IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 1, FEBRUARY2006 305 A New Control Strategy for Single-Phase Shunt Active Power Filters Using a Lyapunov Function Hasan Kömürcügil, Member,IEEE, and Ösman Kükrer, Member,IEEE Abstract—This paper proposes a new control strategy for single- phase shunt active power filters (APFs) based on Lyapunov’s stability theory. The idea in this strategy is to form an energy-like Lyapunov function in terms of the active filter states and then determine the control law that makes the time derivative of the Lyapunov function always negative for all values of the states. It is shown that a globally stable control is possible at the expense of a time-varying reference function for the direct current (dc) capacitor voltage. This method, however, requires the estimation or measurement of the harmonic ripple component on the dc capacitor voltage. Therefore, a modified control is proposed by ignoring this ripple component. The active filter’s current ref- erence is obtained by subtracting the measured load current from the generated supply current reference. The amplitude of the supply current reference can be adjusted by using a proportional–integral (PI) controller that regulates the dc capaci- tor voltage. Experimental results that are obtained for steady-state operation and step changes in the load are presented to verify the correct operation of the proposed control strategy. Index Terms—Lyapunov-based control, shunt active power filters (APFs). I. I NTRODUCTION A CTIVE power filters (APFs) are widely used in all branches of industry as well as by general consumers of electric energy not only to compensate the unwanted harmonic currents produced by nonlinear loads (power electronics-related appliances), but also to improve input power factor. Conven- tionally, passive inductance–capacitance (LC) filters have been used to compensate these harmonic currents and improve input power factor. However, they have many disadvantages, such as resonance, fixed compensation characteristics, large size, tun- ing problems, and inability to compensate changing harmonic current content. Therefore, the control strategies based on the technique of power electronics have become an important issue recently. The shunt APF, as compared with the series APF, is the most widely used active filter because of its excellent performance characteristics and simplicity in implementation, both in single- and three-phase configurations. The study in this paper is concentrated on the single-phase shunt APF. Various control strategies have been proposed in recent pub- lications for this type of active filters [1]–[10]. Generally, these Manuscript received July 28, 2004; revised November 29, 2004. Abstract published on the Internet November 25, 2005. H. Kömürcügil is with the Department of Computer Engineering, Eastern Mediterranean University, Mersin 10, Turkey (e-mail: hasan.komurcugil@ emu.edu.tr). Ö. Kükrer is with the Department of Electrical and Electronic Engineering, Eastern Mediterranean University, Mersin 10, Turkey. Digital Object Identifier 10.1109/TIE.2005.862218 control strategies consist of three parts, namely: 1) the current control of the voltage-source inverter (VSI); 2) calculation of the compensating current reference; and 3) the control of the dc capacitor voltage. The control strategy presented in [1] is based on the calculation of the real part of the fundamental load current. However, its implementation is complicated. The complexity in calculating the real part of the fundamental load current has been reduced in [2] by using the integration and sampling technique. In addition to this advantage, the dc capacitor voltage control, which is based on the energy balance concept has been used to simplify the dc voltage control circuit design. However, due to the integrator, there exists one period delay in the transient response of the supply current. On the other hand, the method presented in [3] eliminates the need for sensing the load current. The least compensation current control method presented in [4] is based on the detection of the harmonic and reactive current of the APF. In [5], genetic algorithm and extended analysis optimization techniques were applied for switched capacitor active filters. A combined ge- netic algorithm/conventional analysis control technique [6] has been considered as a recent control approach. These control strategies have a common drawback concerning the global stability of the closed-loop system. Although, the sliding-mode control method proposed in [7] solves the stability problem, the calculation technique for the compensating current reference is complicated. In [8], a digital repetitive control approach is presented to obtain high gain for the current loop. However, the control strategy in this approach is based on a linearized model of the active filter and does not lead to global stability. A deadbeat control strategy is introduced in [9] for the current loop of single-phase active filters. Although this method has a fast current control due to the deadbeat nature, dependence on parameters is a basic disadvantage. Furthermore, the need for prediction of the current reference requires adaptive signal processing techniques, which complicates the implementation of this technique. Passivity-based controllers [11] based on phasor models of system dynamics have also been proposed in an attempt to improve the stability properties of active filters. In this paper, the Lyapunov-based control strategy presented in [12] is applied to the control of a single-phase shunt APF. The control strategy proposed here has the following advantages compared to the existing ones. 1) A globally stable control is possible if a time-varying reference function is used for the dc capacitor voltage. Note that this reference function is composed of a dc value and a harmonic ripple component at twice the line frequency due to the input power pulsation. This is the 0278-0046/$20.00 © 2006 IEEE