To comply with recent grid code requirements and maintain the internal energy balance of modular multilevel converter (MMC), a careful selection of fault current injection (FCI) methods and control structure design for FCI and energy balancing are required. Although FCI methods applied to voltage-source-converter (VSC) can also be used for MMC, how to integrate them with the total energy balancing remains unclear, especially for flexible positive and negative sequence control (FPNSC). Besides, the participation of AC-side power in total energy balancing causes an interaction between FCI and energy balancing, requiring a control structure that can mitigate it. This paper compares the effect of two FCI methods on grid code compliance, analyses three control structures for integrating FCI with total energy balancing, and discusses the impact of AC-side power-sharing ratios. It was found that FPNSC has better performance on the remaining active power after AC-side faults occur. Inserting the output of total energy balancing after the FCI current calculation can reduce the interaction between FCI and energy balancing control loops, while selecting AC-side power-sharing ratio carefully is essential to avoid overcurrent in this structure.