Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems

The modular multilevel converter (MMC) has been widely used in high-voltage/high-power applications, e.g., high-voltage direct current transmission. However, its nonlinear time-periodic nature leads to complex harmonic interactions and then complicates the small-signal stability modeling and analysis of grid-connected MMC systems. To address this, the linear time-periodic (LTP) theory and the Floquet theory-based monodromy matrix method are applied in this paper. First, an analytical expression of the monodromy matrix (i.e., the state transition matrix over a period) for the LTP model of grid-connected MMC systems is constructed by applying the Chebyshev collocation method. In addition to avoiding time-consuming numerical integration, the analytical matrix facilitates to perform the derivative-based eigenvalue sensitivity analysis. Then, the system free-response solution is efficiently computed by means of a set of analytical state transition matrices. The effective oscillation components in critical LTP modes and relative contributions thus can be identified. On this basis, the participation factor analysis and damping ratio analysis can be performed to gain insightful characterization of system dynamics. The correctness and effectiveness of the proposed method are verified on an exemplary grid-connected MMC system by both numerical and experimental results. •The stability of grid-connected MMC systems with time-periodic nature is analyzed.•An analytical monodromy matrix of LTP systems is derived by the collocation method.•The analytical solution is significantly more efficient than the numerical one.•The derivative-based eigenvalue sensitivity analysis is performed.•The effective oscillation components contained in critical LTP modes are identified.