IEEE Power Electronics Magazine - September 2016 - 24
Figure of Merit for IPT Systems
[22]-[25]
[21], [37]
[8]
[16]-[18]
[9], [10]
[11], [12]
[6], [7]
[19]
[20]
Based on the theoretical analysis of the transformer
equivalent circuit of a series-series compensated
IPT system, it was shown in [41]-[43] that the figure
of merit FOM = kQ limits the transmission (or coilto-coil) efficiency to
2
h max . 1 - kQ ,
[13]-[15]
(1)
(a)
Coupling k
Number of Publications
where k represents the magnetic coupling and Q
the quality factor of the two IPT coils at the operating
frequency ~ 0 . The magnetic coupling accounts for the
magnetizing current [compare i n in Figure 2(b)] that
is necessary to sustain a certain power output Pout ,
while the quality factor represents the ac power
losses Ploss that occur in the coil windings as a
result of the parasitic resistance of the copper litz
wire conductors.
The magnetic coupling is mainly a function of the
ratio between the air gap and the size of the IPT coils,
as shown in Figure 2(c) for an exemplary configuraFIG 1 (a) A geographical overview of selected research and development
tion. Hence, larger IPT coils lead to higher efficiency
activities on IPT for EV charging. (b) The publication numbers obtained
from the following Google Scholar search query: power inductive OR confor a given transmission distance. In addition, the
tactless "electric vehicle"-"induction motor"-"induction machine." (The last
magnetic coupling decreases rapidly with misaligned
two parts exclude electrical machine research with similar titles.)
IPT coils. Therefore, large IPT coils are needed to limit
the variation of the magnetic coupling and to achieve a
sufficient
misalignment tolerance. If, as a first approximation,
out the limitations of IPT technology for EV charging as
the ac effects in the litz wire windings and the losses in the
compared to conventional conductive chargers, based on
magnetic core elements are neglected, the quality factor
the theoretical and experimental results obtained from
the 50-kW prototype. For the sake of brevity, the obserQ . ~ 0 L / R ac is proportional to the transmission frequency
vations are presented as a high-level discussion without
[Figure 2(d)]. In addition, the quality factor also increases with
considering all the technical details, for which interested
the coil size because of the increasing inductance that results
readers are referred to [36]-[40].
from the larger coil area enclosed by the windings. Hence, the
transmission efficiency is defined by
the size of the IPT coils as compared to
the air gap and by the selected transmisIdeal Transformer
L
sion frequency.
2
D /2
L2 - M
L1 - M
i1
i2
For a given area-related power den+
+
iµ
R2,ac
R1,ac
sity a = Pout / A coil of the IPT coils and
u2
u1
k
assuming natural convection coolh
ing, the coil surface-related power
M = k √L1L2
loss density is thermally limited to
L1
-
-
R1,ac
1:1
Psurf, max = Ploss,max /A coil by the heat tr(a)
(b)
ansfer coefficient at the coil surface
and the IPT coil surface area A coil .
This
thermal limit defines a required
3
0.3
minimum efficiency of
2,000
Data Source:
1,750 Google Scholar
1,500
Papers and Patents
1,250
Scientific Papers
1,000
750
500
250
0
2005
2010 2014
1990
1995
2000
Year of Publication
(b)
2
0.2
0.1
0
Q ≈ ωL/
L Rac
ωL/R
D
h
2 3 4 5 6 7 8 9 10
Ratio D /h
(c)
Rac
ωL
R dc
h min . 1 f res
0
Frequency
(d)
FIG 2 (a) A four-turn spiral air coil pair. (b) A transformer equivalent circuit. (c) The
calculated magnetic coupling as a function of the ratio of the coil diameter to the air gap.
(d) The approximate frequency dependency of the coil impedances and the quality factor.
24
IEEE PowEr ElEctronIcs MagazInE
z September 2016
P loss, max
Psurf, max
(2)
a
Pout = 1 -
and, thereby, a required minimum coil
size for the dissipation of the power
losses Ploss, max that result during the
transfer of a given charging power Pout.
Depending on the materials used for
the coil housing and on the power level,
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