# Distribution Electricity Pricing under Uncertainty

## TL;DR

This paper introduces a novel method for calculating distribution locational marginal prices (DLMPs) that accounts for renewable energy uncertainty and risk preferences, enabling efficient and market-compatible pricing in distribution networks.

## Contribution

It presents a new approach using conic duality on chance-constrained AC optimal power flow to derive DLMPs that include detailed pricing components and establish a competitive equilibrium.

## Key findings

- DLMPs can be decomposed into active/reactive power, regulation, and voltage support prices.
- The proposed method ensures a competitive equilibrium in distribution markets.
- Imposing voltage chance constraints can distort market equilibrium.

## Abstract

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.