  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.
