# A Hybrid Active Filter Using the Backstepping Controller for Harmonic Current Compensation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{dc}at its reference value, and a significantly reduced THD according to standards, whereas the conventional PI controller has a very high response time and an error between the setpoint and its reference value. Finally, the fuzzy logic control presents a 5% response time lower than the PI controller, but the system remains slower. The above reflects that the proposed approach achieves the desired performance.

## 2. Proposed Hybrid Filter

- Serial active filter with parallel passive filter;
- Serial active filter connected in series with parallel passive filter;
- Parallel active filter in series with a passive filter.

#### 2.1. Current Reference Algorithm Using p-q Theory

#### 2.2. DC Bus Voltage Regulation

_{dc}) is to maintain the latter following its reference value V

_{dc ref}. For the control of this loop, a PI corrector is used as shown in Figure 3. The reference voltage is considered as input and the measured value as output. The voltage at the capacitor terminals is given by:

_{p}and K

_{i}:

#### 2.3. Regulation of the Current Injected by the Filter

#### 2.4. Fuzzy Logic Control

## 3. Proposed Backstepping Control

_{c}is the voltage across the capacitance C of the passive filter.

_{fα}, i

_{fβ}where voltages v

^{*}

_{fα}, v

^{*}

_{fβ}are considered as control variables.

#### 3.1. Subsystem 1

^{*}

_{fα}represents the command and i

_{fα}its output. The algorithm is given as follows:

_{1}is given by:

#### 3.2. Subsystem 2

_{1}is given by:

#### 3.3. Subsystem 3

_{dc}. It contains a single error variable that is between the DC bus voltage and its reference value ${z}_{3}$. The error variable is defined by:

## 4. Simulation and Interpretation

_{s}

_{1}= V

_{s}

_{2}= V

_{s}

_{3}= 220 V, the passive filter parameters are as follows L = 0.01 H, C = 150 µF, the reference voltage of the DC bus is equal to 620 V, the pollutant load is a three-phase diode rectifier, its output an inductance of 0.003 H, in series with a resistance of 18 Ω, and the energy storage capacity is chosen from 2000 µF. The Simulink model realized is illustrated in Figure 6.

_{dc}to the capacitor terminals C with the identification block. More than one block linked to the identification block allows the regulation of the injected current and transfers the control pulses to the converter for the semiconductors. The model is illustrated in Figure 6.

_{dc}followed the variation of its reference with the backstepping controller at a better speed. The system is stabilized at the time t = 0.06 s, and we notice a good accuracy, but the result with the PI linear controller contains an error between the DC bus voltage V

_{dc}and its reference which varies from 600 V to 620 V (as a ripple in the transient regime) and during the delay as shown in Figure 18. It is noted that V

_{dc}does not follow its reference variation in the transient regime. Also, a high response time is found. The system is only stabilized at the time t = 0.135 s, which translates into a poor speed and consequently a degradation of the performance of the HAPF. Concerning the fuzzy non-linear logic controller, the system is stabilized at the time t = 0.0755 s. The delay of the voltage V

_{dc}deviates from its reference and presents a response time at 5% lower. These make the system slower, and it contains oscillations in the permanent regime, consequently the system degrades the accuracy. The controller’s earnings are elected by test to achieve satisfactory performance. It should be noted that the THD with backstepping is significantly lower than the PI control, and fuzzy logic. We can say that the backstepping command has better control performance in terms of oscillations and response time compared to the PI and fuzzy logic controller. The response of the HAPF can be improved by using the proposed control method that achieves the desired performance.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Akagi, H. Large static converters for industry and utility applications. Proc. IEEE
**2001**, 89, 976–983. [Google Scholar] [CrossRef] - Krastev, I.; Tricoli, P.; Hillmansen, S.; Chen, M. Future of Electric Railways: Advanced Electrification Systems with Static Converters for ac Railways. IEEE Electrif. Mag.
**2016**, 4, 6–14. [Google Scholar] [CrossRef] - Emanuel, A.E. On the assessment of harmonic pollution [of power systems]. IEEE Trans. Power Deliv.
**1995**, 10, 1693–1698. [Google Scholar] [CrossRef] - Redl, R.; Tenti, P.; Daan van Wyk, J. Power electronics’ polluting effects. IEEE Spectr.
**1997**, 34, 32–39. [Google Scholar] [CrossRef] - Singh, B.; Al-Haddad, K.; Chandra, A. A review of active filters for power quality improvement. IEEE Trans. Ind. Electron.
**1999**, 46, 960–971. [Google Scholar] [CrossRef] - Rahmani, S.; Al-Haddad, K.; Kanaan, H.Y. A comparative study of shunt hybrid and shunt active power filters for single-phase applications: Simulation and experimental validation. Math. Comput. Simul.
**2006**, 71, 345–359. [Google Scholar] [CrossRef] - Peng, F.Z.; Adams, D.J. Harmonic sources and filtering approaches-series/parallel, active/passive, and their combined power filters. In Proceedings of the Conference Record of the 1999 IEEE Industry Applications Conference: Thirty-Forth IAS Annual Meeting (Cat. No.99CH36370), Phoenix, AZ, USA, 3–7 October 1999; Volume 1, pp. 448–455. [Google Scholar]
- Peng, F.Z. Application issues of active power filters. IEEE Ind. Appl. Mag.
**1998**, 4, 21–30. [Google Scholar] [CrossRef] - Kim, S.; Enjeti, P.N. A new hybrid active power filter (APF) topology. IEEE Trans. Power Electron.
**2002**, 17, 48–54. [Google Scholar] - Graovac, D.; Katic, V.; Rufer, A. Power Quality Problems Compensation With Universal Power Quality Conditioning System. IEEE Trans. Power Deliv.
**2007**, 22, 968–976. [Google Scholar] [CrossRef] - Routimo, M.; Salo, M.; Tuusa, H. Comparison of Voltage-Source and Current-Source Shunt Active Power Filters. IEEE Trans. Power Electron.
**2007**, 22, 636–643. [Google Scholar] [CrossRef] - Benchaita, L.; Saadate, S.; Salem nia, A. A comparison of voltage source and current source shunt active filter by simulation and experimentation. IEEE Trans. Power Syst.
**1999**, 14, 642–647. [Google Scholar] [CrossRef] - Ghadbane, I.; Benchouia, T.; Tahar, G. Comparative study of backstepping and Proportional Integral Controller to Compensating Current Harmonics. In Proceedings of the International Conference on Systems and Processing Information, Guelma, Algeria, 12–14 May 2013. [Google Scholar]
- Zelloma, L.; Rabhi, B.; Saad, S.; Benaissa, A.; Benkhoris, M.F. Fuzzy logic controller of five levels active power filter. Energy Procedia
**2015**, 74, 1015–1025. [Google Scholar] [CrossRef] - Abdusalam, M.; Poure, P.; Saadate, S. Control of hybrid active filter without phase locked loop in the feedback et feedforward loops. In Proceedings of the ISIE, IEEE International Symposium on Industrial Electronics, Cambridge, UK, 30 June–2 July 2008. [Google Scholar]
- El-Habrouk, M.; Darwish, M.K.; Mehta, P. Active power filters: A review. IEE Proc. Electr. Power Appl.
**2000**, 147, 403. [Google Scholar] [CrossRef] - Akagi, H. Control strategy and site selection of a shunt active filter for damping of harmonic propagation in power distribution systems. IEEE Trans. Power Deliv.
**1997**, 12, 354–363. [Google Scholar] [CrossRef] [Green Version] - Marques, G.D. A comparison of active power filter control methods in unbalanced and non-sinusoidal conditions. In Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (Cat.No.98CH36200), IECON ’98, Aachen, Germany, 31 August–4 September 1998. [Google Scholar]
- Sahnouni, K.; Godfroid, H.; Berthon, A. An optimised variable structure control of a shunt active filter. In Proceedings of the IEEE International Electric Machines and Drives Conference: IEMDC’99. Proceedings (Cat. No.99EX272), Seattle, WA, USA, 9–12 May 1999; pp. 682–684. [Google Scholar]
- Jasim, W.; Gu, D. Integral backstepping controller for quadrotor path tracking. In Proceedings of the 2015 International Conference on Advanced Robotics (ICAR), Istanbul, Turkey, 27–31 July 2015; pp. 593–598. [Google Scholar]
- Ouchatti, A.; Abbou, A.; Akherraz, M.; Taouni, A. Induction motor controller using fuzzy MRAS and backstepping approach. Int. Rev. Electr. Eng.
**2014**, 9, 511–518. [Google Scholar] - Hou, S.; Fei, J. Adaptive fuzzy backstepping control of three-phase active power filter. Control Eng. Pract.
**2015**, 45, 12–21. [Google Scholar] [CrossRef] - Benchouia, M.T.; Ghadbane, I.; Golea, A.; Srairi, K.; Benbouzid, M.E.H. Implementation of Adaptive Fuzzy Logic and PI Controllers to Regulate the DC Bus Voltage of Shunt Active Power Filter. Appl. Soft Comput.
**2015**, 28, 125–131. [Google Scholar] [CrossRef] - Ait Chihab, A.; Ouadi, H.; Giri, F.; El Majdoub, K. Adaptive Backstepping Control of Three-Phase Four-Wire Shunt Active Power Filters for Energy Quality improvement. J. Control Autom. Electr. Syst.
**2016**, 27, 144–156. [Google Scholar] [CrossRef] - Campanhol, L.B.G.; da Silva, S.A.; Goedtel, A. Application of Shunt Active Power Filter for Harmonic Reduction and Reactive Power Compensation in Three-Phase Four-Wire Systems. IET Power Electron.
**2014**, 7, 2825–2836. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Daou, N.; Montoya, F.G.; Ababssi, N.; Djeghader, Y.
A Hybrid Active Filter Using the Backstepping Controller for Harmonic Current Compensation. *Symmetry* **2019**, *11*, 1161.
https://doi.org/10.3390/sym11091161

**AMA Style**

Daou N, Montoya FG, Ababssi N, Djeghader Y.
A Hybrid Active Filter Using the Backstepping Controller for Harmonic Current Compensation. *Symmetry*. 2019; 11(9):1161.
https://doi.org/10.3390/sym11091161

**Chicago/Turabian Style**

Daou, Nora, Francisco G. Montoya, Najib Ababssi, and Yacine Djeghader.
2019. "A Hybrid Active Filter Using the Backstepping Controller for Harmonic Current Compensation" *Symmetry* 11, no. 9: 1161.
https://doi.org/10.3390/sym11091161