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REVIEW 3 major objections 5 minor 24 cited by

The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A curated library turns old grid data into hard AC-OPF benchmarks that expose algorithm differences.

desk verdict A genuinely useful AC-OPF benchmark library, but the validation overstates what the TL-UB cases show and needs a revision to document which constraints actually bind. read the letter →

arxiv 1908.02788 v2 pith:7R7ZQBAO submitted 2019-08-07 math.OC

Sogol Babaeinejadsarookolaee , Adam Birchfield , Richard D. Christie , Carleton Coffrin , Christopher DeMarco , Ruisheng Diao , Michael Ferris , Stephane Fliscounakis
show 15 more authors
Scott Greene Renke Huang Cedric Josz Roman Korab Bernard Lesieutre Jean Maeght Terrence W. K. Mak Daniel K. Molzahn Thomas J. Overbye Patrick Panciatici Byungkwon Park Jonathan Snodgrass Ahmad Tbaileh Pascal Van Hentenryck Ray Zimmerman
This is my paper · ORCID
classification math.OC MSC 90C2690C30
keywords ACoptimalpowerflowbenchmarkingoptimalitygapconvexrelaxationgridtestcasessyntheticnetworkdatageneratorcostmodelsbranchthermallimits
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

This paper aims to fix a reproducibility problem in AC optimal power flow research: studies differ in problem formulation and in data, so algorithms cannot be compared fairly. It proposes a standardized AC-OPF model and a curated, open-access library of networks, PGLib-OPF, in which missing generator costs, injection limits, and branch thermal limits are completed by statistical models. The central claim, backed by a validation study, is that these benchmark networks show much larger optimality gaps than the older standard test cases, making them discriminating tests for different solution methods.

What carries the argument

The load-bearing object is PGLib-OPF itself: a set of creative-commons network cases in a common data format, paired with a single nominated AC-OPF model (Model 1) that includes nodal power balance, Ohm's-law branch flows, thermal limits, and voltage angle difference limits. The argument runs on data-completion models for generators (GF-Stat, AG-Stat, AC-Stat) and branches (TL-Stat, TL-UB), plus two stress-test variants: API, which raises load until thermal limits bind, and SAD, which shrinks angle limits until they bind. The validation metric is the optimality gap, (AC heuristic objective - SOC relaxation bound) / AC heuristic objective.

What would settle it

Take a real network with complete, verified operational data (for example a utility's actual costs and line ratings) and run both a strong AC heuristic and the SOC relaxation on it. Then re-run using PGLib's statistical completion on the same topology. If the optimality gap and the ordering of two reference solvers differ wildly between the real and synthetic data, the benchmarking transferability claim would collapse.

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Extended reading notes

Core claim

The paper demonstrates that the majority of the PGLib-OPF networks exhibit significantly larger optimality gaps than traditional MATPOWER case studies, and hence are useful for benchmarking AC-OPF algorithms. The validation study quantifies this with an optimality gap defined as the relative difference between a local-nonlinear AC feasible solution and a Second-Order Cone relaxation bound. The larger gaps arise both from deliberately congested cases (API) and from cases with tightly constrained voltage angle differences (SAD), which provide a wider variety of difficulty for algorithm testing.

Load-bearing premise

The statistical models for missing costs, generator limits, and line ratings produce numbers that are realistic enough that a solver's ranking on these synthetic cases matches its ranking on real grids.

Editorial extensions

If this is right

  • Different AC-OPF studies become directly comparable because the formulation and data are fixed and shared.
  • Researchers can select cases by gap size, separating the question 'can this heuristic find good feasible points?' from 'is this relaxation bound tight?'
  • The API and SAD variants provide systematic, repeatable ways to probe how an algorithm degrades under thermal congestion and angle congestion, respectively.
  • The creative-commons license allows results to be checked and extended without data-use barriers.
  • The two infeasible legacy cases (case9target and case145) are flagged as data-quality issues rather than solver failures, correcting potential mis-benchmarks.

Reading between the lines

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

  • The same data-completion recipe could generate benchmarks for other grid problems, such as unit commitment or security-constrained OPF, by adding the extra data tables the appendix lists.
  • The API construction is effectively a standardized stress test: a community-standard 'congestion level' could be defined by reporting how close to the thermal limit the load ramping stops.
  • Because the statistical models are drawn randomly, sampling many PGLib instances would let the community report algorithm performance distributions, not single-point gaps.
  • The large gaps in SAD variants suggest that angle-difference limits, not just thermal limits, are a cheap knob for creating hard instances; this could be exploited to generate custom difficulty levels.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This IEEE PES Task Force report introduces PGLib-OPF, a curated, open-access library of AC optimal power flow (AC-OPF) benchmark instances in MATPOWER format, together with a standardized AC-OPF formulation (Model 1). The paper motivates the library by showing that classic MATPOWER cases mostly have optimality gaps below 1% (Section III, Table I), surveys publicly available transmission datasets and their missing parameters (Section IV, Table II), and describes statistical and arithmetic models for completing generator limits, costs, and branch thermal limits (Section V). It then constructs PGLib-OPF cases in three variants -- Typical Operating Conditions (TYP), Active Power Increase (API), and Small Angle Difference (SAD) -- and reports optimality gaps between IPOPT local solutions and a second-order cone relaxation (Section VI, Tables VI--VIII). The paper concludes that the majority of PGLib-OPF networks exhibit significant optimality gaps and are therefore useful for benchmarking AC-OPF algorithms.

Significance. If the claims hold, PGLib-OPF is a valuable community resource: it provides a common, standardized testbed, openly licensed data, reproducible software tooling, and a careful survey of missing data in existing test cases. The paper also ships concrete numerical validation tables and explicitly acknowledges the synthetic nature of much of the data. However, the strength of the central benchmarking claim is limited by the validation methodology: the evidence is based on a single solver pair (IPOPT local solutions versus an SOC relaxation), and the thermal-limit completion used for several large networks is an upper bound rather than a realistic rating. These issues do not negate the value of the library, but they require revision before the headline claims can be accepted as stated.

major comments (3)
  1. [V.B.2 / Eq. (5) and Table V] The thermal-limit model TL-UB in Eq. (5) is not a thermal rating: it is the maximum apparent power flow magnitude compatible with the voltage magnitude and angle difference bounds in Model 1. As a result, any point satisfying constraints (2d) and (2i) automatically satisfies the branch limit (2h), so the TL-UB limits are redundant and cannot create thermal congestion. Table V applies TL-UB to the PEGASE, RTE, IEEE 300, PSERC, and GOC 179 networks, and Table VI reports large optimality gaps in some of these cases, e.g., pglib_opf_case6495_rte TYP at 15.11% and pglib_opf_case6515_rte TYP at 6.40%. Those gaps therefore cannot be interpreted as evidence of congestion-induced hardness, and the Section VII statement that all PGLib-OPF networks have reasonable branch thermal limits is not supported for the TL-UB cases. Please re-run the validation on these networks using TL-Stat or the original partial thermal limits, or explicitly characterize the TL-UB cases as having non-binding thermal limits and adjust the associated claims accordingly.
  2. [VI.A and Tables VI-VIII] The central claim that the PGLib-OPF networks are useful for benchmarking AC-OPF algorithms rests on optimality gaps between one IPOPT local solution and one SOC relaxation. As the paper itself notes, a large gap can be caused by heuristic failure, a weak relaxation, or both; the current experiments do not distinguish these possibilities. More importantly, benchmarking usefulness requires that different algorithms can be distinguished and ranked, which a single solver pair cannot demonstrate. Please add at least one independent solver or a small multi-algorithm comparison on a representative subset of cases to show that the gaps translate into meaningful algorithm differentiation. Without this, the phrase 'useful for benchmarking' is supported only indirectly.
  3. [V.A and Tables III-V] The data-completion models AG-Stat, AC-Stat, and TL-Stat are stochastic and are taken from NESTA [52], and the paper does not report random seeds or a sensitivity analysis for the particular realization used in PGLib-OPF. Since Section VII explicitly acknowledges that the network data are 'by-in-large synthetically generated,' the representativeness of the completed cases is an untested assumption. A small number of independent completions, or a report of the seeds used, would clarify whether the reported optimality gaps are a stable property of the benchmark family or an artifact of a single draw. This is load-bearing because the benchmarking claim presupposes that the synthetic parameters are realistic enough for algorithm comparisons to be meaningful.
minor comments (5)
  1. [Abstract] The phrase 'all the of network data' should read 'all of the network data.'
  2. [III] The phrase 'by-in-large' should read 'by and large'; there is also a grammatical slip in 'cases that where originally designed' (Section IV.A).
  3. [VI.A] The sentence 'This suggest that many of these cases will be useful' contains a subject-verb agreement error and should be corrected.
  4. [Table II] The table lists PEGASE and RTE thermal limits as 'partial,' but Table V shows TL-UB is applied to almost all of those cases; a brief note explaining how 'partial' original data relates to the TL-UB completion would improve clarity.
  5. [V.C] The statement that a 30-degree angle difference bound is 'subsumed by the thermal limits provided with all of the networks considered here' is trivially true for TL-UB cases by construction; please clarify whether it is also asserted for TL-Stat cases.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the validation gaps are computed after dataset construction and do not reduce to the fitted completion models; self-citations to NESTA are independent and not load-bearing.

full rationale

The paper's central claim is that a majority of PGLib-OPF networks exhibit meaningful optimality gaps and are therefore useful for benchmarking AC-OPF algorithms. That claim is supported by numerical results in Tables VI, VII, and VIII, which are obtained by solving Model 1 and its SOC relaxation on the completed datasets. The data-completion models (AG-Stat, AC-Stat, TL-Stat, and TL-UB, Eqs. (4)-(5)) are inputs that define the benchmark instances; the reported gaps are outputs of separate optimization computations. No equation in the paper expresses an optimality gap as an algebraic consequence of the fitted parameters, so there is no self-definitional or fitted-input-called-prediction loop. The paper does rely on NESTA [52] for the statistical completion models, and the corresponding author of the present paper is also an author of NESTA, but [52] is a published, externally grounded body of work built from EIA and SEDS data, and it does not assume the PGLib validation results. Therefore the self-citation is real evidence rather than a circularity. The TL-UB concern raised by skeptics is a legitimate data-quality and external-validity question: Eq. (5) defines an upper bound consistent with voltage and angle limits, so those branch limits may be non-binding and the resulting cases may lack realistic thermal congestion. That concern does not make the derivation circular; it is a critique of whether the benchmark instances faithfully represent real-world networks. The paper itself acknowledges this limitation in the conclusions, stating that the datasets are 'by-in-large synthetically generated' and that there remains a significant gap to industry-grade models. The API and SAD variants are transparently engineered to create congestion and angle stress, which is an explicit construction strategy rather than a hidden circular prediction. Overall, the derivation chain is self-contained: benchmark construction and benchmark evaluation are distinct stages, and no central result reduces by construction to the fitted inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. PGLib-OPF networks are assembled data artifacts, not invented scientific entities, and the paper does not postulate any new mechanism, particle, or conserved quantity. The central claim rests on the fitted statistical models and the solver assumptions listed above.

free parameters (6)
  • TL-Stat thermal limit regression coefficients = a=-5.0886, b=0.4772
    Fitted to thermal limit data in NESTA [52]; used in Eq. (4) to set branch limits for many PGLib cases, directly affecting congestion and observed optimality gaps.
  • AG-Stat exponential rates (PEL, NG, COW) = lambda=0.023254, 0.009188, 0.003201
    Maximum likelihood estimates from EIA data (Table III), used to sample active generation capacities.
  • AG-Stat normal parameters (NUC) = mu=1044.56, sigma=219.27
    Normal distribution for nuclear capacities (Table III), used in generation capacity sampling.
  • AC-Stat fuel cost distribution parameters = PEL 111.34/9.67, NG 34.27/10.98, COW 24.79/8.09, NUC 7.25/0.75 ($/MWh)
    Means and std devs from SEDS fuel cost data (Table IV), used to sample linear generation costs.
  • RG-AM50 reactive capability ratio = 0.5
    Hand-chosen +/-50% of nameplate capacity as reactive bounds when given data exceeds this; a pessimistic modeling choice affecting generator feasibility regions.
  • Voltage angle difference bound = 30 degrees
    Chosen as a generous value based on voltage stability practice; influences SAD variant construction and all cases.
assumptions (5)
  • domain assumption The PI branch model and AC power flow equations (Ohm's law and power balance) accurately represent steady-state grid physics for the test cases.
    Invoked in Model 1 constraints (2e)-(2g); if the model is inappropriate, the benchmarks measure the wrong problem.
  • standard math The SOC relaxation is a valid convex relaxation of Model 1, so infeasibility of the relaxation proves infeasibility of the AC-OPF problem.
    Used in Section III to claim case9target and case145 have no feasible AC-OPF solution.
  • domain assumption Optimality gap between a local AC heuristic and the SOC bound is a meaningful indicator of AC-OPF difficulty.
    Stated in Section III as the premise of the motivating and validation studies; the paper's usefulness claim relies on this heuristic notion.
  • domain assumption The statistical data models from NESTA [52] produce parameter values that are statistically representative of real transmission networks.
    Section V uses these models to fill missing data; if the synthetic parameters are unrealistic, the benchmark conclusions may not transfer to real networks.
  • domain assumption IPOPT converged to a KKT point for the reported AC solutions and the SOC solutions.
    The validation tables assume the reported objective values are reliable; solver failure would change the gap numbers.

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Cite this review

Pith. "Pith review of The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms." pith.science (2026). https://pith.science/paper/7R7ZQBAO

@misc{pith2026190802788,
  author       = {Pith},
  title        = {Pith review of: The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7R7ZQBAO}},
  note         = {Machine review of arXiv:1908.02788}
}
read the original abstract

In recent years, the power systems research community has seen an explosion of novel methods for formulating the AC power flow equations. Consequently, benchmarking studies using the seminal AC Optimal Power Flow (AC-OPF) problem have emerged as the primary method for evaluating these emerging methods. However, it is often difficult to directly compare these studies due to subtle differences in the AC-OPF problem formulation as well as the network, generation, and loading data that are used for evaluation. To help address these challenges, this IEEE PES Task Force report proposes a standardized AC-OPF mathematical formulation and the PGLib-OPF networks for benchmarking AC-OPF algorithms. A motivating study demonstrates some limitations of the established network datasets in the context of benchmarking AC-OPF algorithms and a validation study demonstrates the efficacy of using the PGLib-OPF networks for this purpose. In the interest of scientific discourse and future additions, the PGLib-OPF benchmark library is open-access and all the of network data is provided under a creative commons license.

Figures

Figures reproduced from arXiv: 1908.02788 by the authors.

Figure 1
Figure 1. Π-circuit branch model with an ideal transformer. This is the branch model used by MATPOWER [16]. OPF networks and conducts a baseline validation study to demonstrate that they are suitable for benchmarking the AC￾OPF problem. Section VII provides concluding remarks. An appendix summarizes some variants of the proposed AC-OPF model and discusses the additional data that may be necessary in order to make the PGLIB-OP… view at source ↗
Figure 2
Figure 2. An Empirical Distribution of Generation Fuel Categories by Nameplate [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Reference graph

Works this paper leans on

102 extracted references · 77 canonical work pages · cited by 24 Pith papers

  1. [52]

    NESTA, The N ICTA Energy System Test Case Archive,

    C. Coffrin, D. Gordon, and P. Scott, “NESTA, The N ICTA Energy System Test Case Archive,” CoRR, vol. abs/1411.0359, 2014. [Online]. Available: http://arxiv.org/abs/1411.0359

    arXiv 2014

  2. [1]

    A linear-programming approximation of AC power flows,

    C. Coffrin and P. Van Hentenryck, “A linear-programming approximation of AC power flows,” INFORMS Journal on Computing, vol. 26, no. 4, pp. 718–734, 2014. [Online]. Available: http://dx.doi.org/10.1287/ijoc.2014.0594

    work page arXiv 2014

  3. [2]

    The IV formulation and linear approximations of the AC optimal power flow problem,

    R. P. O’Neill, A. Castillo, and M. B. Cain, “The IV formulation and linear approximations of the AC optimal power flow problem,” Published online at http://www.ferc.gov/industries/electric/indus-act/ market-planning/opf-papers/acopf-2-iv-linearization.pdf, December 2012, accessed: 18/11/2013

    2012

  4. [3]

    Radial distribution load flow using conic programming,

    R. A. Jabr, “Radial distribution load flow using conic programming,” IEEE Transactions on Power Systems , vol. 21, no. 3, pp. 1458–1459, Aug. 2006

    2006

  5. [4]

    Inverter V AR control for distribution systems with renewables,

    M. Farivar, C. R. Clarke, S. H. Low, and K. M. Chandy, “Inverter V AR control for distribution systems with renewables,” in 2011 IEEE International Conference on Smart Grid Communications (SmartGrid- Comm), Oct 2011, pp. 457–462

    2011

  6. [5]

    The QC relaxation: A theoretical and computational study on optimal power flow,

    C. Coffrin, H. L. Hijazi, and P. V . Hentenryck, “The QC relaxation: A theoretical and computational study on optimal power flow,” IEEE Transactions on Power Systems , vol. 31, no. 4, pp. 3008–3018, July 2016

    2016

  7. [6]

    Convex quadratic re- laxations for mixed-integer nonlinear programs in power systems,

    H. Hijazi, C. Coffrin, and P. V . Hentenryck, “Convex quadratic re- laxations for mixed-integer nonlinear programs in power systems,” Mathematical Programming Computation , vol. 9, no. 3, pp. 321–367, Sept. 2017

    2017

  8. [7]

    Semidefinite programming for optimal power flow problems,

    X. Bai, H. Wei, K. Fujisawa, and Y . Wang, “Semidefinite programming for optimal power flow problems,” International Journal of Electrical Power & Energy Systems , vol. 30, no. 6-7, pp. 383 – 392, 2008

    2008

Show all 102 references
  1. [8]

    Moment-based relaxation of the optimal power flow problem,

    D. Molzahn and I. Hiskens, “Moment-based relaxation of the optimal power flow problem,” in Power Systems Computation Conference (PSCC), 2014 , Aug. 2014, pp. 1–7

    2014

  2. [9]

    Optimal power flow as a polynomial optimization problem,

    B. Ghaddar, J. Marecek, and M. Mevissen, “Optimal power flow as a polynomial optimization problem,” IEEE Transactions on Power Systems, vol. 31, no. 1, pp. 539–546, Jan. 2016

    2016

  3. [10]

    Sparsity-exploiting moment-based relaxations of the optimal power flow problem,

    D. K. Molzahn and I. A. Hiskens, “Sparsity-exploiting moment-based relaxations of the optimal power flow problem,” IEEE Transactions on Power Systems, vol. 30, no. 6, pp. 3168–3180, Nov. 2015

    2015

  4. [11]

    Lasserre hierarchy for large scale polynomial optimization in real and complex variables,

    C. Josz and D. K. Molzahn, “Lasserre hierarchy for large scale polynomial optimization in real and complex variables,” SIAM Journal on Optimization , vol. 28, no. 2, pp. 1017–1048, 2018

    2018

  5. [12]

    Convex relaxations in power system op- timization: A brief introduction,

    C. Coffrin and L. A. Roald, “Convex relaxations in power system op- timization: A brief introduction,” arXiv:1807.07227, July 2018, videos available at https://www.youtube.com/watch?v=gB43TmcoUpA&list= PLeuOzWTGxj2ZZ XUutDwNFvNfSWwWCgR5

    2018 arXiv

  6. [13]

    Mathematical programming methods for mi- crogrid design and operations: A survey on deterministic and stochastic approaches,

    G. Wang and H. Hijazi, “Mathematical programming methods for mi- crogrid design and operations: A survey on deterministic and stochastic approaches,” Computational Optimization and Applications , June 2018

    2018

  7. [14]

    A survey of relaxations and approximations of the power flow equations,

    D. K. Molzahn and I. A. Hiskens, “A survey of relaxations and approximations of the power flow equations,” F oundations and Trends in Electric Energy Systems , vol. 4, no. 1-2, pp. 1–221, Feb. 2019

    2019

  8. [15]

    Zero duality gap in optimal power flow problem,

    J. Lavaei and S. H. Low, “Zero duality gap in optimal power flow problem,” IEEE Transactions on Power Systems , vol. 27, no. 1, pp. 92 –107, Feb. 2012. 15 TABLE IX OTHER PROBLEM FORMULATIONS Problem Description Additional Information Required Refs. Power Flow Determine a voltag...

    2012

  9. [16]

    Matpower: Steady-state operations, planning, and analysis tools for power systems research and education,

    R. D. Zimmerman, C. E. Murillo-Sandnchez, 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

    2011

  10. [17]

    Gurobi optimizer reference manual,

    Gurobi Optimization, Inc., “Gurobi optimizer reference manual,” Pub- lished online at http://www.gurobi.com, 2014

    2014

  11. [18]

    IBM ILOG CPLEX Optimization Studio,

    I. IBM, “IBM ILOG CPLEX Optimization Studio,” http://www-01. ibm.com/software/commerce/optimization/cplex-optimizer/, 2014

    2014

  12. [19]

    MOSEK ApS, The MOSEK optimization toolbox. , 2015. [Online]. Available: http://www.mosek.com/resources/doc

    2015

  13. [20]

    Contribution a l’Etude du Dispatching Economique,

    J. L. Carpentier, “Contribution a l’Etude du Dispatching Economique,” Bulletin de la Societe Francoise des Electriciens , vol. 8, no. 3, pp. 431–447, 1962

    1962

  14. [21]

    A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches,

    J. Momoh, R. Adapa, and M. El-Hawary, “A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches,” IEEE Transactions on Power Systems , vol. 14, no. 1, pp. 96 –104, Feb. 1999

    1993

  15. [22]

    A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods,

    J. Momoh, M. El-Hawary, and R. Adapa, “A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods,” IEEE Transactions on Power Systems , vol. 14, no. 1, pp. 105–111, Feb. 1999

    1993

  16. [23]

    Survey of approaches to solving the acopf (opf paper 4),

    A. Castillo and R. P. O’Neill, “Survey of approaches to solving the acopf (opf paper 4),” US Federal Energy Regulatory Commission, Tech. Rep., Mar. 2013

    2013

  17. [24]

    Optimal transmission switching,

    E. Fisher, R. O’Neill, and M. Ferris, “Optimal transmission switching,” IEEE Transactions on Power Systems , vol. 23, no. 3, pp. 1346–1355, 2008

    2008

  18. [25]

    Optimization of AC transmission system planning,

    R. Jabr, “Optimization of AC transmission system planning,” IEEE Transactions on Power Systems , vol. 28, no. 3, pp. 2779–2787, Aug. 2013. 16

    2013

  19. [26]

    Benchmarks for optimization software,

    H. Mittelmann, “Benchmarks for optimization software,” Published online at http://plato.la.asu.edu/bench.html, accessed: 24/11/2014

    2014

  20. [27]

    Power sys- tems test case archive,

    University of Washington, Dept. of Electrical Engineering, “Power sys- tems test case archive,” Published online at http://www.ee.washington. edu/research/pstca/, 1999, accessed: 30/04/2012

    1999

  21. [28]

    Generating realistic infor- mation for the development of distribution and transmission algo- rithms (GRID DATA),

    T. Heidel, K. Hedman, and P. McGrath, “Generating realistic infor- mation for the development of distribution and transmission algo- rithms (GRID DATA),” Published online at https://arpa-e.energy.gov/ ?q=arpa-e-programs/grid-data, January 2016, accessed: 08/08/2018

    2016

  22. [29]

    Power grid security analysis: An optimization approach,

    A. Verma, “Power grid security analysis: An optimization approach,” Ph.D. dissertation, Columbia University, 2009

    2009

  23. [30]

    AC-feasibility on tree networks is NP-hard,

    K. Lehmann, A. Grastien, and P. V . Hentenryck, “AC-feasibility on tree networks is NP-hard,” IEEE Transactions on Power Systems , vol. 31, no. 1, pp. 798–801, Jan. 2016

    2016

  24. [31]

    Examining the limits of the application of semidefinite programming to power flow problems,

    B. Lesieutre, D. Molzahn, A. Borden, and C. DeMarco, “Examining the limits of the application of semidefinite programming to power flow problems,” in 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2011 , Sept. 2011, pp. 1492 –1499

    2011

  25. [32]

    Small test systems for power system economic studies,

    F. Li and R. Bo, “Small test systems for power system economic studies,” in Power and Energy Society General Meeting, 2010 IEEE , July 2010, pp. 1–4

    2010

  26. [33]

    Optimal load flow with steady-state security,

    O. Alsac and B. Stott, “Optimal load flow with steady-state security,” IEEE Transactions on Power Apparatus and Systems , vol. PAS-93, no. 3, pp. 745–751, May 1974

    1974

  27. [34]

    Transaction analysis in deregulated power systems using game theory,

    R. W. Ferrero, S. M. Shahidehpour, and V . C. Ramesh, “Transaction analysis in deregulated power systems using game theory,” IEEE Transactions on Power Systems , vol. 12, no. 3, pp. 1340–1347, Aug. 1997

    1997

  28. [35]

    On-line stability analysis study, RP 90-1,

    G. Bills, “On-line stability analysis study, RP 90-1,” Request online at http://www.osti.gov/scitech/biblio/5984031, Oct. 1970

    1970

  29. [36]

    Pai, Energy Function Analysis for Power System Stability , ser

    A. Pai, Energy Function Analysis for Power System Stability , ser. Kluwer International Series in Engineering and Computer Science. Springer, 1989

    1989

  30. [37]

    Transient stability preventive control of an electric power system using a hybrid method,

    C. M. Ferreira, F. P. M. Barbosa, and C. I. F. Agreira, “Transient stability preventive control of an electric power system using a hybrid method,” in 12th International Middle-East Power System Conference (MEPCON), Mar. 2008, pp. 141–145

    2008

  31. [38]

    Transfer capability calculator,

    Power Systems Engineering Research Center, “Transfer capability calculator,” Published online at http://www.pserc.cornell.edu/tcc/, 2001, accessed: 25/08/2014

    2001

  32. [39]

    IEEE reliability test system. A report prepared by the reliability test system task force of the application of probability methods subcommittee,

    P. F. Albrecht, M. P. Bhavaraju, B. E. Biggerstaff, R. Billinton, G. Elsoe Jorgensen, N. D. Reppen, and P. B. Shortley, “IEEE reliability test system. A report prepared by the reliability test system task force of the application of probability methods subcommittee,” IEEE Tran...

    1979

  33. [40]

    IEEE 24- substation reliability test system, generator data,

    Power Systems Control and Automation Laboratory, “IEEE 24- substation reliability test system, generator data,” Published on- line at http://pscal.ece.gatech.edu/testsys/generators.html, accessed: 22/10/2013

    2013

  34. [41]

    The IEEE reliability test system-1996. A report prepared by the reliability test system task force of the application of probability methods subcommittee,

    C. Grigg, P. Wong, P. Albrecht, R. Allan, M. Bhavaraju, R. Billinton, Q. Chen, C. Fong, S. Haddad, S. Kuruganty, W. Li, R. Mukerji, D. Patton, N. Rau, D. Reppen, A. Schneider, M. Shahidehpour, and C. Singh, “The IEEE reliability test system-1996. A report prepared by the relia...

    1996

  35. [42]

    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,” CoRR, vol. abs/1603.01533, 2016. [Online]. Available: https://arxiv.org/abs/1603.01533

    2016 arXiv

  36. [43]

    Grid structural characteristics as validation criteria for synthetic networks,

    A. B. Birchfield, T. Xu, K. M. Gegner, K. S. Shetye, and T. J. Over- bye, “Grid structural characteristics as validation criteria for synthetic networks,” IEEE Transactions on Power Systems , vol. 32, no. 4, pp. 3258–3265, July 2017

    2017

  37. [44]

    SDET transmission models,

    Sustainable Data Evolution Technology, “SDET transmission models,” Published online at https://egriddata.org/group/ sustainable-data-evolution-technology-sdet, 2018, accessed: 07/31/2018

    2018

  38. [45]

    Grid optimization competition datasets,

    Grid Optimization Competition, “Grid optimization competition datasets,” Published online at https://gocompetition.energy.gov/ competition/beta?page=data, 2018, accessed: 07/31/2018

    2018

  39. [46]

    Reduced network modeling of wecc as a market design prototype,

    J. E. Price and J. Goodin, “Reduced network modeling of wecc as a market design prototype,” in 2011 IEEE Power and Energy Society General Meeting , July 2011, pp. 1–6

    2011

  40. [47]

    Completed projects, M- 21,

    Power Systems Engineering Research Center, “Completed projects, M- 21,” Published online at https://pserc.wisc.edu/research/public reports. aspx, 2018, accessed: 07/31/2018

    2018

  41. [48]

    Matpower,

    R. D. Zimmerman and C. E. Murillo-S ´anchez, “Matpower,” Dec

  42. [49]

    On the implementation of a primal- dual interior point filter line search algorithm for large-scale nonlinear programming,

    A. W ¨achter and L. T. Biegler, “On the implementation of a primal- dual interior point filter line search algorithm for large-scale nonlinear programming,” Mathematical Programming, vol. 106, no. 1, pp. 25–57, 2006

    2006

  43. [50]

    The HSL mathematical software library,

    Research Councils U.K., “The HSL mathematical software library,” Published online at http://www.hsl.rl.ac.uk/, accessed: 30/10/2014

    2014

  44. [51]

    Powermodels.jl: An open-source framework for exploring power flow formulations,

    C. Coffrin, R. Bent, K. Sundar, Y . Ng, and M. Lubin, “Powermodels.jl: An open-source framework for exploring power flow formulations,” in 2018 Power Systems Computation Conference (PSCC) , June 2018, pp. 1–8

    2018

  45. [53]

    Annual electric generator data - eia-860 data file,

    U.S. Energy Information Administration, “Annual electric generator data - eia-860 data file,” Published online at www.eia.gov/electricity/ data/eia860/, 2012, accessed: 25/08/2014

    2012

  46. [54]

    State Energy Data System (SEDS): 1960-2012 (complete),

    ——, “State Energy Data System (SEDS): 1960-2012 (complete),” Published online at http://www.eia.gov/state/seds/seds-data-complete. cfm, 2012, accessed: 25/08/2014

    1960

  47. [55]

    Table 8.2 Average tested heat rates by prime mover and energy source, 2007–2016, form EIA-860, Annual electric generator re- port,

    ——, “Table 8.2 Average tested heat rates by prime mover and energy source, 2007–2016, form EIA-860, Annual electric generator re- port,” Published online at https://www.eia.gov/electricity/annual/html/ epa 08 02.html, 2016, accessed: 29/09/2018

    2007

  48. [56]

    Kundur, Power System Stability and Control

    P. Kundur, Power System Stability and Control . McGraw-Hill Profes- sional, 1994

    1994

  49. [57]

    Accurate load and generation scheduling for linearized DC models with contingencies,

    C. Coffrin, P. Van Hentenryck, and R. Bent, “Accurate load and generation scheduling for linearized DC models with contingencies,” in IEEE Power and Energy Society General Meeting , July 2012, pp. 1–8

    2012

  50. [58]

    Strengthening the SDP relaxation of AC power flows with convex envelopes, bound tightening, and valid inequalities,

    C. Coffrin, H. L. Hijazi, and P. V . Hentenryck, “Strengthening the SDP relaxation of AC power flows with convex envelopes, bound tightening, and valid inequalities,” IEEE Transactions on Power Systems , vol. 32, no. 5, pp. 3549–3558, Sept. 2017

    2017

  51. [59]

    Primal and dual bounds for optimal transmission switching,

    C. Coffrin, H. Hijazi, K. Lehmann, and P. Van Hentenryck, “Primal and dual bounds for optimal transmission switching,” Power Systems Computation Conference (PSCC) , pp. 1–8, 08 2014

    2014

  52. [60]

    Impacts of topology control on the ACOPF,

    T. Potluri and K. W. Hedman, “Impacts of topology control on the ACOPF,” in IEEE Power and Energy Society General Meeting , 2012, pp. 1–7

    2012

  53. [61]

    Local solu- tions of the optimal power flow problem,

    W. Bukhsh, A. Grothey, K. McKinnon, and P. Trodden, “Local solu- tions of the optimal power flow problem,” IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4780–4788, Nov 2013

    2013

  54. [62]

    Security Analysis and Optimization,

    B. Stott, O. Alsac ¸, and A. J. Monticelli, “Security Analysis and Optimization,” Proceedings of the IEEE , vol. 75, no. 12, pp. 1623– 1644, December 1987

    1987

  55. [63]

    Optimal power flow — Basic requirements for real-life problems and their solutions,

    B. Stott and O. Alsac, “Optimal power flow — Basic requirements for real-life problems and their solutions,” self published, available from brianstott@ieee.org, July 2012

    2012

  56. [64]

    Critical review of recent advances and further devel- opments needed in AC optimal power flow,

    F. Capitanescu, “Critical review of recent advances and further devel- opments needed in AC optimal power flow,” Electric Power Systems Research, vol. 136, pp. 57–68, 2016

    2016

  57. [65]

    Interpretation and use of generator reactive capability diagrams,

    J. Y . Jackson, “Interpretation and use of generator reactive capability diagrams,” IEEE Transactions on Industry and General Applications , vol. IGA-7, no. 6, pp. 729–732, November 1971

    1971

  58. [66]

    Estimation of constraint parameters in optimal power flow data sets,

    D. K. Molzahn, Z. B. Friedman, B. C. Lesieutre, C. L. DeMarco, and M. C. Ferris, “Estimation of constraint parameters in optimal power flow data sets,” in 47th North American Power Symposium (NAPS) , October 2015. 17

    2015

  59. [67]

    Examination of three different ACOPF formulations with generator capability curves,

    B. Park, L. Tang, M. C. Ferris, and C. L. DeMarco, “Examination of three different ACOPF formulations with generator capability curves,” IEEE Transactions on Power Systems , vol. 32, no. 4, pp. 2913–2923, July 2017

    2017

  60. [68]

    Optimal voltage man- agement for enhancing electricity market efficiency,

    M. Ili ´c, S. Cviji ´c, J. H. Lang, and J. Tong, “Optimal voltage man- agement for enhancing electricity market efficiency,” in IEEE Power Energy Society General Meeting , July 2015, pp. 1–5

    2015

  61. [69]

    IEEE PES Com- petition on Application of Modern Heuristic Optimization Algorithms for Solving Optimal Power Flow Problems,

    K. Y . Lee, I. Erlich, J. L. Rueda, and S. Wildenhues, “IEEE PES Com- petition on Application of Modern Heuristic Optimization Algorithms for Solving Optimal Power Flow Problems,” Published online at http: //sites.ieee.org/pes-iss/working-groups/, 2013, accessed: 25/08/2014

    2013

  62. [70]

    A progressive method to solve large-scale AC optimal power flow with discrete variables and control of the feasibility,

    M. Ruiz, J. Maeght, A. Mari ´e, P. Panciatici, and A. Renaud, “A progressive method to solve large-scale AC optimal power flow with discrete variables and control of the feasibility,” in Power Systems Computation Conference (PSCC) , Aug. 2014, pp. 1–7

    2014

  63. [71]

    Heuristic MINLP for optimal power flow problems,

    C. Coffrin and H. L. Hijazi, “Heuristic MINLP for optimal power flow problems,” Application of Modern Heuristic Optimization Algorithms for Solving Optimal Power Flow Problems Competition, 2014 IEEE Power & Energy Society General Meeting (PES) , 2014

    2014

  64. [72]

    Some applications of optimization techniques to power systems problems,

    A. M. Sasson and H. M. Merrill, “Some applications of optimization techniques to power systems problems,” Proceedings of the IEEE , vol. 62, no. 7, pp. 959–972, July 1974

    1974

  65. [73]

    J. A. Momoh, Electric Power System Applications of Optimization . CRC Press, 2008

    2008

  66. [74]

    A. J. Wood, B. F. Wollenberg, and G. B. Sheble, Power Generation, Operation and Control , 3rd ed. John Wiley and Sons, Inc., 2013

    2013

  67. [75]

    Review of load-flow calculation methods,

    B. Stott, “Review of load-flow calculation methods,” Proceedings of the IEEE , vol. 62, no. 7, pp. 916–929, July 1974

    1974

  68. [76]

    Recent advances in computational methods for the power flow equations,

    D. Mehta, D. K. Molzahn, and K. Turitsyn, “Recent advances in computational methods for the power flow equations,” in American Control Conference (ACC) , Boston, MA, USA, July 2016, pp. 1753– 1765

    2016

  69. [77]

    Multiperiod optimal power flow using Benders decomposition,

    N. Alguacil and A. J. Conejo, “Multiperiod optimal power flow using Benders decomposition,”IEEE Transactions on Power Systems, vol. 15, no. 1, pp. 196–201, February 2000

    2000

  70. [78]

    Optimal thermal generating unit commit- ment: A review,

    S. Sen and D. P. Kothari, “Optimal thermal generating unit commit- ment: A review,” International Journal of Electrical Power & Energy Systems, vol. 20, no. 7, pp. 443–451, 1998

    1998

  71. [79]

    Unit commitment–A bibliographical survey,

    N. P. Padhy, “Unit commitment–A bibliographical survey,” IEEE Transactions on Power Systems , vol. 19, no. 2, pp. 1196–1205, May 2004

    2004

  72. [80]

    Large- scale unit commitment under uncertainty,

    M. Tahanan, W. Van Ackooij, A. Frangioni, and F. Lacalandra, “Large- scale unit commitment under uncertainty,” 4OR, vol. 13, no. 2, pp. 115–171, 2015

    2015

  73. [81]

    On mixed inte- ger programming formulations for the unit commitment prob- lem,

    B. Knueven, J. Ostrowski, and J. Watson, “On mixed inte- ger programming formulations for the unit commitment prob- lem,” Preprint, http:// www.optimization-online.org/ DB HTML/ 2018/ 11/ 6930.html, Nov. 2018

    2018

  74. [82]

    A review of transmission switching and network topology optimization,

    K. W. Hedman, S. S. Oren, and R. P. O’Neill, “A review of transmission switching and network topology optimization,” in IEEE Power & Energy Society General Meeting , July 2011, pp. 1–7

    2011

  75. [83]

    Optimal AC distribution systems reconfiguration,

    H. L. Hijazi and S. Thi ´ebaux, “Optimal AC distribution systems reconfiguration,” in Power Systems Computation Conference (PSCC) , Wroclaw, Poland, August 2014

    2014

  76. [84]

    Power system state estimation: A survey,

    F. F. Wu, “Power system state estimation: A survey,” International Journal of Electrical Power & Energy Systems , vol. 12, no. 2, pp. 80–87, 1990

    1990

  77. [85]

    Abur and A

    A. Abur and A. G ´omez Exp ´osito, Power System State Estimation: Theory and Implementation . Marcel Dekker, 2004

    2004

  78. [86]

    PSSE redux: Convex relaxation, decentralized, robust, and dynamic approaches,

    V . Kekatos, G. Wang, H. Zhu, and G. B. Giannakis, “PSSE redux: Convex relaxation, decentralized, robust, and dynamic approaches,” arXiv:1708.03981, August 2017

    2017 arXiv

  79. [87]

    C. W. Taylor, Power System V oltage Stability. McGraw-Hill, 1994

    1994

  80. [88]

    V oltage stability assessment: Concepts, practices and tools,

    I. Dobson, T. Van Cutsem, C. V ournas, C. L. DeMarco, M. Venkata- subramanian, T. Overbye, and C. A. Canizares, “V oltage stability assessment: Concepts, practices and tools,” IEEE Power Engineering Society, Power System Stability Subcommittee Special Publication SP101PSS, August 2002

    2002

  81. [89]

    P. W. Sauer and M. A. Pai, Power System Dynamics and Stability . Prentice Hall, 1998

    1998

  82. [90]

    So- lution Techniques for Transient Stability-Constrained Optimal Power Flow – Part I,

    S. Abhyankar, G. Geng, M. Anitescu, X. Wang, and V . Dinavahi, “So- lution Techniques for Transient Stability-Constrained Optimal Power Flow – Part I,” IET Generation, Transmission & Distribution , vol. 11, pp. 3177–3185, August 2017

    2017

  83. [91]

    Solution Tech- niques for Transient Stability-Constrained Optimal Power Flow – Part II,

    G. Geng, S. Abhyankar, X. Wang, and V . Dinavahi, “Solution Tech- niques for Transient Stability-Constrained Optimal Power Flow – Part II,” IET Generation, Transmission & Distribution , vol. 11, pp. 3186– 3193, August 2017

    2017

  84. [92]

    Risk assessment of cascading outages: Methodologies and challenges,

    M. Vaiman, K. Bell, Y . Chen, B. Chowdhury, I. A. Dobson, P. Hines, M. Papic, S. Miller, and P. Zhang, “Risk assessment of cascading outages: Methodologies and challenges,” IEEE Transactions on Power Systems, vol. 27, no. 2, pp. 631–641, May 2012

    2012

  85. [93]

    Test systems and mathematical models for transmission network expansion planning,

    R. Romero, A. Monticelli, A. Garcia, and S. Haffner, “Test systems and mathematical models for transmission network expansion planning,” IEE Proceedings - Generation, Transmission and Distribution, vol. 149, no. 1, pp. 27–36, January 2002

    2002

  86. [94]

    Dynamic simulations of combined transmission and distribution systems using parallel processing tech- niques,

    P. Aristidou and T. Van Cutsem, “Dynamic simulations of combined transmission and distribution systems using parallel processing tech- niques,” in Power Systems Computation Conference (PSCC) , August 2014, pp. 1–7

    2014

  87. [95]

    Experiences integrating transmission and distribution simulations for DERs with the Integrated Grid Modeling System (IGMS),

    B. Palmintier, E. Hale, B. Hodge, K. Baker, and T. M. Hansen, “Experiences integrating transmission and distribution simulations for DERs with the Integrated Grid Modeling System (IGMS),” in Power Systems Computation Conference (PSCC) , June 2016, pp. 1–7

    2016

  88. [96]

    A combined transmission and distribution system co-simulation framework for assessing the impact of V olt/V AR control on transmission system,

    K. Balasubramaniam and S. Abhyankar, “A combined transmission and distribution system co-simulation framework for assessing the impact of V olt/V AR control on transmission system,” in IEEE Power Energy Society General Meeting , July 2017, pp. 1–5

    2017

  89. [97]

    Cyber physical system approach for design of power grids: A survey,

    S. K. Khaitan and J. D. McCalley, “Cyber physical system approach for design of power grids: A survey,” in IEEE Power Energy Society General Meeting , July 2013, pp. 1–5

    2013

  90. [98]

    Coordinated scheduling for interdependent electric power and natural gas infrastructures,

    A. Zlotnik, L. A. Roald, S. Backhaus, M. Chertkov, and G. Andersson, “Coordinated scheduling for interdependent electric power and natural gas infrastructures,” IEEE Transactions on Power Systems , vol. 32, no. 1, pp. 600–610, Jan. 2017

    2017

  91. [99]

    Optimal water-power flow problem: Formulation and distributed optimal solution,

    A. S. Zamzam, E. Dall’Anese, C. Zhao, J. A. Taylor, and N. Sidiropou- los, “Optimal water-power flow problem: Formulation and distributed optimal solution,” IEEE Transactions on Control of Network Systems , vol. 6, no. 1, pp. 37–47, Mar. 2019

    2019

  92. [100]

    Chance-constrained opti- mal power flow: Risk-aware network control under uncertainty,

    D. Bienstock, M. Chertkov, and S. Harnett, “Chance-constrained opti- mal power flow: Risk-aware network control under uncertainty,” SIAM Review, vol. 56, no. 3, pp. 461–495, 2014

    2014

  93. [101]

    A survey of distributed optimization and control algorithms for electric power systems,

    D. Molzahn, F. D ¨orfler, H. Sandberg, S. H. Low, S. Chakrabarti, R. Baldick, and J. Lavaei, “A survey of distributed optimization and control algorithms for electric power systems,” IEEE Transactions on Smart Grid , vol. 8, no. 6, pp. 2939–2940, Nov. 2017. LA-UR-18-29054

    2017

  94. [2016]

    Available: https://doi.org/10.5281/zenodo.3237810

    [Online]. Available: https://doi.org/10.5281/zenodo.3237810

    doi

Pith tools

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