Energy yield estimation of thin-film photovoltaic plants by using physical approach and artificial neural networks

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 130 (2016) 232–243 www.elsevier.com/locate/solener

Energy yield estimation of thin-film photovoltaic plants by using physical approach and artificial neural networks Giorgio Graditi a,⇑, Sergio Ferlito a, Giovanna Adinolfi a, Giuseppe Marco Tina b, Cristina Ventura b a

Italian National Agency for New Technologies, Energy and Sustainable Economic Development, ENEA – Research Center, Piazza E. Fermi 1, 80055 Portici (NA), Italy b Dipartimento di Ingegneria Elettrica, Elettronica e Informatica, University of Catania, Viale Andrea Doria n. 6, 95125 Catania, Italy Received 5 December 2015; received in revised form 8 February 2016; accepted 11 February 2016

Communicated by: Associate Editor Igor Tyukhov

Abstract Nowadays, the estimation of the energy yield of a stand-alone or grid-connected photovoltaic (PV) systems is crucial for ensuring their economic feasibility and the proper sizing of system components. In fact, the energy yield estimation allows to avoid outages and it ensures quality and continuity of supply. In this context, this paper analyzes and compares two different approaches to estimate energy yield of a 1.05 kWp experimental PV plant located at ENEA Portici Research Centre: the first one is based on the physical modelization of the plant; the other one is related to various topologies of Artificial Neural Networks (ANN). In particular, in the second case, a new hybrid method, called Hybrid Physical Artificial Neural Network (HPANN), based on an ANN and clear sky solar radiation curves is proposed and compared with a Multi-Layer Perceptron (MLP) ANN method widely used in the scientific literature. Moreover, using the same structure of the HPANN, a nonlinear AutoRegressive eXogenous (ARX) model, which uses a wavelet network as its nonlinearity estimator, and an approach founded on Adaptive Network based Fuzzy Inference System (FIS) have also been developed. In order to verify the effectiveness of the implemented approaches, measured and estimated data have been compared and errors have been calculated by means of different statistical coefficients. Results demonstrate that the HPANN approach allows a more precise estimation of the ac energy yield, obtaining, in the worst case, values of Relative Root Mean Square Error less than 10%. Ó 2016 Elsevier Ltd. All rights reserved.

Keywords: ANN; Energy yield estimation; HPANN; Nonlinear ARX; Photovoltaic system model

1. Introduction The large scale introduction of renewable nonprogrammable (wind and solar) energy sources into existing energy supply structures is becoming an important ⇑ Corresponding author. Tel.: +39 (0)817723400; fax: +39 (0)817723344.

E-mail addresses: [email protected] (G. Graditi), sergio. [email protected] (S. Ferlito), giovanna.adinolfi@enea.it (G. Adinolfi), [email protected] (G.M. Tina), [email protected] (C. Ventura). http://dx.doi.org/10.1016/j.solener.2016.02.022 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.

challenge. Wind and PV energy sources are certainly the most common, reliable and mature from a technological point of view among the Renewable Energy Sources (RES). In particular, with the continuous fall in the price of PV modules, the rising concern on the greenhouse gas emissions and increasing costs for some generation alternatives, solar energy is rapidly becoming a competitive solution for the production of clean energy. As an example, even during a difficult period of industry consolidation and economic crisis more than 40 GW of PV power systems

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233

Nomenclature ANFIS Adaptive Network based Fuzzy Inference System ac alternating current Tamb ambient temperature a-Si:H amorphous AI artificial intelligence ARX AutoRegressive eXogenous CSM Clear Sky solar radiation Model CC Correlation Coefficient IMPP_STC Current at MPP in STC DAS Data Acquisition System DM Data Mining d day Ya dc yield dc direct current EPIA European Photovoltaic Industry Association EQE External Quantum Efficiency Yf final yield FIS Fuzzy Inference System FL Fuzzy Logic GUI Graphical User Interface h hours HPANN Hybrid Physical Artificial Neural Network IEC International Electrotechnical Commission gmax maximum efficiency MP maximum power MPP Maximum Power Point cPM maximum power temperature coefficient lc-Si:H microcrystalline

were installed worldwide in 2014, according to the European Photovoltaic Industry Association, EPIA (EPIA Global Market Outlook for Photovoltaics 2015–2019, 2015). Nowadays it appears possible to meet the everincreasing energy needs of the planet using the energy coming from RES, particularly in the most industrialized countries, but there are still problems regarding the unpredictability of the amount of energy available to the grid. RES have a dynamic nature and their power generation capabilities are highly dependent on the geographical location and weather conditions. Therefore, there is the need for improving performance of renewable energy technologies, applying suitable techniques for accurate estimation and prediction of their outputs (Shah et al., 2015; Jurusˇ et al., 2013). In fact, the modeling of PV power supply systems is the initial stage that must precede all sizing, identification or simulation applications (Mellit and Kalogirou, 2011). Moreover, the disadvantage of PV systems is that the capital cost compared with conventional energy sources continues to be high. Currently, many research activities

A module area module temperature Tm MLP Multi-Layer Perceptron NN Neural Network NOCT Nominal Operating Cell Temperature VOC open-circuit voltage VOC_STC open circuit voltage in STC PR performance ratio PV photovoltaic POA Plane of Array PMPP_STC power at MPP in STC Pmeas power measured Pac PV plant ac power production Yr reference yield MBE/A Relative Mean Bias Error RMSE/A Relative Root Mean Square Error RES Renewable Energy Sources R2 R-squared STC Standard Test Condition ISC short-circuit current ISC_STC short circuit current in STC Gi solar global radiation aT temperature coefficient TSTC temperature in STC VMPP_STC voltage at MPP in STC WNN Wavelet Neural Network SW wind speed

are focused on the optimization of PV systems which involves: the number of PV modules, capacity of storage battery, capacity of inverter and PV array tilt angle (Tina and Ventura, 2014). Consequently, in any PV plant, sizing represents an important part of the system design, i.e. the optimal selection of the number of solar panels, the size of the storage battery and the regulator to be used for certain applications at a particular site is an important economic task for electrification of villages in rural areas, telecommunications, refrigeration, water pumping, and water heating (Luna-Rubio et al., 2012). In particular, the modeling of PV power systems is a crucial stage that must precede not only sizing, but also placement and optimal power management (Graditi et al., 2014a) under variable climatic conditions. In literature, several models have been developed for the modeling and simulation of the different components of PV power systems based on analytical or numerical techniques (Chouder et al., 2013). In particular, different approaches have been proposed to estimate the output power of PV systems, such as physical approaches (Omar et al., 2014;

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Torres-Ramı´rez et al., 2014; Firth et al., 2010) or numerical and analytical approaches (Navabi et al., 2015; Chouder et al., 2014). The majority of these methods can simulate the PV system based on the mathematical equations of each component of the system and they can be used for analyzing the evolution of the I–V characteristic of the PV-array, state of charge of the battery, regulator characteristics. However, the simple application of standard models/ approaches does not always lead to satisfactory solutions (Maris et al., 2007). These approaches can be applied to PV plants characterized by a simple configurations, otherwise the use of circuit-based models and mathematical equations may be problematic. As for example, in the power plant under study in this paper only the dc voltage and dc current for the whole plant are available, therefore only one set of parameters could be calculated. This can lead to a not accurate calculation of the parameters involved in the circuit based models. Moreover, the values of the unknown parameters depend on the temperature and irradiance. They can be estimated starting from the measured current–voltage (I–V) characteristic at a specific working condition or from the technical data provided by the manufacturer of the PV module, which are relative to reference operative conditions. Then, different formulas should be applied to obtain the value of each parameter in the different working conditions (Chouder et al., 2012). In IEC 60891 the correction procedures according to the temperature and irradiance of the measured I–V characteristics of crystalline silicon PV devices are described. It includes procedures for the determination of temperature coefficients, internal series resistance and correction factor. Anyway, these procedures are valid for a range of irradiation variation of ±30% with respect to the value the I–V characteristic is performed. In order to adapt to the complex and nonlinear reality of the PV production modeling and to obtain more careful forecasts, two are the possible ways:
to use deeply accurate modeling customized to particular situation, using physical knowledge (including important system nonlinearities) as well as other known constraints and external information which the model should respect,
to give up the structured modeling and use a highly adaptive black-box philosophy, which automatically adapts to the local situation. In this context, Artificial Intelligence (AI) techniques represent suitable solutions. They are becoming useful as alternative approaches to conventional techniques or as components of integrated systems, since they can be used for modeling, prediction and optimization of complex systems (Mellit and Kalogirou, 2008). The main advantages of AI techniques are: ability to learn from the input data with or without a proper supervision, generalization ability, fault tolerability in the sense that they have stability of out-

put with respect to input values (incomplete, noisy, not well known, error or variation affected), ability to classify complex patterns and to deal with non-linear problems. In addition, once trained, they can perform high speed prediction and generalization (Tina et al., 2012). They consist of several branches such as ANN, Fuzzy Logic (FL), Adaptive Network based Fuzzy Inference System (ANFIS) and Data Mining (DM) (Kalogirou and Sencan, 2010). Several AI-based methods for PV systems sizing (Mellit et al., 2009; Mellit and Kalogirou, 2011) or for modeling the PV power output (Liu et al., 2014; Saberian et al., 2014) have been presented in literature. In this paper, different approaches are implemented for estimating the power production of a 1.05 kWp experimental micro-morph silicon modules plant. Firstly, a physical model of the power is implemented (Ventura and Tina, 2015), then three AI-based models – a multilayer feedforward network, a nonlinear AutoRegressive eXogenous (ARX) model which uses a wavelet network and an Adaptive Network based Fuzzy Inference System (FIS) – have been developed. The goal of this paper is to compare results obtained using the implemented physical model and the three AIbased models to estimate the power production in terms of advantages and disadvantages and calculating different statistical coefficients. Moreover, a hybrid method, called Hybrid Physical Artificial Neural Network (HPANN), which combines an artificial intelligence technique (ANN) with an analytical physical model is proposed. 2. Experimental PV plant description and performance The developed ANN model makes use of data provided by a Data Acquisition System (DAS) connected to an experimental plant (Fig. 1) consisting of micro-morph silicon modules based on a combination of microcrystalline (lc-Si:H) and amorphous (a-Si:H) silicon technology. In detail, each module is composed of micro-morph double-junction solar cells consisting of a-Si:H top cell and lc-Si:H bottom cell which are stacked on top of each other. The a-Si:H and lc-Si:H materials are characterized by different absorption spectrums and suitable prepared by convenient combined process allow to obtain high quality PV cells. Indeed the micro-morph tandem solar cell is one of the most promising multi-junction candidates for high stabilized efficiency thin film silicon solar cell (So¨derstro¨m et al., 2010). This type of PV module presents better performance at high temperature (due to the presence of a-Si:H cell) and low irradiation values, generally 6250 W/m2 (due to the double junction) compared to traditional crystalline module (Marion, 2008). An improving of the power conversion efficiency substantially owing to better use of the solar spectrum (Keppner et al., 1999; Shah, 2010; So¨derstro¨m et al., 2010) is obtained respect to single a-Si:H and lcSi:H solar cells (Fig. 2).

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Fig. 1. Micro-morph silicon modules PV plant installed at ENEA Portici Research Center.

Fig. 2. External Quantum Efficiency (EQE) of a micro-morph solar cell. Table 1 Comparison of aT between different thin-film modules and traditional c-Si module. ‘‘Error” represents the measurement error for each temperature coefficient (Virtuani et al., 2010). aT

Pmax crel (%/°C)

VOC brel (%/°C)

ISC arel (%/°C)

FF krel (%/°C)

Error a-Si (SJ) CdTe Micro-morph (a-Si:H/lcSi:H) CIGS c-Si wafer-based TF-Si

±0.027 0.13 0.21 0.36 0.36 0.45 0.48

±0.021 0.33 0.24 0.37 0.31 0.33 0.41

±0.019 +0.12 +0.04 +0.05 +0.02 +0.06 +0.15

– +0.10 0.01 0.04 0.08 0.19 0.22

Actual micro-morph tandem cells, containing low VOC bottom cells, show a better thermal behavior than c-Si and all lc-Si:H cells as can be outlined considering the temperature coefficients. In Virtuani et al. (2010) authors tested the temperature coefficients of a set of thin film modules commercially available on the European market. The investigated technologies are: Single Junction (SJ) amorphous Silicon (a-Si), tandem micro-morph (a-Si:H/lc-Si: H), cadmium telluride (CdTe), copper indium gallium selenide CIGS (Cu(In, Ga)Se2), and thin film c-Si (TF-Si). The technologies are listed on an anonymous basis in Table 1. For comparison, relative temperature coefficients (aT) of

a conventional single-crystal c-Si wafer-based module were tested and results are reported in Table 1. All modules, with the exception of CdTe device, were subjected to an outdoor exposure according to relevant IEC standards before testing. This feature should not be underrated, considering that under real working conditions, an important aspect of any solar cell is its temperature performance (Virtuani et al., 2010). The rated power of the plant here analyzed is 1.05 kWp. The PV system architecture is made up of 28 micro-morph silicon modules. They are divided in 14 strings, each of them is made by 2 series modules. PV modules and array details are reported in Table 2. The single module efficiency is closed to 9%. The PV plant is connected to the grid by means of a dcac converter characterized by a maximum efficiency (gmax) P 93%. The used modules are installed at 20° tilt angle, south oriented and they are assembled on a wooden structure to simulate a real roof typical installation (Fig. 1). The PV plant performance indices are calculated according to the European Standard EN 61,724. In detail, considered indices are:





final yield (Yf); dc yield (Ya); reference yield (Yr); performance ratio (PR = Yf/Yr) representing overall losses on array nominal power imputed to module temperature (Tm), partial utilization of total irradiance and system losses or failures.

The block scheme representing the PV plant configuration and performances indices is reported in Fig. 3. The PV plant has been monitored for about 6 years. Its yearly performances are reported in Table 3. 3. AC power estimation 3.1. Physical approach There are several correlations in the literature to estimate the PV electrical power as a function of cell/module

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Table 2 Module/array specifications in Standard Test Conditions (STC). Parameter

Symbol

Unit

Module

Array

Power at MPP in STC Voltage at MPP in STC Current at MPP in STC Open circuit voltage in STC Short circuit current in STC Maximum power temperature coefficient Module area

PMPP_STC VMPP_STC IMPP_STC VOC_STC ISC_STC cPM A

Wp V A V A %/°C m2

37.5 100 0.375 130 0.434 0.16 0.40

1050 200 5.25 260 6.1 0.16 11.2

Fig. 3. PV plant configuration and performance indices definition: block scheme.

Table 3 Annual performance indices. Year

Yf (kW h/kWp)

Yr,d (h/d)

Yf,d (h/d)

PR

2006 2007 2008 2009 2010 2011

1315 1272 1209 1073 1141 1204

4.40 4.41 4.32 4.34 4.03 4.37

3.61 3.48 3.30 3.14 3.12 3.29

0.82 0.79 0.76 0.72 0.77 0.75

operating temperature and basic environmental variables (Skoplaki and Palyvos, 2009). The first solution here implemented is based on a physical modelization of the PV plant (Ventura and Tina, 2015). It depends on the power measured at STC (PMPP_STC) and on the operating condition: P dcphy

1

¼ P MPP

STC



GPOA  ð1  aPM  ðT PV  T STC ÞÞ GSTC

ð1Þ

where GPOA is the plane-of-array irradiance in operating conditions, GSTC is the irradiation in STC (GSTC = 1000 W/m2), aPM is the maximum power temperature coefficient, TPV is the PV cell temperature in operating conditions and, finally, TSTC is the temperature in STC (TSTC = 25 °C). In this case study, the cell/module operating temperature is not available. Anyway, TPV is related to the ambient temperature (Tamb) through the following simple linear formula (Ioannou et al., 2014). T PV ¼ T amb þ ðNOCT  20Þ 

Gi 800

ð2Þ

where Gi is the solar global radiation and NOCT is Nominal Operating Cell Temperature. Using Eq. (1) the power is always overestimated since it takes into account only the power losses due to temperature. Consequently, to better estimate the PV plant ac power production (Pac) other causes of power losses should be modelized and considered. First of all, mismatch losses should be contemplated. They usually are between 1% and 9% (Norton et al., 2011). For sake of simplicity, in this paper, the efficiency due to mismatch losses (gMis) has been taken into account as a constant loss, in particular gMis has been evaluated through the PVSyst software considering the design of the PV plant here studied (gMis = 2%). Then, also the angle of incidence losses (gIAM) should be added. It implies the decrease in irradiance that reaches the cell surface with respect to normal incident irradiance (Rojas et al., 2008). P dcphy

2

¼ gIAM  gMis  P dcphy

1

ð3Þ

Moreover, when power output is generated by solar irradiation on a PV module, Joule heating loss occurs by an electric current to flow through a circuit (Norton et al., 2011). Consequently, the power losses caused by series resistance, gR, can be determined considering the current (I) flowing in a PV modules and the series resistance (R) (Okada et al., 2005). gR ¼

P meas P meas þ R  I 2

ð4Þ

where Pmeas is the measured power and R should be calculated. Considering Eq. (3), Eq. (4) can be written as: P dcphy ¼ P dcphy 2  R  I 2

ð5Þ

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ANNs methods are being widely used in many fields of study as alternative approaches to conventional techniques. An ANN is a mathematical model or computational model based on biological Neural Networks (NNs). It is a complex structure emulating certain ‘‘human” behaviors. Starting from a certain ‘‘experience”, which may have been a priori provided, or which is built up over time with or without human supervision, a Neural Network (NN) becomes able to recognize images, sounds and any other item that is proposed in the right way. It is largely based on the simulation of artificial neurons properly connected. An ANN is an adaptive system that changes its structure based on the information provided during the learning phase. The ANN can be used as a model of complex interconnections between inputs and outputs or to find patterns inside the analyzed data. ANN main properties are:

At the input layer n inputs as xi (i = 1, 2, 3, . . . n) constitute the input signal: e.g. all the variables constitute the available dataset. Each input is weighted before reaching the subsequent layer of neurons, hidden layer, by the connecting strength or the weight factor, wj (j = 1, 2, 3, . . . n). Hence, the signal transferred through the connection strength, is equal to a portion of the original signal as wjxj. ANNs are widely used also in the field of the solar energy to forecast or estimate energy production of solar plants (Mellit and Kalogirou, 2008). In this context, authors would like to pinpoint what, in this paper, is intended with the ‘‘forecast” and ‘‘estimate” terms. The former is used to provide an expectation of future interest variable values (at timestamp t + 1, t + 2, . . . , t + h) based on its previously known/acquired values, eventually considering one or more exogenous variable. The latter is used to represent the relation between output and inputs, at the same timestamp, without recurring to a complex analytical representation. What the two terms ‘‘forecast” and ‘‘estimate” have in common is that the value obtained from the model is always affected by an error although the paramount goal is to minimize this error. In this paper, the attention is focused on NN model and precisely on ANN ability to represent any nonlinear relation; from this point onwards, we are dealing with ANNs estimating capabilities. The design of an ANN consists of the following steps:


Non-linearity: due to the fact that its basic component, the artificial neuron, is non-linear. This property is very important because in this way the network is able to ‘‘learn” non-linear phenomena.
Adaptability: thanks to the presence of modifiable synaptic connections, it is possible to train again the network if the operating conditions are changed.
Ability to create an input/output connection.
Generalization: after the ANN has been trained, it is able to generalize, i.e. to respond ‘‘appropriately” to stimuli never presented during the training phase.
Robustness: thanks to its architecture, the NN can process information in a ‘‘robust” way. The knowledge of the network is stored in a distributed and redundant manner, this means that it is possible to remove some neurons from the network without overly compromising its performance.


inputs and outputs definition; it is possible to relate an output variable to the same input variable (previous values) or use one or more exogenous variables;
inputs/outputs pre-processing to fit an ANN model;
ANN architecture definition by specifying; – number of hidden layer; – number of neurons for each layer; – activation function and transfer function; – training algorithm and performance function definition. In particular, during training, the interest is focused on performance, the magnitude of the gradient of performance and the number of validation checks; – ANN training by submitting the correct map of input/output values; – ANN performance evaluation by measuring error in predicting output values respect to real ones.

In this case, if no other losses are taken into account, R can be calculated by least square fits. Finally, to estimate Pac, the theoretical efficiency of the inverter, gINV, should be considered: P acphy ¼ gINV  P dcphy

ð6Þ

3.2. Neural networks

As human brain similar, where a single neuron is made up of a main cell body, a single artificial neuron can accept x1, x2, . . . xn inputs weighted by w1, w2, . . . wn, providing an output by means of a transfer function f and an appropriate bias B. An ANN is usually made up of several neurons grouped as follow:
one input layer,
hidden layer; one or more than one layer can be arranged,
one output layer.

3.2.1. Neural networks to estimate the AC power generation In this paper, an application of ANNs for the estimation of a thin-film PV plant ac power production (Pac) has been presented. By mean of ANN models, authors were able to evaluate the ac power produced by an experimental PV plant located at the ENEA Research Center of Portici. Different ANNs approaches have been developed. 3.2.1.1. Multi-Layer-Perceptron neural network. Considering solar radiation and PV energy yield estimation, one

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of the most used NNs is the MLP (feed-forward) network consisting of units arranged in layers with only forward connections to units in subsequent layers (Mellit and Kalogirou, 2008). The focus of this work is to estimate Pac, as function of two inputs parameters, i.e. Tamb and Gi. Since the outputinput relation under study is non-linear, the MPL network, with only one hidden layer, is one of the most suited ANN architectures. In fact, this type of ANN has been proven to be (Mellit and Kalogirou, 2008) a universal approximator of these nonlinear functions. The used numerical environment to design the MLP NN is MATLABÒ and its Neural Network Toolbox containing suitable tools to develop the above described model, also by means of a user-friendly Graphical User Interface (GUI). In details, the implemented MLP NN is made up of a single hidden layer with 8 neurons, training is evaluated considering the Mean Squared Error as performance parameter. A maximum of 500 epochs (Graditi et al., 2014b) and a number of validation checks set to 10 are taken into account. Moreover, a radial basis transfer function is used as neuron activation function of the hidden and the output layer, while the used learning algorithm is the Levenberg–Marquardt back-propagation. Weights and bias values are updated according to Levenberg–Marquardt optimization (Chen and Zhang, 2012). The values of the learning period, the size of the used training dataset, the hidden layer neurons and the learning rate were set on a trial and error basis. The other parameters characterizing the MLP NN have been set as the defaults values used in the MATLABÒ Neural Network Toolbox v.8.4. The block diagram of the ANN used to estimate the Pac function using two inputs is shown in Fig. 4. Then, to improve the performance of this first MLP NN, a new hybrid method called HPANN, based on an ANN and the Clear Sky solar radiation Model (CSM), is considered. Clear sky models estimate the terrestrial solar radiation under a cloudless sky as a function of the solar elevation angle, site altitude, aerosol concentration, water

Fig. 4. Structure of the MLP NN used to estimate Pac using as inputs: Gi and Tamb.

vapor, and various atmospheric conditions. It stands for a reference for the daily variance of irradiance and the upper limit for it (Tina et al., 2012). In this case, by a trial and test procedure, an optimal value of 12 neurons has been selected for the hidden layer. The block diagram of the HPANN approach used to estimate the Pac function is shown in Fig. 5. 3.2.1.2. nWavelet neural network. Recently, the Wavelet transform, which is a novel signal processing technique developed from the Fourier transform, has been widely used to signal processing. Its main characteristic is its time frequency localization. Wavelet transformation has versatile basis functions which are selected based on the type of the signal analyzed. Wavelets have generated a great interest in both theoretical and applied areas, especially over the past few years (Mellit et al., 2009). Wavelet Neural Network (WNN) is an approach toward the learning function. They utilize wavelets as the basis function to construct a network. The WNN consists of three layers: input layer, hidden layer and output layer. In this paper, a WNN has been developed to estimate the PV plant’s ac energy yield using the System Identification Toolbox in MATLABÒ environment. In particular, a nonlinear ARX model using a wavelet network, as its nonlinearity estimator, has been adopted. The structure of the developed WNN is equal to the HPANN approach shown in Fig. 5. Considering a trial and error basis, the maximum number of estimation iterations has been set to 1000, while the estimation focus has been set to ‘simulation’ in order to optimize model for simulation applications. No time delay has been set. The other parameters characterizing the nWavelet NN have been set as the defaults values used in the MATLABÒ System Identification Toolbox. 3.2.1.3. Adaptive network-based fuzzy inference system. A fuzzy system can represent a suitable solution to match any set of input-output data. Some advantages of Fuzzy Logic (FL) are: it is conceptually easy to understand, it is

Fig. 5. Structure of the HPANN used to estimate the Pac.

G. Graditi et al. / Solar Energy 130 (2016) 232–243

flexible and it is able to manipulate inaccurate data, it can reproduce functions of arbitrary complexity, it allows to use and manipulate the experience of human users, it can be combined with other control techniques and it is based on a natural language. FL is a methodology that mimics the human capability of imprecise reasoning and uncertain judgment (Mellit and Kalogirou, 2008). This process is made particularly easy by adaptive techniques like ANFIS which are available in FL software Toolbox. The ANFIS is a soft computing method in which a given input-output data set is expressed in a FIS that implements a nonlinear mapping from its input space to the output space. The mapping is obtained by a number of fuzzy ‘‘if-then” rules, each one describing the local behavior of the mapping. The fuzzy membership parameters are optimized either by using a back-propagation algorithm or by combination of both back-propagation and least square method (Mellit and Kalogirou, 2011). The neuro-adaptive learning method works similarly to ANN one, where the method for the fuzzy modeling procedure to learn information about a data set is based on neuro-adaptive learning techniques. Also in this case the structure of the developed ANFIS is equal to the HPANN approach shown in Fig. 5. The ANFIS model has been developed in MATLABÒ environment, considering a trial and error basis. In detail, in the Input MF Type box, the ‘trimf’ has been chosen, the Output MF Type box has been set to ‘constant’, the number of epochs to 500 and the optimization method to ‘‘hybrid”. The other parameters characterizing the ANFIS NN have been set as the defaults values used in the MATLABÒ ANFIS Toolbox. 4. Results evaluation The considered PV plant was monitored since 2006, so a large dataset of experimental data is available to train and test the used models. In particular, 6 years of data sampled with a time step of 5 min were used for NNs training and valuation. Data have been filtered to make them coherent and physically acceptable. The number of available data for each year is reported in Table 4. The theoretical number of available data is 105,120 for all year, except for leap years where it is 105,408. Some statistical indicators have been considered in order to appreciate the effectiveness of the NNs estimation. These parameters, calculated by the following expressions, are:

239


Relative Mean Bias Error (MBE/A) (Eq. (7));
Relative Root Mean Square Error (RMSE/A) (Eq. (8));
Correlation Coefficient (CC) (Eq. (9)). PN

 P x;n Þ  100 N  Px qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 1 n¼1 ðP y;n  P x;n Þ N RMSE=Að%Þ ¼  100 Px PN n¼1 ðP y;n  P y Þ  ðP x;n  P x Þ ffi CC ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 PN 2 n¼1 ðP y;n  P y Þ  n¼1 ðP x;n  P x Þ

MBE ¼ Að%Þ

n¼1 ðP y;n

ð7Þ

ð8Þ ð9Þ

where Px(n) represents the measured data, Py(n) the estimated one, N is the number of available samples, P x and P y are the mean values of the measured and estimated data, respectively. Another commonly used statistic related to the error is the goodness-of-fit R2 (R-squared) statistic. The R2 statistic ranges from a value of 0 for absolutely no relation between the data and the line to a value of 1 which occurs only if all of the data fall exactly on the line, i.e., no error. In some engineering disciplines, an equation fitted to data is acceptable only if R2 > 0.9. Other engineering disciplines might find an R2 as low as 0.7 acceptable for use. The R2 index is mathematically defined as: PN 2 ðP y;n  P x;n Þ 2 R ¼ 1  Pn¼1 ð10Þ 2 N n¼1 ðP x;n  P x Þ Table 5 Values of statistical coefficients obtained estimating the Pac with the physical method described in Section 3.1. The resistance R has been calculated by least square fits using the data relative to the year 2007, R = 3.52 X. Year for test

MBE/A (%)

RMSE/A (%)

CC

R2

2006 2007 2008 2009 2010 2011 2012

4.03 1.99 4.59 1.78 2.32 5.17 9.46

10.59 7.64 9.24 8.69 13.22 10.24 11.60

0.9866 0.9892 0.9872 0.9853 0.9696 0.9831 0.9873

0.9591 0.9768 0.9666 0.9692 0.9368 0.9564 0.9387

Table 4 Number of available data for each year.

Table 6 Values of statistical coefficients relative to the MLP NN with two input (Tamb and Gi) values. Data relative to year 2007 have been used as training dataset.

Year

Available data

Year for test

MBE/A (%)

RMSE/A (%)

CC

R2

2006 2007 2008 2009 2010 2011 2012

34,322 36,823 22,531 22,501 35,394 37,746 14,334

2006 2007 2008 2009 2010 2011 2012

4.36 0.50 1.91 2.24 1.24 3.94 5.25

9.58 6.47 7.61 7.72 10.60 9.40 9.94

0.9887 0.9919 0.9905 0.9886 0.9803 0.9849 0.9863

0.9667 0.9839 0.9785 0.9754 0.9602 0.9641 0.9584

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Table 7 Values of statistical coefficients relative to the HPANN approach. Data relative to year 2007 have been used as training dataset. Year for test

MBE/A (%)

RMSE/A (%)

CC

R2

2006 2007 2008 2009 2010 2011 2012

5.14 0.42 1.22 1.22 0.62 3.04 4.73

9.76 5.91 7.01 7.24 10.09 8.33 8.75

0.9901 0.9934 0.9916 0.9897 0.9824 0.9878 0.9892

0.9660 0.9868 0.9820 0.9788 0.9644 0.9723 0.9681

Table 8 Values of statistical coefficients relative to the nonlinear ARX model using a wavelet network as its nonlinearity estimator. Year for test

MBE/A (%)

RMSE/A (%)

CC

R2

2006 2007 2008 2009 2010 2011 2012

4.72 0.01 1.65 1.47 0.93 3.53 5.23

9.36 5.65 7.13 7.44 10.69 8.33 9.03

0.9903 0.9939 0.9914 0.9892 0.9800 0.9883 0.9890

0.9685 0.9878 0.9812 0.9775 0.9598 0.9721 0.9657

Table 9 Values of statistical coefficients relative to ANFIS. Year for test

MBE/A (%)

RMSE/A (%)

CC

R2

2006 2007 2008 2009 2010 2011 2012

4.76 0.01 1.63 1.30 0.60 3.20 5.11

9.53 5.81 7.07 7.51 10.71 8.41 8.99

0.9897 0.9935 0.9916 0.9890 0.9800 0.9878 0.9889

0.9674 0.9871 0.9816 0.9772 0.9599 0.9717 0.9660

It must be underlined that the closer the correlation index is to unity value, the better the model represents the plant real output. The results obtained using the physical model discussed in Section 3.1 are shown in Table 5.

With regard to the MLP NN, the methodology adopted to evaluate the performance can be described by following steps:
Divide the entire available data set in subsets, each regarding a specific year.
Select a specific year for MLP NN phases of training/ evaluation and testing, according to a percentage division, typically 98% for training, 1% for testing and 1% for evaluation.
Train the network using data relative to the year chosen for the train phase.
Simulate the network output utilizing all the years and compute, for each year, the statistical indexes described before. The designed MLP NN was trained using the year 2007 data and it was simulated with all the other available years (2006, 2008, 2009, 2010, 2011, 2012). The values of statistical coefficients obtained considering the network with two inputs (Tamb and Gi) are reported in Table 6. Then another input, relative to the CSM, has been added to the MLP NN (HPANN approach) and statistical coefficients values (Table 7) have been evaluated. Values of statistical coefficients relative to the nonlinear ARX model using a wavelet network as its nonlinearity estimator and the ANFIS method using the HPANN approach are listed in Tables 8 and 9 respectively. Based on these results some comments can be done:
The AI-based approaches allow to obtain a better estimation of the Pac compared to the physical approach here implemented. In particular, a good estimation of the PV plant ac energy yield have been obtained using only two inputs for the MLP NN here developed, the ambient temperature and the global solar radiation. Moreover, values of statistical coefficients and the correlation index demonstrates that, adding the clear sky

Table 10 Values of Yf calculated using the measured Pac and the estimated one considering the different methods presented in this paper: Physical approach, MPL NN, n-Wavelet NN and ANFIS. Year

Measured Yf (kW h/kWp)

Estimated Yf (kW h/kWp) (Yf%) Physical approach

MP NN

n-Wavelet NN

ANFIS

2006

1166

2007

1166

2008

648

2009

720

2010

1065

2011

1124

2012

407

1119 (95.96%) 1189 (101.97%) 677 (104.47%) 732 (101.66%) 1089 (102.25%) 1182 (105.16%) 446 (109.58)

1109 (95.11%) 1165 (99.91%) 657 (101.38%) 729 (101.25%) 1073 (100.75%) 1161 (103.29%) 421 (103.43%)

1111 (95.28%) 1166 (100.00%) 659 (101.69%) 730 (101.38%) 1075 (100.93%) 1164 (103.55%) 429 (105.40%)

1110 (95.19%) 1166 (100.00%) 658 (101.54%) 729 (101.25%) 1071 (100.56%) 1160 (103.20%) 428 (105.16%)

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Fig. 6. Empirical cumulative distribution function of the measured Pac and the estimated one considering the different methods presented in this paper: Physical approach, MPL NN, n-Wavelet NN and ANFIS. The year 2007 has been used for the training of the AI-based models.

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solar radiation as input to the MLP NN (HPANN), it is possible to obtain a more accurate estimation of the measured Pac.
The main advantage of the AI-based approaches is that only information about temperature, irradiance and geographic data are required to obtain a good estimation of Pac. Moreover, these techniques are relatively insensitive to noise included in the measured data; their disadvantage is that a large number of historical data to train network are needed. On the other hand, using a physical approach, the dc power, the dc current, the main characteristic data of the PV modules and of the inverter and a detailed knowledge of their prevailing physical relationships are needed to estimate Pac. In addition, measurement errors greatly influence the results.
Comparing the results obtained with the HPANN, nonlinear ARX with wavelet and ANFIS approaches, it is possible to affirm that ARX with wavelet and ANFIS approaches results are comparable with a slight improvement in the HPANN case. The values of Yf calculated using the measured Pac and the estimated one considering the different methods presented in this paper are shown in Table 10. It should be taken into consideration that the Yf calculated using the measured Pac is different from that one indicated in Table 3, because it has been calculated only using the available data for each year indicated in Table 4. Table 10 shows the trend of the measured and the estimated Yf. They are very similar in the year 2007 since it is the year used for the training of the AI-based models implemented in the paper. In the year 2006 it is possible to note that value of Yf is underestimated, while after year 2007 it is overestimated. Since Yf is obtained using the sum of the measured or the estimated Pac, in order to underline if results shown in Table 10 are due to compensation issues, the empirical cumulative distribution function of the measured and estimated Pac has been calculated and shown in Fig. 6. Fig. 6 confirms that the estimated Pac during the year used for training (2007) is very closed to the measured Pac. Results obtained the year before the training show how the estimated Pac underestimated the measured Pac, especially for Pac greater than 500 W. Instead for years after 2007 the Pac is overestimated. This can be due to a degradation of the performance of the power plant that the methods presented in this paper, to estimate the Pac, are not able to catch. However, such compensation effects could be studied deeper, analyzing if they are also timedependent. A minor compliance among the physical approach estimated curve and the measured one than the other presented methods, can be observed in Fig. 6. 5. Conclusion The accurate estimation of the power generation is very important for the operations planning of the entire electric

power system. In this paper, an application of different approaches for the estimation of ac energy yield of a thin-film PV plant has been presented. In particular, first of all, an approach based on the physical relationships between variables needed for Pac estimation has been presented. Then a MLP NNs characterized by the measured ambient temperature and the global solar radiation inputs, has been presented. Moreover, for a better estimation of the Pac, a new hybrid method, by means of an ANN mixed with the clear sky solar radiation model, has been proposed and called HPANN. In fact, the clear sky solar radiation can represent a reference value and, since it is a calculated value, can be used to compensate measurement errors on the two inputs of the ANN which surely influence the estimation of Pac both during the training and the test phase. Then, using the hybrid approach, a nonlinear ARX model, which uses a wavelet network as its nonlinearity estimator, and an adaptive neuro-fuzzy inference systems have been also implemented. Available data to train and test the different approaches taken into consideration were relative to seven years of data acquisition, from 2006 to 2012. Only one year of the available data have been used for the training phase and then the data relative to the remained years have been used to test the developed methods. The results from the error assessment, according to the error definitions here explained, lead to the conclusion that AI-based approaches allow to better estimate Pac than the physical method, moreover the hybrid method is more accurate than just the ANN. In particular, using the MLP NN with two inputs, the Relative Mean Bias Error (MBE/A) resulted to be between 0.50% and 5.25%, the Relative Root Mean Square Error (RMSE/A) between 6.47% and 10.60%, the Correlation Coefficient (CC) between 0.9803 and 0.9919, while the R-squared (R2) between 0.9584 and 0.9839. Whereas in the case the HPANN approach is used, the MBE/A resulted to be between 0.01% and 5.11%, the RMSE/A between 5.91% and 10.09%, the CC between 0.9824 and 0.9934, while the R2 between 0.9644 and 0.9868. Furthermore, the comparison between the different AI-based approaches here adopted allows to conclude that there is not an approach that gives better results than the others, but they are comparable. The methods here presented, which are static models to estimate the ac power, can be used also for forecasting purposes. If forecasted variables are used as inputs, in fact, the output will be forecasted ac power. The error on the forecasted output will be the sum of the error of the forecasted temperature and irradiance and the error of the static model. Therefore, reducing the error on the static models will allow an indirect way to diminish the error on the forecasted power. References Chen, Y., Zhang, S., 2012. Research on EEG classification with neural networks based on the Levenberg–Marquardt algorithm. In: Information Computing and Applications, 308, pp. 195–202

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