A method for operating an asynchronous doubly-fed wind turbine generator connected to a power grid in a grid-forming mode to emulate a virtual synchronous machine. The doubly-fed wind turbine generator includes a line-side converter coupled to a rotor-side converter via a direct current (DC) link. The method includes receiving, via a controller, at least one reference command from an external controller. The method also includes controlling rotor flux of the doubly-fed wind turbine generator using the at least one reference command. Further, the method includes providing power droop control for the doubly-fed wind turbine generator through at least one of rotor-side reference frame rotation and d-axis flux control.