| In this paper, we present a new implementation of the harmonic balance method which extends its applicability to circuits 2-3 orders of magnitude larger than was previously practical. The results reported here extend our previous work 1] which only considered large circuits operating in a mildly nonlinear regime. The new implementation is based on quadratically convergent Newton methods and i...

Consider a one-mass system with two degrees of freedom, nonlin-early coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable a stable periodic solution...

This paper detects the disturbing loads in distorted and/or unbalanced three phase three wire power system. It is based on the simultaneous measurement of four non-active power quantities, which are found on the IEEE Std.1459-2000 method. It allows, achieving better knowledge of the power system when both harmonic distortion and un-balance are present. The proposed method requires only the fund...

The influence of permanent dipole moments of quantized states on intersubband second harmonic generation based on quantum-interference induced transparency in semiconductor quantum wells is explored using the harmonic balance method. The permanent moments are found to be quite important: they affect the transparency condition, especially at larger pump intensities. Hence, both the conversion ef...

We present a method to control unbalanced fast dynamics in an ensemble Kalman filter by introducing a weak constraint on the imbalance in a spatially sparse observational network. We show that the balance constraint produces significantly more balanced analyses than ensemble Kalman filters without balance constraints and than filters implementing incremental analysis updates (IAU). Furthermore,...

To predict nonlinear circuit behaviour, harmonic balance (HB) is a popular and useful frequency-domain technique. But given its mathematical nature, it can only converge to mathematical solutions being harmonically related to the input sources into the circuit. Nevertheless, the mathematical solutions to a nonlinear system do not necessarily need to be harmonically related to the input signals ...