In applying virtual synchronous generator (VSG) to solve low inertia problem due to high renewable energy sources (RESs) penetration in the power system, selecting proper value for its parameters is important to maintain frequency stability of the system subject to dynamic events and contingencies. For this purpose, several methods have been proposed. However, in those methods, VSG parameters are selected without considering system frequency protection scheme. Therefore, the setting of the existing frequency protection scheme might be inadequate for the application in low inertia condition. In this paper, a method to select proper virtual inertia constant of VSG by taking the system frequency protection scheme into account is proposed. The dynamic change of the virtual inertia constant is shown under different system inertia and penetration level of RESs. Using the proposed method, optimal virtual inertia support from VSG for different system inertia condition could be achieved in line with the existing system frequency protection scheme and thus, the reconfiguration of the existing frequency protection scheme is not necessary for the application in low inertia condition.