Intelligent Variable Speed Wind Turbine Controller using the Type-2

Fuzzy Logic based on PID

Khaddouj Ben Meziane

, Faiza Dib

and Ismail Boumhidi

Higher Institute of Engineering and Business (ISGA), Department of Engineering, Fez, Morocco

Department of Physics, Faculty of Sciences and Technology, University of Abdelmalek

Essaadi, Al Hoceima, Morocco

Department of Physics, Faculty of Sciences Dhar el Mahraz, SidiMohammedBenAbdellah

University, Fez, Morocco

Keywords: Wind Turbine System, Robust Control, Interval Type-2 Fuzzy System, Oscillations.

Abstract: An Intelligent and optimal Interval Type-2 Fuzzy Logic (IT2FL) based on Proportional, Integral, and

Derivative controller (IT2FLC-PID) is designed in this paper for the robust control of a Wind Turbine System

(WTS) to guarantee high and efficient stability of the system in different operating conditions. To improve

the classical PID controller efficiency and robustness, we used the interval type-2 fuzzy logic controller

(IT2FLC). However, the aim of using the IT2FLC is to overcome oscillations, imprecision, and uncertainty.

This approach is applied in this study to adjust and optimize the gains of the PID controller. We have designed

the proposed (IT2FLC-PID) to achieve considerable stability and to increase the performance of (VS-WT)

system. Furthermore, for the purpose evaluate the effectiveness and the robustness of the proposed controllers

(IT2FLC-PID), the simulation results attest that the (IT2FLC-PID) comparing with (IT1FLC-PID) and (PID)

controller produces robust stability and better response for Wind Turbine systems.

1 INTRODUCTION

Wind energy has an important role and can be

considered the most developed renewable energy

source. The level of efficiency and profitability of a

wind energy system (WES) depends very much on its

control (Apata et Oyedokun, 2020). The most of wind

energy system uses variable speed wind turbines (VS-

WT). Due to their superiority compared to fixed-

speed wind turbines (FS-WT). The characterization

of variable speed wind turbine is the capacity to adapt

the speed of the shaft in the case of changes in wind

speed (Jabbariet al. 2016; Koumir et al. 2017).

Variable speed operation is primarily related to

the type of generator that provides the mechanical-to-

electrical conversion (Wang et al. 2018). Therefore,

several research studies have been carried out on the

use of wind turbine systems (WTS), whose purpose is

the production of electricity. To achieve the

performance and efficiency of the system based on

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the use of conventional controls such as the PID

controller. There is no such thing as the perfect PID;

it is all about compromise. Some applications will

allow an overrun to improve the stabilization time,

while others will not allow it, so it depends on the

specifications. Each of the coefficients (KP, KI, KD)

influences the response of the system. To decrease the

static error, it is necessary to decreases KP and KI.

The overshoot is reduced (ratio between the first peak

and the setpoint) if KP or KI decreases or KD

increases. The rise time decreases if KP or KI

increases or KD decreases (Apata et Oyedokun,

2020). The stabilization time decreases as KP and KI

increase. However, using this classical type of control

(PID) causes many difficulties in guaranteeing robust

performance; because there are many problems in the

wind turbine system, such as the nonlinearity of the

(WTS) systems, the uncertainties; the parameter

variation, and unknown disturbances (Dib et al.

2019).

216

Ben Meziane, K., Dib, F. and Boumhidi, I.

Intelligent Variable Speed Wind Turbine Controller using the Type-2 Fuzzy Logic based on PID.

DOI: 10.5220/0010731300003101

In Proceedings of the 2nd International Conference on Big Data, Modelling and Machine Learning (BML 2021), pages 216-221

ISBN: 978-989-758-559-3

The main objective of this work is to develop a

new and intelligent approach (IT2FLC-PID); the

purpose of this approach is the design of a robust and

efficient controller. Most controllers existing in the

literature use the traditional fuzzy logic system

(IT1FLC). Furthermore, there is an alternative that

uses the interval type-2 fuzzy logic controller

(IT2FLC) (Miccio and Cosenza, 2014; Ben Meziane

et al. 2019). Usually, Lotfi Zadeh has expressed a

fuzzy logic by a set of linguistic rules called fuzzy

rules, which are used to describe the dynamic

behavior of an unknown or ill-defined system (Zadeh,

1965). Since fuzzy systems are built from the

knowledge provided by the human expert, they are

fraught with uncertainties. These uncertainties are

injected at the level of the membership functions of

the antecedent and consequent fuzzy sets, which will

be uncertain. These fuzzy systems, called type-1

fuzzy systems, are unable to model these

uncertainties because they use precise membership

functions, which have a two-dimensional

representation. Therefore, type-2 fuzzy sets, whose

membership functions themselves are fuzzy, are the

extension of type-1 fuzzy systems. Membership

functions type-2 have a three-dimensional

representation, the new (third) dimension of fuzzy

sets provides an additional degree of freedom to

accommodate uncertainties. The main advantage of

type-2 fuzzy logic over type-1 fuzzy logic is its ability

to take into account linguistic and numerical

uncertainties (Mendel et al. 2006). IT2FLC; can be

used in situations where there is uncertainty about the

membership degrees themselves. For example,

uncertainty in the form of the membership function or

some of its parameters.

The (IT2FLC-PID) proposed controller is used in

this study to achieve a high performance of control in

terms of precision, variations, and external

disturbances in the (WT) system; and facilitate the

performance in damping oscillations, and increase the

stability of the (WTS). We have using the IT2FL

controller for adjusting the (Kp), (Ki), and (Kd) gains

of the conventional PID controller to obtain the

optimal parameters.

The paper is organized as follows: Section 2

presents the mathematical model of the wind turbine

system, Section 3 shows the proposed controller, the

simulation results are shown in Section 4, and the

conclusion is given in Section 5.

2 MODELING WIND TURBINE

SYSTEM (WTS)

Variable Speed Wind Turbines Systems are currently

the most widely used in the industry. The term

variable speed designates the fact that the speed of the

turbine is independent of the frequency of the power

system. The main advantage of operating the turbine

at a variable speed is to maximize the capture of the

energy available in the wind (Koumir et al. 2017).

The mathematical model of the aerodynamic

power of the wind turbine (WT) is described by the

following equation (Sid Ahmed et al. 2015):

𝑃





𝜌𝐴𝑣



(1)

The power captured by the rotor is given by the

following equation (Hamedet al. 2016):

𝑃



𝐶





𝜆,𝛽



𝑃



(2)

𝑃





𝜌𝜋𝑅



𝐶





𝜆,𝛽



𝜐



(3)

Where 𝐶



the coefficient of performance of power

and λ presents the tip speed ratio given by:

𝜆

𝜔



𝑅

𝜐

(4)

𝜔



Indicate the tangential speed of the tip of the

blade; 𝑅 design the radius of the area swept by the

rotor. The expression of wind turbine power can be

defined as follows (Lahlou et al. 2019):

𝑃



𝜔



𝑇



(5)

The aerodynamic power extracted 𝑃𝑎 is a non-

linear function of wind speed, rotor speed, and stall

angle. Then, the aerodynamic torque is converted into

mechanical power, which results in an aerodynamic

torque 𝑇𝑎, we have the following equation:

𝑇





2𝜆

𝜌𝜋𝑅



𝐶





𝜆,𝛽



𝜐



(6)

To describe the model of the wind turbine system,

generally, a two-mass model is used, which is

illustrated in Figure.1.

Figure 1: The model of a two-mass wind turbine system

(Dib et al. 2019).

Intelligent Variable Speed Wind Turbine Controller using the Type-2 Fuzzy Logic based on PID

217

The main advantages of variable speed wind turbines

compared to fixed speed ones are as follows (El

Aimani et al. 2003):

• Increased operating range, especially for low wind

speeds where maximum power can be easily

converted.

• Simplicity of the blade orientation system.

• Reduction of mechanical efforts thanks to the

adaptation of the speed of the turbine during

variations in the wind.

• Noise reduction during low power operation

because the speed is slow (Koumir et al. 2017).

The rotor speed 𝜔



is given in the equation (7)

(Hamed et al. 2016):

𝐽



𝜔



𝑇



𝑇



𝐾



𝜔



(7)

The torque of the low-speed shaft 𝑇



is given by

equation (8):

𝑇



𝐵





𝜃



𝜃





𝐾





𝜔



𝜔





(8)

𝐽



𝜔



𝑇



𝐾



𝜔



𝑇



(9)

If an ideal gearbox with a ratio 𝑛



is assumed, one

has (Hamed et al. 2016):

𝑛





𝑇



𝑇







𝜔



𝜔





𝜃



𝜔



(10)

By using (7)–(10), we can model the (WTS) by

equations (11):



𝜔



𝜔



𝑇







𝑐



𝑐



𝑐



𝑐



𝑐



𝑐



𝑐



𝑐



𝑐





𝜔



𝜔



𝑇





𝑏



𝑏



𝑏



𝑇





𝑏



𝑏



𝑏



𝑇



(11)

We define 𝑥



𝜔



,𝑥



𝜔



,𝑥



𝜔



, and 𝑢

𝑇



, the state space of the system is described by

equations (12) (Lahlou et al. 2019):

⎩

⎪

⎨

⎪

⎧

𝑥



𝑥



𝑥



𝑓



𝑥



𝑔



𝑥



.𝑢𝜉



𝑥,𝑡



𝑥



𝑐



𝑥





𝑐



𝑐





𝑥



𝑐



𝑥



𝑏



𝑇





𝑏



𝑢𝑥,𝑡

𝑦𝑥



(12)

The two-mass model becomes a non-linear system.

With two inputs: 𝑇𝑒𝑚 which is a controllable input,

and 𝑣, which is a non-controllable input, and at one

output, it is the rotor speed 𝜔



.To maximize the

energy captured by the wind, the variables λ and β

must be kept at their optimal values to ensure the

maximum value of Cp. Thus, the pitch angle of the

blade is fixed at its optimum value βopt. The rotor

speed ωt must be adjusted by Tem to follow the

optimal reference ω

topt

The nonlinearity of this system comes from the

aerodynamic torque, which depends on 𝜔𝑡 and on the

wind speed, which is a non-controllable, random, and

fluctuating input (Koumir et al. 2017).

3 INTERVAL TYPE-2 FUZZY

LOGIC BASED ON PID

CONTROLLER

3.1 Interval Type-2 Fuzzy Logic System

In recent years, the classical fuzzy logic called type-1

fuzzy logic has been developed to a new generation

called type-2 fuzzy logic. Mendel and his team

contributed a lot to its development (Mendel et al.

2006). The type reducer block is given between the

inference engine and the defuzzification block. The

basic structure of the IT2FLC system, which is

represented by Figure 2, is essentially composed of

three elements namely: the fuzzification interface, the

inference mechanism, and the output processing

module(El-Nagar et al. 2014).

Figure2: Structure described the IT2FLC.

 Fuzzification: Unlike the type-1 membership

function, the type-2 membership function gives multiple

membership degrees (or dimensions) for each input.

Therefore, the uncertainty will be better represented.

 Rule bases: The difference between type-1 and

type-2 lies only like the membership functions;

therefore, the structure of the rules in the case of type-

2 remains the same (Mendel et al. 2002).

 Inference Mechanism: The inference system in

a type-2 fuzzy system uses the fuzzy rule base to

relate the input vector to the scalar output.

 The type-reducer: is used to convert output sets

of type-2 fuzzy into sets of type-1 fuzzy to give finally

a crisp output (Lahlou et al. 2019). The type-reducer

takes into account more information about the

uncertainties of the rules than the defuzzified value (a

number). However, this operation requires intensive

calculations, except for interval type 2 where there is

BML 2021 - INTERNATIONAL CONFERENCE ON BIG DATA, MODELLING AND MACHINE LEARNING (BML’21)

218

a simple procedure for implementing type reduction.

The choice of (IT1FL) may not present the correct

and the optimal solution to all types of control

problems, while a possible alternative is to use

controllers based on type-2 fuzzy logic.

 Defuzzification: The defuzzifier in a type-2

fuzzy system can then defuzzify the reduced set to

obtain an ordinary non-fuzzy output.

The variation in the wind and the change in the

operating point introduce some unpredictable values

into the information collected. All the uncertainties

are reflected at the level of the base of the fuzzy rules

by functions belonging to the premises and uncertain

consequences. We will illustrate how to use the

IT2FLC to minimize the effect of these uncertainties.

3.2 Proposed Interval Type-2 Fuzzy

Logic based on PID Controller

(IT2FL-PID)

The new proposed control used in this study is

obtained as:

𝑈





𝐾





𝑒



𝑡



𝐾





𝑒



𝑡



𝑑𝑡 𝐾





𝑑𝑒



𝑡



𝑑𝑡

(13)

With 𝐾





, 𝐾





, 𝐾





represent respectively the

corrected values of proportional, integral, and

derivative gains, which, are tuned by using the

IT2FLC. We have Exposed the structure of the new

control law based on the IT2FLC-PID controller in

Figure 3.

Figure 3: Structure of IT2FL- PID controllers.

The type-2 interval fuzzy system (IT2FL) is designed

using the MATLAB / Toolbox (Castillo, 2007). The

type-2 Gaussian membership function is chosen for

the two inputs and the outputs. We have chosen seven

membership functions for each input and output.

These membership functions have different ranges in

the universe of discourse.

The interval of outputs gains KP, KI, KD of the two-

area are from:

𝐾









0,20



; 𝐾









0,60



; 𝐾









0,15



In this paper, Figure 4 describes the type-2

membership functions (MF). We have used the

symmetrical and Gaussian (MF).

Figure 4: Gaussian type-2 membership functions.

After the fuzzification of the input and output variables,

we proceed to the design of the inference engine. We have

designed 49 rule bases in the form of a matrix.

Finally, we can get the (IT2FLC-PID), our

proposed controller, which is presented by the

equations (14):

𝑢



𝑢





𝑢





(14)

4 SIMULATION RESULTS

This paper selects one type of the two-mass model of

the wind turbine. We have proposed to test Simulation

in MATLAB Software to validate the validity and the

robustness of the developed and suggested control

device (IT2FLC-PID). The parameters of the wind

turbine are taken from (Orlando et al. 2010).

Simulation Scenario 1: The wind speed profile

applied in the first scenario with more minor

variations. The result of the simulation is illustrated

in Figures:

Intelligent Variable Speed Wind Turbine Controller using the Type-2 Fuzzy Logic based on PID

219

Figure 5: The Rotor Speed response.

Figure 6: The aerodynamic torque.

Figure 7: Comparison of tracking errors.

From this simulation results; it can therefore be

deduced from this case of simulation the efficiency

and the robustness of the proposed controller device

(IT2FLC-PID). The results confirm that this

intelligent controller is capable of eliminating the

oscillations and minimizing the tracking errors.

Comparing with the other controllers and intelligently

controlling the speed of the rotor of a wind turbine in

different wind profiles and offers a better result and

response time.

Simulation Scenario2: The wind speed profile used

in this scenario with high variation:

Figure 8: The Rotor Speed response.

Figure 9: The aerodynamic torque.

Figure 10: Comparison of tracking errors.

From all these results, we can deduce that all the

output response of (IT2FLC-PID) converges to de the

required values rapidly compared to other controllers

(IT1FLC-PID) and (PID). Consequently, the result of

the simulations shows that the suggested approach

makes it possible to minimize the response time with

good convergence despite the variations in wind

speed.

The proposed controller shows good performance in

terms of eliminating disturbances as well as in terms

of pursuing the desired rotational speed. We notice

that the proposed controller quickly converges to the

optimal state with less oscillation even when

changing the wind profile.

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220

5 CONCLUSIONS

In this paper, the intelligent and optimal (IT2FLC-

PID) controller for a Variable Speed Wind Turbine

(VS-WT) System is introduced to ameliorate the

stability of the (WT) system. We have optimized the

gains of the (PID) controller by using the (IT2FLC)

approach to eliminate and overcome the significant

parametric variations, imprecision, and system

nonlinearities, this method strategy is used. We can

also show that the control device we have proposed

(IT2FLC-PID) in this work can ensure the good

performances of tracking which leads to the overall

stability of variable speed wind turbine systems in

various conditions of operating.

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