Due to the nonconvex binary constraints of unit commitment (UC), no uniform linear pricing scheme supports the optimal dispatch. Convex hull pricing (CHP) and copositive duality pricing (CDP) both address this problem. CHP derives the price from the subgradient of the value function of the convex hull relaxation of UC. CDP refers to several different pricing mechanisms that can be constructed from the dual multipliers of the completely positive programming reformulation. In this work, we define a centralized convex hull price over the joint feasible set of UC and prove that, under non-degeneracy, it coincides with the marginal copositive duality price. Numerical experiments on the Scarf example validate this equivalence and quantify the pricing gap introduced by the semidefinite restriction.
The unit commitment (UC) problem is paramount for optimal operation of power systems, but it faces computational limitations in large-scale settings, especially in investment or stochastic models, because of the binary variables that it contains. A lot of research has attempted t…
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