Congestion Structure and Exceedance Bounds for Locational Marginal Emissions

Abstract

Locational marginal emissions (LMEs) give the sensitivity of total operating carbon emissions to nodal power demand. We show that this vector with $n$ entries has a much smaller intrinsic dimension under DC optimal power flow. Within a fixed active constraint set, the LME vector lies in the span of the uniform vector and the power transfer distribution factor rows of the binding lines. Its rank $r$ is therefore at most one more than the number of binding/congested lines. This structure makes $r$ independent scalar observations necessary and sufficient for exact recovery. Across ten systems with nonzero operating emissions, from 14 to 1,354 buses, $r$ ranges from 2 to 15. For instance, on a 300 bus system, 24 dispatch simulations recover all 300 LMEs. We also derive an emissions exceedance bound under uncertain demand. The bound separates variation while the nominal active set remains unchanged, the probability of an active set change, and estimation error. Numerical results show that its usable forecast error range depends on local active set geometry.