Modeling of solar cell under different conditions by Ant Lion Optimizer with LambertW function
Graphical abstract
Introduction
Photovoltaic devices are the alternatives for the conventional electricity production by fossil fuels. Effective modeling is required to design efficient and cost-effective photovoltaic energy systems and predict the energy production in the design of solar cells. The photovoltaic systems require an electrical model to investigate the electrical characteristics, a thermal model to study the performance under various changes in temperature and a radiation model to determine the solar energy absorbed by the system. Usually, manufacturers provide the panel parameters at ambient temperature and insolation. The performance of solar panel changes with the changing weather conditions and the angle of mounting. So, we require a model to study the combined analysis of the performance under varied temperature and insolation as it varies from time to time. The models that include the combined analysis of various changes in the operating conditions include analytical models [1] and empirical models [2] based on the physics of photovoltaic systems. These physical models can quantify the electrical output power extracted by the photovoltaic system with the solar radiation assuming that the maximum power is obtained. In order to determine the maximum power extracted by the solar panel, we require the information of I–V characteristics. However, I–V characteristics of the device under study depends on atmospheric temperature and incoming solar radiation. So, the knowledge of the solar cell parameters considering a wide-range of operating conditions is essential to establish the exact performance of the photovoltaic device. These parameters can only be extracted from the experimental I–V characteristics data of the respective solar cell by fitting the simulated curve with the experimental curve. Further, measuring the I–V data under different weather conditions is next to impossible as we have to artificially simulate the weather conditions or wait for their natural occurrence.
The parameters are estimated using traditional methods like Newton–Raphson, Runge–Kutta method [3], analytical methods [4], [5], [6] and stochastic metaheuristic methods [7], [8]. Many optimization methods such as Genetic Algorithm [9], [10], [11], Artificial Immune System [12], Artificial Bee Swarm Optimization algorithm [13], Simulated Annealing [14], [15], Particle Swarm Optimization [16], [17], [18], Differential Evolution [19], [10], Harmony Search [20], Memetic Algorithm [21], Pattern Search [22], Cuckoo Search [23], Artificial Bee Colony Optimization [24], Biogeography Based Optimization Algorithm with Mutation Strategies [25], Teaching Learning Based Optimization [26], Modified Artificial Bee Colony Optimization [27], Bird Mating Optimizer (BMO) [28] etc., have been used to estimate the solar cell electrical parameters as found in literature.
Although there exist numerous techniques to solve the optimization problem of estimating the intrinsic parameters of the solar cell, it is also required to modify the non-linear transcendental equation of single diode model equation to simulate the exact behaviour of the solar cell. In this study, the LambertW function is used to explicitly represent the single diode model equation under temperature and insolation dependence. The required parameters are extracted using the Ant Lion Optimizer coded in IPython. This strategy is chosen since the performance of ALO does not depend on any specific algorithmic parameters, that needs prior optimization, and the implementation is simple in IPython. In this paper, using the I–V data measured at standard weather conditions, we have tried to extract the internal parameters of solar cell for different weather conditions by the combined analysis of LambertW function and Ant Lion Optimizer.
Ant Lion Optimizer is a nature-inspired optimization algorithm based on the hunting mechanisms of the antlion. Researchers have found that ALO surmounts other famous techniques like Genetic algorithm, Particle Swarm Optimization, etc. for various engineering problems [29]. In this paper, the intrinsic parameters of a photovoltaic device are determined from single diode model [30], considering the varied operating conditions with a LambertW function using Ant Lion Optimizer implemented in IPython.
The paper is organized as follows: Section 2 elaborates the modeling of a photovoltaic cell and the desired single diode model for varied environmental conditions. Section 2.3 describes the estimation of internal parameters by LambertW function, problem formulation and an extensive description of Ant Lion Optimizer algorithm is given in Section 3. Results and discussions are presented in Section 4. The summary and conclusion are given in Section 5.
Section snippets
Single diode model
Solar cells are operated, based on the principle of the photovoltaic effect. When the solar illumination is incident on the solar cell, the semiconductor material absorbs photons and generates charge carriers. This produces a potential difference and current in the external circuit that leads to charge separation in the PN junction and collected at the electrodes. The current generated in response to the solar radiation is termed as photocurrent (Ipv). Eradicating the photovoltaic effect, solar
Ant Lion Optimizer
Ant Lion Optimizer (ALO) is a nature-inspired metaheuristic algorithm, developed by Seyedali Mirjalili in 2015 [29], that simulates the hunting scheme of the antlions in catching its preferred prey. ALO consists of five measures in hunting ants such as, the random walk of ants, constructing traps, entrapment of ants in traps, catching ants, and re-constructing traps. Antlions are usually called as doodlebugs. They have two metamorphic stages in their life cycle namely, larvae and adult. In
Results and discussion
The parameters are estimated from desired single diode equation expressed in LambertW function using ALO implemented in IPython. The program in IPython is executed several times (runs) and 10 best optimal parameters are recorded in Table 2. The average of these 10 sets of values for each parameter is shown in the last row of Table 2. This parameter extraction problem under varied environmental conditions is tested for a commercial 57 mm diameter solar cell (R.T.C. France) operating at 33 °C and
Conclusion
Ant Lion Optimizer is used to estimate the intrinsic photovoltaic parameters from the single diode model in terms of LambertW function under the influence of temperature and solar irradiance with a high degree of accuracy. The different scenarios like the influence of temperature on the parameters of the solar cell with constant irradiation and the influence of irradiation with constant temperature are considered. The 10 parameters involved in describing the influence of temperature and
Conflict of interest
The authors declare that there is no conflict of interest.
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