Challenge 1 Problem Formulation

Formulation Summary

The Challenge 1 problem is a type of a security-constrained (ac based) optimal power flow, or SCOPF. There are many ways to formulate an SCOPF problem. Competitors are strongly encouraged to study the detailed formulation precisely and to engage with the broader community if anything is not clear (e.g., use the Competition forum).

The basic features of this SCOPF problem are the following:

  1. An alternating current (AC) formulation
  2. Security constraints (more information to come)
  3. Pre-contingency (base-case) operational constraints and post-contingency operational constraints
  4. Preventive and corrective actions
  5. Transmission (line/transformer) contingency modeling and the corresponding
  6. Generator contingency modeling
  7. Bus-branch model
  8. Load modeling (more information to come)
  9. Some constraint violations are included in the objective function

Features that are not modeled within this SCOPF include:

  1. Three-winding transformers.
  2. Transformer tap settings
  3. Phase angle regulators
  4. Various flexible ac transmission system (FACTS) devices
  5. Switchable shunts (shunts are included but we are not precisely modeling the binary nature of switchable shunts)
  6. Generator ramp rates and start-up and shut-down costs
  7. Multiple time intervals

The following variables must be supplied explicitly by the solution files and will be subject to bounds that are enforced as hard constraints:

  1. Bus voltage magnitude in the base case and contingencies
  2. Generator real and reactive power in the base case and contingencies
  3. Switched shunt susceptance in the base case and contingencies
  4. Droop control in the base case and contingencies
  5. PV/PQ switching in the base case and contingencies

There are linear penalties on violations on the following constraints:

  1. Bus real and reactive power balance in the base case and contingencies
  2. Line apparent current limit in the base case and contingencies
  3. Transformer apparent power limit in the base case and contingencies


Information about the  Evaluation source code, which reads the input files and the solution output files to calculate the objective function score, is available on the Evaluation page.

SCOPF Problem Formulation: Challenge 1, updated April 9, 2019, is available in PDF format here.

Changes on April 9, 2019, to the previous March 29, 2019 version:

In section (C.9), no initial value of biCS0 was provided, so this symbol was left undefined for buses i with no fixed shunts present and in service. This has been corrected by specifying that biCS0 takes the initial value 0 prior to reading any switched shunt records.

In section (C.9), for each record for an in service switched shunt, a local variable NBL is defined giving the number of valid blocks. The expression for NBL was not well defined in the case where at least one of the fields N1 and B1 is 0. This has been corrected by specifying that NBL = 0 in this case and that the original definition of NBL applies in the case where N1 and B1 are both nonzero.

Changes on March 29, 2019, to the previous November 30, 2018 version:

The treatment of hard constraint violations in the evaluation procedure is modified, where hard constraints are those constraints that do not use penalty variables. A tolerance of 1e-4 p.u. will be used in determining whether these violations constitute infeasibility. Specifically, any violation of a hard constraint > 1e-4 p.u. will result in infeasibility, and any violation of a hard constraint <= 1e-4 (p.u.) will be ignored. This is equivalent to truncating the floating point representation of the violation to 4 digits after the decimal point. The solution procedure is modified to reflect this practice. This change is made in the description of the evaluation procedure (Appendix F.1) and in the evaluation code itself (

See Appendix G.4 for the full list of changes.

Changes on November 30, 2018, to the previous November 14, 2018 version: 

  • The interpretation of the R field of the INL file is clarified in sections (A.4, C.11). Specifically, this field is taken as the participation factor of a generator in post-contingency real power output response, which is a dimensionless, nonnegative, real number. The interpretation of R in Table 3 is excluded from its interpretation in the Appendices.
  • It can be assumed that any (I, ID, CKT) appearing in a record of the CON file appears also in the RAW file as either a line (non-transformer branch) or a transformer but not both. This assumption is posted in section (C.12).

Changes on November 14, 2018, to the previous November 1, 2018 version :

  • Corrected an error in the interpretation of the STATUS field (and other analogous fields with different names) in the Load, Fixed Shunt, and Switched Shunt sections of the RAW file. Previously the STATUS field was ignored. Now we specify that among all loads, fixed shunts, and switched shunts, only those with STATUS = 1 should be added to the model. The changed text appears in Appendix C Construction of Primitive Data from Input Data Files in sections C.4 Load Data from RAW, C.5 Fixed Shunt Data from RAW, and C.9 Switched Shunt Data from RAW.

Changes on November 1, 2018,  to the initial August 28, 2018 version include:

  • Section 2, Table 6 (page 12): added definition of idgat end of table.
  • Fixed some unit descriptions. Some units were missing time, measured in hours (h). This has been added where needed. This change does not affect the equations of the formulation or of the processing of input data into the data of the formulation. It only affects the clarity of the interpretation of the variables and parameters of the model.
  • Appendices added:
    • A. Input Data Format (detailed description of the 4 input files summarized under Input Files and Format)
    • B. Data Construction Reference Table (index to detailed parameter definitions)
    • C. Construction of Primitive Data from Input Data Files (mapping the input data to the formulation)
    • D. Construction of Further Data (transformations of input data needed to match formulation)
    • E. Solution Output (detailed description of solution files summarized under Output Files and Format)
    • F. Solution Evaluation (detailed description of Evaluation procedure summarized under Evaluation)
    • G. Change Log (log of changes made to the document)