PaperlayerView exact revision on arXiv

Source-linked AI summary

A unified power-grid representation for reuse across network structures and computational tasks

Yanhao Huang, Changqing Liu, Zichang Wang, Qianhong Wu

arXiv:2609.07650v1eess.SYcs.SY

TL;DR

Power-system models are often developed for specific grids and tasks, while practical analysis spans changing structures and heterogeneous objectives. This paper proposes a self-supervised grid representation that remains fixed while independent reasoners handle downstream tasks. The results support the feasibility of a common representation across changing grid structures, including transfer to a 70,000-bus grid.

  • Problem

    Models are commonly developed for specific systems, tasks and operating regimes, while applying them to unrepresented grids can require costly additional data, updating and validation.

    Source: Introduction · pp. 1, 3

  • Method

    A self-supervised encoder maps grids into a common latent representation, which remains frozen while independently trained task-specific reasoners use it for downstream computation.

    Source: Discussion · p. 23

  • Results

    Results support the feasibility of a common representation across grid structures, with bus-correspondence accuracy reaching 0.79 on the 70,000-bus grid.

    Source: §3.2.2 · p. 15, Discussion · p. 23

  • Takeaways & Limitations

    Grids retain their system-specific content in a common representation format while task-specific solution procedures remain specialized to their analytical objectives.

    Source: Introduction · p. 3, Discussion · p. 23

    Encoder pretraining was restricted to small- and medium-scale systems, with substantially larger networks held for transfer evaluation.

    Source: Discussion · p. 24

Abstract

from arXiv · show

Data-driven power-system models are typically developed for specific grids and computational tasks, but their performance can deteriorate markedly or even fail when network structures or analytical objectives change. This paper develops a unified grid representation that separates physical-grid description from downstream computation. A self-supervised encoder represents each grid as a variable number of fixed-dimensional node, branch and global vectors under a common latent description. Although pretrained only on systems with at most 270 buses, the frozen encoder transfers without adaptation to a 70,000-bus network, more than 250 times larger in bus count, while preserving 0.7919 bus-correspondence accuracy. The same representation supports four independently trained downstream tasks: power-flow calculation, reactive-power adjustment, operating-condition generation and transient-stability assessment. On the previously unseen 70,000-bus grid, power-flow calculation achieves mean errors of 0.108$^{\circ}$ in phase angle and 3.8$\times$10\textsuperscript{-6} p.u. in voltage magnitude. Reactive-power adjustment achieved a 75\% PSASP-verified correction rate on the previously unseen 70,000-bus grid, while operating-condition generation delivered at least one PSASP-verified feasible state for 82.2\% of requests on previously unseen 400--1,000-bus grid families. For transient-stability assessment, the frozen encoder achieves accuracy within 0.8 percentage points of full encoder adaptation under matched training conditions. These results demonstrate that a unified power-grid representation can be learned once and reused unchanged across structurally different power systems and heterogeneous computational tasks.

Introduction

Power-system models are often developed for specific grids, tasks and operating regimes, despite practical analyses spanning changing topologies and objectives. Prior work has advanced structural transfer and task reuse, but whether one grid representation can remain unchanged across unseen grids and heterogeneous tasks remains open.

Introduction

  • Data-driven models are commonly developed and validated for specific systems, tasks and operating regimes, mismatching the range of conditions encountered in practical analysis.Topology changes and application to unrepresented grids can degrade performance and require additional data, updating and validation.Source: Introduction · pp. 1–3
  • Structural-transfer studies have tested unseen grids and larger systems, but often remain within particular task formulations or include target-grid adaptation.Multi-task frameworks likewise commonly fine-tune shared representations for tasks or grids, leaving unchanged reuse across both dimensions unresolved.Source: Introduction · p. 2
  • Prior work shows reuse among related steady-state tasks and generalization within transient analysis, but offers less evidence for an unchanged representation spanning both.The paper identifies the missing evidence as reuse across steady-state and transient computations.Source: Introduction · p. 2
  • The paper asks whether one grid representation can be learned once and reused unchanged across unseen structures and heterogeneous tasks, leaving task-specific procedures specialized.The representation is intended to provide a common physical description while downstream computation remains task-specific.Source: Introduction · p. 3
  • The paper develops a self-supervised unified representation framework and evaluates unchanged reuse across four tasks, from power flow to transient-stability assessment.The evaluation combines representation analyses, task-specific tests and independent physical verification.Source: Introduction · p. 3

2.1 Framework for unified grid representation and task-specific computation

The framework separates a shared physical-grid representation from task-specific computation. A frozen encoder maps each grid into a common latent space, and independent reasoners use that representation with task-specific conditions.

2.1 Framework for unified grid representation and task-specific computation

  • Each case is encoded as addressable node, branch and global tokens in a common 192-dimensional latent space, then passed to task-specific reasoners.The encoder has eight layers and 16 global tokens, and its parameters, normalization statistics and token semantics remain fixed after pretraining.Source: §2.1 · p. 3
  • The shared encoder maps variable-size grid graphs to node-, branch- and system-level representations while keeping the representation mechanism and feature dimension common across grids.The number of represented elements varies with grid size and topology.Source: §2.1 · p. 3
  • Each independently parameterized reasoner combines the frozen grid representation with its own external task condition to produce an output for numerical or simulator-based verification.Conditions can include voltage-violation descriptors, requested operating conditions or fault information.Source: §2.1 · p. 3
  • The framework instantiates independently trained reasoners for power flow, reactive-power adjustment, operating-condition generation and transient-stability assessment.Downstream supervision does not determine or modify the shared representation.Source: §2.1 · p. 4

2.2 Unified grid representation

The encoder maps variable-size power-grid graphs into aligned node, directed-branch and global representations with shared latent dimensions and token semantics. Self-supervised masked reconstruction trains the encoder before it is frozen for downstream use.

2.2 Unified grid representation

  • Grid cases become aligned node, directed-branch and global representations whose element counts vary by grid while encoder parameters, latent dimension and token semantics remain common.Each physical branch is represented by two directed records; local message passing and global attention provide local and system-level context.Source: §2.2 · p. 4, Figure 2 · p. 5
  • The encoder combines topology and equipment information with operating-state variables, using positional and random-walk structural encodings and within-case identity cues.A directory preserves correspondence between graph records and simulator objects.Source: §2.2 · p. 4, Table 1 · p. 5
  • Masked pretraining reconstructs valid masked grid attributes, using Huber loss for continuous fields and binary cross-entropy for categorical and Boolean fields.Operating-state reconstruction receives twice the weight of other feature groups; an auxiliary identity-reconstruction objective encourages element addressability.Source: §2.2 · p. 6
  • Pretraining uses 6,866 operating cases from 67 topology families, with eight synthetic families for validation and 12 larger synthetic families reserved for transfer evaluation.Normalization statistics are estimated from the encoder-training corpus and fixed after pretraining.Source: §2.2 · p. 6
  • After pretraining, encoder parameters and normalization statistics are fixed, while task-specific quantities are introduced only after grid encoding and supplied to the corresponding reasoners.The input schema describes each variable's physical meaning, unit, normalization and dimensionality; it groups node features into topology, static, dynamic and operating-state fields.Source: Table 1 · p. 5, §2.2 · pp. 6–7

2.3 Task-specific computation and physical verification

All four downstream computations use the same frozen grid representation, with task-specific information added after encoding. Their reasoners combine that representation with task-specific estimates, inputs or event descriptors, and outputs are physically verified.

2.3 Task-specific computation and physical verification

  • All four reasoners read the same frozen node, branch and global tokens, while their task-specific inputs enter only after encoding.Outputs are independently verified, including by PSASP replay.Source: §2.3 · p. 7, Table 2 · p. 7

2.3.1 Power-flow calculation

  • Power-flow calculation predicts the unknown AC state from an unsolved case, then refines it through four jointly trained decoupled-Newton correction rounds.Specified quantities bypass the encoder, and physical estimates provide angle and voltage hints that are omitted in 20% of training samples.Source: §2.3.1 · p. 7, Figure 3 · p. 8

2.3.2 Reactive-power adjustment

  • Reactive-power adjustment predicts generator set-point and shunt actions, then verifies them in PSASP, using ranked alternatives and fallback procedures when needed.Its task-side inputs include voltage-violation depths and a switchable-shunt candidate mask.Source: §2.3.2 · p. 8, Figure 4 · p. 9

2.3.3 Operating-condition generation

  • Operating-condition generation uses a conditional diffusion model to propose up to eight candidates, screens them, and delivers the first PSASP-solved state meeting the voltage criterion.The reported delivery rate characterizes the full propose-screen-solve pipeline, not the diffusion network alone.Source: §2.3.3 · p. 9, Figure 5 · p. 10

2.3.4 Transient-stability assessment

  • Transient-stability assessment combines the frozen faulted-branch token with four fault descriptors and predicts instability, subtype, critical-clearing-time and generator-group outputs.No post-fault trajectory or stability outcome is supplied to the encoder or reasoner.Source: §2.3.4 · p. 10

2.4 Power-system datasets

The study uses PSASP-generated steady-state and transient data across benchmark, synthetic and larger transmission systems. Separate data-generation and evaluation procedures define the training and test settings for encoder representation and four downstream tasks.

2.4 Power-system datasets

  • Datasets span steady-state and transient studies across benchmark, synthetic and large transmission systems, with PSASP used to generate and evaluate cases.Steady-state cases were perturbed and solved, while transient cases were generated by electromechanical time-domain simulation.Source: §2.4 · p. 10

2.4.1 Encoder pretraining and representation-evaluation data

  • Encoder pretraining used 6,866 operating cases from 67 topology families; representation transfer was evaluated on 12 independently generated synthetic families at 400, 700, and 1,000 buses, plus larger transmission systems.For larger synthetic networks, operating conditions used narrower load and voltage-setpoint ranges, without generator decommitment.Source: §2.4.1 · p. 11

2.4.2 Power-flow calculation data

  • Power-flow reasoner training used 9,646 operating cases, and independent evaluation included resampled IEEE118 conditions and retained cases from larger systems.Topology sensitivity used paired N-0, N-1 and N-2 cases with the same load, dispatch and voltage-setpoint realization; retained cases were absent from training corpora.Source: §2.4.2 · pp. 11–12

2.4.3 Reactive-power adjustment data

  • Reactive-power adjustment cases were created by increasing reactive demand until voltage violations occurred in otherwise convergent PSASP cases.Grid-specific voltage bands defined both violation depth and correction success; matched N-0, N-1 and N-2 variants reused the disturbance and were independently checked in PSASP.Source: §2.4.3 · p. 12

2.4.4 Operating-condition generation data

  • Operating-condition generation training used 8,133 cases from 81 topology families, with independent requests testing feasible states under specified load and online-generator conditions.Generated candidates were written back to the corresponding case and evaluated in PSASP for convergence and voltage compliance; topology comparisons kept the requests matched.Source: §2.4.4 · p. 12

2.4.5 Transient-stability assessment data

  • Transient-stability data came from simulated faults on CEPRI36, IEEE39 and IEEE118, with evaluation events separated from training and IEEE39 testing transfer without reasoner-training labels.Fault events were simulated for 12 seconds; critical clearing time was searched over 0–0.5 seconds with 0.01-second tolerance, and stable cases at 0.5 seconds were right-censored.Source: §2.4.5 · pp. 12–13

3.1 Power grids spanning diverse network structures and scales

The experiments span power systems from 36 to 70,000 buses, including benchmark grids, synthetic topology families and large transmission networks. Encoder and reasoner exposure differed across downstream tasks, separating representation-level transfer from task-specific transfer.

3.1 Power grids spanning diverse network structures and scales

  • The testbed spans 36–70,000 buses, with encoder pretraining on 67 topology families and evaluation on larger synthetic families and six real-scale grids.Pretraining synthetic families contained 150–270 buses; transfer grids ranged from 400 to 70,000 buses.Source: §3.1 · p. 13
  • Some grids were absent from encoder pretraining but appeared in reasoner training, while others were unseen by both, distinguishing representation-level from downstream-task transfer.Task-specific evaluations also included IEEE300.Source: §3.1 · p. 13

3.2 The unified grid representation generalizes across structures and scales

The frozen representation preserves physical-element addressability and masked operating-state information, then transfers to larger unseen grids and topology changes. Bus correspondence declines at the largest scale, while paired branch outages leave the reported representation probes nearly unchanged.

3.2.1 The representation preserves element addressability and operating-state information

  • 0.00430–0.00432 p.u. voltage-magnitude MAE and 0.261–0.287 rad phase-angle MAE were achieved when masked bus variables were recovered across encoder realizations.The reported angle precision needed for power-flow calculation is supplied on the task side by physical estimates and correction.Source: §3.2.1 · p. 14

3.2.2 The representation generalizes across unseen grids and topology changes

  • 0.79 bus-correspondence accuracy was retained on the 70,000-bus grid, while accuracy exceeded 0.99 on synthetic grids up to 1,000 buses.Across three encoder realizations, source-grid bus correspondence was 0.9973–0.9976; electrically identical parallel branches remained separable where such pairs existed.Source: §3.2.1 · p. 13, §3.2.2 · p. 15
  • 0.00473–0.00474 p.u. voltage MAE at 400–700 buses and 0.00557 p.u. at 1,000 buses show limited loss on larger synthetic grids, while phase-angle recovery worsened more with scale.On six real-scale grids, voltage MAE was 0.0124–0.0307 p.u. and phase-angle MAE was 0.157–0.626 rad.Source: §3.2.2 · p. 15
  • 0.0002 p.u. voltage-recovery MAE and 0.015 rad phase-angle MAE were the maximum changes across paired N-0, N-1 and N-2 cases.Bus-correspondence accuracy and parallel-branch separation changed by less than 0.001 and 0.0002, respectively.Source: §3.2.2 · p. 15

3.3 A frozen grid representation supports heterogeneous power-system tasks across grid structures

One frozen grid representation supports four heterogeneous tasks through independently trained reasoners, with task specialization outside the encoder. Results test this shared representation across different grid structures and task-specific physical endpoints.

3.3 A frozen grid representation supports heterogeneous power-system tasks across grid structures

  • One frozen representation supported power flow, reactive-power adjustment, operating-condition generation and transient-stability assessment, with task-specific computation performed by separate reasoners.The four tasks span steady-state analysis, corrective control, operating-state generation and dynamic-security assessment.Source: §3.3 · pp. 15–16

3.3.1 Power-flow calculation

  • On the previously unseen 70,000-bus grid, mean θ MAE was 0.108° and mean V MAE was 3.8×10^-6 p.u.; mean errors remained stable under paired N-0 to N-2 tests.The localized ACTIVSg25k tail-error increase occurred when opened branches left adjacent buses weakly connected; mean errors remained unchanged.Source: §3.3.1 · p. 17, Table 7 · p. 17
  • With embedded physics-correction rounds, mean θ MAE fell from 13.8° to 0.108° on ACTIVSg70k and from 0.585° to 0.0038° on ACTIVSg25k.The ablation attributes the initial estimate to the learned representation and reasoner, with correction rounds refining it toward AC-reference agreement.Source: §3.3.1 · p. 18, Table 9 · p. 18

3.3.2 Reactive-power adjustment

  • On grids absent from reasoner training, reactive-power adjustment corrected 0.57–0.75 of paired cases; label-supplying grids reached 1.00 on IEEE118 and 0.77 on ACTIVSg2000.The success measure was PSASP-verified task completion in the deployed procedure.Source: §3.3.2 · p. 19, Table 10 · p. 19
  • On unseen grids, adjustment depended on local control reach; six case3120sp N-1 cases remained at 0.89–0.91 p.u. because outages placed violating buses beyond adjustable-unit reach.The deployed procedure uses a locality prescreen because the reasoner’s first whole-grid choice often lay 5–45 hops from the violation.Source: §3.3.2 · p. 19

3.3.3 Operating-condition generation

  • Generation delivered 74 of 90 requests (0.822) across unseen 400–1,000-bus synthetic families; branch outages left delivery rates within five of 160 and one of 90 requests of intact-grid rates.The 3,120-bus evaluation delivered all 50 requests, while ACTIVSg2000 delivered 56 of 60.Source: §3.3.3 · pp. 20–21, Table 11 · p. 21
  • Aggregate load was controlled exactly, but online-unit count was not effectively controlled by the continuous latent generation pipeline; none of 50 delivered 3,120-bus cases met the requested count within ±1 unit.The passage attributes the differences across grids to their generator-unit data and minimum-output constraints.Source: §3.3.3 · pp. 20–21

3.3.4 Transient-stability assessment

  • On held-out events, median accuracy was 0.929 for IEEE118 and 0.915 for CEPRI36; pooled unstable-event class recall was 88.2–99.2% and precision was 92.9–95.9%.Instability classes merged five labelled subtypes into power-angle, voltage and frequency classes.Source: §3.3.4 · pp. 21–22, Table 12 · p. 22, Table 13 · p. 22

3.4. Sensitivity of transient-stability assessment to encoder adaptation

Under matched training conditions, freezing the encoder kept transient-stability assessment accuracy within one percentage point of full adaptation on average. The larger advantage at independently selected stopping points is secondary because fully adapted models trained longer.

3.4. Sensitivity of transient-stability assessment to encoder adaptation

  • The comparison evaluated frozen, partial and full encoder adaptation using the same TSA formulation, with accuracy measured against time-domain simulation outcomes.Protocols included a fixed 4,000-step budget, five paired runs at matched checkpoints, and independently selected stopping points.Source: §3.4 · p. 22
  • At 4,000 steps, TSA accuracy was 0.8488 with the encoder frozen, 0.8465 with the final two layers adapted and 0.8459 with full adaptation.All three configurations were still undertrained, so this was an early training-trajectory comparison, not evidence that one strategy was superior.Source: §3.4 · p. 22, Table 14 · p. 23
  • Within matched checkpoints, full adaptation led freezing by 0.57 pp, 0.55 pp and 0.77 pp at 6,200, 7,200 and 8,200 steps, respectively; the advantage was not reproduced in all five runs.The section concludes that frozen-encoder accuracy was within one percentage point of full adaptation on average under matched training conditions.Source: §3.4 · p. 23, Table 14 · p. 23
  • At independently selected stopping points, full adaptation led by 2.93 pp, but trained 12,040 steps on average versus 9,000 for frozen runs, confounding the comparison.The independently selected endpoint is treated as secondary evidence.Source: §3.4 · p. 23, Table 14 · p. 23

Discussion

The discussion frames the encoder as a common, fixed latent description of each grid, with separate reasoners handling task-specific computation. It attributes the framework’s scope to cooperation among that representation, selective task readout and physics-aware modules, while identifying broader pretraining and end-to-end latent computation as future directions.

Discussion

  • Each grid retains variable numbers of fixed-dimensional node, branch and global vectors under shared representation format, latent dimensionality and token semantics.Downstream reasoners interpret this fixed representation to extract information for their computational objectives.Source: Discussion · p. 23
  • Multi-field masked pretraining aligns topology, equipment attributes, operating states and element identity; independently trained query reasoners then select and recombine task-relevant information.The encoder weights, normalization statistics and token semantics remain fixed, while task quantities and physics-based hints or checks are supplied outside the encoder.Source: Discussion · p. 23
  • The contribution combines a permanently fixed grid representation and external task reasoners across grid structures and heterogeneous objectives, rather than relying on a frozen backbone alone.Element-level addressability avoids information loss from a single pooled vector, while the observed performance reflects cooperation with selective readout and physics-aware modules.Source: Discussion · pp. 23–24
  • Phase-angle recovery depends more on system-wide active-power transfer and network coupling than voltage-magnitude recovery, consistent with its stronger degradation as grid scale increases.The discussion relates voltage magnitude to local and neighbouring reactive-power balance and regulation, whereas angle recovery may require information from paths beyond a bus’s immediate neighbourhood.Source: Discussion · p. 24
  • Future work includes broader pretraining across network structures and scales, richer physical descriptions, and chaining computations within the shared latent space.Proposed extensions include hybrid AC/DC networks and dynamic model parameters; chaining multiple reasoners remains future work, although the operating-condition generator already synthesizes latent node states.Source: Discussion · p. 24
Loading 2609.07650v1…