Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels

Abstract

This paper presents a class of nonsmooth convex optimization methods for the passivity enforcement of reduced-order macromodels of electrical interconnects, packages, and linear passive devices. Model passivity can be lost during model extraction or identification from numerical field solutions or direct measurements. Nonpassive models may cause instabilities in transient system-level simulation, therefore a suitable postprocessing is necessary in order to eliminate any passivity violations. Different from leading numerical schemes on the subject, passivity enforcement is formulated here as a direct frequency-domain norm minimization through perturbation of the model state-space parameters. Since the dependence of this norm on the parameters is nonsmooth, but continuous and convex, we resort to the use of subdifferentials and subgradients, which are used to devise two different algorithms. We provide a theoretical proof of the global optimality for the solution computed via both schemes. Numerical results confirm that these algorithms achieve the global optimum in a finite number of iterations within a prescribed accuracy level.

LMI-Based Method for Estimating Passive Blackbox Models in Power Systems Transient Analysis

“…this time, Φ il is a column vector of ones in R K P.4) To attain a passive realization of model (10), formulate the search for the optimalθ in objective function (18) as:…”

“…That ends up reducing the computational effort and preserving passivity enforcement constraint via convex optimization. Optimization techniques to address similar problems have also been proposed by [14] and [18]. An algebraic method for the passivity enforcement based on quadratic programming is applied in reference [14] whereas reference [18] uses a class of non-smooth convex optimization subgradient technique.…”

Robust localization methods for passivity enforcement of linear macromodels

“…In this paper we use robust localization based algorithms, such as the ellipsoid algorithm [9] and the cutting plane method [10], to solve the convex continuous but non-smooth passivity enforcement formulation presented in [11]. The algorithms presented in [11] exhibit high sensitivity to given problem parameters and need tuning of the algorithm coefficients for individual cases.…”

“…The algorithms presented in [11] exhibit high sensitivity to given problem parameters and need tuning of the algorithm coefficients for individual cases. Compared to [11], the algorithms implemented in this paper are robust in the sense that they are less sensitive to the given problem parameters and converge with in acceptable number of iterations even for the challenging cases where the subgradient techniques in [11] converge too slowly. In this paper, we also provide a scheme to determine the initial set which is guaranteed to contain the global solution of the problem.…”

Rational Modeling of Multiport Systems via a Symmetry and Passivity Preserving Mode-Revealing Transformation

“…A number of techniques are available for such model extraction (e.g., vector fitting [14]- [19] and Löwner matrix interpolation [20]. With these methods, passivity must be enforced as a second step by perturbation [21]- [25].…”