Primary split with series "cable compensation" capacitor

[741]

I've been handed a part schematic of a circuit used to transfer power.

The front end has something that confuses me immediately: A transformer with a split primary and a series capacitor Cs linking the primary coils.
I gather 'Cs' is intended to compensate for the de-tuning effect of the cable from the sine-wave source.

I do not see why the designers did not simply place 'Cs' in series with a single-winding primary.

I began to enter the circuit into LTSpice (I do not yet have full information like actual values). Having done that, I am not much the wiser.

My guess is the capacitor is for PFC (power factor correction).

[moffy]

Just a brief comment, your coupling factors look very low for a transformer, are they heavily air gapped?, and remember that L1 and L2 couple to one another also. It is certainly symmetrical and is reminiscent of a resonant supply of some sort. The split coils remind me of an LVDT where two coils displaced are excited anti phase and a pickup coil measures the displacement/voltage but that is not a power but sensor application.

[741]

Using K=1 for both stalled the simulation.

The coupling factors 'had to be' 0.5 to get the simulation working.  I decided that could be physically reasonable as only half the secondary is close to either of the primaries.
It might be (?) I do not need L1 to L2 coupling because (assuming Zc is low), it's basically 'as if' there are one coil.

I've slightly ammeded the above because it looks like there is an inductive load.