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Due to the importance of arm inductances in modular multilevel converters (MMC), it is necessary to propose an approach which provide the optimal inductor size considering the technical and manufacturing constraints. The investigations prove that utilizing the coupled inductor enhances converter performance and decreases the required value arm inductance and sub-module capacitor and the final converter volume and mass especially in high power applications. The analytical model of coupled inductors is consisted of circuit, electromagnetic and thermal model which will be combined with MMC circuit model to create the global MMC model. The analytical model of coupled inductor leads to fast convergence of optimization algorithm while it does not provide the accurate results. Another proposed approach is to put a finite element software directly in the optimization loop which intensely increases the optimization time and sometime made it hard to converge. In this paper, a novel hybrid correction loop has been proposed and developed to modify the analytical model parameters while the optimization is running. It effectively increases the results accuracy whereas the optimization does not increase so much. The proposed hybrid correction algorithm was employed in a global optimization loop which tries to minimize the total mass of a high power MMC converter according to the number of series sub-modules per arm. The results show that there is an optimal point which provides the maximum performance dependent to the load specifications, IGBT characteristics, goal function and manufacturing constraints. Also, in this research, the effect of coupled inductors on total converter mass and efficiency was investigated and compared to the state of using uncoupled inductors.