The causes of ferromagnetic series resonance while experimenting on the developed 10 kV/500 A/ 2.5 kA transformer coupling solid-state fault current limiter（SSFCL） with pure capacitance load are analyzed in details. The underlying matter is the nonlinear saturation of the coupling transformer when placed in service on its secondary side equivalent open-circuit. The effective methods are proposed by connecting parallel damping resistance on primary side of the coupling transformer or/and adopting pre-triggering the SCR of the SSFCL when placed in service， for preventing the nonlinear saturation of the coupling transformer and thereby for restraining the ferromagnetic series resonance. Confirmation from simulations is given in the paper.