Demand response (DR) is an ancillary service that provides frequency support to the power grid. However, since its controller considers frequency deviations, the compensation provided by controllable loads such as thermostatically controllable loads (TCLs), may generate undesired harmonics into the power grid. This feature could be included into the controller of the TCLs by filtering the high harmonics. Hilbert-Huang Transform (HHT) uses an empirical decomposition method (EMD) from which the signal is separated into several intrinsic mode functions (IMFs), that can detect the high harmonics to be filtered. This paper proposes a frequency analysis of the power provided by TCLs, using HHT. Moreover, the study case considers variability of renewable generation in a microgrid. This was validated by using real demand and generation data from UK national system and simultaneously, temperature data for the same region and time frame, and implemented in Simulink/MATLAB.