Modern control of a three-phase pulse-width modulated voltage source inverter

In this paper, a linear state space model is realized for a three-phase shunt active power filter used to prevent the propagation of current harmonics into the power source. Different transformations are then applied to this model in order to include a parameter used to extract desired frequency components and achieve decoupling between phases. The latter can be done through the representation of the system in a complex framework in which the design of a stabilizing controller is simplified. The contribution of this work is the application of modern control theory on a three-phase power system. A Linear Matrix Inequality (LMI) based H_∞ synthesis is performed in order to design a static state feedback controller with complex-valued parameters used to command appropriately a three-phase pulse-width modulated voltage source inverter so that the active filter is capable of compensating current harmonics demanded by non linear loads. The effectiveness of the synthesized H_∞ controller is validated through numerical simulations and its robustness with respect to network impedance uncertainties is investigated.