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Switching power converters operating in a multistate switching mode (more than two states) feature multidimensional control over their state variables. In this paper, a large-signal multistate modeling method is developed based on the switching flow-graph method to study the steady-state and dynamic properties of pulse-width-modulated (PWM) multistate-switching power converters for the continuous conduction mode. This modeling method translates a switching power converter directly to its graphic dynamic model and uses graphical representation to reveal the cause and effect relationship of the dynamics within a multidimensional power converter. A three-state buck-boost circuit is conceived with two duty ratios controlling two outputs as an example to test this modeling method. Experimental results confirm the theoretical prediction. This multistate-switching flow-graph modeling method is very general, easy to use and accurate, and it provides deep physical insight for engineering design.
Ma et al. (1997) studied this question.