Performance prediction of PV module using electrical equivalent model and artificial neural network

Solar Energy 176 (2018) 104–117

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Performance prediction of PV module using electrical equivalent model and artificial neural network

T

Manan Mittala, , Birinchi Borab, Sahaj Saxenaa, Anshu Mli Gaura ⁎

a b

Thapar Institute of Engineering & Technology, Patiala, Punjab, India National Institute of Solar Energy, Gurugram, Haryana, India

ARTICLE INFO

ABSTRACT

Keywords: Solar energy PV module Modelling Performance prediction MATLAB Artificial neural network Thin film Electrical equivalent models

Before a photovoltaic (PV) system is installed, a prerequisite modelling and performance analysis are carried out which estimates the performance parameters and reliability in operation of PV system. This paper proposes a neural network approach to performance prediction of PV Modules. Here the feed forward neural networks are used to predict I-V curve parameters as a function on input irradiance and temperature. K Fold cross-validation is used to validate model accuracy for determination of I-V curve parameters for five different technology modules, i.e., CdTe, CIGS, MICROMORPH, MUTICRYSTALLINE, MAXEON. A comparison is also drawn between the neural network predictor and the existing modeling procedures available. Model parameters have been determined following iterative, analytical and regression of known data points for seven and five parameter model of PV Modules. Among the electrical equivalent models, the seven parameter model is the most efficient model for performance prediction however commutation of model parameters in complex and tedious. Neural network model simplifies the computational process at the expense of higher error variance in comparison to electrical equivalent models. Further, a cascade implementation of the above two is designed and tested on Multicrystalline and Maxeon technology modules for higher model accuracy. The results obtained, verify the proposed cascaded model to be the most efficient model in comparison to independent models where mean bias error deviations are less than ± 1% and error variance is reduced significantly. Also, a MATLAB based graphical user interface (GUI) is developed that can be used to predict the performance based on the analysis carried out. The proposed model is tested against a set of operating conditions and compared to the actual experimental values obtained using outdoor tests.

0. Nomenclature In this paper, the mathematical notations in the support of study are presented below: Iph photo current (A) Io reverse saturation current (A) VT = NskT/q thermal voltage (V) Ns cells connected in series q electron charge (1.60217646 × 10−19 C) k Boltzmann constant A diode ideality factor Rse series resistance (Ω) Rsh shunt resistance(Ω) Kv temperature coefficient of voltage (V/K) Ki temperature coefficient of current (A/K) G irradiance (W/m2)

⁎

Tn I-V CIGS MSE MBE Cdte STC PV ANN

temperature at STC (K) current-voltage copper indium gallium selenide mean square error mean bias error cadmium telluride standard testing conditions photovoltaic artificial neural network

1. Introduction With the rapid increase in global warming, carbon emissions, unsustainable use of fossil fuels and a hike in global oil prices, a shift towards a more sustainable, natural and environment-friendly source of energy, is essential. Among other renewable sources of energy, the solar industry has

Corresponding author. Tel.: +91 8427472432. E-mail address: [email protected] (M. Mittal).

https://doi.org/10.1016/j.solener.2018.10.018 Received 13 July 2018; Received in revised form 2 October 2018; Accepted 5 October 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.

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witnessed a massive boom in the past decade. Unlike other conventional sources of energy, use of solar energy does not yield any harmful emissions to the environment besides being a clean and a renewable resource. The absence of moving parts, silent operation, low maintenance, long life (max degradation in Pmax < 1%) and direct conversion of incident solar radiation to direct current are the major advantages associated with PV energy systems. The PV module forms the major part of PV power system. However, the performance of the PV Module is greatly affected by environmental conditions. Solar radiation and module operating temperature are major factors, which affect the performance of the PV Module. Appropriate modelling of PV module based on the variations in temperature and irradiation is essential for prediction of energy yields, performance evaluation, and electrical modelling. A significant work has been presented in literature related to modelling and performance evaluation of PV Module over the past decade. This involves translating a given I-V curve information at known temperature and irradiance to a desirable operating condition. IEC 60891 provides various translational equations based on independent translational equations (IEC 60891, 2009). Bilinear translation involves four I-V curve information to predict I-V characteristics at any desired condition (Marion et al., 2004). Performance evaluation can also be achieved by electrical lumped models of PV Module. Various such models have been proposed till date (Bana and Saini, 2016). Parameter evaluation forms a major part of modelling procedure. This can be achieved using known datasheet values (Sera et al., 2007) or can be independently evaluated using iterative techniques (Ishaque et al., 2011). However, the datasheet values cannot be used reliably as these are determined at standard testing conditions (STC) at the time of manufacturing. However, sparse operating conditions (deviation from STC) and degradation of the PV Module limits its applicability (Sharma and Chandel, 2013). Regression of known data points to evaluate certain parameters has been covered extensively (Hansen, 2015). Further various analytical solutions to the complex transcendental equations of PV modules have been proposed (Chan and Phang, 1987). However extensive computation limits its applicability. Diode ideality factor can be directly used from a given predetermined value based on the type of PV technology used (Tsai et al., 2008). However, this factor is computed for a given module for higher model accuracy. Various SIMULINK subsystems are also proposed which can be used to model PV Modules and arrays (Xiao et al., 2004; Zhou et al., 2007; Pandiarajan and Muthu, 2011). Today is the era of computing using artificial intelligence. Various biological and nature-inspired heuristic techniques have been proposed so far. Among them, computing via an artificial neural network is highly popular. This computing technique is accurate, reliable and robust without computation of additional parameters. These models can be deployed with reasonable accuracy. In the present study, the neural network with a different architecture (i.e., feed forward and radial basis function) and learning (i.e., Levenberg-Marquardt and Resilient Back propagation) are also adapted to model our system. Neural networks can be employed for hourly load forecasting and long-term forecasting (Park et al., 1991) based on time series, fitting, and regression approach. Determination of Maximum power via neural networks is proposed (Lo Brano et al., 2018) wherein the module operating temperature and input irradiance show the highest correlation. Analysis carried out by (Xiao et al., 2017a,b) compares metrological factors such as air temperature, wind speed and humidity as input parameters to neural network. This shows that air temperature also plays an important role in determination of maximum power of solar cell. However the effect of change in ambient temperature and wind speed causes a change in module temperature which can be detected by the temperature sensor with sufficient degree of accuracy. Also this paper compares the accuracy of various models for performance predication of different technologies. Inclusion of another factor in the neural network approach implies, other models cannot be compared on similar grounds. Inclusion of ambient temperature and wind speed in electrical equivalent models will be taken up in further study as a

function of module temperature which is beyond the scope of this paper. A 24 h forecast of solar irradiation using artificial neural networks is also presented (Mellit and Pavan, 2010; Jumaat et al., 2016). Cross validation can be used to validate model accuracy at unknown data points. Here K fold cross validation technique is used to validate the proposed models. Further, the accuracy of K Fold Cross validation technique for performance prediction of various models is covered extensively in Yang and Huang (2014). Keeping the aforementioned points in mind, the main objective of this paper is to propose a modelling procedure to predict the performance of the PV module as a function of irradiance and temperature. Further, this modelling procedure is validated for PV modules of different technologies and the predicted data is compared to the experimental values at I-V curve parameters, i.e., Voc, Isc, Vmax, Imax, and Pmax. Performance prediction via seven parameter, five parameter, four parameter/Rs model and artificial neural networks are carried out. These independent models are compared on the basis of I-V curve parameter evaluation for five different PV technologies. Further a cascade connection of electrical lumped parameters and feed forward neural network is also designed and tested which shows significantly lower deviations between the modelled and experimental values as compared to independent models. The modelling process begins with a brief description of existing electrical equivalent model as discussed in Section 2.1 followed by determination of model parameters in Section 2.2. Performance prediction using artificial neural network as independent and cascaded models is proposed in the further Section 2.3. MATLAB GUI is developed based on the above modelling procedure to simplify the analysis further as shown in Section 4. Section 5 compares the results obtained using the above models on various technology PV Modules following Regression/Error/Benchmark Analysis. 2. Mathematical modelling 2.1. Electrical equivalent circuit of PV module (1) Ideal model The ideal model of a PV Module consists of a single diode connected in parallel with a light generated current source Iph as shown in Fig. 1.

Fig. 1. Ideal model.

(2) Four parameter/Rs model The single diode model which includes the series resistance Rs is shown in Fig. 2. The model is also known as the four-parameter model of a solar cell based on the number of unknown variables in the governing equation. Series resistance accounts for internal resistance and losses within the PV Module such as solar bond resistance, lead resistance, contact drops etc. The output current can be expressed mathematically as: 105

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Fig. 4. Double diode/seven parameter model.

through iteration. This is reported to be the most efficient model until now in the literature (Bana and Saini, 2016).

Fig. 2. Four parameter/Rs model.

(1)

I= Iph Id

2.2. Determination of model parameters

Eq. (1) can be written as:

I = IPH Io exp

V + IRse aVT

(1) Diode ideality factor

1

Accurate performance evaluation of PV cells requires the correct estimation of diode ideality factor. Procedure enlisted by SANDIYA LABS (Hansen, 2015) for estimation of diode ideality factor is based on the measured I-V data for the given PV Module.

(2)

(3) Single diode/five parameter model

Voc Kv (T Tn) = Voco + aVt ln

Eq. (2) does not adequately represent the behaviour of the cell when subjected to environmental variations, especially at low voltages. A more practical model can be seen in Fig. 3, where Rse and Rsh represent the series and parallel resistances respectively. An output current equation using this model can be written as:

I = Iph Io exp

V + IRse aVT

1

V + IRse Rsh

G 1000

(5)

Voco

where is the open circuit voltage rating of the module at the name plate. The determination of diode ideality factor is shown in Fig. 5 as per the above procedure where the slope of the regression line gives the value of diode ideality factor (a). For the regression, I-V characteristic information is required over a range of irradiance, preferably from 400 W/m2 to 1000 W/m2. The data obtained through I-V tracer of the respective modules is manipulated as per the procedure enlisted above. The slope of the above regression equation gives the value of diode ideality factor. For double diode model, a1 = 1 and a2 is evaluated using regression.

(3)

where Rse and Rsh are the equivalent series and parallel resistances, respectively. This model yields more accurate result than the Rs model, but at the expense of longer computational time. This is also called as the five parameter model of a PV Module, based on the number of unknown parameters in the governing equation, i.e., Iph, a, Io, Rse, Rsh

Fig. 3. Single diode/five parameter model.

(4) Double diode/seven parameter model The two diode model is depicted in Fig. 4. The following equation describes the output current of the cell.

I = IPh Io1 exp

V + IRse a1 VT1

1

I02 exp

V + IRse a2 VT 2

1

V + IRse Rsh

Fig. 5. Evaluation of diode ideality factor.

(4)

(2) Temperature coefficients

where Io1 and Io2 are the reverse saturation currents of diode 1 and diode 2, respectively. VT1 and VT2 are the thermal voltages of respective diodes and a1 and a2 represent the diode ideality constants. The Io2 term in (4), compensates the recombination loss in the depletion region. Although greater accuracy can be achieved using this model, it requires the computation of seven parameters, namely Iph, Io1, Io2, Rsh, Rse, a1 and a2. Thus it is also called as the seven parameter model of a PV Module. Furthermore, Io1, Io2, Rsh, and Rse, are obtained

The current and voltage coefficients are used to include the effect of variation of temperature on the nominal values of open circuit voltage and short circuit conditions as enlisted in the datasheet. The datasheets of the panel also include these coefficients as a part of the thermal characteristics of the PV module. These are calculated at the STC conditions however due to degradation, variation in actual operating conditions the actual values of 106

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the temperature coefficients are determined through regression of the operating outdoor data points (Hansen, 2015).

Voc = Voco + aVt ln

G + K v (T Tn) 1000

coefficient of short circuit current of PV Module. (3) Photo current

(6)

According to the literature reviewed, the value of light generated photo current is directly proportional to the incident irradiation. Since the diode current and the shunt current forms only a small percentage of the total load current, the value of nominal short circuit current can be used as the light generated photo current at STC. Incorporating the effect of temperature and appropriate irradiance, the value of photo current can be evaluated as per Eq. (10).

Using the value of diode ideality factor obtained in the above analysis and re-arranging the above (6),

Voc aVt ln

G = Voco + K v (T Tn) 1000

(7)

Now, using the outdoor data, the slope of the regression equation gives the value of Kv as shown in Fig. 6.

I2 = I1 + Isc

G2 1 + Ki (T2 T1) G1

V2 = V1 Rse (I2 I1) + Kv (T2 T1)

Iph = (8)

G (Isc + Ki (T 25)) 1000

(10)

(4) Reverse saturation current

(9)

Eq. (11) is used to evaluate the value of reverse saturation current for dark characteristics.

According to IEC 60891 procedure 1, (8) and (9) represent the basic translational equations. These equations can be used to translate a set of values at given reference conditions to another set of conditions. This can be used to evaluate any unknown parameter from a set of known parameters of the PV Module and the recorded I-V data. Here, (8) is used to evaluate the temperature coefficient of short circuit current Ki for the PV module. Fig. 7 shows the evaluation of temperature

Ion =

Isc qVoc e knT

(11)

1

where Isc, Voc represent short circuit current and open circuit voltage respectively. The saturation current depends on the current density and the effective area of the cell. The intrinsic characteristic determines current density. This is obtained at the nominal temperature of 298 K. Since the generation/flow of charge carriers is greatly affected by temperature variations, the value of reverse saturation current is computed using (12).

Io = Ion

T Tn

3 qEbg 1 e nk Tn

1 T

(12)

For simplicity, Io1 is assumed to be equal to Io2 in double diode model analysis. (5) Shunt/series resistance An iterative approach (Bana and Saini, 2016) has been used to determine the value of series resistance Rse and shunt resistance Rsh This procedure is enlisted by various papers (Ishaque et al., 2011; Bana and Saini, 2016), and can be deployed with reasonable accuracy. The value of Rse is iteratively increased while Rsh is calculated simultaneously. For initializing the iteration process, the appropriate values of Rsh and Rse are considered. Value of Rse is taken as zero and the value of Rsh is obtained using the following equation:

Fig. 6. Evaluation of temperature coefficient of voltage Kv.

Rsh0 =

Vmp

Voc Vmp

Isc Imp

Imp

(13)

Maximum power point for the given values of Rse and Rsh assumed according to (13) is computed using MATLAB and subsequently compared to the experimental value of PMAX. The value of Rse is increased in steps of 0.1 and the value of Rsh is computed using (14) simultaneously.

Vmp + Imp Rse

Rsh = Ipho

Io

Vmp + Imp Rse VT e

+e

Vmp+ Imp Rse n 1VT

2

e Pmax Vmp

(14)

The process is carried out until the calculated value of max power matches the experimentally obtained power at MPP. The following algorithm as shown in Fig. 8 is implemented in MATLAB which is used to evaluate series and shunt resistance

Fig. 7. Evaluation of temperature coefficient of current Ki. 107

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Fig. 9. Block diagram feed forward neural network (Independent).

Fig. 10. Block TER + FFANN).

MBE =

2.3. Artificial neural network In order to develop an artificial neural network which can be used to predict the module performance independently as a function of irradiation and temperature, the neural network has to be trained with a significant amount of data specific to the type of PV technology used. In the proposed model as per Fig. 9, temperature and irradiance were used as the input vector and five I-V curve parameters, i.e., Voc, Isc, Vmax, Pmax, and Imax as the desired vectors Artificial neural networks for various technologies were trained using the data collected for five different technology modules. Training data set includes more the 1000 data points for each technology recorded at regular intervals of time (30 s). The trained neural network has to be validated in order to determine the accuracy of the proposed model. Cross-validation can be used to analyze the network performance to an unfamiliar data set. Validation is carried out by reserving a portion of the dataset for example 15% for validation and using the remaining data set for training. However, a more accurate and systematic approach towards validation is by K fold validation process. Cross-validation carried out in a number of steps using different training and validation sets for each iteration reduces the error variance. Here the input data set is divided into K folds/parts. The network is validated for each Kth fold following a training stage using rest of the dataset. This is repeated for K iterations. After the training stage, a correlation analysis is carried out on the data predicted using the ANN topology and the measured data. The closeness of the measured data points to the predicted values is determined by the R square index. This can be evaluated using (15) and (16).

R2 = 1

MSE =

yiac n i=1 n i=1

(15)

(yi pr yiac )2 (y ac y¯ac )2 i

implementation

(SEVEN

PARAME-

1 n 1 n

n

yi pr yiac i=1

(17)

n

(yi pr yiac ) 2 i=1

(18)

This can be used as selection criteria for network architecture for determination of the number of hidden layers, number of neurons, training algorithm and spread factor (in case of radial basis function). The dependencies of maximum power prediction on the number of neurons in the hidden layer was studied (Xiao et al., 2017a,b) for silicon solar cells. The results show that there is no universal principle for selection of neural network architecture, which further depends on the application. Here the selection of network architecture was carried out using K fold cross validation technique in following a number of iterations. Also the selection of training algorithm and neuron transfer function plays an important role in model accuracy. However, in general aspects of neural networks, it is observed that LM and RP algorithms are known to yield faster response for regression-type problems (Edoras.sdsu.edu, 2018). The LM training algorithm in most of cases was found to be significantly the most efficient, fast converging and accurate in comparison to other training algorithms (Sari, 2014). Following two independent approaches for performance prediction of PV Modules, a more accurate model is proposed (Fig. 10) wherein the two separate blocks are connected in cascade, i.e., the I-V curve parameters as predicted by the seven parameter model are corrected to the accurate values using feed forward artificial neural network. This involves design and implementation of the artificial neural network which uses 5 input parameters and results in five output IV curve parameters. Again Feed forward neural network is employed with 1 hidden layer and 10 neurons as network architecture based on results obtained by simulation on MATLAB GUI. The proposed cascade implementation is tested for Multicrystalline and Maxeon Technology PV Module where percentage errors between the predicted values and measured outdoor values are plotted for IV curve parameters i.e. Voc, Isc, Pmax, Imax and Vmax

n i=1

cascade

where the mean squared error, mean bias error was evaluated for various I-V curve parameters. Mean squared error gives a measure of the absolute deviation of the predicted values from the experimental values while the mean bias error tells the relative closeness of the predicted values to the experimental values. A positive value indicates an overestimation of parameters while a negative value indicates underestimation. This can be evaluated using (17) and (18).

Fig. 8. Algorithm for Rse/Rsh.

1 y¯ac = n

diagram

(16)

A statistical analysis was also carried out on the predicted data 108

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3. Experimental setup

4. Graphical user interface

Validation of accuracy of the proposed model and calculation of diode ideality factor requires I-V tracer data for PV Modules. The data is recorded at an outdoor test facility at National Institute of Solar Energy (NISE), Gurgaon as depicted in Fig. 11 with the geographical location of Latitude 28°47 N and Longitude 77°4 E. This site has a composite type of climate characterized by high solar radiation and temperature levels. The PV Modules of different technologies were mounted on Dual Axis Manual tracker structure and I-V data was recorded after every 30 s for the given PV Module. PV modules were cleaned on regular basis to avoid errors in measurement due to soil deposition. The I-V tracer (2540C) as shown in Fig. 11 was used to record the I-V data for the PV module at regular intervals. Reference cell (SOZ 03) which measures the global irradiation was mounted along the PV Module at the same tilt and temperature sensors (PT100) were used to measure the module temperature.

MATLAB Front end GUI as shown in Fig. 12 can be used to automate the modelling procedure. This can be used to evaluate PV Module I-V characteristics at any module temperature and irradiance of interest based on the PV Module technology chosen by the user. Further, a model can be selected from a number of models available in order to predict the I-V parameters. This interface can be used to compare the results obtained for different models presented in the previous section. This can also be used to study the effect of temperature and irradiance on the I-V characteristics by simulating the above program for a number of operating conditions simultaneously. The results can be exported to a dedicated excel file, which can be used for further analysis. MATLAB GUI provides an iterative environment to the user without having the need to edit MATLAB codes for different operating conditions and PV Modules.

Fig. 11. Outdoor experimental setup at NISE.

Fig. 12. GUI frontend for modelling.

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5. Results and discussions

represents the linear, regression carried out on I-V tracer data for 5 commercially available PV Modules of different technologies, i.e., multicrystalline, MAXEON, CdTe, CIGS, and MICROMORPH. The slope of the linear fit curve indicates the value of desired coefficients; therefore, the accuracy of the above regression analysis and measurement is essential.

As per the above modelling criteria proposed, the outdoor data recorded for each of five modules was used to evaluate diode ideality factor, the temperature coefficient of current and temperature coefficient of voltage as per the above procedure. Figs. 13a–13e

Fig. 13a. Regression analysis for multicrystalline technology module.

Fig. 13b. Regression analysis for Maxeon technology module.

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Fig. 13c. Regression analysis for CdTe technology module.

Fig. 13d. Regression analysis for CIGS technology module.

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Fig. 13e. Regression analysis for MICROMORPH technology module.

5.1. Regression analysis

Table 2 Selection of network architecture (feed forward).

The accuracy of the regression analysis can be verified with the R square value as obtained using the linear fit curve. The R square value determines the closeness of the measured IV data points to the fitted regression line. A value closer to 1 implies better regression. The results obtained below have regression coefficients greater than 0.99 and a standard error in slope measurement of 0.00597 indicating a high degree of accuracy. Table 1 indicates the values of temperature coefficients and diode ideality factor for all of the technologies modeled. The I-V characteristics are predicted using the above modelling procedure for 7 parameters, 5 Parameter and Rs Model for five different technology PV Modules. This is compared to I-V characteristics using the outdoor experimental at a number of different values of module temperature and irradiance. Percentage errors are computed at significant data points of the IV characteristics, i.e., maximum power point (Pmax Imax Vmax), short circuit condition (Isc) and open circuit condition (Voc) for each of the five technology modules.

Feed forward neural network

Current coefficient Ki (A/K)

Voltage coefficient Kv (V/K)

Ideality factor (a)

CDTE CIGS MICROMORPH MAXEON MULTICRYSTALLINE

0.00158 0.01003 0.00488 0.0060 0.0051

−0.1521 −0.1894 −0.1594 −0.1652 −0.1670

1.037 1.707 1.0911 1.264 1.068

No. neurons

MSE

MBE

R2

TRAIN LM 2 2 1 1

[10 10] [5 5] 10 5

0.5034 0.8055 0.6059 0.9563

0.0040 −0.0045 0.000597 0.0042

0.9177 0.7255 0.9349 0.8920

TRAIN RP 2 2 1 1

[10 10] [5 5] 10 5

1.6117 2.8016 11 3.1084

−0.0097 0.0171 0.039 0.0211

0.8603 0.7492 0.87 0.6978

summarizes the results obtained for selection of network architecture and training algorithm carried out on Sunpower (Maxeon) Technology Module. Here MSE, MBE, and R2 values are calculated cumulatively for IV curve parameters for different network topologies for 10 validation sets as per K Fold Analysis (K = 10). Table 3 indicates the variation of spread factor on the performance of radial basis neural networks. The spread factors indicated the sensitivity of the RBNN on the input values. Spread Factor is varied for 0.5–1.1 in order to observe the effect of spread on the performance of radial basis neural network. Here multi-layer neural network with one input layer, one hidden layer (10 neurons) and an output layer yielded the best results with Levenberg–Marquardt as the training algorithm. The neural network analysis has been carried out on Laptop computer with Intel Core i3 4 Gb of RAM. The training and validation stage takes less than 2 min. Post the selection of network architecture, the model is used to predict IV curve parameters of different PV Module technologies, i.e., CdTe,

Table 1 Regression analysis. Technology

No. hidden layers

5.2. Neural network Here two different ANN topologies, i.e., feed forward neural and radial basis neural networks are trained and tested for predicting the performance of PV Module independently. Artificial Neural Network Toolbox in MATLAB (version: R2014b) is used to develop the various ANN topologies. The ANN developed can be trained using the built-in training functions available where Levenberg-Marquardt (LM) and Resilient Back propagation (RP) were tested. Network architecture for a feed forward neural network was selected on trial and error basis where a number for different topologies was tried and tested. Table 2

Table 3 Selection of network architecture (radial basis). Radial basis neural network

112

Spread

MSE (×102)

MBE

R2

0.5 1 1.1

5.048 3.349 3.034

10.301 7.369 6.824

−0.0365 −0.2279 −0.0472

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Table 4 Error analysis (MBE) for FFANN. Feed forward network PV technology

IV curve parameter

MULTICRYSTALLINE SUNPOWER (MAXEON) CDTE CIGS MICROMORPH

ISC

VOC

IMAX

VMAX

PMAX

0.1020 0.1916 −0.6204 −0.0405 0.0127

−0.0079 −0.1631 −0.0657 0.0011 0.0202

0.0948 0.0119 0.2939 0.1427 −0.0090

−0.0077 −0.0564 −0.0692 −0.0367 0.0539

0.0065 −0.1805 −0.0858 −0.1247 −0.0217

CIGS, MICROMORPH, multicrystalline, MAXEON. Table 4 shows MBE variation for different module technologies for different parameters as obtained by the above analysis.

Figs. 14c–14e show the error plots for three thin film technology modules i.e. CdTe, CIGS, and MICROMORPH. Similar results are obtained for thin film technology modules as well with percentage errors subsequently less for seven parameter model as compared to five parameter and Rs model. The plots also show the accuracy of the IV curve parameter prediction using a feed forward neural network. A comparison reveals that the error variance is significantly lower for FF ANN, however, the MBE is considerable when employed independently for performance prediction. The network performs efficiently to input values closer to trained data sets. However, a deviation in input values leads to poor network performance. Thin film modules show comparatively higher deviations in simulated values of I-V characteristics parameters than the crystalline technology modules. This is due to non-linear behavior of thin film modules and temperature/irradiance dependency of temperature

5.3. Error analysis Fig. 14a shows the percentage Error plots for various I-V characteristic parameters i.e. Voc, Isc, Vmax, Imax, Pmax for Maxeon technology Module. A comparison can be made between the proposed models for the PV modules. The plot clearly indicates the seven-parameter model to be the highest efficient model with percentage errors subsequently less the five parameters and Rs Model respectively for I-V curve parameters, i.e., Voc, Isc, Vmax, Imax, Pmax (see Fig. 14b).

Percentage Error =

y pr y ac 100 y ac

Fig. 14a. Error analysis Maxeon technology.

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Fig. 14b. Error analysis multicrystalline technology.

Fig. 14c. Error analysis CIGS technology.

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Fig. 14d. Error analysis micromorph technology.

Fig. 14e. Error analysis CDTE technology.

coefficients of voltage and current. Further, the spectral mismatch observed between the reference cell and the thin film modules create an error in the measurement of I-V characteristics for thin film technology modules. Thus, analysis can be extended to the calculation of effective irradiance based on mismatch factor for different technology modules. Fig. 15a shows the error plots for MAXEON technology module for various I-V curve parameters as obtained using the proposed cascaded model. The predicted values from the seven parameter model are corrected using the feed forward neural network. The ANN takes I-V curve parameters as input and returns the corrected values as the output. The results obtained from the cascaded model are compared with the

outdoor experimental data to deduce percentage errors. The results show significantly lower deviations in the determination of Vmax, Imax, Pmax, Isc, Voc with mean bias errors less the 1%. The same has been repeated for multicrystalline technology module wherein the seven parameter model and training stage of the neural network are specific to multicrystalline technology data. Similar results are obtained as per Fig. 15b where errors deviations are lower in comparison to independent models.

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model parameters required to evaluate IV characteristics at the given temperature and irradiance. Further, the accuracy of the various electrical equivalent models and neural networks is compared to crystalline and thin film technology modules. The deviation between simulated and experimental data for various IV curve parameters, i.e., Voc, Isc, Vmax, Imax, Pmax is compared for various models. Among the electrical equivalent models, the seven parameter model is the most efficient model for performance prediction however commutation of model parameters is complex and tedious. Neural network models simplifies the computational process at the expense of higher error variance A cascaded model is proposed wherein the values are first predicted via the seven parameters model and simultaneously corrected via feed forward neural networks. The results obtained, verify the proposed cascaded model to be the most efficient model in comparison to independent models where mean bias error deviations are less than ± 1% and error variance is reduced significantly. Further, a MATLAB based GUI is developed which is used to effectively evaluate Module parameters and performance of PV Modules at any temperature and irradiance for the above five module technologies. This simplifies the computation process and provides an interactive user interface.

Fig. 15a. Error analysis MAXEON (SEVEN PARAMETER + FFANN).

Acknowledgement The authors are thankful to National Institute of Solar Energy, Gurugram, India for allowing them to use the test set-up. References Bana, S., Saini, R., 2016. A mathematical modeling framework to evaluate the performance of single diode and double diode based SPV systems. Energy Rep. 2, 171–187. Chan, D., Phang, J., 1987. Analytical methods for the extraction of solar-cell single- and double-diode model parameters from I-V characteristics. IEEE Trans. Electron Dev. 34 (2), 286–293. Edoras.sdsu.edu, 2018. Backpropagation (Neural Network Toolbox). (online) Available at: https://edoras.sdsu.edu/doc/matlab/toolbox/nnet/backpr13.html (accessed 22 May 2018). Hansen, C., 2015. Parameter Estimation for Single Diode Models of Photovoltaic Modules. (online) Prod.sandia.gov. Available at: http://prod.sandia.gov/techlib/accesscontrol.cgi/2015/152065.pdf (accessed 22 May 2018). Ishaque, K., Salam, Z., Taheri, H., 2011. Simple, fast and accurate two-diode model for photovoltaic modules. Solar Energy Mater. Solar Cells 95 (2), 586–594. Jumaat, S., Crocker, F., Abd Wahab, M., Mohammad Radzi, N., 2016. Investigate the photovoltaic (PV) module performance using Artificial Neural Network (ANN). 2016 IEEE Conference on Open Systems (ICOS). Lo Brano, V., Ciulla, G., Di Falco, M., 2018. Artificial Neural Networks to Predict the Power Output of a PV Panel. Marion, B., Rummel, S., Anderberg, A., 2004. Current-voltage curve translation by bilinear interpolation. Prog. Photovolt.: Res. Appl. 12 (8), 593–607. Mellit, A., Pavan, A., 2010. A 24-h forecast of solar irradiance using artificial neural network: application for performance prediction of a grid-connected PV plant at Trieste, Italy. Solar Energy 84 (5), 807–821. Pandiarajan, N., Muthu, R., 2011. Mathematical modeling of photovoltaic module with Simulink. 2011 1st International Conference on Electrical Energy Systems. Park, D., El-Sharkawi, M., Marks, R., Atlas, L., Damborg, M., 1991. Electric load forecasting using an artificial neural network. IEEE Trans. Power Syst. 6 (2), 442–449. IEC 60891, 2009. Photovoltaic Devices – Procedures for Temperature and Irradiance Corrections to Measured I-V Characteristics. Sari, Y., 2014. Performance evaluation of the various training algorithms and network topologies in a neural-network-based inverse kinematics solution for robots. Int. J. Adv. Robot. Syst. 11 (4), 64. Sera, D., Teodorescu, R., Rodriguez, P., 2007. PV panel model based on datasheet values. 2007 IEEE International Symposium on Industrial Electronics. Sharma, V., Chandel, S., 2013. Performance and degradation analysis for long term reliability of solar photovoltaic systems: a review. Renew. Sustain. Energy Rev. 27, 753–767. Tsai, H., Tu, C., Su, Y., 2008. Development of Generalized Photovoltaic Model Using MATLAB/SIMULINK. (online) S2i.bordeaux.free.fr. Available at: http://s2i.bordeaux. free.fr/Espace%20Terminale/Ressources/Projet/Projet%202%202013-2014/2. %20Development%20of%20Generalized%20Photovoltaic%20Model%20using %20Matlab.pdf (accessed 22 May 2018). Xiao, W., Dai, J., Wu, H., Nazario, G., Cheng, F., 2017b. Effect of meteorological factors on photovoltaic power forecast based on the neural network. RSC Adv. 7 (88), 55846–55850. Weidong, Xiao, Dunford, W., Capel, A., n.d. A novel modeling method for photovoltaic

Fig. 15b. Error analysis multicrystalline (SEVEN PARAMETER + FFANN).

5.4. Benchmark analysis A comparison between the manufacture data specification of the PV Module and the predicted data obtained via different predictive models at 1000 W/m2 and 25 °C was also drawn in order to benchmark the performance of the model against a standard reference. Table 5 shows the percentage errors for various I-V curve parameters for different predictive models for Multi-Crystalline Module. This again shows that among the various models available, the cascaded model is the most accurate model followed by seven and five parameter model. Table 5 Benchmark analysis (percentage error) for multi-crystalline. Predictive model

Rs model 5 Parameter 7 Parameter FF ANN FF ANN + 7 Parameter

Percentage error (IV curve parameter) Voc

Isc

Pmax

Vmax

Imax

−1.90 0.78 −0.73 −2.18 −0.59

−2.01 0.68 0.39 3.64 0.21

4.28 2.65 −1.80 1.66 −0.77

2.03 1.13 0.17 −1.60 −0.17

2.21 −1.91 −2.98 2.73 −0.87

6. Conclusions This paper presents a general modeling procedure for photovoltaic modules. It follows a systematic approach in order to determine the

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