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SIGMA · physics-informed reliability engine

Physics-informed fault
prediction for microgrids

SIGMA computes a real-time fault probability from power-quality signals and flags incipient faults ~12 seconds before onset. It is interpretable, sub-5 ms per window, and grounded in grid physics.

Published research, validated on a 12 V DC microgrid testbed and Pandapower simulations

Incipient faults hide below the threshold

Self-clearing arcing and resistive events precede permanent failures. They show up as brief voltage sags, current spikes, and harmonic bursts lasting only a few cycles — below the magnitudes that trip a conventional relay, so they go unseen.

Sub-threshold signatures

Incipient faults sit beneath protective settings. Relays designed to trip on large, sustained faults never see them coming.

Microgrids are dynamic

Renewable intermittency and nonlinear data-center loads make modern microgrids volatile, with fast power-quality swings that mask developing faults.

Protection is reactive

Traditional schemes act after a fault. Resilient operation needs proactive detection that recognizes the precursor signature in time.

The model

SIGMA sits between deterministic observers and opaque deep nets: a lightweight, interpretable logistic model that merges measurable physical indicators with probabilistic learning.

Five power-quality features

\(S_v\)
Voltage sag

Short RMS dips from arcing or partial shorts.

\(T_h\)
Total harmonic distortion

Arcing injects nonlinear harmonics; THD rises sharply.

\(P_f\)
Power-factor deviation

Arc or insulation faults shift the V–I phase angle.

\(\dot V\)
Rate of change of voltage

Highlights abrupt sags and recoveries.

\(\dot I\)
Rate of change of current

Captures the current spikes typical of arc ignition.

Fault-probability model

A logistic core maps the feature vector to a calibrated fault probability \(p(t)\) every sample.

$$p(t)=\sigma\!\big(\beta_0+\beta_1 S_v+\beta_2 T_h+\beta_3 P_f+\beta_4 \dot V+\beta_5 \dot I\big)$$ $$\sigma(z)=\frac{1}{1+e^{-z}}$$

Coefficients are constrained \(\beta_i \ge 0\) to enforce monotonicity: worse power quality always implies higher fault risk.

Regularized training

Parameters are learned by \(\ell_2\)-regularized maximum likelihood over labeled windows.

$$\min_{\beta_0,\,\boldsymbol{\beta}\ge 0}\; -\sum_t\big[y_t\ln p_t+(1-y_t)\ln(1-p_t)\big]+\lambda\lVert\boldsymbol{\beta}\rVert_2^2$$

A sliding window updates \(p(t)\) on every sample for continuous, online estimation.

State machine

The probability stream is classified into operating states that drive alerting.

NORMAL · \(p<0.45\) AHEAD · \(0.45\le p<0.85\) FAULT · \(p\ge 0.85\) RECOVERY

Probability rises smoothly in anticipation of a fault rather than spiking only after it occurs.

Kalman residual preprocessing

An optional extended Kalman filter models nominal feeder behavior; residuals emphasize deviations and suppress noise.

$$x_{k+1}=A x_k+B u_k,\qquad y_k=C x_k$$ $$r_k=y_k-\hat y_k$$

Residual filtering cut the false-alarm rate by roughly half in testing.

System architecture

A real-time pipeline from sensing and simulation through inference to alerting — benchmarked at under 5 ms per window.

sensors + Pandapower twin feature extraction logistic + Kalman state machine API + alerts

Sensing

Arduino + INA226 sensors sample \(V\), \(I\), power factor, and THD at 1 Hz on a 12 V DC microgrid testbed.

Digital twin

A Pandapower model generates labeled fault runs — line-to-line, line-to-ground, overload, and harmonic distortion.

Inference

Logistic core with optional EKF preprocessing, on rolling 30 s windows, at under 5 ms latency per window.

Serving

Python 3.11, FastAPI, TimescaleDB, and a Streamlit dashboard — output routes into existing monitoring with no new hardware.

Measured results

On a 12 V DC microgrid testbed and Pandapower digital-twin simulations, leave-one-run-out cross-validation.

~12 s

lead time before onset

>93%

average detection rate

0.96

ROC AUC

<5 ms

inference per window

Fault type Lead time (s) Detection (%) False alarms (/h)
Voltage sag 12.4 95 0.09
Overload 11.8 92 0.10
Line-to-line / line-to-ground 13.1 94 0.08

Kalman preprocessing reduced the false-alarm rate by roughly 50%, and probability output rose smoothly in anticipation of each event — prognostic, not reactive.

Published research

PHYSICS-INFORMED AI · RELIABILITY MODELING

SIGMA: A Physics-Informed AI Framework for Predictive Fault Probability Modeling in Microgrids

R. Monemi and S. Monemi · Electrical and Computer Engineering

SIGMA (Smart Infrastructure Grid Monitoring AI) computes a real-time fault probability from power-quality features using a logistic core and sliding windows, with an optional Kalman filter for noise rejection. The approach bridges classical reliability analysis and modern AI-based predictive maintenance.

smart grids fault prediction physics-informed AI Pandapower reliability modeling
Read the paper (PDF)

Where it goes next

Ensemble models and adaptive online learning — recursive Bayesian updating — for robustness across operating conditions.

Distributed implementation for multi-node, grid-scale microgrids.

Extension to AI data centers and industrial facilities, where nonlinear loads and the cost of a missed fault are highest.

About the creator

Ryan Monemi

Ryan Monemi

Engineer at SKM Systems Analysis · M.S. candidate

Built by one man. He designed the physics-informed model, the simulation and sensing pipeline, and the real-time serving layer that connects them, and is lead author of the paper behind it, “SIGMA: A Physics-Informed AI Framework for Predictive Fault Probability Modeling in Microgrids” (R. Monemi and S. Monemi).

At SKM Systems Analysis he validates PTW and PTX power studies. He holds a B.S. in Electrical and Computer Engineering and previously designed electric-distribution infrastructure for SDG&E and for SpaceX propellant generation.

Get in touch

If you work on microgrids, power-system protection, or data-center power and want to talk about SIGMA, reach out directly.

founder@monegrid.com