  Distribution locational marginal prices (DLMPs) facilitate the efficient
operation of low-voltage electric power distribution systems. We propose an
approach to internalize the stochasticity of renewable distributed energy
resources (DERs) and risk tolerance of the distribution system operator in DLMP
computations. This is achieved by means of applying conic duality to a
chance-constrained AC optimal power flow. We show that the resulting DLMPs
consist of the terms that allow to itemize the prices for the active and
reactive power production, balancing regulation, and voltage support provided.
Finally, we prove the proposed DLMPs constitute a competitive equilibrium,
which can be leveraged for designing a distribution electricity market, and
show that imposing chance constraints on voltage limits distorts the
equilibrium.
