The adsorption of nicotinic acid molecules from their solution in the aqueous phase was studied in batch mode by using magnetically activated carbon (M-AC) as the adsorbent. Activated carbon was magnetized by a coprecipitation method. The effects of the amount of adsorbent (0.25 to 5 g•L −1 ), initial acid concentration (2.46 to 14.77 g•L −1 or 0.02 to 0.12 mol•L −1 ), contact time (0 to 120 min), and temperature (298 to 333 K) on the percentage removal were investigated. Theoretically (from the Langmuir isotherm), an adsorption capacity of 23.28 g•g −1 was obtained by M-AC for acid removal. Equilibrium isotherms such as the Langmuir, the Freundlich, and the Temkin were applied to determine equilibrium parameters and to fit the equilibrium data, out of which the Langmuir gave the best match to the results. Nicotinic acid adsorption kinetics was modeled with pseudo-first order, pseudo-second order, and intraparticle diffusion models. The kinetic data was best described by the pseudo-second-order model. Thermodynamic parameters such as ΔH o , ΔS o , and ΔG o were calculated, and their values pointed out that the adsorption of acid molecules onto M-AC was exothermic and the process was spontaneous.
Summary
This paper develops a novel hybrid parameter estimation technique of the solar photovoltaic (PV) cell. First, a mathematical model of the solar PV cell, which is a function of three unknown parameters, namely, series resistance, shunt resistance, and thermal voltage, is developed. Then, trust‐region algorithms are used to evaluate these three unknown parameters. The accuracy and efficacy of the proposed technique are tested with five different PV modules of mono‐ and poly‐crystalline materials by estimating their various benchmarks, such as relative maximum power error (RMPE), root mean square error (RMSE) and mean absolute error (MAE) of the current. In addition, the results of the proposed technique are compared with the experimental as well as the results obtained from other established techniques. The %RMSE, as obtained with the proposed technique, is found in order of 10−4 while the other techniques provide the value in the range between 10−1 and 10−3. Similarly, %MAE and %RMSE, as obtained with the proposed technique, are found 0.064 and 0.17, respectively, which is smaller than the other existing techniques. Hence, the proposed hybrid technique provides characteristics that are almost similar to the real characteristics of solar PV.
Highlights
The characteristic equation is developed in terms of Rs, Rp, and Vth.
The hybrid technique is used to evaluate five unknown parameters of solar PV.
Various performance indicators have been estimated for different types of solar PV.
Characteristics obtained with the proposed technique are similar to real characteristics.
The proposed technique reduces the complexity of parameter estimations.
The estimation of the electrical model parameters of solar PV, such as light-induced current, diode dark saturation current, thermal voltage, series resistance, and shunt resistance, is indispensable to predict the actual electrical performance of solar photovoltaic (PV) under changing environmental conditions. Therefore, this paper first considers the various methods of parameter estimation of solar PV to highlight their shortfalls. Thereafter, a new parameter estimation method, based on multi-objective optimisation, namely, Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is proposed. Furthermore, to check the effectiveness and accuracy of the proposed method, conventional methods, such as, ‘Newton-Raphson’, ‘Particle Swarm Optimisation, Search Algorithm, was tested on four solar PV modules of polycrystalline and monocrystalline materials. Finally, a solar PV module photowatt PWP201 has been considered and compared with six different state of art methods. The estimated performance indices such as current absolute error matrics, absolute relative power error, mean absolute error, and P-V characteristics curve were compared. The results depict the close proximity of the characteristic curve obtained with the proposed NSGA-II method to the curve obtained by the manufacturer’s datasheet.
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