This work studies numerical modelling of electrochemical systems by using Python programming language. The method of preparation and examination of data used in this work is similar to papers reported in the electrochemical impedance spectroscopy (EIS) studies. In order to examine the influence of the number of parameters of the equivalent electric circuit (EEC) and the amount of noise on data modelling using the Levenberg-Marquardt algorithm (LMA), different artificial ZARC data that mimics the electrochemical system are used. ZARC data in Nyquist's impedance (i.e. Z) diagram are characterized with depressed semicircle (i.e. ARC). In this work EECR(QR) and EECR(QR)(QR) models are applied for the modelling of the different artificial ZARC data (with and without noise). Optimal EEC parameters are determined by the LMA application, i.e. by minimizing the least-square difference (S-value) between the artificial data and data generated using EEC models. Impedance data are presented in diagrams to show the matching of artificial data and those obtained from EEC models. Also, the values of the optimal parameters of EEC models used to optimize artificial data are given in Tables. Due to the different numbers of EEC parameters and diverse noise magnitude, it was possible to comment on the convergence of LMA algorithm during the minimization process. The increase in the number of optimized parameters and an increase in the noise magnitude hinder the convergence of LMA algorithm.