  The reduced inertia levels in low-carbon power grids necessitate explicit
constraints to limit frequency's nadir and rate of change during scheduling.
This can result in significant curtailment of renewable energy due to the
minimum generation of thermal plants that are needed to provide frequency
response (FR) and inertia. Additional consideration of fast FR, a dynamically
reduced largest loss and under frequency load shedding (UFLS) allows frequency
security to be achieved more cost effectively. This paper derives a novel nadir
constraint from the swing equation that, for the first time, provides a
framework for the optimal comparison of all these services. We demonstrate that
this constraint can be accurately and conservatively approximated for moderate
UFLS levels with a second order cone, resulting in highly tractable convex
problems. Case studies performed on a Great Britain 2030 system demonstrate
that UFLS as an option to contain single plant outages can reduce annual
operational costs by up to {\pounds}559m, 52% of frequency security costs. The
sensitivity of this value to wind penetration, abundance of alternative
frequency services, UFLS amount and cost is explored.
