A general misalignment case is the third case presented above. Suppose that the projection of
O2 in the Tx plane is O2', using the vector O1O2' to indicate the direction of the x axis we can
establish the Cartesian coordinate system, shown in Fig. 3(c). Then for mutual inductance analy-
sis and e±ciency optimization, we assume the angle µ is formed around the x axis. In paper [10],
Soma had demonstrated that there is no strong interaction between the lateral misalignment e®ect and the angular misalignment e®ect. And paper [11] had studied the two displacement con¯gura-
tions independently for the maximum permissible angular and lateral displacements for di®erent
applications.
Any theoretical investigation of the mutual inductance in the misalignment cases is extremely
complex due to the heavy work required to solve the double integral as (4) and the analytical solution
is almost impossible to be derived. Hence, in this study, Matlab is used to obtain the numerical
solution of the mutual inductance in varied misalignment cases with the separate distance of 15 cm
as shown in Fig. 4.
In Fig. 4, the positive and negative of l and µ just stand for the position in the special coordinate
system and the direction of rotation (anticlockwise or clockwise), respectively. It is evident that
in lateral misalignment, the mutual inductance is become smaller with the increase of the lateral
distance l. And in incorporated misalignment, the mutual inductance is varied with the lateral
distance and tilt angle, and there are partial optimal solutions in their ranges shown in Fig. 4(b).
It is also worth noting that with a speci¯c separate distance, the peaks of the mutual inductance in
Fig. 4(b) do not occur in perfect alignment. This implies that in inductively coupled WPT system,
there are some constraints to guarantee the maximum power transfer occurs in perfect alignment.