Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 618 https://internationalpubls.com Artificial Rabbits Optimization Algorithm for PV Cell Parameter Extraction Vimalakeerthy Devadoss1, Mohana Sundaram.K2, Annamalai Muthu3, Periasamy Selvaraju4 1Lecturer, University of Technology and Applied Sciences, Nizwa, Sultanate of Oman. Email: vimalakeerthy.devadoss@utas.edu.om 2Professor, Department of EEE, KPR Institute of Engineering and Technology, Coimbatore, India. Email: mohanasundaram.k@kpriet.ac.in 3Lecturer, Electrical Section, Engineering Department, University of Technology and Applied Science – Nizwa, Oman. Email: annamalai.muthu@utas.edu.om 4Professor of Computer Science and Engineering, Saveetha School of Engineering, Saveetha Institute of Medical and Technological Sciences (SIMATS), Thandalam, Chennai-602105) India. Email: pselvar@yahoo.com Article History: Received: 06-08-2024 Revised: 26-09-2024 Accepted: 08-10-2024 Abstract: Solar energy is available in abundance and the energy obtained from solar is economical. The accurate Modelling of solar module is however more important before its installation. The manufacturers of Solar Panel would provide only few parameters in datasheet that which is not enough for modeling. Metaheuristics algorithms was applied and to obtain those few parameters of module. Artificial rabbits optimization has been applied to obtain the unknown parameters in 250Wp SVL0250P photovoltaic module at varying temperature and irradiance. A performance comparison is made with flower pollination, Jaya algorithm and it is found that Artificial rabbits optimization provides excellent results with respect to precision and convergence. Keywords: Artificial rabbits optimization, Irradiance, Photo-Voltaic (PV), FPA, Jaya Algorithm. Introduction Global warming driven by rise in greenhouse gases such as methane, and nitrous oxide, carbon di oxide in atmosphere, are high owing to the combustion of fossil fuel such as coal to produce electricity which alarms threat to entire country and its critical problem to be addressed urgently. As alternate renewable energy sources produces electricity without the use of fossil fuel are harmless. Compare with the various renewable energy sources, energy obtained from solar is non polluting and clean energy with less maintenance [1]. Photovoltaic (PV) represents one of the most significant advancements in solar power generation. The exact modeling of PV modules is essential for PV characterization, fault detection, MPPT, and efficiency and it should be done before installation part. The equivalent circuit models can be useful in simulating input and output characteristics for Photovoltaic systems. Various analytical and optimization methods were applied to achieve optimal parameters of PV systems. The analytical method is based on the peculiar spots on the current-voltage (I-V) curve whereas the I-V curve varies in different conditions and it will produce a large data error. mailto:mohanasundaram.k@kpriet.ac.in mailto:annamalai.muthu@utas.edu.om Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 619 https://internationalpubls.com The optimization approaches adhere to the principle of fitting the I-V curve in a way that minimizes errors between the simulated and measured data, resulting in a more accurate and dependable solution. The parameters given in the datasheet of solar module are limited. The parameters: series resistance (Rs), Shunt Resistance (Rsh), diode saturation current(Io), Photogenerated current(Ipv), and factor (a) not in the datasheets[2-5]. GS and NR methods were used initially used to find the unknown parameters but while solving objective function, they are sensitive to initial conditions and iterations to obtain the fitness function is also high[6-10]. Optimization approaches such as particle swarm optimization, and genetic algorithm was already applied to determine the unknown parameters [11-19]. Nevertheless, in literature, Artificial rabbits optimization have not been used. Thus, ARO is applied to parameter identification of PV models. Further, the results are compared with another metaheuristic algorithm. 2. PV Cell Mathematical Modelling The single diode model has been analyzed depicted in the fig1. Figure 1. Single diode model The MATLAB Modelling of PV Cell is shown in figure 2. The commercially available solar model has series and parallel resistance that are connected parallel to the diode. Rs represent the structural resistance of the device, Rp represents the loss in the device due to leakage current through resistive path [7] in parallel. Figure 2. Mathematical Modelling of PV Cell Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 620 https://internationalpubls.com The current is given by: 𝐼 = 𝐼𝑃𝑉 βˆ’ 𝐼𝐷 βˆ’ 𝑉𝐷 𝑅𝑃 (1) The current equation of diode is represented as 𝐼𝐷 = 𝐼0(𝑒π‘₯𝑝 ( 𝑉𝐷 𝛼𝑉𝑑 ) βˆ’ 1) (2) I0 is saturation current of diode, Vt thermal voltage can be written as 𝑉𝑑 = π‘π‘ π‘˜π‘‡/π‘ž (3) Where k represents Boltzmann constant, T represents temperature in Kelvin, q represents electron charge and Ns indicate the series connected solar cells. The PV Module equation of current [6]-[9] is given as: 𝐼 = 𝐼𝑃𝑉 βˆ’ 𝐼0[exp⁑ ( 𝑉+𝑅𝑆𝐼 π‘‰π‘‘π‘Ž ) βˆ’ 1] βˆ’ (𝑉 + 𝑅𝑆𝐼)/𝑅𝑃 (4) Hence, these five parameters such as IPV, Rp, Rs, a, I0 in the PV Module are unknown and is mandatory for accurate solar cell modelling. To reduce intricacy, the suggested work calculates β€˜IPV’, β€˜I0’ is analytically. The β€˜a’ is chosen randomly between 1 to 2 depends on the other parameters of the solar module [24]-[25]. The remaining two parameters of β€˜RS’, β€˜RP’ are calculated using optimization approaches. It is discovered that these parameters are modified with regard to irradiance and temperature and then adjusted to an optimum point that is based on the minimal error between computed and actual power. The Photo generated current of PV Module [7] is given by 𝐼𝑃𝑉 = (𝐼𝑆𝐢 + π‘˜π‘–π‘‘π‘‡) βˆ— 𝐺 𝐺𝑛 ⁄ (5) Where G & Gn represents actual solar irradiance and irradiance at STC. The Magnitude of I0 is based on the IPV and Voc [8]. 𝐼0 = 𝐼𝑃𝑉/exp ( (𝑉𝑂𝐢+π‘˜π‘£π‘‘π‘‡)βˆ—π‘‰π‘‘ π‘Ž ) βˆ’ 1 (6) The voltage obtained from Solar module is Vmp, and current is Imp When PV curve is at maximum power point (MPP). Further, at this point, the differentiation of power as function of voltage becomes zero [8]. In this circumstance, the unknown parameters are extracted in this study. 𝑑𝑃 𝑑𝑉 = 0 (7) 𝑑(π‘‰βˆ—πΌ) 𝑑𝑉 = 𝑉 ( 𝑑𝐼 𝑑𝑉 ) + 𝐼 (8) 𝑑𝐼 𝑑𝑉 + ( 𝐼 𝑉 ) = 0 (9) |( 𝑑𝐼 𝑑𝑉 ) |(π‘‰π‘šπ‘,πΌπ‘šπ‘) = (𝐼0πœ“ exp{πœ“(π‘‰π‘šπ‘ + πΌπ‘šπ‘π‘…π‘†)} βˆ’ 𝑍𝑃) /(1+ 𝐼0πœ“π‘…π‘† exp{πœ“(π‘‰π‘šπ‘ + πΌπ‘šπ‘π‘…π‘†)} βˆ’ 𝑍𝑃𝑅𝑆 (10) Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 621 https://internationalpubls.com Where ZP=1/RP, πœ“ =1/aVt 𝐽 = | ( 𝑑𝐼 𝑑𝑉 ) |π‘‰π‘šπ‘,πΌπ‘šπ‘ + ( πΌπ‘šπ‘ π‘‰π‘šπ‘ ) (11) The measured solution is achieved when the fitness function (J) approaches zero[8]. Artificial rabbits optimization Algorithm based solar cell Extraction: ARO is originated from the survival strategies of rabbits in nature The ARO has three phases, namely exploration (detour foraging), exploitation (random hiding) and balancing exploration and exploitation (energy shrink). The flow chart is given below. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 622 https://internationalpubls.com Result analysis: A 250 Watts SVL 0250P datasheet was taken and it provides the values of OC voltage, SC current, maximum power point current, kv, ki. The parameters that are unknown such as Ipv, I0, Rs, a, Rp. The Ipv, I0, are calculated analytically and Rs and Rp are accurately measured using ARO, JA, FPA. The value of Rs is selected arbitrarily between [0 to 2] and initial boundary limit for Rp between 50 to 500. The measured Rs and Rp values using ARO, Jaya Algorithm, and FPO for different environmental conditions is shown below. Table 1. Solar module unknown parameters measured with ARO, JA, and FPO for different Temperature (T) and Irradiance (G) Parameters SVL 0250P FPO JA ARO T=250C & G=1000W/m2 Rs(Ω) Rp(Ω) 0.91778 63.254 0.916811 50.0028 0.814 221.62 T=47.40C & G=525W/m2 Rs(Ω) Rp(Ω) 0.341673 123.46722 0.772148 50.00964 1.3489 131.4698 T=45.90C & G=368W/m2 Rs(Ω) Rp(Ω) 1.92697 82.63984 1.485236 50 1.4589 322.8952 From the observation of table, it is seen that magnitude of Rs is very small and magnitude of Rp is high. According to which, smaller value of Rs and higher value of Rp moves the P-V curve towards MPP. Accordingly, a lower value of Rs and a higher value of Rp shift the PV curve towards MPP. Figure 3 (a-d) shows the simulation results of I vs V and P vs V Characteristics of 250Wp PV module for two environmental conditions such as STC, T=47.40C & G=525W/m2, and T=45.90C & G=368W/m2. (a) (b) 0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 X: 27.63 Y: 4.2 V[V] I[ A ] I-V CURVE 0 5 10 15 20 25 30 35 40 0 20 40 60 80 100 120 X: 27.63 Y: 116 V[V] P [W ] P-V CURVE Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 623 https://internationalpubls.com (c) (d) Figure 3. (a&b) I vs V & P vs V characteristics for G=525W/m2 and T=47.40C ,(c&d) I vs V & P vsV characteristics for G= 368W/m2 and T =45.90C With the obtained results, we can identify that at T=47.40C & G=525W/m2, the voltage(mpp) and current(mpp) are 26.53 V and 4.1A. With T=45.90C & G=368W/m2, the voltage(mpp) and current(mpp) are 26.18 V and 3A. The figures clearly indicate the variation of significant PV parameters i.e., Voc, Isc, MPP voltage and current based on irradiance, temperature. The figure 4 shows the fitness of various algorithms such as ARO, JA and FPO. Figure 4. Convergence Curve Comparison of ARO, JA and FPA With the study of convergence, it can be observed that convergence rate of (ARO) is fast compared to JA and FPA. The ARO has been converged at thirtieth iteration, JA at 160th iteration, and FPO at 180th iteration. ARO, JA, and FPO performance comparison has been depicted in the table 2. Table 2. Comparison of ARO, JA, and FPA. Technical criteria FPO JA ARO Solution Accuracy Low Medium High Convergence Speed Medium Medium High Computational Complexity High Medium Low 0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 X: 27.18 Y: 3 V[V] I[ A ] I-V CURVE 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 90 100 X: 27.18 Y: 81.53 V[V] P [W ] P-V CURVE Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 3 (2025) 624 https://internationalpubls.com With the above table, one can conclude that, it displays that ARO had the best convergence performance proved to be an appropriate optimization technique for PV module unknown parameters extraction in terms of solution accuracy, Convergence speed, and computational complexity. 5. Conclusion ARO has been implemented to measure the PV model parameters, Rs and Rp accurately without sub- optimal traps. These parameters have been extracted with a fitness function of differentiation of power with respect to voltage at maximum power point. 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