IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 6, NOVEMBER 2007 2261 A Model-Based Controller for A Three-Phase Four-Wire Shunt Active Filter With Compensation of the Neutral Line Current Gerardo Escobar, Member, IEEE, Andres A. Valdez, Student Member, IEEE, Raymundo E. Torres-Olguin, and Misael F. Martinez-Montejano Abstract—This paper presents a model-based controller for a three-phase four-wire shunt active filter, which uses a three-leg split-capacitor topology to implement the voltage source inverter. The controller is aimed to compensate reactive power and har- monic distortion in the general case of distorted and unbalanced source voltages and load currents, including distorted loads con- nected between a phase and the neutral line. In addition, the con- troller is able to compensate for the homopolar component of the load current, that is, the current flowing to the source via the neu- tral line can be considerably reduced without modifying the actual topology. The complete model in (fixed frame) -coordinates is presented. Special attention is given to the homopolar compo- nent (referred here as the -component) of the line current, source voltage and control input, which are instrumental for the control design purpose. Experimental results in a 2 kVA prototype are pro- vided to illustrate the benefits of the proposed solution. Index Terms—Active filters, adaptive signal detection, reactive power control. I. INTRODUCTION T HREE-PHASE four-wire shunt active filters arise as effective devices to compensate reactive power, harmonic distortion and unbalance currents caused by the increasing nonlinear loads, such as, computer equipment, electronic ballasts, speed motor drives, switching-mode power supplies and others. The idea behind these converters is to provide a connection path to the neutral wire, so compensation of the homopolar component can be possible. Two basic topologies can be identified. First, a three-leg split capacitor topology, also referred as the conventional topology, where the midpoint of the dc link is tied to the neutral wire (see Fig. 1). Second, using a four-leg topology [1]–[3]. The four-legged topology presents an extra control input, at the expenses of the cost and complexity increase, however the three-leg split capacitor topology, which is the topology studied here, is preferred for its reduced number of semiconductor devices employed. In the split capacitor topology, the connection path allows the homopolar current to flow towards the capacitors, which are aimed to absorb such a current, and thus, to remove it from the line neutral Manuscript received November 2, 2006; revised February 21, 2007. This work was supported by the Bilateral Laboratory of Applied Control France Mexico LAFMAA under Grant MOPOFA-II. Recommended for publication by Associate Editor S. Pekarek. The authors are with the Laboratory of Processing and Quality of En- ergy, IPICYT, Luis Potosí 78216, Mexico (e-mail: gescobar@ipicyt.edu.mx; avaldez@ipicyt.edu.mx; rtorres@ipicyt.edu.mx; fmartinez@ipicyt.edu.mx). Digital Object Identifier 10.1109/TPEL.2007.909297 Fig. 1. Three-phase four-wire shunt active filter based on the three-leg split- capacitor topology. wire. However, this is not possible unless explicit provisions are taken in the controller to eliminate this component. It has been observed that this issue gets worse in the case that the source voltage contains an homopolar component as well [4], [5]. Notice also that, as a consequence of the existence of two capacitors, the control problem becomes more challenging as the controller should deal now with the voltage balance issue as well. Summarizing, in addition to the usual issues found in three-phase three-wire systems, it is demanded to compensate the load homopolar current, and simultaneously, to balance the voltage of both capacitors. Several control methods have been proposed to alleviate the issues found in the split capacitor topology. Most of these works present extensions to instantaneous power theory [6] or to the Fryze-based work (See [4] for a detailed comparison between the -based work and the Fryze-based work). In [7] the authors present a controller that uses the average ac- tive power produced by the zero sequence components and also consider the zero sequence current for the homopolar current compensation. Moreover, they propose a time varying hysteresis band for the voltage balance. An extension is also presented that considers the fundamental positive sequence component of the source voltage in the computations. A similar approach is pre- sented in [9] where the authors present an alternative form of computing the mains voltages to be used in the process of com- puting the current reference. Basically, they propose the use of 0885-8993/$25.00 © 2007 IEEE