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.

The small amount of measurements in distribution grids makes their monitoring difficult. Topological observability may not be possible, and thus, pseudo-measurements are needed to perform state estimation, which is required to control elements such as distributed generation or transformers at distribution grids. 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 an NP-hard optimization problem whose optimal solution is unpractical to obtain for large networks. For that reason, we develop a computationally efficient convex optimization algorithm to compute a lower bound on the possible value of the optimal solution, and thus check the gap between the bound and heuristic solutions. We test the method on a large test feeder, the standard IEEE 8500-node, to show the effectiveness of the approach.