Impact of PLL dynamics on the small-signal stability of the MMC using dynamic phasor modeling in the ABC frame

This paper presents a small-signal dynamic phasor model of the modular multilevel converter including phaselocked loop (PLL) dynamics. A simple PLL model including a low-pass filter at its input and accounting for the harmonic content of the voltage at the point of common coupling is developed to assess the impact of the PLL on small-signal stability. Nonlinear models of the converter, its controllers and the PLL are separately developed and linearized. The linearized models are combined using the component connection method to obtain the overall system matrices. The developed model is verified against a nonlinear averaged model in MATLAB/ Simulink, and dynamic phasor models including different harmonic content are compared in terms of their accuracy. Eigenvalue analysis is carried out to study the impact of the PLL and its filter cutoff frequency on the small-signal stability of the converter.