Estimating DLMP confidence intervals in distribution networks with AC power flow model and uncertain renewable generation

This study proposes a systematic approach for estimating intervals of distribution locational marginal price (DLMP) and corresponding confidence levels without requiring an exact probability distribution of renewable generation. The DLMP is evaluated based on a variant of the alternating current (AC) power flow model, namely, the branch flow model, in which network losses, bus voltage, and reactive power are taken into account. Based on the exactness of convex relaxation of optimal power flow, the authors developed a linear AC power flow model by applying second-order cone relaxation and global polyhedral approximation. Given a set of renewable power volatility, interval prediction of the DLMP is formulated as a bilevel linear program, which is solved via a mixed-integer linear program (MILP). Considering variances and unimodality of renewable power forecast error, a conservative estimation of the confidence level is expressed by a generalised Gauss inequality, which comes down to semidefinite programming. The proposed method is a natural extension of existing interval and probabilistic forecast methods, leveraging the proposed linear AC power flow model and inexact probability distributions of renewable power output, and could be promising in future distribution power markets. Case studies corroborate the effectiveness of the proposed method.