Research Article Artificial Neural Networks to Predict the ...downloads.hindawi.com/journals/ijp/2014/193083.pdf · power from the measures of the PV generator s voltage and current

Research ArticleArtificial Neural Networks to Predict the Power Outputof a PV Panel

Valerio Lo Brano Giuseppina Ciulla and Mariavittoria Di Falco

DEIM Universita degli studi di Palermo Viale Delle Scienze Edificio 9 90128 Palermo Italy

Correspondence should be addressed to Valerio Lo Brano lobranodreamunipait

Received 28 May 2013 Accepted 29 November 2013 Published 23 January 2014

Academic Editor David Worrall

Copyright copy 2014 Valerio Lo Brano 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

The paper illustrates an adaptive approach based on different topologies of artificial neural networks (ANNs) for the power energyoutput forecasting of photovoltaic (PV) modules The analysis of the PV modulersquos power output needed detailed local climatedata which was collected by a dedicated weather monitoring system The Department of Energy Information Engineering andMathematical Models of the University of Palermo (Italy) has built up a weather monitoring system that worked together with adata acquisition system The power output forecast is obtained using three different types of ANNs a one hidden layer Multilayerperceptron (MLP) a recursive neural network (RNN) and a gamma memory (GM) trained with the back propagation In orderto investigate the influence of climate variability on the electricity production the ANNs were trained using weather data (airtemperature solar irradiance and wind speed) along with historical power output data available for the two test modules Themodel validation was performed by comparing model predictions with power output data that were not used for the networkrsquostraining The results obtained bear out the suitability of the adopted methodology for the short-term power output forecastingproblem and identified the best topology

1 Introduction

Among renewable energy sources (RES) solar energy has thegreatest energy potential and PV arrays permit to produceelectric power directly from sunlight furthermore duringthe operational phase the energy production occurs withoutfossil-fuel consumption or noise and not posing health andenvironmental hazards These features will make the PVdevices one of the most important among the technologiesbased on the exploitation of RES [1ndash5] Nevertheless the tech-nological and environmental benefits of PV technology arehindered by economic and technical factors The high cost ofproduction and installation make the PV technology feasibleto the customer only if there are public funding opportunitiesFurthermore there are various concerns associated with PVmodules such as the impact of their interconnection tothe grid [6] Some studies have been carried out on thisfor example [7] but in general there is little informationon the topic The most severe disturbance caused by theconnection of a large amount of PV generation to the grid

would be encountered when a band of cloud sweeps overan area with a large concentration of PV generators Thiscould result in a fairly large and sudden variation in the PVoutput The condition would be aggravated if this changein irradiance occurred during a rapid increase in load [8]For these reasons it is clear that the availability of reliablepredictive tools is very important for the dissemination of PVtechnologies to optimize the performance of PV systems inthe planning and operational phase and finally to correctlyassess the economic return In order to evaluate the realperformance of PV panels is very important the correctprediction of power output an increase of even a few degreesof the PV panel together with a lower solar irradiance canconsiderably reduce the conversion efficiency of the systemthus reducing the power output [9] Indeed an importantconsideration in achieving the efficiency of a PV panel isto evaluate the performance for any weather conditions andto match the maximum power point Many methods basedon the MPPT (maximum power point technique) have beenreported in the literature many others applied empirical

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 193083 12 pageshttpdxdoiorg1011552014193083

2 International Journal of Photoenergy

V

I

I0IL

Rs

RLRsh

Figure 1 One diode simplified equivalent circuit for a solar cellclosed on a resistive load 119877

119871

correlations to evaluate the thermoelectrical performance ofa PV system However these approaches require detailedknowledge of physical parameters of the PV system andman-ufacturing specifications Another approach is representedby adaptive systems An adaptive system is a system thatis able to adapt its behaviour according to changes in itsenvironment or in parts of the system itself An adaptivesystem such as artificial neural networks (ANN) does notrequire any physical definitions for a PV array but shouldallow predicting in a fast and reliable procedure the poweroutput of the PVmodule varying theweather conditionsThispaper presents a comparison of different types of ANNs thatbetter forecasts the PV power outputThe authors have testedthe use of ANN to predict the power output of a PV panelusing the data monitored in a test facility

2 The Power Output of a PV Module

To design and assess the performances of a PV system anaccurate PV model should predict a reliable current-voltage(I-V) and power-voltage (P-V) curves under real operatingconditions

The ldquofive-parameters modelrdquo represents the most com-mon equivalent circuit that better describes the electricalbehaviour of a PV systemThe equivalent circuit is composedof a photocurrent source 119868

119871 a diode in parallel with a shunt

resistance 119877sh and a series resistance 119877119904 as shown in Figure 1Based on this simplified circuit the mathematical model

of a photovoltaic cell can be defined in accordance with thefollowing expression that permits to retrieve the I-V curve

119868 = 119868119871minus 1198680(119890(119881+119868sdot119877

119904)119899119879119888 minus 1) minus

119881 + 119868 sdot 119877119904

119877sh (1)

in which 119868119871depends on the solar irradiance 119868

0is the diode

reverse saturation current and is affected by the silicontemperature n is the ideality factor and 119879

119888is the cell absolute

temperatureAs it is known the performance of a photovoltaic panel

is defined according to the ldquopeak powerrdquo which identifiesthe maximum electric power supplied by the panel when itreceives a solar irradiance 119866 of 1 kWm2 at a cell temperatureof 25∘C For given values of G 119879

119888and 119877

119871 the operating point

can be identified by drawing lines of the different loads 119877119871on

the I-V characteristic (Figure 2) the maximum power pointsare indicated by red circles

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30 35

Pow

er (W

)

Voltage (V)

1Ω 25Ω

5Ω

18Ω

P-V curves for different insolation [1000ndash200] Wm2

(a)

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30 35

Pow

er (W

)

Voltage (V)

1Ω 25Ω

5Ω

18Ω

P-V curves for different temperature [25ndash75]∘C

(b)

Figure 2 Working point of a generic PV panel at constanttemperature (25∘C) varying solar irradiance (1000ndash200Wm2) andelectric load (a) and at constant irradiance (1000Wm2) varyingtemperature (25ndash75∘C) and electric load (b)

In actual conditions it is essential to evaluate the oper-ating condition under all possible circumstances of G 119879

119888

wind speed W air temperature 119879air and electric load 119877119871

The 119879119888temperature thus is a key parameter that affects the

energy conversion efficiency of a PV panel increasing thetemperature decreases the delivered power

Furthermore in the literature it is possible to finddifferent algorithms for seeking the maximum power point

International Journal of Photoenergy 3

[10ndash12] In detail the indirect methods have the particularfeature that the MPP is estimated from the measures of thePV generatorrsquos voltage and current PV the irradiance orusing empiric data bymathematical expressions of numericalapproximations In the most of the maximum power pointtracking (MPPT) methods described in the literature theoptimal operation point of a generic PV system is estimatedby linear approximations [13 14] as

119881mpp = 119896V sdot 119881OC or 119868mpp = 119896119894 sdot 119868sc (2)

where 119881mpp and 119868mpp are the maximum voltage and currentrespectively 119896V and 119896119894 are two constants of proportionality(voltage and current factors) dependents on the characteris-tics of the PV array used 119881oc is the open circuit voltage and119868sc is the short circuit current

Nevertheless the direct methods can also be used theyoffer the advantage that they obtain the actual maximumpower from the measures of the PV generatorrsquos voltage andcurrent PV In that case they are suitable for any irradianceand temperature [15] All algorithms direct and indirect canbe included in some of the DCDC converters maximumpower point tracking (MPPTs) for the stand-alone systems[10]

Recently the fuzzy logic controllers (FLCs) and artificialneural network (ANN) methods have received attention andincreased their use very successfully in the implementationfor MPP searching [16ndash26] The fuzzy controllers improvecontrol robustness and have advantages over conventionalones They can be summarized in the following way [27]they do not need exact mathematical models they can workwith vague inputs and in addition can handle nonlinearitiesand are adaptive in nature likewise their control gives themrobust performance under parameter variation load andsupply voltage disturbances Based on their heuristic natureand fuzzy rule tables these methods use different parametersto predict the maximum power output the output circuitvoltage and short circuit current [17] the instantaneousarray voltage and current [18ndash20] instantaneous array voltageand reference voltage (obtained by an offline trained neuralnetwork) [16] instantaneous array voltage and current ofthe array and short circuit current and open circuit voltageof a monitoring cell [21 22] and solar irradiance ambienttemperature wind velocity and instantaneous array voltageand current used in [23 25 26]

Next three different ANNs are proposed with the aim toforecast power output of PV modules

3 Generalities on Adaptive and ANN Systems

Adaptive systems and ANNs are nonlinear elaboration infor-mation systems whose operation function draws its inspira-tion by biological nervous system When there is no clearrelationship between the inputs and outputs it is not easy toformulate the mathematical model for such as system on thecontrary the ANN canmodel this system using samples [27]

Their ability to learn from experimental data makesANN very flexible and powerful than any other parametricapproaches Therefore neural networks have become very

Adaptive or neural system

Training algorithm

Cost

Output vector

Error

Parameters or weights updating

Input vector

Figure 3 Adaptive or neural systemrsquos design

popular for solving regression and classification problemsin many fields [28] Because the neural network does notrequire any detailed information about the system or processit operates like a black box [29]

4 The Artificial Neuron

An ANN consists of many interconnected processing nodesknown as neurons that act as microprocessors (Figure 3)

Each artificial neuron (Figure 4) receives a weighted setof inputs and produces an output

The activation potential 119860119894of an AN is equal to

119860119894=

119873

sum

119895=1

119908119894119895119909119895minus 119887119895 (3)

where 119873 is the number of elements in the input vector 119909119894

120596119894119895are the interconnection weights and 119887

119894is the ldquobiasrdquo for

the neuron [30] the bias is a coefficient that controls theactivation of the signal handled by theANTheneuron outputdepends only on information that is locally available at theneuron either stored internally or arrived via the weightedcoefficients

5 The Activation Function

The neuron output 119910119894is calculated by the summation of

weighted inputs with a bias through an ldquoactivate on functionrdquoas follows

119910119894= Φ (119860

119894) = Φ[

119873

sum

119894=1

120596119894119895119909119894minus 119887119894] (4)

The activation function is intended to limit the outputof the neuron usually between the values [0 1] or [ndash1 +1]Typically it is used the same activation function for allneurons in the network even if it is not necessary [31] Themost commons activate functions are the step function thelinear combination and the sigmoid function as shown inFigure 5

In the step function the output Φ(119860119894) of this transfer

function is binary depending on whether the input meets


Φ

Transfer function

WeightsInputs

Activation function

Threshold

Activation

x1

x2

x3

xi

w1j

w2j

w3j

wij

yj

sum

Figure 4 Schema of artificial neuron

0

02

04

06

08

1

12

0 2 4 6minus2minus4minus6

(a)

012345

0 2 4 6minus2minus4minus6minus1

minus2

minus3

minus4

minus5

(b)

0

02

04

06

08

1

12


(c)

Figure 5 The most common activation functions (a) step function (b) linear function (c) sigmoid function

a specified threshold The ldquosignalrdquo is sent that is the outputis set to one if the activation meets the threshold

119910119894= Φ (119860

119894) =

1 if 119860 ge threshold0 if 119860 lt threshold

(5)

The step activation function is especially useful in the lastlayer of an ANN to perform a binary classification of theinputs

A linear combination usually more useful in the firstlayers of an ANN where the weighted sum input of theneuron plus a linearly dependent bias becomes the systemoutput A number of such linear neurons perform a lineartransformation of the input vector as

119910119894= Φ (119860

119894) = 119896119860

119894 (6)

in which 119896 is a scale parameter


A sigmoid activation function produces an output valuebetween 0 and 1 Furthermore the sigmoid function iscontinuous and differentiable Due to these reasons this acti-vation function is used in ANNmodels in which the learningalgorithm requires derivatives Often sigmoid function refersto the special case of the logistic function defined by theformula

Φ(119860119894) =

1

1 + 119890minus119896119860 (7)

where 119896 is a constant that control the shape of the curveThe sigmoid function such as the logistic function also hasan easily calculated derivative which can be important whencalculating the weight updates in the network It thus makesthe network more easily mathematically manipulable andwas attractive to early computer scientists who needed tominimize the computational load of their simulations

6 Architecture or Topology of an ANN

Generally an ANN is usually divided into three parts theinput layer that collects the inputs 119909

119894 the hidden layer ℎ

119894 and

the output layer that issues the outputs 119910119894 If a neural network

is composed by a single layer of unidirectional connectionsfrom the input nodes to output nodes is called Perceptron

This configuration is the simplest and is not able to solvenot linearly separable problems For these kind of complexproblems ismore useful to use amultilayer perceptron (MLP)ANN that is a feed forward ANN model that maps sets ofinput data onto a set of appropriate outputsThe feed forwardwas the first and arguably simplest type of ANN developedIn a feed forward ANN the connections between the units donot form a directed cycle the information moves in only onedirection forward from the input nodes through the hiddennodes (if any) and to the output nodes By this way there areno cycles or loops in the network

According to the above definitions a feed forward MLPconsists of multiple layers of nodes in a directed graph witheach layer fully connected to the next one Except for theinput nodes each node is a neuron (or processing element)with a nonlinear activation function

On the contrary a radial neural network (RNN) is a classof neural network where connections between units form adirected cycle This creates an internal state of the networkthat allows the ANN to exhibit a dynamic behaviour Unlikefeed forward ANN RNNs can use their internal memoryto process arbitrary sequences of inputs This makes themapplicable to tasks such as the recognition of time serieswhere they have achieved the best known results

7 Training Algorithm

Before the neural network can be used to a specific problemits weights have to be tuned This task is accomplished bythe learning process in which the network is trained Thisalgorithm iteratively modifies the weights until a specificcondition is verified In most applications the learning algo-rithm stops when the error between desired output and the

calculated output produced by the ANN reach a predefinedvalue The error is updated by optimizing the weights andbiases After the training process the ANN can be used topredict the output parameters as a function of the inputparameters that have not been presented before An epoch isa collection of all available samples it is also the term used fora training iteration of the system when one epoch has passedthe adaptive system has been presented with the availabledata once As adaptive systems are for the most part trainediteratively many epochs are usually required to fully train asystem

Concerning the learning algorithm there are generallytwo typologies of ANN learning algorithm [32]

(i) supervised learning(ii) unsupervised learning

Supervised learning is characterised by a training setcomposed of pairs of inputs and corresponding desiredoutputs The error produced by the ANN is then used toupdate the weights (back propagation)

In unsupervised learning algorithms the network is onlyprovided with a set of inputs and without desired outputThe algorithm guides the ANN to self-organize and to adaptits weights This kind of learning is used for tasks such asdatamining and clustering where some regularities in a largeamount of data have to be found

The information in the previous layers obtained byupdating the weighting coefficients is supplied to the nextlayers through the intermediate hidden layers More hiddenlayers can be added to obtain a quite powerful multilayer net-work The MLP architecture has been successfully employedas a universal function approximation in many modellingsituations [28]

8 Generalities on the PV Panel Behaviour

The electrical power produced by PV devices is linked to thesolar irradiance on the panel and the operating temperaturebut also depends on the connected electrical load119877

119871as shown

in Figure 2 indeed the load defines the operating pointon the P-V characteristic For given values of irradiancetemperature and electrical load the operating point can beidentified by drawing on the P-V characteristic the linesof the different 119877

119871 Therefore in correspondence with a

generic constant load connected to a photovoltaic panel theworking point will move along the load curve under theeffect of temperature variations and solar irradiance duringthe day The maximum power point (MPP) is identifiedby a red circle and its coordinates in the P-V plane are(119875max(119866 119879) 119881mpp(119866 119879)) in the I-V plane the coordinates ofMPP are (119868mpp(119866 119879) 119881mpp(119866 119879)) A careful analysis of P-V curves permits to immediately recognize as the electricalbehaviour of a generic PV panel can be represented in threemodes or regimens

(i) when the ratio between the working voltage119881 and thevoltage ofmaximumpower119881mpp at given temperatureis less than 095 the characteristic P-V is practically


linear and the power is strongly correlated to the inci-dent solar irradiance for constant solar irradiancethere is no temperature influence in the power output

(ii) when the ratio119881119881mpp for a given solar irradiance andtemperature is greater than 105 the P-V characteris-tics of the panel decreases muchmore rapidly and theinfluence of solar irradiance becomes less significant(saturation conditions) for constant solar irradiancethere is a linear correlation between temperature andthe power output

(iii) the regimen identified by a ratio 095 lt 119881119881mpp lt

105 characterizes the state of a PV panel connectedto a maximum power point tracking system (MPPT)in which the load dynamically adapts to generate themaximum power (red circle)

9 Data Acquisition System Input Data Vector

To employ and train an ANN a large database of specificdata that represent the analysed physical system is requiredTo this aim a test facility was built up on the roof of theDepartment of Energy Information Engineering and Math-ematical Models (DEIM) at the University of Palermo Themonitoring system consists of two photovoltaic modules anda pyranometer tilted at 38∘ facing south a precision resistanceset used as calibrated load and a multimeter Concerning thedata acquisition of climate parameters a network of weatherstations was built up [33] The thermal regimen of the PVmodules has been measured with thermocouples (type Tcopper-constantan) installed at the rear film of the moduleAll data were collected every 30 minutes and stored for thefurther calculations and comparisonsThe physical data usedfor the training of the ANN were as follows

(i) air temperature 119879air [∘C]

(ii) cell temperature 119879119888[∘C]

(iii) solar irradiance 119866 [Wm2](iv) wind speed119882 [ms](v) open circuit voltage 119881OC [V](vi) short circuit current 119868SC [A]

These last two parameters are important to improve theevaluation the PV panel power output Their values areevaluated by using the following expressions [34]

119868SC = 119868scref119866

119866ref+ 120583119868SC(119879119888minus 119879ref)

119881OC = 119881OCref + 119899119879 ln( 119866

119866ref) + 120583119881OC

(119879119888minus 119879ref)

(8)

where the subscript ref identifies the reference conditions(119866 = 1000Wm2 119879 = 25

∘C) and 120583119868SC

and 120583119881OC

are theshort circuit current and open circuit voltage temperaturecoefficients respectively [35]

The dataset used for the following analyses consists inmore than 6000 data points The 15 of data will be used as atest dataset (not used for the ANN training phase)

Table 1 Data sheet of Kyocera KC175GH-2

Maximum power 119875max [W] 175Maximum voltage 119881mpp [V] 236Maximum current 119868mpp [A] 742Open circuit voltage 119881OC [V] 292Short circuit current 119868SC [A] 809119881OC thermal coefficient 120583

119881OC[V∘C] minus0109

119868SC thermal coefficient 120583119868SC

[mA∘C] 318

Table 2 Data sheet of Sanyo HIT240HDE4


119881OC[V∘C] minus0109


[mA∘C] 221

The monitoring campaign involved the measurementof the performances of two different photovoltaic panelsa Kyocera KC175-GH-2 polycrystalline panel and a SanyoHIT240 HDE4 monocrystalline panel The principal charac-teristic of the two panels are showed in Tables 1 and 2

The measurement campaign about the power output ofthe PV modules took several months and was characterizedby a frequent change of the resistive loads to the aim ofacquiring data relating to the entire P-V curve All data aresubject to a preprocessing step that consists in a preliminaryanalysis that permits to identify possible outliers to removeuncorrected values to carry out a statistical analysis and toperform a correlation analysis

To simulate the presence of a MPPT device individualrecords characterized by a 095 lt 119881119881mpp lt 105 wereextracted from the original database

After the preprocessing step the database was validatedand the correlation analysis has permitted a first evaluationof the mutual relationships among the considered variables

Figures 6 and 7 show the linear correlation betweenthe power output 119875 and all the other features The higherthe bar goes the more the features are correlated In bothcases the preliminary correlation analysis identified a strongcorrelation between 119875 and the solar irradiance a moderatecorrelation with air temperature 119879air and wind speed wasfound

A statistical analysis permitted to assess the maximum(Max) mean (Mean) and minimum (Min) values and thestandard deviation (StDev) of all considered features (Tables3 and 4)

In our study for the topology of the tested ANN wedecided to use an input vector with six components 119879airG 119879cell W 119881oc(119866 119879cell) and 119868sc(119866 119879cell) the output vectorhas only one component the power output P as shown inFigure 8


Table 3 Preliminary statistics evaluation of weather thermal and electric data pertaining Kyocera panel

119879air [∘C] 119879cell [

∘C] 119866 [Wm2] 119882 [ms] 119868SC [A] 119881OC [V]Max 272 511 10782 72 87 302Min 99 157 1264 0 10 265Mean 195 360 7293 231 59 281StDev 23 73 2932 123 23 07

Table 4 Preliminary statistics evaluation of weather thermal and electric data pertaining Sanyo panel

119879air [∘C] 119879cell [


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc

Figure 6 Correlation analysis between the power output and allinput data of the Kyocera panel

1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc

Figure 7 Correlation analysis between the power output and allinput data of the Sanyo panel

10 ANN Topologies

After the preprocessing phase the authors explored differenttopologies of ANN In the following part will be describedonly the best ANN solutions

Input vector

Output vector

ANN system P

Ta

G

W

Tc

Isc

Voc

Figure 8 Definition of input and output vectors of the tested ANNs

(i) one hidden layer MLP(ii) RNNMLP(iii) gamma memory ANN

For each topology are analysed the design and thealgorithm eachneural networkwas trained andwas validatedwith a post processing phase

11 Description of the ImplementedANN Topology

111 One Hidden Layer MLP The one hidden layer MLP is akind of ANN consisting of three layers of ANs in a directedgraph with each layer fully connected to the next one Inthis work except for the input ANs each node is a neuronwith a sigmoid activation function and a common supervisedlearning technique for training the network was used Thetested topology is one of the simplest available for ANNs andis composed by two input sources two function blocks twoweight layers one hiddenweight layer and one error criterionblock


Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc

PANN calculatedPmeasured

Tair Tc W G

Tair Tc W G

Figure 9 Schema of one hidden layer MLP topology for the power output evaluation

minus(1 minus120583)


Isc Voc

Isc VocPANN calculatedPmeasured

Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G

Figure 10 Schema of RNNMLP topology for the power output evaluation

Figure 9 schematizes the tested one hidden layer MLPtopology to evaluate power output of a PV panel

112 RNN MLP The RNN MLP is a simple ANN topologythat employs a recursive flow of the signal to preserve and touse the temporal sequence of events as a useful informationThis topology is composed of two input sources two weightlayer one hidden weight layer two recursive function blocksand one error criterion

Figure 10 shows the RNN MLP topology for the poweroutput evaluation The recursivity is iconized by a feedbackconnectionwhere 120583 is the weight of the feedback used to scalethe input In our test each signal flowing into the recursivefunction block is linked to a different value of 120583

113 GammaMemory ANN The gammamemory (Figure 11)processing element (PE) is used in dynamic systems toremember past signals [36] It enables the usage of pastinformation to predict current and future states The gammaneuron is ideal for neural networks since the time axis isscaled by the parameter 120583 which can be treated as any weightand adapted using back propagation

The application of gamma memory permitted to employan ANN to emulate the 119875 trends In this work was proposedan ANN constituted by two input sources three gammamemory blocks threeweight layer three function blocks andone error criterion block (Figure 12)

12 Postprocessing Phase PerformanceAssessment of ANNs

After the training for each ANN the postprocessing phaseevaluate the difference between the calculated and the mea-sured output vector The data used for this phase are notused for the training process The performance assessment iscarried out by means of three indexes

(i) the mean error (ME) is

ME = 1

119873

119873

sum

119894=1

(119875measured119894 minus 119875ANN calculated119894) (9)

where119873 is the number of samples

(ii) the mean absolute error (MAE) represents the quan-tity used to measure how close forecasts or predic-tions are to the eventual outcome

MAE = 1

119873

119873

sum

119894=1

1003816100381610038161003816119875measured119894 minus 119875ANN calculated1198941003816100381610038161003816

(10)

(iii) the standard deviation 120590 shows how much variationor ldquodispersionrdquo exists from the average (mean orexpected value) A low standard deviation indicatesthat the sample data tend to be very close to themean


G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum

Figure 11 Schema of the gamma memory processing element topology

Tair Tc W GIsc Voc

Tair Tc W GIsc Voc

PANNcalculatedPmeasured

Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source

Figure 12 Schema of gamma memory topology for the power output evaluation

high standard deviation indicates that data are spreadout over a large range of values

120590 = radic1

119873 minus 1

119873

sum

119894=1

(119875measured119894 minus 119875ANN calculated119894)2

(11)

13 Results and Discussions

As previously described each ANN was characterized by atraining phase a postprocessing phase evaluates the errorand the absolute error between the measured and the cal-culated operating temperature data To better analyse thevalidity of the ANN different simulations were carried outchanging the time of the training phase andor the epochsIn all cases the training phase has been suspended in orderto avoid the over-fitting Furthermore for each topology wasidentified the confidence plot that contains the 95 of theoutputs

To better understand how ANNs performance can beevaluated Figure 13 shows the calculated power output versusmeasured power output (data points not used for trainingphase)

In Tables 5 and 6 the results of several ANNs testedtopologies are reported

The result coming from the ANNs designed to predictthe power output produced by a PV panel shows that thiskind of approach is very promising Mean errors appear tobe generally very low (1W) ANN topologies based on MLP

OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Confidence plot output + minus2465466 is within desired with95 confidence

Figure 13 Calculated power output versus measured power outputfor the Sanyo module (MlP 1 topology)

for both panels were very good in terms of prediction erroreven if they required a longer time for the training phaseThe results of the RNNs and gamma memory ANNs arecharacterized by good performances with shorter trainingtime for the Kyocera module The Sanyo panel has generallyrequired longer training time but with excellent results intermofmean error especially with the gammamemoryANN


Table 5 ANNs results for the Kyocera panel bold identifies the ANNs with the best performance

Topology Error distribution [W] Absolute error distribution [W] Epochs Time [s]Mean Median Stdev Mean Median Stdev

Mlp 1 005 minus05 81 53 30 62 15417 31Mlp 2 minus01 05 73 43 23 59 2854 5Mlp 3 minus19 minus11 81 53 30 64 6354 12Mlp 4 minus09 minus03 76 46 28 61 993 1RNN 1 minus06 minus06 48 33 21 36 4976 102RNN 2 98 71 112 112 82 98 533 10RNN 3 07 14 86 57 32 65 555 11Gamma 1 minus10 04 89 58 32 68 126 2Gamma 2 minus30 minus15 83 57 34 67 346 6

Table 6 ANNs results for the Sanyo panel bold identifies the ANNs with the best performance


Mlp 1 minus01 minus08 91 49 30 78 3162 3Mlp 2 minus38 minus31 53 46 34 47 16176 16RNN 1 minus13 minus01 101 57 38 84 3361 29RNN 2 minus17 004 103 59 40 86 305 3Gamma 1 002 04 94 601 45 73 182 9Gamma 2 02 07 59 45 40 38 3134 27

14 Conclusions

In the paper different network architectures have beentested in order to forecast the electric power generated bya PV module in real conditions Data used to train thenetworks were acquired using two different types of PVmodules connected to calibrated electrical loads Climaticvariables were acquired by means of a weather station Theperformances evaluation of the ANNs was performed bycomparing the prediction with the real power output and theerrors were generally contained within the 005ndash1 of themodule peak power output ANNs with simpler architecturegenerally required longer training time while more complexANNshave requested shorter training time Results show thatadaptive techniques are able to predict the power output of aPV panel with great accuracy and short computational timeThese algorithms canplay a dominant role concerning remotemanagement of PV in a probable future when this technologywill be extremely widespread in the territory

Nomenclature

119860119894 Activation potential

AN Artificial neuronANN Artificial neural network119887119894 Bias coefficient

FLCs Fuzzy logic controllers119866 Solar irradiance [Wm2]119868 Current [A]1198680 Diode reverse saturation current [A]

119868mpp Maximum current [A]119868119871 Photocurrent [A]

119868sc Short circuit current [A]119896 Scale parameter119896119894 Constants of current proportionality

119896V Constants of voltage proportionalityMPP Maximum Power PointMPPT Maximum Power Point technique119899 Ideality factor119873 Number of elements in the input vector119875 Power output [W]PV Photovoltaic119877119871 Electric load [Ω]

RNN Radial neural network119877sh Shunt resistance [Ω]119877119904 Series resistance [Ω]

119879air Air temperature [∘C]119879119888 Cell absolute temperature [∘C]

119881 Voltage [V]119881mpp Maximum voltage [V]119881oc Open circuit voltage [V]120596119894119895 Weights

119882 Wind speed [ms]119909119894 Interconnection

119910119894 Neuron output

120583119868SC Short circuit current temperature coefficients

[mA∘C]120583119881OC

Open circuit voltage temperature coefficients[V∘C]


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] VVossos KGarbesi andH Shen ldquoEnergy savings fromdirect-DC in US residential buildingsrdquo Energy and Buildings vol 68pp 223ndash231 2014

[2] W D Thomas and J J Duffy ldquoEnergy performance of net-zeroand near net-zero energy homes in New Englandrdquo Energy andBuildings vol 67 pp 551ndash558 2013

[3] M Cellura L Campanella G Ciulla et al ldquoThe redesign of anItalian building to reach net zero energy performances a casestudy of the SHC Task 40mdashECBCS Annex 52rdquo in Proceedings ofthe ASHRAETransactions vol 117 part 2 pp 331ndash339 June 2011

[4] J G Kang J H Kim and J T Kim ldquoPerformance evaluation ofDSC windows for buildingsrdquo International Journal of Photoen-ergy vol 2013 Article ID 472086 6 pages 2013

[5] F Asdrubali F Cotana and A Messineo ldquoOn the evaluation ofsolar greenhouse efficiency in building simulation during theheating periodrdquo Energies vol 5 no 6 pp 1864ndash1880 2012

[6] C Rodriguez and G A J Amaratunga ldquoDynamic stabilityof grid-connected photovoltaic systemsrdquo in Proceedings of theIEEE Power Engineering Society General Meeting pp 2193ndash2199June 2004

[7] L Wang and Y-H Lin ldquoRandom fluctuations on dynamicstability of a grid-connected photovoltaic arrayrdquo in Proceedingsof the IEEE Power Engineering SocietyWinterMeeting vol 3 pp985ndash989 February 2001

[8] Y T Tan and D S Kirschen ldquoImpact on the power system ofa large penetration of photovoltaic generationrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash8June 2007

[9] E Skoplaki and J A Palyvos ldquoOn the temperature dependenceof photovoltaic module electrical performance a review ofefficiencypower correlationsrdquo Solar Energy vol 83 no 5 pp614ndash624 2009

[10] V Salas E Olıas A Barrado and A Lazaro ldquoReview of themaximum power point tracking algorithms for stand-alonephotovoltaic systemsrdquo Solar Energy Materials and Solar Cellsvol 90 no 11 pp 1555ndash1578 2006

[11] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[12] J Surya Kumari and C Sai Babu ldquoComparison of maximumpower point tracking algorithms for photovoltaic systemrdquo Inter-national Journal of Advances in Engineering and Technology vol1 no 5 pp 133ndash148 1963

[13] M A S Masoum H Dehbonei and E F Fuchs ldquoTheoret-ical and experimental analyses of photovoltaic systems withvoltage- and current-based maximum power-point trackingrdquoIEEE Transactions on Energy Conversion vol 17 no 4 pp 514ndash522 2002

[14] J Ahmad and H-J Kim ldquoA voltage based maximum powerpoint tracker for low power and low cost photovoltaic applica-tionsrdquo World Academy of Science Engineering and Technologyvol 60 pp 714ndash717 2009

[15] V Lo Brano and G Ciulla ldquoAn efficient analytical approachfor obtaining a five parameters model of photovoltaic modules

using only reference datardquoApplied Energy vol 111 pp 894ndash9032013

[16] M Veerachary T Senjyu and K Uezato ldquoNeural-network-based maximum-power-point tracking of coupled-inductorinterleaved-boost-converter-supplied PV system using fuzzycontrollerrdquo IEEE Transactions on Industrial Electronics vol 50no 4 pp 749ndash758 2003

[17] B M Wilamowski and J Binfet ldquoMicroprocessor implementa-tion of fuzzy systems and neural networksrdquo in Proceedings of theInternational Joint Conference on Neural Networks (IJCNN rsquo01)vol 1 pp 234ndash239 Washington DC USA July 2001

[18] C-Y Won D-H Kim S-C Kim W-S Kim and H-S KimldquoNew maximum power point tracker of photovoltaic arraysusing fuzzy controllerrdquo in Proceedings of th 25th Annual IEEEPower Electronics Specialists Conference (PESC rsquo94) vol 1 pp396ndash403 June 1994

[19] A E-S A Nafeh F H Fahmy and E M Abou El-ZahabldquoEvaluation of a proper controller performance for maximum-power point tracking of a stand-alone PV systemrdquo Solar EnergyMaterials and Solar Cells vol 75 no 3-4 pp 723ndash728 2003

[20] N Patcharaprakiti S Premrudeepreechacharn and Y Sri-uthaisiriwong ldquoMaximum power point tracking using adaptivefuzzy logic control for grid-connected photovoltaic systemrdquoRenewable Energy vol 30 no 11 pp 1771ndash1788 2005

[21] THiyama S Kouzuma andT Imakubo ldquoIdentification of opti-mal operating point of PV modules using neural network forreal time maximum power tracking controlrdquo IEEE Transactionson Energy Conversion vol 10 no 2 pp 360ndash367 1995

[22] T Hiyama S Kouzuma T Imakubo and T H OrtmeyerldquoEvaluation of neural network based real timemaximumpowertracking controller for PV systemrdquo IEEE Transactions on EnergyConversion vol 10 no 3 pp 543ndash548 1995

[23] T Hiyama and K Kitabayashi ldquoNeural network based estima-tion of maximum power generation from PV module usingenvironmental informationrdquo IEEE Transactions on Energy Con-version vol 12 no 3 pp 241ndash246 1997

[24] A Cocconi and W Rippel ldquoLectures from GM sunracer casehistory lecture 3-1 the Sunracer power systemsrdquo Number M-101 Society of Automotive Engineers Warderendale Pa USA1990

[25] G Ciulla V Lo Brano and EMoreci ldquoForecasting the cell tem-perature of PVmodules with an adaptive systemrdquo InternationalJournal of Photoenergy vol 2013 Article ID 192854 10 pages2013

[26] V Lo Brano G Ciulla and M Beccali ldquoApplication of adaptivemodels for the determination of the thermal behaviour of a pho-tovoltaic panelrdquo in Proceedings of the International Conferenceson Computational Science and Its Applications (ICCSA rsquo13) pp344ndash358 Springer Ho Chi Minh City Vietnam 2013

[27] K S Yigit and H M Ertunc ldquoPrediction of the air temperatureand humidity at the outlet of a cooling coil using neuralnetworksrdquo International Communications in Heat and MassTransfer vol 33 no 7 pp 898ndash907 2006

[28] M T Hagan H B Demuth and M Beale Neural NetworkDesign PWS Publishing Company Boston Mass USA 1995

[29] S Danaher S Datta I Waddle and P Hackney ldquoErosionmodelling using Bayesian regulated artificial neural networksrdquoWear vol 256 no 9-10 pp 879ndash888 2004

[30] S Haykin Neural Networks A Comprehensive FoundationMacMillan New York NY USA 1994


[31] V Pacelli and M Azzollini ldquoAn artificial neural networkapproach for credit risk managementrdquo Journal of IntelligentLearning Systems andApplications vol 3 no 2 pp 103ndash112 2011

[32] E Angelini G di Tollo andA Roli ldquoAneural network approachfor credit risk evaluationrdquo Quarterly Review of Economics andFinance vol 48 no 4 pp 733ndash755 2008

[33] V Lo Brano A Orioli G Ciulla and S Culotta ldquoQuality ofwind speed fitting distributions for the urban area of PalermoItalyrdquo Renewable Energy vol 36 no 3 pp 1026ndash1039 2011

[34] V Lo Brano A Orioli and G Ciulla ldquoOn the experimentalvalidation of an improved five-parameter model for siliconphotovoltaic modulesrdquo Solar Energy Materials and Solar Cellsvol 105 pp 27ndash39 2012

[35] V Lo Brano A Orioli G Ciulla and A di Gangi ldquoAn improvedfive-parameter model for photovoltaic modulesrdquo Solar EnergyMaterials and Solar Cells vol 94 no 8 pp 1358ndash1370 2010

[36] J C Principe N R Euliano and W C Lefebvre Neuraland Adaptive Systems FundamentalsThrough Simulations JohnWiley amp Sons New York NY USA 1999

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


V

I

I0IL

Rs

RLRsh

Figure 1 One diode simplified equivalent circuit for a solar cellclosed on a resistive load 119877

119871

correlations to evaluate the thermoelectrical performance ofa PV system However these approaches require detailedknowledge of physical parameters of the PV system andman-ufacturing specifications Another approach is representedby adaptive systems An adaptive system is a system thatis able to adapt its behaviour according to changes in itsenvironment or in parts of the system itself An adaptivesystem such as artificial neural networks (ANN) does notrequire any physical definitions for a PV array but shouldallow predicting in a fast and reliable procedure the poweroutput of the PVmodule varying theweather conditionsThispaper presents a comparison of different types of ANNs thatbetter forecasts the PV power outputThe authors have testedthe use of ANN to predict the power output of a PV panelusing the data monitored in a test facility

2 The Power Output of a PV Module

To design and assess the performances of a PV system anaccurate PV model should predict a reliable current-voltage(I-V) and power-voltage (P-V) curves under real operatingconditions

The ldquofive-parameters modelrdquo represents the most com-mon equivalent circuit that better describes the electricalbehaviour of a PV systemThe equivalent circuit is composedof a photocurrent source 119868

119871 a diode in parallel with a shunt

resistance 119877sh and a series resistance 119877119904 as shown in Figure 1Based on this simplified circuit the mathematical model

of a photovoltaic cell can be defined in accordance with thefollowing expression that permits to retrieve the I-V curve

119868 = 119868119871minus 1198680(119890(119881+119868sdot119877

119904)119899119879119888 minus 1) minus

119881 + 119868 sdot 119877119904

119877sh (1)

in which 119868119871depends on the solar irradiance 119868

0is the diode

reverse saturation current and is affected by the silicontemperature n is the ideality factor and 119879

119888is the cell absolute

temperatureAs it is known the performance of a photovoltaic panel

is defined according to the ldquopeak powerrdquo which identifiesthe maximum electric power supplied by the panel when itreceives a solar irradiance 119866 of 1 kWm2 at a cell temperatureof 25∘C For given values of G 119879

119888and 119877

119871 the operating point

can be identified by drawing lines of the different loads 119877119871on

the I-V characteristic (Figure 2) the maximum power pointsare indicated by red circles

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30 35

Pow

er (W

)

Voltage (V)

1Ω 25Ω

5Ω

18Ω

P-V curves for different insolation [1000ndash200] Wm2

(a)

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30 35

Pow

er (W

)

Voltage (V)

1Ω 25Ω

5Ω

18Ω

P-V curves for different temperature [25ndash75]∘C

(b)

Figure 2 Working point of a generic PV panel at constanttemperature (25∘C) varying solar irradiance (1000ndash200Wm2) andelectric load (a) and at constant irradiance (1000Wm2) varyingtemperature (25ndash75∘C) and electric load (b)

In actual conditions it is essential to evaluate the oper-ating condition under all possible circumstances of G 119879

119888

wind speed W air temperature 119879air and electric load 119877119871

The 119879119888temperature thus is a key parameter that affects the

energy conversion efficiency of a PV panel increasing thetemperature decreases the delivered power

Furthermore in the literature it is possible to finddifferent algorithms for seeking the maximum power point












Training algorithm

Cost

Output vector

Error


Input vector







119860119894=

119873

sum

119895=1

119908119894119895119909119895minus 119887119895 (3)








119910119894= Φ (119860

119894) = Φ[

119873

sum

119894=1

120596119894119895119909119894minus 119887119894] (4)





Φ

Transfer function

WeightsInputs

Activation function

Threshold

Activation

x1

x2

x3

xi

w1j

w2j

w3j

wij

yj

sum


0

02

04

06

08

1

12


(a)

012345


minus2

minus3

minus4

minus5

(b)

0

02

04

06

08

1

12


(c)



119910119894= Φ (119860

119894) =


(5)



119910119894= Φ (119860

119894) = 119896119860

119894 (6)




Φ(119860119894) =

1

1 + 119890minus119896119860 (7)





119894 and
















119871as shown
















119868SC = 119868scref119866

119866ref+ 120583119868SC(119879119888minus 119879ref)

119881OC = 119881OCref + 119899119879 ln( 119866

119866ref) + 120583119881OC

(119879119888minus 119879ref)

(8)


∘C) and 120583119868SC

and 120583119881OC





119881OC[V∘C] minus0109


[mA∘C] 318



119881OC[V∘C] minus0109


[mA∘C] 221










119879air [∘C] 119879cell [



119879air [∘C] 119879cell [


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


10 ANN Topologies


Input vector

Output vector

ANN system P

Ta

G

W

Tc

Isc

Voc







Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc


Tair Tc W G

Tair Tc W G




Isc Voc


Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G










ME = 1

119873

119873

sum

119894=1




MAE = 1

119873

119873

sum

119894=1


(10)



G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of












Training algorithm

Cost

Output vector

Error


Input vector







119860119894=

119873

sum

119895=1

119908119894119895119909119895minus 119887119895 (3)








119910119894= Φ (119860

119894) = Φ[

119873

sum

119894=1

120596119894119895119909119894minus 119887119894] (4)





Φ

Transfer function

WeightsInputs

Activation function

Threshold

Activation

x1

x2

x3

xi

w1j

w2j

w3j

wij

yj

sum


0

02

04

06

08

1

12


(a)

012345


minus2

minus3

minus4

minus5

(b)

0

02

04

06

08

1

12


(c)



119910119894= Φ (119860

119894) =


(5)



119910119894= Φ (119860

119894) = 119896119860

119894 (6)




Φ(119860119894) =

1

1 + 119890minus119896119860 (7)





119894 and
















119871as shown
















119868SC = 119868scref119866

119866ref+ 120583119868SC(119879119888minus 119879ref)

119881OC = 119881OCref + 119899119879 ln( 119866

119866ref) + 120583119881OC

(119879119888minus 119879ref)

(8)


∘C) and 120583119868SC

and 120583119881OC





119881OC[V∘C] minus0109


[mA∘C] 318



119881OC[V∘C] minus0109


[mA∘C] 221










119879air [∘C] 119879cell [



119879air [∘C] 119879cell [


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


10 ANN Topologies


Input vector

Output vector

ANN system P

Ta

G

W

Tc

Isc

Voc







Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc


Tair Tc W G

Tair Tc W G




Isc Voc


Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G










ME = 1

119873

119873

sum

119894=1




MAE = 1

119873

119873

sum

119894=1


(10)



G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Φ

Transfer function

WeightsInputs

Activation function

Threshold

Activation

x1

x2

x3

xi

w1j

w2j

w3j

wij

yj

sum


0

02

04

06

08

1

12


(a)

012345


minus2

minus3

minus4

minus5

(b)

0

02

04

06

08

1

12


(c)



119910119894= Φ (119860

119894) =


(5)



119910119894= Φ (119860

119894) = 119896119860

119894 (6)




Φ(119860119894) =

1

1 + 119890minus119896119860 (7)





119894 and
















119871as shown
















119868SC = 119868scref119866

119866ref+ 120583119868SC(119879119888minus 119879ref)

119881OC = 119881OCref + 119899119879 ln( 119866

119866ref) + 120583119881OC

(119879119888minus 119879ref)

(8)


∘C) and 120583119868SC

and 120583119881OC





119881OC[V∘C] minus0109


[mA∘C] 318



119881OC[V∘C] minus0109


[mA∘C] 221










119879air [∘C] 119879cell [



119879air [∘C] 119879cell [


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


10 ANN Topologies


Input vector

Output vector

ANN system P

Ta

G

W

Tc

Isc

Voc







Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc


Tair Tc W G

Tair Tc W G




Isc Voc


Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G










ME = 1

119873

119873

sum

119894=1




MAE = 1

119873

119873

sum

119894=1


(10)



G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



Φ(119860119894) =

1

1 + 119890minus119896119860 (7)





119894 and
















119871as shown
















119868SC = 119868scref119866

119866ref+ 120583119868SC(119879119888minus 119879ref)

119881OC = 119881OCref + 119899119879 ln( 119866

119866ref) + 120583119881OC

(119879119888minus 119879ref)

(8)


∘C) and 120583119868SC

and 120583119881OC





119881OC[V∘C] minus0109


[mA∘C] 318



119881OC[V∘C] minus0109


[mA∘C] 221










119879air [∘C] 119879cell [



119879air [∘C] 119879cell [


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


10 ANN Topologies


Input vector

Output vector

ANN system P

Ta

G

W

Tc

Isc

Voc







Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc


Tair Tc W G

Tair Tc W G




Isc Voc


Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G










ME = 1

119873

119873

sum

119894=1




MAE = 1

119873

119873

sum

119894=1


(10)



G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of












119868SC = 119868scref119866

119866ref+ 120583119868SC(119879119888minus 119879ref)

119881OC = 119881OCref + 119899119879 ln( 119866

119866ref) + 120583119881OC

(119879119888minus 119879ref)

(8)


∘C) and 120583119868SC

and 120583119881OC





119881OC[V∘C] minus0109


[mA∘C] 318



119881OC[V∘C] minus0109


[mA∘C] 221










119879air [∘C] 119879cell [



119879air [∘C] 119879cell [


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


10 ANN Topologies


Input vector

Output vector

ANN system P

Ta

G

W

Tc

Isc

Voc







Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc


Tair Tc W G

Tair Tc W G




Isc Voc


Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G










ME = 1

119873

119873

sum

119894=1




MAE = 1

119873

119873

sum

119894=1


(10)



G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119879air [∘C] 119879cell [



119879air [∘C] 119879cell [


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


1

09

08

07

06

05

04

03

02

01

0Tair Tc G W Voc

P

Isc


10 ANN Topologies


Input vector

Output vector

ANN system P

Ta

G

W

Tc

Isc

Voc







Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc


Tair Tc W G

Tair Tc W G




Isc Voc


Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G










ME = 1

119873

119873

sum

119894=1




MAE = 1

119873

119873

sum

119894=1


(10)



G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Input source

Weightslayer

Functionblock

Errorcriterion

Weightslayer

Functionblock

Weightslayer

Input source

Isc Voc

Isc Voc


Tair Tc W G

Tair Tc W G




Isc Voc


Errorcriterion

Weightslayer

Functionblock

Input source

Weightslayer

Functionblock

Input source

Tair Tc W G

Tair Tc W G










ME = 1

119873

119873

sum

119894=1




MAE = 1

119873

119873

sum

119894=1


(10)



G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


G(z)

G(z)

G(z) G(z)Zminus1

X1 X2 X3 Xn

Input sum


Tair Tc W GIsc Voc

Tair Tc W GIsc Voc


Gm Gm

Gm

Gammamemory

Gammamemory

Gammamemory

Errorcriterion

Weightslayer

Weightslayer

Weightslayer

Functionblock

Functionblock

Functionblock

Input source

Input source



120590 = radic1

119873 minus 1

119873

sum

119894=1


(11)






OutputHigh

LowDesired

Sample

250240230220210200190180170160150140130

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28











14 Conclusions


Nomenclature













[mA∘C]120583119881OC





References
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of








14 Conclusions


Nomenclature













[mA∘C]120583119881OC





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










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Documents

Research Article Artificial Neural Networks to Predict the ...downloads.hindawi.com/journals/ijp/2014/193083.pdf · power from the measures of the PV generator s voltage and current