The native saturable transformer model of SPS has no linear part in its magnetization branch. The magnetization branch is instead modeled entirely by a current injection. The current injection is computed from a table of the phi=f(i), with the flux being computed from the integral of voltage across the magnetization branch.
In the SPS model, the non-linear Lsat component of the transformer is completely modeled by a current injection computed from the phi=f(i) characteristics.
In SPS in particular, one can specify a residual flux only when the segment 1-2 has infinite slope as mentioned in the SPS documentation.