PARAMETER EXTRACTION OF SINGLE-DIODE PV-MODULE MODEL USING ELECTROMAGNETISM-LIKE ALGORITHM

The performance of photovoltaic (PV) module mainly depends on the parameters of electrical equivalent circuit of module. The parameters are unknown and sensitive to meteorological condition of PV location. Thus, an accurate estimation method should be used to extract the parameters. In this paper, an evolutionary algorithm proposed to optimize the parameters under various operation conditions. The root mean square error between the computed current based estimated parameters and experimental PV output current is proposed as a fitness function to obtain the optimal solution. The results are verified by seven different experimental I-V sets under various meteorological conditions. Furthermore, the results are verified by another work, which based on analytical method that proposed in literature. The results refer to high consistency with realistic data. In addition to that, the proposed method offers an average root mean square error and average absolute error under seven operation conditions were 0.07248 and 0.05316, respectively.


Introduction
The electrical energy (EE) is one of the most important factor for development any society in the world. Therefore, the EE demand is increasing for realizing the requirements of modern life [1,2]. *Corresponding Author deia_muhsen@yahoo.com ISSN 2520-0917 In the fact, the conventional EE resources comprise many disadvantages such as, environmental pollution and fluctuation of fuel prices worldwide. Furthermore, the fuel resources are gradually being lead to depletion [3]. Thus, the researchers are focusing on clean, environmental friendly, renewable and sustainable resources for electrical energy. Solar energy is represented one of the most popular source for generating electrical energy using photovoltaic (PV) technology. However, the modeling of PV array/module plays an essential role in the performance and productivity of PV systems.
The modeling of PV module can be considered by estimating the parameters of the electrical equivalent circuit of PV module.
In general, there are three main PV modeling methods namely; analytical, numerical, and artificial intelligent (AI) methods. In analytical method, the parameters of PV module under real operating condition is derived in terms of them under standard test condition (STC) based on manufacturer data [4] It is worth to mention that some key points that belong to I-V curve are used in analytical methods. The advantages of analytical method are simple and it needs to less computation time as compared to other methods [5]. The inaccurate parameter estimation is represented the main drawback of analytical method, because the PV performance is influenced by environmental conditions [6]. Moreover, the accuracy of estimation is strongly dependent on the key points of I-V curve. A simple PV module model based on the correlation that correlated the parameters of PV module and meteorological variables (ambient temperature and solar irradiance) proposed by Tamer et al. in [7]. An analytical method proposed by Lim et al. [8] to estimate the parameters of single diode PV module model using I-V curve and extensive computation.
On the other hand, another method such as numerical has been proposed by [9][10][11][12][13] to overcome the drawback of analytical method. The numerical method is more accurate than analytical method, because it utilized all the I-V curve points. The Newton Raphson and Levenberg-Marquardt algorithms are widely used in PV module modeling as numerical methods [9,10,[12][13][14]. The main drawbacks of numerical method that it needs to extensive computation as well as the accuracy of estimation depends on the type of fitting algorithm, the cost function, and the initial values of the extracted parameters. A compound methods proposed by [15,16], these methods combine between analytical and numerical methods to estimate the parameters of PV module. The drawbacks of both analytical and numerical methods are presence in compound method as well as to the complexity of method.
In the last decade, the AI is widely used for extracting the parameters of PV module model. Artificial neural network (ANN) based method used for estimation the parameters, but it is still as a black box as well as it needs for a huge I-V points for training the network. Due to the high reliability and efficiency of evolutionary algorithms (EA), the last used for modeling PV module [17][18][19]. The reliability of EA can be defined by the ability to candidate the optimal values of PV parameters. Meanwhile, the efficiency of EA refers to the ability to optimize the PV parameters with less computation time compared with numerical method. The EA can handle nonlinear functions without need for derivative information. Furthermore, EA can deal with multi-modal objective functions.
In this paper, a robust evolutionary algorithm is called electromagnetism-like (EM) algorithm is used to extract the optimal parameters of PV module based on experimental data. Experimental I-V data for seven different meteorological conditions used to validate the results of the proposed model. In addition, the results verified with another model that proposed in literature based on many statistical tools.

Optimization of PV module model's parameters
As aforementioned, the modeling of PV module affects on the designing and planning of PV systems productivity. Thus, accurate modeling is important target for researchers those work in PV field. However, accurate estimation of PV module parameters leads to accurate module modeling. It is worth to mention that the PV module parameters are sensitive to solar cell temperature and solar irradiance

Single Diode PV Module Model
The electrical equivalent circuit of single diode PV module model is illustrated in Fig. 1. The output current of PV module can be depicted by; where; nd are the output voltage (V) and the current (A) of PV module, respectively, nd are the diode saturation current (A) and photocurrent ( A), respectively, nd are the series nd p r llel resist nces (Ω), respectively, nd is the diode thermal voltage and expressed by; , (2) where; is the diode ideality factor, is the Boltzm nn's const nt (1.3806503E-23 J/K), is the cell temperature (K) and is the electron charge (1.60217646E-19 C). According to eqn (1) and (2), the five parameters ( , nd ) affects on the productivity of PV module. The single diode model is used in this paper, because it offers simple computation with satisfactory level of accuracy.

Formulating the Parameters estimation problem
The parameters of PV module are unknown and variable with solar cell temperature and solar irradiance. Thus, the parameter estimation problem can be represented as optimization problem, where an evolutionary algorithm is used to find the optimal parameter values. The root mean square error between the computed PV module current and experimental current over n data set of I-V points is represented as objective function of optimization problem. The objective function that utilized to optimize the parameters of single diode PV module model is formulated as, where; is the objective function, nd are the experimental PV module output current (A) and voltage (V), respectively, and is the length of the I-V data points.

EM Algorithm For Optimizing PV Module Model's Parameters
In this paper, electromagnetism-Like algorithms is utilized to model a PV module. Electromagnetism-Like (EM) algorithm is a population-based search algorithm utilizes the attraction and repulsion mechanism to move the -dimensional individual vectors toward the global optimal values. EM comprises four stages namely, initialization, local search strategy, calculation of exerted force, and new population generation [20].

Initialization
The first step of EM algorithm is the generation of a population randomly. This population parameters that are required to individual vectors while each vector comprises consists of be distributed uniformly dimensional individual vectors are initialized to -be optimized. The ) limits of the search domain as depicted ) and lower ( between the corresponding upper ( in Eq. 4.

Local Search
The local search procedure is used to explore the neighborhood of the -parameter of the individual vector [21]. Two control parameters are used in the local search strategy namely and . The is the number of the iteration that the local search repeats and is a multiplier factor for the neighborhood search. The local search of EM algorithm can be described as follows; The maximum step length for each parameter of the individual vector is calculated first by subtracting the corresponding lower limits from the upper limits. After that, is used to weight the difference.
Secondly, each individual vector is improved by searching the coordinates, whereas the individual vector is stored in a temporary vector and the last vector is moved by adding the random step length to the initial value of .
After that, the individual vector is replaced by if the objective function value of is less than vector within the iteration of local search.

Calculation of Exerted Force
In this stage, the total force exerted on each -dimensional individual vector by all other -dimensional individual vectors in the population is calculated. Here, each -dimensional individual vector will have -dimensional individual vectors exerting force on it. The force exerted on an individual vector by another individual vector that is calculated based on the charges of these vectors [22]. The charge of individual vector is computed by,

Generating new population
After the total force exerted on, an individual vector is computed, the new -parameters individual vector is generated, as in Eq. (8), by moving along the direction of by a magnitude that is randomly selected from the range [0, 1].
The is a vector has components refer to the allowed feasible movement towards the lower or upper limit of the jth parameter of individual vector based on the jth value of the total force vector which is greater or less than zero [21].
The last three stages of EM algorithm are repeated until the maximum number of iteration ( ) is reached or a good fitness value is obtained. Fig. 2 shows the flow chart of EMalgorithm.

Results
An experimental I-V data performance of a multicrystalline Kyocera KC 120-1 photovoltaic module is used in this research. The manufacturer specification of PV module are illustrated in Table 1.
The effectiveness and results accuracy of the proposed modeling method is verified by comparing the results with experimental I-V data and another analytical model that proposed in the literature in [7]. The comparison is achieved under seven various operational conditions Four statistical tools used as evaluation criteria in the comparison; the criteria are root mean square error (RMSE), mean bias error (MBE), coefficient of determination (R 2 ), and absolute error (AE). The RMSE refers to the standard deviation between the experimental and computed currents for a given voltage value in the I-V curve under a specific operational conditions as follows: Where, Ic is the computed PV module current by the proposed model (A), Ie is the experimental PV module current (A), and n is the length of the data set of I-V points. The MBE is another evaluation criteria that used to evaluate the performance of the proposed model under n-data set of I-V points. The MBE is defined by; The third criterion is R 2 that reflects the level of variation in the experimental I-V data. The high consistency between the experimental and simulation results leads to R 2 value close to 1. R 2 can be formulated by; Where ̅ is the arithmetic mean value of experimental current under n-data set of I-V points and it is calculated by; The last criteria used for evaluation the results is AE which is the absolute difference between the experimental and computed current for a given voltage value belong to I-V curve under a specific operation condition. Therefore the AE can be formulated by; The unknown PV module model parameters are Rs, Rp, , Ip, and I o . Thus, the dimension of the current optimization problem is chosen to be five as the parameters of PV module. In the meanwhile, the population size (N) and maximum number of iteration (MAXITER) are set to be 10D and 500, respectively. The control parameters S and LSITER are assumed 0.01 and 30, respectively to obtain better results according to many attempts of running the algorithm. The five extr cted p r meters of single diode PV module's model b sed on EM lgorithm under various operational conditions are tabulated in Table 2.
The I-V and P-V curve under seven operation conditions are shown in Fig. 3 and Fig. 4, respectively. According to Fig. 3, the results of the proposed model are more close to experiment data. Thus, the proposed modeling method is effectiveness to extract the parameters of single diode PV module's model.
A detailed comparison between the proposed modeling method and the method proposed by Tamer et al. in [7] is illustrated in Table 3. According to Table 3, the RMSE, MBE, and AE values of the proposed method are always less than those offered by [7]. The proposed method exhibits average value of RMSE, MBE, and AE around 0.072, 0.007, and 0.053, respectively. On the other hand, the method proposed by [7] offered 0.381, -0.042, and 0.188 for average RMSE, MBE, and AE, respectively. Furthermore, the R 2 values offered by the proposed method is greater than and more close to 1 than obtained from the method proposed by [7] under various operation conditions. The average R 2 of the proposed method and [7] are 0.990 and 0.909, respectively. Fig. 5 shows the evolution of fitness function over the generation number for seven operation conditions that denominated from G1 to G7. The proposed algorithm to estimate the parameter is fast and offered low final fitness function value, especially for low irradiance cases, because these cases has less I-V points.

Number of cells connected in series 36
Temperature coefficient of ( ) 1.325 mA/K Temperature coefficient of ( ) -77.5 mV/K

Conclusions
An electromagnetism-like algorithm is used to estimate the parameters of PV module as a single diode model under various meteorological conditions. Five decision variables ( nd ) are optimized based on objective function that represented as the root mean square error between the experimental and computed PV output current for a realistic set of I-V data points. Experimental I-V data under seven different levels of solar irradiance and ambient temperature are used. The proposed method offers I-V characteristics more close to experimental values than other methods that proposed in literature. The proposed method exhibits an average mean bias error and coefficient of correlation under seven different operation conditions were 0.00733 and 0.99041, respectively.