H∞Static Control Law for a Three-phase Shunt Active Power Filter

The aim of this work is to design a static feedback gain used to force a three-phase shunt active power filter to act as a current source capable of delivering the appropriate harmonics demanded by non-linear loads. This filter is connected in parallel to a three-phase power distribution system in order to keep the current supplied by the latter almost sinusoidal. The control design is performed using the H ∞ suboptimal control theory based on linear matrix inequalities (LMIs), with both partial and full state feedback. Numerical simulations will be presented in order to investigate the advantages of the full state feedback structure over the partial state feedback one, and to compare the performances of the corresponding H ∞ static control laws.