Adaptive Nonlinear Control of Three-Phase Shunt Active Power Filters

The problem of controlling three-phase shunt active power filters (SAPF) is addressed in presence of nonlinear loads supplied with three-phase power grids. The SAPF-load system is shown to be modeled, in the ( , ) coordinate frame, by a third-order nonlinear state-space representation. The control objective is twofold: (i) compensating for the current harmonics and the reactive power absorbed by the nonlinear load; (ii) regulating the inverter DC capacitor voltage. To this end, a nonlinear adaptive controller is developed on the basis, on the average system model, using the backstepping design technique. The controller is made adaptive for compensating the uncertainty on the unknown SAPF components and on the switching loss power. The performances of the proposed adaptive controller are formally analyzed using tools from the Lyapunov stability and the averaging theory. The theoretical results are confirmed by numerical simulations.