Source-linked AI summary
State Estimation as In-context Tabular Prediction
Ayushi Jolotia, Parikshit Pareek
TL;DR
WLS depends on Gaussian measurement errors and observability, while learned estimators can require retraining for changes in network, measurement configuration, or topology. ICTP uses historical measurement and state pairs as context for pretrained tabular foundation models, whose weights remain fixed while predicting a state from a new measurement query. ICTP returned a full state vector at every level and stayed below the context mean; with six buses biased by 8σ, angle error rose 1.8 to 5× for ICTP versus 2.5 to 12.7× for WLS.
Problem
WLS depends on Gaussian measurement errors and observability, while learned estimators can require retraining for changes in network, measurement configuration, or topology.
Source: §I · p. 1, §III · p. 3Method
ICTP uses historical measurement and state pairs as context for pretrained tabular foundation models, whose weights remain fixed while predicting a state from a new measurement query.
Source: §II · pp. 1–2Results
ICTP returned a full state vector at every level and stayed below the context mean; with six buses biased by 8σ, angle error rose 1.8 to 5× for ICTP versus 2.5 to 12.7× for WLS.
Source: §III · pp. 2–3Takeaways & Limitations
Across the tested measurement levels, ICTP provides estimates when WLS may return none or exceed the context mean, and degrades less than WLS under injected bias.
Source: §III · pp. 2–3, §IV · p. 3
Abstract
from arXiv · showhide
This letter poses state estimation (SE) as an in-context tabular prediction (ICTP) problem. The key idea is a tabular arrangement in which historical measurement vectors and corresponding state estimates serve as the context, and a new measurement vector forms the query for which we predict a state vector. We propose to use tabular foundation models (TFMs), pretrained on synthetic data, whose weights are never updated, so power system data is needed only as context. With frozen TFM weights we estimate the state of 14-, 30-, 33-, 70-, and 118-bus transmission and distribution networks, and do so where weighted least squares (WLS) fails or degrades, under low observability and with bad data. ICTP errors are 11 to 57$\times$ below the per-bus average of the context at full metering, and 1.3 to 4.0$\times$ below it with only 5% of measurements available. With measurements at six buses biased by 8$\sigma$, the ICTP angle error rises 1.8 to 5.0$\times$ over its bias-free value against 2.5 to 12.7$\times$ for WLS with bad-data detection. Without retraining, ICTP has lower voltage error than DSS$^2$ on both of its feeders, and lower than a retrained TAPINE on two of three reconfiguration sets.
I. INTRODUCTION
WLS can fail when measurements are non-Gaussian or the system is unobservable, while learned estimators often require network-specific retraining. The paper proposes in-context tabular prediction to address these limitations using pretrained tabular foundation models.
I. INTRODUCTION
- WLS assumes Gaussian errors and observability, conditions that can fail with gross meter errors or meters lost to outages and communication failures.A gross error at a leverage point can pull the estimate onto itself and escape residual-based detection.Source: §I · p. 1
- DSS2 and TAPINE are learned estimators mapping measurements to states from historical data, and both require network-specific retraining when the network, measurement configuration, or topology changes,.Source: §I · p. 1
- ICTP uses historical measurements and estimated states as context so pretrained tabular foundation models can predict a new query without network-specific training.The TFMs are pretrained on synthetic tables and learn relationships between columns and targets,.Source: §I · p. 1
- ICTP returns a full state vector at every tested measurement level; on the 118-bus system, WLS returns no estimate once half the meters are gone, despite 362 readings for 235 states.Across the dark-bus sweep, ICTP angle error grows at most 4.4× over its full-metering value on all three networks.Source: §I · p. 1
II. PROPOSED IN-CONTEXT STATE ESTIMATION
ICTP casts state estimation as tabular prediction: historical measurement snapshots and their state estimates form the context, and current measurements form the query. Pretrained TFM weights remain fixed; network connectivity is used afterward to recover absolute angles.
II. PROPOSED IN-CONTEXT STATE ESTIMATION
- WLS solves for the state by iteratively minimizing weighted residuals, but its normal equations become singular when the measurement Jacobian loses full column rank.Having at least as many measurements as states is necessary but not sufficient for observability.Source: §II · p. 1
- ICTP uses historical measurement snapshots and corresponding state estimates as context, then predicts a state vector for a new measurement query.The input columns are noisy voltage magnitudes, bus injections, and from-end branch flows; targets are bus voltage magnitudes and line angle differences.Source: §II · p. 1, Figure 1 · p. 2
- With pretrained parameters held fixed, the TFM predicts target values from the context and query without using the measurement Jacobian, admittance matrix, or network connectivity.The same weights serve any network; connectivity is used afterward to recover absolute angles from predicted differences through a linear least-squares solve with the slack angle fixed.Source: §II · pp. 1–2
III. RESULTS AND DISCUSSIONS
Across meter-loss, noise, and bad-data tests, ICTP returns state estimates where WLS may fail and often beats the context-mean baseline. The comparisons also test ICTP against learned estimators on distribution feeders and reconfigured topologies.
Meter loss
- ICTP stayed below the context mean by 11 to 57× at full metering and 1.3 to 4.0× at 5% metering; injection thinning changed its angle error by at most 0.006°.WLS returned no estimate at some low-metering levels; the 33-bus case became unobservable after a single dark bus.Source: Figure 2 · p. 2, §III · p. 2
Measurement-type thinning
- Losing flow meters to 5% raised 118-bus WLS angle error 7.7× to 0.249°, while losing injection meters to 5% raised it 1.6× to 0.051°.Thinning any single measurement type reduced accuracy, but H remained full rank at every tested level.Source: §III · p. 2
WLS and context-based baselines
- At full metering, ICTP voltage error was 0.69 to 1.05× WLS and angle error 1.46 to 2.03×; both ratios moved in ICTP’s favor as measurements fell.At 500 context rows, ridge regression was competitive on voltage, while at 50 rows TabPFN was 4.3× better on voltage and 7.3× better on angle on the 118-bus system.Source: §III · pp. 2–3
Noise and bad data
- With six buses biased by 8σ, WLS angle error rose 2.5 to 12.7× versus 1.8 to 5× for ICTP, while raised noise increased errors similarly across methods.Under raised noise, voltage errors rose 1.8 to 3.1× and angle errors 2.0 to 2.7× against each method’s base-noise result.Source: Figure 3 · p. 3, §III · p. 3
Learned-estimator comparison
- On both TU-Delft feeders, TabPFN and TabICL had lower voltage error than DSS2 and WLS on the 1080-snapshot test file.WLS converged on only 501 of 1080 snapshots on the 70-bus feeder, despite a full-rank H.Source: Figure 4 · p. 3, §III · p. 3
Feeder reconfiguration
- Across reconfiguration sets T1–T3, ICTP voltage MAPE stayed within 0.358 to 0.421 [10−2 %] and was below retrained TAPINE on T2 and T3.ICTP used 500 WLS-estimated context labels per topology and required no weight update.Source: Figure 5 · p. 3
IV. CONCLUSION
Across three stress tests, ICTP returned full state vectors and stayed below the context mean, while WLS could return nothing or exceed that mean when rank fell short. ICTP also degraded less than WLS under injected bias and matched or beat published learned estimators on their benchmarks without retraining.
IV. CONCLUSION
- Across three stress tests, ICTP returned full state vectors and stayed below context mean, while WLS sometimes returned nothing or exceeded context mean when rank fell short.The measurement count and WLS bad-data checks did not reveal rank loss.Source: §IV · p. 3
- Under injected bias, ICTP degraded less than WLS with bad-data detection and reached or beat two published learned estimators on their benchmarks without retraining.The comparisons cover the learned estimators on their own benchmarks.Source: §IV · p. 3
- Past measurements and their state estimates form ICTP context, and a new measurement vector is the query for predicting the state.Source: §IV · p. 3
- On the 118-bus system, 100 ICTP estimations cost 239 to 393 s, compared with 81 s for WLS.Reducing the per-target loop is left to future work.Source: §IV · p. 3