Multi-oscillatory LQR for a three-phase four-wire inverter with L3nC output filter

The paper presents control system synthesis for a true sine wave four-leg inverter with an LC output filter. Our main goal is to ensure high quality voltage waveform for unbalanced and nonlinear loads. An LQR approach was chosen. The LQR design approach has proven effective in many industrial applications. Although weights in a cost function are usually set by guess and check method, the LQR in proposed system gives satisfactory results as far as some general and very intuitive rules are applied, e.g. the penalty coefficient for an integral of control error is a few orders of magnitude away from penalty coefficients related to plant state variables. In order to immunise system against nonlinear loads oscillatory terms are included in the control scheme. They can be tuned for typical harmonics like 5th, 7th, 11th and 13th. A novelty of the proposed solution lies in the fact that all controller gains (including all integral and oscillatory terms) are determined altogether in one LQR procedure call. Controls are calculated in rotating reference frame. Simulation (continuous and discrete) and experimental results (at the level of 10kW) are included. They establish consistent set of tests that validates effectiveness of the design approach.