Parameter identification of the photovoltaic panel’s two-diode model

ABSTRACT


INTRODUCTION
Due to the damage caused to our environment as a result of the widespread use of petroleum factories and cars, attention is turning to the use of renewable and environmentally friendly energies such as solar energy.This latter depends on PV panels to convert sunlight into electricity.The market has many types of PV panels.The difference lies in the material from which it is made and the size, in addition to the number of PV cells used.Each PV panel has its own data sheet, which does not include the values of the photocurrent source, the resistances, nor the quality factors of the diode and its reverse saturation current.These parameters are required to adjust the PV panel models.Three equivalent circuits can be used for the PV panel, namely: the one-diode model, the double-diode model, and the three-diode model.Our work is focused on the two-diode model.Many techniques have been used and developed for the two-diode model of solar cell/module during the last few years.Among these techniques are: the salp swarm algorithm [1], the biogeography-based heterogeneous cuckoo search algorithm [2], the performance-guided JAYA algorithm [3], the hybridized interior search algorithm [4], the sine cosine algorithm [5], the flexible particle swarm optimization algorithm [6], a modified flower algorithm [7], and the Lozi map algorithm [8].The particle swarm optimization algorithm based on anarchic universal heterogeneous learning [9], the cuckoo search algorithm and grey wolf optimizer [10], the interval branch and bound algorithm [11], a multitask optimization technique that is evolutionary [12], the levy flight backtracking search algorithm [13], the Nelder-Mead moth-based orthogonal flame technique [14], the farmland fertility optimization algorithm [15], and the differential vectors reusing backtracking search algorithm [16].
The particle swarm optimization algorithm based on multi-swarm spiral leader [17], the algorithm for Laplacian Barnacles mating based on neighborhood strategy [18], a logistic chaotic JAYA algorithm [19], the slime Mould algorithm [20], a differential evolution algorithm based on an ensemble of self-adaptive [21], the salp swarm algorithm based on opposition learning [22], the improved equilibrium optimizer algorithm [23], and the Harris Hawks optimization algorithm [24].The adaptive teaching-learning algorithm [25], the particle swarm algorithm based on parallel computing of the niches [26], the vertical and horizontal crossover of the Nelder-Mead Simplex and Harris Hawks algorithms [27], the ant lion optimizer algorithm [28], the particle swarm optimization technique based on the ensemble of the fractional chaotic [29], the backtracking search algorithm [30], the JAYA algorithm [31], and an optimization algorithm for generalized normal distribution [32].The equilibrium optimizer algorithm [33], the distribution algorithm [34], a shuffled frog-leaping algorithm [35], the reinforcement learning differential evolution algorithm [36], the spherical evolution algorithm [37], the supply-demand-based optimization algorithm [38], an improved slime Mould algorithm [39], and the combined self-adapting algorithm with Newton-Raphson method [40].The non-uniform mutation genetic algorithm [41], the marine predators' algorithm [42], the frog-leaping algorithm [43], the Rao-1 algorithm [44] and its logistic chaotic optimization algorithm [45], an advanced slime Mould algorithm [46], an enhanced algorithm to optimize the adaptation of the butterfly [47], and a combination of two algorithms: experience learning with teaching-learning [48].The whippy Harris Hawks Optimization Algorithm [49], a combination of two algorithms: the adaptive grey wolf optimizer and its chaotic algorithm [50], a combined shuffled frog leaping algorithm with a driven ensemble by multi-strategy [51], an enhanced gaining-sharing knowledge algorithm [52], an enhanced equilibrium optimization algorithm [53], the Laplace cross search algorithm has been combined with the Nelder-Mead simplex algorithm [54], the improved JAYA algorithm [55], and a combination of two algorithms: gradient-based optimization and random learning [56].In addition to the arithmetic optimization algorithm [57], the heap-based optimizer algorithm [58], the heterogeneous differential evolution algorithm [59], the bio-inspired metaheuristic algorithms [60], and a combination of two algorithms: Crisscross and Nelder-mead [61].In this paper, the MATLAB/Simulink simulator has been used to build the proposed mathematical equations for the identification of the parameters of the solar panel.Per-unit representations of the current-voltage and power-voltage characteristics of a PV panel have been represented at and NOCT.Moreover, unknown parameters have been calculated for three atmospheric conditions, namely: STC, NOCT, and random atmospheric conditions.

PARAMETER IDENTIFICATION OF PHOTOVOLTAIC PANEL
The basic components of a solar panel are the solar cells.Therefore, the modeling of a solar panel is based on the solar cell's equivalent electrical circuit.Figure 1 represents the equivalent electrical circuit of the two-diode model for a solar panel.This circuit consists of a photocurrent source,  ℎ , in parallel with the two diodes, 1 and 2, in addition to the parallel and series resistances,  ℎ and   , respectively.The characteristic equation of the PV panel's current has been obtained using Kirchhoff's laws with consideration of Shockley's diode equation, as given by (1).This equation has seven unknown parameters: the photocurrent source,  ℎ , the two diode reverse saturation currents,  1 and  2 , the two thermal voltages,  ℎ1 ,  ℎ2 , the series resistance,   , and the parallel resistance,  ℎ .In this paper, MATLAB/Simulink software has been used to implement the proposed mathematical equations for simultaneously calculating these seven unknown parameters at different atmospheric conditions.The thermal voltages can be determined using ( 2) and (3).nP1 and nP2 are the quality factors of the two diodes.Kb is the constant of Boltzmann (1.38065*10 -23 J/K), q is the magnitude of the electronic charge (1.602*10 −19 C), Ta is the ambient temperature (K), NS is the number of solar cells connected in series, and TSTC is the temperature at STC (298K).) 0.7 The short-circuit current and the open-circuit voltage can be calculated using ( 4) and ( 5), respectively.
The temperature coefficients of the short-circuit current and the open-circuit voltage, ki and kv, respectively, are usually given in the data sheet of a PV panel.IR is the solar irradiation at an ambient temperature, and IRSTC is the solar irradiation at STC (1000 W/m 2 ).  has to be adjusted to obtain the value of the short circuit current.Moreover, the value of the open circuit voltage can be obtained by varying   .The two saturation currents' values can be calculated using ( 6) and (7).Moreover, the value of the photocurrent source can be obtained using (8).
The series and parallel resistances are given by ( 9) and (10), respectively.The number of the parallel solar cells is Np.S is the surface of the solar panel.The resistance rS must be varied until the maximum power point (MPP) of the solar panel is attained at STC.For any other atmospheric condition, kRS has to be varied to attain the PV panel's MPP.

RESULTS AND DISCUSSION
In this section, the MATLAB/Simulink simulator has been used to implement (1)- (10).It has the ambient temperature, solar irradiation, and the data sheet as inputs, while its outputs are the current and power of the PV panel.Different sizes of PV panels for different markets have been used, such as Suntech of 50W, SW 85 poly RNA of 85 W, and JAM60S01 of 320 W. The parameters of these PV panels have been obtained at STC and NOCT.Moreover, the parameters of the Suntech PV panel have been obtained under random atmospheric conditions.

Results at STC and NOCT
We achieved the MPP of each used panel by varying only the value of rS for the series resistance given by ( 9) at STC.We adjusted the variable   of the series resistance for each used PV panel to achieve its maximum power point under NOCT (Gr = 800 W/m 2 , Ta = 20 °C).The data sheets of the used panels are given in Table 1.Table 2 shows the adjusted values of rS and   in addition to the calculated parameters.Figure 2 shows the per-unit curves of I-V and P-V for the used panels (a) at STC and (b) under NOCT.Pds and Ids are used for the per-unit values of the power and the current, which are given in the data sheet, respectively.There are three highlighted points for each used panel.The per-unit points of the short circuit current and open circuit voltage are equal to one, so their calculated values are equal to the data sheet's values.The third point is the maximum power point.Its per-unit values are very close to one.Therefore, the calculated values are very close to the data sheet values.This closeness is calculated using (11).Table 3 shows the obtained values for the absolute relative error.

Results at arbitrary atmospheric conditions
One experiment had been done at the university using a Suntech PV panel.The atmospheric temperature was 17 °C and the solar irradiation was 1176 W/m 2 .By taking atmospheric circumstances into account, we adjusted the variables,   kVoc and kIsc, to make the characteristic curves as close as possible to the measured curves.Therefore, the parameters are obtained simultaneously.Figure 3 shows the characteristic curves of the Suntech panel at arbitrary atmospheric conditions.The adjusted values of the variables and calculated parameters are given in Table 4.The measured and calculated data for the three points, in addition to the resulting absolute relative error, are given in Table 5.

CONCLUSION
The goal of this paper is the calculation of the parameters for the photovoltaic panel with a twodiode model.Therefore, mathematical equations have been proposed and implemented using the MATLAB/Simulink simulator.Per-unit representations of the current and power of the solar panel with comparisons were obtained for STC as well as NOCT.Moreover, comparisons have been made under arbitrary meteorological circumstances.For the three cases, the absolute relative error of the MPP did not reach 0.0008%.

Figure 1 .
Figure 1.Equivalent electrical circuit of the double-diode model for PV panel

Figure 2 .
Figure 2. Per-unit curves of I-V and P-V for the used PV panels: (a) at STC and (b) under NOCT

Figure 3 .
Figure 3. Suntech solar panel: I-V and P-V characteristics at arbitrary atmospheric conditions

Table 1 .
Values from the data sheet of PV panels

Table 2 .
Calculated parameters of PV panels

Table 4 .
Calculated parameters at arbitrary atmospheric conditionsThe parameter Calculated value The parameter Calculated value Parameter identification of the photovoltaic panel's two-diode model (Saida Madi) 2359

Table 5 .
PV panel under random atmospheric conditions