Do nodal loss penalty factors repair the DC OPF's merit order on the IEEE 30-, 39- and 118-bus cases?

research/infra-plf

Nodal loss penalty factors (AC loss sensitivities) in a DC OPF on the IEEE 30-, 39- and 118-bus cases: on the 118-bus case they recover 23 to 38 % of plain DC's excess cost at 0.6 to 1.0 of load, but the iteration does not converge at 0.8 and above and at 1.1 of load the dispatch is worse than plain DC (modelled benchmark, not a measured system).

3 tests

What it found

A lossless DC OPF orders generators by raw marginal cost; the classical fix scales each generator's cost by a penalty factor 1/(1−∂Loss/∂P_i). Sensitivities come from an AC power flow by finite difference, the DC OPF is re-solved with scaled costs and losses added to load, and the dispatch is scored by AC power flow at the original costs against the AC OPF (pandapower, MATPOWER cases, load 0.6–1.1). IEEE 118-bus: excess cost over the AC optimum falls from 0.73, 0.75, 1.48 % (plain DC) to 0.56, 0.46, 0.97 % at 0.6, 0.8, 1.0 of load, versus 0.64, 0.58, 1.18 % for a uniform loss share; at 1.1 it is 2.45 %, worse than both. The damped fixed-point iteration hit its 20-pass cap at 0.8, 1.0 and 1.1 (dispatch still moving 2.5–75 MW per pass), so those rows are not fixed points. Case30 and case39 differences are within 0.1 % and change sign; voltage violations are identical to plain DC. Checks: a three-bus case and two case118 inequalities. Limits: non-converged rows, no AC OPF solution at 1.1 of load on case30/39, no binding branch limits, no prices. Modelled benchmark cases, not measured systems.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.