Improved artificial neural network method for predicting photovoltaic output performance

0 Introduction

Due to the restriction by resource reserves and environmental problems of fossil energy,the development and utilization of renewable energy has become the inevitable trend of the energy transition worldwide[1,2].As a clean energy application with broad prospects,photovoltaic (PV) power is becoming a major direction of the energy transition and has been rapidly developing in recent years [3].The positive energy price policy and electricity price mechanism have also promoted the fast growth of PV [4,5].Evolving technologies for smart energy networks have opened up new opportunities for integrating solar power systems into grids [6].However,the fluctuations in PV power output significantly hinder the grid from taking it in [7].Fluctuations or intermittency can be caused by many factors such as sunlight intensity and changes in environmental conditions [8].Accurate prediction of the PV system is crucial to the stability of the power grid.Therefore,a useful solution to this problem is to establish an accurate prediction model for PV power generation [9].

Many methods have been proposed to describe the PV models.Three main methods have been used to describe PV models:the analytic model [10],single diode model [11],and double-diode model [12].The single-diode model and analytic model are the most widely used because they combine simplicity and sufficient accuracy.The classical single diode physical model uses the structure of a controlled current source inverse parallel diode and resistance to simulate the acceleration power supply and reverse current.In the single diode model,the nonlinear IV relationship is represented by five physical parameters,including the PV current (Iph),reverse saturation current of the diode (Io),diode ideal factor (n),shunt resistance (Rsh),and series resistance (Rs).

The I-V equation of the PV system is nonlinear and implicit,and many methods have been proposed to solve it,including analytical methods [13,14,15],numerical methods [16,17],and curve fitting [18,19].In most studies,only the photocurrent and diode saturation current changed with irradiation and temperature,respectively[20].However,all of the circuit parameters depend on both irradiation and cell temperature.The other three parameters have no clear relationship with irradiance and temperature,so the advantage of the neural network can be reflected.In summary,the five parameters have clear physical meaning and are more accurate than other parameters,making the prediction more accurate.

With the continuous improvement of PV power generation technology,the scale of PV power grid connection is expanding day by day.However,PV power generation has the characteristics of randomness,indirectness,and volatility,and is affected by climatic factors.The power and parameters can be predicted using PV models,and a variety of methods are used to improve these predictions.It has been proven that the power and I-V curves are closely related to the temperature and irradiance and are directly proportional to the temperature and irradiance.However,the direct relationship between irradiance and temperature and the I-V curve and power cannot be accurately expressed by analytical formulas.Instead,neural network can be used to predict this relationship based on the relationship between physical and environmental parameters.Karatepe et al.[12]established neural networks with irradiance and temperature as inputs and the parameters of the single diode model as outputs.They determined the relationship between the diode model parameters,irradiance,and temperature.They trained the neural networks once using some measured current voltage curves and estimated the equivalent circuit parameters by only reading the samples of solar irradiation and temperature very quickly without solving any nonlinear implicit equations [21].Sometimes,the neural network can be combined with wavelet decomposition to reduce the prediction error and improve the accuracy [22].

The relationship between the five parameters,irradiance,and temperature has been discussed in many papers [23].Neural networks can be used to accurately determine the relationship between physical parameters and weather conditions [20].Inputs and outputs may follow different patterns under different weather conditions.Mellit et al.used two neural networks considering cloudy and sunny days,and three neural networks considering sunny,partly cloudy,and overcast days to predict PV power directly.Through error calculation and image analysis,the weather classification neural network was found to be more accurate in predicting the relationship between physical parameters and weather conditions than conventional methods [24,25].

Considering the different weather conditions,the dependence of the output performance of the PV module on the solar irradiance and temperature is complicated.The main objective of this study is to develop a simple and accurate artificial neural network (ANN) model that considers the irradiance and temperature for the accurate estimation of the PV module output performance.The proposed neural network is composed of separate neural networks and is thus called multi-ANN (MANN).The electrical properties of PV modules,including the I-V curves,P-V curves,and normalized root mean square error(NRMSE),are obtained and discussed.The effectiveness and accuracy of the MANN proposed method is verified by experimental data for different types of PV modules and by comparisons with the traditional single-ANN method.

The rest of this paper is organized as follows.In Section 2,we introduce the single diode model,the theory of neural networks,and the theoretical basis of the proposed model.In Section 3,we discuss how to evaluate neural network systems,draw images,and obtain results.In Section 4,we present the conclusions.

1 Improved artificial neural network (ANN)

1.1 Single-diode model

Fig.1 shows the one-diode equivalent circuit of a solar cell,which consists of a diode,current source,series resistance,and parallel resistance.The current source generates the photocurrent (Iph),which is a function of the incident solar irradiation and cell temperature.The diode represents the p-n junction of a solar cell.The temperature dependence of the diode saturation current (Io) and constant diode ideality factor (n) are included in the modeling.In real solar cells,a voltage loss is observed on the way to the external contacts.This voltage loss is expressed by the series resistance (Rs).Furthermore,leakage currents are described by a parallel resistance (Rsh).Using Kirchhoff’s first law,the equation for the extended I-V curve is derived as follows:

where I is the output current of the PV module,Ns is the number of solar cells in series in a module,V is the terminal voltage of the module,q is the electric charge,k is the Boltzmann constant,and T is the cell temperature (K).

1.2 Neural network for predicting PV output performance

Multilayer perceptron is the most widely used neural network,mainly owing to its nonlinear mapping,generalization,and fault-tolerant capabilities [26].The nonlinear mapping capability is mainly used to improve the resolution and compensate for lack of expertise.Then,man problems can be transformed into pattern recognition or nonlinear mapping problems.Without data during training,the ability of the neural network to map correctly from the input space to the output space is called generalization ability.Fault tolerance is the ability to allow input samples with large errors or even individual errors.Based on the above problems,the multilayer perceptron (MLP) neural network has incomparable advantages.In this study,we adopt multilayer perceptron using the back projection algorithm,which has a single hidden layer feedforward network.The neural network consists of three layers:an input layer,a hidden layer,and an output layer.The number of nodes in the input and output layers are based on the input and output dimensions,respectively.According to [21],which considered the same problem considered in this study,the number of hidden layers is 20.Consequently,the input layer has two nodes,the hidden layer has 20 nodes,and the output layer has five nodes(Fig.1).The input layer in this case consists of a twodimensional vector of irradiance and temperature,and the output vector is a four-dimensional vector comprising n,Iph,Io,Rsh,and Rs.To reduce the computational effort,we consider a small network when we find an appropriate network size.When considering the prediction accuracy of the network,the speed of network training must also be considered.Therefore,when the prediction accuracy of the two networks are the same,a small network is usually adopted because the training speed of the small network is faster.This is very important during the testing phase of the network,where fast responses are usually required.In general,the neuron model used in many ANN models consists of a group of connecting links called synapses,each of which has its own weight wkj.This weight is multiplied by its own input xi before summing all weighted inputs as well as an external bias bik that is responsible for lowering or increasing the summation’s output n2k.Then,an activation function f2 is applied to that output to decrease the amplitude range of the output signal a2k to a finite value.

The input vector x = [solar irradiance,cell temperature]is applied to the input layer of the network,as shown in Fig.1.The net input of the jth hidden unit is

where wij is the weight on the connection from the ith input unit,and bhj,with j = 1,2,…,20,represent the bias for the hidden layer neurons.The output of the neurons in the hidden layer is and the net input to the neurons in the output layer is

Fig.1 Configuration of artificial neural network (ANN)

where wkj is the weight on the connection from the jth input unit,b2k,for k =1,2,3,4,5 represent the bias for the second layer,a2k,is the network output of interest,and these outputs are labeled yk.

In Fig.2,a detailed training neural network and prediction flow chart are presented.In the training phase,the method proposed by Laudani et al.[27](hereinafter referred to as the N.L method) is used to calculate five parameters,divide all data into four parts according to the temperature and irradiance,and train the four neural networks.In the prediction stage,the predicted data is input into the corresponding neural network for prediction based on the irradiance and temperature.In this paper,the ANNs are denoted as follows:ANN1 denotes a neural network with irradiance below 600 W/m2 and temperature below 310 K;ANN2 denotes a neural network with irradiance below 600 W/m2 and temperature above 310 K;ANN3 denotes a neural network with irradiance above 600 W/m2 and temperature below 310 K.ANN4 denotes a neural network with irradiance above 600 W/m2 and temperature above 310 K.Furthermore,G represents irradiance and T represents temperature.

Fig.2 Flow charts of neural network training (left)and validation (right)

1.3 Error analysis

The errors discussed in this paper are mainly due to two factors:one is the calculation of the five parameters,and the other is the prediction of the power.There are many methods for obtaining the five parameters under certain conditions.To ensure the accuracy of neural network training and prediction,the AL method is used to calculate the five parameters.To verify the accuracy of the AL method in obtaining the five parameters,the difference between the I-V curve drawn with the calculated five parameters and the actual I-V curve is determined under different irradiances.As can be seen from Table1,the magnitude of the error of the AL method is calculated to be approximately between − 3 and −4.This indicates that the five-parameter training network calculated with the AL method is relatively accurate.

To evaluate the quality of the prediction of neural networks,several evaluation criteria can be used,including the mean square error (MSE),mean relative error(MRE),mean absolute error (MAE),root mean square error (RMSE),NRMSE,coefficient of variance (COV),correlation coefficient (CC),coefficient of determination(COD),efficiency coefficient (EC),overall index of model performance (OIMP),and coefficient of residual mass(CRM) [28].In this study,the NRMSE was used to evaluate the accuracy of the model.Moreover,the NRMSE was used to determine the similarity between the predicted and experimental value.

Table1 Normalized root mean square error obtained with the method proposed by Laudani et al.[27]

Solar irradiance W/m2 Root mean square error of AL method (A)200-400 9.9955e−4 400-600 9.3958e−4 600-800 0.0025 800-1000 0.0029＞1000 0.0018

In general,the best value for the NRMSE is 0,which indicates the highest performance of the model.

In Eqs.(8)-(10),n is the actual number of measured voltages and currents,Iiactual is the actual current,Iicul is the predicted current,Iscactual is the actual short circuit current,and a is the number of curves of the irradiance in a certain range.

2 Results and discussion

We used outdoor-measured I-V data of different PV modules recorded by the National Renewable Energy Laboratory (NREL) [29],which has flat-plate PV modules installed in Cocoa,Florida;Eugene,Oregon;and Golden,Colorado.The data include a wide range of irradiances and temperatures,and the I-V curves of different PV modules associated with meteorological data were recorded nearly every ten minutes from sunrise to sunset in every season for each location for approximately one year.The application of single-crystalline silicon (x-Si) PV modules,multicrystalline silicon (m-Si) PV modules,cadmium telluride(CdTe) PV modules,and copper indium gallium selenide(CIGS) PV modules with a very regular module verifies the applicability of the proposed MANN method.In this study,the data of the single-crystalline silicon PV modules were used to verify the proposed method.The singlecrystalline silicon PV modules were located in Cocoa and had 36 series cells,one parallel cell,area of 0.647 m2,short-circuit current of 4.98327 A,open circuit voltage of 21.9461 V,operating current at maximum power point of 4.48661 W,and operating voltage at the maximum power point of 17.39 V.All values were measured under standard test conditions (STC) of 1000 W/m2,25 °C,and AM1.5.

In this paper,we mainly discuss the relationship between the five parameters,irradiance,and temperature.To intuitively illustrate the randomness of the selected data and the effectiveness of the training network,the distribution of training and validation data of the irradiance and temperature are shown in Figs.3 and 4,respectively;as indicate by the color bar,darker colors indicate smaller densities of the data distribution.

There were 1000 training data points,which were randomly selected from different seasons and different weather conditions.As can be seen from Fig.3,the irradiance at the geographical location of the PV module was mostly distributed around a low irradiance of 200 W/m2 and a high irradiance of 1000 W/m2.In Fig.4,a total of 10,000 data points were selected to verify the accuracy of the neural network prediction,and the same data were randomly selected from each season and weather.Most of the data were at irradiances of 200 and 1000 W/m2,indicating the geographical location of the PV module and the long irradiation time with low and high irradiances.It can be concluded that the selection of neural network training data is universal,and the range of training data covers all irradiance,avoiding the error introduced when not considering the irradiance during neural network training.

Fig.3 Distribution of the training data

To assess the performance of the single-ANN and MANN,the NRMSE was used to calculate the error of the predicted power and I-V curves,and the results are shown in Fig.5.The solar irradiance is represented by G in the figure.From the figure,it can be seen that,overall,the error decreases with the decrease in irradiance,and the error of the MANN is lower than that of the single-ANN.

Fig.6 shows boxplots of the NRMSE obtained with the MANN and single-ANN.From the figure,it can be seen that both the median line and most of the data errors of the MANN are lower than those of the single-ANN.

Table2 lists the irradiance and temperature obtained with eight curves selected randomly,four showing a gradual increase in irradiance at low temperature and four showing a gradual increase in irradiance at high temperature.

Table2 Different operating conditions of a PV module

Irradiance (W) Temperature (K)C1 205.1 298.15 C2 410.0 305.75 C3 709.5 299.35 C4 907.9 299.35 C5 203.5 316.15 C6 411.6 325.65 C7 701.7 321.55 C8 915.2 320.15

Fig.4 Distribution of the validation data

Fig.5 Normalized root mean square error (NRMSE) of I-V of four panels:(a) low irradiance and low temperature (b) high irradiance and low temperature(c) low irradiance and high temperatur (d) high irradiance and high temperature

Fig.7 shows the I-V and P-V curves obtained with the two methods.From Fig.7,it can be seen that the I-V and PV curves predicted with the MANN are more accurate than those predicted with the single-ANN.In addition,in the P-V curves,the maximum power point is marked with a red point.It can be seen that the method proposed in this paper is more accurate in predicting the maximum power point.

3 Conclusion

This paper presents a four ANN method,called the MANN,to predict the output performance of a PV module under varying operating conditions.The four-ANN model is built with different solar irradiance and module temperatures.Each neural network is a traditional threelayer feed-forward neural network.The inputs are the solar irradiance and module temperature,and the outputs are the fives parameters of the single diode model.The neural network is trained using experimental data under different operating conditions.Using the proposed method,the I-V characteristics are determined from the solar irradiance and temperature without solving any nonlinear implicit equation.The proposed MANN is applied to experimental data and compared with a single-ANN.The results indicate that the proposed MANN method has a more accurate output performance prediction,including the I-V and P-V curves and the maximum power point,than the single-ANN.

Fig.6 Boxplots of the NRMSE obtained with the MANN and single-ANN methods for four panels (a) low temperature and low irradiance (b) low temperature and high irradiance (c) high temperature and low irradiance (d) high temperature and high irradiance

Fig.7 I-V curves obtained with the MANN and single-ANN methods at:(a) low temperature and low irradiance (b) high temperature and low irradiance P-V curves obtained with the MANN and single-ANN methods at：(c) low temperature and high irradiance (d) high temperature and high irradiance

Acknowledgments

This work was supported by the National Key Research and Development Program of China (Grant No.2018YFB0904200).

Declaration of Competing Interest

We declare that we have no conflict of interest.