The large-scale access of new energy sources to distribution networks has led to its safe and stable operation. Therefore, this study considers a multi-timescale interaction of a coupled electricity-hydrogen-natural gas (EHG) system with a distribution grid for dynamic games. First, a multifaceted interaction mechanism between the coupling system and the distribution network balancing service mechanism, demand response service mechanism, and frequency regulation service mechanism was designed. Furthermore, an interaction framework between the coupled system and the distribution network was proposed, and a three-level time-scale interaction strategy between the distribution network and the coupled system was constructed considering the dynamic game in the medium- and long-term, short-term, and ultrashort terms. Subsequently, the presence and uniqueness of the interactive equilibrium solution of the dynamic game was proven. Finally, a region was used as an example for arithmetic analysis. The results of the calculation example indicate the following: 1) the ranges of interaction deviation under the medium-to long-term, short-term, and ultra-short-term time scales are [-3.76%, 2.84%], [-2.37%, 1.43%], and [-0.43%, 0.87%], respectively, indicating that the interaction deviation between the coupling system and the distribution grid can be reduced via adjusting and correcting the medium-to long-term, short-term, and ultra-short-term time scales. 2) Compared with the scenario in which only a single service is provided, the distribution network operation cost in the present study decreased by 15.92% and the revenue increased by 30.59%, signifying that the coupling system and distribution network diversification mechanism can expand revenue channels. 3) Compared with Scenario 1, without considering the cost of energy storage loss, and Scenario 3, with a single energy storage configuration, the actual service life of the battery in this study was the longest, 23.72% longer than Scenario 1, and 47.90% longer than Scenario 3, revealing that hybrid energy storage can achieve coordinated optimization and optimal allocation of resources at different time scales. 4) The interaction between the distribution network and coupling system, considering dynamic games, can form a fair price and guide to improved interaction between the distribution network and coupling system.
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