  A standard operational requirement in power systems is that the voltage
magnitudes lie within prespecified bounds. Conventional engineering wisdom
suggests that such a tightly-regulated profile, imposed for system design
purposes and good operation of the network, should also guarantee a secure
system, operating far from static bifurcation instabilities such as voltage
collapse. In general however, these two objectives are distinct and must be
separately enforced. 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
approximation of the power flow equations we arrive at a convex reformulation
which can be efficiently solved for the optimal injections. We also address the
planning problem of allocating the resources by recasting our problem in a
sparsity-promoting framework that allows us to choose a desired trade-off
between optimality of injections and the number of required actuators. Finally,
we present a distributed algorithm to solve the optimization problem, showing
that it can be implemented on-line as a feedback controller. We illustrate the
performance of our results with the IEEE30 bus network.
