W IRELESS P OWER T RANSFER (WPT) FOR E LECTRIC V EHICLE C HARGING
2.3. C APACITIVE P OWER T RANSFER (CPT)
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Table 2.4. Reference levels for occupational exposure to time-varying electric and magnetic fields [79].
Frequency (MHz)
E-field Strength (V/m)
H-field Strength (A/m, RMS)
B-field (µT)
up to 1 Hz - 1.63 x 105 2 x 105
1-8 Hz 20,000 1.63 x 105/f 2 2 x 105/f 2
8-25 Hz 20,000 2 x 104/f 2.5 x 104/f
0.025-0.82 kHz 500/f 20/f 25/f
0.82-65 kHz 610 24.4 30.7
0.65-1 MHz 610 1.6/f 2/f
1-10 MHz 610/f 1.6/f 2/f
10-400 MHz 61 0.16 0.2
400-2,000 MHz 3f 0.5 0.008f 0.5 0.01f 0.5
2-300 GHz 137 0.36 0.45
Frequency, ƒ, is in MHz.
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displacements of coils and electrodes in the horizontal and vertical directions. These values give an indication of power transmitting characteristics.
Figure 2.15. The x and z displacement of electrode: (a) IPT system, (b) CPT system.
Figure 2.16. The electrode displacement behaviour to the efficiency:
(a) x directions, (b) z directions.
In x-direction, the coupling capacitance keeps constant within a range of primary electrode size while mutual inductance decreases immediately as the secondary coil starts to shift. This result shows the robustness of capacitive-coupling for the movement in a horizontal direction if the primary electrode is larger than the secondary one. In case of z-direction, coupling capacitance decreases more rapidly than mutual inductance when the shift begins, which means that capacitive-coupling is more sensitive than inductive one in z-direction.
(a) (b)
z
x Primary coil
Secondary coil
0 r x
z
x Primary electrode Secondary electrode
0 r
(a) (b)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0 5 10 15 20 25
M, C (a.u.)
x (mm)
Cx Mx
Inductive coupling
Capacitive coupling
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0 5 10 15 20 25
M, C (a.u.)
z (mm)
Cz Mz
Inductive-Capacitive
Page | 27 2.3.2. FUNDAMENTAL OF CAPACITIVE COUPLING
Basic equivalent circuit model for capacitive coupling is shown in Figure 2.17. It can be described with two capacitors CC1 and CC2, load resistance RL and AC power source E0. Equivalent capacitance Cc represents the combination of the two interface capacitances that can be expressed as
1 2
1 2
c c
C
c c
C C C
C C
, (2.1)while power gain of the circuit can be derived as
2 2 2
1
c L P
c L
C R Gain P
S C R
, (2.2)
where S is the incident (instantaneous) power that is equal to the reactive power (Qp) plus the real power (P) and ω is the angular frequency (= 2πf).
The spectrum of output over input power ratio is drawn in Figure 2.18. Here the input power is defined as an apparent power composed of a reactant power and an effective power.
When the load resistance of coupling capacitance is larger than the sum of internal and load resistances, the output power decreases as the frequency decreases. It means the output power is limited by the coupling capacitance. In the other case, the output power gets constant at the level of maximum value fixed by R0 and RL. The critical frequency is described by this equation
1
C
2
c L
f C R
, (2.3)when f is larger than fC and R0=RL then the gain of power GainP = 50%. This condition will give the largest output power P. From (2.3), to transfer a large power to the system, higher f with larger Cc and larger RL are required. However, in ideal application of WPT, which has a large gap between the coupler, it was difficult to obtain the required condition. For this state, resonance circuit is introduced in next subsection.
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Figure 2.17. Basic equivalent circuit of capacitive coupling.
Figure 2.18. The frequency response of the power gain.
2.3.3. RESONANT CIRCUIT
Resonant circuits are commonly used in power electronics, especially in transmitters, receivers, or pieces of test equipment in existence, to selectively pass a certain frequency or group of frequencies from a source to a load while attenuating all other frequencies outside of this passband. In order to use the resonant conditions, an inductors LS1 and LS2 connects in
-160 -120 -80 -40 0
1.E+05 1.E+06 1.E+07 1.E+08
P/S (dB)
f (Hz)
Cc=1pF Cc=10pF
Cc=100pF Cc=1nF
1
C 2
c L
f C R
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series with the coupling capacitors CC1 and CC2 as shown in Figure 2.19. The power gain GainP
of this circuit now can be calculated as
1 2
2 2 2 2c L P
c s c L
C R Gain P
S C L C R
, (2.4)
1 2
s s s
L L L
, (2.5)Compared to the CPT system presented in Figure 2.17, the gain peak can be achieved at much lower frequency in the case tuning inductor is added (see Figure 2.19). Figure 2.20 shows the frequency dependence of output power as a function of CC assuming the LS of 1 µH. Each spectrum has a peak at resonant frequency with the same maximum power gain even in small CC. The resonant frequency (fr) can be obtained when
2 1
r S 2
r C
f L f C
, (2.6)1
r 2
S C
f
L C , (2.7)Figure 2.19. Basic equivalent circuit of resonant capacitive coupling.
V → S RL → P
Cc1
Cc2
Transmitter Receiver
Ls1
Ls2
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Figure 2.20. The frequency response of the resonant output power gain.
2.3.4. STRUCTURE OF CPT FOR EV
The more simplest interface of CPT has been introduced in series to increase the efficiency and the safety [36,48,71,88,89]. Two pair of plate, normally, constructs the wireless coupling interface between source and load as shown in the basic diagram for CPT system (see Figure 2.21). This system has ability to deliver a kilowatt amount of power with high efficiency.
However, it has lack of shield in electrical field emission surround the coupler. The emission limits by the regulation related to the safe level of human body radiated by EF [79,80,90].
Figure 2.21. Diagram of basic CPT system.
DC Power Supply
High freq Power converter
(DC/AC)
Rectifier
(AC/DC) Load
Primary side transmitter
Secondary side receiver Coupling
interface -160
-120 -80 -40 0
1.E+05 1.E+06 1.E+07 1.E+08
P/S (dB)
f (Hz)
Cc=1pF Cc=10pF
Cc=100pF Cc=1nF
1
r 2
s c
f L C
Ls=1 μH
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The typical system of CPT for EV charging system is shown in Figure 2.22. It can be divided into three part, there is a switching network that operates in high frequency and high amplitude of voltage. To obtain high voltage, a step-up transformer is connected to the switch.
A compensation network, to maintain the resonant condition of the system, is coupled. Those all module are structured as a primary part of the CPT system. Next part is the coupling interface which is consists of, commonly, a 4-plate conductive materials coupled between the primary and the secondary part of the system. The part can be containing a resonant network, a step-down transformer, and an AC to DC rectifier, an DC to DC voltage converter or a buck/-boost converter) to deliver the power to the load.
Figure 2.22. Coupling interface structure of conventional CPT system for EV charging system (car image source: Tesla Motors).
Currently, many scientists tried to find best approach of CPT system that match to the application needed in the market. Previous research in low power [34,35,84,85] and high power [59] application of CPT has been conducted with efficiency was reported more than 90%. A new approach of coupling structure has been introduced to make an interface more simple, efficient and safe [36,48,71,88].
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Figure 2.23. Coupling interface structure of CPT system.
Coupling interface structure of the conventional CPT system is shown in Figure 2.23. The main coupling plates are notified with P1, P2, P3, and P4. The coupling CC, as well as the operating frequency, f, is an essential factor on affecting the power transfer efficiency. As for analysis, an AC approximation method was used assuming the parasitic resistances are neglected for all components. A circuit model for basic CPT system can be seen in Figure 2.24.
Figure 2.24. A coupling interface circuit model of basic CPT system.
For a given CC, the EF between the plates is restricted to the dielectric media breakdown voltage (Emax = 3 kV/m). The transformer magnetic flux in IPT system is governed by V/Hz comparing to the electric flux which is governed by A/Hz [91]. The capacitance of coupling plate CC can be modelled as [92]:
Electric Field
Coupling plate dCC
dCX
P4
P2 P1
P3
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0 r C C
CC
C A d
, (2.8)while the voltage across or voltage stress (VC), appeared for each CC, can be calculated as follows:
Cc C
C
V I
C , (2.9)
where ICc, 0, r, AC and dCC denotes the current in the capacitive coupling link (A), the dielectric constant in vacuum (8.854x10-14 F/cm), relative dielectric constant of material used between the plates (air, 1.00059 at 1 atm), the coupling area of the plate (cm2), and the gap distance between the plate in vertical (cm), respectively.
2.3.5. ELECTRIC FIELD EMISSIONS
Radiation of EF is the main issue for CPT system since it works with EFR through the coupling plate interface. With a limitation of capacitance in size and value, a higher frequency and a higher voltage is implemented to the CPT system. Electrostatic simulation software introduces the radiation surround the CPT coupling interface system. Figure 2.25 illustrates the radiation of EF simulated by QuickField™ electrostatic software. It can be seen that for the basic CPT system which consist of two pair of coupling interface, the radiation of EF behind the coupling plate were exposed when high voltage applied to the coupler. The exposed EF can affects to the human body as mentioned in the previous subsection.
(a)
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Figure 2.25. EF radiation of basic CPT system:
(a) phase >0°, (b) phase ~90°, (c) phase 180°.