Passivity Enforcement by Residue Perturbation via Constrained Non-Negative Least Squares

Abstract

Passivity is a fundamental requirement for rational models to guarantee stable behavior when included in general time domain simulations. This paper introduces a new variant of one passivity enforcement scheme that is based on residue matrix perturbation. The constrained least squares problem associated with the passivity condition is transformed into a least distance problem which is solved as a non-negative least squares problem while utilizing the sparsity pattern that arises with multi-terminal problems. The resulting method is very fast and requires only a small amount of computer memory, thereby being applicable to models with many terminals and high orders. The method is demonstrated to be suitable for frequency-dependent modeling of subnetworks, transformer winding branch impedances, and measured transformer admittance data.

Inclusion of Neutral Points in Measurement-Based Frequency-Dependent Transformer Model

“…is approximated with a 60 th order pole-residue model using vector fitting [18] with relaxation [19] and fast implementation [20]. The model is subjected to passivity enforcement by residue perturbation [21] with the fast implementation in [22] (RP-NNLS). The perturbed model is finally transformed back by applying the inverse MRT to the individual residue matrices 4 4 ˆ( )…”

A Waveform Relaxation Solver for Transient Simulation of Large-Scale Nonlinearly Loaded Shielding Structures

“…This entire procedure is well-documented in [27] and [30], including application to the very same shielding enclosures considered in this work, and is not repeated here. This optimized macromodel generation flow includes of course a dedicated passivity verification and enforcement, based on an iterative perturbation algorithm [31] of passivity violations identified through the adaptive sampling process [32].…”

LMI‐based passivation of LTI systems with application to marine structures

“…Remark 6. We stress that, in contrast to state-of-the-art passivation techniques, for example, [13][14][15][16] (see also the discussion provided in Section 1), Problem 1 does not require a-priori identification of the specific (frequency) location of any passivity violation, but rather directly computes the minimum norm perturbation required to ensure passivity without such knowledge, hence easing the application of the proposed technique. Furthermore, unlike the technique developed in [13] for marine systems, the presented strategy does not require the definition of an augmented system, being especially suitable for real-time control/state-estimation design and synthesis applications.…”

“…Motivated by this, a number of techniques have been proposed to enforce the passivity of identified models, that is, to achieve passivation, both within, and beyond, the scope of marine engineering (see, for instance, [13][14][15][16]). Aiming to keep this paper reasonably self-contained, we provide a brief discussion on the aforementioned techniques in the following.…”

“…for control/state‐estimation purposes). [14] and [16] assume a pole‐residue description for the target model, and introduce a constrained optimisation procedure to enforce passivity by perturbing the associated residues, with a‐priori knowledge of the specific location of passivity violations in the frequency‐domain. Finally, [15] introduces a passivation method based upon perturbation of the Hamiltonian matrices associated with the specific target system.…”