# Comparison of Bounds for Optimal PMU Placement for State Estimation in Distribution Grids

## TL;DR

This paper investigates optimal sensor placement in large, unbalanced distribution grids to enhance state estimation accuracy, comparing bounds and proposing methods for near-optimal solutions in complex network scenarios.

## Contribution

It introduces and compares bounds for optimal PMU placement, leveraging properties like convexity and modularity, to efficiently approximate solutions in large-scale distribution grids.

## Key findings

- Bounds effectively estimate optimal sensor placement performance.
- Proposed methods improve state estimation accuracy in large networks.
- Validated approach on IEEE benchmark feeders.

## Abstract

The lack of measurements in distribution grids poses a severe challenge for their monitoring: since there may not be enough sensors to achieve numerical observability, load forecasts (pseudo-measurements) are typically used, and thus an accurate state estimation is not guaranteed. However, an estimation is required to control distribution grids given the increasing amount of distributed generation. Therefore, we consider the problem of optimal sensor placement to improve the state estimation accuracy in large-scale, 3-phase coupled, unbalanced distribution grids. This is a combinatorial optimization problem whose optimal solution is unpractical to obtain for large networks. We explore the properties of different metrics in the context of optimal experimental design, like convexity and modularity, to propose and compare several tight lower and upper bounds on the performance of the optimal solution. Moreover, we show how to use these bounds to choose near-optimal solutions. We test the method on two IEEE benchmark test feeders, the 123-bus and the 8500-node feeders, to show the effectiveness of the approach.