Stochastic fractional order solution of buck converter with uncertain parameters

Abstract

This study introduces a novel Monte Carlo-based analysis of parameter uncertainties in fractional-order buck converters, systematically evaluating their sensitivity to individual variations in the fractional inductor, capacitor, and load, as well as their combined interactions. The results show that inductor uncertainties yield asymmetric voltage distributions with left-tailed characteristics, exhibiting the smallest impact on the mean and standard deviation of the voltage. The capacitor variations lead to symmetric fluctuations with moderate mean shifts below 2.8 %. Load variations exhibit the most significant impact, generating extreme output ranges of 0.5917. When combined, these uncertainties create nonlinear interactions that result in peaked distributions at specific frequencies, particularly near 12.8 krad/s, with substantially widened operational bounds. A critical vulnerability window emerges during the system's transition phase between ${7.70\times 10}^2$ and ${6.46\times 10}^5$ rad/s, where parameter uncertainties have their greatest effect. The comprehensive statistical analysis, including probability density functions, standard deviations, and output voltage bounds, provides valuable quantitative guidelines for converter design. The study offers practical insights for developing robust fractional power electronic systems capable of reliable operation under real-world parameter variations, establishing clear safety margins for component tolerances and operational frequency ranges.