Lyapunov stability of the single-leg flying capacitor converter natural voltage balancing mechanism

Purpose - The flying capacitor converter (FFC) balances the clamping capacitor voltages naturally when phase shifted carrier modulation is used. Several models that describe this mechanism are discussed in the literature. However, due to the model complexity, the stability of the mechanism is inferred from the circuit operation. This paper aims to show that the expressions describing the balancing mechanism can be simplified and used to prove Lyapunov stability. Design/methodology/approach - The FCC is analysed in the frequency domain. An equivalent circuit that describes the converter operation in terms of total and difference parameters is used. A concerted effort is made to simplify the resulting convolution expressions to their most basic forms by using the characteristics of the phase shifted switching functions' Fourier series coefficients. Findings - It is shown that the system matrix decomposes naturally into the sum of a symmetric and a skew-symmetric matrix. Through use of Lyapunov's theorem it is shown that the system is stable if the symmetric part of the decomposition is positive definite. A proof is provided that this matrix is positive semidefinite and the system is therefore Lyapunov stable. Research limitations/implications - The simplified expressions describing the convolution and the decomposition of the system matrix can be used in future studies to provide maximum bounds on the rebalancing time constant. Originality/value - This study provides a proof that the natural voltage balancing mechanism is stable. This stability had to be inferred from circuit operation in previous studies. Secondly, the decomposition of the system matrix provides an avenue for future research.