Hilbert space techniques for reactive power compensation with limited current bandwidth

The paper formulates and solves an optimization problem related to reactive power compensation with limited current bandwidth. The current bandwidth limitation is essential for all practical compensators that are built around switching power converters. We use the Hilbert space terminology stated in H. Lev-Ari and A.M. Stankovic (2003) to formulate and solve the corresponding constrained optimization problem. It turns out that our solution generalizes some results from the literature. Under operating conditions that are prevalent in practice, our solution leads to a decomposition of reactive power into three components - a component that can be compensated without energy storage, a component that can be compensated when energy storage is available, and a component that can not be compensated at all because of the limited bandwidth of the compensator.