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

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, so load forecasts (pseudo-measurements) are typically used, and thus an accurate state estimation is not guaranteed. However, 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, such as convexity and modularity, of different metrics in the context of optimal experimental design, 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.