Voltage Analytics for Power Distribution Network Topology Verification

TL;DR

This paper introduces a statistical learning framework leveraging smart meter voltage data to verify power distribution network topology, providing reliable results with limited data and balancing accuracy with computational complexity.

Contribution

It proposes a novel non-convex optimization approach for topology verification using non-synchronized voltage data, with convex relaxations and prior information integration.

Findings

Reliable topology estimates with few data points

Non-convex schemes outperform in line verification accuracy

Convex relaxation guarantees asymptotic optimality

Abstract

Distribution grids constitute complex networks of lines often times reconfigured to minimize losses, balance loads, alleviate faults, or for maintenance purposes. Topology monitoring becomes a critical task for optimal grid scheduling. While synchrophasor installations are limited in low-voltage grids, utilities have an abundance of smart meter data at their disposal. In this context, a statistical learning framework is put forth for verifying single-phase grid structures using non-synchronized voltage data. The related maximum likelihood task boils down to minimizing a non-convex function over a non-convex set. The function involves the sample voltage covariance matrix and the feasible set is relaxed to its convex hull. Asymptotically in the number of data, the actual topology yields the global minimizer of the original and the relaxed problems. Under a simplified data model, the function turns out to be convex, thus offering optimality guarantees. Prior information on line statuses is also incorporated via a maximum a-posteriori approach. The formulated tasks are tackled using solvers having complementary strengths. Numerical tests using real data on benchmark feeders demonstrate that reliable topology estimates can be acquired even with a few smart meter data, while the non-convex schemes exhibit superior line verification performance at the expense of additional computational time.