Transformer winding hot-spot estimation and dynamic loading envelopes, from three signals a utility already logs.
Load current, ambient temperature, top-oil temperature. From those plus a handful of hot-spot calibration reads, CoreField identifies the four IEC 60076-7 thermal parameters (Δθ_or, τ_o, Δθ_hr, τ_w) for a specific unit, then runs the identified model in service to answer the question that carries commercial value: how much extra load can this transformer carry, and for how long?
Those four parameters are the ones the standard says can otherwise only be obtained from a prolonged heat-run test on a transformer fitted with fibre-optic sensors.
This is a complement to that test, not a replacement for it. For a new transformer the heat-run is part of procurement verification and characterises the unit as built. What it cannot do is follow what the unit has become after twenty years of service, and it was never performed at all on most of the installed fleet. Those two cases — the aged unit and the undocumented one — are what this addresses. The framing was corrected on the advice of a reviewer who builds thermal models for a transmission operator; the earlier "replaces the heat-run test" was overreach.
1. IEC 60076-7 provenance. The two-exponential structure and the ONAF constants were checked against the published text of IEC 60076-7:2018 Edition 2.0 on 25 Aug 2026 and match it — all five cooling-class constants, both tabulated time constants, and the assignment of each time constant to its branch. Three numerical checks in
corefield.verificationconfirm that assignment independently of any document.This repository reproduces no text, table or figure from the standard. IEC standards are copyrighted and sold. If you claim standards compliance, hold your own copy from an authorised distributor — the constants here are used as engineering facts, not as a substitute for it.
2. Field validation: none. Every number in this repository was produced from synthetic data. No measurement from a real transformer has ever entered it. See Limitations — that section is not softened, and should not be.
Three model structures were fitted on the same ordinary day (0.6–1.2 pu), then asked about a 2-hour emergency overload at 1.30 pu — outside the load range they were fitted over.
| Model | Structure | RMSE | Worst-case peak error at 1.30 pu | Verdict |
|---|---|---|---|---|
| A | single-exponential, K² drive | 2.59 K | +6.17 K | FAIL |
| B | single-exponential, free exponent | 1.77 K | +3.17 K | FAIL |
| C | IEC two-exponential | 0.11 K | +0.32 K | PASS |
This separation belongs to ON.. cooling classes, where k21 = 2.0 gives the winding a
transient overshoot that only a two-exponential model can follow. For directed-flow (OD/ODAF)
units the standard sets k21 = 1.0: the slow branch vanishes, the overshoot with it, and the
three models converge. Do not quote this table for a directed-flow transformer.
Models A and B read the hot spot several kelvin high at high load — triggering derating exactly when spare capacity is worth the most. That is the commercial argument, and it is why the production engine is classical nonlinear least squares on the IEC two-exponential structure rather than anything more fashionable.
Two things make this table stronger than it looks. Models A and B were driven by the
noise-free top-oil signal while Model C had to fit a noisy one — the comparison is
handicapped in their favour and they still fail. And every value is re-derived on every test
run rather than quoted: python -m pytest reproduces the whole campaign in about 17 seconds.
pip install -e .python -m pytestGet a blank telemetry file to hand to a site engineer:
corefield --template site_A.csvCheck whether a filled-in record can support a fit — before fitting anything:
corefield validate site_A.csvRun the demo:
pip install -e ".[app]"streamlit run app/streamlit_app.py --server.address localhost--server.address localhost is not optional housekeeping. Streamlit binds to all interfaces by
default and prints an external URL, which on a laptop sharing a conference or client network
means anyone on it can open your demo — including whatever telemetry you last uploaded. Bind to
localhost unless you have deliberately decided otherwise.
from corefield.ingest import load_telemetry
from corefield.estimator import identify
from corefield.envelope import LoadingLimits, loading_envelope
from corefield.iec60076_7 import InitialState
frame = load_telemetry("site_A.csv")
print(frame.report.report()) # the gate: sampling, coverage, load hull, load events
frame.require_fittable() # refuses records that cannot determine four parameters
result = identify(
frame.time_s, frame.load_pu, frame.ambient_C, frame.top_oil_C, frame.hotspot_refs
)
print(result.report())
limits = LoadingLimits(
hotspot_limit_C=..., # from YOUR licensed copy of the standard
top_oil_limit_C=...,
label="normal cyclic loading, medium power",
source="IEC 60076-7:2018 Table N, licensed copy, checked 2026-08-24 by AB",
)
envelope = loading_envelope(
result.params, limits, ambient_C=30.0, duration_h=2.0,
initial_state=InitialState(top_oil_C=70.0, prior_load_pu=0.9),
nameplate_MVA=63.0,
)
print(envelope.summary())These are design decisions, not gaps.
It will not fit without ambient. Ignoring a varying ambient under-predicts the hot-spot peak
by 3.09 K — in the dangerous direction, because the ambient maximum coincides with the
afternoon load peak. load_telemetry raises AmbientMissingError rather than warning. The fix
is cheap: ambient reaches the winding through a ~75-minute oil low-pass, so an hourly public
weather feed is sufficient.
It will not supply loading limits. LoadingLimits has no defaults and
iec_loading_limits() exists only to raise NotImplementedError explaining why. This is
unchanged by the constants having been checked: verifying Table 4's thermal characteristics
says nothing about the permissible temperature limits, which are a different table and were
deliberately not read. More importantly, the limits decide the temperature at which this
software tells an operator it is safe to overload a transformer, and they vary with loading type,
transformer category and each utility's own policy. That number must be owned by the person
relying on it. You supply the limits and a provenance string, and that string travels into every
result.
It will not return a railed fit. If every optimiser start converges onto a bound,
identify raises rather than returning the best of a bad set. A solution pinned to a bound is an
optimiser artifact that a caller cannot distinguish from a measurement. During this project's
history an independent implementation railed its optimiser in 9 of 9 runs and reported the result
as evidence of an identifiability problem in the physics; it was an implementation failure.
It will not interpolate observations. Load and ambient are model inputs and are interpolated onto the integration grid. Top-oil is an observation and is not — interpolating it would invent measurements and correlate their noise, making the residual RMSE flatter than the data earns.
It contains no neural networks. That is a result, not a preference: see the table above, and WITHDRAWN.md for the geometry-PINN branch that was retracted.
Efficiency. On the IEC two-exponential structure, the four-parameter estimator is unbiased to better than 0.12 % and sits on the Cramér–Rao bound — 0.97 / 1.01 / 0.95 / 0.97× the folded-Gaussian expectation at 400 seeds. No estimator, classical or learned, can do materially better on this data.
Commissioning. The bound is a property of the record, not the method, so it yields an actionable spec. One load event leaves a ~12 % floor under τ_w that nothing can beat; two events drop it to ~4 %. Commission over at least two load events. Take calibration reads at 3, 8, 18 and 48 minutes after each load change, plus one after ~4 h of steady load — the first three carry the rate, the 48-minute point anchors the amplitude, and sampling a transient without anchoring its own asymptote leaves the two correlated.
Sampling rate. Load sampling dominates; oil sampling barely matters. τ_w error is +2.1 % with 1-minute load logging and +8.4 % with 5-minute — the ~90-second load ramps get aliased. Insist on 1-minute load current; 5-minute top-oil is fine.
The quiet failure modes are the dangerous ones. Telemetry spikes and integer-degree quantisation cost nothing — a dense oil channel drowns them. Slow sensor drift and systematic calibration bias are invisible on any plot and poison the parameters while the trajectory still passes its gate. A winding-temperature-indicator replica reading +3 K high produces an engine that looks perfectly calibrated against that replica while carrying +14.5 % on Δθ_hr and +4.1 K at the true peak — and it distorts the dynamics, not just the level, so a "relative trends only" positioning does not escape it. Commissioning requires at least one bias-audited hot-spot reference per unit.
Hot-spot location is not observable from outside. Top-oil is exactly invariant to where in the winding the hot spot sits — moving it from 10 % to 90 % of winding height changes the reading by 0.0000000 K, because every external measurement is a function of total winding loss and location changes only its distribution. The Cramér–Rao bound on location from every external channel combined is ±40 % of winding height; two probes inside the winding give ±0.33 %. See ASSESSMENT.md; this is why the package has no field-reconstruction module.
Read this section before quoting anything from this repository.
- Everything here is synthetic. There is no field validation whatsoever. Every parameter recovery, every RMSE, every gate verdict was computed against a truth model this package also generated. The estimator has never seen a real transformer.
- Model C is structure-matched to the synthetic truth. The mismatch test killed models A and B; it did not test C. The day-C result certifies parameter-error propagation under extrapolation — it does not certify structural risk on a real unit whose physics may differ from the standard's.
- One synthetic unit. A single illustrative ONAF-scale parameter set. No unit-to-unit spread, no cooling-class variation beyond a constants swap, no ageing.
- IEC text is mirror-sourced and unverified (see the banner above).
- Corruption magnitudes are plausible instrument bounds, not measured values. Drift, spike rate, CT gain error and calibration bias were chosen as engineering estimates.
- The uncertainty band covers parameter error only. It excludes model structural error and ambient/load forecast error, and it is drawn from the Cramér–Rao bound, which is a lower bound on estimator covariance. True uncertainty is larger than reported.
- WTI bias was tested as a constant offset. Gain-type or load-dependent replica error is untested.
- The observability analysis in
corefield.observabilityuses a simplified 1-D axial model with a prescribed oil-rise profile, not CFD. Its leading-order conclusion follows from energy conservation and is robust to that simplicity; its second-order magnitudes are not.
| File | What it holds |
|---|---|
| REPRODUCTION.md | Which published numbers reproduce, which do not, and why |
| ASSESSMENT.md | Prior-art review, and why 2D/3D field reconstruction was not built |
| EVIDENCE.md | (a)/(b)/(c) label index for every claim in this README |
| PREDICTIONS.md | Pre-registered prediction ledger, misses kept |
| WITHDRAWN.md | The retracted geometry-PINN branch and its mesh-convergence failure |
docs/ |
Figures, regenerated from the package by python scripts/make_readme_figures.py |
Python 3.11+, NumPy, SciPy, pandas. CPU-only — measured at 137 MiB peak resident memory for the full campaign, against a 2 GB budget. No GPU, no network, no paid services. The demo adds Streamlit and Matplotlib.
Code — Apache License 2.0. See LICENSE. Apache-2.0 rather than MIT for its explicit patent grant and its requirement that modifications be marked; both matter for engineering software that may end up in a regulated decision path.
Documentation — Creative Commons Attribution 4.0 International. See LICENSE-docs. The prose files carry the evidence and the retractions, and CC BY lets them be quoted and built on with attribution intact.
See NOTICE for the attribution notice, the split between the two licences, and two things the licences do not cover: no IEC standard text is redistributed here, and nothing in this repository has been validated against a real transformer. Loading decisions on electrical plant carry safety and asset consequences; this software must not be the sole basis for one.