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The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms
Sogol Babaeinejadsarookolaee, Adam Birchfield, Richard D. Christie, Carleton Coffrin, Christopher DeMarco, Ruisheng Diao, Michael Ferris, Stephane Fliscounakis, 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
TL;DR
Existing AC-OPF benchmarks often lack modern, comprehensive network and generation data, making comparisons among emerging methods difficult. The report standardizes an AC-OPF formulation and introduces the open-access PGLIB-OPF library, whose curated variants and validation study provide benchmark cases with useful optimality gaps. The report also identifies limitations in the formulation’s treatment of reactive-power controls.
Problem
Existing network datasets often lack parameters such as branch thermal limits and generator cost functions needed to evaluate AC-OPF algorithms.
Method
The report specifies a standardized AC-OPF formulation and curates MATPOWER-format PGLIB-OPF networks using data-driven models and challenging variants.
Results
The validation study finds that the majority of PGLIB-OPF networks exhibit significant optimality gaps and are useful for benchmarking AC-OPF algorithms.
Takeaways & Limitations
PGLIB-OPF supplies benchmark networks with reasonable generation limits, generation costs, and branch thermal limits, plus active-power-increase and small-angle-difference variants.
Takeaways & Limitations
The proposed AC-OPF formulation includes limited reactive-power control devices, which may bias feasible solutions toward a specific voltage profile.
Abstract
from arXiv · showhide
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.
NOMENCLATURE
The paper standardizes an AC-OPF model over complex network variables and specifies the network, generator, branch, and voltage parameters required to encode it. It motivates this formulation within the expanding literature on AC power-flow approximations and relaxations and the need for comparable benchmark data.
- Background: The paper situates AC-OPF benchmarking amid expanding approximations and relaxations of steady-state AC power-flow equations.Examples include LPAC, IV-Flow, SOC, CDF, QC, SDP, and moment/sum-of-squares methods.
- Benchmark library: PGLIB-OPF provides creative-commons AC transmission networks in MATPOWER format with data required for the proposed AC-OPF problem.The report introduces the library to improve evaluation of AC-OPF algorithms and includes a validation study of its networks.
- Required data: The model requires bus, generator, branch, reverse-branch, demand, shunt, voltage, cost, admittance, transformer, thermal-limit, and reference-bus parameters.Most parameters are specified in MATPOWER data files, while some are computed from raw data.
- AC-OPF formulation: The proposed AC-OPF model is a non-convex nonlinear program that minimizes active-power injection costs subject to voltage, generation, balance, and branch-flow constraints.The formulation uses a Π-circuit branch model with an ideal transformer and represents branch flows consistently with Ohm’s Law.
III. MOTIVATION
The motivating study evaluates AC-OPF difficulty and data adequacy in MATPOWER v6.0 cases using feasible solutions and an SOC relaxation. It finds generally small gaps, infeasible cases attributable to data quality, and missing dataset information that motivates PGLIB-OPF curation.
- Study design: The preliminary study examines thirty-five MATPOWER v6.0 AC transmission datasets using optimality gaps as an indicator of AC-OPF difficulty.The gap compares the objective value of a feasible AC-OPF solution with the objective bound from a convex relaxation.
- Study design: The study uses IPOPT to obtain KKT-point feasible solutions and a Second-Order Cone relaxation to provide objective bounds.Both mathematical programs were formulated and solved with PowerModels.jl.
- Results: Most MATPOWER cases have optimality gaps below 1%, while no feasible solution was found for case9target and case145.The study treats large gaps as an indication of challenging instances, while noting that large gaps are not necessary for AC-OPF hardness.
- Results: The SOC relaxation provides a numerical proof that case9target and case145 have no feasible AC-OPF solution, suggesting data quality rather than algorithmic difficulty causes infeasibility.This result limits the interpretation of failed heuristic solutions as evidence of difficult instances.
IV. PUBLICLY AVAILABLE NETWORK DATA
The survey finds that few publicly available transmission networks contain all data required for the proposed AC-OPF model, while some cases are redundant, infeasible, atypical, or restricted by dataset requirements.
- Few surveyed networks include all data required for Model 1, especially generation capacity limits, generation cost functions, and branch thermal limits.Table II identifies where these data are available or missing; missing entries must be added before studying the model.
- The collection considers notable networks separately because some are nearly identical to existing cases and would add no additional value.The IEEE 30 test case is described as nearly identical to the IEEE 30 case and excluded for that reason.
- The Ferrero, Shahidehpour, and Ramesh 30 Bus System was removed because it closely resembles another 30 Bus System and adds no additional value.
- One test case cannot satisfy all Model 1 constraints in its specified state because it does not converge to an AC power flow solution.A feasible solution requires increasing active-generation upper bounds and widening voltage bounds, but still produces significant voltage drops and atypical line parameters.
- The survey restricts the considered collection to creative commons datasets to comply with PGLIB data requirements.
- Another omitted network has generation units one or two orders of magnitude larger than documented U.S. units, suggesting they may represent imports and exports rather than generators.Its atypical characteristics compared with other test cases motivate omission.
4) SDET 2000 System:
The SDET 2000 system motivates data completion because transmission datasets often omit generator descriptions and costs. Its fuel-category model infers generator types from active limits and treats zero-capability devices as synchronous condensers.
- The SDET 2000 system is omitted from later PGLIB-OPF versions because it resembles systems already represented in the Grid Optimization Competition networks.
- Most AC transmission datasets provide only generator injection limits and a dispatch point, often omitting the active-power cost function needed by Model 1.
- The model uses EIA generator and fuel-cost data together with fuel-type-dependent mechanical properties to infer missing generator information.It focuses on Petroleum, Natural Gas, Coal, and Nuclear Fuel categories.
- A generator’s active power injection limit serves as a proxy for nameplate capacity when probabilistically assigning its fuel category.The classifier selects the corresponding capacity bin and rolls a weighted die to choose the fuel type.
- Generators with active-generation upper and lower bounds equal to zero receive a special SYNC category identifying synchronous condensers.Together with the empirical fuel distribution, this special case forms the GF-Stat classification model.
2) Generation Capacity Models:
The paper develops statistical and arithmetic models to fill missing generation and branch data in AC transmission cases, using fuel-specific capacity, cost, and thermal-limit assumptions.
- Generation Capacity Models: Two generation-capability models address AC transmission datasets with unreasonable or missing generation injection limits.
- Generation Capacity Models: AG-Stat samples a fuel-specific nameplate-capacity distribution until it exceeds a generator’s current active output or upper limit, then updates that limit.Exponential distributions model Petroleum, Natural Gas, and Coal, while a normal distribution models Nuclear Fuel.
- Generation Capacity Models: RG-AM50 constrains reactive capability using the observation that synchronous-machine reactive limits are roughly ±50% of nameplate capacity.Given reactive bounds are retained unless they exceed 50% of the nameplate capacity.
- Generation Cost Model: The generator cost model focuses on marginal generation costs in an idealized noncompetitive environment and fits normally distributed fuel costs from SEDS data.
- Branch Thermal Limit Models: Because datasets often provide only impedance, line charging, and sometimes nominal voltage, the paper uses data-driven and arithmetic approaches to estimate branch thermal limits.
- Branch Thermal Limit Models: TL-Stat estimates thermal limits from branch impedance and nominal voltage, using resistance-to-impedance ratio as a clue about conductor type and configuration.The ratio is intended to be independent of line length.
2) A Reasonable Upper Bound:
The statistical thermal-limit model is useful when branch resistance, reactance, and nominal voltage are available, but it fails for networks missing these data. TL-UB provides an alternate way to compute reasonable thermal limits using bounded voltage magnitudes and angle differences.
- Limitations of the statistical model: The statistical model cannot produce branch thermal limits when r, x, or nominal voltage data are missing.This affects cases such as transformers and ideal lines.
- Limitations of the statistical model: Transformers and ideal lines are notable examples requiring an alternate thermal-limit method.Transformers may have different nominal voltages on each side, while ideal lines may lack an r value.
- Alternate upper bound: TL-UB computes a reasonable thermal limit for a branch using the voltage-magnitude and voltage-angle bounds included in Model 1.The section introduces this construction for branches in E and refers to TL-UB as the resulting model.
- Angle-difference assumptions: PGLIB-OPF assigns generous ±30° voltage angle-difference bounds that are justified by practical voltage-stability requirements.These bounds are also subsumed by the thermal limits of the considered networks and do not affect their best-known solutions.
VI. THE PGLIB-OPF NETWORKS
PGLIB-OPF networks are developed by applying the proposed models to complete missing network data. Table V summarizes which models convert the base network data into the benchmark instances.
- Network construction: The PGLIB-OPF networks are developed by leveraging proposed models to complete missing data in the base network datasets.The completed data support construction of the benchmark networks.
- Network construction: Table V summarizes the models used to convert base network data into PGLIB-OPF networks.
A. Results
A validation study formulates the proposed AC-OPF model and its SOC relaxation with PowerModels.jl and solves both using IPOPT. Most PGLIB-OPF TYP cases have gaps below 1%, while several cases show substantial gaps suitable for benchmarking.
- Validation setup: PowerModels.jl v0.17 formulated Model 1 and its SOC relaxation, and IPOPT 3.12 solved both models using the HSL linear algebra library.The experiments ran on a server with two 2.10GHz Intel CPUs and 128GB of RAM.
- Validation results: Most PGLIB-OPF TYP networks have optimality gaps below 1%.The TYP cases are the base PGLIB-OPF networks evaluated under typical operating conditions.
- Validation results: Several networks exhibit significant optimality gaps, including case5 pjm, case30 ieee, case162 ieee dtc, case6495 rte, and case6515 rte.These cases are identified as interesting candidates for benchmarking AC-OPF algorithms.
B. Building More Challenging Test Cases
PGLIB-OPF extends its typical cases with Active Power Increase and Small Angle Difference variants designed to create more challenging AC-OPF benchmarks. The API cases substantially enlarge optimality gaps, while the reported gaps can reflect either heuristic failure or weak SOC relaxations.
- Typical operating conditions: Typical operating-condition networks provide a suitable starting point for benchmarking AC-OPF algorithms.
- Active Power Increase cases: Active Power Increase cases proportionally raise active power demands until branch thermal limits become binding.The construction solves an optimization problem for each standard PGLIB-OPF network and then updates other parameters, including generator capabilities and cost functions.
- Active Power Increase cases: API cases have optimality gaps above 1% in 60% of cases, including eight cases with gaps above 10%.These results suggest that many API cases are useful for benchmarking AC-OPF algorithms.
- Small Angle Difference cases: Small Angle Difference cases are constructed to emphasize the impact of voltage angle-difference bounds on power-system optimization approaches.Their construction is motivated by research showing that these bounds can significantly affect optimization methods.
- Interpreting the gaps: Significant optimality gaps may result from failed heuristic searches for global AC-OPF solutions or weak SOC relaxations.Both factors are presented as research opportunities for AC-OPF algorithm development.
VII. CONCLUSIONS
PGLIB-OPF addresses shortcomings in existing AC-OPF benchmark datasets by providing realistic, challenging networks with validated benchmarking value. The report also identifies important boundaries for future industry-grade and real-world extensions.
- VII. CONCLUSIONS: PGLIB-OPF networks use data-driven models to provide reasonable generation limits, generation costs, and branch thermal limits.Active-power-increase and small-angle-difference variants add further challenging benchmark cases.
- VII. CONCLUSIONS: A validation study found significant optimality gaps in the majority of PGLIB-OPF networks, supporting their use for AC-OPF benchmarking.
- VII. CONCLUSIONS: Industry-grade AC-OPF studies still require configurable assets, N-1 contingencies, differentiated thermal limits, and generator capability curves.
- VII. CONCLUSIONS: PGLIB-OPF datasets remain largely synthetic, leaving continued need for industry engagement and more detailed real-world benchmark networks.
APPENDIX EXTENSIONS AND ALTERNATIVE APPLICATIONS
The appendix describes modifications to the benchmark formulation and alternative power-system applications requiring data beyond the standard PGLIB-OPF model. It covers current-flow limits, branch-charging generalizations, generator capability curves, reactive controls, and broader optimization settings.
- A. Current Flow Limits: Current-flow limits can replace or augment apparent-power limits in the AC-OPF formulation.The associated current limit is often treated as equivalent in per-unit value to the apparent-power limit.
- B. Branch Charging Model: The generalized branch-charging model distinguishes from- and to-side charging admittances and includes conductance and asymmetrical charging effects.
- Generator Capability Curves: Capability-curve generator models couple active and reactive power limits to constrain heating from internal generator currents.
- D. Voltage & Reactive Power Control: Reactive power controls such as bus shunts and transformer taps affect voltage management, but Model 1 includes limited control devices.This limitation may bias feasible solutions toward the voltage profile supplied with the network data.
- Alternative Applications: The single-period steady-state AC-OPF model does not provide all information needed for other power-system optimization and control problems.Those applications may require augmenting PGLIB-OPF with additional data.