An Enhanced Steady-State Model and Capacitor Sizing Method for Modular Multilevel Converters for HVdc Applications

An analytical steady-state model of the modular multilevel converter (MMC) can be used for component sizing and assessment of the impact of different parameters on the MMC performance. Thus, this paper proposes an enhanced steady-state model for the MMC, which enables one to calculate the amplitudes of the harmonic components of MMC arm currents, submodule capacitor voltages, and arm voltages. In addition, the proposed model allows for the calculation of the amplitude and phase angle of the modulating signal, and it also presents a criterion for resonance of the arm currents. This is achieved by means of a polynomial function of the modulation index, and through checking the stability criteria established by the proposed model. The capability of formulating the modulating signal enables a more accurate calculation of the steady-state amplitudes of the variables, as compared to the previously published models. This paper also presents an accurate method of submodule capacitor sizing, based on the proposed steady-state model. The proposed method gives the exact value of the submodule capacitance (i.e., the capacitance that results in dc voltage fluctuations within a desired range) for a prespecified submodule capacitor voltage variation and a given circulating current amplitude. The stability criterion given by the proposed steady-state model, used for sizing the arm inductance, and the submodule capacitor voltage variation given by the proposed capacitor sizing method, used for sizing the submodule capacitor, allows for the determining of the operating limits of the MMC in terms of its parameters. Extensive simulation results are presented to demonstrate the efficacy of the proposed steady-state model and the capacitor sizing method. Further, the results obtained from the proposed capacitor sizing method are compared with experimental results from the literature.