This paper investigates a delay compensation control for coordinating aggregated energy storage systems (ESSs) of dissimilar characteristics to provide fast frequency regulation, particularly the UK National Grid enhanced frequency response (EFR) service. The dynamic model of a generic micro-grid system comprising synchronous generator, load, and EFR-providing ESS is established. Theoretical analyses of the compensation effects are conducted using describing function techniques to model the EFR nonlinearities. The theoretical study indicates the compensation control's beneficial effects through an increase in the micro-grid system's equivalent regulating energy (the inverse of the frequency droop coefficient). The analytical results are validated by RTDS simulations of a representative micro-grid system, which is based on the measured characteristics of a real aggregated ESS fleet, including a 180kWh/240kW commercial battery ESS asset and a 1MWh/2MW battery asset located 100 miles apart. Simulations show that the frequency deviation of the micro-grid system in response to a 10% sinusoidal power imbalance at the network's natural angular frequency could be reduced by 74% through the inclusion of two BESSs providing EFR with a total capacity of 10% of the micro-grid; a further reduction of 42% can be obtained through the implementation of the proposed delay compensation method.