Research proposal · Post-classical grid stability
Grid stability was written for a world where synchronous generators dominated the mix. That world is going away, and the classical models are silent on the failure modes that actually matter now.
IEEE 39-bus inter-machine modal spectrum (Hz). Mode 1 is the inter-area mode at 0.621 Hz — the operator that determines whether the New England footprint holds synchronism through a large disturbance. PHAETHON's static K recovers every mode to a max relative error of 3.8 × 10⁻¹⁵ against the classical small-signal answer.
PHAETHON identifies the stability operator as the curvature of a section in the sense of the Davis Duality — a single geometric object that reproduces the classical A-matrix analysis exactly where it applies, and extends into the regimes where it doesn't. One master identity sits above every reading in the tool:
On grids, K is the inertia-weighted Hessian of the swing-Lyapunov function at the operating point. Its eigenvalues are the classical modal frequencies. But the framework also lifts the dynamic state to an augmented pair (Φ, r), where the discrete component r tracks winding-number transitions on the universal cover — i.e., pole slips — and it proves a strictly positive lower bound on the inter-sector energy barrier. That barrier is the operator's warning that a disturbance is close to taking the system out of synchronism.
Where classical small-signal analysis reads "stable" past the point of danger, PHAETHON reads how close the operating point is to the edge — and, at the inverter-driven bifurcation locus, how far past it.
Machine-precision equivalence at the conservative skeleton is a precondition, not the headline. It earns the right to make predictions outside the linearization — which is where the novel content lives.
Hyperscaler AI datacenters are the largest new grid loads on the planet, and the grids they sit on — CAISO, ERCOT, MISO, PJM — are becoming exactly the kind of unstable the classical math misses. Every additional gigawatt of inverter-based generation displaces synchronous rotating mass, which is the substrate the classical stability tooling was built to reason about.
The operational failure mode is not that the utility's stability analysis is wrong. It's that the standard analysis returns "stable" for regimes that are, in fact, unstable — as ERCOT's 2023 West Texas oscillation and Australia's 2016 black-system event both demonstrated on real networks in production. When that gap widens, the risk lands on the grid's largest, most infrastructure-dependent customers first.
PHAETHON's contribution is a mathematically principled reading of that gap, with pre-registered falsifiers already deposited against three historical events. It is the diagnostic layer a serious grid-dependent operator will want in place before it is needed.
Four workstreams over 12–18 months. Each has a bounded scope, a concrete deliverable, and a public artifact.
The 8-state Kinv derivation for grid-following inverters — PLL phase, outer P/Q integrators, inner current-control integrators, LC filter. Closes the SCR-bifurcation curve and, if tractable, the all-k simultaneity conjecture. Yields the operator that reads inverter-driven instability — the exact class Paper 1 is currently silent on.
Move beyond archival 30 Hz test recordings to streaming PMU ingest from CAISO, ERCOT, or MISO. Deploy PHAETHON as a shadow analytic against 6–12 months of PMU archives; publish agreement and disagreement with the ISO's own stability studies. Requires a data-sharing MOU — a hyperscaler letter of support accelerates that measurably.
The three pre-registered falsifier sets — AEMO 2016, 2003 NE blackout, ERCOT 2023 — evaluated publicly against event data, whether they confirm or refute. Pre-registration with honest reporting is the strongest scientific-credibility signal available; a serious result on any of the three is a headline-grade outcome.
A quarterly index scoring the stability trajectory of every ISO on which hyperscaler datacenters have meaningful load. Delivered as a business-intelligence artifact for internal use — PPA renegotiation, siting decisions, 24×7 CFE strategy — backed by the WS 01–03 math. First release month six; recurring thereafter.
Scale: PI + one research engineer, 18-month runway. A phase-1 minimum viable version at $250K funds WS 04 alone as a hyperscaler-specific consulting engagement, seeded by the WS 03 event reconstruction as anchor case study.
The paper is deposited on Zenodo with a permanent DOI, including the LaTeX source, pre-registered falsifiers, and a self-contained numpy+scipy verifier that reproduces every headline number in one command. The live tool — the Rust API plus React frontend that produced the validation numbers — runs on request during a call.