# FOUR LEGGED ACTIVE POWER FILTER COMPENSATION FOR A UTILITY DISTRIBUTION SYSTEM

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2 A. Chaghi A. Guettafi A. Benoudjit: FOUR LGGD ACTIV POWR FILTR COMPNSATION FOR A UTILITY... r s l s i s (t) i L (t) r c l c L d R d Nonlinear loads AC mains i sh (t) C dc r f l f I N 4-leg VSc Fig.. Basic shunt compensation scheme using a 4-leg VSC is no longer needed in such a case, which turns out to be a conventional three-phase inverter case. V (X) X Î (;) D SPAC VCTOR MODULATION Space vector modulation for a four-legged inverter is based on the representation of the phase voltage space vectors in the α β γ plane as shown in Fig.. In the conventional inverter, there are eight possible switch combinations. With an additional leg, the total number of switch combinations increases to sixteen. V V V Fig.. Representation of topology () in α - β - γ The phase voltage V abc can be presented in the orthogonal coordinate α β γ in the three dimensional space by applying (). Thus, each switching combination can be represented with a space vector: [ X α X β X γ ] = T [ X a X b X c ] where T is the transformation matrix: T =. () The projection of all space vectors in the α-β plane will result in the known hexagon of the conventional space vector modulation for three phase voltage source inverter as shown in Fig.. V 4 (X) 4 V 5 (X) X 5 X V (X) V (X) Fig.. Projection of the sixteen vector into α - β plane Table shows the switching combinations and the corresponding voltages in α- β - γ coordinates. Distribution of the switching vectors is shown in Fig. 4. There are two zero switching vectors (, ), and 4 non-zero vectors. These vectors form six prisms in the space, each prism can be defined by six non zero vectors and two zero vectors. / / -/ - / - Fig. 4. Switching vectors of a three-phase four legged inverter

3 Journal of LCTRICAL NGINRING, VOL. 55, NO. -, 4 Table. Switching combination in the α - β - γ coordinates tats V α V β V γ () () () () () () () () () () () () () () () () Table. Switching variables used in the space vector d α d β d k e α (k) e β (k) e (k) e dc e dc e dc e dc e dc 4 e dc 5 e dc e dc e dc e dc e dc e dc e dc e dc e dc e dc 4 SYSTM MODLLING AND CONTROL The extension of the instantaneous active and reactive current component i d I q method is based on the it original definition [7] plus the introduction of the zero sequence current component. In this method the APF currents ic i are obtained by previous calculation on the mains voltage u i and non linear load currents il i in a stationary reference frame, ie, in α-β - components by equation () and (). Nonzero values are assumed for zero components in both voltage and current. [C αβ ] =, () [u αβ ] = [C αβ ] [u ], [il αβ ] = [C αβ ] [il ]. (4) In order to obtain the d q load current components a synchronous reference frame is used applying the transformation (4) where θ represent the instantaneous voltage vector angle. i i i o i i d d d o i eprom G G G G 4 I dc i i 4-leg inverter Fig. 5. Space vector based current controller for the 4-leg APF i ld i lq i l cos θ sin θ = sin θ cos θ e i i i il α il β il i N. (5) Decoupling between αβ and zero sequence voltage components allows to obtain a transformation which is a function of only two variables. Then performing the elimination of average current components by high-pass filters the currents that should be compensated are obtained. ic d = ĩ ld, ic q = ĩ lq, and i = il. Finally the converter currents in phase co-ordinates can be determined as indicated by (4) ic α ic β ic u α u β = u β u α u α + u β A). Current control u α + u β ic d ic q ic. () The APF based on the 4-leg VSC topology is presented in Fig. 4. Variable g i (k), where i =,, stand for the phase number and k is the VSC state number, are the switching functions. A value g i (k) = / means that the lower/upper IGBT is conducting. Obviously, in any leg, the IGBT s conduction is non simultaneous.the variable g 4 (k) is also a switching function, related with the fourth leg which is connected to the neutral wire. The 4-leg VSC topology enable to generate sixteen, k = (,..., 5) voltage space vectors, e αβ (k). The current control in the APF is achieved with space vector based current controller shown in Fig. 5. This current controller is implemented with hysteresis comparators acting in the current errors.

4 4 A. Chaghi A. Guettafi A. Benoudjit: FOUR LGGD ACTIV POWR FILTR COMPNSATION FOR A UTILITY... AC source V mes Transformation /(ab) L G,G,G,G4 I c (ab) i s I c (ab) i c Command i l V dc control i h Currents identification i n e dc i l,mes Non-linear Load In (A) ILabc (A) Vabc (V) Fig.. Active power filter control circuit based on a 4-leg VSC Time (s) Fig. 7. Before compensation V abc : load voltage, I abc : load currents, I N : neutral current Table presents the switching variables d αβ, VSC state number and voltages, e αβ (k) used in the space vector based current controller for the 4-leg VSC. Using this control strategy only eight (k =,, 5,,,,, 4) of sixteen possible states are used. However, there is always an approximated state k, that satisfy all the voltage components required. The three-phase 4-wire APF control circuit proposed in Fig., is based on the above VSC topology. The space vector based current control is used to achieve the current injection of the reference currents ic αβ or ic dq. B). DC Voltage control Assuming that the active power flow between mains and the VSc is equal to the active power in the Dc side, ie, neglecting zero sequence power, losses in the inductance and switching devices, the state equation for capacitor voltage is: where C e dc de dc = p (7) p = v i h + v i h + v i h (8) therefore considering the variable K P and K i as the proportional and integrator gains of the PI controller, the state equation for capacitor becomes: de dc de dc ( = K p + K ) i (e )v + v + v s dc e dc, Ce dc (9) ( = K p + K ) i (e ) v s dc e dc. Ce dc () The simplified transfer function is e dc e dc v = s + (K i /K p ) K p Ce dc s + ξ e w ne s + wne. () The design of the PI controller is realised verifying that is a prototype second-order system. The variable values considered are damping ration ζ = /, a natural undamped frequency ω n = ω/5, a capacitor c = 4.4 mf, a DC voltage e dc = e dc = 84 V and a mains voltage U = V. K p = Ce dc V and 5 SIMULATION RSULTS K i = Ce dc V wne. () In the simulations the non-linear load is composed of independent single-phase bridge rectifiers connected between each phase and neutral wire and with a parallel RL load. As it can be observed in Figures 8 and 9 before and after compensation. The dynamic response of the control strategy (and overall active power filter) is studied by switching the three single phase inverter feeding unbalanced load with the same commutation angle: α =, under the following parameters: Ac source V/5 Hz, R s =. mω, L s =.8 µh, R c =. mω, L c = 5 µh, R L =. Ω, L L = mh, R L =. Ω, L L =. mh and R L = Ω, L L = 4 mh

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