Adaptive non-linear control of three-phase four-wire Shunt active power filters for unbalanced and non- linear loads

The problem of controlling three-phase, four-leg shunt active power filters (SAPF) is addressed in presence of nonlinear and/or unbalanced loads. A new control model for four-leg SAPF, taking into account for the electrical grid line impedance, is developed. The control objective is threefold: (i) compensating for the current harmonics and the reactive power absorbed by the nonlinear load; (ii) annulations of neutral line current (iii) regulating the inverter DC capacitor voltage. To this end, based on the new model, a nonlinear controller is developed, using the Lyapunov technical design. It is therefore able to ensure good performances over a wide range variation of the load current. Moreover, the controller is made adaptive for compensating the uncertainty on the switching loss power. The performances of the proposed adaptive controller are formally analyzed using tools from the Lyapunov stability and averaging theory. The supremacy of the proposed controller with respect to standard control solutions is illustrated through simulation