Artificial neural network-based model for estimating the produced power of a photovoltaic module

Renewable Energy 60 (2013) 71e78

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Artificial neural network-based model for estimating the produced power of a photovoltaic module lam c, S.A. Kalogirou d A. Mellit a, b, *, S. Sag a

Faculty of Sciences and Technology, Renewable Energy Laboratory, Jijel University, Ouled-Aissa, P.O. Box .98, Jijel 18000, Algeria Unité de développement des équipements solaires (UDES), Bousmail, Tipaza 42000, Algeria c Technical Education Faculty, Marmara University, Istanbul 34722, Turkey d Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, P.O. Box 50329, Limassol 3603, Cyprus b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 November 2012 Accepted 23 April 2013 Available online 18 May 2013

In this paper, a methodology to estimate the profile of the produced power of a 50 Wp Si-polycrystalline photovoltaic (PV) module is described. For this purpose, two artificial neural networks (ANNs) have been developed for use in cloudy and sunny days respectively. More than one year of measured data (solar irradiance, air temperature, PV module voltage and PV module current) have been recorded at the Marmara University, Istanbul, Turkey (from 1-1-2011 to 24-2-2012) and used for the training and validation of the models. Results confirm the ability of the developed ANN-models for estimating the power produced with reasonable accuracy. A comparative study shows that the ANN-models perform better than polynomial regression, multiple linear regression, analytical and one-diode models. The advantage of the ANN-models is that they do not need more parameters or complicate calculations unlike implicit models. The developed models could be used to forecast the profile of the produced power. Although, the methodology has been applied for one polycrystalline PV module, it could also be generalized for largescale photovoltaic plants as well as for other PV technologies. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic module Modelling Produced power ANN Forecasting

1. Introduction As reported by the IEA [1], global photovoltaic capacity has been increasing at an average annual growth rate of more than 40% since 2000 and it has significant potential for long-term growth over the next decades. By 2050, PV will provide 11% of global electricity production (4500 TWh per year), corresponding to 3000 GW of cumulative installed PV capacity. In countries like Turkey, photovoltaic research and development activities are still mainly undertaken across a range of universities, government and industry facilities and the projects are mainly financed by the research programme of State Planning Organization (DPT) and The Scientific & Research Council (TUBITAK) [2,3]. As the performance of photovoltaic systems is influenced by the magnitude of the insolation and atmospheric conditions, more accurate models of photovoltaic cell/module are required to estimate the produced power and generally to analyse the photovoltaic systems performance. As the modelling of photovoltaic cells/

* Corresponding author. Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11, 34151 Trieste, Italy. Tel.: þ213 (0)551 998 982. E-mail addresses: [email protected], [email protected] (A. Mellit). 0960-1481/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2013.04.011

modules is one of the most essential areas in photovoltaics research, numerous methods have been developed for modelling the IeV characteristic and estimating the maximal power. These can be generally classified into two types: explicit I ¼ f(V) and implicit I ¼ f(I, V) models. Explicit models employ a simple analytical expression based on assumptions and they need less computational effort. However, implicit models are relatively more accurate than the explicit ones, and they have the disadvantage of introducing a series of parameters which are difficult or even impossible to obtain from solar cell’s manufacturers (i.e., the series resistance, RS; the shunt resistance, RSh; the dark saturation current, I0; photogenerated current Iph and the diode ideality factor, n). Even if these parameters can be obtained empirically, designers of photovoltaic systems often find difficulties in applying such models [4]. Artificial neural networks (ANNs), genetic algorithm (GA), neuro-fuzzy inference system (ANFIS) and particle swarm optimization (PSO) techniques have been investigated in order to model and extract the PV cell/module parameters, as well as to estimate the maximum power. In Ref. [5] the authors used a neural network to estimate the maximum power generation from a PV module using environmental information. The proposed network can be utilized for the prediction of the next day’s generation from the PV systems by

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using the predicted information from the weather offices. According to the authors, the proposed method gives more accurate prediction compared to the prediction obtained by using the conventional multiple regression models. An application of radial basis function (RBF) for solar array modelling and maximum-power point (MPP) prediction was presented by Al-Amoudi and Zhang [6]. The proposed RBF model can lead to energy saving and it can calculate MPPs accurately without searching around the optimal power point. Abdulhadi et al. [7] have developed a neuro-fuzzy model to predict solar cell short-circuit current and open-circuit voltage. According to the authors, the model can be extended beyond the bounds of measured data by incorporating a priori knowledge derived from theory and manufacturer’s data. In Ref. [8] the authors used a neural network-based approach for improving the accuracy of the electrical equivalent circuit of a PV module. The equivalent circuit parameters of a PV module mainly depend on solar irradiation and temperature. The dependence on environmental factors on the circuit parameters is investigated by using a set of currentevoltage curves. It is shown that the relationship between these two parameters is nonlinear and cannot be easily expressed by any analytical equation. Almonacid et al. [9] developed a method to obtain the characteristic curve of a PV module at any given condition using an MLP taking into account that the voltage could be given as a function of the current, irradiance and the module temperature. It has been reported that, the proposed ANN introduces an accurate prediction for Si-crystalline PV modules performance when compared with the measured values. A particle swarm optimization (PSO) algorithm and a cluster analysis are performed to fit the calculated currentevoltage characteristic of a PV module by Sandrolini et al. [10]. This approach allows one to obtain a set of parameters, which is reasonable and representative of the physical system. In Ref. [11] the authors applied a genetic algorithm to identify the electrical parameters of PV cells/modules, which were used to determine the maximum power. According to the authors, the GA is a very efficient technique compared to other methods. Implementation of an intelligent photovoltaic module on reconfigurable Field Programmable Gate Array (FPGA) was developed by Mekki et al. [12]. The authors designed an MLPphotovoltaic module, which permits the performance evaluation of the PV module using only environmental parameters and involves less computational effort. According to the authors, the device can also be used for predicting the output electrical energy from the PV module and for a real time simulation. Almonacid et al. [13] developed an ANN model to generate the IeV curves of thin-film PV Copper Indium Selenide (CIS) modules for any solar irradiance and module cell temperature. According to the authors, the results obtained were very promising and the developed ANN performs better than other conventional techniques. Generalised regression neural network (GRNN) used to predict the operating current of the photovoltaic module was developed in Ref. [14]. The proposed GRNN model accepts as an input the PV cell temperature, irradiance and PV voltage, while the PV current was the output of the network. Results demonstrated that the GRNN provides a better prediction of the current than a five-parameter analytical model. In Ref. [15] the authors used an ANFIS for modelling and simulation of photovoltaic power supply system. The ANFIS was developed to model the delivered and consumed power generation by the PV power supply (PVPS) system. It has been demonstrated that, the developed model can predict and simulate the different

electrical data of the PVPS-system from only the ambient temperature, solar irradiation and clearness index. RBF networks are utilized to predict the output characteristic of a commercial PV module, using as an input the solar irradiance and temperature [16]. Results show that the numerical values of the computed IeV and PeV characteristics match closely those obtained from the experimental data. The RBF network can also be used for other modelling purposes of solar cells such as the five or seven circuit parameters estimation. Recently, in Ref. [17] a novel methodology based on artificial neural networks is proposed to determine the IeV curve of a PV module operating under different conditions. The main contribution consists in incorporating the measurement of the spectrum as an input of the model. According to the authors, the performance of the network trained with spectral information improves over the one without spectral information. As can be concluded from the above brief review, modelling of PV cell/array based on artificial intelligence techniques such as ANNs, GA, PSO, Neuro-Fuzzy, etc., was applied in different circumstances. These techniques have been proved more beneficial than classical models specifically from the point of view of simplicity and accuracy. The main objective of this paper is to develop a simple and accurate ANN-model taking into account the kind of day (cloudy or sunny) and then to examine its capability in order to estimate the profile of the power produced for a 50 Wp Si-polycrystalline PV module. For this purpose, two ANN-based models have been investigated, the first one (ANN-model 1) is used to estimate the power produced in the case of cloudy days, and the second one (ANN-model 2) is used for sunny days. To assess the performance of the designed models, a comparison between polynomial regression, one-diode, analytical and multiple linear regression models is carried out. The rest of this paper is organized as follows. Section 2 provides information on the database used and the system description. The methodology of developing ANN-based models is presented in Section 3. Evaluation of ANN-models and a comparative study are given in Section 4. 2. System monitoring and database The system consists of one PV module (ASE-50-DG/16) and an MPP unit connected to a load resistance of 100 U, 5 W as indicated in Fig. 1. In this experiment, system current and voltage values are measured with a power analyzer. The power analyzer is connected to a PC via an RS232 serial port. To avoid problems of possible power outages, the PC and the power analyzer are fed by a UPS. Ohmmeter measurements show that set resistance value is 5.5 U including contact resistance. A power analyser (Lutron DW-6090) data-logger has been used for recording data every 2 min (PV current and PV voltage). A weather station (Davis Vantage Pro2 Plus) has been used for recording the meteorological data with 5 min time intervals (air temperature and solar irradiance). These have been recorded at the Marmara University, Istanbul, Turkey from 1-1-2011 to 24-2-2012. As an example of recorded data, Fig. 2 shows the evolution of solar irradiance, air temperature, PV power, PV current and PV voltage (20 cloudy days and 16 sunny days). 3. Models development An ANN-based schematic block diagram used to estimate the profile of the power produced of the PV module is depicted in Fig. 3. The employed ANN has 3 layers, an input layer, a single hidden layer and an output layer. The input layer has 2 inputs: solar

A. Mellit et al. / Renewable Energy 60 (2013) 71e78

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Fig. 1. Photo of the monitoring photovoltaic system with weather station.

20 cloudy days

irradiance and air temperature, and its output layer has a single output node which is the power produced by the PV module. Therefore, the problem is to find a relationship between the inputs and the output based on the experimental data included in the database described before. In other words, the problem can be formulated as, whether it is possible to find a simple formula, which can be useful to estimate the power produced based on solar irradiance and air temperature. The investigated relationship can be given as:

16 sunny days

Irradiance (W/m²)

1000

500

Air temperature (°C)

0

PV Power (W) PV Current (A)

100

200

300

400 500 Time, (h)

600

700

800

900

~ ¼ ~f ðG; TÞ P

(1)

where, ~f is an approximate function. Pre-processing of the data included in the dataset is carried out by using the following expression:

40 30 20

y ¼ ymin þ ðx  xmin Þðxmax  xmin Þ1 ðymax  ymin Þ

(2)

10 0

PV Voltage (V)

0

40

0

100

200

300

400 500 Time, (h)

600

700

800

900

0

100

200

300

400 500 Time (h)

600

700

800

900

20 0

4 2 0

0

100

200

300

400 500 Time (h)

600

700

800

900

0

100

200

300

400 500 Time (h)

600

700

800

900

20 10 0

Fig. 2. An example of monitored data (solar irradiance, air temperature, PV power, PV current and PV voltage).

where xmin  x  xmax and ymin  y  ymax, x is the original data value and y is the corresponding normalized variable. The parameters ymin and ymax have been assumed to 1 and 1 respectively. This pre-processing step on the data (input/output) allows the network to perform more efficiently. From the dataset described above, two sub-databases have been extracted: - The first one consists of data (T, G and P), which has met the condition that the average daily solar irradiation is lower or equal 400 W/m2/day (considered as cloudy days). In this subdatabase we have 5760 samples, 70% of samples have been used for training the network (ANN-model 1), while the rest 30% were used to validate the network. The majority of these days are from the period from 16th September to 14th May. - The second set includes data, which has a condition that the average daily solar irradiation is higher than 400 W/m2/day (considered as sunny days). In this sub-database we have 2280 samples, 70% of samples have been used for training the network (ANN-model 2), while the rest 30% were used to validate the network. The majority of these days are from the period from 15th May to 15th September.

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4. Results and discussion 4.1. Evaluation of the ANN-models Different architectures have been evaluated and the best one was chosen by trial and error. The optimized one consists of 2 units in the input layer, 3 units in the hidden layer and one unit in the output layer as shown in Fig. 4. This structure is applicable for both ANN-models with different weights and bias. Thus, the relationship between the inputs and output can be formulated as:

~ ¼ P

Fig. 3. ANN-based schematic block diagram.

3 X i¼1

w00i ai þ b00

(6)

where, ai ðG; TÞ ¼ 2ð1 þ expð2½w0i;1 G þ w0i;2 T þ b0i ÞÞ1  1, i ¼ 1, 2, 3 Therefore, we try to develop two ANN-models: -

ANN-model 1 used to estimate the profile of power produced in the case of cloudy days. ANN-model 2 used to estimate the profile of the power produced in the case of sunny days.

A set of pre-processed input and output data is used to train the network during the training step. After application of each input, the network computes its output (P) which is then compared with the target output to produce an error (e). The performance function used for training feed-forward neural networks is the mean ~ given squared error with regularization performance function E as [18]:

0 1 n n X 1@ X 2 2A ~ g E ¼ ei þ ð1  gÞ wj n i¼1 j¼1

(3)

where g is the performance ratio. This modified error is used in the LevenbergeMarquardt optimization to update the weights and biases of the network. After sufficient number of iterations, the mean square error between the target and network outputs settles down to a minimum value. Linear, logarithmic sigmoid and hyperbolic tangent sigmoid are the three most common transfer functions. In this study, a linear function is used for the output layer while a hyperbolic tangent sigmoid transfer function is used for the input and the hidden layers given by:



y ¼

2

1þe

2 PN i¼1

1

(4)

wi xi þb

w00i ; w0i;1 ; w0i;2 are the weights and b00 ; b0i are the bias values of the network. The weight and bias values for both ANN models are reported in the Appendix. In order to examine the capability of the designed ANN models to estimate the profile of the produced power accurately, four days for each class (sunny and cloudy) have been considered. These have not been used for the training of the ANN. Fig. 5 shows the evolution of the performance error for both ANN-models. As can be observed the mean squared error (measured versus estimated energy) during the training process is about 104 for the first model, while for the second model is about 107. These results indicate that the network weights and bias of the networks are well adjusted and the models could reproduce the output data with good accuracy especially for the second model used in the case of sunny days. Fig. 6 depicts the superposition curves between the monitored and estimated profiles of the power produced by the PV module. As can be seen, the monitored power values are relatively close to the estimated ones for both ANN-models. However, to assess the performance of the designed ANN-models, the correlation coefficient (R), the root mean square error (RMSE), and the mean bias error (MBE) between monitored (actual) and predicted energy produced (this value is the cumulative sum of the power values along the day) are estimated. These results are reported in Table 1.With reference to the first ANN-model 1 (cloudy days), it should be noted that the correlation coefficient is between 93% and 97%, which means that, both measured and estimated energy are relatively close. The MBE varies in the range of 0.7 and 1.1%, and the RMSE is less than 0.2%. Concerning the second model ANN-model 2 (sunny days), the correlation coefficient is between 96% and 97%, the MBE varies in

The network weights and biases are updated based on the following expression:

 1 Xkþ1 ¼ Xk  J T J þ mI E

(5)

where J is the Jacobian matrix that contains first derivatives of the network errors with respect to the weights and biases, E is a vector of network error and m is the Marquardt adjustment parameter. Thus, the training of the network is completed and now the network is ready for evaluating the produced power. A soft computing program for hourly estimation of the produced power of the considered PV module is developed under MatLabÓ (Ver. 7.8, 2009) [19].

Fig. 4. The multi-layer perceptron architecture used for both ANN models.

A. Mellit et al. / Renewable Energy 60 (2013) 71e78

75

Fig. 5. Evolution of the performance error.

between 350 W/m2/day and 450 W/m2/day both models could be used. After the evaluation step, ANN models can be used with an approximate error of 5% for estimating the profile of the produced power. Furthermore, the developed ANN models can also be used to forecast the profile of the produced power based on forecasted solar irradiance and air temperature. In this case, numerical weather prediction (NWP) models could be used to forecast the solar irradiance and air temperature. The total error is the sum of errors generated by the ANN model and forecaster model, so this error should be considered in the estimation the power produced. If the ANN-models are employed to forecast the power produced (based on the forecasted solar irradiation and air temperature by the NWP), the average daily solar irradiation can be calculated in order to choose which ANN-model (cloudy or sunny days) is suitable for each day. Additionally, the designed ANN-models could be employed to detect faults in the PV module based on the losses in power (comparison between measured and predicted), and then a procedure could be integrated in order to detect which kind of fault is occurred, (shadow, PV module degradation, dust accumulation,

the range of 0.94 and 0.98%, and the RMSE is also less than 0.2%. Both are well within acceptable performance values. With reference to the aforementioned results, it is clearly shown that the second ANN-model 2 (sunny days) is relatively more accurate than the first ANN-model 1 (cloudy days), which is confirmed by the performance evolution of the MSE plotted in Fig. 5. The mean error of the ANN models is less than 2% and therefore taking into account the accuracy in the measurement of solar irradiance, air temperature, PV module current, voltage, and losses in connection wires, which is approximately 3%, hence, the total error is approximately 5%. It should be noted that, the classification of the days into sunny and cloudy, improves significantly the ANN-based models, unlike a single database containing all days, reported in almost all reviewed papers that used ANNs. Therefore, the ANN-model 1 could be applied in the period from 16th September to 14th May, whereas the ANN-model 2 is suitable for the period from 15th May to 15th September. However, in some days (frequently occurred in spring and autumn period) where the mean average daily solar irradiation is approximately in the range

Cloudy days: 15 -18 November 2011 14

Sunny days: 7- 10 August 2011

40

Estimated

Estimated Monitored

12

30

6

4

25

ANN model 2

8

PV module power (W)

ANN model 1

10 PV module power (W)

Monitored

35

20 15

10 2

0 160

5

180

200

220 Time(h)

240

260

280

0 160

180

200

220 Time(h)

240

260

280

Fig. 6. Comparison between measured (monitored data) and estimated (ANN) profile of the produced power of the employed PV module for four days (cloudy and sunny).

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Table 1 Comparison between measured (actual) and ANN predicted energy in both cloudy and sunny day models. Type of days

Mean daily measured energy (kWh/day)

Cloudy days 1st day 15/11/2011 2nd day 16/11/2011 3rd day 17/11/2011 4th day 18/11/2011 Sunny days 1st day 7/8/2011 2nd day 8/8/2011 3rd day 9/8/2011 4th day 10/8/2011

Mean daily estimated energy (kWh/day)

ANN-model 1 2.51 3.26 0.81 1.93 1.46 2.57 1.55 2.51 ANN-model 2 11.66 12.21 11.89 12.73 11.51 12.09 11.42 12.39

RMSE (%)

MBE (%)

R (%)

(10). The designed models for sunny and cloudy days are given as:

 2 ~ PR ¼ 0:16550:0016TCell Gþ0:0371Gþ0:0001G sunny days P 0:18620:0018TCell Gþ0:0328Gþ0:0001G2 cloudy days (12)

0.11 0.12 0.12 0.11

0.74 1.11 1.10 0.96

97.1 93.5 96.5 96.1

0.13 0.10 0.10 0.11

0.94 0.83 0.98 0.97

96.3 97.0 96.5 96.7

4.2.3. One diode model The well-known equivalent circuit of a single junction solar cell is shown in Fig. 7. The IeV characteristic of a photovoltaic module is given by Markvart [21]:

 VþIRs  V þ IRs I ¼ Iph þ I0 enVt Ns  1  Rsh

(13)

etc.). This application is more beneficial for large-scale photovoltaic plants.

where: Iph is the photocurrent of the cell; I0 is the dark saturation current of the diode, n is the diode ideality factor, Vt is the thermal voltage and Ns is the number of cells connected in series. The thermal voltage is given by:

4.2. Comparative study

Vt ¼

In this subsection, we try to compare the performance of the designed ANN-models with different models (e.g. polynomial regression, multiple linear regression, analytical and one-diode). A brief review of each model is given below.

where: K is Boltzmann’s constant, q is the charge of the electron, TSTC ð KÞ. As Eq. (13) is an implicit {I ¼ f(I, V)} formula, an iterative method (NewtoneRaphson) is used to identify the five parameters (I0, Iph, Rs, Rsh and n) of the one-diode model, and then we calculate the maximum power for different irradiance and PV cell temperature. Fig. 8 shows the IeV and PeV characteristics of the photovoltaic panel employed at STC conditions. The estimated maximum power is 51.02 W, and the error between the nominal power provided by the manufacturer on the datasheet and the one estimated by the one-diode model is approximately 0.05%. The values of the identified five parameters of the PV panel employed are: Rsh ¼ 675.9409 (U), Rs ¼ 0.1991 (U), I0 ¼ 3.3963  107 (A), Iph ¼ 3.3010 (A) and n ¼ 1.3925.

4.2.1. Multiple linear regression model In multiple linear regression (MLR), the relationship between the inputs and outputs is given as:

Yi ¼ a þ b1 Xi;1 þ b2 Xi;2 þ ::: þ bp Xi;p þ εi

(7)

where a and bj are coefficients, Xi and Yi are the measured variables and εi are the errors. A least squares approach is used for estimating the coefficients. In our case, we have two input variables and one output variable, so that Eq. (7) can be written as:

PðG; TÞ ¼ a þ b1 G þ b2 T þ ε

(8)

The same database has been used for estimating the coefficients of the multiple linear regression model given by Eq. (8). The designed MLR models for sunny and cloudy days are given as:

~ MLR ¼ P



0:2716 þ 0:0415G þ 0:295T sunny days 0:7644 þ 0:0157G þ 0:121T cloudy days

(9)

4.2.2. Polynomial regression model A generic polynomial regression (PR) model to simulate the performance of a selected PV system is given by International Energy Agency [20]:

P ¼ A þ B,Tcell ,G þ C,G þ D,G2

(10)

A K TSTC q

(14)

4.2.4. Analytical model A simplified algebraic equation was proposed in Ref. [22] to give the maximum power:

P ¼

   G Pref 1  g T  Tref Gref

Subscript ‘ref’ refers to standard testing conditions (Gref ¼ 1000 W/m2, Tref ¼ 25  C) and g is the maximum power correction factor for temperature; it ranges from 0.005 to 0.003  C1 in crystalline silicon, whereas good results are achieved assuming g ¼ 0.0035  C1. In order to make a comparison between ANN-models and the aforementioned models (multiple linear regression, polynomial regression, analytical and one-diode model), two days (cloudy and sunny) have been chosen that were not included in the subdatabases used in the training step.

where A, B, C and D are polynomial coefficients. For variations in air temperature and irradiance, the cell temperature (in  C) can be estimated quite accurately with linear approximation, given by:

Tcell ¼ T þ

  NOCT  20 G 0:8

(11)

The same database has been also used for estimating the coefficients of the polynomial regression model given by Eq.

(15)

Fig. 7. The one-diode equivalent circuit.

A. Mellit et al. / Renewable Energy 60 (2013) 71e78

77

STC conditions

STC conditions

4

50 45

3.5

40 3 35 PV power (W)

PV current (A)

2.5

2

1.5

30 25 20 15

1 10 0.5

5 0

0 0

5

10

15 PV Voltage

20

25

0

5

10

15 PV Voltage

20

25

Fig. 8. The IeV and PeV characteristics of the photovoltaic module employed at STC conditions.

Simulation results are depicted in Fig. 9. As can be seen, the profile of the power estimated by the ANN-models is very close to the measured one for both days. Table 2 reports the mean relative error and the correlation coefficient between the measured (actual) and the estimated energy.

10 Measured Polynomial model ANN-model 1 One diode model MLR model Analytical model

9 8

PV Power (W)

7

Cloudy day : 22/01/2012

6 5 4 3 2 1 0

0

5

10

15

20

Time (h)

50 Measured Polynomial model ANN-model 2 One diode model MLR model Analytical model

45 40

PV Power (W)

35

Sunny day : 15/08/2011

With reference to Table 2, the following key statements can be made: - ANN-based models estimate the profile of the produced power with reasonable accuracy. - The ANN-model 2 (sunny days) is more accurate than the ANNmodel 1 (cloudy days) - Polynomial regression, multiple linear regression and analytical models provide good results for sunny days since the correlation coefficient (R) is between 94% and 96% and the mean relative error (MRE) does not exceed 5% but is not so accurate for the cloudy days. The multiple linear regression model is the least accurate. - One-diode model provides nearly the same MRE (4.4%) for both days, and it provides also good results for sunny days. At STC conditions, the one-diode model provides good accurate results (the error was 0.05%), however, in outdoor tests the results are not as accurate. - According to the MRE the models accuracy can be classified as: B Sunny days: ANN-model, polynomial regression model, analytical model, one-diode model and multiple linear regression model. B Cloudy days: ANN-model, multiple linear regression model, one-diode model and analytical model polynomial regression model. The effectiveness of the split of the available one-year dataset into two different ones representative of two typical days (sunny

30

Table 2 Comparison between measured and estimated energy by ANN-models and other models (polynomial regression, analytical, multiple linear regression and one-diode model) for both days considered.

25 20 15

Models 10 5 0

0

5

10

15

20

Time (h)

Fig. 9. Measured versus estimated power by different models (polynomial, ANN, onediode, multiple linear regression and analytical models) in a day.

ANN-model Polynomial regression Multiple linear regression One-diode model Analytical model

Cloudy day 22/1/2012

Sunny day 15/8/2011

R (%)

MRE (%)

R (%)

MRE (%)

96.40 91.30 92.10 93.68 91.20

2.50 5.30 3.21 4.44 5.27

97.22 96.81 94.45 94.87 95.10

2.30 2.42 5.67 4.38 4.22

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and cloudy) has been shown. As it is proved, this enhanced the prediction accuracy of the developed models.

ANN-model 2 (sunny day)

2

5. Conclusion

w0ij

A simple ANN architecture has been developed for modelling and estimating the profile of the power produced by a 50 Wp polycrystalline photovoltaic module. The capability of the ANN for estimating the PV power produced has been verified with reasonable accuracy (error is about 5%). It has been demonstrated that the ANN-models perform better than polynomial regression, multiple linear regression, analytical and one-diode models. The developed ANN models can be applied to forecast the PV power produced based on the forecasted solar irradiance and air temperature (e.g. from forecaster or numerical weather prediction models). Furthermore, if we consider the developed ANN models as a basic particular model of the employed PV panel, they could be used also to estimate the produced power output of PV arrays in stand-alone or grid-connected photovoltaic systems in this location. The advantage of the ANN-models is that, they do not need additional parameters, which are not always available, unlike implicit models that need more complicated calculations and parameters which are not readily available. For example, the implicit model needs calculations that are more complicated and some parameters (like, Rs and Rsh) which are not given by the manufacturer (in the datasheet). These parameters could be estimated experimentally, which is difficult, or by a numerical approach. Simplicity, accuracy and practicability are the main advantages of the developed ANN models when a sufficient quantity of experimental data is available to estimate the PV power produced. Although the method has been applied for polycrystalline silicon, it could be also used for other type of photovoltaic technologies such as a-Si, CIGS, CIS and CdTe. Acknowledgements The first author would like to thank the ICTP, Trieste (Italy) for providing materials and the computer facilities for achieving the present work. Appendix ANN-model 1 (cloudy day)

2

0:0509 w0ij ¼ 4 0:0241 0:3236 w00i ¼ ½ 3:7164 b0i ¼ ½ 5:7524

3 0:0163 0:0127 5 0:0007

1:4567

2:1704

0:0695 

3:3267 T and b00 ¼ 5:0774

4:3399 ¼ 4 0:0523 0:6371

w00i ¼ ½ 1:5126 b0i ¼ ½ 219:30

3:2848

3 0:1201 0:0033 5 0:0285 20:2166

0:4951 

18:617 T and b00 ¼ ½20:5570

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