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.

This paper deals with the useless active powers and the reactive powers included in the unbalance power (S_U1), and in the nonfundamental effective apparent power (S_eN) defined in IEEE Standard 1459. Only the fundamental positive-sequence active power (P₁⁺) must be delivered to loads under ideal supply operating conditions. Fundamental negative- and zero-sequence active powers (P₁^- and P₁⁰ , respectively), and the harmonic active power (P_H) are considered useless active powers because they increase the power losses in the load and in the distribution lines, reducing the global efficiency of the electrical power systems. S_U1 and S_eN are calculated in this paper for two cases, resolving the effective apparent power (S_e) by means of the product between the terms of the effective voltage (V_e) and the effective current (I_e). It yields to expressions of some useless active powers and reactive powers that differ from the definitions included in IEEE Standard 1459. New definitions of V_e, I_e, and S_e are proposed to avoid the disagreements detailed in this paper. The new definitions are compared with the IEEE Standard 1459 definitions by means of one numerical example. Magnitudes calculated by means of the IEEE Standard 1459 definitions present a general overvaluation that arrives at a maximum of 83% for S_U1.

Based on an instantaneous analysis approach to the IEEE Std. 1459, the authors demonstrated in previous works that the effective apparent power should not be calculated including the rms neutral current and the rms line to line voltage terms. The use of these terms drives to expressions of power magnitudes that are overvaluated and disagree with well-accepted definitions. By using the instantaneous approach, new power terms are proposed. Based on these terms, new power quality indices and new expressions of the unbalanced power terms are presented in this paper. An experimental case is used to compare the power magnitudes and power quality indices obtained with both approaches. Results demonstrate than the most significant power terms are over evaluated when IEEE Std. 1459 power definitions are used. (C) 2015 Elsevier B.V. All rights reserved.

Current control has, for decades, been one of the more challenging research fields in the development of power converters. Simple and robust nonlinear methods like hysteresis or sigma-delta controllers have been commonly used, while sophisticated linear controllers based on classical control theory have been developed for PWM-based converters. The one-cycle current control technique is a nonlinear technique based on cycle-by-cycle calculation of the ON time of the converter switches for the next switching period. This kind of controller requires accurate measurement of voltages and currents in order achieve a precise current tracking. These techniques have been frequently used in the control of power converters generating low-frequency currents, where the reference varies slowly compared with the switching frequency. Its application is not so common in active power filter current controllers due to the fast variation of the references that demands not only accurate measurements but also high-speed computing. This paper proposes a novel one-cycle digital current controller based on the minimization of the integral error of the current. Its application in a three-leg four-wire shunt active power filter is presented, including a stability analysis considering the switching pattern selection. Furthermore, simulated and experimental results are presented to validate the proposed controller.