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

Cédric Josz, Stéphane Fliscounakis, Jean Maeght, Patrick Panciatici

arXiv:1603.01533v3math.OC

TL;DR

The paper addresses the need for realistic, shared power-grid data and improved power-flow computation methods. It publishes nine MATPOWER cases from iTesla, RTE, and PEGASE, provides a MATLAB QCQP conversion tool, and evaluates OPF solutions with lower-bound methods. Knitro solutions are reported as 0.87% to 2.14% optimal, while semidefinite results are limited by solver maturity and numerical problems.

  • Problem

    Power-systems researchers need shared realistic datasets to develop faster and more reliable optimal power flow methods.

  • Method

    The paper publishes nine MATPOWER test cases, provides MATLAB conversion to standard QCQP format, and computes OPF lower bounds with DCOPF, Knitro, and SDPOPF.

  • Results

    0.87% to 2.14% optimality is reported for all Knitro local solutions, while the largest cases achieve only 1.7% and 1.3% proven global optimality with Mosek.

  • Takeaways & Limitations

    The published cases and QCQP converter are intended to help researchers address large-scale power-system optimization without requiring power-system expertise.

Abstract

from arXiv · show

In this paper, we publish nine new test cases in MATPOWER format. Four test cases are French very high-voltage grid generated by the offline plateform of iTesla: part of the data was sampled. Four test cases are RTE snapshots of the full French very high-voltage and high-voltage grid that come from French SCADAs via the Convergence software. The ninth and largest test case is a pan-European ficticious data set that stems from the PEGASE project. It complements the four PEGASE test cases that we previously published in MATPOWER version 5.1 in March 2015. We also provide a MATLAB code to transform the data into standard mathematical optimization format. Computational results confirming the validity of the data are presented in this paper.

I. INTRODUCTION

The paper publishes realistic power-grid datasets in MATPOWER format to support improved power-flow and optimal-power-flow methods. The cases draw on iTesla simulations, RTE SCADA snapshots, and the fictitious PEGASE pan-European network.

  • The datasets are intended to help develop faster and more reliable optimal power flow methods.
  • The MATPOWER format provides a standardized representation compared with other available public grid-data formats.
  • Nine test cases are published in MATPOWER format, with four generated from iTesla, four from RTE snapshots, and one from PEGASE.
  • The iTesla cases use sampled loads and uncontrollable generation to construct full AC network states.
  • The RTE cases originate from French SCADA data processed through Convergence, RTE’s main network analysis tool.
  • PEGASE data represent the size and complexity of the European high-voltage network but are fictitious and unsuitable for grid operation or planning.

III. CONVERSION OF THE DATA

The published cases were adapted to MATPOWER despite representation differences between the source tools and MATPOWER. Some transformations preserve power-flow equations while modifying OPF constraints or omitting operational distinctions.

  • Some modifications to the original grid data were required to fit the MATPOWER format.
  • MATPOWER cannot represent pumped-storage generators directly because negative generation values are treated as dispatchable loads.
  • The source snapshots distinguish pumped-storage operation from dispatchable loads in both market behavior and reactive-power production.
  • Ward equivalents and equivalent three-winding transformers can produce small negative reactances or resistances in the snapshot data.
  • For asymmetric PEGASE shunts, line charging susceptance was set to zero and shunts were represented nodally; power-flow equations remain unchanged, but OPF line-flow constraints change.
  • The section introduces network-case figures and notes that previously published PEGASE cases are included in the description and result tables.

A. General figures

The general-figures section inventories the structural properties of the test cases, including equipment counts, voltage levels, and branches with negative parameters.

  • The case tables report the numbers of buses, generating units, branches, and transformers for each network.
  • A separate table reports the voltage-level range included in each case.
  • The voltage-level distribution is also summarized by counting buses in each main voltage-level category.
  • The cases are characterized by counts of branches with negative resistance and negative reactance, with no branch having both.

B. Impedances and voltages

The paper illustrates network impedances and bus voltages through two graph types: ordered impedance norms and complex-plane voltage plots with 0.9 and 1.1 p.u. reference circles.

  • The impedance graphs plot all line-impedance norms in descending order on a logarithmic scale.
  • The voltage graphs plot the complex values of all bus voltages and mark 0.9 and 1.1 p.u. reference circles.
  • The illustrations use case2868rte for the iTesla cases, case6515rte for the RTE snapshots, and case13659pegase for PEGASE.
  • The selected cases each have separate impedance and complex-plane voltage figures.

V. NUMERICAL RESULTS

The numerical results use Knitro to obtain feasible OPF solutions, including a parameter adjustment that allowed all OPF instances to be solved. The paper also outlines alternative ways to improve feasible solutions.

  • Adjusting Knitro’s xtol parameter through knitro.opt enabled all OPF instances to be solved.MATPOWER’s default xtol setting was considered too large.
  • A. Using Knitro to find feasible solutions: Knitro provides feasible OPF solutions even though solving a nonconvex problem is expected to yield only local optimality conditions.The paper uses feasibility rather than local optimality as the relevant property of these solutions.
  • A. Using Knitro to find feasible solutions: Alternative methods or heuristics could also be used to find better feasible OPF solutions.
  • A. Using Knitro to find feasible solutions: One proposed approach modifies the OPF for numerical improvement, solves the modified problem globally, and transfers its solution to the original OPF.Suggested modifications include node aggregation and penalty terms.
  • A. Using Knitro to find feasible solutions: Improving feasible OPF solutions alone is insufficient; stronger lower bounds are also needed to establish global optimality.

B. Basic evaluation of optimality gap

The paper evaluates OPF optimality gaps by comparing ACOPF solutions with basic DCOPF lower bounds. Knitro’s local solutions are reported as 0.87% to 2.14% optimal, with a specific caveat for two PEGASE cases.

  • Semidefinite programming can provide good OPF lower bounds, but comparisons with basic lower bounds remain necessary.
  • DCOPF without flow limits supplies a trivial lower bound for ACOPF when linear unit costs equal 1.Under these costs, the DCOPF objective minimizes total generation, equivalently minimizing losses in the stated setup.
  • The optimality gap is computed by comparing the ACOPF value from Knitro with the basic lower bound obtained from DCOPF.
  • For case9241pegase and case13659pegase, negative-resistance branches invalidate DCOPF as a strict OPF lower bound, making the final optimality values uncertain.
  • 0.87% to 2.14% optimality was obtained for all Knitro local solutions.The paper notes that these solutions lack information establishing whether they are globally optimal.

C. OPF with or without flow constraints

The experiments compare OPF with apparent-power limits, current limits, and no flow limits. The resulting objective values are very similar across constrained and unconstrained cases, including the largest case.

  • Three computation series use apparent-power limits, current limits, or no flow limits.MATPOWER options ’S’ and ’I’ specify the apparent-power and current-limit formulations, respectively.
  • Values with and without flow limits are very similar, and identical for the largest case, case13659pegase.The paper attributes this pattern to realistic constructed or observed snapshot data and normal grid operation practices.
  • RTE snapshots, PEGASE data, and iTesla data were designed or observed to represent realistic grid conditions.

D. Lower bounds with SDPOPF

The paper uses SDPOPF semidefinite relaxations to obtain lower bounds for large OPF instances and compare them with DCOPF bounds and feasible Knitro solutions. The computations show that very large cases are tractable, but solver numerical failures limit confidence in several optimality certificates.

  • SDPOPF computes semidefinite-relaxation lower bounds, compared against DCOPF lower bounds and feasible OPF solutions from Knitro.The comparison orders DCOPF, SDP-relaxation, and feasible OPF values as lower and upper bounds.
  • 6 to 13 thousand buses could be addressed by SDPOPF without exceeding the 48GB RAM computer limit.
  • Sedumi reported numerical problems in all cases, while Mosek reported MSK_RES_TRM_STALL(), requiring caution when interpreting SDP results.
  • Sedumi produced an SDP lower bound larger than the OPF/Knitro value for case6494rte, indicating that this bound was not correctly computed.
  • For the two largest cases, Mosek proved global optimality only to 1.7% and 1.3%, while case1888rte reached 0.36%.
  • Knitro OPF results were unchanged when feastol was tightened to 1e-10, excluding that precision setting as an explanation for the reported values.

E. Global optimality quest

The paper frames global optimality as a foundation for extending OPF optimization beyond continuous problems. It aims to prove optimality for the published cases with precision 10^-5 or 10^-6 and then address discrete and bilevel grid-operation problems.

  • The stated goal is to prove global optimality for all cases with precision 10^-5 or 10^-6.
  • The paper places continuous global OPF optimization within a broader view of grid operations and development, including future bilevel optimization.
  • The authors present global optimality as relevant to future optimization of OPF with discrete variables such as generator statuses, transformer taps, shunts, and topology choices.

VI. MATHEMATICAL FORMAT

The paper converts MATPOWER optimal power flow test cases into large-scale sparse QCQPs, providing a standard format for mathematical optimization methods. The resulting instances are sparse enough that the authors believe global optimization may be possible.

  • VI. MATHEMATICAL FORMAT: The qcqp_opf.m code converts MATPOWER test cases into large-scale sparse quadratically-constrained quadratic programs.The conversion is intended to let applied mathematicians evaluate methods without requiring power-systems knowledge.
  • VI. MATHEMATICAL FORMAT: The QCQP formulation treats the optimal power flow objective as linear in active power and discards higher-degree objective terms.For rte and pegase cases, this formulation remains equivalent to OPF with current line-flow constraints.
  • VI. MATHEMATICAL FORMAT: The standard format uses a column vector x with nVAR variables, equality constraints, and inequality constraints.The supplied matrices and vectors may be complex, Hermitian, or real symmetric depending on an input parameter.
  • VI. MATHEMATICAL FORMAT: The reported QCQP instances are sparse, with the table measuring nonzero monomials against all possible monomials in a fully dense QCQP.The authors therefore believe these OPF instances may be solvable to global optimality.

VII. CONCLUSION

The paper publishes realistic grid data used by a large transmission system operator, together with preliminary OPF results and a QCQP conversion code. The authors plan future versions with additional numerical results and provide files to support use and reproduction.

  • VII. CONCLUSION: The paper publishes very realistic data used daily by a large transmission system operator and includes preliminary OPF results.The data are accompanied by elementary descriptions of their origin.
  • VII. CONCLUSION: Future document versions are intended to add numerical results, including better upper or lower bounds from the authors or other public academic work.This identifies ongoing expansion of the reported computational results.
  • VII. CONCLUSION: A MATLAB code transforms OPF data into standard QCQP mathematical optimization format for mathematicians without power-systems expertise.The stated aim is to help the mathematical optimization community address these problems.
  • VII. CONCLUSION: The paper includes m-files intended to help the scientific OPF community use the data and reproduce results.The PEGASE cases had already been published in MATPOWER in 2015, while the other cases are included in the arXiv source archive.
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