The increasing integration of renewable energy sources weakens system frequency security, requiring enhanced primary frequency regulation (PFR) from conventional thermal power units (TPUs). In this case, integrating energy storage system (ESS) with TPUs offers a promising solution. However, most existing methods primarily focus on turbine dynamics while overlooking multiscale coordination among ESS, turbine, and boiler, thereby limiting sustained power support and safe operation of TPUs. To this end, this paper firstly analyzes the multiscale energy dynamics of TPUs under power disturbances, revealing that insufficient boiler thermal storage can cause secondary frequency dips (SFDs). An analytical energy balance equation is then established to quantify the ESS energy requirement for compensating thermal storage. Based on this, a novel multiscale energy coordination method for the integrated thermal power energy storage system (TPESS) is developed, including three dedicated controls: a deviation-based power control (DPC) for ESS, a coordinated energy allocation (CEA) between thermal storage and ESS, and a fuel-assisted restoration (FAR) for state of charge (SOC). This method enables the ESS to take the leading role in PFR while simultaneously coordinating with the boiler thermal storage and fuel systems to ensure safe operation and state recovery. Simulation in DIgSILENT/PowerFactory validates the effectiveness of the proposed method in enhancing system frequency security and boiler safety.