Optimal compensator currents for the reduction of the harmonic distortion in networks part 1: analytic solution

Abstract

Abstract Fast harmonic compensators have been developed and will come into practical use in power systems for the reduction of harmonic currents exchanged between an installation and the feeding network or for the reduction of the voltage distortion at a single node, e. g. a central bus. In order to reduce the harmonic voltage level of an entire network a special strategy is necessary to optimize the compensator current injected into the node. The optimization problem consists in finding the minimum of the proper objective function, which can be defined e. g. as the quadratic sum of the harmonic voltages at all network nodes or of the harmonic currents in all network branches. In addition constraints such as the rated compensator current or/and the limitation of nodal harmonic voltages have to be observed. The proposed solution considers stepwise (I) a single compensator for only a single harmonic order, (II) a single compensator for multiple harmonic orders, and (III) several compensators spread over a system for a single or multiple harmonic orders. The analytic solution, in the first step under at maximum one constraint, is presented in this paper. The validity of this method has been verified by the simulating computation for a real simplified 20 kV distribution system.