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 DC objective (constant cost term included) is compared against the published DC ($/h). The per-unit cost scaling cancels exactly, so the comparison is in dollars per hour directly.

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.