Marcos Netto

Xingyu Zhao, Marcos Netto, Junbo Zhao

Dynamic state estimation (DSE) is becoming increasingly important for monitoring inverter-dominated power systems. Due to their cascading control structures, inverter-based resources (IBRs) exhibit multi-timescale dynamics, leading to stiff system models that pose significant challenges for conventional DSE methods. In particular, explicit discretization schemes often require impractically small sampling intervals to maintain numerical stability, increasing computational and communication burdens. To address this issue, this paper proposes a stiffness-aware decentralized DSE method for inverter-dominated power systems. The statistical linearization is used to construct a local linear surrogate model for the nonlinear dynamics, which allows matrix-exponential discretization to enable analytical uncertainty propagation in discrete time, rather than relying on explicit integration schemes. This enables stable DSE at lower sampling rates. Numerical results reveal the mechanism by which stiff dynamics destabilize conventional DSE and demonstrate that the proposed method achieves efficient and accurate estimation under coarse sampling conditions.

Huy Hoang Le, Haoguang Wang, Christian Moya et al.

Neural surrogates for stiff differential-algebraic equations (DAEs) face two key challenges: soft-constraint methods leave algebraic residuals that stiffness amplifies into large errors, while hard-constraint methods require trajectory data from computationally expensive stiff integrators. We introduce an extended Newton implicit layer that enforces algebraic consistency and quasi-steady-state reduction within a single differentiable solve. Given slow-state predictions from a physics-informed DeepONet, the proposed layer recovers fast and algebraic states, eliminates the stiffness-amplification pathway within each time window, and reduces the output dimension to the slow states alone. Gradients derived via the implicit function theorem capture a stiffness-scaled coupling term that is absent in penalty-based approaches. Cascaded implicit layers further extend the framework to multi-component systems with provable convergence. On a grid-forming inverter DAE (21 states), the proposed method (7 outputs, 1.42 percent error) significantly outperforms penalty methods (39.3 percent), standard Newton approaches (57.0 percent), and augmented Lagrangian or feedback linearization baselines, which fail to converge. Two independently trained models compose into a 44-state system without retraining, achieving 0.72 to 1.16 percent error with zero algebraic residual. Conformal prediction further provides 90 percent coverage in-distribution and enables automatic out-of-distribution detection.

Bukunmi G. Odunlami, Marcos Netto, Hai Lin

Discrete events alter how parameter influence propagates in hybrid systems. Prevailing Fisher information formulations assume that sensitivities evolve smoothly according to continuous-time variational equations and therefore neglect the sensitivity updates induced by discrete events. This paper derives a Fisher information matrix formulation compatible with hybrid systems. To do so, we use the saltation matrix, which encodes the first order transformation of sensitivities induced by discrete events. The resulting formulation is referred to as the salted Fisher information matrix (SFIM). The proposed framework unifies continuous information accumulation during flows with discrete updates at event times. We further establish that hybrid persistence of excitation provides a sufficient condition for positive definiteness of the SFIM. Examples are provided to demonstrate the merit of the proposed approach, including a three bus generator wind turbine differential algebraic power system

Marcos Netto, Yoshihiko Susuki, Lamine Mili

This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique generalizes the original definition of the linear mode-in-state participation factors. Two numerical examples are provided to demonstrate the performance of our approach: one relying on a canonical nonlinear dynamical system, and the other based on the two-area four-machine power system. The Koopman mode decomposition is capable of coping with a large class of nonlinearity, thereby making our technique able to deal with oscillations arising in practice due to nonlinearities while being fast to compute and compatible with real-time applications.