A method for controlling a wind turbine power system connected to an electrical grid, the wind turbine power system having a double-fed wind turbine generator coupled to a power converter having a line-side converter and a rotor-side converter coupled together via a DC link, the method comprising: determining, via a controller, at least one non-linear magnetizing parameter (Xm) of the double-fed wind turbine generator, wherein determining the at least one non-linear magnetizing parameter (Xm) of the double-fed wind turbine generator further comprises: (a) providing a plurality of data arrays comprising, at least, a data array of operating data points and a data array of non-linear magnetizing parameter (Xm) data points; (b) enabling rotor control of the double-fed wind turbine generator with a stator switch open; (c) setting an operating set point of the double-fed wind turbine generator equal to a first operating data point in the data array of operating data points; (d) controlling the rotor-side converter to the operating set point and frequency for a time period; (e) collecting current and voltage feedbacks (VS_Fbk_xy, IS_Fbk_xy) for the time period; and (f) calculating the at least one non-linear magnetizing parameter (Xm) based on the current and voltage feedbacks (VS_Fbk_xy, IS_Fbk_xy) for the time period; developing, via the controller, a model of the at least one non-linear magnetizing parameter (Xm) of the double-fed wind turbine generator; and, using, via the controller, the model in a stator voltage regulator of the double-fed wind turbine generator to provide grid-forming control of the double-fed wind turbine generator. determining, via a controller, at least one non-linear magnetizing parameter (Xm) of the double-fed wind turbine generator, wherein determining the at least one non-linear magnetizing parameter (Xm) of the double-fed wind turbine generator further comprises: (a) providing a plurality of data arrays comprising, at least, a data array of operating data points and a data array of non-linear magnetizing parameter (Xm) data points; (b) enabling rotor control of the double-fed wind turbine generator with a stator switch open; (c) setting an operating set point of the double-fed wind turbine generator equal to a first operating data point in the data array of operating data points; (d) controlling the rotor-side converter to the operating set point and frequency for a time period; (e) collecting current and voltage feedbacks (VS_Fbk_xy, IS_Fbk_xy) for the time period; and (f) calculating the at least one non-linear magnetizing parameter (Xm) based on the current and voltage feedbacks (VS_Fbk_xy, IS_Fbk_xy) for the time period; (a) providing a plurality of data arrays comprising, at least, a data array of operating data points and a data array of non-linear magnetizing parameter (Xm) data points; (b) enabling rotor control of the double-fed wind turbine generator with a stator switch open; (c) setting an operating set point of the double-fed wind turbine generator equal to a first operating data point in the data array of operating data points; (d) controlling the rotor-side converter to the operating set point and frequency for a time period; (e) collecting current and voltage feedbacks (VS_Fbk_xy, IS_Fbk_xy) for the time period; and (f) calculating the at least one non-linear magnetizing parameter (Xm) based on the current and voltage feedbacks (VS_Fbk_xy, IS_Fbk_xy) for the time period; developing, via the controller, a model of the at least one non-linear magnetizing parameter (Xm) of the double-fed wind turbine generator; and, using, via the controller, the model in a stator voltage regulator of the double-fed wind turbine generator to provide grid-forming control of the double-fed wind turbine generator.