  In modern power systems, shiftable loads contribute to the flexibility needed
to increase robustness and ensure security. Thermal loads are among the most
promising candidates for providing such service due to the large thermal
storage time constants. This paper demonstrates the use of Variable-Speed
Refrigeration (VSR) technology, based on brushless DC motors, for
fast-frequency response. First, we derive a detailed dynamic model of a
single-phase VSR unit suitable for time-domain and small-signal stability
analysis in low-inertia systems. For analysing dynamic interactions with the
grid, we consider the aggregated response of multiple devices. However, the
high computational cost involved in analysing large-scale systems leads to the
need for reduced-order models. Thus, a set of reduced-order models is derived
though transfer function fitting of data obtained from time-domain simulations
of the detailed model. The modelling requirements and the accuracy versus
computational complexity trade-off are discussed. Finally, the time-domain
performance and frequency-domain analyses reveal substantial equivalence
between the full- and suitable reduced-order models, allowing the application
of simplified models in large-scale system studies.
