Abstract The high-temperature superconductor (HTS) plays a crucial role in power grids due to its ability to carry high current densities and withstand strong magnetic fields, making it ideal for applications like superconducting magnetic energy storage (SMES). However, integrating SMES systems with the grid introduces challenges, particularly regarding the generation of AC losses during cyclic operations, which can lead to temperature increases in HTS tape. This article presents a method for calculating AC losses and determining the magnetic field formulation at the critical state of HTS using numerical techniques. The study focuses on analyzing the charging and discharging operations of a grid-integrated SMES system based on silicon-controlled rectifiers. Additionally, the critical current of the HTS tape is determined using the four-probe method to characterize its I-V characteristics.