Optimal voltage support and Stress Minimization in power networks

A standard operational requirement in power systems is that the voltage magnitudes must lie within pre-specified bounds. Conventional wisdom suggests that such a tightly regulated voltage profile should also guarantee a secure system, operating far from static bifurcation instabilities such as voltage collapse. Here we demonstrate that this conclusion is generally false, and that the distance from voltage collapse is a systems-level objective distinct from ensuring voltage limits. We formulate an optimization problem which maximizes the distance to voltage collapse through injections of reactive power, subject to power flow and operational voltage constraints. By exploiting a linear reformulation of the power flow equations we arrive at a convex reformulation which can be efficiently solved for the optimal reactive power injections. We illustrate the performance of our results with the IEEE30 bus network.