As more renewable energy sources, especially more wind turbines (WTs) are installed in the power system; grid codes for wind power integration are being generated to sustain stable power system operation with non-synchronous generation. Common to most of the grid codes, wind power plants (WPPs) are requested to stay connected and inject positive-sequence reactive current in order to boost positive-sequence grid voltage during short-circuit grid faults, irrespective of the fault type; symmetrical or asymmetrical. However, as shown in this study, when WPPs inject pure positive-sequence reactive current in case of asymmetrical faults, as a conventional method (CM) in accordance with the grid code requirement, positive-sequence grid voltage is boosted, but also higher negative sequence voltage in the grid and higher overvoltages at the non-faulty phases occur. In this study, an alternative injection method, where WTs are injecting both positive and negative sequence currents during asymmetrical faults, providing improved grid support, is given and compared with the CM. In addition, effect of coupling between positive, negative and zero sequences when WPPs are injecting currents during asymmetrical faults, is investigated, which was not considered in the wind power impact studies before.