In this paper, we outline measures that can be implemented to improve the resilience of the power system. The effect that severe weather/natural hazards may have on the transmission/generation network is considered. Power system response to a high-impact low-probability event is analysed and the conclusion is made about the impact the power system instability has on the entire resilience of the system. Power system stability problems are considered of paramount importance in an attempt to improve the network survivability and lessen the system recovery time. A particular problem of intentional controlled separation of the network in response to angular instability of the network is considered. An overview of various methods and approaches which could be used in preventing and mitigating the consequences of angular instability of the network is provided.