Comparison of broad-scale power converter modeling. A hard switched synchronous buck converter is used as an example to show the difference in error convergence to achieve steady-state waveforms with each method.

The goal of this project is to create a design framework to assist researchers in finding the optimal topology, operation, and device selection for an arbitrary set of design objectives. An important aspect of the framework is a database of components, such as inductors and FETs. While tabular data is already available for commercial devices, the parameters given are typically high-level and do not represent the losses or requirements to completely analyze a high frequency, power-dense circuit. An indexed standardized database containing curves and experimental data integrated into a modeling framework will allow broad analysis and comparisons of devices to occur rapidly.
Discrete time state-space modeling provides a generalized method to rapidly find the steady-state of switched circuits [1-3]. If a converter can be approximated as a linear equivalent circuit within each switching interval, it can be modeled using state-space equations. Iterating through the linear equivalent models captures the switching behavior of the converter. By solving the state-space equation over the set of linear equivalent circuits for a converter, the periodic steady-state solution is

$$ \mathbf{x_{ss}}[n] = \left(\mathbf{I}-\prod_{i=1}^ne^{\mathbf{A}_it_i} \right)^{-1}\left(\sum_{i=1}^n\left(\prod_{k=i+1}^ne^{\mathbf{A}_kt_k} \right){\mathbf{A}_i}^{-1}\left(e^{\mathbf{A}_it_i}-\mathbf{I} \right)\mathbf{B}_i\mathbf{u} \right) ~. $$

To solve for the steady-state of a circuit, each linear equivalent model and the transition time between linear equivalent models must be known. For active transitions caused by gate-controlled FETs, the timing can be easily determined. However, state dependent transitions such as diode conduction are unknown prior to solving the converter. This research has shown if states surrounding a diode conduction transition have nearly constant slopes, then the correct transitions can be derived by utilizing partial differential equations [3]. Current research hopes to better discern state dependent transitions without resorting to time-stepping simulation in any circuit. Future work will combine the standardized database with the discrete time state-space modeling method via an optimization process to create a design framework.