The increased penetration of large-scale renewable energy resources results in the significant reduction of the system short-circuit current (SCC) level, challenging current protection systems. In real-time operation, several conventional synchronous generators are committed to maintaining the SCC level at a range that can be identified by the protection system. This limits the hosting capacity of renewable energy integration. This paper investigates the impacts of transmission switching (TS) and unit commitment (UC) on SCC magnitude and derives several linear expressions of SCC constraints for optimal control to restrain the SCC level to the desired range. Besides, an error compensation algorithm is developed to mitigate the linearization error. Numerical results carried out on the standard IEEE test systems show that the proposed method can effectively confine the SCC magnitude to the desired range while increasing the penetration of renewable energy. Comparison results with other methods highlight that the proposed method can achieve a higher level of renewable energy integration without violating SCC constraints.