Circuit-to-Circuit Cosimulation for Closed-Loop Electrical Systems Using Waveform Relaxation

A computational time saving approach is proposed for the co-simulation of a buck-boost converter using waveform relaxation (WR) and time windowing. This study implements the Gauss-Seidel (GS) method, an iterative process that is employed to solve systems of linear and nonlinear equations using the WR technique, improving the convergence speed and accuracy of closed-loop system dynamic simulations. The proposed technique is applied to a 3.3 V buck-boost converter working both in buck and boost modes, therefore, simulations and measurements are carried out with a 1.8 to 5.5 V input voltage range. A comparative analysis between GS-WR without and with time windowing demonstrates that with time windowing, the number of iterations increases by 60% and 67.8%, while the elapsed time is reduced by 22.3% and 26.6% with respect to a single time windows in buck and boost modes, respectively. Moreover, the optimal number of time windows (i.e., 4), computed by simulation, yields a 8.1% and 18.1% faster simulation time compared to the highest considered value in the study (i.e., 10). The outcome of this comparison reveals that a higher number of time windows does not necessarily result in a quicker computation compared to a lower value. More specifically, the GS-WR technique was found to be the main contributor to the acceleration, while time windowing ensures the convergence to the same results as the full system simulation.