CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com Wireless Power Transfer System for Electrical Vehicle Charging Dr. Christian Kremers
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Wireless Power Transfer System for
Electrical Vehicle Charging
Dr. Christian Kremers
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Motivation
Wireless Power Transfer is one of the
key technologies for widespread
acceptance electrical vehicles.
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Outline
Accurate broadband simulation of a magnetic
coupler system
How to deal with Litz Wires ?
Maximum achievable efficiencies as
Design Parameter
Extraction of equivalent circuit
Construct compensation network
System Simulation
Efficiency …
Stray Field and Safety Concerns
Discussion …
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Magnetic Coupler: 3D Model
Aluminum
shield
PEC wire with
12 number of turns
TDK/EPCOS N87 core
described by complex
𝜇 = 𝜇′ + 𝑗 𝜇′′
Winding and core
embedded in PVC with
휀 = 4 and 𝑡𝑎𝑛𝛿 = 0.06
Transmitter = Receiver
Ferrite Core
lossy PVC
𝑑𝑥
𝑑𝑧
M. Budhia et al, IEEE Trans. Power Electronics., vol. 26, no. 11, 2011
discrete
Port
PEC wire
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Magnetic Coupler: 3D Model
Aluminum
shield
PEC wire with
12 number of turns
TDK/EPCOS N87 core
described by complex
𝜇 = 𝜇′ + 𝑗 𝜇′′
Winding and core
embedded in PVC with
휀 = 4 and 𝑡𝑎𝑛𝛿 = 0.06
Transmitter = Receiver
Ferrite Core
lossy PVC
𝑑𝑥
𝑑𝑧
M. Budhia et al, IEEE Trans. Power Electronics., vol. 26, no. 11, 2011
discrete
Port
PEC wire
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Litz Wire Homogenized bundle
M. Etemadrezaei et al, IEEE ECCE, 3833-3840, 2012
1. Analytic formulas for skin effect and
proximity losses on strand level
2. Assumption: Each strand contributes in the
same manner to the overall losses
3. Skin effect losses (𝜔) 𝜎 𝜔 휀′′(𝜔)
Proximity losses (𝜔) 𝜇′′ 𝜔
𝑑𝑠𝑡𝑟𝑎𝑛𝑑 = 0.1 𝑚𝑚 𝑑𝑏𝑢𝑛𝑑𝑙𝑒 = 3.6 𝑚𝑚 𝑛𝑠 = 810
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Litz Wire: Resistance
homogenized material
8.9 meter
wire length
Touchstone for
lumped resistance With TOUCHSTONE describing broadband
resistance of the litz wire, winding losses can be
taken into account in the Schematic
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Magnetic Coupler incl. Litz Wire
𝑑𝑧 = 150 𝑚𝑚 𝑑𝑥 = 0 𝑚𝑚
Inducta
nce /
Henry
Range of validity for MQS (0 − 200 𝑘𝐻𝑧)
coupling coefficient:
quality factor:
Equivalent Circuit extraction @ 100 kHz is possible with MQS
𝐿11 = 6.7 ⋅ 10−5 𝐹
𝑀 = 4 ⋅ 10−6 𝐹
𝑄 = 277
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Extract Equivalent Circuit
𝑑𝑧 = 150 𝑚𝑚 𝑑𝑥 = 0 𝑚𝑚
@ 100 kHz
𝑅𝑤𝑖𝑛𝑑𝑖𝑛𝑔 ≈ 0.09 Ω
Optimization:
• 𝐶1 = 𝐶𝑤𝑖𝑛𝑑𝑖𝑛𝑔 = 127.41 𝑝𝐹
• 𝐶12 = 𝐶𝑐𝑜𝑢𝑝𝑙𝑖𝑛𝑔 = 0.86 𝑝𝐹
𝐿12 = 𝑀
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Matching and Efficiency (AC Analysis) One particular choice: SP configuration
• 𝐶2𝑝 in resonance with 𝐿11
• 𝐶1𝑠 so that ∠ 𝑈𝑖𝑛 , 𝐼𝑖𝑛 = 0
@ 100 𝑘𝐻𝑧, 𝑅𝐿 = 600 Ω
Pow
er
Eff
icie
ncy 𝜂
@ 100 kHz
Load Resistance RL / Ω
Real
Imag
𝜂𝑚𝑎𝑥 @ 𝑅𝐿 ≈ 624 Ω
𝐶1𝑠 𝐶2𝑝
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System Simulation (I)
230V, 50 Hz
Rectifier Inverter
Matched Coupler
t_dead
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System Simulation (II) In
put
Pow
er
𝑃𝑖𝑛
/ W
att
Eff
icie
ncy 𝜂
∠
𝑃𝑖𝑛
,𝑄𝑖𝑛
/ d
eg
Dead Time / ms
𝑅𝐿 = 600 Ω
Check to judge
whether non-linear
effects have to be
considered
Dead Time / ms
Curr
ent
/ A
Safe: “Outside” 𝐁𝑅𝑀𝑆 < 70 𝜇𝑇
Curr
ent
/ A
𝐼1 𝐼2
𝐼1
𝐼2
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Influence of the Car Steel Plate (Lossy Metal)
≡ car chassis
Tabulated Surface Impedance representing Concrete
≡ Floor
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Equivalent Circuit Again
Up to now:
• Magnetic Coupler in WPT System is driven with
small spectral width around fundamental
frequency 𝑓
• At 𝑓 = 100 𝑘𝐻𝑧 we are in the MQS domain
Stranded Coil with
𝑛 turns and resistance 𝑅
MQS at 𝑓 can be used to determine the impedance matrix equivalent circuit
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Sweep Relative Positions 𝑑𝑥
𝑑𝑧
Q-Factor max efficiency k
𝑑𝑥 = 0
𝑑𝑧 = 160
𝑑𝑧 = 220
𝑑𝑧 = 70
𝑑𝑥 = 0
𝑑𝑥 = 280
coupling coeff. k determines the efficiency !
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Solver Technologies: Pro and Cons
Broadband
Full wave
Easy connection to circuit world
Winding of the coil has to be
modelled
Stranded Coil can be used
Winding resistance is a
coil property
Magneto Quasi Static (MQS)
Connection to circuit via
equivalent circuit
Pro
Con
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S. Li et al, “Wireless Power Transfer for Electric Vehicle
Applications”, IEEE Journal of Emerging and Selected Topics in
Power Electronics, vol. 3, no. 1, 2015
M. Budhia et al, “Design and Optimization of Circular Magnetic
Structures for Lumped Inductive Power Transfer Systems”, IEEE
Transactions on Power Electronics, vol. 26, no. 11, 2011
M. Etemadrezaei et al, “Equivalent Complex Permeability and
Conductivity of Litz Wire in Wireless Power Transfer Systems”,
IEEE Energy Conversion Congress and Exposition, 3833-3840, 2012
Citations