Fault ride-through capability studies of MMC-HVDC connected wind power plants have focused primarily on the DC link and onshore AC grid faults. Offshore AC faults, mainly asymmetrical faults have not gained much attention in the literature despite being included in the future development at national levels in the ENTSO-E HVDC code. The proposed work gives an event-triggered control to stabilize the system once the offshore AC fault has occurred, identified, and isolated. Different types of control actions such as proportional-integral (PI) controller and super-twisted sliding mode control (STSMC) are used to smoothly transition the post-fault system to a new steady state operating point by suppressing the negative sequence control. Initially, the effect of a negative sequence current control scheme on the transient behavior of the power system with a PI controller is discussed in this paper. Further, a non-linear control strategy (STSMC) is proposed which gives quicker convergence of the system post-fault in comparison to PI control action. These post-fault control operations are only triggered in the presence of a fault in the system, i.e., they are event-triggered. The validity of the proposed strategy is demonstrated by simulation on a ±525 kV, three-terminal meshed MMC-HVDC system model in Real Time Digital Simulator (RTDS).