Power quality improvement using fuzzy logic controller for five-level shunt active power filter under distorted voltage conditions

Abstract

In this paper, a five-level inverter is used as a shunt active power filter (APF), taking advantages of the multilevel inverter such as low harmonic distortion and reduced switching losses. It is used to compensate reactive power and eliminate harmonics drawn from a thyristor rectifier feeding an inductive load (RL) under distorted voltage conditions. The APF control strategy is based on the use of self-tuning filters (STF) for reference current generation and a fuzzy logic current controller. The use of STF instead of classical extraction filters allows extracting directly the voltage and current fundamental components in the α-β axis without phase locked loop (PLL). The MATLAB fuzzy logic toolbox is used for implementing the fuzzy logic control algorithm. The obtained results show that the proposed shunt APF controller has produced a sinusoidal supply current with low harmonic distortion and in phase with the line voltage.

Keywords

active power filter (APF) / harmonics isolator / distorted voltage conditions / self-tuning filters (STF) / fuzzy logic control

Introduction

The extensive use of static converters in industrial activities and public consumers leads to an increase in harmonic injection in the network and a lower power factor. This causes various problems in power systems and in domestic appliances such as equipment overheating, capacitor blowing, motor vibration, excessive neutral currents and low power factor.

Active power filter (APF) involving two levels voltage source inverters have been widely studied and used to eliminate harmonics and compensate reactive power [1]. Due to power handling capabilities of power semiconductors, these APFs are limited in medium power applications. Then hybrid topologies have been proposed to achieve high power filters [2,3]. Recently, the interest in using multilevel inverters for high power drives, reactive power and harmonics compensation has increased [4]. Multilevel pulse width modulation inverters can be used as APF for high power applications to solve the problem of power semiconductor limitations. The use of neutral-point-clamped (NPC) inverters allows equal voltage shearing of the series connected semiconductors in each phase. The performances of different reference current generation strategies under balanced, sinusoidal, alternating current (AC) voltages conditions are well referenced [5,6], such as the so-called p-q theory and synchronous reference frame theory (SRF) which provide similar performances. Differences arise when one works under distorted and unbalanced AC voltages which is the case in real conditions, where the mains voltages are distorted that decreases filter performances [7].

In this paper, the reference current generation for shunt APF control under distorted voltage conditions is based on the use of STFs. The STF is used to extract the fundamental component directly from electrical signals (distorted voltage and current) in the α-β reference frame under distorted voltage conditions [8].

The major advantages of the STF are efficient operation under steady state and transient conditions; no phase delay and unity gain at the fundamental frequency; no PLL required; and easy to implement in digital or analog control system.

The controller is the main part of the APF operation and has been a subject of many researches in recent years [9,10]. Conventional PI voltage and current controllers have been used to control the harmonic current and DC voltage of the shunt APF. However, they require precise linear mathematical model of the system, which is difficult to achieve under parameter variations, non linearity and load disturbances. These limitations are overridden by using fuzzy logic technics. Thus, in this paper, fuzzy logic control schemes are proposed for harmonic current and inverter DC voltage control to improve the performances of the five levels shunt APF. The performance of fuzzy controllers and reference current generation strategies are evaluated through computer simulations under distorted voltage conditions. The obtained results show that the proposed APF controller provides a sinusoidal supply current with low harmonic distortion and in phase with the line voltage.

System configuration

Figure 1 presents the shunt active filter topology based on a three-phase voltage source inverter, using insulated gate bipolar transistor (IGBT) switches, connected in parallel with the AC three-phase three-wire system through three inductors. The capacitors are used in the DC side to smooth the DC terminal voltage. A three-phase thyristor rectifier supplying a RL load represents the non-linear load.

The main task of the proposed shunt APF is to reduce the harmonic currents and to compensate reactive power. The structure in Fig. 1 describes this shunt APF based on a three-phase five-level voltage source inverter (VSI). In order to produce an inverter (active filter) of N levels, N-1 capacitors are required. The voltage across each capacitor is equal to v_dc / (N-1), while v_dc is the total voltage of the DC source. Each couple of switches (T₁₁, T₁₅) form a cell of commutation, the two switches are ordered in a complementary way. The inverter provides five voltage levels according to Eq. (1).

(1)v_{io}=k_i{\displaystyle \frac{v_{dc}}{\mathrm{2}}},

(1)where v_io is the phase-to-middle fictive point voltage; k_i, the switching state variable (k_i =1, 1/2, 0, -1/2, -1); v_dc, the DC source voltage; and i, the phase index (i = a, b and c). The five voltage values are shown in Table 1 (v_dc/2, v_dc/4, 0, - v_dc/4, - v_dc/2).

Reference current calculation

Self tuning filter

Song [11] had presented in his PhD work the recovery of the equivalent transfer function of the integration in the synchronous references frame SRF by

(2)v_{xy}(t)=e^{jwt}{\displaystyle \int e^{-jwt}{u}_{xy}(t)dt},

where u_xy and v_xy are the instantaneous signals, respectively before and after integration in the synchronous reference frame. Equation (2) can be expressed by the following transfer function after Laplace transformation.

(3)H(s)={\displaystyle \frac{v_{xy}(s)}{u_{xy}(s)}}={\displaystyle \frac{s+jw}{s^{\mathrm{2}}+w^{\mathrm{2}}}}.

A constant k is introduced in the transfer function H(s) in this paper to obtain a STF with a cut-off frequency w_c, so Eq. (3) becomes

(4)H(s)={\displaystyle \frac{v_{xy}(s)}{u_{xy}(s)}}={\displaystyle \frac{(s+k)+j{w}_c}{{(s+k)}^{\mathrm{2}}+w_c^{\mathrm{2}}}}.

By replacing the input signals u_xy(s) by x_{\alpha \beta }(s) and the output signals v_xy(s) by {\widehat{x}}_{\alpha \beta }(s), Eqs. (5) and (6) can be obtained.

(5){\widehat{x}}_{\alpha }(s)={\displaystyle \frac{k}{s}}\left[x_{\alpha }(s)-{\widehat{x}}_{\alpha }(s)\right]-{\displaystyle \frac{w_c}{s}}{\widehat{x}}_{\beta }(s),

(6){\widehat{x}}_{\beta }(s)={\displaystyle \frac{k}{s}}\left[x_{\beta }(s)-{\widehat{x}}_{\beta }(s)\right]-{\displaystyle \frac{w_c}{s}}{\widehat{x}}_{\alpha }(s).

The block diagram of the STF tuned at the pulsation w_c is depicted in Fig. 2 while the frequency response of the STF versus different values of the parameter k for f_c = 60 Hz is depicted in Fig. 3. It can be noticed that no displacement is introduced by this filter at the system pulsation.

It can be observed that the small value of k increases filter selectivity. Thus, by using a STF, the fundamental component can be extracted from distorted electrical signals (voltage or current) without any phase delay and amplitude changing.

Harmonic isolator

The load currents, i_La,i_Lb and i_Lc of the three-phase three-wire system are transformed into the α-β axis (Fig. 4) as

(7)\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\end{array}\right]=\sqrt{{\displaystyle \frac{2}{3}}}\left[\begin{array}{lll}1\hfill & -{\displaystyle \frac{1}{2}}\hfill & -{\displaystyle \frac{1}{2}}\hfill \\ 0\hfill & {\displaystyle \frac{\sqrt{3}}{2}}\hfill & {\displaystyle \frac{-\sqrt{3}}{2}}\hfill \end{array}\right]\left[\begin{array}{c}{i}_{La}\\ i_{Lb}\\ i_{Lc}\end{array}\right].

As is known, the currents in the α-β axis can be respectively decomposed into DC and AC components by

(8)i_{\alpha }={\widehat{i}}_{\alpha }+{\tilde{i}}_{\alpha },

(9)i_{\beta }={\widehat{i}}_{\beta }+{\tilde{i}}_{\beta }.

Then, the STF extracts the fundamental components at the pulsation w_c directly from the currents in the α-β axis. Afterwards, the α-β harmonic components of the load currents are computed by subtracting the STF input signals from the corresponding outputs (Fig. 4.). The resulting signals are the AC components, {\tilde{i}}_{\alpha } and{\tilde{i}}_{\beta }, which correspond to the harmonic components of the load currents i_La,i_Lb and i_Lc in the stationary reference frame.

For the source voltage, the three voltages v_sa, v_sb and v_sc are transformed to the α-β reference frame as

(10)\left[\begin{array}{c}{v}_{\alpha }\\ v_{\beta }\end{array}\right]=\sqrt{{\displaystyle \frac{2}{3}}}\left[\begin{array}{lll}1\hfill & -{\displaystyle \frac{1}{2}}\hfill & -{\displaystyle \frac{1}{2}}\hfill \\ 0\hfill & {\displaystyle \frac{\sqrt{3}}{2}}\hfill & {\displaystyle \frac{-\sqrt{3}}{2}}\hfill \end{array}\right]\left[\begin{array}{c}{v}_{sa}\\ v_{sb}\\ v_{sb}\end{array}\right].

Then, self-tuning filtering is applied to these α-β voltage components. This filter allows suppressing of any harmonic component of the distorted mains voltages and consequently leads to improvement of the harmonic isolator performance.

After computation of the fundamental component {\widehat{v}}_{\alpha \beta } and harmonic currents{\tilde{i}}_{\alpha \beta }, the p and q powers are given as

(11)p=i_{\alpha }{\widehat{v}}_{\alpha }+i_{\beta }{\widehat{v}}_{\beta },(Instantaneous active power)

(12)q=i_{\beta }{\widehat{v}}_{\alpha }-i_{\alpha }{\widehat{v}}_{\beta },(Instantaneous reactive power)

where

(13)p=\widehat{p}+\tilde{p},

(14)q=\widehat{q}+\tilde{q},

in which \widehat{p} nd\widehat{q}are fundamental components and \tilde{p} nd \tilde{q}are alternative components.

The power components \tilde{p} and \tilde{q} related to the same α-β voltages and currents can be written as

(15)\left[\begin{array}{c}\tilde{p}\\ \tilde{q}\end{array}\right]=\left[\begin{array}{cc}{\widehat{v}}_{\alpha }& {\widehat{v}}_{\beta }\\ -{\widehat{v}}_{\beta }& {\widehat{v}}_{\alpha }\end{array}\right]\left[\begin{array}{c}{\tilde{i}}_{\alpha }\\ {\tilde{i}}_{\beta }\end{array}\right].

After adding the active power required for regulating DC bus voltage, p_c, to the alternative component of the instantaneous real power \tilde{p} (Fig. 4), the current references in the α-β reference frame, i_{\alpha \beta }^{\ast }, are calculated by

(16)i_{\alpha }^{\ast }={\displaystyle \frac{{\widehat{v}}_{\alpha }}{{\widehat{v}}_{\alpha }^{\mathrm{2}}+{\widehat{v}}_{\beta }^{\mathrm{2}}}}\left(\tilde{p}+p_c\right)-{\displaystyle \frac{{\widehat{v}}_{\beta }}{{\widehat{v}}_{\alpha }^{\mathrm{2}}+{\widehat{v}}_{\beta }^{\mathrm{2}}}}\tilde{q},

(17)i_{\beta }^{\ast }={\displaystyle \frac{{\widehat{v}}_{\beta }}{{\widehat{v}}_{\alpha }^{\mathrm{2}}+{\widehat{v}}_{\beta }^{\mathrm{2}}}}\left(\tilde{p}+p_c\right)+{\displaystyle \frac{{\widehat{v}}_{\alpha }}{{\widehat{v}}_{\alpha }^{\mathrm{2}}+{\widehat{v}}_{\beta }^{\mathrm{2}}}}\tilde{q}.

Then, the filter reference currents in the a-b-c coordinates are defined by

(18)\left[\begin{array}{l}{i}_{fa}^{\ast }\hfill \\ i_{fb}^{\ast }\hfill \\ i_{fc}^{\ast }\hfill \end{array}\right]=\sqrt{{\displaystyle \frac{2}{3}}}\left[\begin{array}{cc}1& 0\\ 1/2& \sqrt{3}/2\\ -1/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{i}_{\alpha }^{\ast }\\ i_{\beta }^{\ast }\end{array}\right].

Inverter control using phase distortion PWM

This control implements a fuzzy logic controller which starts from the difference between the injected current (active filter current) and the reference current (identified current) that determines the reference voltage of the inverter (modulating wave). This standard reference voltage is compared with four carrying triangular identical waves.

These carrier waves have the same frequency and are arranged on top of each other, with no phase shift, so that they together span from maximum output voltage to minimum output voltage [12,13]. The switching states of one five-level phase leg are summarized in Table 2.

The general block diagram of current control is illustrated in Fig. 5.

Fuzzy logic control application

The synoptic scheme of Fig. 6 shows a fuzzy controller, which possesses two inputs and one output. The inputs are the error (e), which is the difference between the reference current(harmonic current) and the active filter current (injected current) (e = i_ref -i_f) and its derivative (de) while the output is the command (cde).

APF current control

The objective is to get sinusoidal source currents in phase with the supply voltages. This consists of replacing the conventional controllers by fuzzy logic controllers [14].

The establishment of the fuzzy rules is based on the error (e) sign, variation and knowing that (e) is increasing if its derivative (de) is positive, constant if (de) is equal to zero, decreasing if (de) is negative, positive if (i_ref>i_f), zero if (i_ref = i_f), and negative if (i_ref<i_f). Then fuzzy rules are summarized as following:

1) If (e) is zero (ZE), then the command is zero (ZE).

2) If (e) is positive (P), then the command is large positive (LP).

3) If (e) is negative (N), then the command is large negative (LN).

4) If (e) is zero (ZE) and (de) is positive (P), then the command is negative (N).

5) If (e) is zero (ZE) and (de) is negative (N), then the command is positive (P).

DC capacitors voltages stabilization

A DC link voltages stabilization system is introduced to balance the four DC input voltages, avoid NP potential drift and improve the performances of the five level APFs [14]. The structure of the bridge balancing is demonstrated in Fig. 7.

If the voltage u_cx gets higher than an impose reference u_ref (200 V), the transistor T_x is opened to slow down the charging of C_x. The transistors are controlled as follows:

u_{cx}-u_{cref}={\mathrm{\Delta }}_x\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}x=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4.}

If{\mathrm{\Delta }}_x>\mathrm{0}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}{F}_x=\mathrm{1}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}{i}_{rx}=F_x{\displaystyle \frac{u_{cx}}{R_x}}.

Else{F}_x=\mathrm{0.}

DC capacitor voltage control

In this application, the fuzzy control algorithm is implemented to control the DC capacitor inverter voltage based on DC voltage error e(t) processing and its variation Δe(t) in order to improve the dynamic performance of APF and reduce the total harmonic source current distortion.

In the design of a fuzzy control system, the formulation of its rule set plays a key role in improving the system performance. The rule table contains 49 rules, as listed in Table 3, where (LP, MP, SP, ZE, LN, MN, and SN) are linguistic codes (LP—large positive; MP—medium positive; SP—small positive; ZE—zero; LN—large negative; MN—medium negative; and SN—small negative).

Simulation is performed using system parameters presented in Table 4.

Results and discussion

The resulting switching signals in Fig. 8 illustrates a low frequency commutation process showing, thus, the advantages of the multilevel inverter. Figure 9 illustrates that the supply voltage is not sinusoidal and includes a 5th harmonic component (THD=11.11%). The total harmonic distortion (THD) of the load current (supply current without filter) is equal to 21.82% (Fig. 10), whereas, in Fig. 11, the THD of the supply current under this condition is equal to 1.10% after filtering. The proposed harmonic isolation and fuzzy control schemes allow harmonic currents and reactive power compensation simultaneously under distorted voltage conditions. The obtained current and voltage waveforms are in phase as exhibited in Fig. 12. The five-level shunt APF performances are related to current references quality. The STF theory is used for harmonic currents identification and calculation, and the obtained current is presented in Fig. 13.

The line to line output voltage v_ab is shown in Fig. 14. The five level active filter with the proposed harmonic isolation and fuzzy control schemes has imposed a sinusoidal source current waveform as illustrated in Fig. 12, and a constant and ripple free DC voltage in Fig. 15. The different voltages obtained by using the stabilization bridge are displayed in Figs. 16 to 19. It can be seen that the output voltages of the DC side of the five level active filter (u_c1, u_c2, u_c3, u_c4) stabilize around 200 V.

Conclusions

This paper has discussed the control and performance improvement of a shunt APF under distorted voltage conditions, using a fuzzy logic controller for a five level shunt APF based on the optimization of the reference current generation and using a modified version of the p-q theory and PDPWM to generate switching signals. Simulation results have shown high performances in reducing harmonics and power factor correction. The use of the STF leads to satisfactory improvements since it perfectly extracts the harmonic currents under distorted conditions. With the fuzzy logic control, the active filter can be adapted easily to more severe constraints, such as unbalanced conditions. In addition, the results have demonstrated the major advantages of using STF and fuzzy logic controller in filter control. The five-level APF provides numerous advantages such as improvement of supply current waveform, less harmonic distortion and possibilities to use it in high power applications.

As a final conclusion, the obtained results showed that the proposed APF controller have provided a sinusoidal supply current with low harmonic distortion and in phase with the line voltage.

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