Self Tuning Filter Based Fuzzy Logic Controller for Active Power Filter

In recent years, the world has experienced a sharp increase in electrical disturbances due to the increasing use of non-linear loads. These absorb non-sinusoidal currents and therefore produce harmonic pollution current in the grid electrical causing damage to other devices; hence a custom power device should be used to mitigate this pollution harmonic [1-6]. Among the traditional solutions, the passive power filter (PPF). It eliminates current harmonics and improves reactive energy compensation, but it has many disadvantages such as the series and parallel resonance with the system impedance which can step-up the harmonic voltage and current at specified locations [7]. The active power filter (APF) that can be either a FACTS-based device is a well-developed solution to ensure reactive power compensation and harmonic mitigation [8-10].

The performance of the APF depends on the identification strategy of the reference currents and their control. Several control strategies for the extraction of reference currents have been proposed in the literature, especially the widely used p-q theory and the id-iq theory [11]. However, the performance of APF is poor under unbalanced and distorted source voltage conditions for both strategies [11].

In this paper, a control strategy based on self-tuning filter (STF) is used for extraction of the reference harmonic currents. The major advantages of the STF are cited in the paper [12].

The STF filter extracts the fundamental component directly from the load currents and the source voltages in α-β reference frame while fixing two important parameters, namely, the pulsation ω and the proportional gain K, however, no technique existed in the literature for identification of the proportional parameter [13]. For this purpose, a fuzzy regulator has been associated with the STF filter in order to adjust in real time its proportional parameter K to obtain a perfect extraction of the reference harmonic currents.

The control of the reference currents is accomplished by a hysteresis current controller. The hysteresis control is a simple implemented classical method, it ensures a satisfactory control of the current without requiring a thorough knowledge of the model of the system to be controlled [13, 14]. The purpose of this study is to adjust the K parameter of the STF filter by a FLC controller to obtain a better improvement of the quality of the electric currents in a transmission line feeding a nonlinear load.

The control strategy of the APF can be divided into two steps: The first step is the extraction of the reference currents by the STF filter equipped by the FLC controller. The second one is the control of the reference currents by the hysteresis strategy.

3.1 Harmonic currents identification

In order to have a good performance of the APF, the control strategy for the extraction of the reference current harmonics is based on the STF filter. The STF filter extracts the fundamental component directly from the load currents i_Labc and the source voltages v_Sabc in α-β reference frame using the Concordia transformation. The current harmonics in α-β reference frame are calculated by subtracting the current fundamental components from the load currents [15].

The transformation of three-phase voltages and currents in the α-β frame is given by the following expressions:

$\left[ \begin{matrix} {{v}_{\alpha }}  \\  {{v}_{\beta }}  \\\end{matrix} \right]=\sqrt{\frac{2}{3}}\left[ \begin{matrix}   1 & -\frac{1}{2} & -\frac{1}{2}  \\  0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}  \\\end{matrix} \right]\left[ \begin{matrix}  {{v}_{a}}  \\   {{v}_{b}}  \\  {{v}_{c}}  \\\end{matrix} \right]$      (1)

$\left[ \begin{matrix}  {{i}_{\alpha }}  \\  {{i}_{\beta }}  \\\end{matrix} \right]=\sqrt{\frac{2}{3}}\left[ \begin{matrix}  1 & -\frac{1}{2} & -\frac{1}{2}  \\   0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}  \\\end{matrix} \right]\left[ \begin{matrix}   {{i}_{a}}  \\   {{i}_{b}}  \\   {{i}_{c}}  \\\end{matrix} \right]$    (2)

The instantaneous active power p and the instantaneous reactive power q are defined by [16]:

$\left[ \begin{matrix}   p  \\   q  \\\end{matrix} \right]=\left[ \begin{matrix}   {{v}_{\alpha }} & {{v}_{\beta }}  \\   -{{v}_{\beta }} & {{v}_{\alpha }}  \\\end{matrix} \right]\left[ \begin{matrix}   {{i}_{\alpha }}  \\   {{i}_{\beta }}  \\\end{matrix} \right]$     (3)

$p={{v}_{\alpha }}.{{i}_{\alpha }}+{{v}_{\beta }}.{{i}_{\beta }}$       (4)

$q={{v}_{\alpha }}.{{i}_{\beta }}-{{v}_{\beta }}.{{i}_{\alpha }}$       (5)

The instantaneous active and reactive powers can be written as follows:

$\left\{ \begin{align}  & p=\bar{p}+\tilde{p} \\  & q=\bar{q}+\tilde{q} \\ \end{align} \right.$     (6)

where, $\bar{p} \text { and } \bar{q}$ denote the continuous components and $\tilde{p}$ and $\tilde{q}$ denote the harmonic components of p and q.

From Eq. (3), the expressions of the load current components in the α-β reference frame are:

$\left[ \begin{matrix}   {{i}_{\alpha }}  \\   {{i}_{\beta }}  \\\end{matrix} \right]={{\left[ \begin{matrix}   {{v}_{\alpha }} & {{v}_{\beta }}  \\   -{{v}_{\beta }} & {{v}_{\alpha }}  \\\end{matrix} \right]}^{-1}}\left[ \begin{matrix}   p  \\   q  \\\end{matrix} \right]=\frac{1}{v_{\alpha }^{2}+v_{\beta }^{2}}\left[ \begin{matrix}   {{v}_{\alpha }} & -{{v}_{\beta }}  \\   {{v}_{\beta }} & {{v}_{\alpha }}  \\\end{matrix} \right]\left[ \begin{matrix}   p  \\   q  \\\end{matrix} \right]$       (7)

By replacing Eq. (6) in Eq. (7), the expressions of the currents in α-β reference frame are expressed by:

$\left[ \begin{matrix}   {{i}_{\alpha }}  \\   {{i}_{\beta }}  \\\end{matrix} \right]=\frac{1}{v_{\alpha }^{2}+v_{\beta }^{2}}\left[ \begin{matrix}   {{v}_{\alpha }} & -{{v}_{\beta }}  \\   {{v}_{\beta }} & {{v}_{\alpha }}  \\\end{matrix} \right]\left[ \begin{matrix}   {\bar{p}}  \\   {\bar{q}}  \\\end{matrix} \right]+\frac{1}{v_{\alpha }^{2}+v_{\beta }^{2}}\left[ \begin{matrix}   {{v}_{\alpha }} & -{{v}_{\beta }}  \\   {{v}_{\beta }} & {{v}_{\alpha }}  \\\end{matrix} \right]\left[ \begin{matrix}   {\tilde{p}}  \\   {\tilde{q}}  \\\end{matrix} \right]$      (8)

Since we are interested in the simultaneous compensation of current harmonics and reactive energy, the continuous power p_c needed to maintain the DC voltage V_dc at constant value, will be added to the harmonic component $\tilde{p}$ (Figure 3).

The reference harmonic currents denoted i_α-ref and i_β-ref, are expressed in the α-β reference frame by:

$\left[ \begin{matrix}   {{i}_{\alpha -ref}}  \\   {{i}_{\beta -ref}}  \\\end{matrix} \right]=\frac{1}{v_{\alpha }^{2}+v_{\beta }^{2}}\left[ \begin{matrix}   {{v}_{\alpha }} & -{{v}_{\beta }}  \\   {{v}_{\beta }} & {{v}_{\alpha }}  \\\end{matrix} \right]\left[ \begin{matrix}   \tilde{p}+{{p}_{c}}  \\   {\tilde{q}}  \\\end{matrix} \right]$   (9)

3.png

Figure 3. Extraction of reference current harmonics with STF filter

The reference harmonic currents in the three phase reference frame can be determined using the inverse Concordia transformation as follows:

$\left[ \begin{matrix}   {{i}_{a-ref}}  \\   {{i}_{b-ref}}  \\   {{i}_{c-ref}}  \\\end{matrix} \right]=\sqrt{\frac{2}{3}}\left[ \begin{matrix}   1 & 0  \\   -\frac{1}{2} & \frac{\sqrt{3}}{2}  \\   -\frac{1}{2} & -\frac{\sqrt{3}}{2}  \\\end{matrix} \right]\left[ \begin{matrix}   {{i}_{\alpha -ref}}  \\   {{i}_{\beta -ref}}  \\\end{matrix} \right]$      (10)

The principle of the STF consists of extracting the fundamental components $\hat{\imath}_{\alpha \beta}$ at the pulsation ω_c of the currents i_ab, the harmonic components are calculated by subtracting the STF outputs from the corresponding input signals (Figure 4).

4.png

Figure 4. Self-tuning filter

The authors [13] presented the expressions of the fundamental components $\hat{X}_{\alpha \beta}$ according to the real quantities X_ab , (X can be a current or a voltage):

$\begin{align}  & {{{\hat{X}}}_{\alpha }}(s)=\frac{K}{s}\left( {{X}_{\alpha }}(s)-{{{\hat{X}}}_{\alpha }}(s) \right)-\frac{{{\omega }_{c}}}{s}{{{\hat{X}}}_{\beta }}(s) \\ & {{{\hat{X}}}_{\beta }}(s)=\frac{K}{s}\left( {{X}_{\beta }}(s)-{{{\hat{X}}}_{\beta }}(s) \right)+\frac{{{\omega }_{c}}}{s}{{{\hat{X}}}_{\alpha }}(s) \\\end{align}$     (11)

In this system of equations the K parameter plays an important role for the extraction of the fundamental quantities $\hat{X}_{\alpha \beta}$, however there is no method which allows its dimensioning. Indeed, a value too low or too important of K does not allow the filter to effectively eliminate all the harmonics. In this study, a fuzzy controller was associated with the STF filter to adjust the value of the K parameter based on the operating point of the system. The new FLC-STF filter thus obtained makes it possible to extract the fundamental quantities efficiently and independently of the initial value given to the K parameter.

3.2 Fuzzy logic controller

This type of controller does not require any knowledge of the mathematical model of the system. It is composed of four main blocks (Figure 5): the knowledge base, the inference system, the fuzzification interface and the defuzzification interface [17-20].

5.png

Figure 5. Synoptic diagram of the fuzzy controller

3.2.1 FLC-STFControllerconfiguration

The purpose of the FLC-STF filter developed in this study (Figure 6) is to extract the fundamental quantities $\hat{\imath}_{\alpha \beta}$ necessary in the identification phase of the reference harmonic currents. The role of the FLC regulator is to adjust in real time the parameter K of the STF filter to extract the harmonics of currents as much as possible.

A study was conducted to determine the effect of the K parameter of the STF filter on low order current harmonics (Figure 7). This study consists to varying the K parameter and calculating, for each value of K, the amplitudes of the 3rd order harmonic (h3), the 5th order harmonic (h5) and the 7th order harmonic (h7), and the corresponding THD while exploiting the potential of the MATLAB/Simulink^® software. Figure 7 and Figure 8 show, respectively, the variations of the THD and the magnitudes of some low order harmonics of current as functions of K parameter of the STF filter for a non linear load composed of a three phase full bridge rectifier with an RL connection.

6.png

Figure 6. The proposed FLC-STF scheme for active power filter

7.png

Figure 7. The variation of THD as a function of the K parameter of the STF filter for a nonlinear load

8.png

Figure 8. Curves of harmonic variations h3, h5 and h7 as a function of K parameter of the STF filter for nonlinear load

This study showed that K parameter can affect three parameters, which are: the THD, h5, and h7. The 3^rd harmonic is not affected by the variations applied to K parameter.

For this purpose, the designed FLC controller has three input variables are: THD, h5 and h7, then the output variable of the FLC is the K parameter of the STF filter.

The fuzzy controller is characterized by:

• Three membership functions for each variable (inputs and output) as can be seen in Figure 9.
• Fuzzification based on min-max operator.
• Defuzzification based on center gravity method

The inference system consists of five rules as follows:

• If THD is small AND h5 is medium AND h7 is medium THEN K is large.
• If THD is small AND h5 is large AND h7 is large THEN K is small.
• If h5 is medium AND h7 is medium THEN K is medium.
• If h5 is small AND h7 is small THEN K is large.
• If h5 is large AND h7 is large THEN K is large.

9.png

Figure 9. Membership functions defined for the inputs variables (a) and output variable (b) of FLC controller

3.3 Hysteresis controller

In the hysteresis current controller presented by Figure 10, the current produced by the filter i_f is forced to follow reference current i_ref within a hysteresis band by the switching action of the inverter.

The hysteresis controller is fed by the error signal, which is the difference between the reference current i_refand the current produced by the filter i_f, this error is compared with a fixed tolerance band in order to driving the switching signals [21-23].

10.png

Figure 10. Hysteresis current controller.

3.4 DC capacitor voltage control

The control of the DC-link capacitor voltage is necessary to improve the compensation performance of the APF. In fact, the DC-link capacitor voltage control maintains the voltage V_dc at constant value [11]. This voltage is compared with its reference V_dc-ref, and then the error voltage is applied to the input of a standard type PI corrector as shown in Figure 11. According to the error between the reference voltage and the DC capacitor voltage, the PI controller generates a signal proportional to the power absorbed or supplied by the DC link capacitor [24-26]. Then it is added to the harmonic component of active power.

11.png

Figure 11. The control loop of the DC capacitor voltage