Novel control strategy for the global model of wind turbine

ABSTRACT


INTRODUCTION
In recent decades, the most widely used source of renewable energy has been the wind energy conversion system [1]- [5].The interest in the wind turbine (WT) goes back to it is benefits as a sustainable, renewable, clean energy source, it is simplicity of installation, and its small surface occupation.The general idea of wind power is to harness the kinetic energy of wind by transforming it into electrical energy.The modern WT as depicted in Figure 1 is the horizontal axis variable speed wind turbine (VSWT) with threeblade [6], [7].The VSWT contains an aeroturbine coupled to a doubly-fed induction generator (DFIG) as depicted in Figure 1(a) [8], [9].The WT has a highly non-linear mathematical model as depicted in Figure 1(b) and its dynamics change rapidly with fluctuations in wind speed [10].
The wind is an uncontrollable parameter that causes parametric variations in the structure of the WT, cannot stabilize it, and affects its economic viability.Therefore, researchers and engineers are thinking of developing more effective control laws to increase the WT's efficiency and improve the performance of the WT that operate under turbulent, random, and unpredictable wind speed.In the literature, some works have been done on the control of the mechanical subsystem without taking into consideration the control of the electrical part [11], while other research has been done on the control of the electrical part without taking into account the mechanical part [12]- [15].This is the main contribution that motivates us in this paper to ISSN: 2088-8708  Novel control strategy for the global model of wind turbine (Yattou El Fadili) 259 perform work concerning the control of the global WT while taking into account both studies of the mechanical and electrical parts.Among the existing control methods in the literature, the linearization technique is a common strategy that aims to surmount the problem of nonlinearity.However, controllers designed mainly using the technique of WT linearization around their operating points [16] lead to reduced system performance [17].Other non-linear techniques for the control of WT of which the most used is the sliding mode control (SMC) law.The SMC law is a powerful nonlinear control approach that has been deeply studied and applied in different practical applications [18], [19] among them the WT systems [20]- [22].Unfortunately, the SMC has a major drawback named the chattering phenomenon that results from the discontinuity of the control law and the real dynamic behavior of the WT.The chattering problem is undesirable because causes rapid control signal variations which lead to high-frequency oscillations that damage the WT [23].The strong contribution of this article is to tackle the major drawback of SMC (i.e., the chatter phenomenon).This paper presents a developed law for controlling the whole model of WT including both mechanical and electrical parts.The proposed new technique of control is extensively studied and analyzed which is an extension of the classical SMC law by transforming its sliding surface into a sliding sector as in [24].The developed control law is called the sliding sector control (SSC).The good performances of the developed control strategy are demonstrated by the simulation results using MATLAB toolboxes in terms of precise tracking of the rotor speed and its reference signal, maximum extracting of wind energy whatever the climatic change, reducing aerodynamic loads in order to increase the lifespan of WT, achieving stability and robustness against modeling uncertainties and external disturbances represented by rapid wind speed variations, eliminating the chattering phenomenon, and using a high value of switching gain.
The main sections are as follows: section 2 gives the mathematical models of the mechanical part, the electrical part, and the whole WT followed by the proposed control for the entire WT.In section 3, the WT's performances are depicted and compared to classical SMC.The conclusion is given in section 4 which summarizes the highlights of this present paper.

MODEL OF WIND TURBINE SYSTEM
The three-blade horizontal axis VSWT is divided into two subsystems which are the mechanical and the electrical subsystems which are connected together.To model this type of wind turbine, the models of the mechanical and the electrical subsystems are necessary.In the context of controlling the entire wind turbine, some notations are adopted throughout this paper, presented in Table 1 to help the readers and researchers, are listed to refer to the specific coefficients easily and understand the proposed design control.

Mechanical part model
The mechanical part of WT is depicted in Figure 1(b).To model the mechanical part, the two-mass model is used.The modeling of the mechanical part is given in (1) [24].

Electrical part model
The analysis of the electrical part of the modern WT goes back to analyzing the DFIG.The WT's DFIG is described by its stator which is linked to the network, and its rotor is coupled to the network through a power converter [25].Figure 1(a) shows the overall WT design including the connection of the aeroturbine and the DFIG.To simplify this analysis, two simplifying assumptions are taken into account.The first is that the stator resistance is neglected.The second is that the q-axis of the Park's reference is aligned with the stator voltage.These hypotheses will lead to the equations as in (2) [26], [27].(2)

Overall model of wind turbine
The entire WT model is modeled as in (3).The whole WT model is obtained by combining the mechanical subsystem model using the two-mass model presented in subsection 2.1 and the electrical subsystem model given in subsection 2.2.The entire WT model is given by taking into account the system's input is the rotor q-axis voltage noted by u and the system's output is the rotor speed.The main used coefficients in (3)

Application of sliding sector control for wind turbines
The proposed novel control law that is called SSC.This novel law is developed based on the classical strategy of SMC by transforming its sliding surface into a sliding sector.The sliding sector consists of multiple sliding sub-surfaces [24].The number of the sub-surfaces depends on the system's relative degree which is determined through the calculation of successive derivatives of the tracking error.The main objective of the SSC is to eliminate the chattering phenomenon that appears during the reaching phase.In this paper, the relative degree is three which means the utility of three sub-surfaces that define the boundaries of the sliding sector which represents their center.The fundamental steps of SSC are selecting the sliding sector, constructing the control law, and establishing the existence conditions.To design of SSC controller for the whole WT model, the system's input is rotor q-axis voltage and the system's output is rotor speed.The controller should ensure the rotor speed follows its reference signal.The tracking error noted by e(t) and it is successive derivatives are defined as in (4) which is the main objective of the controller that minimizes this error to ensure accurate tracking.The sliding sector noted by S(t) and its three sub-surfaces (S1, S2, and S3) are given in (5). where, , and The control law consists of two terms the equivalent control term ( , ) and the switching control term ( , ) which are expressed as in (6).Where the three regions R1, R2, and R3 divide the entire state space.These regions are defined in (7).The stability is proven outside the sliding sector i.e., () ∈  1 ∪  2 , and inside the sliding sector i.e., () ∈  3 through the powerful Lyapunov function (LF) as in (8).This LF is positive and it is first-time derivative is negative.

SIMULATION RESULTS AND DISCUSSION
The developed nonlinear control law, which is called SSC law, is applied to the overall WT model.The modern WT consists of an aeroturbine connected to the DFIG.The principal characteristics of the WT used in this paper are mentioned in Table 2.The performance of the SSC control applied to the WT is investigated under a random and fast variable wind speed as depicted in Figure 2. The wind speed profile in Figure 2(a) presents the external perturbation of the WT over a duration of 40 seconds with its average wind speed is about 12 m/s.The simulation results are performed using MATLAB toolboxes.The purpose of these simulation results is proving the effectiveness of the developed SSC technique by comparing it with the traditional SMC law under fast and unpredictable wind speed fluctuations.The two control laws (SMC and SSC) are tested for the same values of the switching gain during the same simulation time.The values of the control gains are indicated in Table 3. 1 st test of simulation 0.5 0.9 0.61 0.77 1.9 0.99 10.95 2 nd test of simulation 3 0.9 0.61 0.77 1.9 0.99 10.95 Figure 3 shows the temporal variation in generator torque.Figure 3(a) shows that both control laws SMC and SSC can maintain the generator torque within its limit.However, the chattering phenomenon appears in Figure 3(b) for the SMC law.The major inconvenience of the SMC is the chattering because it can lead to strong vibrations on the drive shafts of WT, and it affects the accuracy of the control system by introducing variability in the input variables.The same discussion of Figures 3(a 4(c) and 4(d).When the value of the switching gain is increasing (here the power of the SSC law appears), the chattering becomes more important for SMC.In contrast, the chattering problem does not appear by using a high value of switching gain for the developed control law.
To show clearly the effectiveness of the proposed control law in this paper, Figure 5 depicts the sliding surface of SMC, and the sliding sector of SSC strategy and its three sub-surfaces by using the high switching gain value.Figure 5(a) shows that the three sub-surfaces of the SSC technique converge gradually towards the sliding sector.Additionally, SSC law exhibits no oscillations that could lead to the chattering problem as illustrated in Figure 5

CONCLUSION
This paper presents a novel nonlinear control strategy for the entire wind energy conversion system operating under a variable speed wind by tacking it as a strong external disturbance.The proposed control is improved by transforming the sliding surface of the known classical sliding mode control into a sliding sector with the main objective of optimizing the performance of the wind turbine by making it more profitable.The simulation results obtained by MATLAB toolboxes prove the effectiveness of the proposed nonlinear control approach in terms of obtaining the maximum wind power available whatever the climatic conditions associated with the wind, achieving a precise tracking of the optimal value of the rotor speed, reducing the aerodynamic loads of the turbine devices, eliminating the chattering phenomenon, and easy implementation in real-time.

Figure 1 .
Figure 1.Complete wind turbine model (a) DFIG electrical model, and (b) two-mass mechanical model

Figure 2 Figure 2 .
Figure 2 depicts the wind speed curve and the temporal variation in rotor speed.Figure 2(b) illustrates the precise tracking of the rotor speed and its reference signal for both control laws SMC and SSC.From Figure 2(c), the value of the switching gain increases, and the rotor speed can quickly follow its reference signal.The good result shown in Figures 2(b) and 2(c) is the capability of achieving accurate tracking between the rotor speed and its desired signal.The precise tracking aims to extract the maximum power available whatever the climatic conditions of the wind.

Figure 3 .
Figure3shows the temporal variation in generator torque.Figure3(a) shows that both control laws SMC and SSC can maintain the generator torque within its limit.However, the chattering phenomenon appears in Figure3(b) for the SMC law.The major inconvenience of the SMC is the chattering because it can lead to strong vibrations on the drive shafts of WT, and it affects the accuracy of the control system by introducing variability in the input variables.The same discussion of Figures3(a) and 3(b) concerns Figures3(c) and 3(d).When the value of the switching gain is increasing (here where the main contribution of SSC is represented), the chattering phenomenon becomes more important for the traditional SMC

Figure 4 .Figure 5 .
Figure4(a) shows the DFIG rotor q-axis voltage to be imposed by the controller to reach the reference of the rotor speed.Therefore, the control strategy developed aims to obtain good performances by comparing it with the classical SMC when the chattering problem appears in the SMC as shown in Figure4(b).The same discussion of Figures4(a) and 4(b) concerns Figures4(c) and 4(d).When the value of the switching gain is increasing (here the power of the SSC law appears), the chattering becomes more important for SMC.In contrast, the chattering problem does not appear by using a high value of switching gain for the developed control law.To show clearly the effectiveness of the proposed control law in this paper, Figure5depicts the sliding surface of SMC, and the sliding sector of SSC strategy and its three sub-surfaces by using the high switching gain value.Figure5(a) shows that the three sub-surfaces of the SSC technique converge gradually towards the sliding sector.Additionally, SSC law exhibits no oscillations that could lead to the chattering problem as illustrated in Figure5(b).

Table 1 .
WT notations of the different coefficients of the whole WT model are identified at the end of this subsection 2.3.

Table 2 .
Wind energy conversion system characteristics Novel control strategy for the global model of wind turbine (Yattou El Fadili) 263

Table 3 .
Control gains values