Stochastic Polynomial-Chaos-Based Average Modeling of Power Electronic Systems

Abstract

With the introduction of variable-frequency generators in next-generation more-electric aircraft, both voltage and frequency are to reveal significant tolerance levels. In this study, a method based on the combination of polynomial chaos and nodal analysis is developed to identify and quantify the impact of such tolerance in ac/dc diode rectifiers and dc/dc switch-mode converters. The resulting stochastic average models track the transients of the tolerance limits and related information in the time domain both accurately and efficiently. The relative merits of the method are substantiated through a comparative analysis with the Monte Carlo and root-sum-square methods.

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

“…Hence, different PC-based techniques have been developed over the years by the research community tailored on the types of devices or components considered: lumped element circuits [42][43][44], multiconductor transmission lines [45][46][47], generic linear multiport systems [37,39,48], and nonlinear systems [38,[49][50][51][52][53]. Additional details are given in the next section, where a review of the main applications of the PC method in electrical and electronics problem is presented.…”

Polynomial chaos based variability analysis of multiport systems

“…• choosing on the number of basis functions M ; • computing the PC coefficients of the state-space matrices; • calculating the corresponding Galerkin projection [7] to determinate the coefficients of the PC expansion of X; • calculating the PC expansion of Y by means of a suitable combination of the results previously obtained. In our approach, the number of basis functions M is chosen upfront, according to (4).…”

“…The desired state-vector coefficients can now be calculated through Galerkin projection [7]. For example, let us assume that the transfer function of the multiport system depends on one RV and M = 2 basis functions are used for the PC model.…”

“…Over the last years, several techniques were developed to study the stochastic variations of electrical circuits by means of the Polynomial Chaos (PC) expansion [1]- [4], PC-based methods are much more efficient with respect to the computationally cumbersome MC-based techniques. These PC-based techniques were designed to handle specific systems: multiconductor transmission lines [5], [6] and lumped elements circuits [7].…”

Stochastic macromodeling for hierarchical uncertainty quantification of nonlinear electronic systems

“…In PC-based approaches, a stochastic process is represented as a series of orthogonal polynomials with suitable coefficients. The PC methodology has been extensively applied to the variability analysis of linear systems, such as lumped elements circuits [9], [10], multiconductor transmission lines [11]- [13] and generic linear multiport systems [14]. Also, the PC methodology has been proposed for the variability analysis of nonlinear electronic circuits [15]- [18].…”