In recent years, the increased application of inverter-based resources in power grids, along with the gradual replacement of synchronous generators, has made the grid support capability of inverters essential for maintaining system stability under large disturbances. Critical clearing time provides a quantitative measure of fault severity and system stability, and its sensitivity can help guide parameter adjustments to enhance the grid support capability of inverters. Building on previous researches, this paper proposes a method for calculating critical clearing time sensitivity in power systems with a high proportion of power electronic devices, accounting for the new dynamic characteristics introduced by these devices. The current limit and switching control of inverter-based resources are considered, and the critical clearing time sensitivity under controlling periodic orbits is derived. The proposed critical clearing time sensitivity calculation method is then validated using a double generator single load system and a modified 39-bus system.