INDUCTIVE power transfer (IPT) systems are emerging

Finite Element Based Design Optimization of Magnetic Structures for Roadway Inductive Power Transfer Systems Masood Moghaddami, Arash Anzalchi and Arif I. Sarwat Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, Email: asarwat@fiu.edu Abstract Design optimization of magnetic structures for roadway inductive power transfer (IPT) systems based on 2D finite element analysis (FEA) is proposed. The proposed method can be used to find the optimal structure for IPT systems based on prioritization of different objectives such as efficiency, cost, etc. A Multi-objective genetic algorithm (MOGA) coupled with 2D FEA is used for the co-optimization of primary and secondary magnetic structures. Also, Electromagnetic field (EMF) emissions of the pads are considered to meet human exposure regulations in compliance with standards as defined by International Commission on Non-Ionizing Radiation Protection (ICNIRP). A 1 kw roadway IPT system is investigated as the case study and the results of the optimization are presented using different objective functions. Index Terms inductive power transfer, finite element method, multi-objective optimization. I. INTRODUCTION INDUCTIVE power transfer (IPT) systems are emerging technology for transferring electric power to a wide range of applications without any physical contacts. It offers robustness, high reliability and high efficiency typically between 85-90%, even when used in hazardous environments, as it is unaffected by dust or chemicals and eliminates sparking and the risk of electrical shocks [1], [2]. Therefore, it is a safe, robust and clean way of transferring power and has rapidly gained increased interest in the commercial and industrial applications. The IPT technology has been successfully employed in many applications, including systems for materials handling [3], [4], biomedical implants [5] [8] and transportation systems [9]. Especially this innovative technology can be used for roadway dynamic wireless power transfer for electric vehicles (EVs) [1], [10]. A roadway IPT system is a safe, robust and clean way of transferring power to EVs with high flexibility and convenience and is unaffected by weather and dirt. Roadway IPT system has already been proposed for more than two decades [11]. However, due to technological barriers, commercial developments have been slow. A typical roadway inductive power transfer system and its components are shown in Fig. 1. This system is composed of primary tracks, secondary power pad, compensation capacitors, power converters, controllers and wireless communication modules. The primary tracks which are built as loops are placed underground. Track loops This work was funded by the National Science Foundation under grant number CRISP-1541069. Primary Compensation 10kHz- 85kHz Secondary Compensation AC/AC Converter Controller Battery Energy Storage System AC/DC Converter Pick-up Power Pad 50/60Hz Three-phase main Wireless Communication Controller Fig. 1. A typical roadway IPT system. Wireless Communication Primary Tracks are longer than pickup pads and due to large air gap, the magnetic coupling coefficient between transmitter and receiver would be lower than 10% [11]. Many studies have been established to improve the efficiency of the magnetic structures with ferrites both in primary tracks and secondary pad. But the use of ferrites in primary are very costfull and may not be applicable. Fig. 2 shows the structure of a circular power pad which is composed of a coil, ferrite bars and shielding plate. In this paper optimization of roadway IPT systems using FEA-based optimization is presented. The proposed method can find the optimal structure for IPT systems by prioritizing the different objective functions. Efficiency, cost, weight, etc. can be defined as objective functions. The Co-optimization of primary and secondary magnetic structures are performed using a multi-objective genetic algorithm (MOGA) coupled with 2D FEA model. The electromagnetic field (EMF) emission of the IPT system is defined as a constraint in the optimization problem to meet human exposure regulations in compliance with standards as defined by International Commission on Non-Ionizing Radiation Protection (ICNIRP). Furthermore, the operational quality factor of the primary and secondary are taken into account to be within the limitations of primary and secondary power converters. A 1 kw roadway IPT system is investigated as the case study and the results of the optimization are presented using different objective functions. 978-1-5090-0403-4/16/$31.00 2016 IEEE

Aluminum Ring Aluminum Shielding Plate Ferrite Bar D ic D if Coil L f D p θ Fig. 2. The structure of a circular power pad. II. DESIGN OPTIMIZATION The power output of an IPT system can be calculated as follows [9]: P out = ωi1 2 M 2 Q 2 (1) L 2 where ω is the angular frequency of the primary track current I 1, M is the mutual inductance between the primary track and secondary pad and L 2 is the inductance of the secondary pad with the primary track open-circuited. Equation (1) shows that the output power can be determined based on the power supply current and frequency (ωi 2 1 ), magnetic coupling between the primary track and secondary pad (M 2 /L 2 ) and switch-mode controller (Q 2 ). The term ωi 2 1 Q 2 is limited to the operational limitations of the power electronic converters. Therefore, it is essential that the power pads have a high magnetic coupling between the pads to ensure the overall feasibility, cost effectiveness, and efficiency of the IPT system. The magnetic coupling between pads (M 2 /L 2 ) is determined by the vertical and horizontal separation between the pads and the structure of the pads. The VA rating of each pad can be calculated as follows [9]: S pad = P out Q2 + 1 (2) Using the rated VA of the pad given by (2), the rated current can be calculated. Thereby, the magnetic structure can be analyzed using the FEA based on electrical and geometrical parameters. The IPT model is parametrized based on parameters which are defined in Table I. The flowchart of the multi-objective optimization is shown in Fig. 4. The objective functions and constraints of the multi-objective optimization problem are presented in the following sections. A. Optimization Objectives The proposed optimization of circular pads includes the following objectives: 1) Total Loss (P t ): The total loss incorporates all the losses in the coils and tracks, ferrite cores and shielding plates both in the primary tracks and secondary pads, which are all described in Section III. The total losses are dependent to D and Ē vectors and can be calculated as follows: W f W c Fig. 3. Geometrical parameters of a circular power pad. P t = P coil + P core + P plate (3) where P coil, P core, P plate can be calculated using (9), (11), and (13) respectively. 2) Total Cost (C t ): The total material cost of each circular pad can be calculated by calculating the length of Litz wire, ferrite core volume, and shielding plate area as follows: C t = π(d c + W c )N c C c + L f W f H f N f C f + π D2 p 4 C p (4) where vector D contains the geometrical parameters of the circular power pad and vector Ē contains the electrical parameters of the primary converter, which both are defined in Table I, and C c, C f, C p are the cost coefficients of the Litz wire, ferrite core and aluminum plate respectively. B. Optimization Constraints There are different types of constraints, which limit the search space of the optimization problem. These constraints include geometric constraints, EMF exposure limitations, as well as converter limitations. 1) Geometric Constraints: The geometric constraints are determined based on the space limitations for the transmitter and receiver pads under the electric vehicle. Therefore, the outer diameter of the pads should be less than a maximum allowable value: D p D max (5) 2) EMF Exposure Limitations: The EMF emission of the IPT system should be in compliance with standards such as those defined by International Commission on Non-Ionizing Radiation Protection (ICNIRP). EMF EMF max (6) where EMF max is the maximum EMF allowed at the track current s frequency.

TABLE I THE PARAMETERS OF A ROADWAY IPT STRUCTURE. Parameter D p D ic W c d c N s D if L f H f L t Prioritization: Weights vector [w 1 w 2 ] Description shielding plate diameter internal diameter of the coil width of the coil diameter of the Litz wire number of turns in the secondary pad internal diameter of the ferrite ends ferrite bar length ferrite bar thickness track distance Design Specifications: P: Output Power g: Air gap ω: Frequency I 1 : Primary current FEM based MOGA Optimal Magnetic Structure: Shield plate diameter (D p ) Ferrite length (L f ) Ferrite internal diameter (D if ) Coil internal diameter (D ic ) Number of turns in Secondary (N s ) Track distance (L t ) Constraints: Topology constraints EMF limitations Converter constraints Fig. 4. The flowchart of the FEM based optimization of the magnetic structures for roadway IPT systems. 3) Converter Limitations: The VA rating of the power converters as well as operating frequency are limited by those power electronic switches presently available. In practical applications, the operating quality factors Q, is constrained to 4-10: 4 Q 1, Q 2 10 (7) This limitations are due to component VA ratings and tolerances of the power converter. C. Multi-Objective Optimization Formulation The multi-objective optimization problem (MOP) can be formulated as follows: min(w 1 P t + w 2 C t ) (8) subject to constraints which are defined in IV.B, where w 1, w 2 are the weighting coefficients which are used for prioritization of power loss (P t ) and cost (C t ). Different methods can be used to solve the MOP, such as genetic algorithms (GA), differential evolution (DE), particle swarm optimization (PSO) [12]. In this study, a elitist non-dominated sorting genetic algorithm (NSGA-II) is used to find the optimal solutions for the MOP. An elitist GA always favors individuals with better fitness rank and as a result, it converges relatively fast [13]. III. FINITE ELEMENT MODELING OF IPT SYSTEMS The calculation of different parameters related to IPT systems is essential for design optimization purposes. Due to complexity of IPT systems, finding analytical solutions for electromagnetic field distribution may not be possible. However, different numerical analysis methods can be employed for electromagnetic field analysis. In this study finite element analysis (FEA) using ANSYS software is used for electromagnetic field analysis of any IPT system design. A 2D quasi-static electromagnetic finite element model is used for FEAs. A Dirichlet boundary condition is used at the outer boundaries of the FE models to model the space out of the drawing region as infinitely large. The tracks and coils are modeled as a stranded coil domain. A. Coil Losses In the design optimization of circular power pads for IPT systems, accurate prediction of high-frequency coil loss is of great importance. Eddy-current winding loss increases rapidly with frequency, and can be divided into skin-effect loss and proximity-effect loss. Due to the complexity of pad geometries and interactions between conductors in windings, it is difficult to find a general analytical solution for the eddy current losses in coils. The coils are constructed using Litz wire to minimize the eddy current loss due to skin effect and proximity effect. The Litz wire consists of many thin wire strands, individually insulated and twisted or woven together, following one of several carefully prescribed patterns, often involving several groups of twisted wires are twisted together. The losses associated with the coils can be computed as follows: P coil = F r i 2 rmsr dc (9) where F r is the ratio of AC resistance (R ac ) to DC resistance (R dc ), which accounts for skin and proximity coil losses, given a sinusoidal current with RMS amplitude i rms. The loss factor F r can be approximated as follows [14]: F r = 1 + π2 ω 2 µ 2 0N 2 n 2 d 2 ck 768ρ 2 cg 2 (10) where ω is the angular frequency of a sinusoidal current, n is the number of strands, N is the number of turns, d c is the diameter of the copper in each strand, ρ c is the resistivity of the copper conductor, g is the air gap between transmitter and receiver power pads, and k is a factor accounting for field distribution in multiwinding coils, normally equal to one. B. Ferrite Core Losses The ferrite cores, which are used to increase the magnetic coupling between the power pads, produce losses due to high frequency magnetic flux. Therefore, calculation of losses in ferrite cores is essential. The losses in the ferrite cores can be calculated using Steinmetz equation as follows: P core = kf α ˆBβ (11) where P is the time-average core loss per unit volume, ˆB is the peak flux density, f is the frequency of sinusoidal excitation,

TABLE II DESIGN SPECIFICATIONS AND CONSTRAINTS THE IPT SYSTEM WITH CIRCULAR POWER PADS. Description Air gap (g) 200 mm Output power (P 2) 1 kw Track current (I 1) 100 A Frequency (f) 20 khz Max. pad diameter (D p) 750 mm Max. EMF (EMF m) 5 mg Operating quality factor range 4-10 and k, α, β are Steinmetz constants, which can be found by curve fitting. Since (11) gives the unit volume loss, by integrating this equation over the ferrites volume in any power pad structure, the total core loss can be calculated. C. Shielding Plate Losses At the boundaries, where the magnetic field penetrates only a short distance into the boundary, the Impedance Boundary Condition (IBC) is used for approximating the magnetic field penetration into the boundary. IBC is a combination of Dirichlet and Neumann boundary conditions. The IBC can be used to model a bounded domain as an unbounded region and it is a valid approximation if the skin depth is small compared to the size of the conductor. The penetration depth δ is measured using the following equation: 2 δ = (12) ωµσ Since in circular power pads, shielding plates are made of aluminum and the penetration depth of aluminum at high frequencies is much smaller than the dimensions of the shielding plates (for example, at 20 khz is less than 1 mm), in 2D FEA model of the IPT system, IBC can be applied to the exterior boundaries of the shielding plates. This will further simplify the FEA model by reducing the number of required mesh elements. Also the plate losses can be calculated as follows [15]: ωµ P plate = 2σ H2 rms (13) where P plate is the unite area power loss and H rms is the rms magnetic field at the surface of the boundary. IV. CASE STUDY ANALYSIS A 1 kw roadway IPT system with a ground clearance of 200 mm is considered. It is assumed that the primary converter can provide 100 A, 20 khz high-frequency current for underground tracks. The design specifications and constraints are presented in Table II. The optimization method is applied to this IPT system with different prioritization. The prioritization is set using the weighting coefficients w 1 and w 2 in (8). A minimum number of 100k elements is set for each 2D FEA model to ensure the accuracy of the calculations. The cost coefficients which are presented in Table III, are used for calculation of cost for each magnetic structure. Efficiency (%) Cost ($) 100 95 90 85 80 75 70 65 900 800 700 600 500 400 TABLE III THE COEFFICIENTS USED FOR COST CALCULATION. Coefficient Description C c Litz wire cost in unit length ($/m) 2.04 C f Ferrite cost in unit volume ($/cm 3 ) 0.18 C p Aluminum plate cost in unit volume ($/m 2 ) 333.68 TABLE IV MULTI-OBJECTIVE OPTIMIZATION PARAMETERS. Description Population size 40 Cross-over probability 0.8 Mutation probability 0.8 Number of generations 104 Total optimization time 227 min. Efficiency function vs. no. of iterations 60 (a) Cost function vs. no. of iterations (b) Fig. 5. Efficiency optimization of the sample 1kW IPT system: a) convergence of the efficiency function, b) convergence of the cost function. 1) Efficiency Optimization: By prioritizing the efficiency optimization defining the weight vector presented in (8) as [w 1, w 2 ] = [10, 1], the optimization is carried out on the 1 kw case study IPT system and the results are shown in Figs. 5a, 5b, 6 and Table V. Results show that the optimized magnetic structure has 96.1% efficiency with the cost of $596. 2) Cost Optimization: By prioritizing the cost optimization using the weight vector presented in (8), the optimization

200 200 TABLE V DIMENSIONS OF THE EFFICIENCY-OPTIMIZED MAGNETIC STRUCTURE OF THE ROADWAY IPT SYSTEM. (ALL DIMENSION ARE IN MILLIMETERS) Parameter Shield plate diameter (D p) 800 Ferrite length (L f ) 383 Ferrite internal diameter (D if ) 34 Coil internal diameter (D ic) 100 Number of turns in Secondary (N s) 50 Track distance (L t) 446 Efficiency (%) 90 85 80 75 70 Efficiency function vs. no. of iterations 304 383 800 34 100 446 Fig. 6. The optimal magnetic structure for maximum efficiency. (All dimension are in millimeters). 65 60 500 450 400 (a) Cost function vs. no. of iterations TABLE VI DIMENSIONS OF THE COST-OPTIMIZED MAGNETIC STRUCTURE OF THE ROADWAY IPT SYSTEM. (ALL DIMENSION ARE IN MILLIMETERS) Cost ($) 350 300 Parameter Shield plate diameter (D p) 424 Ferrite length (L f ) 170 Ferrite internal diameter (D if ) 84 Coil internal diameter (D ic) 100 Number of turns in Secondary (N s) 25 Track distance (L t) 340 is performed on the 1 kw IPT system and the results are shown in Figs. 7a, 7b, 8 and Table VI. Results show that the optimized magnetic structure has $254 production cost with 86.4% efficiency. V. CONCLUSION The proposed multi-objective optimization method based on FEA, provides an effective tool for design optimization of roadway IPT systems for contactless dynamic electric vehicle battery charger. The efficiency and cost which are both of great importance in an IPT system, are considered as the objective functions. Also, practical limitations associated with power electronic converters are defined as constraints. Using the proposed multi-objective optimization, the optimal solutions for roadway IPT structure is carried out based on the prioritization of the objectives. The optimal solutions comply with ICNIRP standard and are compatible with power electronic converters to work in operational limits. REFERENCES [1] C.-S. Wang, O. H. Stielau, and G. A. Covic, Design considerations for a contactless electric vehicle battery charger, IEEE Transactions on Industrial Electronics, vol. 52, no. 5, pp. 1308 1314, Oct 2005. [2] S. Y. R. Hui and W. W. C. Ho, A new generation of universal contactless battery charging platform for portable consumer electronic equipment, IEEE Transactions on Power Electronics, vol. 20, no. 3, pp. 620 627, May 2005. 250 200 (b) Fig. 7. Cost optimization of the sample 1kW IPT system: a) convergence of the efficiency function, b) convergence of the cost function. 140 170 424 84 100 340 Fig. 8. The optimal magnetic structure for minimum cost. (All dimension are in millimeters) [3] P. Sergeant and A. V. D. Bossche, Inductive coupler for contactless power transmission, IET Electric Power Applications, vol. 2, no. 1, pp. 1 7, Jan 2008. [4] J. de Boeij, E. A. Lomonova, and A. J. A. Vandenput, Optimization of contactless planar actuator with manipulator, IEEE Transactions on Magnetics, vol. 44, no. 6, pp. 1118 1121, June 2008. [5] F. Sato, T. Nomoto, G. Kano, H. Matsuki, and T. Sato, A new contactless power-signal transmission device for implanted functional electrical stimulation (fes), IEEE Transactions on Magnetics, vol. 40, no. 4, pp. 2964 2966, July 2004. [6] Q. Chen, S. C. Wong, C. K. Tse, and X. Ruan, Analysis, design, and control of a transcutaneous power regulator for artificial hearts, IEEE Transactions on Biomedical Circuits and Systems, vol. 3, no. 1, pp. 23 31, Feb 2009. [7] G. Wang, W. Liu, M. Sivaprakasam, and G. A. Kendir, Design and

analysis of an adaptive transcutaneous power telemetry for biomedical implants, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 10, pp. 2109 2117, Oct 2005. [8] P. Li and R. Bashirullah, A wireless power interface for rechargeable battery operated medical implants, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 10, pp. 912 916, Oct 2007. [9] J. T. Boys, G. A. Covic, and A. W. Green, Stability and control of inductively coupled power transfer systems, IEE Proceedings - Electric Power Applications, vol. 147, no. 1, pp. 37 43, Jan 2000. [10] O. H. Stielau and G. A. Covic, Design of loosely coupled inductive power transfer systems, in Power System Technology, 2000. Proceedings. PowerCon 2000. International Conference on, vol. 1, 2000, pp. 85 90 vol.1. [11] W. Zhang, S. C. Wong, C. K. Tse, and Q. Chen, An optimized track length in roadway inductive power transfer systems, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 2, no. 3, pp. 598 608, Sept 2014. [12] I. Giagkiozis and P. Fleming, Methods for multiobjective optimization: An analysis, Information Sciences, vol. 293, pp. 338 350, 2015. [Online]. Available: http://www.sciencedirect.com/science/article/pii/s0020025514009074 [13] K. Deb, Multi-objective optimization using evolutionary algorithms. John Wiley & Sons, 2001, vol. 16. [14] C. R. Sullivan, Optimal choice for number of strands in a litz-wire transformer winding, IEEE Transactions on Power Electronics, vol. 14, no. 2, pp. 283 291, Mar 1999. [15] K. Ishibashi, Eddy current analysis by boundary element method utilizing impedance boundary condition, IEEE Transactions on Magnetics, vol. 31, no. 3, pp. 1500 1503, May 1995.