A system and method are provided for operating a power generating asset. Accordingly, a controller detects a fault condition impacting the power generating asset. The controller then determines whether the fault condition is occurring in the power generating asset or is occurring in the power grid. When the fault condition is occurring in the power generating asset, a first response control scheme is implemented. However, when the fault condition is occurring in the power grid, a second response control scheme is implemented. The response control schemes include a first current threshold and a second current threshold respectively, with first current threshold being less than the second current threshold. Additionally, a control action is implemented in response to an approach of a current to the respective current threshold.