Accurate state space realisations of resonant filters for high performance inverter control applications

Controllers based on resonant Second Order Generalised Integrators (SOGIs) are attractive for AC conversion applications because they provide infinite loop gain at the target resonant frequency, which is required to eliminate AC steady state error in the regulated converter output. Furthermore the simple dual integrator based architecture of a SOGI filter facilitates frequency adaptation, for example as is used in motor drive applications. However a consequence of this simple architecture is that the digital form of the SOGI filter is highly susceptible to discretization errors which can compromise the converter steady state tracking accuracy. This paper now presents an alternative state-space approach to realise accurate discrete SOGI filters using Hold and Tustin (pre-warp) methods. The effectiveness of the proposed approach has been verified using simulation and experimental investigations of an inverter interfaced to a distorted grid and controlled using multiple harmonic SOGI filters.