcould be extended by changing the resistance using anotherdynamical load eg DC motor or by applying differentoptimization techniques on the FO-INC

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors would like to thank Prince Sultan UniversityRiyadh Saudi Arabia for supporting and funding this workSpecial acknowledgment to Robotics and Internet-of--ingsLab (RIOTU) at Prince Sultan University Riyadh SA

References

[1] M A Jusoh M F Naim Tajuddin S M Ayob andM A Roslan ldquoMaximum power point tracking chargecontroller for standalone PV systemrdquo TELKOMNIKA (Tele-communication Computing Electronics and Control) vol 16no 4 pp 1413ndash1426 2018

[2] P G Bueno F J Ruiz-Rodriguez and J C HernandezldquoStability assessment for transmission systems with largeutility-scale photovoltaic unitsrdquo IET Renewable Power Gen-eration vol 10 no 5 pp 584ndash597 2016

[3] B-R Peng K-C Ho and Y-H Liu ldquoA novel and fast mpptmethod suitable for both fast changing and partially shadedconditionsrdquo IEEE Transactions on Industrial Electronicsvol 65 no 4 pp 3240ndash3251 2018

[4] H Bahri and A Harrag ldquoVariable step size PampO MPPTcontroller to improve static and dynamic PV system per-formancesrdquo Journal of Advanced Engineering and Compu-tation vol 2 no 2 pp 86ndash93 2018

[5] S Motahhir A El Ghzizal S Sebti and A DerouichldquoModeling of photovoltaic system with modified incrementalconductance algorithm for fast changes of irradiancerdquo In-ternational Journal of Photoenergy vol 2018 Article ID3286479 13 pages 2018

[6] M Seyedmahmoudian T Kok Soon E Jamei et al ldquoMaxi-mum power point tracking for photovoltaic systems underpartial shading conditions using bat algorithmrdquo Sustain-ability vol 10 no 5 p 1347 2018

[7] L Li H Wang X Chen et al ldquoHigh efficiency solar powergeneration with improved discontinuous pulse width mod-ulation (dpwm) overmodulation algorithmsrdquo Energiesvol 12 no 9 p 1765 2019

[8] J Li and H Wang ldquoA novel stand-alone PV generationsystem based on variable step size INC MPPT and SVPWMcontrolrdquo in Proceedings of the 2009 IEEE 6th InternationalPower Electronics and Motion Control Conference pp 2155ndash2160 IEEE Wuhan China May 2009

[9] C Milici G Draganescu and J T Machado Introduction toFractional Differential Equations vol 25 Springer BaselSwitzerland 2019

[10] K-N Yu C-K Liao and H-T Yau ldquoA new fractional-orderbased intelligent maximum power point tracking controlalgorithm for photovoltaic power systemsrdquo InternationalJournal of Photoenergy vol 2015 Article ID 493452 8 pages2015

[11] M A Ebrahim and R Mohamed ldquoComparative study andsimulation of different maximum power point tracking(MPPT) techniques using fractional control amp grey wolfoptimizer for grid connected pv system with batteryrdquo inElectric Power Conversion IntechOpen London UK 2019

[12] M Dorigo and T Stutzle ldquoAnt colony optimization overviewand recent advancesrdquo in Handbook of Metaheuristicspp 311ndash351 Springer 2019

[13] J Kumar K V Azar Ahmad Taher and R K P SinghldquoDesign of fractional order fuzzy sliding mode controller fornonlinear complex systemsrdquo in Mathematical Techniques ofFractional Order Systems pp 249ndash282 Elsevier 2018a

[14] Y Sun and Y Yihan ldquoNon-inverting buck-boost convertercontrolrdquo US Patent App 15729366 2018

[15] A Mohapatra Optimized parameter estimation array con-figuration and MPPT control of standalone photovoltaic sys-tem PhD thesis National Institute of Technology RourkelaIndia 2018

[16] K Sundareswaran V Vigneshkumar P Sankar S P SimonP S R Nayak and S Palani ldquoDevelopment of an improvedPampO algorithm assisted through a colony of foraging ants formppt in PV systemrdquo IEEE Transactions on Industrial In-formatics vol 12 no 1 pp 187ndash200 2015

[17] S Duman N Yorukeren and I H Altas ldquoA novel MPPTalgorithm based on optimized artificial neural network byusing FPSOGSA for standalone photovoltaic energy systemsrdquoNeural Computing and Applications vol 29 no 1 pp 257ndash278 2018

[18] R Sahu and B Shaw ldquoDesign of solar system by imple-menting alo optimized pid based mppt controllerrdquo Trends inRenewable Energy vol 4 no 3 pp 44ndash55 2018

[19] B Oubbati M Boutoubat M Belkheiri and A RabhildquoExtremum seeking and PampO control strategies for achievingthe maximum power for a PV arrayrdquo in International Con-ference in Artificial Intelligence in Renewable Energetic Sys-tems pp 233ndash241 Springer Cham Switzerland 2018

[20] R Pradhan S Pradhan and B B Pati ldquoDesign and per-formance evaluation of fractional order PID controller forheat flow system using particle swarm optimizationrdquo inComputational Intelligence in Data Mining pp 261ndash271Springer Cham Switzerland 2019

[21] N A Kamal and A M Ibrahim ldquoConventional intelligentand fractional-order control method for maximum powerpoint tracking of a photovoltaic system a reviewrdquo in Frac-tional Order Systems pp 603ndash671 Elsevier AmsterdamNetherlands 2018

[22] YMichimura K Komori A Nishizawa et al ldquoParticle swarmoptimization of the sensitivity of a cryogenic gravitationalwave detectorrdquo Physical Review D vol 97 no 12 p 1220032018

[23] P M Kumar U Devi G G Manogaran R SundarasekarN Chilamkurti and R Varatharajan ldquoAnt colony optimi-zation algorithm with internet of vehicles for intelligent trafficcontrol systemrdquo Computer Networks vol 144 pp 154ndash1622018b

12 Complexity

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

[24] E Emary and H M Zawbaa ldquoFeature selection via levyantlion optimizationrdquo Pattern Analysis and Applicationsvol 22 no 3 pp 857ndash876 2018

[25] A A Heidari H Faris S Mirjalili I Aljarah and M MafarjaldquoAnt lion optimizer theory literature review and applicationin multi-layer perceptron neural networksrdquo in Nature-In-spired Optimizers pp 23ndash46 Springer Cham Switzerland2020

Complexity 13

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

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Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

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