research article data-driven photovoltaic system modeling...

Research ArticleData-Driven Photovoltaic System Modeling Based onNonlinear System Identification

Ayedh Alqahtani1 Mohammad Alsaffar2 Mohamed El-Sayed2 and Bader Alajmi1

1Electrical Engineering Department Public Authority for Applied Education amp Training (PAAET) 42325 Kuwait Kuwait2Electrical Engineering Department Kuwait University 42325 Kuwait Kuwait

Correspondence should be addressed to Ayedh Alqahtani aalqahtanipaaetedukw

Received 11 March 2016 Revised 6 June 2016 Accepted 14 June 2016

Academic Editor Prakash Basnyat

Copyright copy 2016 Ayedh Alqahtani et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Solar photovoltaic (PV) energy sources are rapidly gaining potential growth and popularity compared to conventional fossil fuelsources As the merging of PV systems with existing power sources increases reliable and accurate PV system identification isessential to address the highly nonlinear change in PV system dynamic and operational characteristics This paper deals withthe identification of a PV system characteristic with a switch-mode power converter Measured input-output data are collectedfrom a real PV panel to be used for the identification The data are divided into estimation and validation sets The identificationmethodology is discussed A Hammerstein-Wiener model is identified and selected due to its suitability to best capture the PVsystem dynamics and results and discussion are provided to demonstrate the accuracy of the selected model structure

1 Introduction

The modern power system is increasingly taking advantageof renewable energy sources entering the marketplace Tra-ditional central power stations with their pollution relatedproblems will likely be replaced with cleaner and smallerpower plants closer to the loads The energy generated bythe sun is one of the most promising nonpolluting freesources of energy [1] Among their benefits solar-poweredsystems are easily expanded Despite their still relatively highcost photovoltaic (PV) systems installed worldwide show anearly exponential increase [2] A PV cell directly convertssunlight into electricity and the basic elementary device ofPV systems is the PV cell [3] PV systems have proven thatthey can generate power to very small electronic devices upto utility-scale PV power plants The basic building blockfor PV systems is a PV panel consisting of a number ofprewired cells in series [4] Panels are then connected inseries to increase voltage and in parallel to increase currentthe product is power A PV array is formed by series andparallel combinations of panels [5] Figure 1 represents ageneric PVarray structureTheperformance of a PV system isnormally evaluated under the standard test condition (STC)

where an average solar spectrum at 15 Air Mass (AM) isused the irradiance is normalized to 1000Wm2 and thecell temperature is defined as 25∘C [6] However underreal operating conditions (ie varying irradiance as well assignificant temperature changes) most commercial panelsdo not necessarily behave as in the specifications given bythe manufacturers [7 8] In addition PV panels performdifferently according to the location time of day and seasonof the year

For PV system the relationship between environmentalconditions and electrical output parameters (current andvoltage) is highly nonlinear For this reason the process ofmodeling the dynamics of the PV system and identifying themodel structure that captures real-life behavior is extremelyessential for the purpose of controlling the output powerAnother important purpose is to predict future performanceof the system for maintenance and troubleshooting

Modeling and simulation of PV systems have been thesubject of many research studies [3 9ndash12] However thefocus of the studies was on the PV panelarray stage withoutincluding the power electronics of the complete systemmdashthat is identifying only the nonlinear I-V characteristic of

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2016 Article ID 2923731 9 pageshttpdxdoiorg10115520162923731

2 International Journal of PhotoenergyPa

nels

conn

ecte

d in

serie

s

Panels connected in parallel

Panel Cell

IArray

VArraymiddot middot middot

Figure 1 Generic PV array structure

the PV system In this work the PV system identificationincorporated the entire setup considering a PV system powerconverter maximum power point tracker (MPPT) and aload

Identification of linearnonlinear systems became a hottopic in the 1960s probably because proper models wereneeded to design good controllers [13] At this stage the sys-tem identification fieldwas rather immatureThefirst attemptto put the field into order was the published pioneeringwork of Eykhoff [14] Afterward the field became completelystructured when the books of Ljung [15] and Soderstrom andStoica [16] laid out a complete theoretical framework andpractical methodology to the identification process

The core of the system identification process is to con-struct a mathematical model from observed input-outputdata It is widely applied in different engineering disciplinesto help understand the studied process predict the systemresponses and create better design with new specifications

This work is organized as follows Section 2 presentsa description of the studied PV system Section 3 detailsthe system identification methodology Section 4 discussesthe results associated with implementing the PV systemidentification from applied input-output data dividing thedata into estimation and validation sets Finally Section 5concludes the work

2 PV System Description

The PV system illustrated in Figure 2 is considered forthis study The PV panel performance is affected by sev-eral environmental conditions however irradiance has thestrongest impact on the panel output power The panel is amultipurpose module consisting of 36 polycrystalline siliconcells connected in series Under STC the open circuit voltage(119881oc) is 216 V the short circuit current (119868sc) is 516 A themaximum power voltage (119881mp) is 173 V and the maximumpower current (119868mp) is 463A Figure 3 presents the I-V andP-V characteristics under different irradiances These dataare obtained experimentally [17] and they are not the data

IPV PPV

minus

PV panel

DCDCbuck converter

MPPTcontroller

Voltage and current measurements

Load

Power

+Environmental

condition

Input Output

t (s) t (s)

Figure 2 PV panel MPPT DCDC buck converter and a DC load

G = 1200 Wm2 Vmax = 166 V

G = 1000 Wm2 Vmax = 171 V

G = 800 Wm2 Vmax = 175 V

G = 600 Wm2 Vmax = 177 V

G = 400 Wm2 Vmax = 179 V

G = 400 Wm2 Pmax = 308 WG = 600 Wm2 Pmax = 477 WG = 800 Wm2 Pmax = 649 WG = 1000 Wm2 Pmax = 825 WG = 1200 Wm2 Pmax = 100 W

1

2

3

4

5

6

7

Curr

ent (

A)

5 10 15 200Voltage (V)

0

20

40

60

80

100

120

Pow

er (W

)

5 10 15 200Voltage (V)

Figure 3 I-V and P-V characteristic of the PV panel at 119879 = 2515∘C

that will be used for the system identification procedurenevertheless prior information about the system is beneficialWhatwe are interested in is the currentmeasurement as inputand the power measurement as output with respect to timeas indicated in Figure 2

The I-V and P-V characteristic curves show the standardPV panelarray behavior as the irradiance increases the

International Journal of Photoenergy 3

panel current is directly proportional to the solar intensityper unit area Cutting the irradiance in half leads to a dropin current by half Decreasing irradiance also reduces voltagebut it does so following a logarithmic relationship that resultsin a relatively modest change of voltage

In general the operating point of the PV panel is not themaximum power point (MPP) along the I-V curve at whichthe panel operates with maximum efficiency and producesmaximum power Thus a switch-mode power converter(DCDC buck converter in our case) with aMPPT is utilizedto maintain the PV panel operating point at the MPP TheMPPT controller retains this operating point by controllingthe PV panelrsquos voltage or current independently of those ofthe load

Depending on the application the DCDC converterstage could be a buck converter boost converter or buck-boost converter Several MPPT control algorithms havebeen proposed in different publications Perturbation andobservation (PampO) or the hill climbing algorithm is the mostcommonly employed method in commercial PVMPPTs [18ndash22] Among other control mechanisms for MPPT are fuzzylogic [23ndash27] neural network [28ndash32] and incremental con-ductance (IncCond) control [33ndash37]The IncCond algorithmis adapted in this study because it is more convenient andlends itself well to DSP and microcontroller control

3 Identification Methodology

In this section the principle of system identification isdescribed Dynamic models depend heavily on the amountof a priori knowledge about the dynamic process that is to beincorporated Generally modeling any dynamical system canbe categorized into two approaches first-principle modelingand data-driven modeling

First-principle modeling uses an understanding of thesystemrsquos physics to derive a mathematical representationwhereas data-driven modeling involves using empirical datato construct a model for the system The two approachesclassify the modeling process in terms of known parametersand structure into black box grey box and white boxmodeling as suggested by Figure 4

According to [38] white box modeling is when a modelis perfectly known it is possible to construct the modelentirely from prior knowledge and physical insight Greybox modeling is when some physical insight is available butseveral parameters remain to be determined from observeddata In black box modeling no physical insight is availableor used but the chosen model structure belongs to candidatemodels that are known to have good flexibility and have beensuccessful in the past

The black box modeling is used for this work It is usuallya trial-and-error process where one estimates the parametersof various structures and compares the resultsThePV systemconstructed and implemented in Figure 2 is used for data col-lection purposes The measured input-output data will thenbe utilized to select model structure and identify the system

31 The PV System Identification Process Figure 5 illustratesthe measured data collected to be used for the system

Black box

Grey box

White box

Unknown

Structure

Structure

Structure

Structure

Structure

Parameter

Parameter

Parameter

Parameter

Parameter

Known

Figure 4 Classification of dynamical systems by model structureand parameter

0 1 2 3 4 5 6 7 8 9 10

80

1

2

3

4

Curr

ent (

A)

20

40

60

Pow

er (W

)

1 2 3 4 5 60 8 9 107Time (sec)

Time (sec)

Figure 5 Measured input-output data for the PV system

identification The measured input-output data were takenfrom the PV system setup shown in Figure 2 When theirradiance is changingwith time the outputmaximumpowerwill vary according to themaximumpower values in Figure 3The STC (1000Wm2) power is 825W for the selectedpanel The irradiance fluctuates thereby causing the inputcurrent outputted from the panel to change This results incontinuous change of the output power of the system

The flowchart in Figure 6 summarizes the identificationprocess using the measured data The input-output data area sampled time domain signal The next step is to selecta suitable structure for the model Selecting the modelstructure is themost difficult step in the identification processbecause there are a multitude of possibilities Next one canuse the Matlab System Identification Toolbox and comparemodels to choose the model with the best performance Thefinal step is to evaluate the resulting model with a validationdata set It is worth mentioning that system identification

4 International Journal of Photoenergy

Start

Collect input-outputdata

Select a modelstructure

Find best modelin a structure

Evaluated resultacceptable

Yes

End

No

Figure 6 Flowchart for system identification procedure

u(t)Input

nonlinearityf

y(t)Liner block

BFh

nonlinearityOutput OutputInput x(t)w(t)

Figure 7 Hammerstein-Wiener nonlinear model structure

is not a straightforward technique rather it is an iterativeprocedure involving several decisions to be made during theprocess

32Hammerstein-WienerModel Anonlinear block-orientedmodel is frequently applied for an adequate description ofthe nonlinear behavior of a system over a range of operatingconditions The identified system is generally subdividedinto a linear dynamic block and a nonlinear static blockThe Hammerstein-Wiener model is a nonlinear model thatis used in many domains for its simplicity The model ispopular because it has convenient block representation hasa transparent relationship to linear systems and is easier toimplement than heavy-duty nonlinear models such as neuralnetworks and Volterra models It can be used as a black boxmodel structure because it offers flexible parameterization fornonlinear models The model describes a dynamical systemusing one or two static nonlinear blocks in series with a linearblock Only the linear block contains dynamic elements Thelinear block is a discrete-time transfer function and the non-linear blocks are implemented using nonlinearity estimatorssuch as saturation wavelet and dead zone Figure 7 depictsthe structure of the nonlinear Hammerstein-Wiener model

The input signal passes through the first nonlinear block alinear block and a second nonlinear block to produce theoutput signal [39]

The Hammerstein-Wiener structure can be described bythe following general equations

119906 (119905) = 119891 (119906 (119905))

119909 (119905) =

119861119895119894(119902)

119865119895119894(119902)

119908 (119905)

119910 (119905) = ℎ (119909 (119905))

(1)

where 119906(119905) and 119910(119905) are the inputs and outputs for the systemrespectively 119891 and ℎ are nonlinear functions that correspondto the input and output nonlinearities respectively Formultiple inputs and multiple outputs 119891 and ℎ are definedindependently for each input and output channel 119908(119905) and119909(119905) are internal variables that define the input and output ofthe linear block respectively119908(119905) has the same dimension as119906(119905) 119909(119905) has the same dimension as 119910(119905) 119861(119902) and 119865(119902) inthe linear dynamic block are linear functions For 119899119910 outputsand 119899119906 inputs the linear block is a transfer function matrixcontaining entries in the following form

119861119895119894(119902)

119865119895119894(119902)

(2)

where 119895 = 1 2 119899119910 and 119894 = 1 2 119899119906 If only the inputnonlinearity is present the model is called a Hammersteinmodel If only the output nonlinearity is present the model iscalled a Wiener model

The available nonlinearity estimators to be used in theidentification process by estimating the parameters of theinput and output blocks are dead zone piecewise linearsaturation sigmoid network and wavelet network [40]

321 Dead Zone Function The dead zone function generateszero output within a specified region that is called the deadzone The lower and upper limits of the dead zone arespecified as the start and the end of the dead zone parametersrespectively The dead zone defines a nonlinear function 119910 =

119891(119909) where 119891 is a function of 119909 There are three intervalswhich can be identified as follows

119891 (119909) = 119909 minus 119886 119909 lt 119886

119891 (119909) = 0 119886 le 119909 lt 119887

119891 (119909) = 119909 minus 119887 119909 ge 119887

(3)

119891(119909) = 0 when 119909 has a value between 119886 and 119887 this zone iscalled the ldquozero intervalrdquo zone See Figure 8

322 Piecewise Linear Function The piecewise linear func-tion is defined as a nonlinear function 119910 = 119891(119909) where 119891is a piecewise linear (affine) function of 119909 and there are 119899

breakpoints (119909119896 119910119896) where 119896 = 1 119899 and 119910

119896= 119891(119909

119896) 119891

is linearly interpolated between the breakpoints 119910 and 119909 arescalars


F(x) = x minus a

F(x) = x minus bF(x) = 0

x lt a a le x lt b x ge b

a b

Figure 8 Dead zone function

F(x) = a F(x) = bF(x) = x


a b

Figure 9 Saturation function

323 Saturation Function The saturation function can bedefined as a nonlinear function 119910 = 119891(119909) where 119891 is afunction of 119909 There are three intervals as shown in Figure 9and they can be identified as follows

119891 (119909) = 119886 119909 lt 119886

119891 (119909) = 119909 119886 le 119909 lt 119887

119891 (119909) = 119887 119909 ge 119887

(4)

324 Sigmoid Network Function The sigmoid network non-linear estimator uses neural networks comprising an inputlayer an output layer and a hidden layer employing sigmoidactivation functions as represented by Figure 10

It combines the radial basis neural network functionusing a sigmoid as the activation function The estimator isbased on the following expression

119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119891 ((119906 minus 119903)119876119887

119894minus 119888119894) + 119889 (5)

where 119906 is the input and 119910 is the output 119903 is the regressor119876 isa nonlinear subspace and 119875 is a linear subspace 119871 is a linearcoefficient 119889 is an output offset 119887 is a dilation coefficient 119888is a translation coefficient and 119886 is an output coefficient 119891 isthe sigmoid function given by the following equation

119891 (119911) =1

119890minus119911 + 1 (6)

Input layer Hidden layer Output layer

Input (u) Output (y)

Weights Weights

Activation function

Figure 10 Sigmoid network function

325 Wavelet Network Function The wavelet estimator isa nonlinear function combining wavelet theory and neuralnetworksWavelet networks are feedforward neural networksusing a wavelet as an activation function based on thefollowing expression

119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119904119894lowast 119891 (119887119904 (119906 minus 119903)119876 + 119888119904)

+

119899

sum

119894

119886119908119894lowast 119892 (119887119908

119894(119906 minus 119903)119876 + 119888119908

119894) + 119889

(7)

where 119906 is the input and 119910 is the output 119876 is a nonlinearsubspace and 119875 is a linear subspace 119871 is a linear coefficient119889 is an output offset 119886119904 is a scaling coefficient and 119886119908 isa wavelet coefficient 119887119904 is a scaling dilation coefficient and119887119908 is a wavelet dilation coefficient 119888119904 is a scaling translationcoefficient and 119888119908 is a wavelet translation coefficient Thescaling function 119891(sdot) and the wavelet function 119892(sdot) are bothradial functions and can be written as follows

119891 (119906) = 119890minus05lowast119906

1015840lowast119906

119892 (119906) = (dim (119906) minus 1199061015840lowast 119906) lowast 119890

minus05lowast1199061015840lowast119906

(8)

In the system identification process the wavelet coefficient119886 the dilation coefficient 119887 and the translation coefficient 119888are optimized during model learning steps to obtain the bestperformance model

4 Results and Discussion

Asmentioned earlier in Section 3 themeasured input-outputdata collected in Figure 5 are the system identification datato be used for the estimation Table 1 shows the values ofirradiance current and power with time for the PV system

Once the identification process results in finding the bestmodel in a structure another data set (validation data) is usedto validate the model The identification procedure followsthe flowchart steps in Figure 6

41 Model Estimation Table 1 represents the variation inpower for the data set collected for the estimation The time


System identification

Parametric model

Linear model Nonlinear model

(i) Autoregressive (AR)(ii) Autoregressive exogenous

(iii) Box-Jenkins (BJ)(iv) Linear state space (LSS)(v) Laplace transfer function (LTF)

(vi) Output error (OE)(vii) Autoregressive moving average

exogenous (ARMAX) model

(i) Nonlinear output error (NOE)(ii) Nonlinear Box-Jenkins (NBJ)

(iii) Nonlinear state space (NSS)(iv) Nonlinear autoregressive exogenous

(NARX) model(v) Hammerstein-Wiener

(vi) Nonlinear autoregressive movingaverage exogenous (NARMAX)

(ARX) model

model

(a)

Estimated (7748) Measured

10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(b)

Estimated (9451)Measured

10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(c)

Validated (9398) Measured

20

30

40

50

60

70

80Po

wer

(W)

1 2 3 4 5 6 7 8 9 100Time (sec)

(d)

Figure 11 (a) System identification classifications (b) Power output for the identified nonlinear ARXmodel with the estimation data set (c)Power output for the identified Hammerstein-Wiener model with the estimation data set (d) Power output for the identified Hammerstein-Wiener model with the validation data set

Table 1 Variation in power for the data set collected for theestimation

Irradiance (Wm2) Current (A) Power (W) Time (s)400 178 308 6ndash8500 231 393 2ndash4600 285 477 0ndash2600 285 477 8ndash10800 375 649 4ndash6

domain data in Figure 5 are imported to the system identifica-tion toolbox in Matlab Such a toolbox integrates techniquesfor nonlinear and linear models so that the complex problem

of estimating and analyzing nonlinear models appears simpleand systematic

In our case a model is to be identified for the PV systemfrom the current data as input to the system and the recordedpower is to be identified as the system output A nonlinearautoregressive exogenous (NARX) model was selected as areference pointThere are several models that can be selectedfrom the toolbox Figure 11(a) demonstrates the availableclassifications of system identification however discussingthe detail of each one is beyond the scope of this paper

Figure 11(b) shows the result of a nonlinear ARX modeltype with wavelet network nonlinearity The figure indicatesthe model output matches the measured output with 7748accuracy However this match does not best describe the


Table 2 Best fit with different input and output nonlinearity

Hammerstein-Wiener modelInput nonlinearity Output nonlinearity Final predicted error (FPE) Loss function Best fit ()Piecewise linear Piecewise linear 6723 6723 8025Piecewise linear Sigmoid network 5036 5036 8611Piecewise linear Saturation 1751 1751 9283Piecewise linear Dead zone 1023 1023 9224Piecewise linear Wavelet network 2083 2082 8811Sigmoid network Piecewise linear 1265 1265 7794Sigmoid network Sigmoid network 3547 3547 8105Sigmoid network Saturation 2016 2016 8945Sigmoid network Dead zone 4952 4951 8537Sigmoid network Wavelet network 01694 01693 6309Saturation Piecewise linear 1262 1262 9222Saturation Sigmoid network 1199 1199 9244Saturation Saturation FE FE FESaturation Dead zone FE FE FESaturation Wavelet network 07606 07601 8583Dead zone Piecewise linear 03974 03974 934Dead zone Sigmoid network 1464 1464 9398Dead zone Saturation FE FE FEDead zone Dead zone FE FE FEDead zone Wavelet network 02972 02972 9086Wavelet network Piecewise linear 1717 1716 9142Wavelet network Sigmoid network 2038 2037 8961Wavelet network Saturation 1315 1315 minus07279Wavelet network Dead zone 2054 2054 9009Wavelet network Wavelet network 03643 0364 9381FE failed estimation

dynamics of the PV system The input and output data eachcontain 100001 samples with sampling interval of 00001seconds

After the iterative processmdashby selecting different nonlin-ear models with their associated input-output nonlinearitysearching methods and manipulating numerous estimationconfigurationsmdashHammerstein-Wiener was found to be thebest model that captures the main system dynamics with a9451 fit See Figure 11(c)

42 Model Cross-Validation Similarly the model perform-ance is evaluated using cross-validation In cross-validationthe Hammerstein-Wiener model is confronted with a newdata set that is different from the data used to estimatethe model Figure 11(d) provides the new measured dataset collected from the PV system this time with differentirradiances namely 800Wm2 600Wm2 400Wm2 and800Wm2 This situation emulates an effect of a cloudblocking the irradiance from the PV system In the samefigure it can be seen that the output of the Hammerstein-Wiener model matches the validation data set well with9398 accuracy This shows that the estimation process isrobust enough to handle different input and that the modelestimation is successful Table 2 lists the results of the bestfit with different input and output nonlinearity showing the

9398 accuracy The table as well displays an assessment ofthe estimation in terms of final prediction error (FPE) andloss function

5 ConclusionsThe results of this work showed that the nonlinearHammerstein-Wiener model was able to provide an accuratedescription of the PV system dynamics The model wasselected after an iterative process involving trial and errorThe model must produce an accurate fit to the data and theHammerstein-Wiener model showed an accuracy of 9398applying estimation and validation data sets Developingsuch a black boxmodel frommeasured input-output data cancontribute to the design and implementation of nonlinearcontrol strategies In addition researchers and engineerswill be able to predict future performance of PV systems formaintenance and troubleshooting

Competing InterestsThe authors declare that they have no competing interests

References

[1] W T da Costa J F Fardin L D V B M Neto and D S LSimonetti ldquoIdentification of photovoltaic model parameters by


differential evolutionrdquo in Proceedings of the IEEE InternationalConference on Industrial Technology (ICIT rsquo10) pp 931ndash936IEEE March 2010

[2] D Sera R Teodorescu and P Rodriguez ldquoPV panel modelbased on datasheet valuesrdquo in Proceedings of the IEEE Interna-tional Symposium on Industrial Electronics (ISIE rsquo07) pp 2392ndash2396 Vigo Spain June 2007

[3] M G Villalva J R Gazoli and E R Filho ldquoComprehensiveapproach to modeling and simulation of photovoltaic arraysrdquoIEEE Transactions on Power Electronics vol 24 no 5 pp 1198ndash1208 2009

[4] G M Masters Renewable and Efficient Electric Power SystemsJohn Wiley amp Sons Hoboken NJ USA 2004

[5] R Ramaprabha and B L Mathur ldquoMATLAB based modelingto study the influence of shading on series connected SPVArdquoin Proceedings of the 2nd International Conference on EmergingTrends in Engineering and Technology (ICETET rsquo09) pp 30ndash34IEEE Nagpur India December 2009

[6] W Xiao W G Dunford and A Capel ldquoA novel modelingmethod for photovoltaic cellsrdquo in Proceedings of the IEEE 35thAnnual Power Electronics Specialists Conference (PESC rsquo04) vol3 pp 1950ndash1956 Aachen Germany June 2004

[7] E Saloux M Sorinand and A Teyssedou ldquoExplicit model ofphotovoltaic panels to determine voltages and currents at themaximum power pointrdquo CETC Number 2010-156 CanmetEN-ERGY Ottawa Canada 2010

[8] A H Alqahtani M S Abuhamdeh and Y M AlsmadildquoA simplified and comprehensive approach to characterizephotovoltaic system performancerdquo in Proceedings of the IEEEEnergytech Conference pp 1ndash6 Cleveland Ohio USA May2012

[9] J J Soon and K-S Low ldquoPhotovoltaic model identificationusing particle swarm optimization with inverse barrier con-straintrdquo IEEE Transactions on Power Electronics vol 27 no 9pp 3975ndash3983 2012

[10] Y A Mahmoud W Xiao and H H Zeineldin ldquoA parame-terization approach for enhancing PV model accuracyrdquo IEEETransactions on Industrial Electronics vol 60 no 12 pp 5708ndash5716 2013

[11] S A Rahman R K Varma and T Vanderheide ldquoGeneralisedmodel of a photovoltaic panelrdquo IET Renewable Power Genera-tion vol 8 no 3 pp 217ndash229 2014

[12] L Cristaldi M Faifer M Rossi and S Toscani ldquoAn improvedmodel-based maximum power point tracker for photovoltaicpanelsrdquo IEEE Transactions on Instrumentation and Measure-ment vol 63 no 1 pp 63ndash71 2014

[13] J Schoukens ldquoSystem identificationwhat does it offer to electri-cal engineersrdquo in Proceedings of the 60th Anniversary of theFoundation of the Faculty of Electrical Engineering and Informat-ics of the Technical University Budapest December 2009

[14] P Eykhoff System Identification-Parameter and State Estima-tion Wiley London UK 1974

[15] L Ljung System IdentificationmdashTheory for the User Prentice-Hall Englewood Cliffs NJ USA 1987

[16] T SoderstromandP Stoica System Identification Prentice-HallHemel Hempstead UK 1989

[17] C Osorio Model-Based Design for Solar Power Systems TheMathWorks Natick Mass USA 2009

[18] K Ishaque and Z Salam ldquoA review of maximum power pointtracking techniques of PV system for uniform insolation andpartial shading conditionrdquo Renewable and Sustainable EnergyReviews vol 19 pp 475ndash488 2013

[19] A R Reisi M H Moradi and S Jamasb ldquoClassification andcomparison of maximum power point tracking techniquesfor photovoltaic system a reviewrdquo Renewable and SustainableEnergy Reviews vol 19 pp 433ndash443 2013

[20] MAG deBrito LGalotto L P SampaioGDeAzevedoMeloand C A Canesin ldquoEvaluation of the main MPPT techniquesfor photovoltaic applicationsrdquo IEEE Transactions on IndustrialElectronics vol 60 no 3 pp 1156ndash1167 2013

[21] E B Youssef P Stephane E Bruno andA Corinne ldquoNew PampOMPPT algorithm for FPGA implementationrdquo in Proceedings ofthe 36th Annual Conference of the IEEE Industrial ElectronicsSociety (IECON rsquo10) pp 2868ndash2873 IEEEGlendale Calif USANovember 2010

[22] E Setiawan I Hodaka Y Yamamoto and I Jikuya ldquoImprove-ment of maximum power point tracking based on nonlinearcontrol of boost converterrdquo in Proceedings of the 1st IEEEConference on Control Systems amp Industrial Informatics (ICCSIIrsquo12) pp 180ndash184 Bandung Indonesia September 2012

[23] C-S Chiu and Y-L Ouyang ldquoRobust maximum power track-ing control of uncertain photovoltaic systems a unified T-Sfuzzy model-based approachrdquo IEEE Transactions on ControlSystems Technology vol 19 no 6 pp 1516ndash1526 2011

[24] N Patcharaprakiti and S Premrudeepreechacharn ldquoMaximumpower point tracking using adaptive fuzzy logic control forgrid-connected photovoltaic systemrdquo in Proceedings of the IEEEPower Engineering Society Winter Meeting pp 372ndash377 IEEEJanuary 2002

[25] S A Khan and M I Hossain ldquoDesign and implementationof microcontroller based fuzzy logic control for maximumpower point tracking of a photovoltaic systemrdquo in Proceedingsof the International Conference on Electrical and Computer Engi-neering (ICECE rsquo10) pp 322ndash325 IEEE Dhaka BangladeshDecember 2010

[26] J Li and H Wang ldquoMaximum power point tracking of pho-tovoltaic generation based on the fuzzy control methodrdquo inProceedings of the 1st International Conference on SustainablePower Generation and Supply (SUPERGEN rsquo09) pp 1ndash6 Nan-jing China April 2009

[27] S-J Kang J-S Ko J-S Choi et al ldquoA novel MPPT Controlof photovoltaic system using FLC algorithmrdquo in Proceedings ofthe 11th International Conference on Control Automation andSystems (ICCAS rsquo11) pp 434ndash439 IEEE Gyeonggi-do Republicof Korea October 2011

[28] W-M Lin C-M Hong and C-H Chen ldquoNeural-network-based MPPT control of a stand-alone hybrid power generationsystemrdquo IEEE Transactions on Power Electronics vol 26 no 12pp 3571ndash3581 2011

[29] M Syafaruddin E Karatepe and T Hiyama ldquoArtificial neuralnetwork-polar coordinated fuzzy controller based maximumpower point tracking control under partially shaded condi-tionsrdquo IET Renewable Power Generation vol 3 no 2 pp 239ndash253 2009

[30] T Esram Modeling and control of an alternating-current pho-tovoltaic module [PhD thesis] Department of Electrical Engi-neering University of Illinois at Urbana-Champaign UrbanaIll USA 2010

[31] Y-H Liu C-L Liu J-W Huang and J-H Chen ldquoNeural-network-based maximum power point tracking methods forphotovoltaic systems operating under fast changing environ-mentsrdquo Solar Energy vol 89 pp 42ndash53 2013

[32] A BG BahgatNHHelwaG EAhmad andE T El ShenawyldquoMaximumpower point traking controller for PV systems using


neural networksrdquo Renewable Energy vol 30 no 8 pp 1257ndash1268 2005

[33] B-J JeonK-HKimK Lee J-H ImG-BCho andY-OChoildquoBattery controller design of stand-alone photovoltaic systemusing IncCondmethodrdquo in Proceedings of the 15th InternationalConference on Electrical Machines and Systems (ICEMS rsquo12) pp1ndash5 October 2012

[34] C Osorio Webinar Model-Based Design for Solar Power Sys-tems The MathWorks Natick Mass USA 2009

[35] H Kumar and R K Tripathi ldquoSimulation of variable incre-mental conductance method with direct control method usingboost converterrdquo in Proceedings of the Students Conference onEngineering and Systems (SCES rsquo12) March 2012

[36] A Safari and SMekhilef ldquoSimulation and hardware implemen-tation of incremental conductance MPPT with direct controlmethod using cuk converterrdquo IEEE Transactions on IndustrialElectronics vol 58 no 4 pp 1154ndash1161 2011

[37] A Safari and S Mekhilef ldquoImplementation of incrementalconductance method with direct controlrdquo in Proceedings of theIEEE Region 10 Conference (TENCON rsquo11) pp 944ndash948 BaliIndonesia November 2011

[38] J Sjoberg Q Zhang L Ljung et al ldquoNonlinear black-boxmod-eling in system identification a unified overviewrdquo Automaticavol 31 no 12 pp 1691ndash1724 1995

[39] L Ljung System Identification Toolbox 7 Userrsquos Guide TheMathWorks Natick Mass USA 2008

[40] N Patcharaprakiti K Kirtikara K Tunlasakun et al ldquoModelingof photovoltaic grid connected inverters based on nonlinearsystem identification for power quality analysisrdquo in ElectricalGeneration and Distribution Systems and Power Quality Distur-bances InTech Rijeka Croatia 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of

2 International Journal of PhotoenergyPa

nels

conn

ecte

d in

serie

s

Panels connected in parallel

Panel Cell

IArray

VArraymiddot middot middot

Figure 1 Generic PV array structure

the PV system In this work the PV system identificationincorporated the entire setup considering a PV system powerconverter maximum power point tracker (MPPT) and aload

Identification of linearnonlinear systems became a hottopic in the 1960s probably because proper models wereneeded to design good controllers [13] At this stage the sys-tem identification fieldwas rather immatureThefirst attemptto put the field into order was the published pioneeringwork of Eykhoff [14] Afterward the field became completelystructured when the books of Ljung [15] and Soderstrom andStoica [16] laid out a complete theoretical framework andpractical methodology to the identification process

The core of the system identification process is to con-struct a mathematical model from observed input-outputdata It is widely applied in different engineering disciplinesto help understand the studied process predict the systemresponses and create better design with new specifications

This work is organized as follows Section 2 presentsa description of the studied PV system Section 3 detailsthe system identification methodology Section 4 discussesthe results associated with implementing the PV systemidentification from applied input-output data dividing thedata into estimation and validation sets Finally Section 5concludes the work

2 PV System Description

The PV system illustrated in Figure 2 is considered forthis study The PV panel performance is affected by sev-eral environmental conditions however irradiance has thestrongest impact on the panel output power The panel is amultipurpose module consisting of 36 polycrystalline siliconcells connected in series Under STC the open circuit voltage(119881oc) is 216 V the short circuit current (119868sc) is 516 A themaximum power voltage (119881mp) is 173 V and the maximumpower current (119868mp) is 463A Figure 3 presents the I-V andP-V characteristics under different irradiances These dataare obtained experimentally [17] and they are not the data

IPV PPV

minus

PV panel

DCDCbuck converter

MPPTcontroller

Voltage and current measurements

Load

Power

+Environmental

condition

Input Output

t (s) t (s)

Figure 2 PV panel MPPT DCDC buck converter and a DC load

G = 1200 Wm2 Vmax = 166 V

G = 1000 Wm2 Vmax = 171 V

G = 800 Wm2 Vmax = 175 V

G = 600 Wm2 Vmax = 177 V

G = 400 Wm2 Vmax = 179 V

G = 400 Wm2 Pmax = 308 WG = 600 Wm2 Pmax = 477 WG = 800 Wm2 Pmax = 649 WG = 1000 Wm2 Pmax = 825 WG = 1200 Wm2 Pmax = 100 W

1

2

3

4

5

6

7

Curr

ent (

A)

5 10 15 200Voltage (V)

0

20

40

60

80

100

120

Pow

er (W

)

5 10 15 200Voltage (V)

Figure 3 I-V and P-V characteristic of the PV panel at 119879 = 2515∘C

that will be used for the system identification procedurenevertheless prior information about the system is beneficialWhatwe are interested in is the currentmeasurement as inputand the power measurement as output with respect to timeas indicated in Figure 2

The I-V and P-V characteristic curves show the standardPV panelarray behavior as the irradiance increases the











Black box

Grey box

White box

Unknown

Structure

Structure

Structure

Structure

Structure

Parameter

Parameter

Parameter

Parameter

Parameter

Known


0 1 2 3 4 5 6 7 8 9 10

80

1

2

3

4

Curr

ent (

A)

20

40

60

Pow

er (W

)

1 2 3 4 5 60 8 9 107Time (sec)

Time (sec)





Start





Yes

End

No


u(t)Input

nonlinearityf

y(t)Liner block

BFh







119906 (119905) = 119891 (119906 (119905))

119909 (119905) =

119861119895119894(119902)

119865119895119894(119902)

119908 (119905)

119910 (119905) = ℎ (119909 (119905))

(1)


119861119895119894(119902)

119865119895119894(119902)

(2)





119891 (119909) = 119909 minus 119886 119909 lt 119886

119891 (119909) = 0 119886 le 119909 lt 119887

119891 (119909) = 119909 minus 119887 119909 ge 119887

(3)




119896= 119891(119909

119896) 119891



F(x) = x minus a



a b


F(x) = a F(x) = bF(x) = x


a b



119891 (119909) = 119886 119909 lt 119886

119891 (119909) = 119909 119886 le 119909 lt 119887

119891 (119909) = 119887 119909 ge 119887

(4)



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119891 ((119906 minus 119903)119876119887

119894minus 119888119894) + 119889 (5)


119891 (119911) =1

119890minus119911 + 1 (6)



Weights Weights

Activation function



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119904119894lowast 119891 (119887119904 (119906 minus 119903)119876 + 119888119904)

+

119899

sum

119894

119886119908119894lowast 119892 (119887119908

119894(119906 minus 119903)119876 + 119888119908

119894) + 119889

(7)


119891 (119906) = 119890minus05lowast119906

1015840lowast119906



(8)








Parametric model










(ARX) model

model

(a)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(b)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(c)


20

30

40

50

60

70

80Po

wer

(W)

1 2 3 4 5 6 7 8 9 100Time (sec)

(d)

















References






















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of











Black box

Grey box

White box

Unknown

Structure

Structure

Structure

Structure

Structure

Parameter

Parameter

Parameter

Parameter

Parameter

Known


0 1 2 3 4 5 6 7 8 9 10

80

1

2

3

4

Curr

ent (

A)

20

40

60

Pow

er (W

)

1 2 3 4 5 60 8 9 107Time (sec)

Time (sec)





Start





Yes

End

No


u(t)Input

nonlinearityf

y(t)Liner block

BFh







119906 (119905) = 119891 (119906 (119905))

119909 (119905) =

119861119895119894(119902)

119865119895119894(119902)

119908 (119905)

119910 (119905) = ℎ (119909 (119905))

(1)


119861119895119894(119902)

119865119895119894(119902)

(2)





119891 (119909) = 119909 minus 119886 119909 lt 119886

119891 (119909) = 0 119886 le 119909 lt 119887

119891 (119909) = 119909 minus 119887 119909 ge 119887

(3)




119896= 119891(119909

119896) 119891



F(x) = x minus a



a b


F(x) = a F(x) = bF(x) = x


a b



119891 (119909) = 119886 119909 lt 119886

119891 (119909) = 119909 119886 le 119909 lt 119887

119891 (119909) = 119887 119909 ge 119887

(4)



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119891 ((119906 minus 119903)119876119887

119894minus 119888119894) + 119889 (5)


119891 (119911) =1

119890minus119911 + 1 (6)



Weights Weights

Activation function



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119904119894lowast 119891 (119887119904 (119906 minus 119903)119876 + 119888119904)

+

119899

sum

119894

119886119908119894lowast 119892 (119887119908

119894(119906 minus 119903)119876 + 119888119908

119894) + 119889

(7)


119891 (119906) = 119890minus05lowast119906

1015840lowast119906



(8)








Parametric model










(ARX) model

model

(a)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(b)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(c)


20

30

40

50

60

70

80Po

wer

(W)

1 2 3 4 5 6 7 8 9 100Time (sec)

(d)

















References






















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Start





Yes

End

No


u(t)Input

nonlinearityf

y(t)Liner block

BFh







119906 (119905) = 119891 (119906 (119905))

119909 (119905) =

119861119895119894(119902)

119865119895119894(119902)

119908 (119905)

119910 (119905) = ℎ (119909 (119905))

(1)


119861119895119894(119902)

119865119895119894(119902)

(2)





119891 (119909) = 119909 minus 119886 119909 lt 119886

119891 (119909) = 0 119886 le 119909 lt 119887

119891 (119909) = 119909 minus 119887 119909 ge 119887

(3)




119896= 119891(119909

119896) 119891



F(x) = x minus a



a b


F(x) = a F(x) = bF(x) = x


a b



119891 (119909) = 119886 119909 lt 119886

119891 (119909) = 119909 119886 le 119909 lt 119887

119891 (119909) = 119887 119909 ge 119887

(4)



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119891 ((119906 minus 119903)119876119887

119894minus 119888119894) + 119889 (5)


119891 (119911) =1

119890minus119911 + 1 (6)



Weights Weights

Activation function



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119904119894lowast 119891 (119887119904 (119906 minus 119903)119876 + 119888119904)

+

119899

sum

119894

119886119908119894lowast 119892 (119887119908

119894(119906 minus 119903)119876 + 119888119908

119894) + 119889

(7)


119891 (119906) = 119890minus05lowast119906

1015840lowast119906



(8)








Parametric model










(ARX) model

model

(a)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(b)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(c)


20

30

40

50

60

70

80Po

wer

(W)

1 2 3 4 5 6 7 8 9 100Time (sec)

(d)

















References






















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


F(x) = x minus a



a b


F(x) = a F(x) = bF(x) = x


a b



119891 (119909) = 119886 119909 lt 119886

119891 (119909) = 119909 119886 le 119909 lt 119887

119891 (119909) = 119887 119909 ge 119887

(4)



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119891 ((119906 minus 119903)119876119887

119894minus 119888119894) + 119889 (5)


119891 (119911) =1

119890minus119911 + 1 (6)



Weights Weights

Activation function



119910 (119905) = (119906 minus 119903) 119875119871 +

119899

sum

119894

119886119894119904119894lowast 119891 (119887119904 (119906 minus 119903)119876 + 119888119904)

+

119899

sum

119894

119886119908119894lowast 119892 (119887119908

119894(119906 minus 119903)119876 + 119888119908

119894) + 119889

(7)


119891 (119906) = 119890minus05lowast119906

1015840lowast119906



(8)








Parametric model










(ARX) model

model

(a)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(b)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(c)


20

30

40

50

60

70

80Po

wer

(W)

1 2 3 4 5 6 7 8 9 100Time (sec)

(d)

















References






















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



Parametric model










(ARX) model

model

(a)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(b)


10

20

30

40

50

60

70

Pow

er (W

)

1 2 3 4 5 6 7 8 9 100Time (sec)

(c)


20

30

40

50

60

70

80Po

wer

(W)

1 2 3 4 5 6 7 8 9 100Time (sec)

(d)

















References






















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










References






















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article data-driven photovoltaic system modeling...

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