Environmental Engineering Reference
In-Depth Information
The basic configuration of the transmitting and receiving coils is assumed
to be the same dimensions, and the WPT system is in tuned resonance. By
doing so, Equation 6.13 can be further elaborated, by substituting L 1
=
L 2
and the radius of both coils to be equal, r
=
r b ,asfollows:
o
r 3
N
=
(6.14)
a o
o
o
( r 2
D 2 ) 1 . 5
+
1
+ Nr 3
4
2
6 c 4
Referring to Equation 6.14 , it can be observed that there are some prominent
factors in the equation that have effects on the coupling-to-loss ratio, hence
the efficiency of the WPT system. These factors include the conductivity and
radius of the wire, the coil size (i.e., radius and number of turns), the distance
between two coils, and the operating frequency of the WPT system. As can
be seen in Equation 6.14 , the equation is highly interdependent on various
design factors; hence, there is a need to find an optimum configuration for the
WPT system. By conducting simulations and experiments, the relationships
between these design factors and the efficiency of the system are determined.
6.2.2
Simulation Results
In order to improve the efficiency of the WPT system, four different simula-
tions were conducted to determine the relationships between the efficiency of
the system and the design factors: (1) frequency f , (2) coil radius r , (3) num-
ber of winding turns in a coil N , and (4) distance D between two coils [173].
All the simulations were based on the efficiency and coupling-to-loss ratio
expressed in Equations 6.6 and 6.14 , respectively.
6.2.2.1 Simulation of Efficiency versus Frequency
The basic configuration of the two cylindrical coils used in this simulation
was defined as follows: The coil radius r of 7.5 cm was made of 5 winding
turns N of copper wire (SWG12) with conductor radius a of 0.13208 cm and
conductivity of 59.6*10 6 S/m. The separation distance D between the two
coils was 10 cm. The efficiency
of the WPT system was simulated over a
range of operating frequencies from 1 Hz to 1000 GHz, and the simulation
results are plotted in Figure 6.16 .
It is observed from Figure 6.16 that there exists a band of frequencies be-
tween 1 and 1000 GHz whereby the efficiency of the WPT system was opti-
mal. This band of optimum efficiency is the strongly coupled regime where
/
1 and maximum power transfer took place. As the operating fre-
quency shifted away from the strongly coupled regime, the WPT system
efficiency started to decrease. At the lower-frequency region, the coupling
between the coils became weak, as illustrated in Equation 6.7 . Similarly, at
the higher-frequency region, the power losses in the ohmic and radiative re-
sistances became prominent, as illustrated in Equation 6.9 . Only when the
coupling-to-loss ratio balances will the efficiency of the WPT system be high.
 
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