IEEE Electrification Magazine - September 2017 - 28

Normalized Power
Transfer (Pout/P0)
∠ (Zsend) (°)

4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Normalized Frequency (f/f0)
(a)
40
30
20
10
0
-10
-20
-30
-40
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Normalized Frequency (f/f0)
(b)
Outside Bifurcated Region
At Bifurcation Limit
In Bifurcated Region

Figure 6. Typical frequency characteristics of an inductive power transfer
system, outside the bifurcated region, at bifurcation and within the bifurcated region, for (a) power transfer and (b) impedance phase angle.

impedance observed from the terminals of the sendingside converter, undergo a fundamental change. This phenomenon is known as bifurcation, and an example is
shown in Figure 6. Figure 6(a) shows the frequency characteristics of the normalized power transfer capability, while
Figure 6(b) shows the phase angle of the input impedance.
It can be seen from Figure 6(b) that a system outside the
bifurcated region has an impedance angle that is continuously increasing with the frequency and crossing zero only
at the resonance frequency. At the bifurcation limit, the
phase angle still crosses zero only at the resonance frequency, but the derivative of the phase angle with respect
to the frequency at this point becomes zero. When the system enters the bifurcated region, the phase angle crosses
zero at three frequencies, i.e., at two additional points
below and above the resonance frequency. Thus, the slope
of the phase angle with respect to frequency is negative in
the region around the resonance frequency. In the bifurcated region, the power transfer capability of the system
also has two strongly pronounced peaks below and above
the resonance frequency, as shown in Figure 6(a).
Most systems for inductive power transfer are designed
to operate outside of the bifurcated region, to avoid the
impact that the sudden change of phase characteristics at
the bifurcation limit can have on the control of the system. Furthermore, many systems are designed far away
from the bifurcated region, where the power transfer
characteristics have only one single peak that appears at

I E E E E l e c t r i f i c ati o n M agaz ine / SEPTEMBER 2017

the resonance frequency. In such cases, operation at an
off-resonant frequency will reduce the power transfer,
while the phase angle is always increasing with the frequency. This characteristic has been utilized in control
strategies for regulating the power flow in inductive
charging systems at frequencies above the resonant frequency. However, the high phase angle resulting from
increased frequency implies reduced power factor for offresonant operation, and this prevents operation with
close-to-zero current at the switching instants of the sendingside converter.
To avoid the large overrating required for maintaining
resonant operation over the entire expected range of coupling conditions and the low power factor resulting from
conventional frequency control outside the bifurcated
region, the developed high-power inductive charging system presented in this article is designed to operate within
the bifurcated region. Thus, the system must be designed to
operate in the region between the resonance frequency and
one of the peaks in the power transfer characteristics. The
peak values of the power transfer characteristics can also
be influenced by tuning the resonant capacitors and unbalancing the voltages at each side of the system, thus extending the power control capabilities of the method.
If the characteristics of the system in the bifurcated
region are properly utilized, a set of power-frequency characteristics at different coupling conditions as indicated by
the general example in Figure 7 can be obtained. In this figure, it is shown how the power transfer capability at high
coupling conditions and a fixed input voltage can be
increased by operation at off-resonant frequencies. The figure also shows how the rated power flow can be maintained at high coupling conditions by reducing the
operating frequency in the off-resonant region. Furthermore, this ensures a slightly inductive operation of the
sending-end converter, which will help in minimizing the
switching losses. It could also be possible to maintain
the power transfer capability in response to increasing
magnetic coupling by increasing the frequency. This will be
disadvantageous with respect to switching losses since the
current in the sending-end converter will become capacitive, resulting in higher turn-on losses. However, the voltage stress on the resonant capacitors will be reduced due
to the higher frequency of operation.
For a practical high-power system, the design can be
based on operation in resonance when the coils are in
positions corresponding to the minimum (or nominal)
coupling coefficient. If the coupling increases, the operating frequency should be reduced to maintain the power
flow, as shown in Figure 7. The frequency can also be used
to regulate the power flow to a lower value than the full
rated power. However, for regulating less than rated power
at the minimum coupling conditions, the voltage at the
sending end must be reduced by introducing zero voltage
states in the converter output voltage. Thus, a combined
voltage-frequency control must be implemented for

Table of Contents for the Digital Edition of IEEE Electrification Magazine - September 2017