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title: Eigenvalue early warning for power grid stability — the physical basis AI transfer-learning models learn to detect
emoji: 📚
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license: mit
short_description: Eigenvalue early warning for power grid stability — the phys
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Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference

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**TaiScience CSD-EWS** is an educational simulator for *critical slowing down* (CSD) as an early-warning signal in power grid stability. It visualizes how system eigenvalues (poles) approach the stability boundary, using a Jacobian eigenvalue proxy and damping-ratio thresholds.

This work is part of the TokaMind transfer-learning framework, which adapts a tokamak-plasma foundation model to power-grid dynamics. While Microsoft's GridSFM addresses static AC-OPF feasibility, this system targets *dynamic* CSD precursors — complementary directions for grid security analysis, relevant to cascading-failure events such as the 2025 Iberian blackout and the 2016 South Australia blackout.

## What It Shows

- **Complex s-plane map** — conjugate pole pair (s = σ ± jω) with real-time position relative to the stability boundary (Re = 0)
- **Damping ratio** — ζ = −σ / √(σ² + ω²), with a 5% threshold separating adequate damping from warning and danger zones
- **Time-domain response** — illustrative y(t) = e^(σt)·cos(ωt) showing how a near-critical mode decays or diverges

## Core Concept

Critical slowing down is a generic precursor to instability across dynamical systems: as a control parameter pushes a system toward a bifurcation, its dominant eigenvalue's real part approaches zero, recovery from perturbations slows, and damping collapses. In power systems, detecting this slowing *before* a mode crosses into the right-half plane provides an early-warning window for operators.

The full CSD detection pipeline (time-domain Jacobian proxy + spectral LFPR engine) is released as open source:
https://github.com/chihsingwu/CSD-dual-engine

## Use Case

Teaching and intuition-building for power-system stability monitoring, transient stability assessment (TSA), and PMU-based early-warning research. This page is a manual teaching demo — not a live PMU or Toeplitz identification system. The waveform shows e^(σt)·cos(ωt) only, without modal amplitude or phase.

## Related Work

- TaiScience Research Group (Fu Jen Catholic University): https://taiscience.org
- StromaPath platform: https://stromapath.com
- TokaMind PMU transfer-learning preprint: https://arxiv.org/abs/2605.11033
- CSD dual-engine (open source): https://github.com/chihsingwu/CSD-dual-engine

## Keywords

`critical slowing down` · `power grid early warning system` · `Jacobian eigenvalue proxy` · `damping ratio monitoring` · `transient stability assessment` · `PMU` · `TokaMind transfer learning` · `s-plane pole map`