Real time implementation of feedback linearization control based three phase shunt active power filter

These last years, the increasing use of the devices of power electronics, the electric systems involved more and more problems in disturbances or harmonic distortions of the electrical supply networks. This phenomenon touches the whole of the industrial sectors (use of graduators, rectifiers, speed variations....), tertiary sector (data-processing or lighting of the offices, trades…) and domestic (television sets, apparatuses electric household appliances general public…) The harmonic distortion is generated by the nonlinear loads connected to a network and which absorbs non-sinusoidal currents (Abdelmadjid et al., 2006; Afonso et al., 2000; AitChihab et al., 2014).

These harmonics of current go to their turn to generate harmonic tensions at the various points of connection to the network. For other electric components connected in these points, this harmonic pollution has harmful effects. Among these effects, one can in particular quote the deformation of the tension network with not connection whereas the distributor of energy is held to provide a power clean. This pollution can also lead to the heating of the cables and of electric components or even with the sudden stop of revolving machines, even total destruction of all this equipment (Hasan & Osman, 2007; Leszek & Zarnecki, 2006;).

To decrease or remove these disturbances and thus to improve quality of energy distributed, several solutions exist the reduction of the impedance of short-circuiting, modification of the static inverter polluting in terms of topology and/or the order in order to intervene directly with the source of the harmonic disturbances, devices of filtering. The use of devices attracted great attention since two decades ago. Since its introduction some twenty years ago, the Active Power Filter (APF) presents a good solution for disturbance treatment, particularly for harmonic currents and/or voltages (Mohamed et al., 2008; Nadhir et al., 2014; Sabir et al., 2017; Singh et al., 2000).

APF is an up-to-date solution to power quality problems. The shunt APF allows the compensation of current harmonics and unbalance, together with the power factor correction, and can be a much better solution than the conventional approach (capacitors and passive filters) The performance of the APF is determined by the kind of control used. It is more emphasized when the voltages of the electrical network contain harmonics and/or are unbalanced.

Moreover, the Self Tuning Filter STF is proposed for extracting harmonic currents instead of classical harmonics extraction based on High Pass or Low Pass Filters (Lorenzo et al., 2007; Abdusalam et al., 2008) The three-phase currents/voltages are detected using current/voltage sensors. The inverter currents are controlled by using hysteresis comparators. The hysteresis control is characterized by its simplicity and its intrinsic speed. (Beaulieu & Ouhrouche, 2007; Ghamri et al., 2012; Saetieo et al., 1995).

The identification method chosen effect the quality of the compensation of current harmonics. Many theories of instantaneous power exist in scientific literature the extension of the reactive power to non-sinusoidal waveforms is now a subject of controversy. Many new theories have been proposed. Akagi (Beaulieu & Ouhrouche, 2007). proposed a theory based on instantaneous values in three-phase power  systems with or without neutral wire, and is valid for steady-state or transitory operations, as well as for generic voltage and current waveforms called as Instantaneous Power Theory or Active-Reactive (p-q) Theory which consists of an algebraic transformation (Clarke Transformation) of the three-phase voltages in the a-b-c coordinates to the α-β coordinates, followed by the calculation of the p-q theory instantaneous power components by eliminating the DC component of the instantaneous active power (corresponding to the fundamental component of load current) using a selective Filter STF, so the harmonic components can be identified. Figure 3 shows the modified scheme for the identification of reference currents during simultaneous compensation of harmonic currents and reactive power using the method of instantaneous power by using STF.

3.png

Figure 3. The method of instantaneous active and reactive power

This method is based on measuring the instantaneous three-phase variables present on the grid with or without zero-sequence components. This method is valid both in steady-state phase. In this control algorithm (Figure 2), measurements of voltages and currents expressed as a three phase (abc) are converted to two-phase system (α-β) is equivalent to using the transform from Concordia leaving the power invariant:

                                    (1)

                                   (2)

The power is composed of three parts, In the presence of harmonics: reactive (Q) active(P) and deformed (D) as shown by the following equation:

                                          (3)

The instantaneous active power, denoted P(t) is defined by the following equation:

                                (4)

In the stationary reference can be written:

                           (5)

Can be written, the instantaneous imaginary power as follows:

       (6)

Q power meaning than the usual reactive power. In fact, unlike the reactive power, which considers only the fundamental frequency, the imaginary power takes into account all the harmonic components of voltage and current that is why it is given a different name (imaginary power) as a unit with the volt-ampere imaginary (VAI). The part of the relations (5) and (6), we can establish the following matrix:

                                        (7)

with:  Continuous power related to the fundamental component of active power and voltage,  Continuous power related to the fundamental component of reactive current and tension,  and  Powers of alternatives related to the sum of the components of disruptive current and voltage.

By inverting the relation (7), we can recalculate the currents in the coordinate α β as shown in the following equation

                            (8)

Considering equations (8) and (9), we can separate the current bench mark in the three components, active and reactive at the fundamental frequency and harmonics.

Finally, it is easy to obtain the reference currents along the axes abc by the inverse transformation of Concordia

                         (9)

                           (10)

To obtain a satisfactory extraction, the dynamic mode is slow. In general, cut-off frequency is selected enough low, between 5 Hz and 35 Hz, which generates then an instability of the active filter of power during fast variations of the load.

In the contrary case, if more raised cut-off frequency is chosen, precision determination of the alternate component is altered and can prove to be insufficient.

The self-tuning filter is the most important part of this control which allows to make insensible the PLL to the disturbances and filtering correctly the currents in α-β axis. Hong-Scok Song (Abdelmadjid et al., 2006) had presented in his PhD work how recovered the equivalent transfer function of the integration expressed by the block diagram of the STF tuned at the pulsation ωc is shown in the figure 5. The transfer function of this filter is:

According to the α-β axes, the expressions linking the components   FMV output xαβ to input xαβ components are:

                     (11)

We obtain the following block diagram for STF

4.jpg

Figure 4. Self-tuning filter

The voltage regulation Vdc is provided by the subsystem1. To achieve this object requires we must choose y=Vdc as output, then, we seek its relative degree.

                                (15)

Its derivative is given by:

                              (16)

And as Lie derivatives, we write:

                                  (17)

With:

It follows that:

                                             (18)

The law of order is expressed by:

                         (19)

                              (20)

                                        (21)

5.jpg

Figure 5. The photograph of the shunt APF prototype

                                (22)

The second sub-system of order 2, is characterized by its vector state

 We can write the system of equations (22) under the form:

                           (23)

Now we will apply the state feedback control on models (22) and (23).

The main goal of this article presented is articulated basically on two ideas, we have shown the effectiveness of the shunt active power filtering especially with the application of Non-linear control. After compensation The THD of the source voltage and the source current is well below 5%, the IEEE-519 standard imposes the harmonics limit. Further studies the power factor was corrected (power supply current and voltage became in phase). The control of the active power filter was divided into two parts, the first one realized by the DSpace system to generate the reference currents and the second one an analog card, implementing a hysteresis current controller. the proposed modified version of the p-q theory instead of classical extraction filters (low pass filters or high pass and) have been introduced by STFs, for both grid load currents and voltages. The use of this filter experimentally leads to satisfactory performances since it extracts the harmonic currents at high performances. Several tests have been performed in order to prove the efficiency of the controller. The experimental results presented in this article show that the method of feedback remarkably improves the operation of the active power filter in terms of the THD.