Modular multilevel converter losses model for HVdc applications

Multi-terminal high voltage dc (HVdc) grids can eventually became a feasible solution to transport energy to remote and/ or distant areas and its exploitation depend, among other things, on the performance of the converter terminals. Therefore, to optimize the power transmission strategy along such a grid, it is necessary to recognize the efficiency of all the converters in all points of operation, namely with the different load conditions. In this vision, the aim of this work is to provide the methodology to model the modular multilevel converter (MMC) efficiency by means of a mathematical expression that can describe, over a broad range of active and reactive power flow combinations, the power losses generated by the semiconductors. According to the presented methodology, a polynomial-based model with a reduced number of coefficients is deducted, in such a way that can be directly used for optimal power flow (OPF) studies. The accuracy of the proposed model is characterized by an absolute relative error, at the worst scenario, approximately equal to 3%.