Electrical Power and Energy Systems 43 (2012) 90–98

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

MPPT control design and performance improvements of a PV generator powered DCmotor-pump system based on artificial neural networks

Ahmed M. KassemControl Technology Dep., Beni-Suef University, Beni Suef, Egypt

a r t i c l e i n f o

Article history:Received 23 August 2011Received in revised form 21 April 2012Accepted 23 April 2012Available online 18 June 2012

Keywords:PhotovoltaicMaximum power point trackingDrive systemsArtificial neural network controller

0142-0615/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijepes.2012.04.047

E-mail address: Kassem_ahmed53@hotmail.com

a b s t r a c t

This paper presents the optimum photovoltaic (PV) water pumping system using maximum power pointtracking technique (MPPT). The optimum is suspended to reference optimal power. This optimal tech-nique is developed to assure the optimum chopping ratio of buck–boost converter. The presented MPPTtechnique is used in photovoltaic water pumping system in order to optimize its efficiency. An adaptivecontroller with emphasis on Nonlinear Autoregressive Moving Average (NARMA) based on artificial neu-ral networks approach is applied in order to optimize the duty ratio for PV maximum power at any irra-diation level. In this application, an indirect data-based technique is taken, where a model of the plant isidentified on the basis of input–output data and then used in the model-based design of a neural networkcontroller. The proposed controller has the advantages of fast response and good performance. The PVgenerator DC motor pump system with the proposed controller has been tested through a step changein irradiation level. Simulation results show that accurate MPPT tracking performance of the proposedsystem has been achieved. Further, the performance of the proposed artificial neural network (ANN) con-troller is compared with a PID controller through simulation studies. Obtained results demonstrate theeffectiveness and superiority of the proposed approach.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Photovoltaic (PV) energy has increased interest in electricalpower applications. It is crucial to operate the PV energy conver-sion systems near the maximum power point to increase the effi-ciency of the PV system. The current and power of the PV arraydepends on the array terminal operating voltage. In addition, themaximum power operating point varies with insolation level andtemperature. Therefore, the tracking control of the maximumpower point is a complicated problem. To overcome these prob-lems, many tracking control strategies have been proposed suchas perturb and observe [1,2], incremental conductance [3], para-sitic capacitance [4], constant voltage [5], reactive power control[6], neural network [7–12] and fuzzy logic controller (FLC) [13–19]. Some applications need constant output voltage with suitableMPPT or constant output current [20,21]. These strategies havesome disadvantages such as high cost, difficulty, complexity andinstability. Also, In [7–9,12] the neural networks are used onlyfor maximum power estimation while a different controller is usedto adjust the inverter output. But in this proposed system the adap-tive artificial neural network controller is used to adjust the inver-ter output and there is no any more controller else needed.

ll rights reserved.

The general requirements for maximum power point tracking(MPPT) are simplicity and low cost, quick tracking under changingconditions, and small output power fluctuation. A more efficientmethod to solve this problem becomes crucially important.

In photovoltaic pumping system, maximum power transfer isexpected between photovoltaic solar panel (PV) and pump motorat wide irradiance interval. If not, performance may drop to low val-ues to be removed. If the load voltage and or current are controlledto be constant these lead to maximum power decreases [20].

This paper proposes a method to operate the motor pumpingsystem at the high available efficiency. That is by tracking the max-imum power point using adaptive neural NARMA-L2 controller.The NARMA L2 neurocontroller was first trained to cancel boththe nonlinearity and dynamic of the system. Then, it was reconfig-ured to become a controller. Once the NARMA L2 neurocontrollersuppresses both the nonlinearity and dynamic behavior, the closedloop system becomes implicit algebraic relation between the inputand the output. Consequently, the system is able to perfectly fol-low a smooth reference trajectory even it is generated in real-time.A photo sensor and maximum power point tracker algorithm areused to generate the controller reference power. Also, the principledifferent between the proposed method and any other trackingmethod is that the proposed method attempts to track and com-pute the maximum power and controls directly the extractedpower from the PV to that computed value through ANN controller.

Nomenclature

Vg PV generator voltageIg PV generator currentIphg insolation photo current of the PV generatorIog PV generator reverse saturation currentRsg PV generator series resistanceVgm PV generator maximum voltageIgm PV generator maximum currentVa DC motor armature voltageIa DC motor armature currentRa armature resistanceLa armature inductancex rotor shaft speedxm rotor shaft speed at maximum powerEb back emf voltage

Kt torque constantKb back emf constantb friction coefficientJ moment of inertiaTL load torquen load torque constantD duty ratioPmot motor input powerDm maximum duty ratioEbm maximum back emf voltageG insolation levelA1 motor frictionA2 load frictionK torque and back emf constant

A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98 91

While, any other method attempts to reach the maximum point bythe knowledge of the voltage or the current corresponding to thatoptimum point.

In this work, The effectiveness of the PV generator, pumpingsystem together with the proposed ANN controller have been dem-onstrated through computer simulations. Moreover, the proposedcontroller is compared with a conventional PID controller. Simula-tion results have proved that the proposed controller can give bet-ter overall performance.

2. System dynamics

The proposed isolated generation system mainly consists of PVgenerator, DC–DC buck–boost converter and a DC motor coupled toa centrifugal pump as shown in Fig. 1. In the following subsections,a mathematical model for each device is developed and they com-bined together to form the complete model, which is to be used inthe controller design and simulation studies.

2.1. PV generator model

The PV generator consists of solar cells connected in series andparallel fashion to provide the desired voltage and current requiredby the DC motor system. This PV generator exhibits a nonlinearvoltage–current characteristic that depends on the insolation (so-lar radiation), as given by (1) [22,23].

Vg ¼1Ag

lnGIphg � Ig þ Iog

Iog

� �� IgRsg ð1Þ

where Vg is the PV generator voltage; Ig is the PV generator current;Ag = K/Ns is the PV generator constant; K = q/(e � Z � U), is the so-lar cell constant; q = 1.602 � 10�19 C. is the electron charge;Z = 1.38 � 10�23 J/K is Boltzmann constant; U = 298.15 �C is theabsolute temperature; e = 1.1 is the completion factor; Ns = 360 isthe series-connected solar cells; Np = 3 is the parallel paths;

Fig. 1. The proposed PV-generator DC motor pump system.

Rsg = Rs � (Ns/Np) is the PV generator series resistance;Rs = 0.0152 X is the series resistance per cell; Iphg = Iph � Np is theinsolation-dependent photo current of the PV generator; Iph = 4.8 Ais the photo current per cell; Iog = Io � Np is the PV generator reversesaturation current; Io = 2.58e�5 A is the reverse saturation currentper cell; G is the solar insolation in per unit, and 1.0 per unit ofG = 1000 W/m2.

The PV generator voltage–current and voltage–power charac-teristics at five different values of G are shown in Figs. 2 and 3respectively. From which, at any particular value of G, there is onlyone point at which the PV generator power is maximum. This pointis called the Maximum Power Point (MPP). To locate its position,the corresponding voltage (Vgm) and current (Igm) must be deter-mined first.

2.2. DC motor model

The dynamics of the permanent magnet DC motor and its loadare represented by the following set of differential equations withconstant coefficients:

Va ¼ RaIa þ LadIa

dtþ Kx ð2Þ

KIa ¼ A1 þ bxþ Jdxdtþ TL ð3Þ

Fig. 2. I–V characteristics of the PV generator at five different values of G.

Fig. 3. P–V characteristics of the PV generator at five different values of G.

92 A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98

The load (pump) torque can be represented by:

TL ¼ A2 þ nx1:8 ð4Þ

where the name-plate parameters are: Voltage Va = 110 V; CurrentIa = 7.3 A.; Inertia J = 0.02365 kg m2; Resistance Ra = 1.5 X; Induc-tance La = 0.2 H; Torque and back emf constant K = 0.67609 N m A�1;Motor friction A1 = 0.2 N m; Load friction A2 = 0.3 N m; dampingcoefficient b = 0.002387 N m s rad�1; Load torque constant n =0.00059 N m s rad�1.

2.3. DC–DC converter model

The most important parameter of the buck–boost converter isits chopping ratio Y that depends on the duty ratio D through anonlinear relation given by Eq. (5). In this study we modeled theconverter as lossless element:

Y ¼ D1� D

ð5Þ

This converter is inserted between the PV generator and the DC mo-tor to match the PV generator output characteristics to the DC mo-tor input characteristics. Assuming the converter is ideal, then itsinput and output powers are equal resulting in the following rela-tion [24,25]:

Va

Vg¼ Ig

Ia¼ D

1� Dð6Þ

2.4. Power regulator model and MPPT algorithm

There is a unique point on the PV voltage–current (I–V) andvoltage–power (V–P) characteristic curves as shown in (Figs. 2and 3) respectively, called the Maximum Power Point (MPP), atwhich the array produces maximum output power for each G. Ingeneral, when the load is direct-coupled, the operation point isnot at the PV array’s MPP, resulting an oversized PV array. How-ever, because of the small scale of a PV array (less than 200 W),the over-sizing is cheaper than a commercial MPPT. But if the PVscale became more than 200 W, it will be preferable to operate itat the MPPT and with an economical method.

In this paper we chose a very simple method for MPPT algo-rithm as following:

(1) The insolation level is measured on-line using photo sensor.(2) The reference maximum power for each value of insolation

level is calculated on line using Eq. (7).(3) The extract actual power from the PV generator is measured

(VaIa) and compared with the reference maximum power.

(4) The duty ratio of the buck–boost converter is adjusted suchthat the actual generated power equal the reference maxi-mum power using the proposed controller.

Pref ¼ 205� 1429:167Gþ 7208:33G2 � 9270:833G3 þ 4166:67G4

ð7Þ

The power output of the PV generator (delivered to the motor pumpsystem) can be adjusted via controlling the duty ratio of the DC–DCconverter using integral controller according to the following differ-ential equation:

D ¼ZðPref � PmotÞdt ð8Þ

where Pmot = IaVa.

2.5. Complete system model

The subsystem models can be interfaced to form the unifiednonlinear model. The complete nonlinear dynamic model of thePV generator motor pump system can be described as:

dIa

dt¼ 1

LaVa �

Ra

LaIa �

Kb

Lax ð9Þ

dxdt¼ Kt

JIa �

A1

J� b

Jx� 1

JðA2 þ nx1:8Þ ð10Þ

dDdt¼ Pref � Pmot ð11Þ

where

Ia ¼1� D

DIg

Va ¼D

1� DVg ¼

D1� D

1Ag

ln GIphg�IgþIog

Iog

h i�IgRsg

( )

2.6. Linearized model

Small signal linear model of the solar motor-pumped system isformed around an operating point to study the system dynamicswhen subjected to small perturbations. The linearized model canbe described by the following equation:

px ¼ Axþ Blþ dd ð12Þ

where

x ¼ ½DIa Dx DD�; l ¼ ½Pref �; d ¼ ½G�;

andA is a 3 � 3 matrix containing the system parameters.

3. MPPT condition

For tracking maximum power points of PV with DC motor, sys-tem uses a DC/DC converter. This converter may be buck, boost orbuck–boost type in respect of normal (direct coupled) operatingcharacteristic of PV-pump motor. In this work, a buck–boost DC–DC converter is used. Assuming power converter is ideal, all ofPV power is delivered to motor. Under MPPT conditions, motor isdriven by maximum power of PV.

VaIa ¼ VgmIgm ð13Þ

Motor input characteristics are defined by chopper ratio (D) of DC/DC converter. For maximum power tracking, there is a critical value

Fig. 7. Optimal duty ratio versus G irradiance.

Fig. 4. Power versus G irradiance with and without MPPT.

Fig. 5. Shaft speed versus G irradiance with and without MPPT.

Fig. 6. Torque versus G irradiance with and without MPPT.

A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98 93

of D with respect to a given irradiance level (D = Dm). Hence motorinput voltage and current expressions:

Va ¼Dm

1� DmVgm ð14Þ

Ia ¼1� Dm

DmIgm ð15Þ

In order to determine Dm, the steady-state equations of DC motor-pump system can be written as follows:

Va ¼ IaRa þ Kx ð16Þ

Eb ¼ Kx ð17Þ

T ¼ KIa ¼ A1 þ bxþ nx1:8 ð18Þ

Pmech ¼ VaIa � I2aRa ¼ Tx ð19Þ

For a given G, the maximum power (Pref) is equal to maximum ofVgm � Igm values. At maximum power condition, the current is Igm,voltage is Vgm. Hence as a function of G, Pref is;

Pref ðGÞ ¼ VgmðGÞIgmðGÞ ð20Þ

Using Eqs. (14)–(20) firstly, Vgm is obtained from (Fig. 2) to givemaximum power for different values of G(insolation level). Then,Igm which meet the obtained Vgm is obtained using Fig. 3. The backemf Ebm at maximum power is function in rotor speed at maximumpower xm, Eq. (17) can be written as following:

Ebm ¼ Kxm ð21Þ

When motor input values (current and voltage) are transformed toPV side by use of Dm, the following equation is obtained:

ðVgm � RaIgm þ EbmÞD2m þ ð2RaIgm � EbmÞDm � RaIgm ¼ 0 ð22Þ

Also referred to converter side, Eq. (18) can be written as following:

KIgm1� Dm

Dm¼ A1 þ bxm þ nx1:8

m ð23Þ

The optimized duty ratio Dm, Ebm and xm can be obtained by solvingthe three Eq. (23) in Dm, Ebm and xm at different insolation level (Igm

and Vgm). The optimal duty ratio versus G irradiance is shown inFig. 7.

Because, we would like to compare the system in normal casewith the system at maximum power condition, the Ia and x arecalculated using Eqs. (16) and (18) for certain values of Va, whereD is kept constant in this case.

Hence using Eqs. (14) and (15) motor input values are obtained.And then performance can be analyzed under MPPT condition. Fornormal system without MPPT, PV output current and voltage val-ues are equal to those of motor input.

For analysis, PV pumping system is simulated based on Matlab/Simulink program environment. These results are shown by Figs.4–6. For the average mechanical power at sampled irradiance lev-els, PV system with MPPT improves the system performance com-pared to normal system. Motor input power (Pmot = Va�Ia) matchesto PV maximum power point for overall irradiance levels.

Also using MPPT, higher speed and torque are provided at sameirradiance conditions. Assuming least operating torque of system isequal to 2 N m, normal system must wait until irradiance gets to0.4 pu. Whereas for system with MPPT, approximately 0.2 pu irra-diance level is sufficient to actively operate the system. Thus activeoperating region of pumping system is expanded by MPPT.

Fig. 8. NARMA-L2 controller schematic.

Fig. 10. Training data of ANN controller.

94 A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98

4. Nonlinear Autoregressive Moving Average (NARMA-L2)controller

NARMA-L2 is one of the popular neural network architecturesfor prediction and control. The principle idea of this control schemeis to apply the input output linearization method where the outputbecomes a linear function of a new control input [26].

Basically, there are two steps involved when using NARMA L2control: system identification and control design. In the systemidentification stage design, a neural network of the plant thatneeds to be controlled is developed using two subnetworks forthe model approximation. The network is then trained offline inbatch form using data collected from the operation of the plant.Next, the controller is simply the rearrangement of two subnet-works of the plant model. Computation of the next control inputto force the plant output to follow a reference signal is materializedthrough simple mathematical equation.

4.1. NARMA-L2 plant model identification

In this work, the ANN architecture is applied with the aid of theNeural Network Toolbox of MATLAB software. The identificationcan be summarized by the flowing:

The model structure used is the standard NARMA model [26]adapted to the feedback linearization of affine system. A compan-ion form system (control affine) is used as the identification model,i.e.:

Fig. 9. Block diagram of the PV generator motor-pump system with the MPPTalgorithm and the proposed ANN controller.

yðkþ 1Þ ¼ fyðkÞ; yðk� 1Þ; . . . ; yðk� nþ 1Þ;uðk� 1Þ

; . . . ;uðk�mþ 1Þ

� �

þgyðkÞ; yðk� 1Þ; . . . ; yðk� nþ 1Þ;uðk� 1Þ

; . . . ;uðk�mþ 1Þ

� �� uðkÞ

ð24Þ

In essence, the NARMA-L2 approximate model will be parameter-ized by two neural networks f and g that will be used to identifythe system of Eq. (24), i.e.:

yðkþ 1jhÞ ¼ fyðkÞ; yðk� 1Þ; . . . ; yðk� nþ 1Þ;uðk� 1Þ

; . . . ;uðk�mþ 1Þ;w

� �

þgyðkÞ; yðk� 1Þ; . . . ; yðk� nþ 1Þ;uðk� 1Þ

; . . . ;uðk�mþ 1Þ;v

� �� uðkÞ

ð25Þ

The two subnetworks are used for the model approximation; thefirst multilayer neural network (MLNN1) and the second multilayerneural network (MLNN2), which are used to approximate nonlinearfunctions f and g respectively.

The plant model identification in NARMA-L2 Control starts offwith a dataset of input output data pairs collected using the plantmathematical model. Then, the neural nets model is trained andvalidated. Here, the MLNN1 subnetwork is a feedforward neuralnetwork with five hidden layer with p neurons of hyperbolic tan-gent (tanh) activation function and an output layer of one neuronwith linear activation function. Also, the MLNN2 subnetwork is a

Fig. 11. Validation data of ANN controller. Fig. 12. Testing data of ANN controller.

A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98 95

feedforward neural network with q tanh hidden layer neurons andone output neuron.

For each subnetwork, the number of past output n and the pastinput m; which compose the input vector and the number of neu-rons (p and q) of the hidden layer are determined. Subsequently,the selected neural network structure is trained using the inputpattern and the desired output from the dataset. Here, the param-eters (weights and biases) of the two MLNN subnetworks thatproperly approximate the nonlinear modeling representing theoptimized PV motor pump system power regulator is estimated.

Finally, to measure the success at approximating the dynamicalsystem plant model using the neural network model, the predic-tion error ek should be uncorrelated with all linear and nonlinearcombination of past inputs and outputs. Thus, the validation andcross validation tests are carried out to ascertain the validity ofthe obtained neural network model [27,28].

4.2. NARMA-L2 controller design

There are two neural networks are used which are called f and g.Each one is a feed forward with three layers, i.e., an input, a hiddenand an output layers. The input layer of f network has two nodesfor the output power and a bias signal of 1.0. The input layer of gnetwork has two nodes for the duty ratio and a bias signal of 1.0.The hidden layer has three nodes. The output layer has only one

node. The output signal represent the duty ratio signal for the max-imum power point.

The NARMA-L2 controller design is uncomplicated. The controlaction can be simply implemented using the obtained NARMA-L2model based on Eq. (25) in which the functions f and g are defined.In order that a system output, y(k + 1), to follow a reference trajec-tory yr(k + 1), we set: y(k + 1) = yr(k + 1). The NARMA-L2 controlleris designed through substituting y(k + 1) with yr(k + 1) in Eq. (25).Then the resolving controller output would have the form of:

uðkÞ¼yrðkþ1Þ� f ½yðkÞ;yðk�1Þ;...yðk�nþ1Þ;uðk�1Þ;...;uðk�mþ1Þ�g½yðkÞ;yðk�1Þ;...;yðk�nþ1Þ;uðk�1Þ;...;uðk�mþ1Þ�

ð26Þ

Fig. 8 shows the block diagram of NARMA-L2 controller whichclearly a rearrangement of the NARMA-L2 plant approximatedmodel.

5. System configuration

The main objectives of the proposed NARMA controller is totrack and extract the maximum available power from PV generatorfeeding motor pump system. That is done by adjusting the suitablevalue of the duty ratio to give the maximum power. The NARMAcontroller output signal D is given by:In this controller, the armaturepower Pa is used as a feedback signal by measuring the armature

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5300

400

500

600

700

800

900

time (sec.)

Sola

r ins

ulat

ion

leve

l (W

/met

er s

quar

e)

Fig. 13. Solar insolation level variations.

Fig. 14. Dynamic responses of power due to step change in the insolation level.

Fig. 15. Dynamic responses of armature current due to step change in the insolation level.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5105

110

115

120

125

130

135

140

time (sec.)

roto

r spe

ed (r

ad/s

ec)

PIDNARMA-L2

Fig. 16. Dynamic responses of rotor speed due to step change in the insolation level.

96 A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.4

0.45

0.5

0.55

time (sec.)

duty

ratio

PIDNARMA-L2

Fig. 17. Dynamic responses of duty ratio due to step change in the insolation level.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 550

60

70

80

90

100

110

120

time (sec.)

arm

atur

e vo

ltage

(V)

PIDNARMA-L2

Fig. 18. Dynamic responses of armature voltage due to step change in the insolation level.

A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98 97

voltage and current using suitable sensors. The block diagram of thePV generator motor-pump system with the MPPT algorithm and theproposed NARMA controller is shown in Fig. 9. The entire systemhas been simulated on the digital computer using the neuralnetworks tool box in Matlab/Simulink [29] software package.

DðkÞ ¼ Pref ðkþ 1Þ � f ½PaðkÞ; Paðk� 1Þ; . . . ; Paðk� nþ 1Þ;DðkÞ;Dðk� 1Þ; . . . ;Dðk�mþ 1Þ�g½PaðkÞ; Paðk� 1Þ; . . . ; Paðk� nþ 1Þ;DðkÞ;Dðk� 1Þ; . . . ;Dðk�mþ 1Þ�Dðkþ 1Þ ð27Þ

6. Simulation results

Computer simulations have been carried out in order to validatethe effectiveness of the proposed scheme. As mentioned previouslythe Neural networks are trained offline and in batch form. We haveused five hidden layers and 10,000 sample data, which are gener-ated to train the network. 100 training epochs and employingtraining as a training function were enough to get good results.The training, validation and testing data of the ANN controllerare shown in Figs. 10–12 respectively. The PID controller parame-ters are tuned using trial and error with values of kp = 18, Ki = 2.6and Kd = 1.2.

The performance of the proposed system has been tested with astep change in solar insolation level. Thus, the solar insolation levelassumed to vary abruptly between 400 W/m2 and 800 W/m2 asshown in Fig. 13, which mean that the reference maximum powervary also abruptly between 480 watts and 635 as shown in Fig. 14.Figs. 14–18 illustrate the dynamic responses of the actual and ref-erence power, armature current, shaft speed, duty ratio and arma-ture voltage respectively for both PID controller and the proposedANN controller.

It has been noticed in the Figs. 14–18 that as the solar insolationlevel increases from 600 W/m2 to 800 W/m2, the power output ofthe PV-generator (reference power) will increase related to themaximum power algorithm, the duty ratio will increase such thatthe output power of the DC–DC converter equal the PV-generator

maximum power, also both armature current and voltage will in-crease to meet the increasing in power and by the way the motorshaft speed will increase. And vice versa if the solar insolation leveldecreases. The response of the ANN controller is compared withthe PID one for the same conditions. Tuning of the PID controllerwas done by trial and error. In addition, these figures show thatthe power delivered to the motor-pump system follow the PV max-imum output power with small settling time and with zero steadystate error. Also these figures indicate that the dynamic responsesbased on the proposed ANN controller is better than the conven-tional PID controller in terms of fast response and small maximumovershoot.

Simulation results show also that a motor pump system can besupplied from a PV-generator with the maximum available power,which is needed by the load.

7. Conclusions

In this study, the ANN controller has been used in order to de-sign a state feedback static controller for a PV pumping system. The

98 A.M. Kassem / Electrical Power and Energy Systems 43 (2012) 90–98

controlled system consists of a PV generator that supplies a DC mo-tor pump system through buck–boost DC–DC converter. The con-trol objective aims to track and operate the motor-pump systemat the MPPT of the PV generator. This is carried out via controllingthe duty ratio of the DC–DC converter. The results show that theMPPT techniques add about 38% more performance than at normalcondition. The amount of efficiency increasing is coming from thedifference of motor power with and without MPPT controller. Theresults also show that the maximum power tracker is achievedwith zero steady state error and with settling time less than onesecond and accurate tracking performance of the proposed systemhas been achieved. Also the results show that the proposed ANNcontroller has significantly better performance than the classicalPID controller.

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