Validation

tellegen is checked against the published PGLib reference solves. For each case and variant, $PGLIB_OPF_PATH/BASELINE.md tabulates the PowerModels.jl with IPOPT reference: DC ($/h), AC ($/h), QC Gap (%), and SOC Gap (%). The Methodology chapter describes how the harness produces the comparison; this chapter records what each comparison asserts. The measured figures are in benchmark results, a committed snapshot of a full harness run with its provenance.

DC objective

tellegen’s declared DC objective, including its constant cost term, is compared against the published DC baseline. Both values come from the same PGLib cost data. Per-unit power scaling cancels; tellegen does not assign a currency to objectives from other sources.

Relaxation lower bound

The SOCWR objective (socwr_opf objective) must be a lower bound on the published AC optimum (AC ($/h)):

$$ \text{socwr} \le \text{AC} + \text{tol}. $$

A bound violation is a correctness failure.

SOC gap

The gap is

$$ \text{gap} = \frac{\text{AC} - \text{socwr}}{\text{AC}} \cdot 100, $$

compared against the baseline SOC Gap (%). tellegen’s SOCWR is the Jabr SOC relaxation, the same family as the baseline SOC column, so a near-zero difference in gap is the expected result. The published SOC bound is recovered as $\text{AC} \cdot (1 - \text{SOC gap}/100)$.

All three variants are exercised: typical, congested (API), and small-angle (SAD). tellegen’s AcNetwork carries the angle difference limits and the SOCWR enforces them in W-space, so the SAD relaxation tracks the published SAD SOC. Where a case shows a large SOC gap, that measures relaxation quality, not a failure.