APEM PF Relaxations

APEM PF Relaxations#

The power_flow_relaxations module provides a runner for comparing power-flow relaxation formulations on ARPA-derived subscenarios.

Requirements#

  • A working MOSEK installation is required to run this module.

  • A valid MOSEK license must be available in your environment.

Scope#

  • Run DCOPF and ACOPF relaxation models on connected network subgraphs.

  • Compare model behavior across runtime, solve time, memory footprint, welfare, and feasibility violations.

  • Produce CSV result files per model and subscenario size.

Data#

  • The workflow uses the ARPA unit-based dataset (loaded via ParseARPA).

  • Experiments are run on connected subgraphs sampled from the ARPA network.

  • Buyers/sellers are filtered to the sampled nodes before solving each subscenario.

Implemented Relaxations#

  • NodalBaseModel: shared nodal optimization scaffold with common variables, bid constraints, and network-balance handling.

  • DCOPF: linear DC approximation using voltage angles and active-power flow constraints.

  • Shor SDP: semidefinite relaxation of AC power flow with a stronger but more expensive convex envelope.

  • Chordal SDP: chordal decomposition of the SDP model to reduce computational cost on larger networks.

  • Jabr SOCP: second-order-cone relaxation based on Jabr-type formulations, typically lighter than full SDP.

  • QC variants: quadratic-convex relaxations with different approximation degrees and sampling modes (local/global).

Default Run Behavior#

run_relaxations.py currently defaults to:

  • --batch-size 1

  • subscenario sizes 32, 64, 96, ..., 640 nodes (attempted; invalid/oversized samples are skipped)

  • full model list and full scenario-size list are used by default (--model all, --model-start-index 0, --model-end-index -1, --scenario-start-index 0, --scenario-end-index -1)

Results are written under:

  • relaxation_results/<MODEL_TAG>_<SIZE>_results.csv

Entrypoints#

  • power_flow_relaxations.run_relaxations: runs the relaxation experiments, builds subscenarios, solves selected models, and writes per-model CSV results.

  • power_flow_relaxations.create_figures: reads the generated result CSV files and creates comparison plots (runtime, memory, welfare, and feasibility metrics).