Module parameter extraction and simulation with LTSpice software model in sub-Saharan outdoor conditions

1 Laboratoire Electronique, Informatique, Télécommunication et Energies Renouvelables, Université Gaston Berger, Sénégal. 2 GeePs-CentraleSupelec, Laboratoire de Génie Electrique et Electronique de Paris, Universités de Sorbonne, France, UPMC Univ Paris 06, UMR 8507, F-91190 Gif sur Yvette, Paris, France. 3 LESEE-2iE, Laboratoire Energie Solaire et Economie d'Energie, Institut International d'Ingénierie de l'Eau et de l'Environnement, 01 BP 594 Ouagadougou 01, Burkina Faso.


INTRODUCTION
The electric performance of photovoltaic module is described by mathematic equations that model currentvoltage (I-V) curves.Seven mathematical models divided into three groups are usually used (Table 1).The widely used model is the single diode model.These equations are non-linear and need the appropriate methods to extract their parameters.In the literature, several authors have presented reviews of the methods used to extract module parameters (Rabeh Abbassi et al, 2018) (Ashwini Kumari, 2018;Tamrakar and Gupta, 2015).Table 2 shows a non-exhaustive list of various methods used in literature to determine model parameters.Even if these different methods are powerful, most of them, mainly iterative methods as Levenberg-Marquardt (LM) algorithm require *Corresponding author.E-mail: kata.ndetigma@ugb.edu.sn.Tel: 33 961 23 40.Fax: 33 961 53 38.
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Group Model Parameters
One diode model

MATERIALS AND METHODS
The equivalent mathematical model of one diode (five parameters) for the solar cell is given by Equation 1: (1) where and are a photo-generated current, dark saturation current, ideality factor, series resistance, and shunt resistance, respectively.These parameters are to be determined.The initial values required by LM algorithm to perform calculation are calculated with the empiric analytic method exposed after LM algorithm presentation.The LM algorithm combines the methods of the gradient descend and the Gauss-Newton's.This led the algorithm to be robust and fast.A vector ( is the number of points measured for the current-voltage curve) is considered.For each measured voltage value VI, a theoretical current is calculated from the equivalent model with a function Lp (V) of 5 parameters ( and ).A residue vector is obtained from the theoretical current and the measured current as shown in the Equation 2. The values of the parameters p which minimize the norm f(p) (Equation 3) of the residue r(p) are the parameters which model the module.For each iteration i, the norm of the vector residue r(p) is calculated.The parameter  (Figure 1) varies in the same direction as the error to adjust the influence of the hessian (H) on the convergence of the solution.This adjustment may result in an increase or decrease in the parameter .Knowing the vector pi of the parameters at iteration i, the parameters at iteration are obtained using Equation 6.The optimal parameters are obtained after several iterations.
The method process is assumed as shown in Figure 1, where , and are given by Equations 2 to 6. ( The initial parameters are calculated based on an empiric analytical method proposed by Senturk et al. (2017).This method performed in six calculation steps uses the electric data at reference conditions from module datasheet given by the manufacturer.Even if Senturk's method saves calculation time, it allows lot of assumption.The number of equations is reduced by taking the diode ideality factor as a constant value.Consequently, the method accuracy can be affected because the ideality factor characterizes the recombination mechanism that takes place in the solar cells.Elsewhere, Singh et al. (2013) reported an increasing maximum output power with the diode ideality factor.Assuming this factor as a constant value, may affect the maximum output power also.Then, we prososed to use the parameters calculated by Senturk's method as the initial Kata et al.The LTSpice photovoltaic cell model shown in Figure 2 is used to evaluate the extracted parameters ( ) in the sub-Saharan outdoor conditions.The model takes as input, the parameters of the cell in the reference conditions (extracted with hybrid method) and the climatic data (temperature of the module, the irradiation) as shown in Figure 3.The solar cell parameters vary according to climatic variables (irradiation, temperature, wind speed).The influence of the wind speed is implicitly integrated in the model through the relation established by (Kratochvil et al., 2004) between this one and the temperature of the module:  (a-Si:H/mc-Si:H).The study was conducted under different conditions ranging from clear to cloudy skies.At the end of the study, they concluded that the least fair method is the LM method.It was reported that the RMSE obtained in the comparison of the daily evolution of main electrical parameters of the PV systems is below 8% in all cases except the case of using LM.The extraction of PV cell parameters requires to initialize the parameters values.An improper initial values can affect the accuracy of the algorithm as reported by Sofiane kichou et al. (2016).
In order to evaluate the contribution of the present method, the results of the study are compared with the results of the methods developed by Senturk et al. (2017)empirical method and Alain and Tossa et al. (2014) LM for the polycrystalline module SQ175.Tables 3 and 4 show the used modules datasheet and the extracted parameters of module SQ175, respectively.The proposed method presents the best value of RSME (0.9%).Considering the number of iteration points, the present hybrid method improves the calculation time of the LM algorithm.
Furthermore, the solar cell parameter obtained with hybrid LM and empiric method is used in an LTSpice solar cell model.A single junction polycrystalline silicon module (VSP50P-12V in Table 3) is proposed to compare the measurement results with those obtained by simulating the extracted parameters.The I-V characteristic measurements were performed in Laboratory of Solar Energy and Energy Saving (LESEE) of international institute of water and environment engineering (2iE) of Burkina Faso using outdoor monitoring test facility named ''IV bench''.The module temperature and sun irradiation were measured at the same time as module I-V characteristic.Three multimeters are used to measure simultaneously module voltage and module current whereas a pyranometer was used to measure the sun irradiation.The module temperature was measured by a PT100 temperature sensor stuck on solar cell with thin aluminium tape at the back of the module.The two measurements of I-V data were separated by a 5 min interval and the time required to complete I-V curve was less than 2 s.Then, the solar irradiation can be considered constant for each I-V measurement.The range of -0.5V to 105% of Voc voltage were applied to module.All I-V data stemming from measurements are stored in CSV Excel format on PC.
The maximum power output of the module was calculated from measurements and LTSpice simulation.The results are as shown in Figure 4a and 4b, respectively for the current-voltage (V-I) and the voltagemaximum power output (V-P) characteristic.The correlation coefficient between the measured and simulated maximum power values was also calculated for different climatic conditions.This coefficient remains higher than 97% under each of these conditions.
The module daily output power is examined with the proposed method and compared to the measurement.Figure 5a, 5b and 5c shows the daily result for 05th October 2014, 15th October 2014 and 21st October 2014, respectively.A relative error of less than 10% is obtained for each simulation.The module performance ratio is as shown in Figure 5d.It shows a good performance of the hybrid and LTSpice model to evaluate the module performance.

Conclusion
A hybrid Levenberg-Marquardt and empiric analytic algorithm is proposed to extract module parameters.The proposed method aims to avoid divergence and a long computation time due to the improper initial value.The hybrid algorithm is shown to be more accurate than Levenberg-Marquardt and empiric algorithm taken separately.Elsewhere, LTSpice photovoltaic cell model is developed to simulate the extracted parameters in outdoor conditions.The LTSpice model with virtual components gives advantage of conceptualizing and anticipating the characterization of solar module in outdoor conditions.Measurements performed with VSP50P-12V polycrystalline module are compared to simulation results.The RMSE value of 0.9% and correlation one greater than 97% for simulated irradiation indicate computation efficiency and accuracy of the proposed algorithm.An improvement in the accuracy of the LM algorithm, will contribute to the accuracy of system performance estimated under real operating conditions.
values.Generally, the user gives these initial values intuitively.Then, if the values entered are far from the real initial values, the algorithm's calculation time will be long or at worst there will occurred a convergence problem.It would be desirable to have a method to obtain these initial values, because the algorithm accuracy, it convergence and the calculation time can be affected by the inappropriate initial values.In this paper, we propose to calculate the initial values from the electrical specifications of the module given by the manufacturer using the empiric analytic method developed by Ali Senturk et al. ().Then, this method is incorporated in extraction algorithm of LM to form a hybrid algorithm.The present approach should contribute to improving the accuracy of the LM algorithm as well as saving valuable calculation time.Furthermore, the LTSpice solar cell model is proposed to evaluate the extracted parameters in sub-Saharan outdoor condition.The LTSpice software is a high performance professional variant of Simulation Program with Integrated Circuit Emphasis (Spice) running on graphical interface base.It is an open source software that can contribute to evaluate the influence of the photovoltaic module model parameters and the climatic factors variation on the module performance.

Figure 1 .
Figure 1.Diagram of the parameter extraction process.

Figure 3 .
Figure 3. Illustrative diagrams of the inputs and outputs of the LTSpice model.
18 allow to translate module performance in the real operating conditions using LTSpice model presented earlier.The photocurrent Iph : al. (2016), compared the accuracy of five methods of extracting parameters.These methods are: Levenberg-Marquardt (LM), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Diff erential Evolution (DE) and Artificial Bee Colony (ABC).Two models (the five-parameter model (5PM) and the Sandia Array Performance Model (SAPM)) were used to model three PV modules of different technologies: crystalline silicon (c-Si), amorphous silicon (a-Si:H) and micromorph silicon

Figure 4 .Figure 5 .
Figure 4.The measured and simulated I-V (a) and P-V (b) curves for different operating conditions.

Table 1 .
Photovoltaic cell equivalent model classification.

Table 2 .
The non-exhaustive list of various extraction methods.

Table 3 .
Solar module electrical specifications.

Table 4 .
Comparison of the extracted parameters between Hybrid algorithm and LM or empiric analytic method.