Coupling coefficient variation in Wireless power transfer
What would be the best method to transfer a considerable amount of power while the coil moves aka changes coupling coefficient?


If you are after the maximum power transfer, you need to design your wireless power transfer setup such that the input impedance seen by the source is matched with the source impedance (i.e. zero imaginary part and real part as minimum as possible in this case because your source is an ideal source).

The best parameter that you can control is the operating frequency of your source. When the coupling is strong (\$k&gt;k_{critical}=1/\sqrt{Q_1 Q_2}\$), the maximum power transfer occurs at two different frequencies away from the resonance \$\left(f_{\pm}=f_0/\sqrt{1 \mp k}\right)\$ see the below simulation: if you can tune your source to high or low resonance frequencies (\$f\pm\$), then you can obtain the maximum power from the available setup.

Other options include dynamic tuning of compensation, the use of adaptive impedance matching, active rectifier circuits, and resistance compression networks etc. which are more complex and difficult to implement.




Few other point to note here is that


Maximum power transfer will not give the maximum efficiency! In fact, in theory, maximum efficiency will be limited to 50% in perfectly match condition. The best option is to get a compromise between efficiency and the power transfer.
The value of the load plays an important role in both efficiency and power transmission.
Improvement of coil quality factors will always be better to improve the maximum efficiency as well as the power transfer capabilities. Quality factor of 24 \$\rm{\mu H}\$ coil can easily reach quality factor of 500 with proper optimization using Litz wire and ferrite materials.