International Journal of Interactive Mobile Technologies(iJIM) – eISSN: 1865-7923 – Vol 16 No 11 (2022) Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… 500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with Ferrite Core https://doi.org/10.3991/ijim.v16i11.30097 Nadia Nazieha Nanda(), Nur Shahida Midi, Siti Hajar Yusoff, Ahmed Samir Abed Badawi Electrical and Computer Engineering Department, International Islamic University Malaysia, Kuala Lumpur, Malaysia nnazieha.nanda@gmail.com Abstract—The efficiency of wireless pad designs with ferrite cores has been established in several investigations. However, they seldom offered a viable solu- tion to the problem of modifying the ferrite form’s geometric shape. The use of a ferrite core in the primary and secondary coils has been suggested by several researchers. The ferrite core design, on the other hand, is still in the works. Using the wrong ferrite core design might result in unnecessary extra weight and higher production costs. The circular coil design in the primary and secondary for wire- less power transfer (WPT) in electric vehicles is studied in this research. The suggested coil design is used to develop mathematical design utilizing numerical solutions. Later, using Multisims software, this coil design is produced in simu- lation. The suggested coil design’s power efficiency is examined and contrasted between computed and simulated results. Finally, based on the results of the power efficiency, a definitive discussion is presented. Keywords—electric vehicle (EV), numerical, mathematical, coil design, circular, wireless power transfer (WPT) 1 Introduction In a wireless power transfer system, the coupling power transmission idea is utilised to transport electric power from the transmitter coil to the receiver coil beneath the electric vehicle (EV) chassis [1–2]. Capacitive wireless power transfer (CWPT) and inductive wireless power transfer (IWPT) are two types of wireless power transmission (WPT) [3–7]. The coupling of two coils produces an electric field, which is the basis of CWPT. The generated voltage from the transmitter coil produces an electromagnetic field, which creates an electrostatic field on the receiver coil [8]. The connection of the transmitter and receiver coils in the IWPT, on the other hand, creates an electric field. Ampere’s Law and Faraday’s Law [9] are responsible for the magnetic field created. Most researchers have attempted to identify the way to charge the EV by using the wireless concept several years back [10–11]. Inductive charging, as depicted in Figure 1, is viewed as the most suitable alternative for finding a sustainable solution to petroleum iJIM ‒ Vol. 16, No. 11, 2022 149 https://doi.org/10.3991/ijim.v16i11.30097 mailto:nnazieha.nanda@gmail.com Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… depletion where electromagnetic coupling generates electricity. This cutting-edge technology enables the EV to charge securely and without the use of cables. The public energy grid is connected to a transmitter coil. Electricity passes through the transmitter coil as soon as the driver starts charging, generating a magnetic field [12]. An electric current flows via the receiver coil, which is placed beneath the EV chas- sis, as a result of the magnetic field. Induced electricity is used to charge the batteries of electric vehicles [13]. Fig. 1. Wireless battery charging system in EV [12] For the wireless charging of electric vehicles, a variety of coil configurations are available. The most frequent designs are circular pads [1], [4], [10], [12], rectangular pads [1], [12], [13], Double-D pads [11], [14], and Double-D pads [1]. In this work, the circular coil pair design is the sole topic of discussion. The following is how it’s laid out: Section II describes the project’s approach, while Section III includes mathemat- ical and numerical solutions as well as Multisims simulation data. Finally, the essay draws to a close in Section IV. 2 Methodology In order to transfer power wirelessly, energy is delivered from the primary side to the secondary side without any physical contact [16]. As the power transfer mechanism, the core magnet component generates this magnetic field. This section will provide a summary of the methodologies employed throughout the research. This approach is divided into main two parts, one for coil parameter calcula- tions and the other for simulation. The coil parameters will be determined first, and the calculated and simulated power at both primary and secondary plates will be compared. The coupling coefficient (k) of the coil pair determines the IWPT capabilities, which is controlled by the coil structure, also known as coil geometric design [17]. The trans- mitted power from the transmitter coil to the reception coil is used in the IWPT circuit. 150 http://www.i-jim.org Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… A magnetic field is created between the transmitter coil Lp and the reception coil Ls [18–19]. The mutual inductance, M, increases as the coupling coefficient (k) increases, increasing the power transfer. Changes in k have an impact on the output power. The coupling coefficient must be less than or equal to the critical coupling coefficient. (k < kc), the most optimum k is chosen, as shown in Figure 2 [20–21]. Fig. 2. The proposed methodology flowchart iJIM ‒ Vol. 16, No. 11, 2022 151 Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… Based on the proposed methods in Figure 2, the geometry characteristics for primary and secondary coils are calculated. The following is an example of the basic notion of a WPT schematic circuit, as shown in Figure 3. This circuit is in ideal work conditions order, which means it has no internal resistance (Rp = Rs = 0). The schematic circuit for WPT is built using the simulation software NI Multisim, which is listed below. Fig. 3. Basic concept of WPT schematic circuit The proposed 500W circular coil parameters needed to construct the schematic cir- cuit are summarised in Table 1 below. Table 1. Coil parameters needed Primary voltage Vp Secondary voltage Vs Primary capacitance Cp Secondary capacitance Cs Primary resistance Rp Secondary resistance Rs Load resistance RL Primary inductance Lp Secondary inductance Ls Mutual inductance M Coupling coefficient k When designing the transmitter and receiver coils for the proposed coil pair, the required self-inductance of each inductance coil is given by equation (1) and equa- tion (2). Lp refers to the transmitter self-inductance, whereas Ls refers to the receiver self-inductance. To continue the calculation procedure, the values of receiver quality factor, Qs, operating frequency in 0, mutual inductance, M, and coupling coefficient, k must be determined before the requisite self-inductance for both transmitter and receiver coils can be calculated. The quantity of inductance that connects the transmit- ter coil to its neighbouring coil, the receiver coil, is denoted by M. The strength of M can be affected by the distance between the two inductance coils. Equation is used to find value of M. (3) as shown below: 152 http://www.i-jim.org Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… L M L kp s = 2 2 (1) L Q R ws s L o = (2) M I R I w s rms L p rms o = , , (3) Equation (4) is used to compute the load resistance, whereas equation (5) is used to get the essential coupling coefficient, kc. The value of the coupling coefficient, k, should be less than the value of the critical coupling coefficient, kc, for a bifurcation-free operation, (k < kc). To pick the appropriate k for the coil coupling, use equation (5) below to calculate the appropriate critical coupling coefficient, kc. R V PL o o = ( )2 (4) k Q Qs C s � � 1 1 1 4 2 (5) Equations (6) and (7) may be used to compute the RMS values of current in the primary and secondary sides: I P Vp rms o p , = (6) I V Rs rms L , = 0 (7) The validity of the parameters is validated by simulating the ideal outcome; if the power on the primary and secondary sides is the same, there is no internal or external resistance. Running the NI Multisim software will give the current and voltage values. Equation (8) can be used to compute power on both the primary and secondary sides. P V x I= † † (8) Four pairs of circular coils have been proposed for this study. The recommended coil will either be ferrite-free or contain ferrite. If ferrite is available, the preferred coil will be either double in-phase or double out-phase. The proper number of turns for the primary and secondary coils will be computed in the next section, which dives into the mathematical design of the coil characteristics. Table 2 shows a summary of the suggested coil designs. iJIM ‒ Vol. 16, No. 11, 2022 153 Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… Table 2. Primary and secondary coil proposed designs Pair Primary Coil Designs Secondary Coil Designs 1 Ferrite-less Ferrite-less 2 With double ferrites Ferrite-less 3 With double ferrites (in-phase) Ferrite-less 4 With double ferrites (out-phase) Ferrite-less 3 Results 3.1 Numerical solutions for coil parameters This model is based on a 500 W operation with a resonance frequency of 40 kHz and a voltage output of 48 V. Below is the numerical solution for the proposed coil parameters. This mathemati- cal computation begins by determining the ideal circuit’s inductance and capacitance values. Po = 500 W; Vp = 120 V; Vo = 48 V; f = 40 kHz w k krad so � �2 40 251327 41� ( ) . (9) R V PL o o � � � ( ) ( ) . 2 248 500 4 6� (10) Where Qs = 4 is specified; using equation (11) below, calculate an appropriate cou- pling coefficient: k Q Qs kC s C� � � 1 1 1 4 0 248 2 , . (11) The value of kc derived from the computation is 0.248. As a result, the value of k is chosen to be 0.2 as it must be smaller than kc. I P V Ap rms o p , .= = = 150 120 4 167 (12) I V R As rms L , . .= = =o 48 4 6 10 435 (13) L Q R w Hs s L o � � � 4 4 6 251327 41 73 211 ( . ) . . � (14) 154 http://www.i-jim.org Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… M I R I w s rms L p rms o � � �, , ( . )( . ) ( . )( . ) . 10 435 4 6 4 167 251327 41 45 834 �HH (15) L M L k Hp s � � � 2 2 2 2 45 834 73 211 0 2 716 363 . ( . )( . ) . � � � (16) w L C C nFo s s s� � 1 2 216 244 � , . (17) w L C C nFo p p p� � 1 2 22 100 � , . (18) The list of parameters obtained from these equations are summarised in Table 3. Table 3. Circuit parameters Parameters Values Vp,rms 120 V Vs,rms 48 V Ip,rms 4.167 A Is,rms 10.4 A RL 4.6 Ω Lp 716.363 µH Ls 73.211 µH M 45.834 µH Cp 22.100 nF Cs 216.244 nF 3.2 Simulation results discussion Equations (19) and (20) showed a comparison of computed and simulated values for the schematic circuit simulation in NI Multisims software. Efficiency, � � Power Power received transmitted �100% (19) Simulated, Efficiency � � 479 25 493 100 99 4 . % . %� (20) Figure 4 and Figure 5 showed the bar graph of the calculated and simulated primary and secondary voltages and currents. iJIM ‒ Vol. 16, No. 11, 2022 155 Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… Fig. 4. Differences in primary and secondary voltages computed and simulated Fig. 5. Differences in primary and secondary currents computed and simulated The differences between the calculated and simulated values of the system circuit are quite modest, as shown in Figures 4 and 5. Because the differences are very small, the results may be trusted to be further investigated. The findings are then analysed further to determine the transmitted and received power. The efficiency percentages for transmitted and received power are summarised in Figure 6, and the bar graph of the power analyses is depicted in Figure 7. Because this circular coil is meant to have a 500 W output power, the calculated transmitted and received power are predicted to be 500 W. In practise, though, it is nat- ural to experience a loss of efficiency. The results were summarised in Figures 6 and 7. 156 http://www.i-jim.org Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… Fig. 6. Differences in power transmitted and received computed and simulated Fig. 7. Differences in power efficiency percentages calculated and simulated In a perfect circumstance, there would be no internal resistance, therefore the power transfer efficiency would be 100%. When comparing the calculated and simulated data, it can be inferred that the efficiency of the simulated circuit is 99.4%. 3.3 Numerical analsyis Primary and secondary coil geometry properties: L N D D D D out in out in � � � 2 2 8 15 7 2 54 ( ) ( ) . (21) iJIM ‒ Vol. 16, No. 11, 2022 157 Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… For circular coil diameter design, 716 363 30 0 10 0 8 15 30 0 7 10 0 2 54 58 8 58 2 2 . . . ( ( . ) ( . )) . , . ( ) � � � � � N N tp p uurns (22) 73 211 30 0 10 0 8 15 30 0 7 10 0 2 54 18 8 18 2 2 . . . ( ( . ) ( . )) . , . ( ) � � � � � N N tus s rrns (23) Table 4 summarises the primary and secondary parameters employed in the proposed circular coil design. The circular coil on the transmitter side (primary coil) is varied with four distinct ferrite variants for this research. Meanwhile, for the four primary coil modifications, the circular coil on the receiver side (secondary coil) remains the same. Table 4. Summary of calculated geometry properties Coil Dimensions Number of turns (N) Number of ferritesInner Diameter (cm) Outer Diameter (cm) Primary Coil (P1) 10.0 30.0 58 None Primary Coil (P2) 2 Primary Coil (P3) 2 (double), in phase Primary Coil (P4) 2 (double), out phase Secondary Coil 10.0 30.0 18 None The transmitted power may be monitored by altering the primary coil, and the most suitable suggested primary coil can then be selected as the most compatible primary coil to couple with the proposed secondary coil. The magnetic flux density of the find- ings may be determined using the JMAG Designer software or any other compatible software. The magnetic flux density assessments of the suggested circular coil design will not be detailed in this paper. 4 Conclusion The inner and outer diameters, as well as the number of turns necessary for both the main and secondary coils, were calculated using the inductance values. NI Multisims software was used to build the circuit diagram. The design overview was supplied, which included all of the dimensions and number of turns. According to calculations, the transmitted power efficiency from the primary coil to the secondary coil is just 0.6% loss. As a consequence, the new recommended coil has a power efficiency of 99.4%, making this research a success. 5 Acknowledgement This work was partially supported under IIUM-UMP-UITM SUSTAINABLE RESEARCH COLLABORATION GRANT 2020 (SRCG) number SRCG20-049-0049. 158 http://www.i-jim.org Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… 6 References [1] A. Zaini, S. H. Yusoff, A. A. Abdullah, S. Khan, F. A. Rahman, and N. N. Nanda, “Inves- tigation of magnetic properties for different coil sizes of dynamic wireless charging pads for electric vehicles (EV),” IIUM Eng. J., vol. 21, no. 1, pp. 23–32, 2020, https://doi. org/10.31436/iiumej.v21i1.1108 [2] K. 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Abed Badawi, “Mathematical Design of Coil Parameter for Wireless Power Transfer using NI Multisims Software,” in 8th International Conference on Computer and Communication Engineering (ICCCE), 2021, pp. 99–103. https://doi.org/10.1109/ICCCE50029.2021.9467166 [21] A. A. Abdullah et al., “Design of U and I Ferrite Core On Dynamic Wireless Charging for Electric Vehicle,” in 8th International Conference on Computer and Communication Engi- neering (ICCCE), 2021, pp. 104–109. https://doi.org/10.1109/ICCCE50029.2021.9467217 [22] W. Zheng, and J. Liu, “Hybrid sliding mode control technology of electric vehicle based on wireless sensor,” International Journal of Online Engineering (IJOE), vol. 13, no. 05, p. 97, 2017. https://doi.org/10.3991/ijoe.v13i05.7052 [23] M. Han, “Application of artificial intelligence detection system based on multi-sensor data fusion,” International Journal of Online Engineering (IJOE), vol. 14, no. 06, p. 31, 2018. https://doi.org/10.3991/ijoe.v14i06.8696 [24] F. Hussein, L. ben Aissa, A. Abdalla Mohamed, I. Alruwaili, S. and A. Alanzi, “Develop- ment of a secured vehicle spot detection system using GSM,” International Journal of Inter- active Mobile Technologies (IJIM), vol. 15, no. 04, p. 85, 2021. https://doi.org/10.3991/ijim. v15i04.19267 7 Authors In June 2019, Nadia Nazieha Nanda graduated from the International Islamic Uni- versity Malaysia (IIUM) with a bachelor’s degree in Communication Engineering. In addition, she graduated with a Master of Science majoring in Computer and Information-Electronics Engineering in October 2021 from the same university. She worked on multiple coil pair geometrics for inductive wireless power transfer, which included designing the coil pairs as well as their magnetic coupling. Her research includes using the Multisims software to simulate the coil pairs design and the JMAG Designer software to calculate the magnetic flux density of the designed coil pairs. Her area of interest is coupling coil and power transmission efficiency. She currently works as the Structural Design Engineer (GT) at Intel. Nur Shahida Midi received a M.Eng degree in Electrical and Electronic System from Tokai University, Japan and a Ph.D degree from Tokai University, Japan, in 2012 and 2015 respectively. She has been appointed as Assistant Professor in Department of Electrical and Computer Engineering, Faculty of Engineering, International Islamic University Malaysia (IIUM). Her current research interests include high voltage 160 http://www.i-jim.org https://doi.org/10.1109/TTE.2017.2771619 https://doi.org/10.1109/TIE.2011.2114312 https://doi.org/10.3233/JAE-150029 https://doi.org/10.1109/TMAG.2012.2202642 https://doi.org/10.1109/ICCCE50029.2021.9467166 https://doi.org/10.1109/ICCCE50029.2021.9467217 https://doi.org/10.3991/ijoe.v13i05.7052 https://doi.org/10.3991/ijoe.v14i06.8696 https://doi.org/10.3991/ijim.v15i04.19267 https://doi.org/10.3991/ijim.v15i04.19267 Paper—500W Circular Coil Parameters Mathematical Design for Wireless Power Transfer with… phenomenon, energy harvesting, power management, Internet of Things (IoT), and waste management. E-mail: nurshahida@iium.edu.my Siti Hajar Yusoff received the M.Eng. degree in electrical engineering (First Class Honors) and a PhD degree in electrical engineering from the University of Nottingham, UK, in 2009 and 2014, respectively. In 2015, she became an Assistant Professor in the Department of Electrical and Computer Engineering at International Islamic University Malaysia, Gombak. She is now a lecturer in control of power electronics systems and electrical power systems. Her research interests include control of power converters and drives, Matrix and multilevel converters, IoT, smart meter, wireless power trans- fer for dynamic charging in electric vehicles (EVs), and renewable energy. E-mail: sitiyusoff@iium.edu.my Ahmed Badawi received his PhD in International Islamic University Malaysia (IIUM). His study is about maximum power point tracking for small scale wind tur- bine under Electrical Engineering. Badawi have finished his Master degree in Wind Energy, Control Dept. (2013) and B.Sc. Electrical Engineering Communication & Con- trol Dept. (08th June, 2010) from Islamic University of Gaza, Gaza, Palestine. E-mail: ab1005100@gmail.com Article submitted 2022-02-02. Resubmitted 2022-03-04. Final acceptance 2022-03-04. Final version published as submitted by the authors. iJIM ‒ Vol. 16, No. 11, 2022 161 mailto:nurshahida@iium.edu.my mailto:sitiyusoff@iium.edu.my mailto:ab1005100@gmail.com