Online distributed voltage stress minimization by optimal feedback reactive power control

A standard operational requirement in power systems is that the voltage magnitudes lie within prespecified bounds. Conventional engineering wisdom suggests that having a tightly regulated voltage profile should also guarantee that the system operates 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 that 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 then propose a distributed feedback controller, based on a dual-ascent algorithm, to solve for the prescribed optimization problem in real time. This is possible, thanks to a further manipulation of the problem into a form that is amenable for distributed implementation. We also address the planning problem of allocating control resources by recasting our problem in a sparsity-promoting framework. This allows us to choose a desired tradeoff between optimality of injections and the number of required actuators. We illustrate the performance of our results with the IEEE 30-bus network.