This paper presents a new method based on piecewise analytical formulas to evaluate the valve losses of the modular multilevel converter based high-voltage direct current (MMC-HVDC) transmission systems. According to the generating mechanism, the total valve losses of the MMC are divided into three parts: 1) conduction losses; 2) essential switching losses; and 3) additional switching losses. Due to the large number of arm submodules in MMC-HVDC links, the harmonic components in the arm voltages and currents are omitted. Therefore, the conduction losses and the essential switching losses can be precisely represented by analytical formulas. The additional switching losses are described by an analytical upper limit. The case studies are performed on a 400-MW ±200-kV MMC-HVDC system under 12 typical operating conditions. Both the relative errors of the conduction losses and the essential switching losses between the analytical and the simulated results are within ±4%. The analytical upper limits cover almost all of the simulated results for additional switching losses. Finally, an acceptable number for the analytical method is described based on the simulation results, which proves the effectiveness of this method and clarifies the potential to take advantage of this method in engineering applications.
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Zhang et al. (2014) studied this question.
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