Dynamic Phasor Modeling of the Single-Phase MMC under Modulation PSC-PWM

Abstract

This paper develops a model, based on the dynamic phasor approach, for the single-phase modular multilevel converter (MMC), where the switching sequences are generated by the phase-shifted carrier-based pulse-width modulation (PSC-PWM) scheme. The modeling process begins with the MMC state space model, from which the DC and the fundamental complex Fourier coefficients, called dynamic phasors, are extracted for both the original state variables and the switching functions. It is worth noting that, in the developed dynamic phasor-based model (DPhM) of the MMC, all capacitor voltages per phase are considered separately in the modeling process, which contrast with the usual definition of variables based on the sum and difference of the capacitor voltages on the arms. Experimental results are presented to demonstrate the validity of the MMC DPhM as compared to the response of the switched MMC under the PSC-PWM scheme. In particular, it is observed that the developed MMC DPhM is able to reproduce the steady-state waveforms of all original state variables, including the ripple amplitude, as compared to the results obtained with the switched MMC. Furthermore, it is shown that, both in the switched MMC under the PSC-PWM and in the derived DPhM MMC, all capacitors converge to the same steady-state average value without adding an external balance controller, but only due to the natural balancing action of the PSC-PWM scheme, despite arbitrary initial conditions of capacitor voltages.