Optimization Algorithm for Selective Compensation in a Shunt Active Power Filter

This paper proposes an optimization algorithm based on linear matrix inequalities (LMIs) to be implemented in a shunt active power filter (SAPF) enabling it to perform a selective compensation of nonefficient powers when the rated power of the SAPF is limited. The system uses the IEEE Standard 1459 to identify the different power terms (active, reactive, unbalance, and harmonics) demanded by local loads in a three-phase four-wire system. Then, the algorithm solves a quadratically constrained quadratic program by means of an LMI formulation and calculates the optimal reference currents that allow the SAPF to cancel a selection of the previously identified nonefficient power terms. For this selection, the algorithm presents different weighting coefficients in the cost index to be optimized. These coefficients assign a relative importance to each different nonefficient power term, giving priority to some over the others. Moreover, the optimization performed in this work to calculate the reference currents considers that the SAPF presents a power limitation. Finally, the reference currents´ tracking has been implemented using a proportional feedforward controller which assures a constant commutation frequency of the SAPF. Experimental results demonstrate the validity of the proposal.