Enhanced Convergence Rate Of Inequality Constraint Shadow Prices In Pmp Algorithm Cleared Distribution Power Markets

The extension of Transmission Locational Marginal Cost Prices (LMP) to Distribution node LMPs, or DLMPs, is a prerequisite for efficient demand response that may support significant integration of Renewables. AC load flow and non-linear distribution cost modeling needed to this end, render centralized market clearing Algorithms intractable, with Distributed Proximal Message Passing (PMP) Algorithms offering what appears to be the only scalable and tractable alternative. DLMPs of real and reactive power are associated with equality power balance constraint shadow prices at each distribution node, while, allowable voltage limit inequality constraints are associated with inequality constraint shadow prices. This paper addresses the slower convergence rate of voltage constraint shadow price estimates in PMP algorithms. In particular, we use first order optimality conditions to derive relations that characterize the interaction of equality and inequality shadow prices across the distribution network, and employ them to construct a filter that enhances the estimation accuracy of voltage inequality constraint shadow prices. We show that use of this filter results in a significant speedup of the PMP algorithm's convergence rate for both voltage shadow prices as well as DLMPs.