How wrong is the DC approximation of optimal power flow on the IEEE 30-, 39- and 118-bus cases?

research/infra-dcopf

DC against AC optimal power flow in pandapower on the IEEE 30-, 39- and 118-bus cases: the DC model's cost is 1 to 3 % below the AC optimum (it ignores losses); on the 118-bus case its dispatch is feasible but costs 0.7 to 1.7 % more than the AC optimum once losses are paid, and on the 39-bus case it breaks voltage limits (15 buses at 0.6 of load) at almost no cost difference (modelled benchmark, not a measured system; tightened-limit runs often had no solution). Feeding the AC losses back into the DC model (a loss-adjusted DC) brings the 118-bus cost estimate to within 0.6 to 1.2 % of the AC optimum, but repairs only 13 to 32 % of the dispatch's excess cost and none of case39's voltage violations.

8 tests

What it found

The DC optimal power flow is the workhorse of dispatch and price studies; how much does it lose against the AC OPF? On pandapower's MATPOWER cases with their own quadratic costs, load scaled 0.6 to 1.1, both OPFs are solved and the DC set-points are run through an AC power flow (slack pays the losses). IEEE 118-bus (no branch limit binds): DC cost is 1.9–2.9 % below the AC optimum and its dispatch costs 0.7–1.7 % above it, with no violations. IEEE 39-bus: DC cost 1.0–1.5 % below, dispatch within 0.06 % of the optimum but 15, 5 and 1 buses out of voltage limits at 0.6, 0.8 and 1.0 of load. IEEE 30-bus: DC 1.3–2.3 % below; at full load the DC dispatch overloads a branch to 111 % and is 0.31 % cheaper than the AC optimum, i.e. a violated constraint. Checks: a two-bus closed form and agreement of the cost function with pandapower. Limits: tightened-limit sweeps frequently returned no solution from the solver and non-convergence is not separated from infeasibility; 118-bus branch limits never bind so it is a losses-only comparison; no prices (LMPs), unit commitment or N-1; costs are the cases' own, not market prices. Modelled benchmark cases, not measured systems. Loss-adjusted DC (AC losses spread uniformly over loads, iterated 2–4 passes): the 118-bus cost estimate falls within 0.6–1.2 % of the AC optimum, but the AC cost of its dispatch is still 0.58–1.18 % above it (13–32 % of plain DC's excess recovered) and case39's voltage violations are unchanged; a uniform loss share fixes the price level, not the merit order.

A figure from its own output

Figure produced by research/infra-dcopf: gap_vs_load — infra-dcopf/experiments/gap_vs_load.svg, written by the project's own experiment code.

Paper, code and results

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What it found

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Paper, code and results

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