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 (a,β) 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, using the Backstepping design, on the basis of the averaged system model. The controller is made adaptive to compensate for the uncertainty that prevails on the unknown SAPF switching loss power. The average performances of the adaptive controller are formally analyzed using system averaging theory. The theoretical results are confirmed by numerical simulations.