Fast and accurate simulation of bifurcations in naturally sampled PWM control loops

This paper proposes a fast and accurate algorithm to simulate the operation of naturally-sampled PWM control loops. The algorithm is based on exact analytical solutions of the systems of differential equations that describe the converter and feedback loop. Newton's method is used to calculate the intersection between the PWM reference signal and the carrier. It can easily be implemented by means of a Matlab or Python script and is particularly useful when long simulation periods are required. Its execution time is orders of magnitudes shorter that of commercial software. As an example, a synchronous buck converter with a PI voltage regulator is simulated. Bifurcation diagrams were generated to analyse its stability.