Fuzzy Logic and Selectivity of Control for Controlling the Paralleling of Four Leg Shunt Active Power Filters Based on Three Dimensional Space Vector Modulation Ali Chebabhi
Mohammed-Karim Fellah
Abdelhalim Kessal
Mohamed-Fouad Benkhoris
ICEPS Laboratory Department of Electrical Engineering University of Sidi Bel-Abbes. Algeria
[email protected]
ICEPS Laboratory Department of Electrical Engineering University of Sidi Bel-Abbes. Algeria
[email protected]
Faculty of Science and Technology University of Bordj BouArreridj. Algeria
[email protected]
IREENA Laboratory University of Nantes at Saint-Nazaire. France
[email protected]
Abstract— A new structure of paralleling four leg shunt active power filters is presented in order to compensate the four-wire electrical network supplying the high power of non-linear singlephase loads. An effective selectivity of control with fuzzy logic and Three Dimensional Space Vector Modulation (3D-SVM) introduced in this configuration of SAPFs to maintain the same amplitude and frequency of output current of each inverter, this is necessary to determine the numbers of inverters in service and their frequency of commutation according to the power of nonlinear single-phase loads, to make operating or stopping the inverters without disturbing the performance of paralleling SAPFs. The fuzzy logic controller (FLC) and Three Dimensional Space Vector Modulation (3D-SVM) is necessary to robustness, minimizing the harmonics of source currents, reducing the magnitude of neutral current, eliminating the zero-sequence current, compensating reactive power in the four–wire distribution network, stabilizing the DC bus voltage, switching losses, and to fixe switching frequency in inverters. Also, an instantaneous real, imaginary and zero-sequence powers pq0 theory in the αβο-axes is presented to generate the reference currents which should be injected by the paralleled four leg SAPFs. Keywords— Paralleling of four-leg shunt active power filters; Selectivity of control; (FLC); 3D-SVM; pq0 theory; Zero-sequence current; Harmonic; Reactive power compensation.
I.
INTRODUCTION
Three phase four-wire four-leg shunt active power filter are the main compensating reactive power, harmonic currents, and reduce zero-sequence current given by non-linear singlephase loads in the world today [1-3], [9-10]. This SAPF consists in using a four leg inverter that injects harmonic currents in the electrical network, equal to that given by nonlinear single-phase loads, but in phase opposition therewith. However, the increases of non-linear single-phase loads power caused problems appear in four-leg inverter. Static switches of four-leg inverter must switch high currents and it’s often necessary to place several paralleling of four-leg inverters [45]. A given power, reducing of switched currents goes through
increase the switches voltage. The four-leg inverters with PWM require high voltage gradient, this may causing accelerated of aging insulating. This paper propose a new operation configuration of shunt active power filter, it developed to connect the increasing number of SAPF into the four-wire network, and this configuration offers an interesting alternative for reducing the switches constraints [4-7]. Indeed, the increase in the number of SAPF allows the fractionation of power and thereby reducing switches voltage at given current. Furthermore, this paralleling four leg SAPF allow to reducing the amplitude of the injected current if. Also in this paper the selectivity for controlling these new structure are introduced to determine the number of four-leg inverters in service and their switching frequency according to the power of non-linear single-phase loads connected to the four-wire network, for operating or stopping the inverters without disturbing functioning of the complete paralleling SAPFs. The reference signals, switching signals generate, and the harmonic current and DC bus voltage control, are very important for controlling this new structure. In our study, we use a Three Dimensional Space Vector Modulation (3D-SVM) for switching signals generate using the pq0 theory in the αβοaxes [1-3], [9], the harmonic currents and DC voltage controls are realized by fuzzy logic control [3]. The structure of paralleling four-leg SAPFs is shown in Fig. 1. The main circuit composed of m SAPF connected each other in parallel, this m SAPF are connected in shunt to the three phase source supplying the three single phase loads in a point called the Point of Common Coupling (PCC) [1-3], the DC bus supply of these inverters is a capacitor common for the all parallel inverters [6-7].
Fig. 2. Circulation of the zero sequence current in the paralleling of two four-leg inverters Fig. 1. The paralleling four-leg shunt active power filters topology
II.
IV.
MODELING OF THE FOUR-LEG SHUNT ACTIVE POWER FILTER
The differential equations describing the dynamic model of the four-leg shunt active power filter are defined in αβο-axes, as given in equation (1): [2-3] ⎧ di f α ⎪ ⎪ dt ⎪ di ⎪ fβ ⎪⎪ dt ⎨ ⎪ di f 0 ⎪ dt ⎪ ⎪ dVdc ⎪ ⎪⎩ dt
=− =− =− =
Rf Lf
ifα +
1 1 vfα − vlα Lf Lf
if β +
1 1 vf β − vl β Lf Lf
if 0 +
1 1 vf 0 − vl 0 Lf Lf
Rf Lf Rf Lf
(1)
Pdc* C Vdc
III. MODELING OF THE ZERO-SEQUENCE CURRENT In the paralleling three-phase converters the circulation directly of current is a distinctive particularity [6]. Fig. 2 illustrates the path of the circulating current in the two paralleling four-leg inverter. It can be observed in Fig. 2 that there is more than one path of circulation current. Instead of watching all the individual circulation currents, a zero sequence current is normally defined to represent the global circulating current. The zero sequence current is defined as a one third of the sum of all phase currents in an inverter, as given in eq (2): 1 1 (2) io = in = ( is1 + is 2 + is3 ) 3 3 We consider the equation (2) and Fig. 2, which shows the paralleling of four-leg shunt active power filters, the zero sequence current is not zero. Therefore, appropriate controls must be applied to reduce the zero sequence current due to its undesirable effects, such as additional conduction losses, distorted waveforms, etc.
MODELING OF THE PARALLELING FOUR-LEG SHUNT ACTIVE POWER FILTERS
Using the model of four-leg shunt active power filter in eq (1) and the basic scheme of fig. 2 we obtain the model of the paralleling four-leg shunt active power filters given by. Rf ⎧ di f α 1 1 1 if α1 + v fα1 − vlα =− ⎪ dt L L L f f f ⎪ ⎪ di R 1 1 ⎪ f β1 = − f i f β1 + v f β1 − vl β Lf Lf Lf ⎪ dt ⎪ ⎪ di f 01 = − R f i + 1 v − 1 v f 01 f 01 l0 ⎪ dt Lf Lf Lf ⎪ ⎪. ⎪ ⎪⎪. ⎨. ⎪ 1 1 ⎪ di f α m = − R f i vfαm − vlα fαm + ⎪ dt Lf Lf Lf ⎪ Rf ⎪ di f β m 1 1 if βm + vf βm − vl β =− ⎪ Lf Lf Lf ⎪ dt ⎪ di R ⎪ f 01 = − f i f 0 m + 1 v f 0 m − 1 vl 0 Lf Lf Lf ⎪ dt ⎪ ⎪ i = C dVdc dc ⎪⎩ dc dt
V.
(4)
THE PQ0 THEORY
The real, imaginary and zero-sequence instant powers (pq0) theory has been successfully employed in a wide field of applications, and many contributions have been made in order to generalize it. It has also been applied successfully in controllers of four-leg shunt active power filter [2-3]. VI.
THREE DIMENSIONAL SPACE VECTOR MODULATION
In three dimensional space vector modulation (3D-SVM), there are 16 possible switching vectors: fourteen active nonzero vectors and two null vectors. Six prisms in the 3D space vector diagram can be identified and numbered as Prisms I through VI, each of these six prisms is decomposed into four tetrahedrons are labeled T1-T4. Within the selected prism, there are six non-zero switching state vectors and two zero switching state vectors.
This method is represented and described in detail as [1-3], [910]. VII. FUZZY LOGIC CONTROL The block diagram of a fuzzy controller is shown in Fig. 3.
Fig. 3. Basic configuration of fuzzy logic controller (FLC)
A. Control currents The reference voltages vfαβo at the input of 3D-SVM block generates by the fuzzy logic controllers (FLC) are used to control the currents ifαβo will be determined depending on the error between the reference currents and currents injected by the four leg inverters. Each of these fuzzy logic controllers has two inputs, the error of the current (εifαβo), the derivative of the error (Δεifαβo) and a single output namely the command vfαβo [3], [11-14]. B. DC-bus voltage control The direct power Pdc at the output of fuzzy logic controller (FLC) used to control the DC bus voltage and for compensate the losses power of four leg inverters, will be determined according to the error between the reference voltage and the compensating voltage. This fuzzy controller has two inputs, the error (εVdc), the derivative of this error (ΔεVdc) and a single output namely the command Pdc. Selectivity of control in the paralleling of four-leg shunt active power filters [3], [11-14]. 1.
4 ⎧* * ⎪ i f α β o ,s − 1 = 3 .k 1 .i f αβ o − 1 ⎪* 4 f ⎪ i f α β o ,s − 2 = .k 2 .i*f αβ o − 2 ' , f s = 4 sn ⎨ 3 4 ⎪* * ki ∑ ⎪ i f α β o ,s − 3 = 3 .k 3 .i f α β o − 3 i=1 * ⎪ i* ⎩ f α β o ,s − 4 = k 4 .i f αβ o − 4 elseif (p>= x3), k1=1; k2=1; k3=1; k4=1; ⎧ i*f αβ o ,s − 1 = k 1 .i*f αβ o − 1 * ⎪⎪ i* f f αβ o ,s − 2 = k 2 .i f αβ o − 2 , f s' = 4 sn ⎨ i* * = k .i 3 f αβ o − 3 ⎪ *f αβ o ,s − 3 ki * ∑ ⎩⎪ i f αβ o ,s − 4 = k 4 .i f αβ o − 4 i=1 2.
SIMULATION MODEL OF A FOUR LEG SHUNT ACTIVE POWER FILTRE
In this section, we intend to present the results of simulation. A. Before filtering The Fig. 6 shows the current waveform of the loads. It is a highly non-sinusoidal current and deformed and there is not in synchrony with the corresponding voltages (power factor is Pf = 0), the form of the neutral current with a maximum value of 22A in the balanced case and 70A in the unbalanced case. Fig. 7 (i and ii) shows the first phase source current's THD. before unbalanced loads (t0.4s) it’s 10.51%.
SELECTIVITY OF CONTROL
The selectivity of control between the pq0 theory and reference currents controls for controlling these new structures are introduced to determine the number of inverters in service, partitioned their switching frequency and total currents injected by the new structures in the network according to the power of single-phase loads, also to make operating or stopping inverters without disturbing the functioning of complete paralleling SAPFs. This algorithm is given as follows. if (p>=0 && p= x2 && p
