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• A novel dynamic model of cascading failures in power systems is established. • Increased wind penetration and fast frequency responses are obtained. • Impact of increased wind penetration on cascading risks is quantified. • Behaviour characteristics of fast frequency responses are demonstrated. The ever-growing penetration of renewable based generation is leading to significant increases in the risk of cascading failures in low-inertia, and interconnection-rich, power systems. This paper proposes a framework for quantifying the risk of cascading failures in renewable-rich power systems with fast frequency response (FFR) services. This is achieved by developing a novel time-based dynamic model of cascading failures to capture the transient behaviours of the system response and quantify the risk of blackout. This dynamic cascading failure model is complemented by unit commitment for representative dispatch and includes the provision of FFR. The proposed framework is illustrated using a modified version of the Illinois 200-bus synthetic system. As key outputs, the results emphasize the importance of accurate modelling of ancillary services associated with frequency regulation in cascading failure analysis, and indicate that increased wind penetration can lead to a higher probability of power outages. Adopting FFR services can help to mitigate the cascading risk but may introduce rotor angle instability issues. [ABSTRACT FROM AUTHOR]