Lyapunov theory for fully inverter-based systems

Develop a complete theoretical framework for Lyapunov-exponent-based transient-stability assessment in fully inverter-dominated power systems with nonsmooth switching dynamics, including low-voltage ride-through, current limiting, and mode transitions.

Background

Classical Lyapunov-exponent stability assessment was developed primarily for inertia-dominated synchronous-generator systems with smooth dynamics. Inverter-based resources introduce fast control loops and nonsmooth switching, making classical smooth-theory assumptions inadequate. Existing generalized voltage-damping and switching-MLE methods are identified as important but incomplete advances.

References

(3) LLE under IBR dynamics. The theoretical basis for LLE-based stability assessment was developed for inertia-dominated SG systems. IBR control loops operate on microsecond timescales and introduce non-smooth switching dynamics (LVRT, current limiters, mode transitions) that are fundamentally incompatible with classical smooth Lyapunov theory. The GVD/pGVD framework [2], [34] and switching MLE [36] represent important advances, but a complete theoretical framework for LLE-based TSA in fully IBR-dominated systems is still lacking.

— Lyapunov Exponents in Power Systems: A Survey of Theory and Applications in Stability, Control, Forecasting, and Protection  (2610.23809 - Almomani et al., 16 Oct 2026) in Section III-K, p. 13

Despite the substantial literature reviewed above, several critical gaps remain. (1) IBR model realism. The vast majority of chaos studies use simplified integer-order or fractional-order ODE models of synchronous generators. The dynamics of GFM and GFL converters under large disturbances are governed by control-loop switching and saturation, not swing-equation nonlinearities. The hidden-attractor work [109], [110] is the only systematic study that begins from a converter-native model. More work is needed to determine whether the control synthesis methods of Sections IV-F–IV-H are applicable to IBR-dominated networks.

— Lyapunov Exponents in Power Systems: A Survey of Theory and Applications in Stability, Control, Forecasting, and Protection  (2610.23809 - Almomani et al., 16 Oct 2026) in Section IV-J, p. 17

Whether load and renewable time series remain chaotic (in the classical sense) under high IBR penetration and demand-response programs, and whether λ1-based predictability bounds remain meaningful in this regime, is an open and important question.

— Lyapunov Exponents in Power Systems: A Survey of Theory and Applications in Stability, Control, Forecasting, and Protection  (2610.23809 - Almomani et al., 16 Oct 2026) in Section V-I, p. 22

(1) A unified LE framework for IBR-dominated grids. The GVD/pGVD framework addresses STVS; the SMLE addresses commutation-failure transients; hidden-attractor theory addresses microgrid sub-synchronous oscillations. A single, mathematically consistent framework covering all three phenomena for fully IBR-dominated networks (zero synchronous inertia) has not yet been established.

— Lyapunov Exponents in Power Systems: A Survey of Theory and Applications in Stability, Control, Forecasting, and Protection  (2610.23809 - Almomani et al., 16 Oct 2026) in Section VII-H, p. 29

No paper in the corpus provides a full worst-case analysis of how communication degradation propagates into LLE estimation error, which is an important gap for industrial deployment.

— Lyapunov Exponents in Power Systems: A Survey of Theory and Applications in Stability, Control, Forecasting, and Protection  (2610.23809 - Almomani et al., 16 Oct 2026) in Section VII-G, p. 29