A Control Strategy for Four-Wire Shunt Active Filters Using Instantaneous Active and Reactive Current Method Aniel Silva de Morais Ivo Barbi Federal University of Santa Catarina – UFSC Federal University of Santa Catarina – UFSC Power Electronics Institute – INEP Power Electronics Institute – INEP Caixa Postal: 5119 | CEP: 88040-970 Caixa Postal: 5119 | CEP: 88040-970 Florianópolis, Brazil Florianópolis, Brazil aniel@inep.ufsc.br ivobarbi@inep.ufsc.br Abstract – This paper presents a three-phase four-wire active filter control strategy using the instantaneous active and reactive currents. Analyses of the currents including their harmonic components are presented, as well as simulation results that compare the mentioned theories. I. INTRODUCTION Studies dealing with reactive power compensation date from 1976 [1], but the p-q theory was proposed only in 1983 [2]. This theory is valid for any current and voltage waveforms, and is widely used in the control of active filters. The p-q theory is extremely attractive due to the efficiency and relative simplicity, fundamental in times when analog electronics reigned. Shunt active filters are supposed to compensate the load current implying more balanced and sinusoidal input current. The basis of p-q theory is the control of instantaneous powers, what allows the indirect control of the converter currents. However, the use of dq0 transformation causes the currents to be controlled directly. This paper presents a control technique that using the dq0 transformation (7) acts in instantaneous active ( d I ), reactive ( q I ) and zero ( 0 I ) sequence currents. II. P-Q THEORY The p-q theory is based on the 0 transformation, also known as the Clark transformation (1). 0 1 1 1 2 2 2 2 1 1 1 2 2 3 3 3 0 2 2 C αβ       = ⋅ - -       -   (1) One advantage of this theory is the independence of zero sequence components [3]. Another important definition is the three-phase instantaneous active power (2), that describes the total instantaneous energy flow per time unit between two subsystems, and the three-phase instantaneous reactive power (3), representing the power quantities that do not contribute to the three-phase instantaneous active power. ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 1 1 2 2 3 3 p t v t i t v t i t v t i t φ = ⋅ + ⋅ + ⋅ (2) () () () ( ) () () () ( ) () () () ( ) () 1 2 3 2 3 1 3 3 1 2 1 3 v t v t i t v t v t i t q t v t v t i t φ   - ⋅ + - ⋅   = ⋅   + - ⋅   (3) The instantaneous powers defined in the dq0 system are the real power () p t , the imaginary power () qt , and the zero sequence power () 0 p t ( ) () () () () () () () ( ) () () 0 0 0 0 0 0 0 d q d q d q p t i t v t p t v t v t i t v t v t qt i t             = ⋅             -        (4) Such powers can be divided in continuous and alternated components according to (5). () j () i ()  0 0 0 p t p p p t p p qt q q  = +   = +   = +   (5) For balanced systems only the continuous parts p and q exist, while () 0 p t is null. The presence of zero sequence components in the voltage and current causes the appearance of power () 0 p t , while negative sequence components provide the appearance of alternate powers i p and  q . Fig. 1 shows the physical meaning of instantaneous powers () p t , () qt and () 0 p t . 1 2 3 N v 1(t) i 1 (t) i 2 (t) i 3 (t) v 2(t) v 3(t) q(t) p(t) p (t) 0 + Fig. 1 – Physical meaning of instantaneous powers ( ) p t , ( ) 0 p t and ( ) qt . Compensating the desired powers, usually i p , () qt and () 0 p t , the reference currents are obtained to be used in the controllers. If the input voltages are distorted, the converter provides distorted currents to the system, since p-q theory is supposed to compensate the power quantities, and not currents. Phase Locked Loop (PLL) is applied to solve this problem, as the fundamental positive sequence component of the input voltage is obtained. 1846 1-4244-0136-4/06/$20.00 '2006 IEEE