Performance Evaluation of a Wireless Power Transfer System using Coupled 3D Finite Element-Circuit Model A.O. Hariri, A. Berzoy, A.A.S. Mohamed, Student Members, IEEE and O.A. Mohammed, Fellow IEEE Energy Systems Research Laboratory, Department of Electrical and Computer Engineering Florida International University Miami, Florida, USA
[email protected] Abstract —This paper presents a performance evaluation procedure for an inductive wireless power transfer (WPT) system with a parallel-parallel compensation network. The effect of the WPT system design parameters on its efficiency is investigated. The WPT system is modeled using a 3D electromagnetic field technique coupled with circuit simulation. The 3D finite element (3DFE) model is created and a MATLABFEA automated routine configures the model parameters. Moreover, the paper proposes a mathematical model for efficiency assessment purposes. The results from the 3DFE and the mathematical model are compared with the results of a Matlab Simulink model for the same system. The results show good agreement between all the models. Index Terms — Coupled electromagnetic-circuit model, Wireless power transfer, Coupled resonators, 3D Finite Element analysis, Mathematical model.
I. INTRODUCTION As more research is being directed for analyzing and developing WPT systems, issues involving electromagnetic resonance, inductive charging and other multi-disciplinary areas are being addressed. These involve power electronics, controls, communication, and electromagnetic design and analysis. Various techniques can be utilized in the applications of WPT and can be categorized into analytical, numerical, and/or experimental techniques. Analytical methods include equivalent circuit modeling and scattering parameter (Sparameters) analysis. The second category include Finite Element Analysis (FEA) for system electromagnetic modeling, high frequency structured simulation, and coupled field and lumped parameter analysis. The third category is the experimental methods including S-parameters measurements, field measurements as well as power and energy emission tests [1]. The literature demonstrates several applications of 3DFE models of WPT coupled resonators in comparative studies and performance analysis studies where FEA have been utilized to accurately obtain the parameters of the coil transfer system, and then using them to evaluate the performance of the link based on the derived analytical equations [2-3]. In this paper, the numerical technique involving coupled electromagnetic field analysis and electric circuit is used. This
coupled model is utilized to evaluate the WPT system efficiency and performance. The efficiency calculation is based on FEA of the WPT system to ensure a high level of modeling accuracy. A MATLAB-FE routine, which serves as an interface from which the changes to the 3DFE model and the circuit parameters are applied automatically, is developed. Then the FE model results are compared with a mathematical model’s results for validation purposes. II. WIRELESS POWER TRANSFER MODELING There are 3 different mechanisms for wireless energy transfer: inductive coupling, self-resonant coupling and modified resonant coupling [4]. The modeling for WPT using inductive resonant coupling mechanism can be done by: (1) the equivalent lumped parameter circuit model (ELPCM) and/or (2) a FE model coupled with an electric circuit. The ELPCM can be used since the characteristic wavelength (separation distance of the coils) of the system under study is smaller than 1/10𝑡ℎ of the relevant wavelength (wavelength of magnetic field) [5]. Also, a mathematical equation for efficiency calculation is presented in the paper for verification purposes. The details for the FE model, and the 2 verification models are further explained below. A. Equivalent Lumped Parameter Circuit Modeling The equivalent circuit model of the WPT system with the parallel-parallel compensation network, which is the basic Tmodel of two coupled inductors, is shown in figure 1 where 𝐿𝐿1 and 𝐿𝐿2 are the leakage inductances for the transmitting and receiving coils, M is the mutual inductance, 𝑅1 and 𝑅2 are the equivalent series resistances (parasitic resistances) of the transmitting and receiving coils, 𝐶1 and 𝐶2 are the capacitors to impose the resonance and 𝑅𝐿 is the load. R1 Iin
+ C1 _
Vin
LL1 IL1
M
LL2
R2
IRL
IL2 C2
RL
+ Vout _
Fig.1. Electric Circuit and modeling of the WPT
978-1-4673-7447-7/15/$31.00 ©2015 IEEE
2
)) (3)
The resonance frequency is chosen to be compatible with the Qi standard [6] that was developed by the Wireless Power Consortium. The resonance is imposed by choosing the capacitance value, C, that will satisfy the resonance criteria in (4), where L is the value of the self-inductance of the coil. 1 1 C1 = , C2 = (4) 2 2 L1 ω
Electric Circuit
100
M
R1
Ll2
8.0547e-008
+ ωR L C2 (1 +
C2
ωM
T2
−RL −R2
) +(
CoilR
M
T1
Ll2 +RL C2 R2 2
T2
A = (1 +
T1
Where ω is the resonance frequency and A can be defined as:
CoilT
Where PRL is the output power, Pin is the input power, IRL is the load current and IL1 and IL2 are the resonant coil currents. Starting from (1), and using simple circuit analysis of the ELPCM, (2) can be derived. 1 η= R1 R 1+A + 2 L 2 R2 (2) RL ω L2
8.0547e-008
(1)
The selection of the best combination of these parameters for maximizing the power transfer efficiency is a complex problem due to the high number of parameters, some of which are electrical and others geometrical, thus making a simple circuit simulation insufficient for solving this problem. Therefore, a MATLAB-FE routine, which serves as an interface from which the changes to the 3DFE model and the circuit parameters are applied automatically, is developed. At each combination of two selected parameters (e.g: coil wire gauge, distance, etc.), a series of steps linking the MATLAB and the FE model are made. The script allows for executing the FE software to perform changes in the circuit or the 3DFE model’s parameters by passing execution. Following the changes made in the FE model, the solver is executed from MATLAB. The needed parameters, such as currents and voltages in the circuit components are passed back to the MATLAB script and used to calculate the efficiency. The complete flowchart of this process is shown in Fig. 3. C1
PRL |IRL | R L = 2 Pin |I | R + |I |2 R + |I |2 R L1 1 L2 2 RL L
SIN
2
η=
separation off the coaxial axis) and symmetry of the two coils (symmetry of shape, area, and turns ratio).
I1
The power efficiency 𝜂 can be derived from the circuit in Fig. 1 as:
Electric Circuit
CoilT
L2 ω
B. 3DFE Modeling The geometry used for the inductive resonant coupling WPT consist of two approximations of Litz coils. The use of these coils allow significant decrease of the undesirable ac resistance caused by the skin effect which is a usual consequence of high frequency level in the application at hand [7]. Fig. 2 shows the complete circuit as modeled in the FEA program (Infolytica-Magnet). The CoilT and CoilR represent the coils modeled in the 3DFE software. The current source and the capacitors (C1 and C2) are modeled as ideal components in this simulation; R1 is the load. The 3DFE coils are modeled each as a copper ring where the cross-sectional area of the ring is AR = 0.785 cm2 , the number of turns is defined as N, and the geometric radius is defined as R= 20 cm. III. THE FINITE ELEMENT AND MATLAB SCRIPT In order to achieve the goal of wirelessly transferring power, across long distance and with high levels of efficiency, it is important to investigate the effect of different system parameters on the transmitted power and efficiency, and then apply a design technique that will provide the optimum combination of these parameters to achieve the best system performance. The design parameters of WPT circuit can be classified as follows: (1) Electric Circuit Parameters: the inductance value (L), the capacitance value (C) and the resonance frequency (ω). (2) Geometrical Parameters: For the coil (to get the required L): number of turns (N), dimensions of the coils (radius R), gauge of the cable (g), shape of the cable, and shape of the coil (circular, triangular, square, etc.). For the setup structure: distance between coils (d), alignment (angle of
3D-FEA Geometry
R
CoilR
Fig.2. The 3DFE coils coupled with an electric circuit START
MATLAB For loop
PLOT RESULTS YES
STOP CRITERIA NO
END
Vary N, G, N1/N2
YES
Invoke Infolityca
NO YES
Infolityca is open
Solve Static 3D
Vary f, R, d
NO
Get Energy W
Invoke Infolityca
Return W to MATLAB
Calculate L, C and asigned Solve Time Harmonics
Get Io, Vo, Ii, Vi
Calculate Efficiency
Fig.3. Platform interface methodology MATLAB and FEA.
IV. RESULTS AND VERIFICATION A. 3DFE Model Results and Validation Fig. 4 shows the 3D model in the FEA software, Infolytica, showing the magnetic field density on 2 slices defined in the
For purpose of corroboration, the electric variable waveforms obtained from the FE software and from the ELPCM are compared as shown in Fig. 6. It is clear that they highly correlated. P2 P1
CoilT
CoilT
V out
P3
CoilR
0.005
0.01
0.015
0.02 (b)
0.005
0.01
0.015
0.02
0
(c)
L2
0.005
0.01
0.015
0.02
0.005
0.01 Time (msec)
0.015
0.02
0
I Vertical Slice
Slice
FE model (a)
-200 0 10 CoilR
Horiz ontal
Simulink model
200 0 -200 0 10 0 -10 0 200
V in
Fig. 5 shows the variation of the magnetic field density along the line P1 (line midway between the two coils (on the horizontal slice)), along P3 (coplanar with coilR), and along P2, (axial direction of the two coils (on the vertical slice)). The figure shows, as expected, that the magnetic field decreases as the distance increases away from the center (Fig. 5(a)). Also, the field magnitude through CoilT is larger than through CoilR (Fig. 5(b)). The two maxima that are depicted in (Fig. 5(c)) correspond to the positions where the plane intersects the copper ring of the coil.
on the efficiency is graphed at different distances. As the distance between the two coils is an important parameter that directly affects the coupling factor of the two resonators, the effect of the change of these parameters is expected to be attenuated with an increase of the distance. The simulation results in figures show that, as expected, efficiency decrease as the distance of separation of the coils increase. Examining the obtained graphs, Fig. 7 shows that as the number of turns are varied, the efficiency reaches a maximum value at a specific number of turns. Therefore, at each specified distance, it is required to determine this number of turns that will give the maximum efficiency. The same figure also shows that as the distance increase, the number of turns that give maximum efficiency is not the same, but rather decreases as distance increases.
IL1
model. A zoom view on the transmitting coil, and how the generated field linking the coils appear on the two slices, is shown.
(d)
-10 0
Fig.6. Simulink and FE model results (a) input voltage (V) (b) primary coil current (A) (a) output voltage (V) (b) secondary coil current (A)
Fig.4. Magnetic Field Plots from 3DFEA Using Slices
100
5
x 10
(a) 0 0
Bmag (T)
-4
80
x 10 1
(b)
0 0 -3
Bmag (T)
20 40 60 Distance along P1 (cm)
x 10 1.5 1 0.5 0 0
20 40 60 Distance along P2 (cm)
80
Transfer Effeciency (%)
Bmag (T)
-5
80
60
40
20
0 0
(c) 20 40 60 Distance along P3 (cm)
80
Fig.5. Magnetic field density magnitude (a) along line P1 (b) along line P2 (c) along line P3
B. 3DFE-MatLab Script Results The number of turns, turns ratio and the coil wire gauge are the key design parameters which directly affect the equivalent series resistance of the resonating coils. They were chosen for studying the effect of varying them on the power transfer efficiency. The results are presented in figures 7 through 10. These results were obtained using the FE-MATLAB script introduced earlier. The influence that these parameters have
d=2 cm d=20 cm d=38 cm d=56 cm d=76 cm d=94 cm
5
10 15 Number of Turns (N)
20
25
Fig.7. Efficiency versus number of turns at different distances
Fig. 8 shows the efficiency versus turns ratio, where the turns of the transmitting coil is fixed to 5, and the number of turns of the receiving coil is varied from 1 to 23. The behavior of this figure is similar to Fig. 7. Nevertheless, as the distance increase, in this case, the turns’ ratio should be increased to get a more efficient link. Figure 9 also shows the efficiency versus turns’ ratio while fixing the number of turns of the receiving coil to 5, and varying the number of turns of the transmitting coil from 1 to 23. In this case, the efficiency increases with an increase of the turns ratio, but with a
decreasing rate. Figure 10 shows the efficiency versus coil gauge, which is varied from 6 to 21 AWG. As expected, increasing the coil wire gauge decreases the efficiency, as the coil ESR increases, increasing the losses. d=2 cm d=20 cm d=38 cm d=56 cm d=76 cm d=94 cm
Transfer Effeciency (%)
100 80 60 40 20
TABLE I VERIFICATION OF SEVERAL OF THE SIMULATED POINTS
0 0
1
2 3 4 Turns Ratio (N1/N2) 5:v
5
Fig.8. Efficiency versus Turns Ratio N1=5 N2=variable at different distances.
Transfer Effeciency (%)
100
d=2 cm d=20 cm d=38 cm d=56 cm d=76 cm d=94 cm
80
40 20 0 1
2 3 Turns Ratio (N1/N2) v:5
4
5
Fig. 9. Efficiency versus Turns Ratio N1=variable N2=5 at different distances.
Transfer Effeciency (%)
100 80 d=2 cm d=20 cm d=38 cm d=56 cm d=76 cm d=94 cm
60 40 20 0 5
10
15 Coil Gauges (AWG No)
20
N1:N2
Distance
5:5 20:20 5:20 5:5 5:5
38 56 76 38 56
Gauge (𝒄𝒎𝟐 ) 0.034 0.034 0.034 0.00823 0.106
Eff. Script 66.49 7.004 0.298 31.14 48.21
Eff. Cir. Sim. 65.64 6.605 0.288 30.95 45.77
Eff. Eqn. 66.44 6.996 0.298 31.15 48.19
V. CONCLUSION
60
0
parameters of one of the models, and a comparison between: the efficiency obtained by using the circuit signals obtained from the FE-MATLAB script (Efficiency Script), the efficiency obtained from simulating the T-model shown in Fig. 1 (Efficiency Circuit Simulation), and the efficiency obtained by using equation 2 (Efficiency Equation). The points shown in the table were chosen randomly from among all the points verified to show that all the graphs displayed earlier have been successfully verified. It is noticed that the efficiency calculated from the equation was closer to the efficiency obtained from the FE than was the efficiency obtained from circuit simulation.
25
Fig. 10. Efficiency versus Coil Gauges at different distances
C. Verification of the Script Table 1 provides the verification of the developed script both, by circuit simulation (Efficiency Circuit Simulation) and by equation 2 (Efficiency Equation), showing some of the simulated points. Along each row in the table is the
A procedure using electromagnetic field analysis coupled with electric circuit was developed for the performance evaluation of a WPT system. This coupled model was implemented as a 3DFE-MATLAB automated script which was utilized for the performance evaluation of the WPT coupled resonators link. The result obtained were verified using both circuit simulation, and mathematical equation. REFERENCES [1] C. Mi, S. Bhattacharya, and M. K. Mallela, “Study Methods of Wireless Power Transfer Technology in Electric Vehicle Charging - IEEE Transportation Electrification Initiative Web Portal.”. [2] S.-H. Lee and R. D. Lorenz, “Development and Validation of Model for 95%-Efficiency 220-W Wireless Power Transfer Over a 30-cm Air Gap,” IEEE Trans. Ind. Appl., vol. 47, no. 6, pp. 2495–2504, Nov. 2011. [3] H. Fujibe and K. Kesamaru, “Magnetic field analysis of wireless power transfer via magnetic resonant coupling for electric vehicle,” in 2013 International Conference on Electrical Machines and Systems (ICEMS), 2013, pp. 884–887. [4] K. Y. Kim, Wireless Power Transfer: Principles and Engineering Explorations. Intech, 2012. [5] U. S. Inan and A. S. Inan, Engineering Electromagnetics and Waves. Boston, MA: Addison Wesley, 1999. [6] “Wireless Power Consortium – creating a standard for wireless charging.” [Online]. Available: http://www.wirelesspowerconsortium.com/. [Accessed: 06-Feb2015]. [7] C. Deqing, W. Lifang, L. Chenling, and G. Yanjie, “The power loss analysis for resonant wireless power transfer,” in Transportation Electrification Asia-Pacific (ITEC Asia-Pacific), 2014 IEEE Conference and Expo, 2014, pp. 1–4.
