Steady-state analysis of nonlinear circuits with periodic inputs

Harmonic Issues Assessment on PWM VSC-Based Controlled Microgrids Using Newton Methods

“…Each method differs from each other on how the approximation is done, and in the number of full cycles required for the full identification of Φ. In [22] the Aprille and Trick method (AT) was proposed, and the identification of Φ requires only the integration of one full cycle and the computation of the Jacobian of (1) along the trajectory xpt, t 0 ; x i 0 q for t 0 ď t ď t 0`T . Later, based on the Poincaré map approach, the Numerical Differentiation (ND) and Direct Approach (DA) methods were proposed [24].…”

“…Average models fall within this type of systems, but they have evident limitations to evaluate adverse effect of the harmonic distortion on the performance of the MG. Alternatively, the harmonic domain modeling approach is able to consider the distorted nature of microgrids and also leads to time-invariant representations; however, the proper modeling of closed-loop controls and nonlinearities are still a bottleneck in this domain [20]. In order to deal with these problems, the fast time-domain methods were proposed [21], [22] and based on these seminal papers, other methods have been proposed and some of them will be presented in the following sections. Depending on the kind of system, these techniques are referred as shooting methods, Poincaré map methods or simply Newton methods [15]; in particular for non-autonomous systems, the shooting and the Poincaré map methods are essentially the same.…”

Robust Periodic Steady State Analysis of Autonomous Oscillators Based on Generalized Eigenvalues

“…The PSS solution can be found by long time integration, starting from perturbing the DCsolution. It is needed for phase noise analysis [2] [1,7,11]. In these methods the period T or the frequency f is an additional unknown.…”

Rapid and Accurate Latch Characterization via Direct Newton Solution of Setup/Hold Times

“…In this paper, we adapt ideas from mixed-signal/RF simulation [10]- [12] to propose a new technique for finding this skew directly, by expressing it as the solution to a scalar nonlinear equation h(τ) = 0, where τ can be the setup or the hold time. Our formulation uses the nonlinear state-transition function [13], [14] of the differential equations describing the latch, and incorporates a threshold condition to detect onset of metastability.…”