Analysis of distribution locational marginal prices

Low-voltage distribution networks are emerging as an increasingly important component of power system operations due to the deployment of distributed renewable resources (e.g. rooftop solar supply) and the need to mobilize the flexibility of consumers that are connected to the low-voltage grid. The pricing of electric power at distribution nodes follows directly from the theory of spot pricing of electricity. However, in contrast to linearized lossless models of transmission networks, an intuitive understanding of prices at the distribution level presents challenges due to voltage limits, reactive power flows and losses. In this paper we present three approaches towards understanding distribution locational marginal prices by decomposing them: (i) through a duality analysis of the problem formulated with a global power balance constraint, (ii) through a duality analysis of a second order cone program relaxation, and (iii) through an analysis of the impact of marginal losses on price. We discuss the relative strengths and weaknesses of each approach in terms of computation and physical intuition, and demonstrate the concepts on a 15-bus radial distribution network