Pith. sign in

REVIEW 4 major objections 6 minor 42 references

A Two-Stage AI-Powered Motif Mining Method for Efficient Power System Topological Analysis

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that power-system motifs can be mined by a learned ordered embedding and greedy graph growing, without exhaustive subgraph counting.

desk verdict Plausible adaptation of neural subgraph matching to power grids, but the central efficiency and accuracy claims are not backed by measurements or validation at scale. read the letter →

arxiv 2412.05957 v1 pith:VRVEUFS4 submitted 2024-12-08 eess.SY cs.SY

Yiyan Li , Zhenghao Zhou , Jian Ping , Xiaoyuan Xu , Zheng Yan , Jianzhong Wu This is my paper · ORCID
classification eess.SYcs.SY
keywords motifminingpowersystemtopologyorderedembeddinggreedysearchGraphSAGEsubgraphisomorphismrepresentationlearningVF2validation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that motif mining in large power systems, normally an NP-hard search, can be replaced by a learned embedding plus a greedy growth process. It presents a two-stage method: a GraphSAGE-based encoder trained with an order-embedding loss maps small neighborhoods into vectors whose relative positions encode subgraph isomorphism, and a greedy algorithm then grows high-frequency motifs node by node, avoiding enumeration. The study claims the resulting motifs match the domain knowledge of power-system planning and agree with VF2 traversal-searching rankings on rural and urban feeders with 3 to 6 nodes. If the method holds, it would make wide-range topological analysis practical for large transmission grids.

What carries the argument

The ordered embedding space: a high-dimensional vector space in which a graph $G_u$ being a subgraph of $G_v$ is encoded as $[z_u]_i \le [z_v]_i$ for every dimension $i$, so subgraph isomorphism becomes vector comparison. The other half is the greedy motif-growing algorithm, which starts from a random node, expands by attaching adjacent nodes, keeps the expansion with the highest predicted frequency, and repeats to a target size; the learned encoder with skip-connected GraphSAGE layers supplies the frequency estimates.

What would settle it

Take a large synthetic grid, exhaustively count the frequencies of all connected subgraphs of size 7 and 8 that contain the greedy path's final candidate, and check whether any other subgraph has a strictly higher frequency that the greedy search never visits; if one exists, the claim that greedy growth finds the most frequent motif fails.

Watch

Extended reading notes

Core claim

The central claim is that the most frequent subgraphs in a power system can be discovered by walking a monotonic path through an ordered embedding space rather than by enumerating and counting all candidate subgraphs. The authors encode graph neighborhoods so that subgraph relations appear as coordinate-wise "lower-left" ordering of vectors; then the frequency of a query is approximated by counting reference vectors within a threshold, and motifs are grown greedily from a seed node by always adding the neighbor that yields the most frequent expanded graph. On the 61-model database, the discovered motifs are linear and radial structures consistent with planning principles, and the top-ranked motifs for rural and urban feeders reproduce the rankings of the VF2 ground-truth counts.

Load-bearing premise

The greedy growing step assumes that always keeping the locally most frequent expansion leads to the globally most frequent motif of a given size, yet no proof is offered and the validation only covers 3-6 node motifs on two small feeders.

Editorial extensions

If this is right

  • Motif-based vulnerability, contingency selection, and stability studies can move from 4-node structures to larger, more informative subgraphs in transmission-scale systems.
  • The same trained encoder can be reused across grids without retraining, since the subgraph isomorphism patterns it learns are presented as domain-independent.
  • Large synthetic grids can be validated against empirically mined motifs, extending structural validation criteria beyond traditional statistics.
  • The approach may accelerate downstream graph-learning tasks that need frequent subgraph counts, not just graph classification.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the greedy path is only locally optimal, the method may actually be biased toward motifs that are frequent in densely sampled neighborhoods rather than globally frequent; this can be tested by comparing against exhaustive counts on mid-size graphs, which the paper does not do.
  • The ordered embedding might serve as a general subgraph query index for power-system graph databases, turning the motif miner into a broader fast subgraph search primitive.
  • The frequency approximation via thresholded vector comparison could be calibrated with a confidence score, letting users know when the greedy candidate is untrustworthy.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a two-stage AI-powered motif mining method for power-system graphs. In the first stage, a GraphSAGE encoder is trained with an order-embedding loss (Eq. 2) so that subgraph isomorphism can be approximated by a vector comparison rule (Eq. 4). In the second stage, a greedy motif-growing algorithm (Section 2.4) expands a seed node and, at each step, keeps the candidate with the highest embedding-predicted frequency. The method is demonstrated on a database of 61 circuit models, including rural/urban feeder comparisons and US/Europe transmission systems, with VF2 used as a ground-truth check for 3-6 node motifs on two feeders.

Significance. If substantiated, the method would address a real bottleneck: exact motif enumeration is NP-hard and often infeasible for large power-system graphs. The core idea of using ordered embeddings to replace subgraph-isomorphism checks is timely and relevant, and the paper connects its outputs to domain knowledge about radial structures and voltage levels. The work is, however, at the proof-of-concept stage: the central efficiency claim is asserted without runtime or complexity evidence, the greedy search lacks an optimality analysis, and the accuracy validation covers only very small motifs on two feeders. These points must be strengthened before the paper can support its stated contributions.

major comments (4)
  1. [Section 3.5] The central efficiency claim is not supported by any runtime measurement, complexity analysis, or baseline comparison. The statement that the computation efficiency of the proposed algorithm is independent of graph size (Section 3.5) is asserted without data; no wall-clock times, asymptotic complexity, or comparisons with traversal-based tools such as VF2 or ESU are given for the large systems (ACTIVSg70k, PEGASE 13659) where the advantage is claimed. The paper needs quantitative efficiency evidence (e.g., runtime versus graph size, and runtime versus a baseline) before the main contribution can be evaluated.
  2. [Section 2.4] The greedy motif-growing algorithm has no optimality or approximation guarantee. At each expansion step it retains the candidate with the highest frequency predicted by the embedding and threshold t in Eq. (4); no proof or complexity analysis shows that this local choice recovers the globally most frequent k-node motif, and the predicted frequency is itself a threshold-dependent proxy rather than an exact count. The VF2 validation covers only motifs with 3-6 nodes on two feeders (Table II), so the claimed accuracy for 7-30 node motifs (Fig. 10) and for the large transmission systems (Fig. 11) is an untested extrapolation. The authors should either provide a bound on the greedy loss, compare against exact enumeration on a range of small/medium systems, or demonstrate a counterexample analysis.
  3. [Table II] The VF2 validation is difficult to interpret and does not quantitatively establish ranking accuracy. The table reports only frequency values for the proposed method's ranked list and VF2 counts, without identifying the corresponding motif structures, so the reader cannot check whether the same motifs are being compared; the text's 'generally consistent' is not backed by a metric (e.g., top-k agreement, rank correlation). In addition, some cells are ambiguous (e.g., the rural 5-node row appears as '3 2 20 3'), which makes the table unusable as evidence. Please report the isomorphic class of each ranked motif and a quantitative agreement measure.
  4. [Sections 2.1 and 2.2] The method actually mines frequent subgraphs, not network motifs as defined in Section 2.1. The definition there follows Milo et al. (appearing much more frequently than in random graphs), but the proposed algorithm ranks candidates by raw predicted frequency and never compares against a random-graph null model. Hence the structures reported in Figs. 8-12 may not be motifs in the standard statistical sense, and the claim that they reflect 'motif' characteristics of power-system topology is not supported. This relaxation should be stated explicitly and its consequences discussed.
minor comments (6)
  1. [Section 2.3] The text first illustrates a 2-layer GraphSAGE network and later states that K = 8 layers are used; please clarify the actual architecture and the role of the example.
  2. [References] Reference [21] is cited as 'Rex et al.'; the citation should be completed with the full author list.
  3. [Conclusions] In the Conclusions, 'ramdom' should be 'random'.
  4. [Section 3.3] Fig. 8(a) says the motifs 'strictly follow the upper left rule,' whereas Eq. (1) defines a lower-left ordering; this inconsistency should be corrected.
  5. [Section 2.2 and 3.2] No hyperparameter values or sensitivity analyses are reported for threshold t, margin alpha, embedding dimension D, or GraphSAGE neighbor count; at minimum, the values used should be given, and a sensitivity check for t is needed because Eq. (4) directly controls the predicted frequencies.
  6. [Table I] In Table I, 'case69' appears twice in the description of the small radial distribution systems; please check whether this is a typo.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the approximate motif frequencies are checked against an external VF2 ground truth rather than being forced by construction.

full rationale

The derivation chain is not circular. The ordered embedding encoder is trained on subgraph-isomorphism labels (positive and negative pairs) via the order-embedding loss of Eq. (2), not on the final motif-frequency rankings or on VF2 counts. The frequency proxy in Eq. (4) is explicitly an approximation, and the greedy growing step in Section 2.4 simply uses that proxy to rank candidates. The paper then validates the resulting motifs against VF2 traversal counts in Table II, which is an independent ground-truth comparison that could have disagreed; indeed, some rows show imperfect consistency. The lack of an optimality guarantee for the greedy search and the limited 3–6 node validation on two feeders are correctness and generalization concerns, not circularity, because the claimed consistency with VF2 is an empirical claim. No load-bearing self-citation or imported uniqueness theorem is present; the cited prior works [21], [22], and [24] are external. Therefore the central claim has independent content and no circular reduction is exhibited.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the accuracy of the learned embedding, the threshold choice, and the greedy search heuristic. Several hyperparameters are left unspecified. The motif-definition relaxation to frequent subgraph mining is not flagged. No new physical entities are introduced.

free parameters (4)
  • Threshold t in subgraph prediction function Eq. (4) = not reported
    Controls whether a pair of embeddings is counted as a subgraph match; the final motif frequency depends directly on this value and it is never specified or swept.
  • Margin alpha in the ordered embedding loss Eq. (2) = not reported
    Positive hyperparameter in the max-margin loss that shapes the embedding space; its value is not reported.
  • Embedding dimension D = not reported
    Dimension of the ordered embedding vectors in Eq. (1); the value is never stated.
  • GraphSAGE neighbor sample count and layer count = N=4 in the figure example, K=8 stated
    The neighborhood aggregation size and depth determine what subgraph structure is encoded; these architecture choices are set by hand and not systematically justified.
assumptions (4)
  • domain assumption GraphSAGE node embeddings faithfully represent the k-hop neighborhood subgraph of each node.
    The method treats the embedding of a node as the embedding of its neighborhood subgraph, which is an approximation not formally proven; invoked in Section 2.3.
  • domain assumption The learned ordered embedding generalizes from training neighborhoods to arbitrary target graphs and preserves the componentwise inequality in Eq. (1) well enough for threshold-based counting.
    No out-of-sample analysis or formal guarantee establishes that unseen graph pairs satisfy the ordered embedding pattern; the method relies on this in Section 2.2 and Eq. (4).
  • ad hoc to paper Greedy expansion of a random seed, keeping the locally highest-frequency candidate at each step, finds the globally most frequent motif of each target size.
    The algorithm in Section 2.4 provides no proof that local frequency maxima lead to global motif frequency maxima; this is a heuristic search assumption.
  • ad hoc to paper The graph motif definition based on comparison with random graphs is relaxed to simply mining the most frequent subgraphs in the target database.
    Section 2.1 defines motifs using a random-graph null model, but Section 3.3 mines the most frequent subgraphs directly; no null-model comparison is performed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Two-Stage AI-Powered Motif Mining Method for Efficient Power System Topological Analysis." pith.science (2026). https://pith.science/paper/VRVEUFS4

@misc{pith2026241205957,
  author       = {Pith},
  title        = {Pith review of: A Two-Stage AI-Powered Motif Mining Method for Efficient Power System Topological Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VRVEUFS4}},
  note         = {Machine review of arXiv:2412.05957}
}
read the original abstract

Graph motif, defined as the microstructure that appears repeatedly in a large graph, reveals important topological characteristics of the large graph and has gained increasing attention in power system analysis regarding reliability, vulnerability and resiliency. However, searching motifs within the large-scale power system is extremely computationally challenging and even infeasible, which undermines the value of motif analysis in practice. In this paper, we introduce a two-stage AI-powered motif mining method to enable efficient and wide-range motif analysis in power systems. In the first stage, a representation learning method with specially designed network structure and loss function is proposed to achieve ordered embedding for the power system topology, simplifying the subgraph isomorphic problem into a vector comparison problem. In the second stage, under the guidance of the ordered embedding space, a greedy-search-based motif growing algorithm is introduced to quickly obtain the motifs without traversal searching. A case study based on a power system database including 61 circuit models demonstrates the effectiveness of the proposed method.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 24 canonical work pages

  1. [1]

    Introduction After decades of development, the power grid has evolved into a hyper-complex physical system . The large-scale integration of renewable energy resources and flexible loads accelerates the electronization of the power system, leading to low system inertia and high operation uncertainty. Meanwhile, advanced operation modes such as peer-to-peer...

    work page

  2. [2]

    lower left

    Methodology (a) (b) Fig. 2 Overview of the proposed motif mining process. (a) The ordered embedding process to encode graphs into vectors to formulate the ordered embedding space. (b) The motif searching process to iteratively grow the motifs. As shown in Fig. 2, the proposed motif mining method includes two stages: ordered embedding and motif Submitted t...

    work page

  3. [3]

    upper left

    Case Study 3.1 Test Case Setup In this paper, we implement the proposed motif mining method on a power system database including 61 circuit models, as shown in Table I. We evaluate the effectiveness of the proposed method from two aspects. First, we examine the motif mining results to see if they are in consistence with the domain knowledge in power syste...

    work page

  4. [4]

    dead trees

    proposes an efficient topological procedure to calculate the reliability indices and determine the contribution of each system state to those indices. Ref [5] focuses instead on the medium and low voltage grids to analyze the adequacy of the current distribution infrastructure for a decentralized energy market, based on statistical tools from the complex ...

    work page

  5. [5]

    Conclusions In this paper, a two-stage AI-powered motif mining method is introduced to enable efficient and wide-range motif analysis for large-scale power systems. A representation learning model based on graphSAGE network is designed to achieve ordered embedding for the power system topology, based on which the subgraph matching problem can be converted...

    work page

  6. [6]

    Acknowledgement This work was supported in part by National Natural Science Foundation of China under Grant 52307121, and in part by Shanghai Sailing Program under Grant 23YF1419000

    work page

  7. [7]

    Structural vulnerability of the North American power grid,

    R. Albert, I. Albert, and G. L. Nakarado, “Structural vulnerability of the North American power grid,” Phys. Rev. E, vol. 69, no. 2, p. 025103, Feb. 2004, doi: 10.1103/PhysRevE.69.025103

    work page doi:10.1103/physreve.69.025103 2004

  8. [8]

    Topological vulnerability of the European power grid under errors and Submitted to Applied Energy 14 attacks[J]

    Rosas-Casals M, Valverde S, Solé R V. Topological vulnerability of the European power grid under errors and Submitted to Applied Energy 14 attacks[J]. International journal of bifurcation and chaos, 2007, 17(07): 2465-2475

    work page 2007

Show all 42 references
  1. [9]

    Reliability Evaluation of Park-level Electricity-Hydrogen Systems using Explainable Graph Neural Network,

    B. Cao, X. Wu, and X. Wang, “Reliability Evaluation of Park-level Electricity-Hydrogen Systems using Explainable Graph Neural Network,” IEEE Trans. Smart Grid, pp. 1–1, 2024, doi: 10.1109/TSG.2023.3337392

    2024

  2. [10]

    Topological analysis in bulk power system reliability evaluation,

    S. Jonnavithula and R. Billinton, “Topological analysis in bulk power system reliability evaluation,” IEEE Transactions on Power Systems, vol. 12, no. 1, pp. 456–463, Feb. 1997, doi: 10.1109/59.575784

    1997 doi

  3. [11]

    Towards Decentralization: A Topological Investigation of the Medium and Low Voltage Grids,

    G. A. Pagani and M. Aiello, “Towards Decentralization: A Topological Investigation of the Medium and Low Voltage Grids,” IEEE Transactions on Smart Grid, vol. 2, no. 3, pp. 538 –547, Sep. 2011, doi: 10.1109/TSG.2011.2147810

    2011

  4. [12]

    Efficient Topology Design Algorithms for Power Grid Stability,

    S. Bhela, H. Nagarajan, D. Deka, and V. Kekatos, “Efficient Topology Design Algorithms for Power Grid Stability,” IEEE Control Systems Letters, vol. 6, pp. 1100–1105, 2022, doi: 10.1109/LCSYS.2021.3088888

    2022

  5. [13]

    Structural vulnerability of power systems: A topological approach,

    E. Bompard, D. Wu, and F. Xue, “Structural vulnerability of power systems: A topological approach,” Electric Power Systems Research, vol. 81, no. 7, pp. 1334–1340, Jul. 2011, doi: 10.1016/j.epsr.2011.01.021

    2011 doi

  6. [14]

    Extended Topological Metrics for the Analysis of Power Grid Vulnerability,

    E. Bompard, E. Pons, and D. Wu, “Extended Topological Metrics for the Analysis of Power Grid Vulnerability,” IEEE Systems Journal, vol. 6, no. 3, pp. 481–487, Sep. 2012, doi: 10.1109/JSYST.2012.2190688

    2012

  7. [15]

    Higher -order organization of complex networks,

    A. R. Benson, D. F. Gleich, and J. Leskovec, “Higher -order organization of complex networks,” Science, vol. 353, no. 6295, pp. 163–166, Jul. 2016, doi: 10.1126/science.aad9029

    2016 doi

  8. [16]

    Motif-based analysis of power grid robustness under attacks,

    A. K. Dey, Y. R. Gel, and H. V. Poor, “Motif-based analysis of power grid robustness under attacks,” in 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Nov. 2017, pp. 1015– 1019. doi: 10.1109/GlobalSIP.2017.8309114

    2017

  9. [17]

    Assessing European power grid reliability by means of topological measures,

    M. Rosas Casals and B. Corominas Murtra, “Assessing European power grid reliability by means of topological measures,” WIT transactions on ecology and the environment, vol. 121, pp. 527– 537, 2009, doi: 10.2495/ESUS090471

    2009 doi

  10. [18]

    How dead ends undermine power grid stability,

    P. J. Menck, J. Heitzig, J. Kurths, and H. Joachim Schellnhuber, “How dead ends undermine power grid stability,” Nat Commun, vol. 5, no. 1, p. 3969, Jun. 2014, doi: 10.1038/ncomms4969

    2014 doi

  11. [19]

    Detours around basin stability in power networks,

    P. Schultz, J. Heitzig, and J. Kurths, “Detours around basin stability in power networks,” New J. Phys., vol. 16, no. 12, p. 125001, Dec. 2014, doi: 10.1088/1367-2630/16/12/125001

    2014 doi

  12. [20]

    Motif-Based Reliability Analysis for Cyber-Physical Power Systems,

    H. Binqadhi, M. AlMuhaini, H. V. Poor, and H. Huang, “Motif-Based Reliability Analysis for Cyber-Physical Power Systems,” in 2023 IEEE PES Innovative Smart Grid Technologies Europe (ISGT EUROPE), Oct. 2023, pp. 1–5. doi: 10.1109/ISGTEUROPE56780.2023.10407121

    2023

  13. [21]

    The Most Frequent N -k Line Outages Occur in Motifs That Can Improve Contingency Selection,

    K. Zhou, I. Dobson, and Z. Wang, “The Most Frequent N -k Line Outages Occur in Motifs That Can Improve Contingency Selection,” IEEE Transactions on Power Systems, vol. 39, no. 1, pp. 1785 –1796, Jan. 2024, doi: 10.1109/TPWRS.2023.3249825

    2024

  14. [22]

    A combinatorial approach to graphlet counting,

    T. Hočevar and J. Demšar, “A combinatorial approach to graphlet counting,” Bioinformatics, vol. 30, no. 4, pp. 559– 565, 2014

    2014

  15. [23]

    A Survey on Subgraph Counting: Concepts, Algorithms and Applications to Network Motifs and Graphlets,

    P. Ribeiro, P. Paredes, M. E. P. Silva, D. Aparicio, and F. Silva, “A Survey on Subgraph Counting: Concepts, Algorithms and Applications to Network Motifs and Graphlets,” ACM Comput. Surv., vol. 54, no. 2, pp. 1–36, Mar. 2022, doi: 10.1145/3433652

    2022 doi

  16. [24]

    SimGNN: A Neural Network Approach to Fast Graph Similarity Computation,

    Y. Bai, H. Ding, S. Bian, T. Chen, Y. Sun, and W. Wang, “SimGNN: A Neural Network Approach to Fast Graph Similarity Computation,” in Proceedings of the Twelfth ACM International Conference on Web Search and Data Mining, Melbourne VIC Australia: ACM, Jan. 2019, pp. 384–392. doi...

    2019

  17. [25]

    Neural Subgraph Isomorphism Counting,

    X. Liu, H. Pan, M. He, Y. Song, X. Jiang, and L. Shang, “Neural Subgraph Isomorphism Counting,” in Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Virtual Event CA USA: ACM, Aug. 2020, pp. 1959–1969. doi: 10.1145/3394486.3403247

    2020

  18. [26]

    Can graph neural networks count substructures?,

    Z. Chen, L. Chen, S. Villar, and J. Bruna, “Can graph neural networks count substructures?,” Advances in neural Submitted to Applied Energy 15 information processing systems, vol. 33, pp. 10383–10395, 2020

    2020

  19. [27]

    Neural Subgraph Matching,

    Rex et al., “Neural Subgraph Matching,” Oct. 27, 2020, arXiv: arXiv:2007.03092. Accessed: Mar. 21, 2024. [Online]. Available: http://arxiv.org/abs/2007.03092

    2020 arXiv

  20. [28]

    Representation Learning for Frequent Subgraph Mining,

    R. Ying, T. Fu, A. Wang, J. You, Y. Wang, and J. Leskovec, “Representation Learning for Frequent Subgraph Mining,” Feb. 22, 2024, arXiv: arXiv:2402.14367. Accessed: Apr. 13, 2024

    2024 arXiv

  21. [29]

    Network Motifs: Simple Building Blocks of Complex Networks,

    R. Milo, S. Shen -Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, “Network Motifs: Simple Building Blocks of Complex Networks,” Science, vol. 298, no. 5594, pp. 824 –827, Oct. 2002, doi: 10.1126/science.298.5594.824

    2002 doi

  22. [30]

    Order-Embeddings of Images and Language,

    I. Vendrov, R. Kiros, S. Fidler, and R. Urtasun, “Order-Embeddings of Images and Language,” Mar. 01, 2016, arXiv: arXiv:1511.06361. Accessed: May 16, 2024

    2016 arXiv

  23. [31]

    On the bias of BFS (Breadth First Search),

    M. Kurant, A. Markopoulou, and P. Thiran, “On the bias of BFS (Breadth First Search),” in 2010 22nd International Teletraffic Congress (lTC 22), Sep. 2010, pp. 1–8. doi: 10.1109/ITC.2010.5608727

    2010

  24. [32]

    Semi -Supervised Classification with Graph Convolutional Networks,

    T. N. Kipf and M. Welling, “Semi -Supervised Classification with Graph Convolutional Networks,” Feb. 22, 2017, arXiv: arXiv:1609.02907. Accessed: Apr. 14, 2024

    2017 arXiv

  25. [33]

    Inductive representation learning on large graphs,

    W. Hamilton, Z. Ying, and J. Leskovec, “Inductive representation learning on large graphs,” Advances in neural information processing systems, vol. 30, 2017, Accessed: May 16, 2024

    2017

  26. [34]

    Radial distribution test feeders,

    W. H. Kersting, “Radial distribution test feeders,” IEEE Transactions on Power Systems, vol. 6, no. 3, pp. 975–985, 1991

    1991

  27. [35]

    MATPOWER: Steady -State Operations, Planning, and Analysis Tools for Power Systems Research and Education,

    R. D. Zimmerman, C. E. Murillo -Sánchez, and R. J. Thomas, “MATPOWER: Steady -State Operations, Planning, and Analysis Tools for Power Systems Research and Education,” IEEE Transactions on Power Systems, vol. 26, no. 1, pp. 12–19, Feb. 2011, doi: 10.1109/TPWRS.2010.2051168

    2011

  28. [36]

    Available online at:https://sourceforge.net/p/ electricdss/code/HEAD/tree/trunk/Distrib/ EPRITestCircuits/

    EPRI Test Circuits. Available online at:https://sourceforge.net/p/ electricdss/code/HEAD/tree/trunk/Distrib/ EPRITestCircuits/

  29. [37]

    AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE,

    C. Josz, S. Fliscounakis, J. Maeght, and P. Panciatici, “AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE,” Mar. 30, 2016, arXiv: arXiv:1603.01533. doi: 10.48550/arXiv.1603.01533

    2016 doi arXiv

  30. [38]

    Contingency Ranking With Respect to Overloads in Very Large Power Systems Taking Into Account Uncertainty, Preventive, and Corrective Actions,

    S. Fliscounakis, P. Panciatici, F. Capitanescu, and L. Wehenkel, “Contingency Ranking With Respect to Overloads in Very Large Power Systems Taking Into Account Uncertainty, Preventive, and Corrective Actions,” IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4909–4917, ...

    2013

  31. [39]

    Grid Structural Characteristics as Validation Criteria for Synthetic Networks,

    A. B. Birchfield, T. Xu, K. M. Gegner, K. S. Shetye, and T. J. Overbye, “Grid Structural Characteristics as Validation Criteria for Synthetic Networks,” IEEE Transactions on Power Systems, vol. 32, no. 4, pp. 3258– 3265, Jul. 2017, doi: 10.1109/TPWRS.2016.2616385

    2017

  32. [40]

    The neutral -to-earth voltage (NEV) test case and distribution system analysis,

    W. G. Sunderman, R. C. Dugan, and D. S. Dorr, “The neutral -to-earth voltage (NEV) test case and distribution system analysis,” in 2008 IEEE power and energy society general meeting -conversion and delivery of electrical energy in the 21st century, IEEE, 2008, pp. 1–6. Accesse...

    2008

  33. [41]

    IEEE 342-node low voltage networked test system,

    K. Schneider, P. Phanivong, and J.-S. Lacroix, “IEEE 342-node low voltage networked test system,” in 2014 IEEE PES general meeting| conference & exposition, IEEE, 2014, pp. 1–5. Accessed: May 16, 2024

    2014

  34. [42]

    An improved algorithm for matching large graphs,

    L. P. Cordella, P. Foggia, C. Sansone, and M. Vento, “An improved algorithm for matching large graphs,” in 3rd IAPR-TC15 workshop on graph-based representations in pattern recognition, Citeseer, 2001, pp. 149–159. Accessed: May 16, 2024

    2001

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.