modeling and simulation of a stand-alone

ARTICLE IN PRESS

Renewable Energy 32 (2007) 285–313

0960-1481/$ -

doi:10.1016/j

�CorrespoE-mail ad

skalogir@spi1Regular a

www.elsevier.com/locate/renene

Modeling and simulation of a stand-alonephotovoltaic system using an adaptive

artificial neural network: Proposition fora new sizing procedure

A. Mellita,�, M. Benghanemb,1, S.A. Kalogirouc

aDepartment of Electronics, University Centre of Medea, Institute of Science Engineering, 26000, Medea, AlgeriabUniversity of Sciences and Technologies Houari Boumadiene, Faculty of Electrical Engineering,

B. O. Box, 32; El-Alia, Bab-Ezzouar 16111, Algiers, AlgeriacDepartment of Mechanical Engineering, Higher Technical Institute, P.O. Box 20423, Nicosia 2152, Cyprus

Received 2 July 2005; accepted 5 January 2006

Available online 20 March 2006

Abstract

This paper presents an adaptive artificial neural network (ANN) for modeling and simulation of a

Stand-Alone photovoltaic (SAPV) system operating under variable climatic conditions. The ANN

combines the Levenberg–Marquardt algorithm (LM) with an infinite impulse response (IIR) filter in

order to accelerate the convergence of the network. SAPV systems are widely used in renewable

energy source (RES) applications and it is important to be able to evaluate the performance of

installed systems. The modeling of the complete SAPV system is achieved by combining the models

of the different components of the system (PV-generator, battery and regulator). A global model can

identify the SAPV characteristics by knowing only the climatological conditions. In addition, a new

procedure proposed for SAPV system sizing is presented in this work. Different measured signals of

solar radiation sequences and electrical parameters (photovoltaic voltage and current) from a SAPV

system installed at the south of Algeria have been recorded during a period of 5-years. These signals

have been used for the training and testing the developed models, one for each component of the

system and a global model of the complete system. The ANN model predictions allow the users of

SAPV systems to predict the different signals for each model and identify the output current of the

system for different climatological conditions. The comparison between simulated and experimental

see front matter r 2006 Elsevier Ltd. All rights reserved.

.renene.2006.01.002

nding author.

dresses: [email protected] (A. Mellit), [email protected] (M. Benghanem),

dernet.com.cy (S.A. Kalogirou).

ssociate member in ICTP.

www.elsevier.com/locate/renene

ARTICLE IN PRESSA. Mellit et al. / Renewable Energy 32 (2007) 285–313286

signals of the SAPV gave good results. The correlation coefficient obtained varies from 90% to 96%

for each estimated signals, which is considered satisfactory. A comparison between multilayer

perceptron (MLP), radial basis function (RBF) network and the proposed LM–IIR model is

presented in order to confirm the advantage of this model.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Stand-alone PV power system; Sizing procedure; Modeling; Simulation; Artificial neural network

1. Introduction

The technologies for power production from renewable energy sources are available andreliable. Therefore, the penetration of these technologies depends mainly on the economicfeasibility and the proper sizing of the components in order to avoid outages and ensurequality and continuity of supply. Photovoltaic (PV) technology has become one of severalpromising alternatives for use in energy technology [1–4]. Because of the high cost of PVmodules, PV generation systems are attractive only for remote isolated areas and for small-scale applications [3] such as PV refrigerators and water-pumping systems. The rapiddecrease in the PV module cost during the past few years and the recent escalation in theprice of conventional petrochemical fuels used for generating electricity, resulted in thewider employment of PV-generation systems. The advantages of using the photovoltaiceffect to generate electricity include the avoidance of pollutants emissions, silent operation,long lifetime and low maintenance requirement. Moreover, solar energy is abundant, free,clean and inexhaustible. The modeling of PV power systems is an intermediate stage thatmust precede all sizing, identification or simulation applications. Many PV systems operatein stand-alone mode. Such a system consists of a PV generator, energy storage (forexample a battery), DC to AC converters, AC and DC consumers and a powerconditioning system; a stand-alone system is not interacting with the utility grid. A PVgenerator can contain several PV arrays; each array is composed of several modules andeach module is composed of several solar cells. The battery bank stores energy when thepower supplied by the PV modules exceeds load demand and releases it back when the PVsupply is insufficient. The load of stand-alone PV system can feature many types of supply,both DC (television, lighting) and AC (electric motors, heaters, etc.). The powerconditioning system provides an interface between all the elements of a PV system and isused to give protection and control to the system. The most frequently encounteredelements of the power conditioning system are blocking diodes and charge regulators [5,6].In literature, several models have been developed for the modeling and simulation of thedifferent components of stand-alone PV power systems based on analytical or numericaltechniques [7–10]. Other simulation approaches are performed in various programmingenvironments such as Pspice, Matlab Simulinkr and Labview [11–15]. The majority ofthese approaches can simulate the SAPV based on the mathematical equations of eachcomponent of the system, and it can be used for drawing the evolution of the I–Vcharacteristic of the PV-array, state of charge (SOS) of the battery, regulatorcharacteristics and the output current or voltage curves. These models however cannotpredict or estimate the different signals (different current and voltage from eachcomponent of the system, i.e. IPV, VPV, Vb, Ibr, Vbr, Iu, Vu, etc.) of the SAPV systemsfor the next day, i.e., based on the predicted signal the performance of SAPV systems can

ARTICLE IN PRESS

Nomenclature

APV PV-generator area (m2)CS storage capacityCU useful accumulator capacityEAUXj energy supplied by the auxiliary generator in the day j

Eb storage capacity of the battery (Wh)Ebmin battery minimal threshold (Wh)Ebmax battery maximal threshold (Wh)Ec calculated errorEoc battery circuit voltage (V)EPV energy produced by the PV-generator module (Wh)EPV-T total energy produced by the generator (Wh)Es specified errorf1, f2 sizing parameters of PV systemsH average daily irradiation (Wh/m2/day)Ib battery current (A)ID normal diode current (A)IPV PV-generator current (A)Ir regulator current (V)Iu used output current (A)Iph source currentL average daily energy (Wh)LLP specified loss of load probabilityLLP calculated loss of load probabilityNMSE normalized Mean Square ErrorQm normal capacity (Ah)Rb internal resistance of battery (O)Rs series resistance (O)r1, r2 sizing parameters of PV systemsSOC state of chargeVb battery terminal voltage (V)VPV PV-generator voltage (V)Vr regulator voltage (V)

Greek

DEpv difference between produced and demand energy (Wh)Z efficiencyZPV PV-generator efficiency

A. Mellit et al. / Renewable Energy 32 (2007) 285–313 287

be analyzed. In addition, the optimal configuration of SAPV system for the next day(number of solar panel cell and storage battery) can be predicted. Generally, it is verydifficult to develop an analytical equation or numerical model capable of predicting theperformance of the PV system under the variable climatic conditions (influencing the


system) for the next day [16,17]. These systems can be considered non linear, which meansthat are very complex and is very difficult to find a suitable model by classical approaches.For this reason, we considered the artificial neural network (ANN) as a suitable approachfor such a complex system modeling [16,17]. The ANN can simulate the SAPV based on adatabase of several signals for each component of the system recorded along a 5-yearperiod. The main purpose of this study is to develop a suitable adaptive artificial neuralnetwork which could be used for the modeling and simulation of a SAPV system, whichwould improve the results presented in [16,17] and to propose a new PV-system sizingprocedure. The ANN used in this study combines the Levenberg–Marquardt algorithm(LM) with infinite impulse response (IIR) filter in order to accelerate the convergence ofthe network. The signals estimated by this model can also be used to estimate theperformance of the system. Finally, a study comparing the multilayer perceptron (MLP)[16], radial basis function (RBF) [17] and the LM–IIR network, which were used to modelthe same SAPV system, is presented and discussed.The next section presents the general mathematical model for each component of the

SAPV system. Section 3 describes the experimental SAPV system installed at the south ofAlgeria. Section 4 shows, the available data (signals) used for this simulation. Section 5presents the developed LM–IIR model while the use of the developed LM–IIR model forthe modeling and simulation of SAPV system is presented in Section 6. The new sizingprocedure proposed is described in Section 7. The simulation results are presented anddiscussed in the final section.

2. Modeling of SAPV system

In literature, there are several mathematical models available for each component ofstand-alone PV systems [6,10–12]. In this section, the mathematical model for eachcomponent of PV system is presented.

2.1. PV-generator model

In literature, there are several mathematical models available for each component of PVgenerators [5,6]. Such a generator is formed by solar cells with protective connections andsupports. In the present modeling, we focus only on the cell, module and PV array models.

2.1.1. Cells model

A solar cell is usually represented by an equivalent one-diode model [5,6] as shown inFig. 1a. The model contains a current source Iph and series resistance Rs, which representsthe resistance inside each cell and in the connection between the cells. The net current is thedifference between the photocurrent Iph and the normal diode current ID:

I ¼ Iph � ID ¼ Iph � I0 expeðV � IRÞ

mKTab� 1

� �, (1)

where m is the idealizing factor, K is the Boltzmann’s constant, Tab the absolutetemperature of the cell, e electronic charge and V is the voltage imposed across the cell. I0 isthe saturation current, which depends strongly on the cell temperature [5,6].

ARTICLE IN PRESS

+

V

-

RS

ID

NSM

VM

MS

VA

IA

(a)

(b)

(c)

Fig. 1. a. Model for a single solar cell; b. PV-module cell; and c. PV-array.


2.1.2. Module model

Cells are normally grouped into ‘modules’, which are encapsulated with variousmaterials to protect the cells and the electrical connectors from the environment. The cellsin the modules consist of NPM parallel branches, each with NSM solar cells series as shownin Fig. 1b. In order to have a clear specification of which element (cell or module), theparameters in the mathematical model are considered. The following notation is adopted


in this work; the parameters with superscript ‘M’ are referring to the PV module, while theparameters with superscript ‘C’ are referring to the solar cell. A model for the PV module isobtained by replacing each cell in Fig. 1b by the equivalent diagram from Fig. 1a. In thefollowing, the mathematical model of a PV module suggested in Refs. [4,6], is brieflydiscussed. The first advantage of this model is that it can be established to refer to the solarcell. Thus, the applied voltage at the module’s terminals is denoted by VM, while the totalcurrent generated by the module is denoted by IM. The other advantage of this model isthat it can be established to be applied only to standard modules and cells supplied by themanufacturer data. The PV modules current IM under arbitrary operating conditions canthus be described as:

IM ¼ IMSC 1� expVM � VM

OC þ RMS IM

NSMVC

� �� . (2)

2.1.3. PV-array

The modules in a PV system are typically connected in arrays, as shown in Fig. 1c whichillustrates the case of an array with MP parallel branches each with MS modules in series.The applied voltage at the array’s terminals is denoted by VA, while the total current of the

array is given by IA ¼PNP

i¼1

I i. If it is assumed that all the modules are identical and the

irradiation is the same over all modules, then the array’s current is IA ¼MPIM.

2.2. The battery storage model

Another important element of a SAPV system is the battery [5,6]. The battery isnecessary in such a system because of the fluctuating nature of the output delivered by thePV arrays. Thus, during the hours of sunshine, the PV system feeds directly the load andthe excess electrical energy is stored in the battery. During the night, or during a periodwith low solar irradiation, energy is supplied to the load from the battery. Several modelshave been presented in [5,18,19]. For each model, the following parameters are required:

(a)
Nominal capacity (qm)
This is the number of ampere hours (Ah) that can maximally be extracted from thebattery, under the predetermined discharge conditions.

(b)
State of charge (SOC)
This is the ratio between the present capacity and the nominal capacity, i.e.,SOC ¼ q=qmax. Obviously 0oSOCo1. If the SOC ¼ 1, then the battery is totally charged;otherwise, if SOC ¼ 0, the battery is fully discharged.

(c)
Charge (or discharge) regime
This parameter reflects the relationship between the nominal capacity of a battery andthe current at which it is charged (or discharged). It is expressed in hours.

ARTICLE IN PRESSA. Mellit et al. / Renewable Energy 32 (2007) 285–313 291

(d)
Efficiency
This is the ratio of the charge extracted during discharge divided by the amount of thecharge needed to restore the initial state of charging and discharging current.

(e)
Lifetime
This is the number of charge/discharge cycles the battery can sustain before losing 20%of its nominal capacity.

The battery model, which describes the relationship between the voltage, current and thestate of charge, can be found in Ref. [3]. The terminal voltage of the battery can beexpressed in terms of its open circuit voltage and the voltage across the internal resistanceof the battery [3]:

Vb ¼ Eoc þ Ib þ Rb, (3)

where Vb is the battery terminal voltage, Eoc is the battery circuit voltage, Ib batterycurrent and Rb is the internal resistance of the battery.

2.3. The regulator model

All power systems must include a control strategy that describes the interactionsbetween its components [5,6]. The use of batteries for storage implies the presence ofcharge controller. The charge controller is used to manage the PV system’s energy,batteries and loads by collecting information on the battery voltage. There are two mainoperating methods for the regulator. The first is the normal operating condition, whichoccurs when the battery voltage fluctuates between maximum and minimum voltages. Thesecond is an overcharge or over-discharge condition, in which the battery voltage reachessome critical values. To protect the battery against an excessive charge, the PV arrays aredisconnected from the system, when the terminal voltage increases above a certainthreshold Vmax_off and when the current required by the load is less than the currentdelivered by the PV arrays. PV arrays are connected again when the terminal voltagedecreases below a certain voltage Vmax_on.

2.4. The inverter model

As is well known, the PV arrays produce DC and therefore when the SAPV systemcontains an AC load, a DC/AC conversion is required. An inverter is a converter wherethe power flows from DC to AC side, i.e., having a DC voltage as input; it producesAC voltage, as output. The inverter is characterized by a power dependent efficiency. Therole of the inverter is to keep the voltage constant on the AC side, i.e., at the rated voltageof 230V, and to convert the input power Pin into the output power Pout with the bestpossible efficiency [5]. The inverter is characterized by a power-dependent efficiency Zingiven by [5]:

Zin ¼Pout

Pin¼

VacIac cosðjÞVdcIdc

, (4)

ARTICLE IN PRESS

Days

DC-load

AC-load

Ene

rgy

(Wh/

day)

Fig. 2. DC and AC load.

A. Mellit et al. / Renewable Energy 32 (2007) 285–313292

where Idc is the current required by the inverter from the DC source in order to be ableto keep the rated voltage on the AC side, Vdc is the input voltage to the inverter deliveredby the DC source, Vac and Iac are the output voltage and current, respectively.

2.5. The load model

There are two types of loads, AC and DC, determined according to the externalequipment connected to the SAPV system:

DC load—this kind of load is constant and it is used in order to supply a DC equipment.The power curve is similar to the line (see Fig. 2a).

AC load—this kind of load is variable and it needs too much energy in order to satisfy agiven consumption. The power curve is variable along the day (see Fig. 2b).

3. Description of the experimental SAPV system installed in Tahifet location (south of

Algeria)

The SAPV system, shown diagrammatically in Fig. 3 [20], is used in this study. It isinstalled at Tahifet, a site south of Algeria, with geographical coordinates of latitude 221,longitude 61 and altitude 1400m above mean sea level. The SAPV system consists of thePV-generator, regulator, battery and inverter. It is monitored with a data-acquisitionsystem in order to record the different signals.

3.1. PV Generator

The PV array employs 16 ITALSOLAR modules, which include 30 square single crystalsilicon cells each. The total peak power of the system is 720We. The PV-generator voltageis 40V (maximum), the PV-generator current is 20A (maximum) and the area of PVgenerator is 6m2.

3.2. Battery system

The battery system used in this experimental SAPV system consists of 12 accumulators,type FIMM. Each accumulator delivers 2V. These accumulators are connected in series in

ARTICLE IN PRESS

Module

PV Generator

Inverter

Ventilator65*10W

Refrigeratingapparatus

450W

Regulator

Battery2*400Ah

Refrigeratingapparatus60*10W

Lamps8x20W

IPV

VPV

Ta

Vb IbrIrb

TaHu

Iu

Tc

H Hu

Fig. 3. Block diagram of simplified SAPV installation (Tahifet).


order to ensure that the nominal voltage is 24V, and its capacity is 800Ah. The batterysystem is used to supply the stored energy during the night or during periods of low solarradiation.

3.3. Monitoring and regulation of the SAPV system

The regulator of this installation contains the different electricity measuring equipmentfor the automatic regulation of the current coming from the PV-generator and the currentdirected to the load in order to assure the correct operation of the battery. It contains also:

(a)
a voltmeter for the measurement of voltage, (b) a data acquisition system (data logger GRANT) [20] which contains several sensors for
the measurement of temperature, PV-generator voltage, PV-generator current, batteryvoltage, battery current, output current or voltage from the regulator and solarradiation.

3.4. Inverter

The inverter used in this system is characterized by its power rating of 500VA, and itsefficiency depends on the delivered load.

4. Available data

The experimental data used in this study are recorded from the data-acquisition systemof the SAPV system installed at Tahifet and correspond to 5 years of measurements. Fig. 4shows the variation of the different signals recorded from the SAPV system over the

ARTICLE IN PRESS

0 500 1000 1500 20000

20

40

Ta

(C°)

0 500 1000 1500 20000

20

40

Tc

(C°)

0 500 1000 1500 200020

25

30

Vb

(V)

0 500 1000 1500 200020

25

30

Ipv

(A)

0 500 1000 1500 20000

5

10

Iu (

A)

0 500 1000 1500 20000

5

10

0 500 1000 1500 20000

200

400

Vpv

(V

)

0 500 1000 1500 20000

10

20

Hu

(%)

0 500 1000 1500 20000

5

10

Ibr

(A)

Days

0 500 1000 1500 20000

5

Irb

(A)

Days

H (

KW

h/m

² )

Fig. 4. Different signals recorded from the Monitoring of PV system.


5 years. These are the PV generator current (IPV), battery voltage (Vb), PV generatorvoltage (VPV), caisson temperature (Tc), ambient temperature (Ta), used current (Iu),irradiation (H), humidity (Hu) and the current to and from the battery to regulator (Ibr)and (Irb).

5. Artificial neural network

Artificial neural networks (ANNs) have been successfully employed in solving complexproblems in various fields of applications such as pattern recognition, identification,classification, speech, vision and control systems. ANNs can be trained to solve problemsthat are difficult for conventional computer programs or human beings. ANNs, on theother hand, overcome the limitation of the conventional approaches by extracting thedesired information directly from the data. In the literature there are a number of differentlearning algorithms; a popular one is the back-propagation algorithm, which has differentvariants. Back-propagation training algorithms are gradient descent [21]. Gradient descent

ARTICLE IN PRESS

bk

bj

x1 x2 xn

Input layer

Hidden layer

Output layer

wiq

wij

y1 y2 yn

Input data

Output data

Bias

The weight synapses

Σz-1

v

a0

y (k)z-1 z-1

z-1 z-1 z-1

Σ

yi

a1 aM

-1

aM b

0

b1b

N-1

bN

(a)

(b)

Fig. 5. a. Architecture of neural network employed; and b. IIR filter architecture.


with momentum algorithm however, is often too slow for practical problems because itrequires small learning rates for stable learning. In addition, the success of this algorithmstrongly depends on the user specified parameters such as the learning rate and momentumconstant. Faster algorithms such as conjugate gradient, quasi-Newton and Levenberg–Marquadt (LM) use standard numerical optimization techniques [22]. These algorithmseliminate some of the disadvantages mentioned above. In this work, we have used a LMalgorithm in order to train the ANN. Fig. 5a shows the general architecture of multi-layerperceptron (MLP) employed in this study.

5.1. Levenberg– Marquadt (LM) algorithm

LM method is in fact an approximation of the Newton’s method [23]. The algorithmuses the second-order derivatives of the cost function so that a better convergence behaviorcan be obtained. In the ordinary gradient descent search, only the first-order derivativesare evaluated and the parameter change information contains solely the direction alongwhich the cost is minimized, whereas the Levenberg–Marquardt technique extracts a betterparameter change vector. Suppose that we have a function E(X) which needs to beminimized with respect to the parameter vector x. Then Newton’s method would be [24,25]

DX ¼ � r2EðX Þ� ��1

rEðX Þ, (5)


Where r2E(X) is the Hessian matrix and rE(X) is the gradient. If we assume that E(X) isthe sum of square function. Then,

EðX Þ ¼XN

i¼1

e2i ðX Þ, (6)

where e ¼ Y � Y , Y is the output signal and Y is the modeled output. Then it can beshown that:

rEðX Þ ¼ JTðX ÞeðX Þ, (7)

r2EðX Þ ¼ JTðX ÞJðX Þ þ SðX Þ, (8)

where J(X) is the Jacobian matrix:

JðX Þ ¼

@e1ðX Þ@X 1

@e1ðX Þ@X 2

. . . @e1ðX Þ@X n

@e2ðX Þ@X 1

@e2ðX Þ@X 2

. . . @e2ðX Þ@X n

..

. . .. ..

.

@eN ðX Þ@f1

@eN ðX Þ@X 2

. . . @eN ðX Þ@X n

26666664

37777775, (9)

and

SðX Þ ¼XN

i¼1

eiðX Þr2eiðX Þ. (10)

For the Gauss–Newton method it is assumed that SðX Þ � 0 and the update of Eq. (5)becomes:

rX ¼ JTðX ÞJðX Þ� ��1

þ JTðX ÞeðX Þ. (11)

The LM modification to the Gauss–Newton method is:

rX ¼ JTðX ÞJðX Þ þ mI� ��1

þ JTðX ÞeðX Þ. (12)

The parameter m is multiplied by some factor b whenever a step change would result inan increased Y(X). When a step change reduces Y(X), m is divided by b (b ¼ 10 andm ¼ 0:01). Notice that when m is large the algorithm becomes steepest descent (with step1/m), while for small m the algorithm becomes Gauss-Newton. The LM algorithm can beconsidered a trust-region modification to Gauss–Newton [24,25].

5.2. Infinite impulse response (IIR) filter

The Infinite Impulse Response filter (IIR) [26–28] used in this study is shown in Fig. 5b.This filter is connected to the neural network in cascade, in order to accelerate theconvergence of the network based on the LM algorithm. The approximate function of thefiler can be modeled by:

Y_

kðtÞ ¼

XN

i¼1

aiðwi;kÞUi þXMj¼1

bj Y_ðt� jÞV , (13)

where wi,k is the k-th weight coefficients, ai, bj are the coefficient of the filter, N is thenumber of feed-forward delays, M is the number of feedback delays, U and V are the input


and the co-input respectively. The coefficients of the network w, a and b can be calculatedby the LM-algorithm. The key step of this algorithm is the computation of the Jacobianmatrix. For the neural network-mapping problem, the terms in the Jacobian matrix can becomputed by a simple modification of the back-propagation algorithm.

6. ANN-based modeling for SAPV system

The main purpose of this section is to describe the different neural network structures,which were used for the modeling of each component of a SAPV system, i.e., the PV,generator, battery and regulator model. In these, each component of SAPV is consideredas a black box. Initially, the various signals used in the input and in the output of eachmodel (PV-generator, battery and regulator) are determined. Then the database is dividedin two parts; a set of 365� 4 patterns (corresponding to 4-years of data) which have beenused for the training of the network and a second set of 365 patterns (corresponding to1-year) which have been used for the testing and validation of each model based on theLM–IIR algorithm presented above. The algorithm consists of an adaptive neural networktopology in cascade with a local IIR block structure as shown in Figs. 5a and b. The IIRsynopsis network is used to create a double local network architecture that provides acomputationally efficient method of training the network and consequently results in aquicker learning and faster convergence [29]. The neurons of the input and output layersare fixed for each model. However, the number of hidden layers and the neurons withinthese layers are modified until satisfactory performance is obtained for each model(PV-generator, battery and regulator models). Table 1 shows the statistical coefficients ofvarious topologies tried in order to select the best architecture.

6.1. ANN-PV generator model

For the modeling of the PV-generator, the solar radiation data (H), ambienttemperature (Ta) and humidity (Hu), were used as input. The output is the voltage VPV

and current IPV from which the energy provided by the PV-generator, can be estimated.The ANN architecture employed is shown in Fig. 6 and is a 4-layer feed-forward networkwith 12 neurons in each hidden layer [16,17].

6.2. ANN-battery model

In order to model the battery, the caisson temperature (Tc), ambient temperature (Ta)and the current coming from the regulator to the battery (Irb) were used as input. Theoutputs are battery current (Ibr) and the battery voltage (Vb). The ANN architecture shownin Fig. 7 and is a 4-layer feed-forward network with 11 neurons in hidden layers [16,17].

6.3. ANN-regulator model

The regulator allows the management of energy between the load and the battery. Theinput signals for regulator model are the battery current (Ibr), PV generator’s voltage (VPV)and PV generator’s current (IPV) and battery voltage (Vb). The outputs are battery (Irb)current and used current (Iu). The ANN architecture shown in Fig. 8 and is again a 4-layerfeed-forward network with 10 neurons in each hidden layer [16,17].

ARTICLE IN PRESS

Table 1

Statistical test between actual and estimated signals of the SAPV system

ANN

structure

Mean

actual

Mean

estimated

Autocorrelation

Coefficient (%)

Variance Mean relative

error (%)

NMSE

Statistical tests of ANN-generator model

LM algorithm PV-generator current IPV(A)

3� 4� 2 4.091 4.1741 82 0.547 2.02 0.00758

3� 8� 2 4.091 4.0112 87 0.325 1.98 0.00684

3� 10� 8� 2 4.091 4.1453 91 0.451 1.31 0.00587

3� 12� 12� 2 4.091 4.1211 95 0.254 0.73 0.00430

PV-generator voltage VPV(V)

3� 4� 2 13.85 13.543 83 0.973 2.28 0.00758

3� 8� 2 13.85 14.104 85 0.932 1.89 0.00684

3� 10� 8� 2 13.85 13.732 93 0.752 0.88 0.00587

3� 12� 12� 2 13.85 13.771 96 0.712 0.60 0.00430

Statistical tests of ANN-battery model

LM algorithm Battery voltage Vb(V)

3� 6� 2 24.70 24.171 79 2.541 2.30 0.07514

3� 8� 2 24.70 24.212 82 2.514 2.10 0.00741

3� 9� 9� 2 24.70 24.341 87 2.641 1.50 0.06731

3� 11� 11� 2 24.70 24.471 91 2.314 0.93 0.00641

Current from the battery-regulator Irb(A)

3� 6� 2 1.60 1.551 75 0.541 3 0.07815

3� 8� 2 1.60 1.635 83 0.531 2 0.00741

3� 9� 9� 2 1.60 1.571 84 0.556 1.9 0.06731

3� 11� 11� 2 1.60 1.583 90 0.514 1.2 0.00641

Statistical tests of ANN-regulator model

LM algorithm Used current Iu(A)

4� 6� 2 3.65 3.791 79 0.714 3.2 0.07514

4� 8� 2 3.65 3.772 82 0.651 2.2 0.00641

4� 9� 9� 2 3.65 3.593 82 0.632 1.95 0.05731

4� 10� 10� 2 3.65 3.811 91 0.583 1.64 0.00453

Current from the regulator to battery Irb(A)

4� 6� 2 2.32 2.271 84 0.595 2 0.07514

4� 8� 2 2.32 2.282 89 0.584 1.80 0.00641

4� 9� 9� 2 2.32 2.371 89 0.564 1.39 0.05731

4� 10� 10� 2 2.32 2.292 90 0.523 1.31 0.00453

Statistical tests of ANN-Global model for SAPVP system

LM–IIR algorithm Used current Iu(A)

3� 2� 1 3.65 3.751 88 0.60 2.6 0.00684

3� 6� 1 3.65 3.742 90 0.57 2.1 0.00583

3� 8� 2� 1 3.65 3.721 92 0.53 2.0 0.00497

3� 11� 11� 1 3.65 3.753 96 0.51 1.4 0.00354


6.4. ANN-global model

The global model is a combination of the above three models which allows theidentification of the used current Iu from only the climate conditions, such as solarirradiation H, ambient temperature Ta, humidity Hu and Tc [30]. The block diagram ofANN-global model is shown in Fig. 9.

ARTICLE IN PRESS

H

Ta

Hu

IPV

VPV

First hidden layer(12 neurons)

Second hidden Layer(12 neurons)

Input layer

(3 neurons)

Output layer(2 neurons)

Fig. 6. ANN-PV generator model.


7. Proposition of a new sizing procedure of SAPV system

The size of a SAPV system is determined by the size of PV-array and accumulators.A useful definition of such dimensions relates to the load. On a daily basis, the PV-arraycapacity (CA) is defined as the ratio between average PV array energy production and theaverage load energy demand. The storage capacity (CS) is defined as the maximum energythat can be taken out from the accumulators divided by the average energy demand [31].Then,

CA ¼ZPVAPVH

L; and CS ¼

CU

L, (14)

where APV is the PV-array area, ZPV is the PV array efficiency, H is the average dailyirradiation on the PV array, L is the average daily energy consumption, CS is the storagecapacity and CU is the useful accumulator capacity. Note that CA depends on themeteorological conditions of the location, which means that the same PV array for thesame load can be ‘large’ in one site and ‘small’ in another site with lower solar radiation. Inorder to size a PV system so that it can work properly, efficiently and economically to meetthe desired load requirements under the local meteorological conditions, the characteristicperformance of each component in the PV system is required. Normally, the informationprovided about the PV modules and other components from the manufacturers is used forsizing the PV system by a rough estimation of the system output based on average values

ARTICLE IN PRESS

Irb

Ta

Tc

Ibr

Vb

First hidden layer

(11 neurons)

Second hidden Layer

(11 neurons)

Input layer

(3 neurons)

Output layer

(2 neurons)

Fig. 7. ANN-Battery model.


of daily meteorological data inputs. In the literature, different sizing methods have beenpresented [32–36]. Some of these methods are based on analytical approaches, whereas themethod presented here is based on the concept of loss of load probability (LLP) (seeAppendix A). However, both methods allow the estimation of the pair CA and CS, whichlead to the determination of the APV and CU. Other methods combine an analytical and anumerical approach in order to select the optimal parameters of stand-alone PV system(f, u) [31] (see Appendix B). In addition, these models may result in an oversized system forone location and an undersized one for another location [8]. For the oversized case, thesystem cannot have full functional operation, which results in a shortened lifetime of thesystem and higher installation costs. For the undersized case, the system may fail to supplyenough power for the appliances. Moreover, the system lifetime is also shortened. A morerecent model allows the estimating of the optimal coefficients of SAPV systems for anylocation in Algeria [37,38]. However, not all these PV system-sizing models are able toestimate the PV-array area and the useful accumulator corresponding to the next day. Inthis section, a new sizing procedure is present, which allows the prediction of the optimalsizing coefficients of SAPV systems based on predicted signals given by the ANN-globalSAPV model described in last section. Fig. 10, shows the block diagram of the stand-alonePV system incorporated with a new sizing procedure. This diagram consists of anexperimental SAPV connected with the PC via a data acquisition system. The descriptionof this procedure is shown in Fig. 11. It allows the estimation of the PV-system sizingcoefficients for the next day in very simple manner. For this procedure, the predicted

ARTICLE IN PRESS

Ibr

IPV

VPV

Vb

Irb

Iu

First hidden layer

(10 neurons)

Second hidden Layer

(10 neurons)

Input layer

(4 neurons)

Output layer

(2 neurons)

Fig. 8. ANN-Regulator model.

SAPV

System (plan)

Σ

Ta H, Hu, Tc

Iu

e(k)

Iu

+

-

ANN-SAPV

model

LM-IIR

Algorithm

Fig. 9. ANN-Global model for the SAPV system.


ARTICLE IN PRESS

SAPV system

Data-acquisition system and A/N converter

ANN programs

Sizing procedure

Predicted signals

Meteorological data

H, Ta, Hu

PC

APV

CU

RS-232

Received signals (IPV, VPV, Ibr, Vbr, Iu, …etc)

Fig. 10. Block diagram of SAPV connected with PC.


signals from the ANN-model are required in order to operate. Before explaining theprinciple of operation of this procedure, the definition of each parameter presented in thesizing procedure (Fig. 11) are given.The energy produced by the PV-array is defined by EPV ¼ VPVIPV, whereas the total

energy is given by EPV�T ¼R

nEPV dt, where n is the number of PV-array area. It can also be

given by EPV�T ¼ ZPVHAPV: Eb is the energy delivered by the battery, which can beexpressed by Eb ¼ IbrVb. The total capacity of the batteries is defined byEbT ¼

Rn

Eb dt,where m is the number of the batteries. Also the total capacity of the battery system can beexpressed by EbT ¼ ZbCu, where Zb is the efficiency and the useful capacity of the batteriesrespectively. Emax and Emin are the maximum and the minimum thresholds of the battery.In this procedure, the load L is defined by L ¼ IuVu where Iu and Vu is the used currentand voltage respectively; the voltage can be fixed at 12, 24 or 48V according to theapplication. For this procedure, a computer program was developed using Matlabr,Ver. 7, which allows the determination of the optimal sizing coefficients (APV, CU) for thePV system described above. Once the data are submitted to the PC from the dataacquisition system, via the serial bus RS-232 (CAN), the ANN program predicts thedifferent signals for the next day of the SAPV system and the sizing procedure uses thesesignals in order to determine the optimal configuration of PV system. The operation ofthe system is automatic. When the load is more than the power generated by the total PV-array, the regulator starts by extracting energy from the battery until the minimum energyof the battery is reached (Emin). If this energy is not able to satisfy the energy required bythe load then the system automatically adds some PV-array modules to the system in orderto satisfy the load required. On the contrary, if the generated energy by the total PV-arrayis more than the energy required by the load, the regulator charges the battery until themaximum power of the battery is reached. In the case where this energy is more than theenergy required by the load, the regulator automatically disconnects some PV-modules.This configuration of PV system can operate and provide the optimal parameters for thenext day based on the predicted signals by the ANN-model.

ARTICLE IN PRESS

EPV-T/L<1

Ebt/Eb>1 Eb<EbminDisconnect the

load

Eb=Eb-∆EPV

EPV-T=EPV-T-∆Eb

Start

EPV-T/EPV>1

EPV-T=EPV-T-Eb

EPV-T=EPV-T-Eb

y

y y

y

Ebt /Eb<1

Eb<Ebmax

EPV-T=EPV-T-Eb

EPV-T/EPV<1

Stop

yEPV-T=EPV-T-Eb

Disconnect theload

y

y

Read the estimated signals by ANN model(IPV, VPV, Vb, Ibr, Iu, Irb) and Load,

Print EPV-T=> APV and

Ebt=>Cu

Fig. 11. Block diagram of the proposed new sizing procedure.


8. Simulation results

In order to investigate the ability of the simulation model to predict the SAPV systemperformance, the experimental system was tested under a variety of significant operatingconditions corresponding to one year. Five years have been used to train each model andto identify the global model.

Fig. 12 shows the performance of normalized mean square error (MSE) for each model.As can be seen, each model present a good convergence and the number of epochs requiredto obtain good predictions is not more than 700. Figs. 13a–c, show the comparisonbetween actual and ANN predicted signals of the PV system. According to these figures,the simulated values are reasonably close to the observed ones except for somediscrepancies. Figs. 14a–c show the cumulative function Fx for each output signalscorresponding to the different ANN model estimations and actual signals. These curvespresent clearly the good agreement between all cumulative functions. Fig. 15 shows thenormalized MSE for the global model. From this figure, the importance of using the IIR

ARTICLE IN PRESS

0 100 200 300 400 500 600 70010-4

10-3

10-2

10-1

100

700 Epochs

Nor

mal

ized

err

or E

Performance is 0.00841092, Goal is 0.001

ANN architecture: 2x11x11x2Normalized MSE for Battery model performance

0 50 100 150 200 250 300 350 400 450 50010-4

10-3

10-2

10-1

100

101

500 Epochs

Nor

mal

ized

err

or E


ANN architecture: 3x12x12x2 Normalized MSE for PV-generator model performance

0 50 100 150 200 250 300 350 400 450 50010-4

10-3

10-2

10-1

100

500 Epochs

Nor

mal

ized

err

or E


ANN architecture: 2x10x10x2 Normalized MSE for Regulator model performance

Fig. 12. Normalized MSE for each ANN model of the SAPV system.


ARTICLE IN PRESS

1450 1500 1550 1600 1650 1700 1750 1800 1850-2

0

2

4

6

Ibr

(A)

PredictedObeserved

1450 1500 1550 1600 1650 1700 1750 1800 185018

20

22

24

26

Days

Vb

(V)

PredictedObeserved

1450 1500 1550 1600 1650 1700 1750 1800 18500

1

2

3

4

5

Irb

(A)

ObsevedPredicted

1450 1500 1550 1600 1650 1700 1750 1800 18500

2

4

6

8

Days

Iu (

A)

ObsevedPredicted

1450 1500 1550 1600 1650 1700 1750 1800 18500

2

4

6

8Ip

v (A

)ObsevedPredicted

1450 1500 1550 1600 1650 1700 1750 1800 18500

5

10

15

20

Days

Vpv

(V

)

ObsevedPredicted

(a)

(b)

(c)

Fig. 13. a. Comparison between observed and predicted signals for ANN- PV generator model; b. Comparison

between observed and predicted signals for ANN- battery model; and c. comparison between observed and

predicted signals for ANN-regulator model.



filter in order to accelerate the convergence of the network can be clearly seen as the goal oferror equal to 0.001 is obtained in 400 iterations. Fig. 16, provides a comparison betweenthe cumulative function of observed and predicted used current Iu. Fig. 17, illustrates thecomparison between measured useful current and that identified by LM–IIR network. Ascan be seen there is a good agreement between both series. Table 1 summarizes thestatistical comparison between actual and ANN estimated signals for each element of aSAPV system for different ANN structures. From this table it can be concluded thatsatisfactory results have been obtained for each model from almost all architectures but thebest results were obtained by the architectures presented in Section 6, the LM algorithmwith IIR filter. In addition, the used current Iu identified by LM–IIR gives good results.Table 2 presents a comparison between different ANN architectures (using differentalgorithms) and the LM-IIR for the global model. It should be noted that the bestperformance results are obtained by the LM-IIR model. However, the RBF-IIR and the

0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cum

ultiv

e fu

nctio

n F

x

Measured Ipv

ANN estimated Ipv

4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cum

ulat

ive

finct

ion

Fx

Measured Vpv

ANN estimated Vpv

PV-array current IPV

PV-array voltage VPV

(a)

Fig. 14. a. Cumulative functions of measured and ANN estimated IPV and VPV; b. Cumulative functions of

measured and ANN estimated Ibr and Vb; and c. Cumulative functions of measured and ANN estimated Iu and Irb.

ARTICLE IN PRESS

0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Measured Ibr

ANN-estimed Ibr

20 21 22 23 24 25 26 27 28 29 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Measured VbANN-estimed Vb

Cum

ulat

ive

func

tion

Fx

Cum

ulat

ive

func

tion

Fx

Current Ibr

Voltage battery Vb

(b)

Fig. 14. (Continued)


MLP also present acceptable results. In order to validate the new sizing procedure theexperimental sizing parameters of the SAPV system installed at the south of Algeria(Tahifet) have been used. The parameters considered are the PV-array area (APV) and theused storage capacity (CU) which are determined by an empirical technique. Table 3 gives acomparison of the results obtained between the classical methods and the proposedprocedure. According to Table 3 the results obtained by this procedure are generallysatisfactory compared to the other methods such as the analytical, numerical and hybrid.The mean relative error (MRE) between the experimental and ANN results estimated byour model is between 2.5% and 8.5%. The advantage of the present procedure is that thesizing parameters of SAPV system in the next day are estimated based on predicted signalsby the ANN model. This prediction permits the avoidance of anomalies in systemoperation, which can result from the bad sizing of the system. None of the other modelscan estimate these parameters for the next day.

ARTICLE IN PRESS

Current Irb

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cum

ultiv

e fu

nctio

n F

x

Measured IuANN-estimed Iu

1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cum

ultiv

e fu

nctio

n F

x

Measured IrbANN-estimed Irb

Used current Iu

(c)

Fig. 14. (Continued)

0 50 100 150 200 250 300 350 40010-4

10-3

10-2

10-1

100

101

Epochs

Nor

mal

ized

err

or E


Fig. 15. Normalized error for ANN-global model.


ARTICLE IN PRESS

1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cum

ultiv

e fu

nctio

n F

x

Measured Iu (A)ANN estimated Iu (A)

Used current Iu

Fig. 16. Cumulative function for global model (Iu).

1 2 3 4 5 6 71

2

3

4

5

6

7

Measured Iu (A)

AN

N-id

entif

ied

I u (

A)

R²=96%

Fig. 17. Comparison between measured and identified Iu by LM–IIR model.


9. Conclusions

In this paper, a suitable adaptive artificial neural network has been developed for themodeling and simulation of a SAPV system. The ANN combines the LM algorithm withIIR filter in order to accelerate the conversion of the network. The developed ANN models(ANN-generator, ANN-battery and ANN-regulator) can predict the different signals fromthe output of each component of the system within acceptable limits of accuracy givenfrom a comparison between the observed and experimental signals. In addition, the ANN-global model of SAPV can identify the current used by the load of the system, based onlyon solar radiation, ambient temperature and the humidity. This simulation has beenperformed by using a database of different experimental signals recorded from the data-acquisition system of the SAPV installed at the south of Algeria. It can be concluded thatthe proposed model can be used to predict the required system parameters in differentweather conditions. In addition, a new proposed sizing procedure has been presented

ARTICLE IN PRESS

Table 2

Training results for various ANN architecture for global model

ANN architectures Algorithm NMSE performance Number of iteration

RBF

4� 5� 1 Gradient descent back-propagation 0.0236 850



RBF–IIR

4� 10� 1 Gradient descent back-propagation

with IIR filter

0.0095 460

MLP

4� 8� 1 Gradient descent back propagation 0.0354 980

4� 11� 1 FGS quasi-Newton back-

propagation

0.0125 1000

4� 10� 1 Gradient descent with adaptive

learning rate back-propagation

0.0254 840

4� 12� 1 Gradient descent with momentum

and adaptive learning rate back-

propagation

0.0098 860

4� 10� 1 Levenberg–Marquardt back-

propagation

0.0042 700

MLP-IIR

4� 11� 11� 1 Levenberg–Marquardt back-

propagation with IIR filter

0.0034 500

Table 3

Comparison between different sizing model and a new procedure

LLP ¼ 1%, H ¼ 6kWh=m2=day, Zpv ¼ 10%

Sizing method Sizing coefficients PV-generator and battery sizing Mean relative error

Analytic CA CS APV (m2) CU (Wh) % (Apv) %(Cu)

1.65 0.405 5.50 810 9.1 2

Numeric CA CS

1.66 0.398 5.54 792 8.30 1.2

Hybrid f u

1.68 0.4 5.6 — 7.14 —

New sizing procedure Epvt Ebt

3318 781 5.53 781 8.5 2.5

Experimental sizing — — 6 800 — —


based on estimated signals by the ANN model. This procedure has an advantage comparedto the other classical models (analytic, numeric and hybrid) as it can predict the futureoptimal configuration (sizing) of the SAPV. This is proved by the results obtained, whichindicate that the accuracy of the comparison between the measured and estimated sizingpair (APV, CU) is acceptable. On the contrary, the other numerical or analytical models


need several parameters, which are not always available. Additionally, the predictedsignals can be used in:

(a)
Analyzing the performance of SAPV systems [39]. (b) Sizing and control of SAPV systems [40,41]. (c) Studying of the cumulative energy stored in the battery [39]. (d) Predict an optimal configuration of SAPVP system for the next day (number of solar
panels, number of batteries and inclination of the PV generator) [30].
(e) Control the maximum power point tracker (MPPT) [42]. (f) Development of a new configuration of SAPV system [30].
Finally, this methodology offers the possibility to implement an expert system circuitthat can be added to the PV system in order to control each electrical signal for the SAPVsystem.

Acknowledgements

The first author would like to thank Prof A. Guessoum (Supervisor research in BlidaUniversity) and Dr. Hadjarab (Supervisor research in Renewable Energy Centre ofAlgiers) for their help.

Appendix A

The state of the charge of the battery, at the end of the day j is given by:

SOCj ¼ min SOCj�1 þZPVAPVH

CU

� �(A1)

The auxiliary generator is managed in such a way that, at the end of day j it keepsthe battery fully charged if the stored energy is lower than the load requirements.Then,

SCCjXC�1S ) EAUXJ ¼ 0,

SCCjpC�1S ) EAUXJ ¼ 1� SOCj

� � L

CS; and SOCJ ¼ 1.

The LLP value corresponding to the SAPV systems is given by:

LLP ¼XN

j¼1

EAUXj= NjL� �

.

Appendix B

The relation binding the capacity of a PV generator to the capacity of storage is given bythe following expression:

CA ¼ fC�rS ,


where f and r are the parameters which depend on the LLP by a simple regression of thetype:

f ¼ f 1 þ f 2 LogðLLPÞ; and r ¼ exp r1 þ r2 LLPð Þ.

References

[1] Winter CJ, Sizman RL, Vant-hull LL. Solar power plants. USA: Springer-Verlag; 1989.

[2] Markvart T. Solar electricity. Chichester: Wiley; 1994.

[3] Sukamongkol Y, Chungpaibulpatana S, Ongsakul W. A simulation model for predicting the performance of

a solar photovoltaic system with alternating current loads, Renewable Energy 2002;27:237–58.

[4] Rajapakse A, Chungpaibulpatana S. Dynamic simulation of a photovoltaic refrigeration system, RERIC

1994;16(3):67–101.

[5] Hansen D, Sorensen P, Hansen Lars H, Henrik B. Models for a stand-alone PV system. Rio-R-1219 (EN)/

SEC-R-12, 2000.

[6] Lorenzo E. Solar electricity engineering of photovoltaic systems. Spain: Artes Graficas, S.L.; 1994.

[7] Exell RHB, Saligupata C. A computer model for stand-alone domestic photovoltaic systems. In: Proceedings

of the second Asian renewable energy conference. Phuket, Thailand, 1979.

[8] Wrixon GT, McCrathy S. Optimization and analysis of photovoltaic system using a computer model Proc

IEEE 1988;2:1293–7.

[9] Mayer D, Nolay P. Analyze and design methods of Photovoltaic systems. In: Proceedings of the Fifth

international E.C. photovoltaic solar energy conference. Italy: Klawer Academis; 1988. p.406-10.

[10] Hasti DF. Photovoltaic power system application, IEEE power engineering review, Sandia National

Laboratories, 1994. p.8-19.

[11] Negro E. PVDIM: PC program for PV simulation and sizing, EPSEC, vol. 12, 1994. P. 1707-10.

[12] Coupti JB, Lorenzo E, Chenlo F. A general battery model for PV system simulation; Progress in

photovoltaics 1993;1:283–92.

[13] Koutroulis E, Kalaitzakis K. Development of an integrated data-acquisition system for renewable energy

systems monitoring. Renewable Energy 2003;28:139–52.

[14] Gow JA, Manning CD. Development of a photovoltaic array model use in power electronics simulation

studies. IEE Proc Electr Power Appls 1999;146(2):193–200.

[15] Gergraud O, Multon B, Ben AH. Analysis and experimental validation of various photovoltaic system

models. In: Proceedings of the 7th International ELECTRIMACS congress, Montreal, 2002.

[16] Mellit A, Benghanem M, Salhi H. An Adaptive Artificial Neural Network for Modeling and Simulation of a

Stand-Alone Photovoltaic Power System. In: Proceedings of the 3th conference on systems, signals, and

devices. IEEE 2005;4:257.

[17] Mellit A, Benghanem M. Modeling and simulation of stand-alone power system using artificial neural

network. Solar world congress. ISES/ASES 2005.

[18] Manwell J, McGowan JG. Lead acid battery model for hybrid energy system. Sol Energy 1993;50(5):

399–405.

[19] Coptti JB, Lorenzo E, Chenlo F. A general battery model for PV system simulation. Prog Photovoltaics

1993;1:283–92.

[20] Sonelgaz (National Society of Electric and Gas), (ENEL) CREL. Description and instructions for use of the

photovoltaic equipment. Norm for the installation of data acquisition system (GRANT). Installation and

function of the GRAND system. 2000.

[21] Haykin S. Neural Networks: a comprehensive foundation. New York: MacMillan; 1994.

[22] Hagan MT, Menhaj MB. Training feed-forward networks with the Maruardt algorithm. IEEE Trans Neural

Network 1994;5(6):989–93.

[23] Marquardt D. An algorithm for least squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math.

1963:431–41.

[24] Battiti R. First and second order methods for learning: between steepest descent and Newton’s method.

Neural Comput 1992;4(2):141–66.

[25] Hagan MT, Menhaj MB. Training feed-forward networks with the Marquardt algorithm. IEEE Trans

Neural Network 1994;5(6):989–93.


[26] Ji-Nan L, Unbehaen R. Bias-remedy least mean square equation error algorithms for IIR parameter

recursive estimation. IEEE Trans Signal Process 1992;40(1):62–9.

[27] Pasquato L, Kale I. Adaptive IIR filter initialization via hybrid FIR/IIR adaptive filter combination. IEEE

Trans Instrum Meas 2001;50(6):1830–5.

[28] Mellit A, Benghanem M, Hadj A, Guessoum A, Moulai K. Neural network adaptive wavelets for sizing of a

stand-alone PV system. Second IEEE International Conference on Intelligence Systems 2004;1:365–70.

[29] Lekutai G, Vanlandingham HF. Self-tuning control of nonlinear systems using neural network adaptive

frame wavelets. International Conference on Computational Cybernetics and Simulation 1997;2:1017–22.

[30] Mellit A, Benghanem M, Guessoum A. An expert structure of photovoltaic power supply system by using

artificial neural network. In: Proceeding of the 3th conference on systems, signals, and devices. IEEE

2005;4:258.

[31] Egido M, Lorenzo E. The sizing of sand-alone PV systems: a Review and a proposed new method. Solar

Energy Mater Sol Cells 1992;26:51–69.

[32] Klein SA, Beckman WA. Loss of load probabilities for stand-alone PV. Solar Energy 1987;39:499–505.

[33] Bara L, Catalakoti S, Fontana F, Lavorane F. A analytical method to determine the optimal size the

photovoltaic plant. Sol Energy 1984;6:509–14.

[34] Shrestha GB, Goel L. A study on optimal sizing of stand-alone photovoltaic stations. IEEE Trans Energy

Convers 1998;13(4).

[35] Abouzahr I, Ramaknmar R. Loss of power supply probability of stand-alone photovoltaic systems: a closed

form approach. IEEE Trans Energy Convers 1991;6(1).

[36] Maghraby HAM, Shwehli MH, Ghassan K, Al-Bassam GK. Probabilistic assessment of photovoltaic (PV)

generation systems. IEEE Trans Power Energy 2002;17(1):205–8.

[37] Mellit A, BenghanemM, Hadj A, Guessoum A. Modeling of sizing the photovoltaic system parameters using

artificial neural network. Proc IEEE Conf Control Appl 2003;1:353–7.

[38] Mellit A, Benghanem M, Hadj A, Guessoum A. An adaptive artificial neural network for sizing of stand-

alone photovoltaic systems: application for isolated sites in Algeria. Renewable Energy 2005;30(10):1501–24.

[39] Mellit A, Benghanem M, Hadj A, Guessoum A. Prediction and modeling signals from the monitoring of

stand-alone photovoltaic systems using an adaptive neural network model. In: Proceedings of the 5th ISES

European solar conference. 2004; 3: 224–230.

[40] Mellit A, Benghanem M, Hadj A, Guessoum A. Use a fuzzy-logic controller for control of stand-alone

photovoltaic systems. In: Proceedings of the IEEE, 12th Mediterranean conference on control and

automation. June 6–9 2004. Kusadaci, Turkey.

[41] Henze GP, Ddier RH. Adaptive optimal control of grid-independent photovoltaic system. ASME J Sol

Energy Eng 2003;125:35–43.

[42] Himaya T, Kitabayashi K. Neural network based estimation of maximum power generation from the PV

module using environment information. IEEE Trans Energy Convers 1997;12(3):241–7.

modeling and simulation of a stand-alone

Documents