With the growing penetration of intermittent renewable energy resources in power systems, it is a challenge for automatic generation control (AGC) to maintain the required control performance. In recent years, battery energy storage systems (BESSs) have been installed in thermal power plants to provide frequency regulation service bundled with the traditional thermal generating units (TGUs). However, in real projects, the installed BESS typically works as parasitic equipment of the generating unit, which limits the coordination between the TGU and the BESS. In this paper, a complementary cooperation pattern is proposed for the TGU-BESS union to improve the dispatchability of its response to the AGC signal. Then, the correlation between the BESS's energy demand and the TGU's operation states is described by a data-driven method, which combines fuzzy c-means cluster, r-vine copula, and random forest. Finally, a rolling-horizon energy balance strategy is developed to make the control decisions for the TGU-BESS union in response to the stochastic AGC signal. The effectiveness of the proposed method is demonstrated using the historical data from a real union with a 9MW/4.5 MWh BESS and a 350MW coal-fired generator.