IEEE Electrification Magazine - March 2020 - 41

Scaling Considerations for Electric Vehicles and
Wireless-Charging Systems
When scaling down reality, fidelity must always be questioned: Which aspects of the systems can be accurately
replicated and studied, and which characteristics will be
lost in the miniaturization process? It is easy to argue that
downscaling has limited influence on the fundamental
behavior of self-driving systems, since they are designed
to solve a purely geometrical and logical problem. Thus,
the main issue for the truck model is that commercially
available sensors are relatively large compared to the vehicle, while they would be insignificant for a full-scale truck.
However, the scaling of the inductive power-transfer system requires deeper analysis.
A fundamental result of coupled-circuit theory is that
the maximum theoretical efficiency at which nonradiative
power can be transferred between two coils can be
expressed solely in terms of the quality factor of the coils,
Q , and the mutual-coupling coefficient, k:
	

h max =

k2 Q1 Q2
2 ;
_1 + 1 + k2 Q1 Q2 i

~$L
Q = R coil .(1)
coil

Crucially, it turns out that the basic factors determining
the power transfer of resonant inductive charging (namely, the magnetic coupling and quality factors of the coils)
are invariant with geometrical scaling. More specifically,
the scaled-down version of a given multicoil system will
give rise to the same electromagnetic-field pattern as the
original system, and the power transfer between the coils
will take place at exactly the same theoretical efficiency,
albeit at a power level reduced by the cube of the geometric scaling factor and at a resonant frequency equal to the
square of the one of the original system. This very convenient scaling property was exploited when deciding to
build the small-scale demonstration model.
It must be pointed out that while scaling down the
macroscopic details of the coils by a factor of 14 poses no
challenges, there are some important microscopic details
that cannot be easily (or practically) reproduced, leading to
a loss of fidelity. Most notably, the very many thin, insulated copper strands forming the coil conductors (Litz wires)
of typical resonant coils cannot be scaled, generally resulting in a lower efficiency for the reduced-scale model. This
factor, combined with the increased losses in magnetic
materials and the power-electronics converters, often calls
for the operation of the reduced-scale model at a frequency lower than what would follow from the ideal geometrical scaling. A lower operating frequency, however, results
in a lower theoretical efficiency for the inductive powertransfer process, as immediately seen in (1). Perfect geometry and frequency scaling also cause changes to the
properties related to heat management, since the cooling
performance is proportional to the exposed surfaces,
while the heat to be dissipated is proportional to the volume. This means that all things being equal, the actual

full-scale system would be more challenging to cool than
the small-scale model.
The biggest drawback of the scaled-down model is that
it cannot be used to directly gather reliable information
about the energy balance of the driving/charging process.
This is partly due to the difference in the efficiency of the
wireless-charging system discussed previously but mainly
because the driving effort-the power required for driving
the truck along a given route-does not scale with the
same law as the inductive charging power. Even worse,
different components of the total driving power (aerodynamic drag, road friction, drivetrain friction, slope climbing, and so on) scale according to different laws that are
sometimes difficult to assess. Thus, the scaled truck
model will not have the same ratio between the average
and peak power requirements as a real system, and the
operation of the model should not be directly utilized to
evaluate the operation of dynamic wireless-charging
systems in terms of their influence on the available driving range and the infrastructure requirements for ensuring the long-term energy balance of the vehicle. However,
comparative analysis of some general trends and characteristics can be relevant, especially for comparing
design strategies and control methods based on similar
system configurations.
Given the nature of the application, the total amount of
energy that can be transferred to the onboard battery for a
unit length of traveled distance is arguably the most
important criterion, beside the cost, for the comparison of
different solutions. This energy-transfer capability
depends on several factors, including the design of the
road coils (shape, length, mutual distance, and so on), the
capability of the converters in terms of maximum voltages
and currents, and the performance of the control methods
used to regulate the power flow under the variable loading
and coupling conditions that result from driving. Therefore, rather than simply looking at the maximum transfer
efficiency given by (1), the overall energy transfer per unit
length of road should be considered. Using e in to indicate
the total energy supplied by the utility grid to the roadside
infrastructure, normalized to the road distance, the energy-transfer efficiency can be expressed as
	

h road =

e batt 6kWh/km@
# 1.(2)
e in 6kWh/km@

Although the energy efficiency of a small-scale model will
differ from a full-scale system, comparative analysis of the
energy-transfer efficiency can reveal relevant differences
between various concepts for dynamic wireless charging.
When evaluating this figure, the accuracy of the driving
pattern (that is, the alignment between the onboard and
on-road coils) will also have an impact. Thus, self-driving
solutions imply the potential for more accurate and consistent positioning of the vehicle when passing the roadside coils and can thereby improve the utilization of the
infrastructure compared to manual driving.
	

IEEE Elec trific ation Magazine / MARCH 2 0 2 0

41
IEEE Electrification Magazine - March 2020

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