Eigendecomposition of a digital iterative decentralised interleaving for multicellular converters

The decentralised control of multicellular converters is an alternative to the usual control techniques. Multicellular converters use interleaved carriers to reduce filtering elements and potentially improve transient response. Decentralised interleaving techniques are scalable, avoid a complex interleaving controller for a high number of cells, and simplify reconfiguration cases like phase shading. Circular chain of communication (ring, or daisy chain) approaches have been proposed in the literature and implemented in concrete applications. However, the analytical study of the stability and dynamic response of this system involving several identical phase-delay local controllers connected in a dedicated communication chain with their close neighbours has not been conducted yet. This paper presents a behavioural discrete model for a digitally implemented decentralised interleaving device. The eigenvalue study gives the stability criterion and convergence speed to choose the appropriate parameters of the controllers. A modal decomposition technique dissociates the various types of differential interactions to observe their respective time response. Simulation results demonstrate that the system is unconditionally stable when all differential modes are properly damped. An analytical expression for the final disposition of the carriers in steady state depending on the start-up condition is established. Lastly, a more precise operator to overcome the singular discontinuity of the model is presented and discussed. Experimental validation by FPGA implementation have been done for reconfiguration and start-up cases.