Data-Driven Generator Transient Prediction for Digital Twin Decision Support

Emad Sadeghi; Emerson Miller; Kerry Sado; Adel Nasiri

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Data-Driven Generator Transient Prediction for Digital Twin Decision Support

Emad Sadeghi, Emerson Miller, Kerry Sado, Adel Nasiri

arXiv:2609.05356v1Sep 4, 2026eess.SYeess.SP

TL;DR

Generator digital twins need fast forecasts of whether planned active- and reactive-power commands will keep voltage and frequency within acceptable limits. The paper develops an event-conditioned Hankel-DMDc surrogate with conformal joint prediction bands, achieving near-nominal coverage, transient-focused accuracy, and rapid open-loop rollout on a generator testbed.

Problem
Generator digital-twin forecasting must balance transient fidelity, computational efficiency, and calibrated uncertainty when screening planned load commands.
Method
The paper combines delay-coordinate lifting, command-event features, an event-weighted Hankel basis, and event-conditioned joint conformal calibration around a frozen surrogate.
Results
90.17% pointwise joint voltage-frequency coverage was achieved for a nominal 90% target, with event-window RMSE of 1.058 V and 0.155 Hz.
Takeaways & Limitations
The framework supports operator-facing screening of candidate load commands with calibrated voltage/frequency uncertainty and rapid open-loop scenario evaluation.
Takeaways & Limitations
Evaluation is limited to data from the same physical generator, despite using a separate held-out test set.

Abstract

from arXiv · show

This paper develops a calibrated transient forecasting surrogate model for generator digital twin (DT) decision support that evaluates planned active- and reactive power load commands before they are applied. The proposed event-conditioned Hankel Dynamic Mode Decomposition with Control (Hankel-DMDc) model combines delay-coordinate lifting, command-event memory features, and an event-weighted Hankel basis so that sparse load-transition dynamics influence the reduced representation and fitted dynamics. This design targets intervals where voltage/frequency deviations and recovery behavior determine whether a candidate load command keeps the system within acceptable limits. To provide operator-facing confidence information, a split-conformal calibration layer is applied to the frozen surrogate model to form event-conditioned joint prediction bands for voltage and frequency. The experimental results show event-window root-mean-square errors of 1.058 V and 0.155 Hz. For a nominal 90% target, the bands attain 90.17% pointwise joint voltage-frequency coverage, with mean band widths of 3.55 V and 0.566 Hz. A 50-s open-loop rollout is computed in 181 ms on a single CPU core, approximately 280 times faster than real time, with forecast accuracy evaluated over horizons up to 5 s. These results demonstrate a computationally efficient advisory framework for generator DTs that combines transient prediction with calibrated uncertainty.

I. INTRODUCTION

The paper targets fast, data-driven generator transient forecasting for digital-twin decision support, where planned load commands must be screened against voltage and frequency limits. It combines event-sensitive Hankel-DMDc modeling with calibrated joint uncertainty to emphasize sparse operationally important transients.

Motivation: Generator digital twins can forecast whether planned load commands will violate voltage and frequency limits before application, especially in islanded or weak-grid systems.Exceeding operating limits can trigger protection or control actions that disconnect equipment and interrupt critical loads.
Motivation: Physics-based models offer high fidelity, but incomplete parameters, unmeasured states, proprietary controls, aging, and computational cost can limit operational digital-twin use.These constraints motivate complementary data-driven surrogates that learn predictive dynamics from operating data while remaining computationally efficient.
Motivation: Load steps and pulses occupy a small fraction of measured data yet determine voltage/frequency deviations, recovery rates, and margins for keeping converters online.Unweighted identification can therefore be dominated by steady-state behavior rather than transient performance.
Contributions: The proposed framework combines command-event memory, an event-weighted Hankel basis, transient-sensitive model selection, and event-conditioned joint conformal bands.The bands provide simultaneous uncertainty estimates for voltage and frequency in operator-facing decision support.
Related work: Existing generator-transient approaches leave practical data-driven solutions for fast and reliable look-ahead prediction limited by the tradeoff among detail, data dependence, and computational cost.The paper positions its hardware-validated surrogate as a balance between computational efficiency and transient-event accuracy.

III. EVENT-CONDITIONED SURROGATE MODEL

The event-conditioned surrogate forecasts terminal voltage and frequency from recent measurements and planned load commands. Delay-coordinate lifting supplies measured memory, while per-event rollout evaluation isolates the transient windows the model is designed to predict.

Forecasting workflow: The forecasting stage combines recent terminal measurements with planned load-command trajectories to generate open-loop voltage and frequency forecasts.A frozen surrogate is later used for joint conformal-band calibration.
Command-conditioned forecasting: The future command sequence defines the operator-selected scenario, and the model returns the corresponding open-loop voltage and frequency response.The command sequence covers both the recent history and the prediction horizon.
Evaluation: Per-event look-ahead forecasts restart at each detected event and propagate over a fixed horizon, isolating transient windows from steady-state-dominated full-record evaluation.A horizon of Hs seconds corresponds to H = ⌊Hs/∆t⌋ samples.
Hankel lifting: Delay coordinates use recent measurement histories to construct a richer representation of latent dynamics than a single voltage/frequency sample provides.The Hankel window preserves measured memory for dynamics that are not directly observed.

C. Event-Aware Command Features

The command-feature design encodes recent load-change history rather than relying only on instantaneous power levels. Exponentially decaying memory channels and a strided lag window represent fast-to-slow transient and recovery behavior compactly.

Event representation: Transient response depends on the sign, magnitude, and timing of recent command changes, not only instantaneous power levels.The feature construction therefore augments command values with explicit event information.
Event memory: Exponentially decaying memory channels separate initial transient response from slower recovery dynamics across fast-to-slow time constants.Each channel maintains an event-memory state with a corresponding decay factor.
Lagged features: The standardized event features are stacked over a strided lag set to form a compact command-feature vector aligned with the corresponding output Hankel row.This provides recent command activity without requiring future measurements.
Workflow: The Hankel observable supplies measured memory, while the command-feature vector supplies recent command activity for the controlled reduced model.Together they support command-conditioned rollout of the reduced dynamics.

D. Event-Weighted Hankel Basis

The event-weighted Hankel basis modifies offline subspace identification so sparse command transitions and output transients influence the reduced representation. Its weighting emphasizes windows where command changes, transient outputs, and voltage sags coincide while capping amplification.

Motivation: An unweighted Hankel SVD optimizes average reconstruction, but average reconstruction error does not necessarily reflect transient fidelity.The method therefore replaces the standard basis construction with an event-weighted matrix.
Workflow: The deterministic surrogate projects measured voltage/frequency history onto an event-weighted reduced coordinate before rolling out under planned commands and event-memory features.This workflow connects Hankel lifting, weighted reduction, and command-conditioned forecasting.
Weighted basis: The event-weighted basis emphasizes Hankel rows near command transitions and voltage/frequency deviations during offline subspace identification.Online prediction still uses only the measured delay window and planned command profile.
Weight construction: Rows receive the largest emphasis when command changes, output transients, and voltage sags occur together.The cap wmax limits this amplification.

E. Controlled Reduced-Order Evolution

The reduced-order model identifies controlled dynamics from weighted reduced coordinates and command features, then uses a fixed online projection for open-loop forecasting. Stability projection bounds recursive rollouts.

Controlled reduced-order identification: The model identifies A and B from consecutive reduced-state pairs and command-feature vectors using weighted ridge regression.X+ supplies next-step reduced states, while Θ contains current reduced states and corresponding command features.
Controlled reduced-order identification: The same event-sensitive weights shape both the reduced basis and the fitted reduced dynamics.The diagonal regression weight matrix is formed from the weights used during weighted SVD basis construction.
Stability projection: The stability projection maps eigenvalues outside the unit circle to a fixed radius ρ < 1 while preserving their complex arguments.Complex-conjugate pairs are adjusted together so the projected matrix remains real and recursive rollouts stay bounded.
Online forecasting: Online encoding projects the latest measured delay window onto the retained right-singular subspace rather than applying the offline output-dependent weighting.The same encoder is used for tuning, calibration, and testing, and rollout propagates the reduced state under planned command features.

F. Transient-Aware Model Selection

The forecasting procedure selects model order and regularization with a transient-aware criterion, then performs offline identification and online open-loop rollout using commanded P/Q trajectories.

Transient-aware model selection: The transient-aware tuning loss balances global, event-weighted, peak-weighted, and derivative errors for voltage and frequency.This criterion emphasizes command-transition accuracy, large excursions, and response shape rather than steady-state tracking alone.
Experimental setup: The experimental testbed uses a synchronous generator, programmable EGSTON loading, and OPAL-RT commands and terminal-data recording.The setup supports active- and reactive-power command trajectories for transient forecasting.
Offline identification and online forecast: Algorithm 1 preprocesses signals, builds command-event features and event-memory channels, forms weighted Hankel windows, and fits the reduced model.The offline procedure selects q, r, and λ on a tuning interval before online forecasting.
Offline identification and online forecast: The online forecast initializes from a pre-event window and recursively advances the reduced state under planned command features.The procedure outputs an open-loop look-ahead forecast over horizon H.

B. Normalized Coordinates and Preprocessing

The preprocessing pipeline converts measured generator signals and commanded powers into causal, normalized coordinates for identification and calibration while retaining relevant low-inertia dynamics.

Signal preprocessing: Raw electrical channels are filtered and downsampled from 2000 Hz to a 200 Hz model update rate with Δt = 0.005 s.Voltage uses a three-cycle RMS estimate, while frequency is estimated with a 5-Hz-bandwidth PLL.
Signal preprocessing: Filtering suppresses estimator ripple and high-frequency artifacts while retaining approximately 3 V and 0.5 Hz low-frequency oscillations from generator dynamics.The oscillations are attributed to the low-inertia, engine-speed-governed generator rather than the measurement chain.
Normalized coordinates: The measured voltage, frequency, and commanded active and reactive powers are expressed in normalized coordinates using Vnom = 277 V, fnom = 60 Hz, and Sbase = 225 kVA.Errors are later reported in engineering units so predictions remain interpretable as volts and hertz.
Online realizability: All preprocessing stages are causal, adding about 100 ms of group delay and enabling online realization without future samples.The delay is dominated by the three-cycle RMS estimate and frequency and target low-pass filters.
Data partitioning and evaluation: Identification, tuning, calibration, and held-out testing use temporally separated intervals, with testing performed on a separate experimental run containing 96 events.The same event labels are used for conformal direction stratification.

V. DETERMINISTIC PREDICTION RESULTS

The selected reduced model uses a long Hankel window and elevated rank to retain transient structure, and its accuracy is assessed across full-record and per-event measures on held-out data.

Model-order selection: q = 520 samples, r = 100, and λ = 1 were selected by the transient-aware tuning loss.The selected point lies at the longest-window, highest-rank corner of the tested grid, whose loss surface varies by less than 3%.
Hankel diagnostic: Ranks 15 and 45 capture 90% and 99% of Hankel singular-value energy, while r = 100 retains additional capacity for sparse transient components.The effective rank is 15.85 and stable rank is 5.14, indicating compact delay-coordinate structure with a non-negligible tail.
Deterministic prediction accuracy: The evaluation emphasizes event-weighted and per-event errors alongside peak-weighted, derivative, and nadir metrics for screening voltage and frequency limits.Global RMSE mainly reflects steady tracking because long steady intervals dominate the load profile.
Deterministic prediction accuracy: Accuracy remains consistent across training, combined validation and calibration, and the held-out test interval.The held-out evaluation includes a separate experimental run and a representative one-minute segment.

C. Look-Ahead Accuracy by Horizon

Held-out horizon evaluation emphasizes transient-focused accuracy and event-conditioned uncertainty calibration. The model’s prediction bands are constructed from held-out residuals using command-event context while preserving the deterministic point forecast.

Look-Ahead Accuracy by Horizon: Event features reduce per-event voltage RMSE from 1.077 V to 0.967 V relative to the same-preprocessing no-event model.The event-weighted basis does not reduce per-event window RMSE beyond the features-only model, but it improves voltage-nadir fidelity.
Look-Ahead Accuracy by Horizon: Event-conditioned split-conformal calibration uses held-out residuals to adapt joint voltage/frequency band widths to event magnitude, phase, and direction.Calibration modifies the prediction bands after the deterministic surrogate has been selected and frozen, not the point forecast.
Look-Ahead Accuracy by Horizon: The calibration context uses active/reactive event direction and phase, with finer pools backing off to coarser pools when calibration support is sparse.The fallback hierarchy selects the most specific supported calibration pool for each band.
Look-Ahead Accuracy by Horizon: Joint calibration counts a sample as covered only when both voltage and frequency lie inside their intervals at the same instant.The resulting coverage is pointwise rather than containment of an entire event trajectory.

C. Held-Out Coverage Results

Held-out conformal bands achieve coverage close to the nominal target while adapting across command-event phases and types. Coverage is strongest immediately after events and somewhat lower during later recovery, with one sparsely supported event type under target.

Held-Out Coverage Results: 90.17% pointwise joint coverage is achieved on held-out test data against a 90% nominal target.Event-weighted joint coverage is similarly close at 90.08%.
Held-Out Coverage Results: 3.55 V and 0.566 Hz are the mean held-out band widths for voltage and frequency.The reported empirical coverage results are carried by the calibration and held-out test rows, not the diagnostic training row.
Held-Out Coverage Results: Held-out coverage is at or above target immediately after command events, when the bands are widest, and slightly lower during later recovery as bands narrow.The phase-resolved result links wider intervals with the immediate post-event response and narrower intervals with recovery.
Held-Out Coverage Results: Figure 7 organizes representative held-out events by four joint command-event types, with commanded P/Q changes, voltage, and frequency shown across columns.The middle and right panels compare measured and predicted voltage and frequency with conformal bands.
Held-Out Coverage Results: The (P shed, Q step) event type has the lowest joint coverage at 83.12%.It also has the fewest test events and narrowest bands, making limited calibration support the most consistent explanation offered.

VII. DISCUSSION AND DEPLOYMENT SCOPE

The event-conditioned surrogate provides fast forecasting with calibrated voltage/frequency uncertainty, but its deployment scope is bounded by testbed coverage, forecast assumptions, and advisory use.

Computational deployment: 181 ms computes a 50-s forecast on one CPU core, approximately 280 times faster than real time, supporting online screening.The model uses about 15 MB of memory; offline basis construction is the primary computational cost.
Validation scope: The evaluation uses the same physical generator across separate experimental runs, demonstrating transfer to a new operating profile but not cross-asset generalization.The stated boundary includes different generators, controllers, sensor chains, and load magnitudes.
Forecast limitations: Open-loop forecast error can accumulate with horizon, so operational use should consider calibrated bands rather than the point forecast alone.The method assumes the future command is known, so the bands quantify residual model error under calibrated command and state contexts.
Measurement and dynamics: Approximately 3 V voltage and 0.5 Hz frequency steady-state oscillations limit the minimum achievable band width.These oscillations are associated with low-inertia gaseous-engine generator dynamics rather than measurement noise.
Deployment boundary: The surrogate is intended as an advisory screening tool, not a replacement for protection settings or validated stability studies.Commands outside calibrated support should be treated as out of support, with bands recalibrated as operating conditions change.
Overall scope: The framework combines event-conditioned Hankel-DMDc forecasting with conformal joint voltage/frequency bands for generator-DT decision support.Its scope includes limitations related to calibration support, open-loop horizon, measurement bandwidth, and testbed operating range.