A parametric simulation of the wireless power transfer with inductive coupling for electric vehicles, and modelling with artiﬁcial bee colony algorithm Deniz Ustun a , Selami Balci b,⇑ , Kadir Sabanci b a Department of Computer Engineering, Engineering Faculty, Karamanoglu Mehmetbey University, 70200 Karaman, Turkey b Department of Electrical and Electronics Engineering, Engineering Faculty, Karamanoglu Mehmetbey University, 70200 Karaman, Turkey article info Article history: Received 19 March 2019 Received in revised form 9 September 2019 Accepted 19 September 2019 Available online 23 September 2019 Keywords: Electrical vehicles Wireless power transfer Serial resonance circuit Artiﬁcial bee colony algorithm abstract In recent years, electrical power transmission has been intensiﬁed by the use of wireless power transfer (WPT). In this study, a new mathematical expression that calculates the efﬁciency of the charging process for a single phase coreless transformer and the inductive power transmission circuit that can be used in the wireless charging station of electric vehicles was proposed. An experimental design was performed by using central composite design and ranges of a few parameters selected for the transformer and power transmission circuit for 540 simulations. The expression that calculates the charging efﬁciency was obtained by using the artiﬁcial bee colony algorithm. An expression that consists of optimization vari- ables and efﬁciency parameters and also conforms to simulation data was obtained. The variables of expression in the optimization process were determined optimally by harmonizing of the simulation results and the outputs of expression produced by using the artiﬁcial bee colony algorithm. The results show that the analyzes of the WPT circuits related to the charging efﬁciency can be easily calculated with the proposed expression without considering simulation, measurement and sophisticated mathematics. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Electrical vehicles in everyday life are older than fossil fueled internal combustion engine technologies and electric vehicles have been continuously under development since their ﬁrst production in 1836. In connection with technological developments, Industry 1.0 has been the age of steam engines and reigned between 1750 and 1850, and in 1822 after Faraday’s explanation of the principles of the magnetic ﬁeld and with the development of electric motors in the 1824s, Industry 2.0 became the age of Electrical Energy. It has not taken long time for steam-powered vehicles to turn into electric-powered vehicles, and in the early 1900s one of every three vehicles became electric vehicles. The ﬁrst damage to electric vehicles was the discovery of Texas oil in America (1877), followed by the discovery of oil in the Middle East countries and thus, tech- nologies focused on mostly internal combustion motor vehicles. On the other hand, battery problem and long distance requirement, as well as the presence of a starter motor system in fossil fuel con- suming vehicles can be listed as reasons for the removal of electric cars for a long time (1910–1960) [1–4]. Industry 3.0 emerged as a new era in the industry with the development of controlled recti- ﬁer (SCR) silicon semiconductor technology in the 1970s. Thus, both semiconductor switching elements have started to be devel- oped and there has been a small movement for electric vehicles in the context of the initiation of measures against global warming which has become a concern such as the damage of fossil fuels to the environment, but there have not been many breakthroughs. Industry 4.0 Information-Artiﬁcial Intelligence and robotics sys- tems with the latest technology in the 2000s, as the last era of industry, both semiconductor power electronics technologies and advanced sensor applications have led to the development of highly dynamic technology for electric vehicles. Li-Ion battery technology has also contributed greatly to the development of electric vehicles. Nowadays, research and development activities are continuing in order to overcome the problems such as battery systems of elec- tric vehicles and travel restrictions on long distances. In this con- text, charging stations of electric vehicles can be designed as connected/wireless and their numbers are increasing. Wireless charging systems can be provided dynamically by the installation of the system along the road during travel. On the other hand, it is possible to charge the batteries in the areas allocated for wireless power transfer in the car parking areas of the electric vehicles. https://doi.org/10.1016/j.measurement.2019.107082 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: sbalci@kmu.edu.tr (S. Balci). Measurement 150 (2020) 107082 Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement