Modeling, Simulation and Verification of Contactless Power Transfer
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Modeling, Simulation and Verification of Contactless Power Transfer Systems J. Serrano(1,*), M. Perez-Tarragona´ (1), C. Carretero(2), J. Acero(1). (1)Department of Electronic Engineering and Communications. Universidad de Zaragoza. Maria de Luna, 1. 50018 Zaragoza. Spain. (2)Department of Applied Physics. Universidad de Zaragoza. Pedro Cerbuna, 12. 50009 Zaragoza, Spain. (*)E-mail: [email protected] Abstract—This work presents the analysis of a wireless power transfer system consisting of two coupled coils and ferrite slabs acting as flux con- centrators. The study makes use of Finite Element Method (FEM) simulations to predict the key per- formance indicators of the system such as coupling, quality factor and winding resistance. The simula- tions results were compared against experimental measurements on a prototype showing consistence. Keywords—Wireless power transfer, Electro- magnetic modeling, FEM simulation, Inductive Charging. Fig. 1. Wireless power transfer system. I. INTRODUCTION Wireless power transfer (WPT) applications will be later compared against measurements on are taking major importance among market trends a prototype. thanks to their versatility and user convenience. This solution allows the producers to remove In order to address this problem, in Section the cables and connectors which are one of the II, key performance indicators will be defined. main causes of breakdown. As this technology In Section III, the electromagnetic model will be consolidates, WPT systems are becoming more presented. In Section IV, the simulation procedure common and available for a large number of with COMSOL will be detailed. In Section V, devices. The modeling of these systems is, the model will be experimentally validated by therefore, of great interest. characterizing a prototype. Finally, Section VI gathers the main conclusions of the study. Important research efforts were made in the past on the development of this WPT systems [1–4]. The main areas of interest include inductive II. KEY PERFORMANCE INDICATORS OF LOW coupling between the coils [5], power losses POWER INDUCTIVE LINKS in the windings [6–10], and power electronics [11–15]. In terms of the intended application, The operating principle of WPT systems is these systems can be roughly classified in low based on Lenz-Faraday’s Law, according to power magnetic links and high power magnetic which the induced electromotive force in any links. Low power links are highly limited by size closed circuit is equal to the negative of the time restrictions, i.e. small-sized devices and large rate of change of the magnetic flux enclosed separation between coils. These leads to loosely by the circuit [17]. An alternating current is coupled coils and low efficiency in the inductive driven through the primary coil generating and power transference. On the other hand, high alternating magnetic field. This field causes a power links are characterized the use of larger variable flux through the secondary coil, where coils with higher coupling leading to higher an electromotive force is induced. The system inductive power transference efficiencies [16]. can be interpreted as a loosy coupled coreless transformer. In this work, a simulation model for low power transfer will be presented in order to predict the The coupling between two coils, k, is defined key performance indicators of the system. These as usual, Excerpt from the Proceedings of the 2016 COMSOL Conference in Munich M k = p ; (1) L1L2 where L1 is the self-inductance of the primary, L2 is the self-inductance of the secondary, M is the mutual inductance. Moreover, the quality factor of a coil is defined (a) as, rext,2 t !0Li f ,2 Qi = ; (2) tw,2 rint,2 Ri ∆z rint,1 where !0 is the angular frequency of resonance tw,1 t and i = 1; 2 is an index indicating primary or f ,1 ∆r rext,1 secundary coil. The efficiency of a WPT for a certain geometry (b) was proven [16] to be a function of the aforemen- Fig. 2. Cross-section schematic of (a) wireless power tioned variables, being limited by the maximum transfer system with two coils wound with litz wire and efficiency [5]: two slabs of ferrite as flux concentrator. (b) Simulation model. 1 ηmax = q (3) 1 + 2 1 + 1 + (kQ)2 and ∆r represents misalignment. (kQ)2 p where Q = Q1Q2. Once the geometry is defined, the current den- sity can be defined as, As can be inferred from Equation 3, the effi- −! n · I0 ciency is maximized when the parameter kQ is J = ' (5) t (r − r ) b maximized. Therefore, the parameter kQ will be w;1 ext;1 int;1 chosen as a key performance parameter, which being n the number of turns, I0 the current introducing Equations 1 and 2, can be expressed and 'b represents the azimuthal direction of a as, cylindric coordinate system. s M (!0L1)(!0L2) This current generates a magnetic field H and kQ = p : (4) an electric field E, from which the induced elec- L1L2 R1R2 tromotive force can be calculated for both coils: The electromagnetic model in the next section will have as main objective to model and correctly I −! −! 1 Z predict the variables involved in Equation 4: M, Vi = − E · dl = − E'dV (6) Scoil;i Vcoil;i L1, L2, R1 and R2 which are characteristic of the coils. From were the coil’s impedance can be ob- tained, III. ELECTROMAGNETIC MODELING V A. Self and mutual inductance calculation Z = i : (7) i I High frequency devices usually employ 0 multi-stranded litz wire due to its good reduced The calculation of L1, L2 and M is immediate. ac-losses [10]. Litz wire ensures that all the When coil 1 is excited, L1 and M are obtained strands in the cable are equivalent among as: them [8], and therefore the current is equally =m(Z1) shared between all of the strands. Under this L = (8) 1 ! assumption, the primary inductor can be modeled =m(Z ) as a ring-shaped ideal domain with rectangular M = 2 (9) cross-section through which a constant current ! density flows. This simplification is graphically When coil 2 is excited, L2 can be calculated represented in Fig. 2, where tf represents the and M can be verified: ferrite’s thickness, tw represents the winding’s =m(Z2) thickness, rext and rint are the external and L2 = (10) internal radii respectively and indexes 1 and 2 ! represent primary coil (transmitter) and secondary =m(Z1) coil (receiver). ∆z is the separation between coils M = (11) ! Excerpt from the Proceedings of the 2016 COMSOL Conference in Munich Note that as the inductors are ideal domains, no power losses take place on them. Therefore, the resulting resistance from Ri = <e(Zi) would be null. The resistance of the losses are calculated by a separate loss model. B. Winding resistance calculation The power losses in the winding can be divided into two groups, depending on their cause. On one hand, dc and skin effect losses produce an Fig. 3. Model geometry. associated power loss referred as conduction loss, Pcond. On the other hand, induced currents due to TABLE I. System parameters. proximity effects produce proximity losses, P . prox Description Symbol Value Both can be modeled by resistances, R and cond Nr. Turns n 20 Rprox, in such a way that Ri = Rcond;i + Rprox;i. Nr. Strands ns 105 r µ From previous studies [18, 19] the resistance of Strand radius s 40 ( m) t a circular cross-sectional conductor per unit length Ferrite thickness f 2.5 (mm) l (e.g. PCB tracks) is already known: Ferrite side length 50 (mm) Coil external radius rext 22 mm Coil internal radius r 10.12 mm 1 int t Rdc;skin;u:l: = 2 Φdc;skin(r0/δ) (12) Coil thickness w 2.5 mm πr0σ Coil separation ∆z 4 mm Misalignment ∆r 0-44 mm 4π R = Φ (r /δ)jH j2 (13) prox;t;u:l: δ prox 0 t the square of the magnetic field incident on the where r0 is the strand radius, σ is the conductor 2 2 2 conductors, jH¯0j = n jH¯0;1j . Consequently, electrical conductivity, δ is the skin depth, Ht 3 Rprox = n · ns · Rprox;11. is the transversal magnetic field and Φdc;skin and Φprox are functions including the geometric and frequency dependences. Their analytical The resistance of each coil is finally given by expressions where inferred in [20]. n 3 Ri = Rcond;11;i + n · ns · Rprox;11;i: (16) By integrating equations (12) and (13) in in- ns ductor domain, and expressing the resistances in terms of cylindrical coordinates (where the index IV. SIMULATION IN COMSOL k refers to the coordinates r and z ) the conduc- tion resistance Rcond;11 and proximity resistance The model was simulated in COMSOL making Rprox;11 of one turn made of one strand can be obtained: use of the AC/DC Module. The geometry is shown in Fig. 3 and the geometric parameters are lav shown in Table I. Rcond;11 = 2 Φdc;skin(r0/δ) (14) πr0σ The domains representing the coils are defined σ ≈ 0 µ = 1 4π D ¯ 2E as quasi-ideal domains ( S/m, r ), Rprox k;11 = Φprox (r0/δ) 2πr H0 i;1 σ while the ferrites are characterized by their (15) physical properties (σ ≈ 0 S/m, µr = 2000). where lav = π (rext + rint) represents the Firstly, an external current density is set in the ¯ average length of the turns, H0 i;1 corresponds to primary coil. The current density is calculated the magnetic field generated by the single-wire according to Equation (5), with a current of D ¯ 2E turn and 2πr H0 i;1 is the averaged square I0 = 1 A and the geometric parameters in Table magnetic field in the ideal ring-type inductor I.