# Problem Formulation

**Download the Challenge 2 Problem Formulation document, with Data Format Appendices and Change Log, dated May 31, 2021.**

The May 31 changes, described in Appendices F.32 and F.33. F.32 adds a description of the evaluation output files to Section D.1, including Table 26 that describes the fields of the evaluation summary output file at also appears in the eval_detail.csv and eval_detail.json files produced in every successful run. F.33 adds a further explanation that transmission line and transformer switching may only be used in Divisions 3 and 4, NOT in Division 1 and 2 according to the Rules and Scoring documents.

The April 28 change, described in Appendix F.31, clarifies the interpretation of transformer RMA1 and RMI1 when COD1 is -1 or -3. Table 20 describing the fields of the transformer table in the RAW file did not specify the interpretation of RMA1 and RMI1 when COD1 is -1 or -3. This has been corrected.

The April 15 change, in Appendix F.30, replaces the terms *infeasibility solution, infeasibility objective*, and *z ^{inf}* by

*prior point solution, prior point objective*, and

*z*in Appendix D. This change emphasizes the method of construction of these concepts (i.e. from the prior operating point) rather than only one of their possible uses (i.e. to assign a scoring objective in case of infeasibility). The interface of this document to the competition scoring document scoring is addressed at the beginning of Appendix D. Some parts of Appendix D are revised for clarity and precision.

^{pp}The Feb. 19 change, in Appendix F.29, presents an algebraically equivalent linear formulation of generator ramping constraints. The generator ramping constraints are correct as formulated in Equations (87) to (90), however, they make use of some nonlinear, specifically bilinear, expressions. F.29 shows it is possible to formulate these constraints using linear expressions only.

Changes since the initial release on July 20 are explained in the Change Log (Appendix F). The previous releases were dated September 8 and 18, October 4, 13 and 25, November 24, and December 22, 2020.

## Summary

The Challenge 2 problem is a type of a security-constrained (AC based) optimal power flow, or SCOPF. Entrants are tasked with determining the optimal dispatch and control settings for power generation and grid control equipment in order to maximize the market surplus associated with the operation of the grid, subject to pre- and post-contingency constraints. The optimization problem is a mixed integer, non-linear, non-convex (MINLP) problem and includes discrete variables such as unit commitment, control settings (transformer taps with impedance correction tables) and bus shunts. Feasible solutions must conform to operating standards including, but not limited to: minimum and maximum bus voltage magnitude limits, minimum and maximum real and reactive power generation from each generator, thermal transmission constraints, and constraints to ensure the reliability of the system while responding to unexpected events (i.e., a contingency). Feasible solutions must also be able to respond to contingencies of generators and transmission elements. This formulation allows for bus real and reactive power imbalance as well as branch (transmission line and transformer) rating exceedance, both at a cost included in the objective function.

Features added to this formulation since the Challenge 1 Competition include transformer tap settings, phase angle regulators, switchable shunts, transmission branch and transformer switching, generator ramp rate response to contingencies, start up and shut down of qualified generators, and price responsive demand. Please note that shunts are no longer modeled as with continuous variables in this formulation.

Challenge 2 uses power system network models that vary in size and complexity. The size of each network model (number of nodes and branches) as well as the number of contingencies will vary across datasets. The largest models reach the size of the largest independent system operator in the United States, around 32,000 buses. The problem is a two-stage single period problem with a given operating point prior to a base case state and then a post-contingency state. The modeling of the pre-contingency base case is a reflection of the first stage of a two-stage mathematical program whereas the post-contingency state represents the second stage. Limited unit commitment (the commitment/decommitment of generators) is included within the formulation only for generators designated as “fast-start”. Other generators may not change their commitment in either the pre-contingency base case or the post-contingency state. Generator response between states (from the given prior operating point to the pre-contingency base case state, and from the pre-contingency base case to the post-contingency state) is limited to the available ramp rate response within each generator’s operational limit given the length of time between each state. The first priority of post-contingency generator response should be to ensure a feasible post-contingency state, but this problem will also consider the market surplus of both the pre- and the post-contingency states.

**Divisions 1 and 2** will allow competitors to use any feature of the loads, generators, and transmission assets described in the formulation and within the limits of the input datasets to optimize each scenario for both the base case and each contingency response with the exception of topology optimization (line switching).

**Divisions 3 and 4** will allow competitors to employ all these previously described features as well as **topology optimization**. See the Scoring document for details.

**The ‘problem formulation’ document includes more than just the mathematical problem definition. There are** **several appendices that describe properties of the input and output data and their required formats.**