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Control of grid-connected power converters is continuously developing to meet the grid codes, according to which the generation units should keep connected to the grid and further provide ancillary services, such as voltage and frequency support, negative sequence current injection, inertia emulation, etc. A virtual admittance controller is proposed in this paper for the objective of voltage support under asymmetrical grid faults. By using independent and selective admittances for positive and negative sequence current injection, the unbalanced voltage can be significantly compensated during asymmetrical faults. The controller is based on the generic control framework of the synchronous power controller (SPC), which is able to control a power converter with emulated and improved synchronous generator characteristics. Simulation and experimental results based on two paralleled 100 kW grid-connected power converters demonstrate the controller to be effective in supporting unbalanced voltage sags.