Full Order Discrete Time Modelling of High Gain Switched Capacitor Converter

High gain switched capacitor converters are quite popular for integrating low voltage storage devices to the high voltage dc link of DC Microgrids. One of the major challenge for switched capacitor circuit based topologies is to develop accurate dynamic model, as the conventional state space averaging methods can not be applied for these topologies due to the discontinuous nature of the capacitor voltages. In this aspect, discrete time based modelling approaches have been widely used for SC based topologies as it does not involve small ripple approximation. But specifically for SC converters system matrices may become singular for one or more states which can make DT modelling method ineffective. Though some of the existing literature have addressed this issue, but they suffer from different limitations such as reduced system order, loss of information and accuracy. In this paper, a generalized full order discrete time modelling technique for switched capacitor derived high gain topology is proposed considering matrix singularity problem with capacitor charge redistribution. A step by step large and small signal dynamic model is developed for a ladder SC circuit derived bidirectional high gain topology. Further, the dynamic modelling and controller design is validated through experimental results performed in a 500W, 220V laboratory prototype.