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This manuscript presents a new approach MPPT (Maximum Power Point Tracking) for improving and optimizing the performance of a Wind Energy Conversion System (WECS) operating for small variations in wind speed by combining sliding mode control and fuzzy logic control. The proposed method consists of optimizing the sliding mode controller by the fuzzy controller. The main purpose of the Sliding Mode control-Fuzzy Logic controller (SM-FL) is to ensure the robustness (by eliminating certain disadvantages of the sliding mode control such as the phenomenon of chattering) and the stability of the control system in the case of small variations in conditions atmospheric (here variation of the wind). Our system consists of a wind turbine, a Permanent Magnet Synchronous Generator (PMSG) and a DC-DC boost converter connected to a continuous load. The performances of the method suggested are compared with those of fuzzy logic and fuzzy-Proportional Integral (FL-PI) in term speed of convergence, of tracking time and tracking efficiency. The results of numerical simulation of our system confirmed the best performance of this method.

Recently, the production of electrical energy by sources of renewable energy like the wind power increased because of the ecological problems and the increase in the cost of traditional energies and the limitation of their resources [

Various MPPT controllers have been used for Wind Conversion Systems in previous publications such as Sliding Mode controller, thus the performances are reduce by the presence of the phenomenon of chattering [

The objective of this manuscript is to realize a controller combining sliding mode and fuzzy logic in order to improve the maximum operation of a wind generator in areas where wind speeds are low.

The paper is organized as follows: the second section of the manuscript will be dedicated to the description of our study system. A third section is reserved for the SM-FL control strategy. The different simulations performed as well as the discussion of the results found will be the subject of the fourth section. In the fifth section, a conclusion is presented.

In this section, we present wind turbine model, Permanent Magnet Synchronous Generator and boost converter, which makes up the entire Wind Energy Conversion System, will be explained (

The aerodynamic power collected by a wind turbine is written in the following

form [

P a e r o = 1 2 C p ( λ , β ) ρ S V 3 (1)

With:

ρ: Represents the air density (kg/m^{3});

V: wind speed (m/s);

S: the useful surface crossed by the wind given by S = π R 2 ;

R: the radius of the blades;

C p ( λ , β ) : Power coefficient.

The power coefficient C p ( λ , β ) indicates aerodynamic efficiency of wind turbine. It is a function of the speed λ and the blade pitch angle β. It is different from one turbine to another due to its dependence on the characteristic of each. During this work, this coefficient will be modeled by the following analytical expression [

C p ( λ , β ) = 0.5 ( 98 λ i − 0.4 β − 5 ) exp ( − 16 / λ i ) (2)

1 λ i = 1 λ + 0.08 β − 0.035 β 3 + 1 (3)

λ = R ω m V (4)

The aerodynamic torque appearing at the level of the turbine is therefore a function of this power:

Γ a e r o = P a e r o ω m = 1 2 ω m C p ( λ , β ) ρ π R 2 V 3 (5)

where: ω m is the rotor speed of a wind turbine.

For each wind speed, it exists a maximum power of the wind turbine obtained according to the rotor speed (

For applications autonomous of wind energy transformation, the PMSG are used the most considering their reliabilities and robustness. We used the referential d-q

Nominal mechanical output power | 1500 W |
---|---|

Pitch angle | 0^{˚} |

Air density | 0.6125 kg/m^{3} |

Blade radius | 1.125 m |

Wind speed | 6.5 m/s |

transform of park for modeling. The voltage of axis d and q is obtained by the system of Equation (6) [

{ v d s = R s i d s + L d d i d s d t − L q ω r i q s v q s = R s i q s + L q d i q s d t + L d ω r i d s + ω r Ψ r (6)

The Equation (7) gives the electromagnetic torque of PMSG.

г e = 1.5 p [ ( L d − L q ) i q s i d s − Ψ q r i d r − Ψ r i q s ] (7)

with: i d s and i q s the currents of the axis d and q; v d s and v q s the voltages of the axis d and q;

ω r the angular frequency of generator;

L q , and L d are the inductances of the generator;

Ψ r the permanent flux;

R_{s} the stator resistance and p is the pole pairs.

Static converters are very significant for the wind energy transformation at variable speed. In this document, a boost converter is used here (

Rated power | 1500 W |
---|---|

Stator phase resistance | 0.425 Ω |

Machine inertia | 0.085 kg·m^{2} |

Armature inductance | 0.225 H |

Friction factor | 0.00673 N·m/s |

Pole pairs | 5 |

operation of the chopper, the switch is closed with a closing time equal to (D.T), and it is opened in an opening time ((1 − D).T), with: T is the switching period and D the duty cycle of the switch ( D ∈ [ 0 , 1 ] ).

V o u t = V i n 1 − D (8)

where:

V o u t : Output voltage;

V i n : input voltage;

D: duty cycle;

The boost converter parameters are summarized in

In this part, we initially will introduce the sliding mode (SM) controller, in continuation the fuzzy logic (FL) controller, and finally the combination of the two controllers (SM-FL).

The sliding mode control is one of the nonlinear controls effective. The design of this controller is carried out in three essential points: the establishment of the conditions of existence, choice of the sliding surfaces (x), and the determination of the control law [

The maximum power point (MPP) condition is given by [

d P W d V W = 0 (9)

with P_{w}, V_{w}, I_{w} is respectively the power, the voltage, and the current of the wind generator. The switching surface can be chosen as follows [

s ( x , t ) = d P W d V W = I W + V W d I W d V W (10)

Let u be the switching control law defined according to the sign of the sliding surface adopted to increase and decrease the voltage V_{W} according to the position of the operating point with respect to the PPM [

u = { 0 for s ( x ) > 0 1 for s ( x ) < 0 Which can be written too: u = 1 2 ( 1 − sign ( S ) ) (11)

Load | 200 Ω |
---|---|

Inductor | 3.635 mH |

Capacitor | 3.36 mF |

Equation (11) depends on the sign function. The use of this function in the control law makes it possible to force the error to converge asymptotically towards zero. However, this discontinuous function causes the reluctance problem. To remedy this problem in the literature either one applies the boundary layer solution where the sign function is approximated by the hyperbolic tangent function [

The operation of this controller is done in three blocks: fuzzification, inference and defuzzification (

This controller is doing in three blocks: fuzzification, inference and defuzzification (

E = P ( k ) − P ( k − 1 ) I ( k ) − I ( k − 1 ) C E = E ( k ) − E ( k − 1 ) (12)

Linguistic variables are assigned to these quantities: NB (Negative Big), NM (Negative Medium), NS (Negative Small), Z (Zero), PS (Positive Small), PM (Positive Medium) and PB (Positive Big).

In the inference stage, we make decisions (

Finally, in defuzzification, we convert the fuzzy output subsets into a numeric value.

CE E | NB | NM | NS | Z | PS | PM | PB |
---|---|---|---|---|---|---|---|

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

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

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

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

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

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

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

After having realized our two controllers we can now combine them.

In this part, a SM-FL controller is designed in order to overcome the shortcomings of the SM. The SM controller is designed simply on the basis of Equation (10) and in order to have an SM-FL we add to the output of the SM a fuzzy controller and we obtain our structure which is given in

After the text edit has been completed, the paper is ready for the template. Duplicate the In order to test the performance of the SM-FL MPPT controller, we have carried out several cases of simulations following two wind speed profiles of the wind turbine. To verify the theoretical study on the behavior of the MPPT controller, a series of simulations was carried out with the Matlab/Simulink software and a comparison was made with the controllers, fuzzy logic (FL) and fuzzy logic-PI (FL-PI). The gains of the PI controller used are: Kp = 1.852 and Ki = 1.338.

fast response time, higher execution compared with both others during the changing of wind speed. For more details, the tracking efficiency is given in the table below. From these curves, we can see that the SM-FL controller contributed in a more efficient way to extract the maximum power for each wind speed by comparing to the MPPT strategies based on the FL and FL-PI approach. Because it is robust, it converges quickly compared to the compared approaches and it is very simple to achieve. Therefore, we can say that for low to medium wind ranges our controller is performing well.

With the aim of improving the efficiency of wind systems, especially their energy production in areas with low wind speeds; we have developed a smart and simple strategy, based on sliding mode and fuzzy logic. This strategy makes it possible to optimize the power delivered by the wind turbine for both wind speed profiles at all times. So we started with the presentation of the system used. Then we presented the SM and FL controllers. Then, we designed a sliding mode (SM) and fuzzy logic (FL) based controller, the SM-FL controller. The simulation results clearly demonstrate the effectiveness of the strategy adopted. Indeed, the MPPT SM-FL allowed on the one hand the pursuit of the maximum power point according to the weak variations of wind and on the other hand its performance compared to the FL and FL-PI approaches with its rapid convergence and its robustness.

The authors would like to thank the journal editor and all organizations that provided data for this research.

The authors declare no conflicts of interest regarding the publication of this paper.

Malobe, P.A., Djondine, P., Eloundou, P.N. and Ndongo, H.A. (2020) A Novel Hybrid MPPT for Wind Energy Conversion Systems Operating under Low Variations in Wind Speed. Energy and Power Engineering, 12, 716-728. https://doi.org/10.4236/epe.2020.1212042