Abstract: Introducing an inertia market has become imperative with the construction of new power systems. As an independent market participant, how energy storage can participate in various types of electricity markets to maximize profits remains an urgent issue. Research on energy storage participation in electricity markets mainly focuses on energy and frequency regulation markets. However, studies on its participation in the inertia market and further trading in energy-inertia-primary frequency regulation (PFR) multi-markets are almost nonexistent. Therefore, this paper proposes a trading strategy for energy storage to participate in energy- inertia-PFR multi-markets. Firstly, we propose a system dynamic frequency characteristic and energy storage frequency response model based on the combined effects of inertia and PFR resources. Secondly, based on the system and energy storage frequency characteristics and considering energy storage as an independent market participant, we construct a bilevel market trading decision model that includes the state variables of synchronous units. The upper-level model aims to maximize energy storage's revenue by determining its multi-market trading strategy. In contrast, the lower-level model achieves the joint clearing of energy, inertia, and PFR markets. Thirdly, the bilevel model is transformed into a single-level mixed-integer linear programming model and solved using the Karush-Kuhn-Tucker (KKT) conditions and duality theory. Finally, case studies demonstrate that energy storage units can achieve superior economics by simultaneously participating in energy, inertia, and PFR markets.