Power Systems

Power systems encounter severe numerical challenges during stress conditions. Power flow Jacobians become ill-conditioned near voltage collapse, state estimators face rank deficiency with limited measurements, and weak grid analysis struggles with low short-circuit ratios as renewable penetration increases. Traditional approaches use continuation methods or heavy regularization, but these can mask exactly how close the system is to a stability boundary.

ZeroProofML addresses this by recognizing that power flow equations are fundamentally rational structures. Near voltage collapse, the system approaches a bifurcation point (the "nose" of the P-V curve) where the Jacobian determinant vanishes. Standard neural networks struggle to model this sharp turning point, often smoothing it out and overestimating the safety margin.

By using Signed Common Meadows (SCM), ZeroProofML allows neural surrogates to learn the exact rational topology of the grid physics. The Scale-Detached Gradient estimator enables the model to train stably right up to the collapse point, capturing the asymptotic behavior that defines the stability limit.

Potential applications:

• Voltage Stability Analysis: Train fast neural approximations of P-V curves that maintain accuracy through the nose point. This is critical for real-time margin assessment in control rooms.
• Weak Grid Studies: Model inverter interactions at connection points with low Short-Circuit Ratios (SCR), where the effective grid impedance creates a rational singularity.
• Contingency Screening: Improve N-1 analysis tools by maintaining convergence across wider operating ranges, reducing the number of cases that require manual review.
• State Estimation: Handle measurement configurations with redundancy issues without the arbitrary regularization that biases results.