State-Space Representation of ISOP-Systems to Study Natural Power Sharing of Common Frequency Controlled LLC Based Systems

The input series output parallel (ISOP) connection of multiple DC-DC converters enables high input voltage applications with high output currents. These systems require an equal distribution of power and thus input voltage. To avoid the need for isolated input voltage sensing, stable operation is achieved by driving all converter modules with a common control signal. However, parameter mismatches between the modules lead to uneven power distribution. Just like in the previous design process of the single module, studying the applicability of the common control approach requires many simulation runs and therefore a fast and efficient simulation model like time discrete modeling, which is based on the state-space equations of each subcircuit. Directly deriving the state-space representation of the complete ISOP-system is cumbersome due to the number of state variables and switching elements. Therefore, this paper demonstrates how to extend the single module’s state-space representation – previously used in the design process of the single module – to the otherwise hard-to-obtain ISOP-system’s representation. This enables parameter studies by fast time-domain simulation with time discrete modeling. To demonstrate the general applicability of the proposed method, simulation results of an ISOP-system consisting of two LLC converters are compared to measurement, proving the feasibility of the approach. A parameter sensitivity analysis over the input voltage and load range reveals the impact of parameter mismatches on the power sharing in the common frequency controlled system.