Robust Adaptive Super Twisting Algorithm Sliding Mode Control of a Wind System Based on the PMSG Generator
Abstract
:1. Introduction
- Permanent magnet poles provide a high energy density.
- High efficiency, reliability.
- Self-excitation characteristics.
- Lightweight and simplicity of reactive power management.
2. Literature Review
3. The Paper Contribution
4. Problem Formulation
5. Wind Energy Conversion System Modeling
5.1. Wind Turbine Model
5.2. PMSG Modeling
5.3. DC-Link Modeling
5.4. GSC Modeling
6. Sliding Mode Control
- 𝜆 is a positive coefficient.
- n is the order of the system.
- is the error in the output state with:
- , the equivalent command, is calculated based on the system behavior S(x) = 0 to precise linearization of the system.
- is utilized to verify the convergence condition of Lyapunov with , where:
6.1. State-of-the-Art SMC Implementation for PMSG Control
6.2. Higher Order Sliding Mode Control
6.3. Sliding Mode Control Using the Super-Twisting Method (ST-SMC)
6.4. Application of the AST to the PMSG
- Generator rotation speed regulation
6.5. Regulation of Stator Currents
6.6. Adaptive Super Twisting Algorithm (AST)
7. Results and Discussion
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Li, X.; Zhou, Y.; Yu, S.; Jia, G.; Li, H.; Li, W. Urban heat island impacts on building energy consumption: A review of approaches and findings. Energy 2019, 174, 407–419. [Google Scholar] [CrossRef]
- Elavarasan, R.M.; Shafiullah, G.; Padmanaban, S.; Kumar, N.M.; Annam, A.; Vetrichelvan, A.M.; Mihet-Popa, L.; Holm-Nielsen, J.B. A Comprehensive Review on Renewable Energy Development, Challenges and Policies of leading Indian States with an International Perspective. IEEE Access 2020, 8, 74432–74457. [Google Scholar] [CrossRef]
- Thellufsen, J.Z.; Lund, H.; Sorknæs, P.; Østergaard, P.A.; Chang, M.; Drysdale, D.; Nielsen, S.; Djørup, S.R.; Sperling, K. Smart energy cities in a 100% renewable energy context. Renew. Sustain. Energy Rev. 2020, 129, 109922. [Google Scholar] [CrossRef]
- Antonopoulos, I.; Robu, V.; Couraud, B.; Kirli, D.; Norbu, S.; Kiprakis, A.; Flynn, D.; Elizondo-Gonzalez, S.; Wattam, S. Artificial intelligence and machine learning approaches to energy demand-side response: A systematic review. Renew. Sustain. Energy Rev. 2020, 130, 109899. [Google Scholar] [CrossRef]
- Lange, S.; Pohl, J.; Santarius, T. Digitalization and energy consumption. Does ICT reduce energy demand? Ecol. Econ. 2020, 176, 106760. [Google Scholar] [CrossRef]
- Bossoufi, B.; Karim, M.; Taoussi, M.; Aroussi, H.A.; Bouderbala, M.; Deblecker, O.; Motahhir, S.; Nayyar, A.; Alzain, M.A. Rooted Tree Optimization for the Backstepping Power Control of a Doubly Fed Induction Generator Wind Turbine: dSPACE Implementation. IEEE Access 2021, 9, 26512–26522. [Google Scholar] [CrossRef]
- Sanguesa, J.A.; Torres-Sanz, V.; Garrido, P.; Martinez, F.J.; Marquez-Barja, J.M. A Review on Electric Vehicles: Technologies and Challenges. Smart Cities 2021, 4, 372–404. [Google Scholar] [CrossRef]
- Goel, S.; Sharma, R.; Rathore, A.K. A review on barrier and challenges of electric vehicle in India and vehicle to grid optimisation. Transp. Eng. 2021, 4, 100057. [Google Scholar] [CrossRef]
- Chege, S.M.; Wang, D.; Suntu, S.L. Impact of information technology innovation on firm performance in Kenya. Inf. Technol. Dev. 2019, 26, 316–345. [Google Scholar] [CrossRef]
- Lowitzsch, J.; Hoicka, C.E.; van Tulder, F.J. Renewable energy communities under the 2019 European Clean Energy Package—Governance model for the energy clusters of the future? Renew. Sustain. Energy Rev. 2020, 122, 109489. [Google Scholar] [CrossRef]
- Baradei, S.E.; Sadeq, M.A. Effect of solar canals on evaporation, water quality, and power production: An optimization study. Water 2020, 12, 2103. [Google Scholar] [CrossRef]
- Ahmed, S.D.; Al-Ismail, F.S.M.; Shafiullah; Al-Sulaiman, F.A.; El-Amin, I.M. Grid Integration Challenges of Wind Energy: A Review. IEEE Access 2020, 8, 10857–10878. [Google Scholar] [CrossRef]
- Elsisi, M.; Tran, M.-Q.; Mahmoud, K.; Lehtonen, M.; Darwish, M.M.F. Robust Design of ANFIS-Based Blade Pitch Controller for Wind Energy Conversion Systems Against Wind Speed Fluctuations. IEEE Access 2021, 9, 37894–37904. [Google Scholar] [CrossRef]
- Touati, Z.; Pereira, M.; Araújo, R.E.; Khedher, A. Integration of Switched Reluctance Generator in a Wind Energy Conversion System: An Overview of the State of the Art and Challenges. Energies 2022, 15, 4743. [Google Scholar] [CrossRef]
- Laabidine, N.Z.; El Bakkali, C.; Mohammed, K.; Bossoufi, B. Flow-Oriented Control Design of Wind Power Generation System Based on Permanent Magnet Synchronous Generator. In Proceedings of the ICDTA 2021, Fez, Morocco, 29–30 January 2021. [Google Scholar]
- Majout, B.; El Alami, H.; Salime, H.; Laabidine, N.Z.; El Mourabit, Y.; Motahhir, S.; Bouderbala, M.; Karim, M.; Bossoufi, B. A Review on Popular Control Applications in Wind Energy Conversion System Based on Permanent Magnet Generator PMSG. Energies 2022, 15, 6238. [Google Scholar] [CrossRef]
- Guo, G.; Song, Q.; Zhao, B.; Rao, H.; Xu, S.; Zhu, Z.; Liu, W. Series-connected-based Offshore Wind Farms with Full-bridge Modular Multilevel Converter as Gridand Generator-side Converters. IEEE Trans. Ind. Electron. 2019, 67, 2798–2809. [Google Scholar] [CrossRef]
- Xie, C.; Li, K.; Zou, J.; Liu, D.; Guerrero, J.M. Passivity-Based Design of Grid-Side Current-Controlled $LCL$-Type Grid-Connected Inverters. IEEE Trans. Power Electron. 2020, 35, 9813–9823. [Google Scholar] [CrossRef]
- Liu, L.; Liu, Y.-J.; Chen, A.; Tong, S.; Chen, C.L.P. Integral Barrier Lyapunov function-based adaptive control for switched nonlinear systems. Sci. China Inf. Sci. 2020, 63, 132203. [Google Scholar] [CrossRef] [Green Version]
- Liu, Z.; Han, Z.; Zhao, Z.; He, W. Modeling and adaptive control for a spatial flexible spacecraft with unknown actuator failures. Sci. China Inf. Sci. 2021, 64, 152208. [Google Scholar] [CrossRef]
- Qian, Z.; Pei, Y.; Zareipour, H.; Chen, N. A review and discussion of decomposition-based hybrid models for wind energy forecasting applications. Appl. Energy 2018, 235, 939–953. [Google Scholar] [CrossRef]
- Sarmiento, J.; Iturrioz, A.; Ayllón, V.; Guanche, R.; Losada, I. Experimental modelling of a multi-use floating platform for wave and wind energy harvesting. Ocean Eng. 2019, 173, 761–773. [Google Scholar] [CrossRef]
- Laabidine, N.Z.; Errarhout, A.; El Bakkali, C.; Mohammed, K.; Bossoufi, B. Sliding mode control design of wind power generation system based on permanent magnet synchronous generator. Int. J. Power Electron. Drive Syst. (IJPEDS) 2021, 12, 393–403. [Google Scholar] [CrossRef]
- Cui, L.; Zhang, R.; Yang, H.; Zuo, Z. Adaptive super-twisting trajectory tracking control for an unmanned aerial vehicle under gust winds. Aerosp. Sci. Technol. 2021, 115, 106833. [Google Scholar] [CrossRef]
- Ozer, H.O.; Hacioglu, Y.; Yagiz, N. High order sliding mode control with estimation for vehicle active suspensions. Trans. Inst. Meas. Control 2017, 40, 1457–1470. [Google Scholar] [CrossRef]
- Chen, J.; Yao, W.; Zhang, C.-K.; Ren, Y.; Jiang, L. Design of robust MPPT controller for grid-connected PMSG-Based wind turbine via perturbation observation based nonlinear adaptive control. Renew. Energy 2018, 134, 478–495. [Google Scholar] [CrossRef]
- Lara, M.; Garrido, J.; Ruz, M.L.; Vázquez, F. Adaptive Pitch Controller of a Large-Scale Wind Turbine Using Multi-Objective Optimization. Appl. Sci. 2021, 11, 2844. [Google Scholar] [CrossRef]
- El Ouanjli, N.; Derouich, A.; El Ghzizal, A.; Bouchnaif, J.; EL Mourabit, Y.; Taoussi, M.; Bossoufi, B. Real-time implementation in dSPACE of DTC-backstepping for a doubly fed induction motor. Eur. Phys. J. Plus 2019, 134, 566. [Google Scholar] [CrossRef]
- Babaghorbani, B.; Beheshti, M.T.; Talebi, H.A. A Lyapunov-based model predictive control strategy in a permanent magnet synchronous generator wind turbine. Int. J. Electr. Power Energy Syst. 2021, 130, 106972. [Google Scholar] [CrossRef]
- Ayyarao, T.S. Modified vector controlled DFIG wind energy system based on barrier function adaptive sliding mode control. Prot. Control Mod. Power Syst. 2019, 4, 4. [Google Scholar] [CrossRef] [Green Version]
- Naik, K.A.; Gupta, C.P.; Fernandez, E. Design and implementation of interval type-2 fuzzy logic-PI based adaptive controller for DFIG based wind energy system. Int. J. Electr. Power Energy Syst. 2020, 115, 105468. [Google Scholar] [CrossRef]
- Mosaad, M.I.; Abu-Siada, A.; Elnaggar, M. Application of Superconductors to Improve the Performance of DFIG-based WECS. IEEE Access 2019, 7, 103760–103769. [Google Scholar] [CrossRef]
- Chavero-Navarrete, E.; Trejo-Perea, M.; Jáuregui-Correa, J.C.; Carrillo-Serrano, R.V.; Ríos-Moreno, J.G. Expert Control Systems for Maximum Power Point Tracking in a Wind Turbine with PMSG: State of the Art. Appl. Sci. 2019, 9, 2469. [Google Scholar] [CrossRef] [Green Version]
- Gui, Y.; Blaabjerg, F.; Wang, X.; Bendtsen, J.; Yang, D.; Stoustrup, J. Improved DC-Link Voltage Regulation Strategy for Grid-Connected Converters. IEEE Trans. Ind. Electron. 2020, 68, 4977–4987. [Google Scholar] [CrossRef]
- Aschemann, H.; Haus, B.; Mercorelli, P. Second-Order SMC with Disturbance Compensation for Robust Tracking Control in PMSM Applications. IFAC-PapersOnLine 2020, 53, 6225–6231. [Google Scholar] [CrossRef]
- Rajendiran, S.; Lakshmi, P. Performance Analysis of Fractional Order Terminal SMC for the Half Car Model with Random Road Input. J. Vib. Eng. Technol. 2019, 8, 587–597. [Google Scholar] [CrossRef]
- Chojaa, H.; Derouich, A.; Chehaidia, S.E.; Zamzoum, O.; Taoussi, M.; Elouatouat, H. Integral sliding mode control for DFIG based WECS with MPPT based on artificial neural network under a real wind profile. Energy Rep. 2021, 7, 4809–4824. [Google Scholar] [CrossRef]
- Sun, X.; Cao, J.; Lei, G.; Guo, Y.; Zhu, J. A Robust Deadbeat Predictive Controller with Delay Compensation Based on Composite Sliding-Mode Observer for PMSMs. IEEE Trans. Power Electron. 2021, 36, 10742–10752. [Google Scholar] [CrossRef]
- Chen, X.; Li, Y.; Ma, H.; Tang, H.; Xie, Y. A Novel Variable Exponential Discrete Time Sliding Mode Reaching Law. IEEE Trans. Circuits Syst. II Express Briefs 2021, 68, 2518–2522. [Google Scholar] [CrossRef]
- Charfeddine, S.; Boudjemline, A.; Ben Aoun, S.; Jerbi, H.; Kchaou, M.; Alshammari, O.; Elleuch, Z.; Abbassi, R. Design of a Fuzzy Optimization Control Structure for Nonlinear Systems: A Disturbance-Rejection Method. Appl. Sci. 2021, 11, 2612. [Google Scholar] [CrossRef]
- Ali, N.; Ur Rehman, A.; Alam, W.; Maqsood, H. Disturbance Observer Based Robust Sliding Mode Control of Permanent Magnet Synchronous Motor. J. Electr. Eng. Technol. 2019, 14, 2531–2538. [Google Scholar] [CrossRef]
- Lochan, K.; Roy, B.K.; Subudhi, B. Chaotic tip trajectory tracking and deflection suppression of a two-link flexible manipulator using second-order fast terminal SMC. Trans. Inst. Meas. Control 2019, 41, 3292–3308. [Google Scholar] [CrossRef]
- Ouchen, S.; Benbouzid, M.; Blaabjerg, F.; Betka, A.; Steinhart, H. Direct Power Control of Shunt Active Power Filter using Space Vector Modulation based on Super Twisting Sliding Mode Control. IEEE J. Emerg. Sel. Top. Power Electron. 2020, 9, 3243–3253. [Google Scholar] [CrossRef]
- Singh, P.P.; Roy, B.K. Inter network synchronisation of complex dynamical networks by using smooth proportional integral SMC technique. Eur. Phys. J. Spec. Top. 2020, 229, 861–876. [Google Scholar] [CrossRef]
- Ding, S.; Park, J.H.; Chen, C.-C. Second-order sliding mode controller design with output constraint. Automatica 2019, 112, 108704. [Google Scholar] [CrossRef]
- Hong, C.-M.; Chen, C.-H.; Tu, C.-S. Maximum power point tracking-based control algorithm for PMSG wind generation system without mechanical sensors. Energy Convers. Manag. 2013, 69, 58–67. [Google Scholar] [CrossRef]
- Bounar, N.; Labdai, S.; Boulkroune, A. PSO-GSA based fuzzy sliding mode controller for DFIG-based wind turbine. ISA Trans. 2018, 85, 177–188. [Google Scholar] [CrossRef]
- Rhaili, S.E.; Abbou, A.; Hichami, N.E.; Marhraoui, S.; Chojaa, H. Mawimum power extraction of five-phase PMSG WECS by adopting and improved fractional order sliding mode strategy. Jilin DaxueXuebao 2021, 55–74. [Google Scholar]
- Yin, X.-X.; Lin, Y.-G.; Li, W.; Gu, Y.-J.; Liu, H.-W.; Lei, P.-F. A novel fuzzy integral sliding mode current control strategy for maximizing wind power extraction and eliminating voltage harmonics. Energy 2015, 85, 677–686. [Google Scholar] [CrossRef]
- Meghni, B.; Dib, D.; Azar, A.T. A second-order sliding mode and fuzzy logic control to optimal energy management in wind turbine with battery storage. Neural Comput. Appl. 2017, 28, 1417–1434. [Google Scholar] [CrossRef]
- Manzanilla, A.; Ibarra, E.; Salazar, S.; Zamora, Á.E.; Lozano, R.; Muñoz, F. Super-twisting integral sliding mode control for trajectory tracking of an Unmanned Underwater Vehicle. Ocean. Eng. 2021, 234, 109164. [Google Scholar] [CrossRef]
- Saadatmand, M.; Gharehpetian, G.B.; Siano, P.; Alhelou, H.H. PMU-based FOPID controller of large-scale wind-PV farms for LFO damping in smart grid. IEEE Access. 2021, 9, 94953–94969. [Google Scholar] [CrossRef]
Acronym | Version with More Information |
---|---|
PMSG | Permanent Magnet Synchronous Generator |
WECS | Wind Energy Conversion System |
SMC | Sliding Mode Control |
AST | Adaptive Super Twisting |
MSC | Machine-Side Converter |
GSC | Grid-Side Converter |
HOSMC | Higher Order Sliding Mode Control |
MPPT | Maximum Power Point Tracking |
Symbol | Parameter | Value |
---|---|---|
Pole pairs | 75 | |
Nominal stator resistance | 6.25 × 10−3 Ω | |
d axis inductance | 4.229 × 10−3 H | |
Lsq | q axis inductance | 4.229 × 10−3 H |
J | Mechanical inertia moment | 10,000 N·m |
R | Rotor radius | 55 m |
Air density | 1.25 kg/ | |
The rotor angular speed | rad/s | |
Rated power | 1.5 kw | |
C | DC-link nominal voltage | V |
Generator flux | 11.1464 Wb | |
Λopt | Tip-speed ratio | 8 |
Methods | Researchers | |
---|---|---|
Higher order-SMC | Ozer, H. O., Hacioglu, Y., & Yagiz, N. (2017) [26] | |
Second order-SMC | Aschemann, H., Haus, B., & Mercorelli [36] | |
Terminal-SMC | Rajendiran, S., & Lakshmi, [37] Lochan, K., Roy, B. K., & Subudhi, B. [43] | |
Integral-SMC | Singh, P. P., & Roy, B. K. [45] | |
Sliding Mode Control | Backstepping-SMC | Majout, B., El Alami, H., Salime, H., Zine Laabidine, N. [17] |
Direct power control-SMC | Ouchen, S., Benbouzid, M., Blaabjerg, F., Betka, A., & Steinhart, H. [44] | |
Fuzzy logic-SMC | Charfeddine, S.; Boudjemline, A.; Ben Aoun, S.; Jerbi, H.; Kchaou, M.; Alshammari, O.; Elleuch, Z.; Abbassi, [41] | |
Artificial neural network-SMC | Hamid Chojaa, Aziz Derouich, Seif Eddine Chehaidia, Othmane Zamzoum, Mohammed Taoussi, Hasnae Elouatouat [38] | |
Observer-SMC | Ali, N., Ur Rehman, A., Alam, W., & Maqsood, H. [42] | |
Predictive sliding mode | Sun, X., Cao, J., Lei, G., Guo, Y., & Zhu, J. [39] | |
Reaching Law-SMC | Chen, X., Li, Y., Ma, H., Tang, H., & Xie, Y. [40] |
Parameter | Value | Parameter | Value | Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|---|---|---|---|
50 × 105 | 0.15 | 50 | 80 | 1 | |||||
60 × 105 | 0.15 | 66 | 98 | 1 | |||||
58 × 105 | 0.15 | 62 | 100 | 1 |
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Zine Laabidine, N.; Bossoufi, B.; El Kafazi, I.; El Bekkali, C.; El Ouanjli, N. Robust Adaptive Super Twisting Algorithm Sliding Mode Control of a Wind System Based on the PMSG Generator. Sustainability 2023, 15, 10792. https://doi.org/10.3390/su151410792
Zine Laabidine N, Bossoufi B, El Kafazi I, El Bekkali C, El Ouanjli N. Robust Adaptive Super Twisting Algorithm Sliding Mode Control of a Wind System Based on the PMSG Generator. Sustainability. 2023; 15(14):10792. https://doi.org/10.3390/su151410792
Chicago/Turabian StyleZine Laabidine, Nada, Badre Bossoufi, Ismail El Kafazi, Chakib El Bekkali, and Najib El Ouanjli. 2023. "Robust Adaptive Super Twisting Algorithm Sliding Mode Control of a Wind System Based on the PMSG Generator" Sustainability 15, no. 14: 10792. https://doi.org/10.3390/su151410792