# MPPT Improvement for PMSG-Based Wind Turbines Using Extended Kalman Filter and Fuzzy Control System

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- Improving the accuracy of the wind turbine MPPT implementation.
- Increasing the efficiency of the PMSG output power by estimating the generator speed.
- Estimating the unpredictable parameters by employing EKF in PMSG-based wind turbines to the best knowledge of the authors.

## 2. Proposed Method

- The PMSG-based wind turbine is directly driven, which makes it easily controllable.
- This VSWT has a slow rotation speed.
- It has high torque density and very low inertia, which makes it highly efficient.
- This type of VSWTs can be used without the gearbox.

#### 2.1. System Description

#### 2.1.1. SSC Control

_{ds}at zero to achieve a unity power factor. The second one consists of two cascade loops, in which an outer loop is used to maximize power by setting the reference current i

_{qs}for the inner current loop [31].

_{ds}and u

_{qs}. It performs this task through the sinusoidal pulse with modulation (PWM). The PMSG is modeled using Equations (1) and (2), based on stator current and voltages as follows [32]:

_{m}is core magnetic flux and, ${\omega}_{e}$ illustrates the rotor angular speed. Also, R

_{s}and L

_{s}show the stator resistance and inductance, respectively. The controller output voltage signals are obtained through the new variables ${u}_{sd}^{\prime}$ and ${u}_{sq}^{\prime}$ [31]:

_{dc}shows the DC-link voltage. Based on Equations (3) and (4), the following transfer function can be extracted for both ${i}_{ds}$ and ${i}_{qs}$:

#### 2.1.2. GSC Control

_{dg}. Also, the reactive power can be controlled at zero in order to achieve the unity power factor. The grid voltage components are as in Equations (8) and (9) [31].

#### 2.2. Parameter Estimation

_{1}is F

_{1}and x

_{2}is F

_{2}, THEN y is R(i);

_{1}, x

_{2}, and y are input1 variable, input2 variable, and control variable, respectively. F

_{1}and F

_{2}illustrate the fuzzy sets of input1 and input2, and R(i) shows the fuzzy set of the control variable. The control rules are designed to assign a fuzzy set of the control input y for each combination of fuzzy sets of x

_{1}and x

_{2}. Table 1 shows the rules for the FLC.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Yamakawa, C.K.; Qin, F.; Mussatto, S.I. Advances and opportunities in biomass conversion technologies and biorefineries for the development of a bio-based economy. Biomass Bioenergy
**2018**, 119, 54–60. [Google Scholar] [CrossRef] - Honarbari, S.; Bidgoli, M.A. Designing a Quasi-Z-Source Inverter with Energy Storage to Improve Grid Power Quality. IETE J. Res.
**2020**, 1–9. [Google Scholar] [CrossRef] - Zaboli, M.; Ajarostaghi, S.S.M.; Saedodin, S.; Pour, M.S. Thermal Performance Enhancement Using Absorber Tube with Inner Helical Axial Fins in a Parabolic Trough Solar Collector. Appl. Sci.
**2021**, 11, 7423. [Google Scholar] [CrossRef] - Olfian, H.; Ajarostaghi, S.S.M.; Ebrahimnataj, M. Development on evacuated tube solar collectors: A review of the last decade results of using nanofluids. Sol. Energy
**2020**, 211, 265–282. [Google Scholar] [CrossRef] - Roy, S.; Saha, U.K. Review on the numerical investigations into the design and development of Savonius wind rotors. Renew. Sustain. Energy Rev.
**2013**, 24, 73–83. [Google Scholar] [CrossRef] - Javadi, H.; Urchueguia, J.F.; Ajarostaghi, S.S.M.; Badenes, B. Numerical Study on the Thermal Performance of a Single U-Tube Borehole Heat Exchanger Using Nano-Enhanced Phase Change Materials. Energies
**2020**, 13, 5156. [Google Scholar] [CrossRef] - Javadi, H.; Urchueguia, J.; Ajarostaghi, S.M.; Badenes, B. Impact of Employing Hybrid Nanofluids as Heat Carrier Fluid on the Thermal Performance of a Borehole Heat Exchanger. Energies
**2021**, 14, 2892. [Google Scholar] [CrossRef] - Alamian, R.; Shafaghat, R.; Amiri, H.A.; Shadloo, M.S. Experimental assessment of a 100 W prototype horizontal axis tidal turbine by towing tank tests. Renew. Energy
**2020**, 155, 172–180. [Google Scholar] [CrossRef] - Bilandzija, N.; Voca, N.; Jelcic, B.; Jurisic, V.; Matin, A.; Grubor, M.; Kricka, T. Evaluation of Croatian agricultural solid biomass energy potential. Renew. Sustain. Energy Rev.
**2018**, 93, 225–230. [Google Scholar] [CrossRef] - Ezoji, H.; Shafaghat, R.; Jahanian, O. Numerical simulation of dimethyl ether/natural gas blend fuel HCCI combustion to investigate the effects of operational parameters on combustion and emissions. J. Therm. Anal. Calorim.
**2018**, 135, 1775–1785. [Google Scholar] [CrossRef] - Ezoji, H.; Ajarostaghi, S.S.M. Thermodynamic-CFD analysis of waste heat recovery from homogeneous charge compression ignition (HCCI) engine by Recuperative organic Rankine Cycle (RORC): Effect of operational parameters. Energy
**2020**, 205, 117989. [Google Scholar] [CrossRef] - Wang, C.; Wang, L.; Shi, L.; Ni, Y. A Survey on Wind Power Technologies in Power Systems. In Proceedings of the 2007 IEEE Power Engineering Society General Meeting, Tampa, FL, USA, 24–28 June 2007; pp. 1–6. [Google Scholar]
- Lan, J.; Patton, R.J.; Zhu, X. Fault-tolerant wind turbine pitch control using adaptive sliding mode estimation. Renew. Energy
**2018**, 116, 219–231. [Google Scholar] [CrossRef] - Gao, R.; Gao, Z. Pitch control for wind turbine systems using optimization, estimation and compensation. Renew. Energy
**2016**, 91, 501–515. [Google Scholar] [CrossRef] - Wang, C.-N.; Lin, W.-C.; Le, X.-K. Modelling of a PMSG Wind Turbine with Autonomous Control. Math. Probl. Eng.
**2014**, 2014, 85617. [Google Scholar] [CrossRef] - Geng, H.; Yang, G. Output Power Control for Variable-Speed Variable-Pitch Wind Generation Systems. IEEE Trans. Energy Convers.
**2010**, 25, 494–503. [Google Scholar] [CrossRef] - Bianchi, F.; Mantz, R.; Christiansen, C. Gain scheduling control of variable-speed wind energy conversion systems using quasi-LPV models. Control Eng. Pract.
**2005**, 13, 247–255. [Google Scholar] [CrossRef] - Stol, K.A.; Balas, M.J. Periodic Disturbance Accommodating Control for Blade Load Mitigation in Wind Turbines. J. Sol. Energy Eng.
**2003**, 125, 379–385. [Google Scholar] [CrossRef] - Mohamed, A.Z.; Eskander, M.N.; Ghali, F.A. Fuzzy logic control based maximum power tracking of a wind energy system. Renew. Energy
**2001**, 23, 235–245. [Google Scholar] [CrossRef] - Shi, F.; Patton, R. An active fault tolerant control approach to an offshore wind turbine model. Renew. Energy
**2015**, 75, 788–798. [Google Scholar] [CrossRef] - Najafi-Shad, S.; Barakati, S.M.; Yazdani, A. An effective hybrid wind-photovoltaic system including battery energy storage with reducing control loops and omitting PV converter. J. Energy Storage
**2020**, 27, 101088. [Google Scholar] [CrossRef] - Gliga, L.I.; Chafouk, H.; Popescu, D.; Lupu, C. Diagnosis of a Permanent Magnet Synchronous Generator using the Extended Kalman Filter and the Fast Fourier Transform. In Proceedings of the 2018 7th International Conference on Systems and Control (ICSC), Valencia, Spain, 24–26 October 2018; pp. 65–70. [Google Scholar]
- Afrasiabi, S.; Afrasiabi, M.; Rastegar, M.; Mohammadi, M.; Parang, B.; Ferdowsi, F. Ensemble Kalman Filter based Dynamic State Estimation of PMSG-based Wind Turbine. In Proceedings of the 2019 IEEE Texas Power and Energy Conference (TPEC), College Station, TX, USA, 7–8 February 2019; pp. 1–4. [Google Scholar]
- Zhang, Z.; Wang, F.; Si, G.; Kennel, R. Predictive encoderless control of back-to-back converter PMSG wind turbine systems with Extended Kalman Filter. In Proceedings of the 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), Auckland, New Zealand, 5–8 December 2016; pp. 1–6. [Google Scholar]
- Zerdali, E.; Yildiz, R.; Inan, R.; Demir, R.; Barut, M. Improved speed and load torque estimations with adaptive fading extended Kalman filter. Int. Trans. Electr. Energy Syst.
**2021**, 31, 12684. [Google Scholar] [CrossRef] - Bagheri, A.; Ojaghi, M.; Bagheri, A. Air-gap eccentricity fault diagnosis and estimation in induction motors using unscented Kalman filter. Int. Trans. Electr. Energy Syst.
**2020**, 30, e12450. [Google Scholar] [CrossRef] - Ortatepe, Z.; Karaarslan, A. Robust predictive sensorless control method for doubly fed induction generator controlled by matrix converter. Int. Trans. Electr. Energy Syst.
**2020**, 30, 12650. [Google Scholar] [CrossRef] - Wu, Y.-T.; Liao, T.-L.; Chen, C.-K.; Lin, C.Y.; Chen, P.-W. Power output efficiency in large wind farms with different hub heights and configurations. Renew. Energy
**2019**, 132, 941–949. [Google Scholar] [CrossRef] - Ribrant, J.; Bertling, L. Survey of failures in wind power systems with focus on Swedish wind power plants during 1997–2005. In Proceedings of the 2007 IEEE Power Engineering Society General Meeting, Tampa, FL, USA, 24–28 June 2007; pp. 1–8. [Google Scholar]
- Odgaard, P.F.; Stoustrup, J.; Kinnaert, M. Fault-Tolerant Control of Wind Turbines: A Benchmark Model. IEEE Trans. Control Syst. Technol.
**2013**, 21, 1168–1182. [Google Scholar] [CrossRef][Green Version] - Shariatpanah, H.; Fadaeinedjad, R.; Rashidinejad, M. A New Model for PMSG-Based Wind Turbine with Yaw Control. IEEE Trans. Energy Convers.
**2013**, 28, 929–937. [Google Scholar] [CrossRef] - Rosyadi, M.; Muyeen, S.M.; Takahashi, R.; Tamura, J. A Design Fuzzy Logic Controller for a Permanent Magnet Wind Generator to Enhance the Dynamic Stability of Wind Farms. Appl. Sci.
**2012**, 2, 780–800. [Google Scholar] [CrossRef][Green Version] - Mehrzad, D.; Luque, J.; Cuenca, M.C. Vector Control of PMSG for Grid-Connected Wind Turbine Applications. Master’s Thesis, Institute of Energy Technology, Alborg University, Aalborg, Denmark, 2009. [Google Scholar]
- Gao, D.W. Energy Storage for Sustainable Microgrid; Academic Press: Cambridge, MA, USA, 2015. [Google Scholar]
- Wan, E.A.; van der Merwe, R.; Nelson, A.T. Advances in Neural Information Processing Systems 12, Ch. Dual Estimation and the Unscented Transformation; MIT Press: Cambridge, MA, USA, 2000; pp. 666–672. [Google Scholar]

**Figure 13.**Comparison between the generator speed in the proposed system and the conventional method.

y | x_{1} | |||||||
---|---|---|---|---|---|---|---|---|

NB | NM | NS | Z | PS | PM | PB | ||

x_{2} | NB | NB | NB | NM | NM | NS | NS | Z |

NM | NB | NM | NM | NS | NS | Z | PS | |

NS | NM | NM | NS | NS | Z | PS | PS | |

Z | NM | NS | NS | Z | PS | PS | PM | |

PS | NS | NS | Z | PS | PS | PM | PM | |

PM | NS | Z | PS | PS | PM | PM | PB | |

PB | Z | PS | PS | PM | PM | PB | PB |

Fuzzy Sets Labels | Fuzzy Sets |
---|---|

NB | Negative Big |

NM | Negative Medium |

NS | Negative Small |

ZR | Zero |

PS | Positive Small |

PM | Positive Medium |

PB | Positive Big |

**Table 3.**Membership function, fuzzy set labels, and fuzzy numbers representation for Figure 5.

Membership Function Type | Fuzzy Sets Labels | Fuzzy Numbers |
---|---|---|

zmf | NB | [−3k_{1}, −k_{1}] |

trimf | NM | [−3k_{1}, −2k_{1}, 0] |

trimf | NS | [−3k_{1}, −k_{1}, k_{1}] |

trimf | Z | [−2k_{1}, 0, 2k_{1}] |

trimf | PS | [−k_{1}, k_{1}, 3k_{1}] |

trimf | PM | [0, 2k_{1}, 3k_{1}] |

zmf | PB | [k_{1}, 3k_{1}] |

**Table 4.**Membership function, fuzzy set labels, and fuzzy numbers representation for Figure 6.

Membership Function Type | Linguistic Variables | Fuzzy Numbers |
---|---|---|

zmf | NB | [−3k_{1}, −k_{1}] |

trimf | NM | [−3k_{1}, −2k_{1}, 0] |

trimf | NS | [−3k_{1}, −k_{1}, k_{1}] |

trimf | Z | [−2k_{1}, 0, 2k_{1}] |

trimf | PS | [−k_{1}, k_{1}, 3k_{1}] |

trimf | PM | [0, 2k_{1}, 3k_{1}] |

zmf | PB | [k_{1}, 3k_{1}] |

**Table 5.**Membership function, fuzzy set labels, and fuzzy numbers representation for Figure 7.

Membership Function Type | Linguistic Variables | Fuzzy Numbers |
---|---|---|

zmf | NB | [−3k_{3}, −k_{3}] |

trimf | NM | [−3k_{3}, −2k_{3}, 0] |

trimf | NS | [−3k_{3}, −k_{3}, k_{3}] |

trimf | Z | [−2k_{3}, 0, 2k_{3}] |

trimf | PS | [−k_{3}, k_{3}, 3k_{3}] |

trimf | PM | [0, 2k_{3}, 3k_{3}] |

zmf | PB | [k_{3}, 3k_{3}] |

Parameters | Value |
---|---|

Turbine Nominal Power | 900 kW |

Nominal Voltage | 20 kV |

Nominal Frequency | 60 Hz |

Number of Pole Pairs (P) | 4 |

Stator Resistance (R_{s}) | 25 mΩ |

Stator Inductance (L_{s}) | 5 mH |

DC-link Capacitance (C) | 2.5 mf |

GSC Resistance (R_{g}) | 15 m Ω |

GSC Inductance (L_{g}) | 0.2 mH |

Switching Frequency | 1590 Hz |

Wind Speed | 5 to 16 m/s |

SSC Controller (PI_{1}) | $\frac{5\text{}\mathrm{s}+25}{\mathrm{s}}$ |

GSC Current Controller (PI_{2}) | $\frac{0.2\text{}\mathrm{s}+15}{\mathrm{s}}$ |

GSC Voltage Controller (PI_{3}) | $\frac{0.62\text{}\mathrm{s}+0.01}{\mathrm{s}}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Honarbari, A.; Najafi-Shad, S.; Saffari Pour, M.; Ajarostaghi, S.S.M.; Hassannia, A. MPPT Improvement for PMSG-Based Wind Turbines Using Extended Kalman Filter and Fuzzy Control System. *Energies* **2021**, *14*, 7503.
https://doi.org/10.3390/en14227503

**AMA Style**

Honarbari A, Najafi-Shad S, Saffari Pour M, Ajarostaghi SSM, Hassannia A. MPPT Improvement for PMSG-Based Wind Turbines Using Extended Kalman Filter and Fuzzy Control System. *Energies*. 2021; 14(22):7503.
https://doi.org/10.3390/en14227503

**Chicago/Turabian Style**

Honarbari, Amirsoheil, Sajad Najafi-Shad, Mohsen Saffari Pour, Seyed Soheil Mousavi Ajarostaghi, and Ali Hassannia. 2021. "MPPT Improvement for PMSG-Based Wind Turbines Using Extended Kalman Filter and Fuzzy Control System" *Energies* 14, no. 22: 7503.
https://doi.org/10.3390/en14227503