Against the backdrop of continuously increasing penetration of new energy, the phenomenon of low inertia and weak damping has emerged in microgrids. Existing research mainly improves the frequency regulation capability of microgrids by improving control strategies and optimizing scheduling, but the premise is that the microgrid itself has sufficient frequency regulation capacity. In response to this issue, this paper incorporates frequency constraints in grid connection and off grid modes during the microgrid planning phase, and establishes a mixed integer linear capacity optimization model. First, this paper models multiple frequency modulation resources within the microgrid, constructs a comprehensive frequency response model, and derives frequency constraints. Second, an improved adaptive linearization method is used to linearize the frequency constraint and embed it into the model. Finally, the Gurobi solver is used to validate and analyze multiple microgrid examples, and the results show that the proposed microgrid capacity optimization configuration model can achieve the lowest construction and operation costs while ensuring the stability of system grid connection and off grid frequencies.