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A General Economic Dispatch Problem with Marginal Losses
Standard economic dispatch problems that consider line losses are linear
approximations of a non-convex economic dispatch problem formulated by fixing
voltage magnitudes and assuming the decoupling of real and reactive power. This
paper formulates and analyzes the general non-convex economic dispatch problem,
incorporating and generalizing the Fictitious Nodal Demand (FND) model,
resulting in a slack bus independent formulation that provides insight into
standard formulations by pointing out commonly used but unnecessary assumptions
and by deriving proper choices of "tuning parameters." The proper choice of
loss allocation is derived to assign half of the losses of each transmission
line to adjacent buses, justifying approaches in the literature. Line
constraints are proposed in the form of voltage angle difference limits and are
proven equivalent to various other line limits including current magnitude
limits and mid-line power flow limits. The formulated general economic dispatch
problem with marginal losses consistently models flows and loss approximation,
results in approximately correct outcomes and is proven to be reference bus
independent. Various approximations of this problem are compared using
realistically large transmission network test cases.Comment: 8 pages, 2 figures, 1 table, American Control Conference 2019
(Submitted